ScalarEvolution.cpp revision 32efba698df6aa35335eeb44d89288352d04746d
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 106static RegisterPass<ScalarEvolution> 107R("scalar-evolution", "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(FoldingSetNodeID(), 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 = SCEVAllocator.Allocate<SCEVConstant>(); 181 new (S) SCEVConstant(ID, V); 182 UniqueSCEVs.InsertNode(S, IP); 183 return S; 184} 185 186const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 187 return getConstant(ConstantInt::get(getContext(), Val)); 188} 189 190const SCEV * 191ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 192 return getConstant( 193 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 194} 195 196const Type *SCEVConstant::getType() const { return V->getType(); } 197 198void SCEVConstant::print(raw_ostream &OS) const { 199 WriteAsOperand(OS, V, false); 200} 201 202SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 203 unsigned SCEVTy, const SCEV *op, const Type *ty) 204 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 205 206bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 207 return Op->dominates(BB, DT); 208} 209 210bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 211 return Op->properlyDominates(BB, DT); 212} 213 214SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 215 const SCEV *op, const Type *ty) 216 : SCEVCastExpr(ID, scTruncate, op, ty) { 217 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 218 (Ty->isInteger() || isa<PointerType>(Ty)) && 219 "Cannot truncate non-integer value!"); 220} 221 222void SCEVTruncateExpr::print(raw_ostream &OS) const { 223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 224} 225 226SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 227 const SCEV *op, const Type *ty) 228 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 229 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 230 (Ty->isInteger() || isa<PointerType>(Ty)) && 231 "Cannot zero extend non-integer value!"); 232} 233 234void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 236} 237 238SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 239 const SCEV *op, const Type *ty) 240 : SCEVCastExpr(ID, scSignExtend, op, ty) { 241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 242 (Ty->isInteger() || isa<PointerType>(Ty)) && 243 "Cannot sign extend non-integer value!"); 244} 245 246void SCEVSignExtendExpr::print(raw_ostream &OS) const { 247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 248} 249 250void SCEVCommutativeExpr::print(raw_ostream &OS) const { 251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 252 const char *OpStr = getOperationStr(); 253 OS << "(" << *Operands[0]; 254 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 255 OS << OpStr << *Operands[i]; 256 OS << ")"; 257} 258 259bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 261 if (!getOperand(i)->dominates(BB, DT)) 262 return false; 263 } 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 269 if (!getOperand(i)->properlyDominates(BB, DT)) 270 return false; 271 } 272 return true; 273} 274 275bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 276 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 277} 278 279bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 280 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 281} 282 283void SCEVUDivExpr::print(raw_ostream &OS) const { 284 OS << "(" << *LHS << " /u " << *RHS << ")"; 285} 286 287const Type *SCEVUDivExpr::getType() const { 288 // In most cases the types of LHS and RHS will be the same, but in some 289 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 290 // depend on the type for correctness, but handling types carefully can 291 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 292 // a pointer type than the RHS, so use the RHS' type here. 293 return RHS->getType(); 294} 295 296bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 297 // Add recurrences are never invariant in the function-body (null loop). 298 if (!QueryLoop) 299 return false; 300 301 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 302 if (QueryLoop->contains(L)) 303 return false; 304 305 // This recurrence is variant w.r.t. QueryLoop if any of its operands 306 // are variant. 307 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 308 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 309 return false; 310 311 // Otherwise it's loop-invariant. 312 return true; 313} 314 315void SCEVAddRecExpr::print(raw_ostream &OS) const { 316 OS << "{" << *Operands[0]; 317 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 318 OS << ",+," << *Operands[i]; 319 OS << "}<"; 320 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 321 OS << ">"; 322} 323 324bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 325 // All non-instruction values are loop invariant. All instructions are loop 326 // invariant if they are not contained in the specified loop. 327 // Instructions are never considered invariant in the function body 328 // (null loop) because they are defined within the "loop". 329 if (Instruction *I = dyn_cast<Instruction>(V)) 330 return L && !L->contains(I); 331 return true; 332} 333 334bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 335 if (Instruction *I = dyn_cast<Instruction>(getValue())) 336 return DT->dominates(I->getParent(), BB); 337 return true; 338} 339 340bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 341 if (Instruction *I = dyn_cast<Instruction>(getValue())) 342 return DT->properlyDominates(I->getParent(), BB); 343 return true; 344} 345 346const Type *SCEVUnknown::getType() const { 347 return V->getType(); 348} 349 350bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 351 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 352 if (VCE->getOpcode() == Instruction::PtrToInt) 353 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 354 if (CE->getOpcode() == Instruction::GetElementPtr && 355 CE->getOperand(0)->isNullValue() && 356 CE->getNumOperands() == 2) 357 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 358 if (CI->isOne()) { 359 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 360 ->getElementType(); 361 return true; 362 } 363 364 return false; 365} 366 367bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 368 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 369 if (VCE->getOpcode() == Instruction::PtrToInt) 370 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 371 if (CE->getOpcode() == Instruction::GetElementPtr && 372 CE->getOperand(0)->isNullValue()) { 373 const Type *Ty = 374 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 375 if (const StructType *STy = dyn_cast<StructType>(Ty)) 376 if (!STy->isPacked() && 377 CE->getNumOperands() == 3 && 378 CE->getOperand(1)->isNullValue()) { 379 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 380 if (CI->isOne() && 381 STy->getNumElements() == 2 && 382 STy->getElementType(0)->isInteger(1)) { 383 AllocTy = STy->getElementType(1); 384 return true; 385 } 386 } 387 } 388 389 return false; 390} 391 392bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 393 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 394 if (VCE->getOpcode() == Instruction::PtrToInt) 395 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 396 if (CE->getOpcode() == Instruction::GetElementPtr && 397 CE->getNumOperands() == 3 && 398 CE->getOperand(0)->isNullValue() && 399 CE->getOperand(1)->isNullValue()) { 400 const Type *Ty = 401 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 402 // Ignore vector types here so that ScalarEvolutionExpander doesn't 403 // emit getelementptrs that index into vectors. 404 if (isa<StructType>(Ty) || isa<ArrayType>(Ty)) { 405 CTy = Ty; 406 FieldNo = CE->getOperand(2); 407 return true; 408 } 409 } 410 411 return false; 412} 413 414void SCEVUnknown::print(raw_ostream &OS) const { 415 const Type *AllocTy; 416 if (isSizeOf(AllocTy)) { 417 OS << "sizeof(" << *AllocTy << ")"; 418 return; 419 } 420 if (isAlignOf(AllocTy)) { 421 OS << "alignof(" << *AllocTy << ")"; 422 return; 423 } 424 425 const Type *CTy; 426 Constant *FieldNo; 427 if (isOffsetOf(CTy, FieldNo)) { 428 OS << "offsetof(" << *CTy << ", "; 429 WriteAsOperand(OS, FieldNo, false); 430 OS << ")"; 431 return; 432 } 433 434 // Otherwise just print it normally. 435 WriteAsOperand(OS, V, false); 436} 437 438//===----------------------------------------------------------------------===// 439// SCEV Utilities 440//===----------------------------------------------------------------------===// 441 442static bool CompareTypes(const Type *A, const Type *B) { 443 if (A->getTypeID() != B->getTypeID()) 444 return A->getTypeID() < B->getTypeID(); 445 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 446 const IntegerType *BI = cast<IntegerType>(B); 447 return AI->getBitWidth() < BI->getBitWidth(); 448 } 449 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 450 const PointerType *BI = cast<PointerType>(B); 451 return CompareTypes(AI->getElementType(), BI->getElementType()); 452 } 453 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 454 const ArrayType *BI = cast<ArrayType>(B); 455 if (AI->getNumElements() != BI->getNumElements()) 456 return AI->getNumElements() < BI->getNumElements(); 457 return CompareTypes(AI->getElementType(), BI->getElementType()); 458 } 459 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 460 const VectorType *BI = cast<VectorType>(B); 461 if (AI->getNumElements() != BI->getNumElements()) 462 return AI->getNumElements() < BI->getNumElements(); 463 return CompareTypes(AI->getElementType(), BI->getElementType()); 464 } 465 if (const StructType *AI = dyn_cast<StructType>(A)) { 466 const StructType *BI = cast<StructType>(B); 467 if (AI->getNumElements() != BI->getNumElements()) 468 return AI->getNumElements() < BI->getNumElements(); 469 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 470 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 471 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 472 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 473 } 474 return false; 475} 476 477namespace { 478 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 479 /// than the complexity of the RHS. This comparator is used to canonicalize 480 /// expressions. 481 class SCEVComplexityCompare { 482 LoopInfo *LI; 483 public: 484 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 485 486 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 487 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 488 if (LHS == RHS) 489 return false; 490 491 // Primarily, sort the SCEVs by their getSCEVType(). 492 if (LHS->getSCEVType() != RHS->getSCEVType()) 493 return LHS->getSCEVType() < RHS->getSCEVType(); 494 495 // Aside from the getSCEVType() ordering, the particular ordering 496 // isn't very important except that it's beneficial to be consistent, 497 // so that (a + b) and (b + a) don't end up as different expressions. 498 499 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 500 // not as complete as it could be. 501 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 502 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 503 504 // Order pointer values after integer values. This helps SCEVExpander 505 // form GEPs. 506 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 507 return false; 508 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 509 return true; 510 511 // Compare getValueID values. 512 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 513 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 514 515 // Sort arguments by their position. 516 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 517 const Argument *RA = cast<Argument>(RU->getValue()); 518 return LA->getArgNo() < RA->getArgNo(); 519 } 520 521 // For instructions, compare their loop depth, and their opcode. 522 // This is pretty loose. 523 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 524 Instruction *RV = cast<Instruction>(RU->getValue()); 525 526 // Compare loop depths. 527 if (LI->getLoopDepth(LV->getParent()) != 528 LI->getLoopDepth(RV->getParent())) 529 return LI->getLoopDepth(LV->getParent()) < 530 LI->getLoopDepth(RV->getParent()); 531 532 // Compare opcodes. 533 if (LV->getOpcode() != RV->getOpcode()) 534 return LV->getOpcode() < RV->getOpcode(); 535 536 // Compare the number of operands. 537 if (LV->getNumOperands() != RV->getNumOperands()) 538 return LV->getNumOperands() < RV->getNumOperands(); 539 } 540 541 return false; 542 } 543 544 // Compare constant values. 545 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 546 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 547 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 548 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 549 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 550 } 551 552 // Compare addrec loop depths. 553 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 554 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 555 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 556 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 557 } 558 559 // Lexicographically compare n-ary expressions. 560 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 561 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 562 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 563 if (i >= RC->getNumOperands()) 564 return false; 565 if (operator()(LC->getOperand(i), RC->getOperand(i))) 566 return true; 567 if (operator()(RC->getOperand(i), LC->getOperand(i))) 568 return false; 569 } 570 return LC->getNumOperands() < RC->getNumOperands(); 571 } 572 573 // Lexicographically compare udiv expressions. 574 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 575 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 576 if (operator()(LC->getLHS(), RC->getLHS())) 577 return true; 578 if (operator()(RC->getLHS(), LC->getLHS())) 579 return false; 580 if (operator()(LC->getRHS(), RC->getRHS())) 581 return true; 582 if (operator()(RC->getRHS(), LC->getRHS())) 583 return false; 584 return false; 585 } 586 587 // Compare cast expressions by operand. 588 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 589 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 590 return operator()(LC->getOperand(), RC->getOperand()); 591 } 592 593 llvm_unreachable("Unknown SCEV kind!"); 594 return false; 595 } 596 }; 597} 598 599/// GroupByComplexity - Given a list of SCEV objects, order them by their 600/// complexity, and group objects of the same complexity together by value. 601/// When this routine is finished, we know that any duplicates in the vector are 602/// consecutive and that complexity is monotonically increasing. 603/// 604/// Note that we go take special precautions to ensure that we get determinstic 605/// results from this routine. In other words, we don't want the results of 606/// this to depend on where the addresses of various SCEV objects happened to 607/// land in memory. 608/// 609static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 610 LoopInfo *LI) { 611 if (Ops.size() < 2) return; // Noop 612 if (Ops.size() == 2) { 613 // This is the common case, which also happens to be trivially simple. 614 // Special case it. 615 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 616 std::swap(Ops[0], Ops[1]); 617 return; 618 } 619 620 // Do the rough sort by complexity. 621 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 622 623 // Now that we are sorted by complexity, group elements of the same 624 // complexity. Note that this is, at worst, N^2, but the vector is likely to 625 // be extremely short in practice. Note that we take this approach because we 626 // do not want to depend on the addresses of the objects we are grouping. 627 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 628 const SCEV *S = Ops[i]; 629 unsigned Complexity = S->getSCEVType(); 630 631 // If there are any objects of the same complexity and same value as this 632 // one, group them. 633 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 634 if (Ops[j] == S) { // Found a duplicate. 635 // Move it to immediately after i'th element. 636 std::swap(Ops[i+1], Ops[j]); 637 ++i; // no need to rescan it. 638 if (i == e-2) return; // Done! 639 } 640 } 641 } 642} 643 644 645 646//===----------------------------------------------------------------------===// 647// Simple SCEV method implementations 648//===----------------------------------------------------------------------===// 649 650/// BinomialCoefficient - Compute BC(It, K). The result has width W. 651/// Assume, K > 0. 652static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 653 ScalarEvolution &SE, 654 const Type* ResultTy) { 655 // Handle the simplest case efficiently. 656 if (K == 1) 657 return SE.getTruncateOrZeroExtend(It, ResultTy); 658 659 // We are using the following formula for BC(It, K): 660 // 661 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 662 // 663 // Suppose, W is the bitwidth of the return value. We must be prepared for 664 // overflow. Hence, we must assure that the result of our computation is 665 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 666 // safe in modular arithmetic. 667 // 668 // However, this code doesn't use exactly that formula; the formula it uses 669 // is something like the following, where T is the number of factors of 2 in 670 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 671 // exponentiation: 672 // 673 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 674 // 675 // This formula is trivially equivalent to the previous formula. However, 676 // this formula can be implemented much more efficiently. The trick is that 677 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 678 // arithmetic. To do exact division in modular arithmetic, all we have 679 // to do is multiply by the inverse. Therefore, this step can be done at 680 // width W. 681 // 682 // The next issue is how to safely do the division by 2^T. The way this 683 // is done is by doing the multiplication step at a width of at least W + T 684 // bits. This way, the bottom W+T bits of the product are accurate. Then, 685 // when we perform the division by 2^T (which is equivalent to a right shift 686 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 687 // truncated out after the division by 2^T. 688 // 689 // In comparison to just directly using the first formula, this technique 690 // is much more efficient; using the first formula requires W * K bits, 691 // but this formula less than W + K bits. Also, the first formula requires 692 // a division step, whereas this formula only requires multiplies and shifts. 693 // 694 // It doesn't matter whether the subtraction step is done in the calculation 695 // width or the input iteration count's width; if the subtraction overflows, 696 // the result must be zero anyway. We prefer here to do it in the width of 697 // the induction variable because it helps a lot for certain cases; CodeGen 698 // isn't smart enough to ignore the overflow, which leads to much less 699 // efficient code if the width of the subtraction is wider than the native 700 // register width. 701 // 702 // (It's possible to not widen at all by pulling out factors of 2 before 703 // the multiplication; for example, K=2 can be calculated as 704 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 705 // extra arithmetic, so it's not an obvious win, and it gets 706 // much more complicated for K > 3.) 707 708 // Protection from insane SCEVs; this bound is conservative, 709 // but it probably doesn't matter. 710 if (K > 1000) 711 return SE.getCouldNotCompute(); 712 713 unsigned W = SE.getTypeSizeInBits(ResultTy); 714 715 // Calculate K! / 2^T and T; we divide out the factors of two before 716 // multiplying for calculating K! / 2^T to avoid overflow. 717 // Other overflow doesn't matter because we only care about the bottom 718 // W bits of the result. 719 APInt OddFactorial(W, 1); 720 unsigned T = 1; 721 for (unsigned i = 3; i <= K; ++i) { 722 APInt Mult(W, i); 723 unsigned TwoFactors = Mult.countTrailingZeros(); 724 T += TwoFactors; 725 Mult = Mult.lshr(TwoFactors); 726 OddFactorial *= Mult; 727 } 728 729 // We need at least W + T bits for the multiplication step 730 unsigned CalculationBits = W + T; 731 732 // Calcuate 2^T, at width T+W. 733 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 734 735 // Calculate the multiplicative inverse of K! / 2^T; 736 // this multiplication factor will perform the exact division by 737 // K! / 2^T. 738 APInt Mod = APInt::getSignedMinValue(W+1); 739 APInt MultiplyFactor = OddFactorial.zext(W+1); 740 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 741 MultiplyFactor = MultiplyFactor.trunc(W); 742 743 // Calculate the product, at width T+W 744 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 745 CalculationBits); 746 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 747 for (unsigned i = 1; i != K; ++i) { 748 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 749 Dividend = SE.getMulExpr(Dividend, 750 SE.getTruncateOrZeroExtend(S, CalculationTy)); 751 } 752 753 // Divide by 2^T 754 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 755 756 // Truncate the result, and divide by K! / 2^T. 757 758 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 759 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 760} 761 762/// evaluateAtIteration - Return the value of this chain of recurrences at 763/// the specified iteration number. We can evaluate this recurrence by 764/// multiplying each element in the chain by the binomial coefficient 765/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 766/// 767/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 768/// 769/// where BC(It, k) stands for binomial coefficient. 770/// 771const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 772 ScalarEvolution &SE) const { 773 const SCEV *Result = getStart(); 774 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 775 // The computation is correct in the face of overflow provided that the 776 // multiplication is performed _after_ the evaluation of the binomial 777 // coefficient. 778 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 779 if (isa<SCEVCouldNotCompute>(Coeff)) 780 return Coeff; 781 782 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 783 } 784 return Result; 785} 786 787//===----------------------------------------------------------------------===// 788// SCEV Expression folder implementations 789//===----------------------------------------------------------------------===// 790 791const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 792 const Type *Ty) { 793 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 794 "This is not a truncating conversion!"); 795 assert(isSCEVable(Ty) && 796 "This is not a conversion to a SCEVable type!"); 797 Ty = getEffectiveSCEVType(Ty); 798 799 FoldingSetNodeID ID; 800 ID.AddInteger(scTruncate); 801 ID.AddPointer(Op); 802 ID.AddPointer(Ty); 803 void *IP = 0; 804 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 805 806 // Fold if the operand is constant. 807 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 808 return getConstant( 809 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 810 811 // trunc(trunc(x)) --> trunc(x) 812 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 813 return getTruncateExpr(ST->getOperand(), Ty); 814 815 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 816 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 817 return getTruncateOrSignExtend(SS->getOperand(), Ty); 818 819 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 820 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 821 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 822 823 // If the input value is a chrec scev, truncate the chrec's operands. 824 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 825 SmallVector<const SCEV *, 4> Operands; 826 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 827 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 828 return getAddRecExpr(Operands, AddRec->getLoop()); 829 } 830 831 // The cast wasn't folded; create an explicit cast node. 832 // Recompute the insert position, as it may have been invalidated. 833 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 834 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 835 new (S) SCEVTruncateExpr(ID, Op, Ty); 836 UniqueSCEVs.InsertNode(S, IP); 837 return S; 838} 839 840const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 841 const Type *Ty) { 842 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 843 "This is not an extending conversion!"); 844 assert(isSCEVable(Ty) && 845 "This is not a conversion to a SCEVable type!"); 846 Ty = getEffectiveSCEVType(Ty); 847 848 // Fold if the operand is constant. 849 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 850 const Type *IntTy = getEffectiveSCEVType(Ty); 851 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 852 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 853 return getConstant(cast<ConstantInt>(C)); 854 } 855 856 // zext(zext(x)) --> zext(x) 857 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 858 return getZeroExtendExpr(SZ->getOperand(), Ty); 859 860 // Before doing any expensive analysis, check to see if we've already 861 // computed a SCEV for this Op and Ty. 862 FoldingSetNodeID ID; 863 ID.AddInteger(scZeroExtend); 864 ID.AddPointer(Op); 865 ID.AddPointer(Ty); 866 void *IP = 0; 867 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 868 869 // If the input value is a chrec scev, and we can prove that the value 870 // did not overflow the old, smaller, value, we can zero extend all of the 871 // operands (often constants). This allows analysis of something like 872 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 873 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 874 if (AR->isAffine()) { 875 const SCEV *Start = AR->getStart(); 876 const SCEV *Step = AR->getStepRecurrence(*this); 877 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 878 const Loop *L = AR->getLoop(); 879 880 // If we have special knowledge that this addrec won't overflow, 881 // we don't need to do any further analysis. 882 if (AR->hasNoUnsignedWrap()) 883 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 884 getZeroExtendExpr(Step, Ty), 885 L); 886 887 // Check whether the backedge-taken count is SCEVCouldNotCompute. 888 // Note that this serves two purposes: It filters out loops that are 889 // simply not analyzable, and it covers the case where this code is 890 // being called from within backedge-taken count analysis, such that 891 // attempting to ask for the backedge-taken count would likely result 892 // in infinite recursion. In the later case, the analysis code will 893 // cope with a conservative value, and it will take care to purge 894 // that value once it has finished. 895 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 896 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 897 // Manually compute the final value for AR, checking for 898 // overflow. 899 900 // Check whether the backedge-taken count can be losslessly casted to 901 // the addrec's type. The count is always unsigned. 902 const SCEV *CastedMaxBECount = 903 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 904 const SCEV *RecastedMaxBECount = 905 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 906 if (MaxBECount == RecastedMaxBECount) { 907 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 908 // Check whether Start+Step*MaxBECount has no unsigned overflow. 909 const SCEV *ZMul = 910 getMulExpr(CastedMaxBECount, 911 getTruncateOrZeroExtend(Step, Start->getType())); 912 const SCEV *Add = getAddExpr(Start, ZMul); 913 const SCEV *OperandExtendedAdd = 914 getAddExpr(getZeroExtendExpr(Start, WideTy), 915 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 916 getZeroExtendExpr(Step, WideTy))); 917 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 918 // Return the expression with the addrec on the outside. 919 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 920 getZeroExtendExpr(Step, Ty), 921 L); 922 923 // Similar to above, only this time treat the step value as signed. 924 // This covers loops that count down. 925 const SCEV *SMul = 926 getMulExpr(CastedMaxBECount, 927 getTruncateOrSignExtend(Step, Start->getType())); 928 Add = getAddExpr(Start, SMul); 929 OperandExtendedAdd = 930 getAddExpr(getZeroExtendExpr(Start, WideTy), 931 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 932 getSignExtendExpr(Step, WideTy))); 933 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 934 // Return the expression with the addrec on the outside. 935 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 936 getSignExtendExpr(Step, Ty), 937 L); 938 } 939 940 // If the backedge is guarded by a comparison with the pre-inc value 941 // the addrec is safe. Also, if the entry is guarded by a comparison 942 // with the start value and the backedge is guarded by a comparison 943 // with the post-inc value, the addrec is safe. 944 if (isKnownPositive(Step)) { 945 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 946 getUnsignedRange(Step).getUnsignedMax()); 947 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 948 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 949 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 950 AR->getPostIncExpr(*this), N))) 951 // Return the expression with the addrec on the outside. 952 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 953 getZeroExtendExpr(Step, Ty), 954 L); 955 } else if (isKnownNegative(Step)) { 956 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 957 getSignedRange(Step).getSignedMin()); 958 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 959 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 960 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 961 AR->getPostIncExpr(*this), N))) 962 // Return the expression with the addrec on the outside. 963 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 964 getSignExtendExpr(Step, Ty), 965 L); 966 } 967 } 968 } 969 970 // The cast wasn't folded; create an explicit cast node. 971 // Recompute the insert position, as it may have been invalidated. 972 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 973 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 974 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 975 UniqueSCEVs.InsertNode(S, IP); 976 return S; 977} 978 979const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 980 const Type *Ty) { 981 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 982 "This is not an extending conversion!"); 983 assert(isSCEVable(Ty) && 984 "This is not a conversion to a SCEVable type!"); 985 Ty = getEffectiveSCEVType(Ty); 986 987 // Fold if the operand is constant. 988 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 989 const Type *IntTy = getEffectiveSCEVType(Ty); 990 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 991 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 992 return getConstant(cast<ConstantInt>(C)); 993 } 994 995 // sext(sext(x)) --> sext(x) 996 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 997 return getSignExtendExpr(SS->getOperand(), Ty); 998 999 // Before doing any expensive analysis, check to see if we've already 1000 // computed a SCEV for this Op and Ty. 1001 FoldingSetNodeID ID; 1002 ID.AddInteger(scSignExtend); 1003 ID.AddPointer(Op); 1004 ID.AddPointer(Ty); 1005 void *IP = 0; 1006 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1007 1008 // If the input value is a chrec scev, and we can prove that the value 1009 // did not overflow the old, smaller, value, we can sign extend all of the 1010 // operands (often constants). This allows analysis of something like 1011 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1012 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1013 if (AR->isAffine()) { 1014 const SCEV *Start = AR->getStart(); 1015 const SCEV *Step = AR->getStepRecurrence(*this); 1016 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1017 const Loop *L = AR->getLoop(); 1018 1019 // If we have special knowledge that this addrec won't overflow, 1020 // we don't need to do any further analysis. 1021 if (AR->hasNoSignedWrap()) 1022 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1023 getSignExtendExpr(Step, Ty), 1024 L); 1025 1026 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1027 // Note that this serves two purposes: It filters out loops that are 1028 // simply not analyzable, and it covers the case where this code is 1029 // being called from within backedge-taken count analysis, such that 1030 // attempting to ask for the backedge-taken count would likely result 1031 // in infinite recursion. In the later case, the analysis code will 1032 // cope with a conservative value, and it will take care to purge 1033 // that value once it has finished. 1034 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1035 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1036 // Manually compute the final value for AR, checking for 1037 // overflow. 1038 1039 // Check whether the backedge-taken count can be losslessly casted to 1040 // the addrec's type. The count is always unsigned. 1041 const SCEV *CastedMaxBECount = 1042 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1043 const SCEV *RecastedMaxBECount = 1044 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1045 if (MaxBECount == RecastedMaxBECount) { 1046 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1047 // Check whether Start+Step*MaxBECount has no signed overflow. 1048 const SCEV *SMul = 1049 getMulExpr(CastedMaxBECount, 1050 getTruncateOrSignExtend(Step, Start->getType())); 1051 const SCEV *Add = getAddExpr(Start, SMul); 1052 const SCEV *OperandExtendedAdd = 1053 getAddExpr(getSignExtendExpr(Start, WideTy), 1054 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1055 getSignExtendExpr(Step, WideTy))); 1056 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1057 // Return the expression with the addrec on the outside. 1058 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1059 getSignExtendExpr(Step, Ty), 1060 L); 1061 1062 // Similar to above, only this time treat the step value as unsigned. 1063 // This covers loops that count up with an unsigned step. 1064 const SCEV *UMul = 1065 getMulExpr(CastedMaxBECount, 1066 getTruncateOrZeroExtend(Step, Start->getType())); 1067 Add = getAddExpr(Start, UMul); 1068 OperandExtendedAdd = 1069 getAddExpr(getSignExtendExpr(Start, WideTy), 1070 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1071 getZeroExtendExpr(Step, WideTy))); 1072 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1073 // Return the expression with the addrec on the outside. 1074 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1075 getZeroExtendExpr(Step, Ty), 1076 L); 1077 } 1078 1079 // If the backedge is guarded by a comparison with the pre-inc value 1080 // the addrec is safe. Also, if the entry is guarded by a comparison 1081 // with the start value and the backedge is guarded by a comparison 1082 // with the post-inc value, the addrec is safe. 1083 if (isKnownPositive(Step)) { 1084 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1085 getSignedRange(Step).getSignedMax()); 1086 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1087 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1088 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1089 AR->getPostIncExpr(*this), N))) 1090 // Return the expression with the addrec on the outside. 1091 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1092 getSignExtendExpr(Step, Ty), 1093 L); 1094 } else if (isKnownNegative(Step)) { 1095 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1096 getSignedRange(Step).getSignedMin()); 1097 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1098 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1099 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1100 AR->getPostIncExpr(*this), N))) 1101 // Return the expression with the addrec on the outside. 1102 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1103 getSignExtendExpr(Step, Ty), 1104 L); 1105 } 1106 } 1107 } 1108 1109 // The cast wasn't folded; create an explicit cast node. 1110 // Recompute the insert position, as it may have been invalidated. 1111 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1112 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1113 new (S) SCEVSignExtendExpr(ID, Op, Ty); 1114 UniqueSCEVs.InsertNode(S, IP); 1115 return S; 1116} 1117 1118/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1119/// unspecified bits out to the given type. 1120/// 1121const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1122 const Type *Ty) { 1123 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1124 "This is not an extending conversion!"); 1125 assert(isSCEVable(Ty) && 1126 "This is not a conversion to a SCEVable type!"); 1127 Ty = getEffectiveSCEVType(Ty); 1128 1129 // Sign-extend negative constants. 1130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1131 if (SC->getValue()->getValue().isNegative()) 1132 return getSignExtendExpr(Op, Ty); 1133 1134 // Peel off a truncate cast. 1135 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1136 const SCEV *NewOp = T->getOperand(); 1137 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1138 return getAnyExtendExpr(NewOp, Ty); 1139 return getTruncateOrNoop(NewOp, Ty); 1140 } 1141 1142 // Next try a zext cast. If the cast is folded, use it. 1143 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1144 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1145 return ZExt; 1146 1147 // Next try a sext cast. If the cast is folded, use it. 1148 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1149 if (!isa<SCEVSignExtendExpr>(SExt)) 1150 return SExt; 1151 1152 // Force the cast to be folded into the operands of an addrec. 1153 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1154 SmallVector<const SCEV *, 4> Ops; 1155 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1156 I != E; ++I) 1157 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1158 return getAddRecExpr(Ops, AR->getLoop()); 1159 } 1160 1161 // If the expression is obviously signed, use the sext cast value. 1162 if (isa<SCEVSMaxExpr>(Op)) 1163 return SExt; 1164 1165 // Absent any other information, use the zext cast value. 1166 return ZExt; 1167} 1168 1169/// CollectAddOperandsWithScales - Process the given Ops list, which is 1170/// a list of operands to be added under the given scale, update the given 1171/// map. This is a helper function for getAddRecExpr. As an example of 1172/// what it does, given a sequence of operands that would form an add 1173/// expression like this: 1174/// 1175/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1176/// 1177/// where A and B are constants, update the map with these values: 1178/// 1179/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1180/// 1181/// and add 13 + A*B*29 to AccumulatedConstant. 1182/// This will allow getAddRecExpr to produce this: 1183/// 1184/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1185/// 1186/// This form often exposes folding opportunities that are hidden in 1187/// the original operand list. 1188/// 1189/// Return true iff it appears that any interesting folding opportunities 1190/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1191/// the common case where no interesting opportunities are present, and 1192/// is also used as a check to avoid infinite recursion. 1193/// 1194static bool 1195CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1196 SmallVector<const SCEV *, 8> &NewOps, 1197 APInt &AccumulatedConstant, 1198 const SmallVectorImpl<const SCEV *> &Ops, 1199 const APInt &Scale, 1200 ScalarEvolution &SE) { 1201 bool Interesting = false; 1202 1203 // Iterate over the add operands. 1204 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1205 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1206 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1207 APInt NewScale = 1208 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1209 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1210 // A multiplication of a constant with another add; recurse. 1211 Interesting |= 1212 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1213 cast<SCEVAddExpr>(Mul->getOperand(1)) 1214 ->getOperands(), 1215 NewScale, SE); 1216 } else { 1217 // A multiplication of a constant with some other value. Update 1218 // the map. 1219 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1220 const SCEV *Key = SE.getMulExpr(MulOps); 1221 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1222 M.insert(std::make_pair(Key, NewScale)); 1223 if (Pair.second) { 1224 NewOps.push_back(Pair.first->first); 1225 } else { 1226 Pair.first->second += NewScale; 1227 // The map already had an entry for this value, which may indicate 1228 // a folding opportunity. 1229 Interesting = true; 1230 } 1231 } 1232 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1233 // Pull a buried constant out to the outside. 1234 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1235 Interesting = true; 1236 AccumulatedConstant += Scale * C->getValue()->getValue(); 1237 } else { 1238 // An ordinary operand. Update the map. 1239 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1240 M.insert(std::make_pair(Ops[i], Scale)); 1241 if (Pair.second) { 1242 NewOps.push_back(Pair.first->first); 1243 } else { 1244 Pair.first->second += Scale; 1245 // The map already had an entry for this value, which may indicate 1246 // a folding opportunity. 1247 Interesting = true; 1248 } 1249 } 1250 } 1251 1252 return Interesting; 1253} 1254 1255namespace { 1256 struct APIntCompare { 1257 bool operator()(const APInt &LHS, const APInt &RHS) const { 1258 return LHS.ult(RHS); 1259 } 1260 }; 1261} 1262 1263/// getAddExpr - Get a canonical add expression, or something simpler if 1264/// possible. 1265const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1266 bool HasNUW, bool HasNSW) { 1267 assert(!Ops.empty() && "Cannot get empty add!"); 1268 if (Ops.size() == 1) return Ops[0]; 1269#ifndef NDEBUG 1270 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1271 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1272 getEffectiveSCEVType(Ops[0]->getType()) && 1273 "SCEVAddExpr operand types don't match!"); 1274#endif 1275 1276 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1277 if (!HasNUW && HasNSW) { 1278 bool All = true; 1279 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1280 if (!isKnownNonNegative(Ops[i])) { 1281 All = false; 1282 break; 1283 } 1284 if (All) HasNUW = true; 1285 } 1286 1287 // Sort by complexity, this groups all similar expression types together. 1288 GroupByComplexity(Ops, LI); 1289 1290 // If there are any constants, fold them together. 1291 unsigned Idx = 0; 1292 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1293 ++Idx; 1294 assert(Idx < Ops.size()); 1295 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1296 // We found two constants, fold them together! 1297 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1298 RHSC->getValue()->getValue()); 1299 if (Ops.size() == 2) return Ops[0]; 1300 Ops.erase(Ops.begin()+1); // Erase the folded element 1301 LHSC = cast<SCEVConstant>(Ops[0]); 1302 } 1303 1304 // If we are left with a constant zero being added, strip it off. 1305 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1306 Ops.erase(Ops.begin()); 1307 --Idx; 1308 } 1309 } 1310 1311 if (Ops.size() == 1) return Ops[0]; 1312 1313 // Okay, check to see if the same value occurs in the operand list twice. If 1314 // so, merge them together into an multiply expression. Since we sorted the 1315 // list, these values are required to be adjacent. 1316 const Type *Ty = Ops[0]->getType(); 1317 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1318 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1319 // Found a match, merge the two values into a multiply, and add any 1320 // remaining values to the result. 1321 const SCEV *Two = getIntegerSCEV(2, Ty); 1322 const SCEV *Mul = getMulExpr(Ops[i], Two); 1323 if (Ops.size() == 2) 1324 return Mul; 1325 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1326 Ops.push_back(Mul); 1327 return getAddExpr(Ops, HasNUW, HasNSW); 1328 } 1329 1330 // Check for truncates. If all the operands are truncated from the same 1331 // type, see if factoring out the truncate would permit the result to be 1332 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1333 // if the contents of the resulting outer trunc fold to something simple. 1334 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1335 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1336 const Type *DstType = Trunc->getType(); 1337 const Type *SrcType = Trunc->getOperand()->getType(); 1338 SmallVector<const SCEV *, 8> LargeOps; 1339 bool Ok = true; 1340 // Check all the operands to see if they can be represented in the 1341 // source type of the truncate. 1342 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1343 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1344 if (T->getOperand()->getType() != SrcType) { 1345 Ok = false; 1346 break; 1347 } 1348 LargeOps.push_back(T->getOperand()); 1349 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1350 // This could be either sign or zero extension, but sign extension 1351 // is much more likely to be foldable here. 1352 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1353 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1354 SmallVector<const SCEV *, 8> LargeMulOps; 1355 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1356 if (const SCEVTruncateExpr *T = 1357 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1358 if (T->getOperand()->getType() != SrcType) { 1359 Ok = false; 1360 break; 1361 } 1362 LargeMulOps.push_back(T->getOperand()); 1363 } else if (const SCEVConstant *C = 1364 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1365 // This could be either sign or zero extension, but sign extension 1366 // is much more likely to be foldable here. 1367 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1368 } else { 1369 Ok = false; 1370 break; 1371 } 1372 } 1373 if (Ok) 1374 LargeOps.push_back(getMulExpr(LargeMulOps)); 1375 } else { 1376 Ok = false; 1377 break; 1378 } 1379 } 1380 if (Ok) { 1381 // Evaluate the expression in the larger type. 1382 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1383 // If it folds to something simple, use it. Otherwise, don't. 1384 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1385 return getTruncateExpr(Fold, DstType); 1386 } 1387 } 1388 1389 // Skip past any other cast SCEVs. 1390 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1391 ++Idx; 1392 1393 // If there are add operands they would be next. 1394 if (Idx < Ops.size()) { 1395 bool DeletedAdd = false; 1396 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1397 // If we have an add, expand the add operands onto the end of the operands 1398 // list. 1399 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1400 Ops.erase(Ops.begin()+Idx); 1401 DeletedAdd = true; 1402 } 1403 1404 // If we deleted at least one add, we added operands to the end of the list, 1405 // and they are not necessarily sorted. Recurse to resort and resimplify 1406 // any operands we just aquired. 1407 if (DeletedAdd) 1408 return getAddExpr(Ops); 1409 } 1410 1411 // Skip over the add expression until we get to a multiply. 1412 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1413 ++Idx; 1414 1415 // Check to see if there are any folding opportunities present with 1416 // operands multiplied by constant values. 1417 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1418 uint64_t BitWidth = getTypeSizeInBits(Ty); 1419 DenseMap<const SCEV *, APInt> M; 1420 SmallVector<const SCEV *, 8> NewOps; 1421 APInt AccumulatedConstant(BitWidth, 0); 1422 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1423 Ops, APInt(BitWidth, 1), *this)) { 1424 // Some interesting folding opportunity is present, so its worthwhile to 1425 // re-generate the operands list. Group the operands by constant scale, 1426 // to avoid multiplying by the same constant scale multiple times. 1427 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1428 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1429 E = NewOps.end(); I != E; ++I) 1430 MulOpLists[M.find(*I)->second].push_back(*I); 1431 // Re-generate the operands list. 1432 Ops.clear(); 1433 if (AccumulatedConstant != 0) 1434 Ops.push_back(getConstant(AccumulatedConstant)); 1435 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1436 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1437 if (I->first != 0) 1438 Ops.push_back(getMulExpr(getConstant(I->first), 1439 getAddExpr(I->second))); 1440 if (Ops.empty()) 1441 return getIntegerSCEV(0, Ty); 1442 if (Ops.size() == 1) 1443 return Ops[0]; 1444 return getAddExpr(Ops); 1445 } 1446 } 1447 1448 // If we are adding something to a multiply expression, make sure the 1449 // something is not already an operand of the multiply. If so, merge it into 1450 // the multiply. 1451 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1452 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1453 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1454 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1455 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1456 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1457 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1458 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1459 if (Mul->getNumOperands() != 2) { 1460 // If the multiply has more than two operands, we must get the 1461 // Y*Z term. 1462 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1463 MulOps.erase(MulOps.begin()+MulOp); 1464 InnerMul = getMulExpr(MulOps); 1465 } 1466 const SCEV *One = getIntegerSCEV(1, Ty); 1467 const SCEV *AddOne = getAddExpr(InnerMul, One); 1468 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1469 if (Ops.size() == 2) return OuterMul; 1470 if (AddOp < Idx) { 1471 Ops.erase(Ops.begin()+AddOp); 1472 Ops.erase(Ops.begin()+Idx-1); 1473 } else { 1474 Ops.erase(Ops.begin()+Idx); 1475 Ops.erase(Ops.begin()+AddOp-1); 1476 } 1477 Ops.push_back(OuterMul); 1478 return getAddExpr(Ops); 1479 } 1480 1481 // Check this multiply against other multiplies being added together. 1482 for (unsigned OtherMulIdx = Idx+1; 1483 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1484 ++OtherMulIdx) { 1485 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1486 // If MulOp occurs in OtherMul, we can fold the two multiplies 1487 // together. 1488 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1489 OMulOp != e; ++OMulOp) 1490 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1491 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1492 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1493 if (Mul->getNumOperands() != 2) { 1494 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1495 Mul->op_end()); 1496 MulOps.erase(MulOps.begin()+MulOp); 1497 InnerMul1 = getMulExpr(MulOps); 1498 } 1499 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1500 if (OtherMul->getNumOperands() != 2) { 1501 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1502 OtherMul->op_end()); 1503 MulOps.erase(MulOps.begin()+OMulOp); 1504 InnerMul2 = getMulExpr(MulOps); 1505 } 1506 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1507 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1508 if (Ops.size() == 2) return OuterMul; 1509 Ops.erase(Ops.begin()+Idx); 1510 Ops.erase(Ops.begin()+OtherMulIdx-1); 1511 Ops.push_back(OuterMul); 1512 return getAddExpr(Ops); 1513 } 1514 } 1515 } 1516 } 1517 1518 // If there are any add recurrences in the operands list, see if any other 1519 // added values are loop invariant. If so, we can fold them into the 1520 // recurrence. 1521 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1522 ++Idx; 1523 1524 // Scan over all recurrences, trying to fold loop invariants into them. 1525 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1526 // Scan all of the other operands to this add and add them to the vector if 1527 // they are loop invariant w.r.t. the recurrence. 1528 SmallVector<const SCEV *, 8> LIOps; 1529 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1530 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1531 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1532 LIOps.push_back(Ops[i]); 1533 Ops.erase(Ops.begin()+i); 1534 --i; --e; 1535 } 1536 1537 // If we found some loop invariants, fold them into the recurrence. 1538 if (!LIOps.empty()) { 1539 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1540 LIOps.push_back(AddRec->getStart()); 1541 1542 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1543 AddRec->op_end()); 1544 AddRecOps[0] = getAddExpr(LIOps); 1545 1546 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition 1547 // is not associative so this isn't necessarily safe. 1548 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1549 1550 // If all of the other operands were loop invariant, we are done. 1551 if (Ops.size() == 1) return NewRec; 1552 1553 // Otherwise, add the folded AddRec by the non-liv parts. 1554 for (unsigned i = 0;; ++i) 1555 if (Ops[i] == AddRec) { 1556 Ops[i] = NewRec; 1557 break; 1558 } 1559 return getAddExpr(Ops); 1560 } 1561 1562 // Okay, if there weren't any loop invariants to be folded, check to see if 1563 // there are multiple AddRec's with the same loop induction variable being 1564 // added together. If so, we can fold them. 1565 for (unsigned OtherIdx = Idx+1; 1566 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1567 if (OtherIdx != Idx) { 1568 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1569 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1570 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1571 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1572 AddRec->op_end()); 1573 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1574 if (i >= NewOps.size()) { 1575 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1576 OtherAddRec->op_end()); 1577 break; 1578 } 1579 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1580 } 1581 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1582 1583 if (Ops.size() == 2) return NewAddRec; 1584 1585 Ops.erase(Ops.begin()+Idx); 1586 Ops.erase(Ops.begin()+OtherIdx-1); 1587 Ops.push_back(NewAddRec); 1588 return getAddExpr(Ops); 1589 } 1590 } 1591 1592 // Otherwise couldn't fold anything into this recurrence. Move onto the 1593 // next one. 1594 } 1595 1596 // Okay, it looks like we really DO need an add expr. Check to see if we 1597 // already have one, otherwise create a new one. 1598 FoldingSetNodeID ID; 1599 ID.AddInteger(scAddExpr); 1600 ID.AddInteger(Ops.size()); 1601 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1602 ID.AddPointer(Ops[i]); 1603 void *IP = 0; 1604 SCEVAddExpr *S = 1605 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1606 if (!S) { 1607 S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1608 new (S) SCEVAddExpr(ID, Ops); 1609 UniqueSCEVs.InsertNode(S, IP); 1610 } 1611 if (HasNUW) S->setHasNoUnsignedWrap(true); 1612 if (HasNSW) S->setHasNoSignedWrap(true); 1613 return S; 1614} 1615 1616/// getMulExpr - Get a canonical multiply expression, or something simpler if 1617/// possible. 1618const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1619 bool HasNUW, bool HasNSW) { 1620 assert(!Ops.empty() && "Cannot get empty mul!"); 1621 if (Ops.size() == 1) return Ops[0]; 1622#ifndef NDEBUG 1623 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1624 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1625 getEffectiveSCEVType(Ops[0]->getType()) && 1626 "SCEVMulExpr operand types don't match!"); 1627#endif 1628 1629 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1630 if (!HasNUW && HasNSW) { 1631 bool All = true; 1632 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1633 if (!isKnownNonNegative(Ops[i])) { 1634 All = false; 1635 break; 1636 } 1637 if (All) HasNUW = true; 1638 } 1639 1640 // Sort by complexity, this groups all similar expression types together. 1641 GroupByComplexity(Ops, LI); 1642 1643 // If there are any constants, fold them together. 1644 unsigned Idx = 0; 1645 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1646 1647 // C1*(C2+V) -> C1*C2 + C1*V 1648 if (Ops.size() == 2) 1649 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1650 if (Add->getNumOperands() == 2 && 1651 isa<SCEVConstant>(Add->getOperand(0))) 1652 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1653 getMulExpr(LHSC, Add->getOperand(1))); 1654 1655 ++Idx; 1656 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1657 // We found two constants, fold them together! 1658 ConstantInt *Fold = ConstantInt::get(getContext(), 1659 LHSC->getValue()->getValue() * 1660 RHSC->getValue()->getValue()); 1661 Ops[0] = getConstant(Fold); 1662 Ops.erase(Ops.begin()+1); // Erase the folded element 1663 if (Ops.size() == 1) return Ops[0]; 1664 LHSC = cast<SCEVConstant>(Ops[0]); 1665 } 1666 1667 // If we are left with a constant one being multiplied, strip it off. 1668 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1669 Ops.erase(Ops.begin()); 1670 --Idx; 1671 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1672 // If we have a multiply of zero, it will always be zero. 1673 return Ops[0]; 1674 } else if (Ops[0]->isAllOnesValue()) { 1675 // If we have a mul by -1 of an add, try distributing the -1 among the 1676 // add operands. 1677 if (Ops.size() == 2) 1678 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1679 SmallVector<const SCEV *, 4> NewOps; 1680 bool AnyFolded = false; 1681 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1682 I != E; ++I) { 1683 const SCEV *Mul = getMulExpr(Ops[0], *I); 1684 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1685 NewOps.push_back(Mul); 1686 } 1687 if (AnyFolded) 1688 return getAddExpr(NewOps); 1689 } 1690 } 1691 } 1692 1693 // Skip over the add expression until we get to a multiply. 1694 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1695 ++Idx; 1696 1697 if (Ops.size() == 1) 1698 return Ops[0]; 1699 1700 // If there are mul operands inline them all into this expression. 1701 if (Idx < Ops.size()) { 1702 bool DeletedMul = false; 1703 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1704 // If we have an mul, expand the mul operands onto the end of the operands 1705 // list. 1706 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1707 Ops.erase(Ops.begin()+Idx); 1708 DeletedMul = true; 1709 } 1710 1711 // If we deleted at least one mul, we added operands to the end of the list, 1712 // and they are not necessarily sorted. Recurse to resort and resimplify 1713 // any operands we just aquired. 1714 if (DeletedMul) 1715 return getMulExpr(Ops); 1716 } 1717 1718 // If there are any add recurrences in the operands list, see if any other 1719 // added values are loop invariant. If so, we can fold them into the 1720 // recurrence. 1721 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1722 ++Idx; 1723 1724 // Scan over all recurrences, trying to fold loop invariants into them. 1725 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1726 // Scan all of the other operands to this mul and add them to the vector if 1727 // they are loop invariant w.r.t. the recurrence. 1728 SmallVector<const SCEV *, 8> LIOps; 1729 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1730 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1731 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1732 LIOps.push_back(Ops[i]); 1733 Ops.erase(Ops.begin()+i); 1734 --i; --e; 1735 } 1736 1737 // If we found some loop invariants, fold them into the recurrence. 1738 if (!LIOps.empty()) { 1739 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1740 SmallVector<const SCEV *, 4> NewOps; 1741 NewOps.reserve(AddRec->getNumOperands()); 1742 if (LIOps.size() == 1) { 1743 const SCEV *Scale = LIOps[0]; 1744 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1745 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1746 } else { 1747 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1748 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1749 MulOps.push_back(AddRec->getOperand(i)); 1750 NewOps.push_back(getMulExpr(MulOps)); 1751 } 1752 } 1753 1754 // It's tempting to propagate the NSW flag here, but nsw multiplication 1755 // is not associative so this isn't necessarily safe. 1756 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1757 HasNUW && AddRec->hasNoUnsignedWrap(), 1758 /*HasNSW=*/false); 1759 1760 // If all of the other operands were loop invariant, we are done. 1761 if (Ops.size() == 1) return NewRec; 1762 1763 // Otherwise, multiply the folded AddRec by the non-liv parts. 1764 for (unsigned i = 0;; ++i) 1765 if (Ops[i] == AddRec) { 1766 Ops[i] = NewRec; 1767 break; 1768 } 1769 return getMulExpr(Ops); 1770 } 1771 1772 // Okay, if there weren't any loop invariants to be folded, check to see if 1773 // there are multiple AddRec's with the same loop induction variable being 1774 // multiplied together. If so, we can fold them. 1775 for (unsigned OtherIdx = Idx+1; 1776 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1777 if (OtherIdx != Idx) { 1778 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1779 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1780 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1781 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1782 const SCEV *NewStart = getMulExpr(F->getStart(), 1783 G->getStart()); 1784 const SCEV *B = F->getStepRecurrence(*this); 1785 const SCEV *D = G->getStepRecurrence(*this); 1786 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1787 getMulExpr(G, B), 1788 getMulExpr(B, D)); 1789 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1790 F->getLoop()); 1791 if (Ops.size() == 2) return NewAddRec; 1792 1793 Ops.erase(Ops.begin()+Idx); 1794 Ops.erase(Ops.begin()+OtherIdx-1); 1795 Ops.push_back(NewAddRec); 1796 return getMulExpr(Ops); 1797 } 1798 } 1799 1800 // Otherwise couldn't fold anything into this recurrence. Move onto the 1801 // next one. 1802 } 1803 1804 // Okay, it looks like we really DO need an mul expr. Check to see if we 1805 // already have one, otherwise create a new one. 1806 FoldingSetNodeID ID; 1807 ID.AddInteger(scMulExpr); 1808 ID.AddInteger(Ops.size()); 1809 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1810 ID.AddPointer(Ops[i]); 1811 void *IP = 0; 1812 SCEVMulExpr *S = 1813 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1814 if (!S) { 1815 S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1816 new (S) SCEVMulExpr(ID, Ops); 1817 UniqueSCEVs.InsertNode(S, IP); 1818 } 1819 if (HasNUW) S->setHasNoUnsignedWrap(true); 1820 if (HasNSW) S->setHasNoSignedWrap(true); 1821 return S; 1822} 1823 1824/// getUDivExpr - Get a canonical unsigned division expression, or something 1825/// simpler if possible. 1826const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1827 const SCEV *RHS) { 1828 assert(getEffectiveSCEVType(LHS->getType()) == 1829 getEffectiveSCEVType(RHS->getType()) && 1830 "SCEVUDivExpr operand types don't match!"); 1831 1832 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1833 if (RHSC->getValue()->equalsInt(1)) 1834 return LHS; // X udiv 1 --> x 1835 if (RHSC->isZero()) 1836 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1837 1838 // Determine if the division can be folded into the operands of 1839 // its operands. 1840 // TODO: Generalize this to non-constants by using known-bits information. 1841 const Type *Ty = LHS->getType(); 1842 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1843 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1844 // For non-power-of-two values, effectively round the value up to the 1845 // nearest power of two. 1846 if (!RHSC->getValue()->getValue().isPowerOf2()) 1847 ++MaxShiftAmt; 1848 const IntegerType *ExtTy = 1849 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1850 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1851 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1852 if (const SCEVConstant *Step = 1853 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1854 if (!Step->getValue()->getValue() 1855 .urem(RHSC->getValue()->getValue()) && 1856 getZeroExtendExpr(AR, ExtTy) == 1857 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1858 getZeroExtendExpr(Step, ExtTy), 1859 AR->getLoop())) { 1860 SmallVector<const SCEV *, 4> Operands; 1861 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1862 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1863 return getAddRecExpr(Operands, AR->getLoop()); 1864 } 1865 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1866 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1867 SmallVector<const SCEV *, 4> Operands; 1868 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1869 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1870 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1871 // Find an operand that's safely divisible. 1872 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1873 const SCEV *Op = M->getOperand(i); 1874 const SCEV *Div = getUDivExpr(Op, RHSC); 1875 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1876 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1877 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1878 MOperands.end()); 1879 Operands[i] = Div; 1880 return getMulExpr(Operands); 1881 } 1882 } 1883 } 1884 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1885 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1886 SmallVector<const SCEV *, 4> Operands; 1887 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1888 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1889 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1890 Operands.clear(); 1891 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1892 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1893 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1894 break; 1895 Operands.push_back(Op); 1896 } 1897 if (Operands.size() == A->getNumOperands()) 1898 return getAddExpr(Operands); 1899 } 1900 } 1901 1902 // Fold if both operands are constant. 1903 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1904 Constant *LHSCV = LHSC->getValue(); 1905 Constant *RHSCV = RHSC->getValue(); 1906 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1907 RHSCV))); 1908 } 1909 } 1910 1911 FoldingSetNodeID ID; 1912 ID.AddInteger(scUDivExpr); 1913 ID.AddPointer(LHS); 1914 ID.AddPointer(RHS); 1915 void *IP = 0; 1916 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1917 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1918 new (S) SCEVUDivExpr(ID, LHS, RHS); 1919 UniqueSCEVs.InsertNode(S, IP); 1920 return S; 1921} 1922 1923 1924/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1925/// Simplify the expression as much as possible. 1926const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1927 const SCEV *Step, const Loop *L, 1928 bool HasNUW, bool HasNSW) { 1929 SmallVector<const SCEV *, 4> Operands; 1930 Operands.push_back(Start); 1931 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1932 if (StepChrec->getLoop() == L) { 1933 Operands.insert(Operands.end(), StepChrec->op_begin(), 1934 StepChrec->op_end()); 1935 return getAddRecExpr(Operands, L); 1936 } 1937 1938 Operands.push_back(Step); 1939 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1940} 1941 1942/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1943/// Simplify the expression as much as possible. 1944const SCEV * 1945ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1946 const Loop *L, 1947 bool HasNUW, bool HasNSW) { 1948 if (Operands.size() == 1) return Operands[0]; 1949#ifndef NDEBUG 1950 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1951 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1952 getEffectiveSCEVType(Operands[0]->getType()) && 1953 "SCEVAddRecExpr operand types don't match!"); 1954#endif 1955 1956 if (Operands.back()->isZero()) { 1957 Operands.pop_back(); 1958 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1959 } 1960 1961 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1962 if (!HasNUW && HasNSW) { 1963 bool All = true; 1964 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1965 if (!isKnownNonNegative(Operands[i])) { 1966 All = false; 1967 break; 1968 } 1969 if (All) HasNUW = true; 1970 } 1971 1972 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1973 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1974 const Loop *NestedLoop = NestedAR->getLoop(); 1975 if (L->contains(NestedLoop->getHeader()) ? 1976 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1977 (!NestedLoop->contains(L->getHeader()) && 1978 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1979 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1980 NestedAR->op_end()); 1981 Operands[0] = NestedAR->getStart(); 1982 // AddRecs require their operands be loop-invariant with respect to their 1983 // loops. Don't perform this transformation if it would break this 1984 // requirement. 1985 bool AllInvariant = true; 1986 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1987 if (!Operands[i]->isLoopInvariant(L)) { 1988 AllInvariant = false; 1989 break; 1990 } 1991 if (AllInvariant) { 1992 NestedOperands[0] = getAddRecExpr(Operands, L); 1993 AllInvariant = true; 1994 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1995 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1996 AllInvariant = false; 1997 break; 1998 } 1999 if (AllInvariant) 2000 // Ok, both add recurrences are valid after the transformation. 2001 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2002 } 2003 // Reset Operands to its original state. 2004 Operands[0] = NestedAR; 2005 } 2006 } 2007 2008 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2009 // already have one, otherwise create a new one. 2010 FoldingSetNodeID ID; 2011 ID.AddInteger(scAddRecExpr); 2012 ID.AddInteger(Operands.size()); 2013 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2014 ID.AddPointer(Operands[i]); 2015 ID.AddPointer(L); 2016 void *IP = 0; 2017 SCEVAddRecExpr *S = 2018 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2019 if (!S) { 2020 S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 2021 new (S) SCEVAddRecExpr(ID, Operands, L); 2022 UniqueSCEVs.InsertNode(S, IP); 2023 } 2024 if (HasNUW) S->setHasNoUnsignedWrap(true); 2025 if (HasNSW) S->setHasNoSignedWrap(true); 2026 return S; 2027} 2028 2029const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2030 const SCEV *RHS) { 2031 SmallVector<const SCEV *, 2> Ops; 2032 Ops.push_back(LHS); 2033 Ops.push_back(RHS); 2034 return getSMaxExpr(Ops); 2035} 2036 2037const SCEV * 2038ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2039 assert(!Ops.empty() && "Cannot get empty smax!"); 2040 if (Ops.size() == 1) return Ops[0]; 2041#ifndef NDEBUG 2042 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2043 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2044 getEffectiveSCEVType(Ops[0]->getType()) && 2045 "SCEVSMaxExpr operand types don't match!"); 2046#endif 2047 2048 // Sort by complexity, this groups all similar expression types together. 2049 GroupByComplexity(Ops, LI); 2050 2051 // If there are any constants, fold them together. 2052 unsigned Idx = 0; 2053 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2054 ++Idx; 2055 assert(Idx < Ops.size()); 2056 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2057 // We found two constants, fold them together! 2058 ConstantInt *Fold = ConstantInt::get(getContext(), 2059 APIntOps::smax(LHSC->getValue()->getValue(), 2060 RHSC->getValue()->getValue())); 2061 Ops[0] = getConstant(Fold); 2062 Ops.erase(Ops.begin()+1); // Erase the folded element 2063 if (Ops.size() == 1) return Ops[0]; 2064 LHSC = cast<SCEVConstant>(Ops[0]); 2065 } 2066 2067 // If we are left with a constant minimum-int, strip it off. 2068 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2069 Ops.erase(Ops.begin()); 2070 --Idx; 2071 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2072 // If we have an smax with a constant maximum-int, it will always be 2073 // maximum-int. 2074 return Ops[0]; 2075 } 2076 } 2077 2078 if (Ops.size() == 1) return Ops[0]; 2079 2080 // Find the first SMax 2081 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2082 ++Idx; 2083 2084 // Check to see if one of the operands is an SMax. If so, expand its operands 2085 // onto our operand list, and recurse to simplify. 2086 if (Idx < Ops.size()) { 2087 bool DeletedSMax = false; 2088 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2089 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 2090 Ops.erase(Ops.begin()+Idx); 2091 DeletedSMax = true; 2092 } 2093 2094 if (DeletedSMax) 2095 return getSMaxExpr(Ops); 2096 } 2097 2098 // Okay, check to see if the same value occurs in the operand list twice. If 2099 // so, delete one. Since we sorted the list, these values are required to 2100 // be adjacent. 2101 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2102 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 2103 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2104 --i; --e; 2105 } 2106 2107 if (Ops.size() == 1) return Ops[0]; 2108 2109 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2110 2111 // Okay, it looks like we really DO need an smax expr. Check to see if we 2112 // already have one, otherwise create a new one. 2113 FoldingSetNodeID ID; 2114 ID.AddInteger(scSMaxExpr); 2115 ID.AddInteger(Ops.size()); 2116 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2117 ID.AddPointer(Ops[i]); 2118 void *IP = 0; 2119 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2120 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 2121 new (S) SCEVSMaxExpr(ID, Ops); 2122 UniqueSCEVs.InsertNode(S, IP); 2123 return S; 2124} 2125 2126const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2127 const SCEV *RHS) { 2128 SmallVector<const SCEV *, 2> Ops; 2129 Ops.push_back(LHS); 2130 Ops.push_back(RHS); 2131 return getUMaxExpr(Ops); 2132} 2133 2134const SCEV * 2135ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2136 assert(!Ops.empty() && "Cannot get empty umax!"); 2137 if (Ops.size() == 1) return Ops[0]; 2138#ifndef NDEBUG 2139 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2140 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2141 getEffectiveSCEVType(Ops[0]->getType()) && 2142 "SCEVUMaxExpr operand types don't match!"); 2143#endif 2144 2145 // Sort by complexity, this groups all similar expression types together. 2146 GroupByComplexity(Ops, LI); 2147 2148 // If there are any constants, fold them together. 2149 unsigned Idx = 0; 2150 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2151 ++Idx; 2152 assert(Idx < Ops.size()); 2153 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2154 // We found two constants, fold them together! 2155 ConstantInt *Fold = ConstantInt::get(getContext(), 2156 APIntOps::umax(LHSC->getValue()->getValue(), 2157 RHSC->getValue()->getValue())); 2158 Ops[0] = getConstant(Fold); 2159 Ops.erase(Ops.begin()+1); // Erase the folded element 2160 if (Ops.size() == 1) return Ops[0]; 2161 LHSC = cast<SCEVConstant>(Ops[0]); 2162 } 2163 2164 // If we are left with a constant minimum-int, strip it off. 2165 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2166 Ops.erase(Ops.begin()); 2167 --Idx; 2168 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2169 // If we have an umax with a constant maximum-int, it will always be 2170 // maximum-int. 2171 return Ops[0]; 2172 } 2173 } 2174 2175 if (Ops.size() == 1) return Ops[0]; 2176 2177 // Find the first UMax 2178 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2179 ++Idx; 2180 2181 // Check to see if one of the operands is a UMax. If so, expand its operands 2182 // onto our operand list, and recurse to simplify. 2183 if (Idx < Ops.size()) { 2184 bool DeletedUMax = false; 2185 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2186 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2187 Ops.erase(Ops.begin()+Idx); 2188 DeletedUMax = true; 2189 } 2190 2191 if (DeletedUMax) 2192 return getUMaxExpr(Ops); 2193 } 2194 2195 // Okay, check to see if the same value occurs in the operand list twice. If 2196 // so, delete one. Since we sorted the list, these values are required to 2197 // be adjacent. 2198 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2199 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2200 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2201 --i; --e; 2202 } 2203 2204 if (Ops.size() == 1) return Ops[0]; 2205 2206 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2207 2208 // Okay, it looks like we really DO need a umax expr. Check to see if we 2209 // already have one, otherwise create a new one. 2210 FoldingSetNodeID ID; 2211 ID.AddInteger(scUMaxExpr); 2212 ID.AddInteger(Ops.size()); 2213 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2214 ID.AddPointer(Ops[i]); 2215 void *IP = 0; 2216 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2217 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2218 new (S) SCEVUMaxExpr(ID, Ops); 2219 UniqueSCEVs.InsertNode(S, IP); 2220 return S; 2221} 2222 2223const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2224 const SCEV *RHS) { 2225 // ~smax(~x, ~y) == smin(x, y). 2226 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2227} 2228 2229const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2230 const SCEV *RHS) { 2231 // ~umax(~x, ~y) == umin(x, y) 2232 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2233} 2234 2235const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2236 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2237 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2238 C = ConstantFoldConstantExpression(CE, TD); 2239 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2240 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2241} 2242 2243const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2244 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2245 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2246 C = ConstantFoldConstantExpression(CE, TD); 2247 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2248 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2249} 2250 2251const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2252 unsigned FieldNo) { 2253 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2254 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2255 C = ConstantFoldConstantExpression(CE, TD); 2256 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2257 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2258} 2259 2260const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2261 Constant *FieldNo) { 2262 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2263 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2264 C = ConstantFoldConstantExpression(CE, TD); 2265 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2266 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2267} 2268 2269const SCEV *ScalarEvolution::getUnknown(Value *V) { 2270 // Don't attempt to do anything other than create a SCEVUnknown object 2271 // here. createSCEV only calls getUnknown after checking for all other 2272 // interesting possibilities, and any other code that calls getUnknown 2273 // is doing so in order to hide a value from SCEV canonicalization. 2274 2275 FoldingSetNodeID ID; 2276 ID.AddInteger(scUnknown); 2277 ID.AddPointer(V); 2278 void *IP = 0; 2279 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2280 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2281 new (S) SCEVUnknown(ID, V); 2282 UniqueSCEVs.InsertNode(S, IP); 2283 return S; 2284} 2285 2286//===----------------------------------------------------------------------===// 2287// Basic SCEV Analysis and PHI Idiom Recognition Code 2288// 2289 2290/// isSCEVable - Test if values of the given type are analyzable within 2291/// the SCEV framework. This primarily includes integer types, and it 2292/// can optionally include pointer types if the ScalarEvolution class 2293/// has access to target-specific information. 2294bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2295 // Integers and pointers are always SCEVable. 2296 return Ty->isInteger() || isa<PointerType>(Ty); 2297} 2298 2299/// getTypeSizeInBits - Return the size in bits of the specified type, 2300/// for which isSCEVable must return true. 2301uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2302 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2303 2304 // If we have a TargetData, use it! 2305 if (TD) 2306 return TD->getTypeSizeInBits(Ty); 2307 2308 // Integer types have fixed sizes. 2309 if (Ty->isInteger()) 2310 return Ty->getPrimitiveSizeInBits(); 2311 2312 // The only other support type is pointer. Without TargetData, conservatively 2313 // assume pointers are 64-bit. 2314 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!"); 2315 return 64; 2316} 2317 2318/// getEffectiveSCEVType - Return a type with the same bitwidth as 2319/// the given type and which represents how SCEV will treat the given 2320/// type, for which isSCEVable must return true. For pointer types, 2321/// this is the pointer-sized integer type. 2322const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2323 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2324 2325 if (Ty->isInteger()) 2326 return Ty; 2327 2328 // The only other support type is pointer. 2329 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2330 if (TD) return TD->getIntPtrType(getContext()); 2331 2332 // Without TargetData, conservatively assume pointers are 64-bit. 2333 return Type::getInt64Ty(getContext()); 2334} 2335 2336const SCEV *ScalarEvolution::getCouldNotCompute() { 2337 return &CouldNotCompute; 2338} 2339 2340/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2341/// expression and create a new one. 2342const SCEV *ScalarEvolution::getSCEV(Value *V) { 2343 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2344 2345 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2346 if (I != Scalars.end()) return I->second; 2347 const SCEV *S = createSCEV(V); 2348 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2349 return S; 2350} 2351 2352/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2353/// specified signed integer value and return a SCEV for the constant. 2354const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) { 2355 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2356 return getConstant(ConstantInt::get(ITy, Val)); 2357} 2358 2359/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2360/// 2361const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2362 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2363 return getConstant( 2364 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2365 2366 const Type *Ty = V->getType(); 2367 Ty = getEffectiveSCEVType(Ty); 2368 return getMulExpr(V, 2369 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2370} 2371 2372/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2373const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2374 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2375 return getConstant( 2376 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2377 2378 const Type *Ty = V->getType(); 2379 Ty = getEffectiveSCEVType(Ty); 2380 const SCEV *AllOnes = 2381 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2382 return getMinusSCEV(AllOnes, V); 2383} 2384 2385/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2386/// 2387const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2388 const SCEV *RHS) { 2389 // X - Y --> X + -Y 2390 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2391} 2392 2393/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2394/// input value to the specified type. If the type must be extended, it is zero 2395/// extended. 2396const SCEV * 2397ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2398 const Type *Ty) { 2399 const Type *SrcTy = V->getType(); 2400 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2401 (Ty->isInteger() || isa<PointerType>(Ty)) && 2402 "Cannot truncate or zero extend with non-integer arguments!"); 2403 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2404 return V; // No conversion 2405 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2406 return getTruncateExpr(V, Ty); 2407 return getZeroExtendExpr(V, Ty); 2408} 2409 2410/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2411/// input value to the specified type. If the type must be extended, it is sign 2412/// extended. 2413const SCEV * 2414ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2415 const Type *Ty) { 2416 const Type *SrcTy = V->getType(); 2417 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2418 (Ty->isInteger() || isa<PointerType>(Ty)) && 2419 "Cannot truncate or zero extend with non-integer arguments!"); 2420 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2421 return V; // No conversion 2422 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2423 return getTruncateExpr(V, Ty); 2424 return getSignExtendExpr(V, Ty); 2425} 2426 2427/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2428/// input value to the specified type. If the type must be extended, it is zero 2429/// extended. The conversion must not be narrowing. 2430const SCEV * 2431ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2432 const Type *SrcTy = V->getType(); 2433 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2434 (Ty->isInteger() || isa<PointerType>(Ty)) && 2435 "Cannot noop or zero extend with non-integer arguments!"); 2436 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2437 "getNoopOrZeroExtend cannot truncate!"); 2438 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2439 return V; // No conversion 2440 return getZeroExtendExpr(V, Ty); 2441} 2442 2443/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2444/// input value to the specified type. If the type must be extended, it is sign 2445/// extended. The conversion must not be narrowing. 2446const SCEV * 2447ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2448 const Type *SrcTy = V->getType(); 2449 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2450 (Ty->isInteger() || isa<PointerType>(Ty)) && 2451 "Cannot noop or sign extend with non-integer arguments!"); 2452 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2453 "getNoopOrSignExtend cannot truncate!"); 2454 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2455 return V; // No conversion 2456 return getSignExtendExpr(V, Ty); 2457} 2458 2459/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2460/// the input value to the specified type. If the type must be extended, 2461/// it is extended with unspecified bits. The conversion must not be 2462/// narrowing. 2463const SCEV * 2464ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2465 const Type *SrcTy = V->getType(); 2466 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2467 (Ty->isInteger() || isa<PointerType>(Ty)) && 2468 "Cannot noop or any extend with non-integer arguments!"); 2469 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2470 "getNoopOrAnyExtend cannot truncate!"); 2471 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2472 return V; // No conversion 2473 return getAnyExtendExpr(V, Ty); 2474} 2475 2476/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2477/// input value to the specified type. The conversion must not be widening. 2478const SCEV * 2479ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2480 const Type *SrcTy = V->getType(); 2481 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2482 (Ty->isInteger() || isa<PointerType>(Ty)) && 2483 "Cannot truncate or noop with non-integer arguments!"); 2484 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2485 "getTruncateOrNoop cannot extend!"); 2486 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2487 return V; // No conversion 2488 return getTruncateExpr(V, Ty); 2489} 2490 2491/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2492/// the types using zero-extension, and then perform a umax operation 2493/// with them. 2494const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2495 const SCEV *RHS) { 2496 const SCEV *PromotedLHS = LHS; 2497 const SCEV *PromotedRHS = RHS; 2498 2499 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2500 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2501 else 2502 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2503 2504 return getUMaxExpr(PromotedLHS, PromotedRHS); 2505} 2506 2507/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2508/// the types using zero-extension, and then perform a umin operation 2509/// with them. 2510const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2511 const SCEV *RHS) { 2512 const SCEV *PromotedLHS = LHS; 2513 const SCEV *PromotedRHS = RHS; 2514 2515 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2516 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2517 else 2518 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2519 2520 return getUMinExpr(PromotedLHS, PromotedRHS); 2521} 2522 2523/// PushDefUseChildren - Push users of the given Instruction 2524/// onto the given Worklist. 2525static void 2526PushDefUseChildren(Instruction *I, 2527 SmallVectorImpl<Instruction *> &Worklist) { 2528 // Push the def-use children onto the Worklist stack. 2529 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2530 UI != UE; ++UI) 2531 Worklist.push_back(cast<Instruction>(UI)); 2532} 2533 2534/// ForgetSymbolicValue - This looks up computed SCEV values for all 2535/// instructions that depend on the given instruction and removes them from 2536/// the Scalars map if they reference SymName. This is used during PHI 2537/// resolution. 2538void 2539ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2540 SmallVector<Instruction *, 16> Worklist; 2541 PushDefUseChildren(I, Worklist); 2542 2543 SmallPtrSet<Instruction *, 8> Visited; 2544 Visited.insert(I); 2545 while (!Worklist.empty()) { 2546 Instruction *I = Worklist.pop_back_val(); 2547 if (!Visited.insert(I)) continue; 2548 2549 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2550 Scalars.find(static_cast<Value *>(I)); 2551 if (It != Scalars.end()) { 2552 // Short-circuit the def-use traversal if the symbolic name 2553 // ceases to appear in expressions. 2554 if (!It->second->hasOperand(SymName)) 2555 continue; 2556 2557 // SCEVUnknown for a PHI either means that it has an unrecognized 2558 // structure, or it's a PHI that's in the progress of being computed 2559 // by createNodeForPHI. In the former case, additional loop trip 2560 // count information isn't going to change anything. In the later 2561 // case, createNodeForPHI will perform the necessary updates on its 2562 // own when it gets to that point. 2563 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 2564 ValuesAtScopes.erase(It->second); 2565 Scalars.erase(It); 2566 } 2567 } 2568 2569 PushDefUseChildren(I, Worklist); 2570 } 2571} 2572 2573/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2574/// a loop header, making it a potential recurrence, or it doesn't. 2575/// 2576const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2577 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2578 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2579 if (L->getHeader() == PN->getParent()) { 2580 // If it lives in the loop header, it has two incoming values, one 2581 // from outside the loop, and one from inside. 2582 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2583 unsigned BackEdge = IncomingEdge^1; 2584 2585 // While we are analyzing this PHI node, handle its value symbolically. 2586 const SCEV *SymbolicName = getUnknown(PN); 2587 assert(Scalars.find(PN) == Scalars.end() && 2588 "PHI node already processed?"); 2589 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2590 2591 // Using this symbolic name for the PHI, analyze the value coming around 2592 // the back-edge. 2593 Value *BEValueV = PN->getIncomingValue(BackEdge); 2594 const SCEV *BEValue = getSCEV(BEValueV); 2595 2596 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2597 // has a special value for the first iteration of the loop. 2598 2599 // If the value coming around the backedge is an add with the symbolic 2600 // value we just inserted, then we found a simple induction variable! 2601 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2602 // If there is a single occurrence of the symbolic value, replace it 2603 // with a recurrence. 2604 unsigned FoundIndex = Add->getNumOperands(); 2605 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2606 if (Add->getOperand(i) == SymbolicName) 2607 if (FoundIndex == e) { 2608 FoundIndex = i; 2609 break; 2610 } 2611 2612 if (FoundIndex != Add->getNumOperands()) { 2613 // Create an add with everything but the specified operand. 2614 SmallVector<const SCEV *, 8> Ops; 2615 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2616 if (i != FoundIndex) 2617 Ops.push_back(Add->getOperand(i)); 2618 const SCEV *Accum = getAddExpr(Ops); 2619 2620 // This is not a valid addrec if the step amount is varying each 2621 // loop iteration, but is not itself an addrec in this loop. 2622 if (Accum->isLoopInvariant(L) || 2623 (isa<SCEVAddRecExpr>(Accum) && 2624 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2625 bool HasNUW = false; 2626 bool HasNSW = false; 2627 2628 // If the increment doesn't overflow, then neither the addrec nor 2629 // the post-increment will overflow. 2630 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2631 if (OBO->hasNoUnsignedWrap()) 2632 HasNUW = true; 2633 if (OBO->hasNoSignedWrap()) 2634 HasNSW = true; 2635 } 2636 2637 const SCEV *StartVal = 2638 getSCEV(PN->getIncomingValue(IncomingEdge)); 2639 const SCEV *PHISCEV = 2640 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2641 2642 // Since the no-wrap flags are on the increment, they apply to the 2643 // post-incremented value as well. 2644 if (Accum->isLoopInvariant(L)) 2645 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2646 Accum, L, HasNUW, HasNSW); 2647 2648 // Okay, for the entire analysis of this edge we assumed the PHI 2649 // to be symbolic. We now need to go back and purge all of the 2650 // entries for the scalars that use the symbolic expression. 2651 ForgetSymbolicName(PN, SymbolicName); 2652 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2653 return PHISCEV; 2654 } 2655 } 2656 } else if (const SCEVAddRecExpr *AddRec = 2657 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2658 // Otherwise, this could be a loop like this: 2659 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2660 // In this case, j = {1,+,1} and BEValue is j. 2661 // Because the other in-value of i (0) fits the evolution of BEValue 2662 // i really is an addrec evolution. 2663 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2664 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2665 2666 // If StartVal = j.start - j.stride, we can use StartVal as the 2667 // initial step of the addrec evolution. 2668 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2669 AddRec->getOperand(1))) { 2670 const SCEV *PHISCEV = 2671 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2672 2673 // Okay, for the entire analysis of this edge we assumed the PHI 2674 // to be symbolic. We now need to go back and purge all of the 2675 // entries for the scalars that use the symbolic expression. 2676 ForgetSymbolicName(PN, SymbolicName); 2677 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2678 return PHISCEV; 2679 } 2680 } 2681 } 2682 2683 return SymbolicName; 2684 } 2685 2686 // It's tempting to recognize PHIs with a unique incoming value, however 2687 // this leads passes like indvars to break LCSSA form. Fortunately, such 2688 // PHIs are rare, as instcombine zaps them. 2689 2690 // If it's not a loop phi, we can't handle it yet. 2691 return getUnknown(PN); 2692} 2693 2694/// createNodeForGEP - Expand GEP instructions into add and multiply 2695/// operations. This allows them to be analyzed by regular SCEV code. 2696/// 2697const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2698 2699 bool InBounds = GEP->isInBounds(); 2700 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2701 Value *Base = GEP->getOperand(0); 2702 // Don't attempt to analyze GEPs over unsized objects. 2703 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2704 return getUnknown(GEP); 2705 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2706 gep_type_iterator GTI = gep_type_begin(GEP); 2707 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2708 E = GEP->op_end(); 2709 I != E; ++I) { 2710 Value *Index = *I; 2711 // Compute the (potentially symbolic) offset in bytes for this index. 2712 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2713 // For a struct, add the member offset. 2714 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2715 TotalOffset = getAddExpr(TotalOffset, 2716 getOffsetOfExpr(STy, FieldNo), 2717 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2718 } else { 2719 // For an array, add the element offset, explicitly scaled. 2720 const SCEV *LocalOffset = getSCEV(Index); 2721 // Getelementptr indicies are signed. 2722 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2723 // Lower "inbounds" GEPs to NSW arithmetic. 2724 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2725 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2726 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2727 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2728 } 2729 } 2730 return getAddExpr(getSCEV(Base), TotalOffset, 2731 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2732} 2733 2734/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2735/// guaranteed to end in (at every loop iteration). It is, at the same time, 2736/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2737/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2738uint32_t 2739ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2740 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2741 return C->getValue()->getValue().countTrailingZeros(); 2742 2743 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2744 return std::min(GetMinTrailingZeros(T->getOperand()), 2745 (uint32_t)getTypeSizeInBits(T->getType())); 2746 2747 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2748 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2749 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2750 getTypeSizeInBits(E->getType()) : OpRes; 2751 } 2752 2753 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2754 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2755 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2756 getTypeSizeInBits(E->getType()) : OpRes; 2757 } 2758 2759 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2760 // The result is the min of all operands results. 2761 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2762 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2763 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2764 return MinOpRes; 2765 } 2766 2767 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2768 // The result is the sum of all operands results. 2769 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2770 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2771 for (unsigned i = 1, e = M->getNumOperands(); 2772 SumOpRes != BitWidth && i != e; ++i) 2773 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2774 BitWidth); 2775 return SumOpRes; 2776 } 2777 2778 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2779 // The result is the min of all operands results. 2780 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2781 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2782 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2783 return MinOpRes; 2784 } 2785 2786 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2787 // The result is the min of all operands results. 2788 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2789 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2790 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2791 return MinOpRes; 2792 } 2793 2794 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2795 // The result is the min of all operands results. 2796 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2797 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2798 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2799 return MinOpRes; 2800 } 2801 2802 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2803 // For a SCEVUnknown, ask ValueTracking. 2804 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2805 APInt Mask = APInt::getAllOnesValue(BitWidth); 2806 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2807 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2808 return Zeros.countTrailingOnes(); 2809 } 2810 2811 // SCEVUDivExpr 2812 return 0; 2813} 2814 2815/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2816/// 2817ConstantRange 2818ScalarEvolution::getUnsignedRange(const SCEV *S) { 2819 2820 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2821 return ConstantRange(C->getValue()->getValue()); 2822 2823 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2824 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2825 2826 // If the value has known zeros, the maximum unsigned value will have those 2827 // known zeros as well. 2828 uint32_t TZ = GetMinTrailingZeros(S); 2829 if (TZ != 0) 2830 ConservativeResult = 2831 ConstantRange(APInt::getMinValue(BitWidth), 2832 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2833 2834 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2835 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2836 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2837 X = X.add(getUnsignedRange(Add->getOperand(i))); 2838 return ConservativeResult.intersectWith(X); 2839 } 2840 2841 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2842 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2843 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2844 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2845 return ConservativeResult.intersectWith(X); 2846 } 2847 2848 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2849 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2850 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2851 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2852 return ConservativeResult.intersectWith(X); 2853 } 2854 2855 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2856 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2857 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2858 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2859 return ConservativeResult.intersectWith(X); 2860 } 2861 2862 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2863 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2864 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2865 return ConservativeResult.intersectWith(X.udiv(Y)); 2866 } 2867 2868 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2869 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2870 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2871 } 2872 2873 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2874 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2875 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2876 } 2877 2878 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2879 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2880 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2881 } 2882 2883 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2884 // If there's no unsigned wrap, the value will never be less than its 2885 // initial value. 2886 if (AddRec->hasNoUnsignedWrap()) 2887 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2888 ConservativeResult = 2889 ConstantRange(C->getValue()->getValue(), 2890 APInt(getTypeSizeInBits(C->getType()), 0)); 2891 2892 // TODO: non-affine addrec 2893 if (AddRec->isAffine()) { 2894 const Type *Ty = AddRec->getType(); 2895 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2896 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2897 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2898 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2899 2900 const SCEV *Start = AddRec->getStart(); 2901 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2902 2903 // Check for overflow. 2904 if (!AddRec->hasNoUnsignedWrap()) 2905 return ConservativeResult; 2906 2907 ConstantRange StartRange = getUnsignedRange(Start); 2908 ConstantRange EndRange = getUnsignedRange(End); 2909 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2910 EndRange.getUnsignedMin()); 2911 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2912 EndRange.getUnsignedMax()); 2913 if (Min.isMinValue() && Max.isMaxValue()) 2914 return ConservativeResult; 2915 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2916 } 2917 } 2918 2919 return ConservativeResult; 2920 } 2921 2922 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2923 // For a SCEVUnknown, ask ValueTracking. 2924 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2925 APInt Mask = APInt::getAllOnesValue(BitWidth); 2926 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2927 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2928 if (Ones == ~Zeros + 1) 2929 return ConservativeResult; 2930 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 2931 } 2932 2933 return ConservativeResult; 2934} 2935 2936/// getSignedRange - Determine the signed range for a particular SCEV. 2937/// 2938ConstantRange 2939ScalarEvolution::getSignedRange(const SCEV *S) { 2940 2941 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2942 return ConstantRange(C->getValue()->getValue()); 2943 2944 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2945 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2946 2947 // If the value has known zeros, the maximum signed value will have those 2948 // known zeros as well. 2949 uint32_t TZ = GetMinTrailingZeros(S); 2950 if (TZ != 0) 2951 ConservativeResult = 2952 ConstantRange(APInt::getSignedMinValue(BitWidth), 2953 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 2954 2955 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2956 ConstantRange X = getSignedRange(Add->getOperand(0)); 2957 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2958 X = X.add(getSignedRange(Add->getOperand(i))); 2959 return ConservativeResult.intersectWith(X); 2960 } 2961 2962 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2963 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2964 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2965 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2966 return ConservativeResult.intersectWith(X); 2967 } 2968 2969 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2970 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2971 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2972 X = X.smax(getSignedRange(SMax->getOperand(i))); 2973 return ConservativeResult.intersectWith(X); 2974 } 2975 2976 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2977 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2978 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2979 X = X.umax(getSignedRange(UMax->getOperand(i))); 2980 return ConservativeResult.intersectWith(X); 2981 } 2982 2983 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2984 ConstantRange X = getSignedRange(UDiv->getLHS()); 2985 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2986 return ConservativeResult.intersectWith(X.udiv(Y)); 2987 } 2988 2989 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2990 ConstantRange X = getSignedRange(ZExt->getOperand()); 2991 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2992 } 2993 2994 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2995 ConstantRange X = getSignedRange(SExt->getOperand()); 2996 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2997 } 2998 2999 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3000 ConstantRange X = getSignedRange(Trunc->getOperand()); 3001 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3002 } 3003 3004 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3005 // If there's no signed wrap, and all the operands have the same sign or 3006 // zero, the value won't ever change sign. 3007 if (AddRec->hasNoSignedWrap()) { 3008 bool AllNonNeg = true; 3009 bool AllNonPos = true; 3010 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3011 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3012 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3013 } 3014 if (AllNonNeg) 3015 ConservativeResult = ConservativeResult.intersectWith( 3016 ConstantRange(APInt(BitWidth, 0), 3017 APInt::getSignedMinValue(BitWidth))); 3018 else if (AllNonPos) 3019 ConservativeResult = ConservativeResult.intersectWith( 3020 ConstantRange(APInt::getSignedMinValue(BitWidth), 3021 APInt(BitWidth, 1))); 3022 } 3023 3024 // TODO: non-affine addrec 3025 if (AddRec->isAffine()) { 3026 const Type *Ty = AddRec->getType(); 3027 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3028 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3029 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3030 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3031 3032 const SCEV *Start = AddRec->getStart(); 3033 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 3034 3035 // Check for overflow. 3036 if (!AddRec->hasNoSignedWrap()) 3037 return ConservativeResult; 3038 3039 ConstantRange StartRange = getSignedRange(Start); 3040 ConstantRange EndRange = getSignedRange(End); 3041 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3042 EndRange.getSignedMin()); 3043 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3044 EndRange.getSignedMax()); 3045 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3046 return ConservativeResult; 3047 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3048 } 3049 } 3050 3051 return ConservativeResult; 3052 } 3053 3054 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3055 // For a SCEVUnknown, ask ValueTracking. 3056 if (!U->getValue()->getType()->isInteger() && !TD) 3057 return ConservativeResult; 3058 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3059 if (NS == 1) 3060 return ConservativeResult; 3061 return ConservativeResult.intersectWith( 3062 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3063 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3064 } 3065 3066 return ConservativeResult; 3067} 3068 3069/// createSCEV - We know that there is no SCEV for the specified value. 3070/// Analyze the expression. 3071/// 3072const SCEV *ScalarEvolution::createSCEV(Value *V) { 3073 if (!isSCEVable(V->getType())) 3074 return getUnknown(V); 3075 3076 unsigned Opcode = Instruction::UserOp1; 3077 if (Instruction *I = dyn_cast<Instruction>(V)) 3078 Opcode = I->getOpcode(); 3079 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3080 Opcode = CE->getOpcode(); 3081 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3082 return getConstant(CI); 3083 else if (isa<ConstantPointerNull>(V)) 3084 return getIntegerSCEV(0, V->getType()); 3085 else if (isa<UndefValue>(V)) 3086 return getIntegerSCEV(0, V->getType()); 3087 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3088 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3089 else 3090 return getUnknown(V); 3091 3092 Operator *U = cast<Operator>(V); 3093 switch (Opcode) { 3094 case Instruction::Add: 3095 // Don't transfer the NSW and NUW bits from the Add instruction to the 3096 // Add expression, because the Instruction may be guarded by control 3097 // flow and the no-overflow bits may not be valid for the expression in 3098 // any context. 3099 return getAddExpr(getSCEV(U->getOperand(0)), 3100 getSCEV(U->getOperand(1))); 3101 case Instruction::Mul: 3102 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3103 // Mul expression, as with Add. 3104 return getMulExpr(getSCEV(U->getOperand(0)), 3105 getSCEV(U->getOperand(1))); 3106 case Instruction::UDiv: 3107 return getUDivExpr(getSCEV(U->getOperand(0)), 3108 getSCEV(U->getOperand(1))); 3109 case Instruction::Sub: 3110 return getMinusSCEV(getSCEV(U->getOperand(0)), 3111 getSCEV(U->getOperand(1))); 3112 case Instruction::And: 3113 // For an expression like x&255 that merely masks off the high bits, 3114 // use zext(trunc(x)) as the SCEV expression. 3115 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3116 if (CI->isNullValue()) 3117 return getSCEV(U->getOperand(1)); 3118 if (CI->isAllOnesValue()) 3119 return getSCEV(U->getOperand(0)); 3120 const APInt &A = CI->getValue(); 3121 3122 // Instcombine's ShrinkDemandedConstant may strip bits out of 3123 // constants, obscuring what would otherwise be a low-bits mask. 3124 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3125 // knew about to reconstruct a low-bits mask value. 3126 unsigned LZ = A.countLeadingZeros(); 3127 unsigned BitWidth = A.getBitWidth(); 3128 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3129 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3130 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3131 3132 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3133 3134 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3135 return 3136 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3137 IntegerType::get(getContext(), BitWidth - LZ)), 3138 U->getType()); 3139 } 3140 break; 3141 3142 case Instruction::Or: 3143 // If the RHS of the Or is a constant, we may have something like: 3144 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3145 // optimizations will transparently handle this case. 3146 // 3147 // In order for this transformation to be safe, the LHS must be of the 3148 // form X*(2^n) and the Or constant must be less than 2^n. 3149 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3150 const SCEV *LHS = getSCEV(U->getOperand(0)); 3151 const APInt &CIVal = CI->getValue(); 3152 if (GetMinTrailingZeros(LHS) >= 3153 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3154 // Build a plain add SCEV. 3155 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3156 // If the LHS of the add was an addrec and it has no-wrap flags, 3157 // transfer the no-wrap flags, since an or won't introduce a wrap. 3158 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3159 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3160 if (OldAR->hasNoUnsignedWrap()) 3161 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3162 if (OldAR->hasNoSignedWrap()) 3163 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3164 } 3165 return S; 3166 } 3167 } 3168 break; 3169 case Instruction::Xor: 3170 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3171 // If the RHS of the xor is a signbit, then this is just an add. 3172 // Instcombine turns add of signbit into xor as a strength reduction step. 3173 if (CI->getValue().isSignBit()) 3174 return getAddExpr(getSCEV(U->getOperand(0)), 3175 getSCEV(U->getOperand(1))); 3176 3177 // If the RHS of xor is -1, then this is a not operation. 3178 if (CI->isAllOnesValue()) 3179 return getNotSCEV(getSCEV(U->getOperand(0))); 3180 3181 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3182 // This is a variant of the check for xor with -1, and it handles 3183 // the case where instcombine has trimmed non-demanded bits out 3184 // of an xor with -1. 3185 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3186 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3187 if (BO->getOpcode() == Instruction::And && 3188 LCI->getValue() == CI->getValue()) 3189 if (const SCEVZeroExtendExpr *Z = 3190 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3191 const Type *UTy = U->getType(); 3192 const SCEV *Z0 = Z->getOperand(); 3193 const Type *Z0Ty = Z0->getType(); 3194 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3195 3196 // If C is a low-bits mask, the zero extend is zerving to 3197 // mask off the high bits. Complement the operand and 3198 // re-apply the zext. 3199 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3200 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3201 3202 // If C is a single bit, it may be in the sign-bit position 3203 // before the zero-extend. In this case, represent the xor 3204 // using an add, which is equivalent, and re-apply the zext. 3205 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3206 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3207 Trunc.isSignBit()) 3208 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3209 UTy); 3210 } 3211 } 3212 break; 3213 3214 case Instruction::Shl: 3215 // Turn shift left of a constant amount into a multiply. 3216 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3217 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3218 Constant *X = ConstantInt::get(getContext(), 3219 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3220 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3221 } 3222 break; 3223 3224 case Instruction::LShr: 3225 // Turn logical shift right of a constant into a unsigned divide. 3226 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3227 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3228 Constant *X = ConstantInt::get(getContext(), 3229 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3230 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3231 } 3232 break; 3233 3234 case Instruction::AShr: 3235 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3236 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3237 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3238 if (L->getOpcode() == Instruction::Shl && 3239 L->getOperand(1) == U->getOperand(1)) { 3240 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3241 uint64_t Amt = BitWidth - CI->getZExtValue(); 3242 if (Amt == BitWidth) 3243 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3244 if (Amt > BitWidth) 3245 return getIntegerSCEV(0, U->getType()); // value is undefined 3246 return 3247 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3248 IntegerType::get(getContext(), Amt)), 3249 U->getType()); 3250 } 3251 break; 3252 3253 case Instruction::Trunc: 3254 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3255 3256 case Instruction::ZExt: 3257 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3258 3259 case Instruction::SExt: 3260 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3261 3262 case Instruction::BitCast: 3263 // BitCasts are no-op casts so we just eliminate the cast. 3264 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3265 return getSCEV(U->getOperand(0)); 3266 break; 3267 3268 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3269 // lead to pointer expressions which cannot safely be expanded to GEPs, 3270 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3271 // simplifying integer expressions. 3272 3273 case Instruction::GetElementPtr: 3274 return createNodeForGEP(cast<GEPOperator>(U)); 3275 3276 case Instruction::PHI: 3277 return createNodeForPHI(cast<PHINode>(U)); 3278 3279 case Instruction::Select: 3280 // This could be a smax or umax that was lowered earlier. 3281 // Try to recover it. 3282 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3283 Value *LHS = ICI->getOperand(0); 3284 Value *RHS = ICI->getOperand(1); 3285 switch (ICI->getPredicate()) { 3286 case ICmpInst::ICMP_SLT: 3287 case ICmpInst::ICMP_SLE: 3288 std::swap(LHS, RHS); 3289 // fall through 3290 case ICmpInst::ICMP_SGT: 3291 case ICmpInst::ICMP_SGE: 3292 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3293 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3294 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3295 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3296 break; 3297 case ICmpInst::ICMP_ULT: 3298 case ICmpInst::ICMP_ULE: 3299 std::swap(LHS, RHS); 3300 // fall through 3301 case ICmpInst::ICMP_UGT: 3302 case ICmpInst::ICMP_UGE: 3303 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3304 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3305 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3306 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3307 break; 3308 case ICmpInst::ICMP_NE: 3309 // n != 0 ? n : 1 -> umax(n, 1) 3310 if (LHS == U->getOperand(1) && 3311 isa<ConstantInt>(U->getOperand(2)) && 3312 cast<ConstantInt>(U->getOperand(2))->isOne() && 3313 isa<ConstantInt>(RHS) && 3314 cast<ConstantInt>(RHS)->isZero()) 3315 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3316 break; 3317 case ICmpInst::ICMP_EQ: 3318 // n == 0 ? 1 : n -> umax(n, 1) 3319 if (LHS == U->getOperand(2) && 3320 isa<ConstantInt>(U->getOperand(1)) && 3321 cast<ConstantInt>(U->getOperand(1))->isOne() && 3322 isa<ConstantInt>(RHS) && 3323 cast<ConstantInt>(RHS)->isZero()) 3324 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3325 break; 3326 default: 3327 break; 3328 } 3329 } 3330 3331 default: // We cannot analyze this expression. 3332 break; 3333 } 3334 3335 return getUnknown(V); 3336} 3337 3338 3339 3340//===----------------------------------------------------------------------===// 3341// Iteration Count Computation Code 3342// 3343 3344/// getBackedgeTakenCount - If the specified loop has a predictable 3345/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3346/// object. The backedge-taken count is the number of times the loop header 3347/// will be branched to from within the loop. This is one less than the 3348/// trip count of the loop, since it doesn't count the first iteration, 3349/// when the header is branched to from outside the loop. 3350/// 3351/// Note that it is not valid to call this method on a loop without a 3352/// loop-invariant backedge-taken count (see 3353/// hasLoopInvariantBackedgeTakenCount). 3354/// 3355const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3356 return getBackedgeTakenInfo(L).Exact; 3357} 3358 3359/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3360/// return the least SCEV value that is known never to be less than the 3361/// actual backedge taken count. 3362const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3363 return getBackedgeTakenInfo(L).Max; 3364} 3365 3366/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3367/// onto the given Worklist. 3368static void 3369PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3370 BasicBlock *Header = L->getHeader(); 3371 3372 // Push all Loop-header PHIs onto the Worklist stack. 3373 for (BasicBlock::iterator I = Header->begin(); 3374 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3375 Worklist.push_back(PN); 3376} 3377 3378const ScalarEvolution::BackedgeTakenInfo & 3379ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3380 // Initially insert a CouldNotCompute for this loop. If the insertion 3381 // succeeds, procede to actually compute a backedge-taken count and 3382 // update the value. The temporary CouldNotCompute value tells SCEV 3383 // code elsewhere that it shouldn't attempt to request a new 3384 // backedge-taken count, which could result in infinite recursion. 3385 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3386 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3387 if (Pair.second) { 3388 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3389 if (BECount.Exact != getCouldNotCompute()) { 3390 assert(BECount.Exact->isLoopInvariant(L) && 3391 BECount.Max->isLoopInvariant(L) && 3392 "Computed backedge-taken count isn't loop invariant for loop!"); 3393 ++NumTripCountsComputed; 3394 3395 // Update the value in the map. 3396 Pair.first->second = BECount; 3397 } else { 3398 if (BECount.Max != getCouldNotCompute()) 3399 // Update the value in the map. 3400 Pair.first->second = BECount; 3401 if (isa<PHINode>(L->getHeader()->begin())) 3402 // Only count loops that have phi nodes as not being computable. 3403 ++NumTripCountsNotComputed; 3404 } 3405 3406 // Now that we know more about the trip count for this loop, forget any 3407 // existing SCEV values for PHI nodes in this loop since they are only 3408 // conservative estimates made without the benefit of trip count 3409 // information. This is similar to the code in forgetLoop, except that 3410 // it handles SCEVUnknown PHI nodes specially. 3411 if (BECount.hasAnyInfo()) { 3412 SmallVector<Instruction *, 16> Worklist; 3413 PushLoopPHIs(L, Worklist); 3414 3415 SmallPtrSet<Instruction *, 8> Visited; 3416 while (!Worklist.empty()) { 3417 Instruction *I = Worklist.pop_back_val(); 3418 if (!Visited.insert(I)) continue; 3419 3420 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3421 Scalars.find(static_cast<Value *>(I)); 3422 if (It != Scalars.end()) { 3423 // SCEVUnknown for a PHI either means that it has an unrecognized 3424 // structure, or it's a PHI that's in the progress of being computed 3425 // by createNodeForPHI. In the former case, additional loop trip 3426 // count information isn't going to change anything. In the later 3427 // case, createNodeForPHI will perform the necessary updates on its 3428 // own when it gets to that point. 3429 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3430 ValuesAtScopes.erase(It->second); 3431 Scalars.erase(It); 3432 } 3433 if (PHINode *PN = dyn_cast<PHINode>(I)) 3434 ConstantEvolutionLoopExitValue.erase(PN); 3435 } 3436 3437 PushDefUseChildren(I, Worklist); 3438 } 3439 } 3440 } 3441 return Pair.first->second; 3442} 3443 3444/// forgetLoop - This method should be called by the client when it has 3445/// changed a loop in a way that may effect ScalarEvolution's ability to 3446/// compute a trip count, or if the loop is deleted. 3447void ScalarEvolution::forgetLoop(const Loop *L) { 3448 // Drop any stored trip count value. 3449 BackedgeTakenCounts.erase(L); 3450 3451 // Drop information about expressions based on loop-header PHIs. 3452 SmallVector<Instruction *, 16> Worklist; 3453 PushLoopPHIs(L, Worklist); 3454 3455 SmallPtrSet<Instruction *, 8> Visited; 3456 while (!Worklist.empty()) { 3457 Instruction *I = Worklist.pop_back_val(); 3458 if (!Visited.insert(I)) continue; 3459 3460 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3461 Scalars.find(static_cast<Value *>(I)); 3462 if (It != Scalars.end()) { 3463 ValuesAtScopes.erase(It->second); 3464 Scalars.erase(It); 3465 if (PHINode *PN = dyn_cast<PHINode>(I)) 3466 ConstantEvolutionLoopExitValue.erase(PN); 3467 } 3468 3469 PushDefUseChildren(I, Worklist); 3470 } 3471} 3472 3473/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3474/// of the specified loop will execute. 3475ScalarEvolution::BackedgeTakenInfo 3476ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3477 SmallVector<BasicBlock *, 8> ExitingBlocks; 3478 L->getExitingBlocks(ExitingBlocks); 3479 3480 // Examine all exits and pick the most conservative values. 3481 const SCEV *BECount = getCouldNotCompute(); 3482 const SCEV *MaxBECount = getCouldNotCompute(); 3483 bool CouldNotComputeBECount = false; 3484 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3485 BackedgeTakenInfo NewBTI = 3486 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3487 3488 if (NewBTI.Exact == getCouldNotCompute()) { 3489 // We couldn't compute an exact value for this exit, so 3490 // we won't be able to compute an exact value for the loop. 3491 CouldNotComputeBECount = true; 3492 BECount = getCouldNotCompute(); 3493 } else if (!CouldNotComputeBECount) { 3494 if (BECount == getCouldNotCompute()) 3495 BECount = NewBTI.Exact; 3496 else 3497 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3498 } 3499 if (MaxBECount == getCouldNotCompute()) 3500 MaxBECount = NewBTI.Max; 3501 else if (NewBTI.Max != getCouldNotCompute()) 3502 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3503 } 3504 3505 return BackedgeTakenInfo(BECount, MaxBECount); 3506} 3507 3508/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3509/// of the specified loop will execute if it exits via the specified block. 3510ScalarEvolution::BackedgeTakenInfo 3511ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3512 BasicBlock *ExitingBlock) { 3513 3514 // Okay, we've chosen an exiting block. See what condition causes us to 3515 // exit at this block. 3516 // 3517 // FIXME: we should be able to handle switch instructions (with a single exit) 3518 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3519 if (ExitBr == 0) return getCouldNotCompute(); 3520 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3521 3522 // At this point, we know we have a conditional branch that determines whether 3523 // the loop is exited. However, we don't know if the branch is executed each 3524 // time through the loop. If not, then the execution count of the branch will 3525 // not be equal to the trip count of the loop. 3526 // 3527 // Currently we check for this by checking to see if the Exit branch goes to 3528 // the loop header. If so, we know it will always execute the same number of 3529 // times as the loop. We also handle the case where the exit block *is* the 3530 // loop header. This is common for un-rotated loops. 3531 // 3532 // If both of those tests fail, walk up the unique predecessor chain to the 3533 // header, stopping if there is an edge that doesn't exit the loop. If the 3534 // header is reached, the execution count of the branch will be equal to the 3535 // trip count of the loop. 3536 // 3537 // More extensive analysis could be done to handle more cases here. 3538 // 3539 if (ExitBr->getSuccessor(0) != L->getHeader() && 3540 ExitBr->getSuccessor(1) != L->getHeader() && 3541 ExitBr->getParent() != L->getHeader()) { 3542 // The simple checks failed, try climbing the unique predecessor chain 3543 // up to the header. 3544 bool Ok = false; 3545 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3546 BasicBlock *Pred = BB->getUniquePredecessor(); 3547 if (!Pred) 3548 return getCouldNotCompute(); 3549 TerminatorInst *PredTerm = Pred->getTerminator(); 3550 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3551 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3552 if (PredSucc == BB) 3553 continue; 3554 // If the predecessor has a successor that isn't BB and isn't 3555 // outside the loop, assume the worst. 3556 if (L->contains(PredSucc)) 3557 return getCouldNotCompute(); 3558 } 3559 if (Pred == L->getHeader()) { 3560 Ok = true; 3561 break; 3562 } 3563 BB = Pred; 3564 } 3565 if (!Ok) 3566 return getCouldNotCompute(); 3567 } 3568 3569 // Procede to the next level to examine the exit condition expression. 3570 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3571 ExitBr->getSuccessor(0), 3572 ExitBr->getSuccessor(1)); 3573} 3574 3575/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3576/// backedge of the specified loop will execute if its exit condition 3577/// were a conditional branch of ExitCond, TBB, and FBB. 3578ScalarEvolution::BackedgeTakenInfo 3579ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3580 Value *ExitCond, 3581 BasicBlock *TBB, 3582 BasicBlock *FBB) { 3583 // Check if the controlling expression for this loop is an And or Or. 3584 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3585 if (BO->getOpcode() == Instruction::And) { 3586 // Recurse on the operands of the and. 3587 BackedgeTakenInfo BTI0 = 3588 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3589 BackedgeTakenInfo BTI1 = 3590 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3591 const SCEV *BECount = getCouldNotCompute(); 3592 const SCEV *MaxBECount = getCouldNotCompute(); 3593 if (L->contains(TBB)) { 3594 // Both conditions must be true for the loop to continue executing. 3595 // Choose the less conservative count. 3596 if (BTI0.Exact == getCouldNotCompute() || 3597 BTI1.Exact == getCouldNotCompute()) 3598 BECount = getCouldNotCompute(); 3599 else 3600 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3601 if (BTI0.Max == getCouldNotCompute()) 3602 MaxBECount = BTI1.Max; 3603 else if (BTI1.Max == getCouldNotCompute()) 3604 MaxBECount = BTI0.Max; 3605 else 3606 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3607 } else { 3608 // Both conditions must be true for the loop to exit. 3609 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3610 if (BTI0.Exact != getCouldNotCompute() && 3611 BTI1.Exact != getCouldNotCompute()) 3612 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3613 if (BTI0.Max != getCouldNotCompute() && 3614 BTI1.Max != getCouldNotCompute()) 3615 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3616 } 3617 3618 return BackedgeTakenInfo(BECount, MaxBECount); 3619 } 3620 if (BO->getOpcode() == Instruction::Or) { 3621 // Recurse on the operands of the or. 3622 BackedgeTakenInfo BTI0 = 3623 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3624 BackedgeTakenInfo BTI1 = 3625 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3626 const SCEV *BECount = getCouldNotCompute(); 3627 const SCEV *MaxBECount = getCouldNotCompute(); 3628 if (L->contains(FBB)) { 3629 // Both conditions must be false for the loop to continue executing. 3630 // Choose the less conservative count. 3631 if (BTI0.Exact == getCouldNotCompute() || 3632 BTI1.Exact == getCouldNotCompute()) 3633 BECount = getCouldNotCompute(); 3634 else 3635 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3636 if (BTI0.Max == getCouldNotCompute()) 3637 MaxBECount = BTI1.Max; 3638 else if (BTI1.Max == getCouldNotCompute()) 3639 MaxBECount = BTI0.Max; 3640 else 3641 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3642 } else { 3643 // Both conditions must be false for the loop to exit. 3644 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3645 if (BTI0.Exact != getCouldNotCompute() && 3646 BTI1.Exact != getCouldNotCompute()) 3647 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3648 if (BTI0.Max != getCouldNotCompute() && 3649 BTI1.Max != getCouldNotCompute()) 3650 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3651 } 3652 3653 return BackedgeTakenInfo(BECount, MaxBECount); 3654 } 3655 } 3656 3657 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3658 // Procede to the next level to examine the icmp. 3659 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3660 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3661 3662 // If it's not an integer or pointer comparison then compute it the hard way. 3663 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3664} 3665 3666/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3667/// backedge of the specified loop will execute if its exit condition 3668/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3669ScalarEvolution::BackedgeTakenInfo 3670ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3671 ICmpInst *ExitCond, 3672 BasicBlock *TBB, 3673 BasicBlock *FBB) { 3674 3675 // If the condition was exit on true, convert the condition to exit on false 3676 ICmpInst::Predicate Cond; 3677 if (!L->contains(FBB)) 3678 Cond = ExitCond->getPredicate(); 3679 else 3680 Cond = ExitCond->getInversePredicate(); 3681 3682 // Handle common loops like: for (X = "string"; *X; ++X) 3683 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3684 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3685 const SCEV *ItCnt = 3686 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3687 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3688 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3689 return BackedgeTakenInfo(ItCnt, 3690 isa<SCEVConstant>(ItCnt) ? ItCnt : 3691 getConstant(APInt::getMaxValue(BitWidth)-1)); 3692 } 3693 } 3694 3695 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3696 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3697 3698 // Try to evaluate any dependencies out of the loop. 3699 LHS = getSCEVAtScope(LHS, L); 3700 RHS = getSCEVAtScope(RHS, L); 3701 3702 // At this point, we would like to compute how many iterations of the 3703 // loop the predicate will return true for these inputs. 3704 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3705 // If there is a loop-invariant, force it into the RHS. 3706 std::swap(LHS, RHS); 3707 Cond = ICmpInst::getSwappedPredicate(Cond); 3708 } 3709 3710 // If we have a comparison of a chrec against a constant, try to use value 3711 // ranges to answer this query. 3712 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3713 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3714 if (AddRec->getLoop() == L) { 3715 // Form the constant range. 3716 ConstantRange CompRange( 3717 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3718 3719 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3720 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3721 } 3722 3723 switch (Cond) { 3724 case ICmpInst::ICMP_NE: { // while (X != Y) 3725 // Convert to: while (X-Y != 0) 3726 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3727 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3728 break; 3729 } 3730 case ICmpInst::ICMP_EQ: { // while (X == Y) 3731 // Convert to: while (X-Y == 0) 3732 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3733 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3734 break; 3735 } 3736 case ICmpInst::ICMP_SLT: { 3737 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3738 if (BTI.hasAnyInfo()) return BTI; 3739 break; 3740 } 3741 case ICmpInst::ICMP_SGT: { 3742 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3743 getNotSCEV(RHS), L, true); 3744 if (BTI.hasAnyInfo()) return BTI; 3745 break; 3746 } 3747 case ICmpInst::ICMP_ULT: { 3748 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3749 if (BTI.hasAnyInfo()) return BTI; 3750 break; 3751 } 3752 case ICmpInst::ICMP_UGT: { 3753 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3754 getNotSCEV(RHS), L, false); 3755 if (BTI.hasAnyInfo()) return BTI; 3756 break; 3757 } 3758 default: 3759#if 0 3760 dbgs() << "ComputeBackedgeTakenCount "; 3761 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3762 dbgs() << "[unsigned] "; 3763 dbgs() << *LHS << " " 3764 << Instruction::getOpcodeName(Instruction::ICmp) 3765 << " " << *RHS << "\n"; 3766#endif 3767 break; 3768 } 3769 return 3770 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3771} 3772 3773static ConstantInt * 3774EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3775 ScalarEvolution &SE) { 3776 const SCEV *InVal = SE.getConstant(C); 3777 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3778 assert(isa<SCEVConstant>(Val) && 3779 "Evaluation of SCEV at constant didn't fold correctly?"); 3780 return cast<SCEVConstant>(Val)->getValue(); 3781} 3782 3783/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3784/// and a GEP expression (missing the pointer index) indexing into it, return 3785/// the addressed element of the initializer or null if the index expression is 3786/// invalid. 3787static Constant * 3788GetAddressedElementFromGlobal(GlobalVariable *GV, 3789 const std::vector<ConstantInt*> &Indices) { 3790 Constant *Init = GV->getInitializer(); 3791 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3792 uint64_t Idx = Indices[i]->getZExtValue(); 3793 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3794 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3795 Init = cast<Constant>(CS->getOperand(Idx)); 3796 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3797 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3798 Init = cast<Constant>(CA->getOperand(Idx)); 3799 } else if (isa<ConstantAggregateZero>(Init)) { 3800 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3801 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3802 Init = Constant::getNullValue(STy->getElementType(Idx)); 3803 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3804 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3805 Init = Constant::getNullValue(ATy->getElementType()); 3806 } else { 3807 llvm_unreachable("Unknown constant aggregate type!"); 3808 } 3809 return 0; 3810 } else { 3811 return 0; // Unknown initializer type 3812 } 3813 } 3814 return Init; 3815} 3816 3817/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3818/// 'icmp op load X, cst', try to see if we can compute the backedge 3819/// execution count. 3820const SCEV * 3821ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3822 LoadInst *LI, 3823 Constant *RHS, 3824 const Loop *L, 3825 ICmpInst::Predicate predicate) { 3826 if (LI->isVolatile()) return getCouldNotCompute(); 3827 3828 // Check to see if the loaded pointer is a getelementptr of a global. 3829 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3830 if (!GEP) return getCouldNotCompute(); 3831 3832 // Make sure that it is really a constant global we are gepping, with an 3833 // initializer, and make sure the first IDX is really 0. 3834 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3835 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3836 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3837 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3838 return getCouldNotCompute(); 3839 3840 // Okay, we allow one non-constant index into the GEP instruction. 3841 Value *VarIdx = 0; 3842 std::vector<ConstantInt*> Indexes; 3843 unsigned VarIdxNum = 0; 3844 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3845 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3846 Indexes.push_back(CI); 3847 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3848 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3849 VarIdx = GEP->getOperand(i); 3850 VarIdxNum = i-2; 3851 Indexes.push_back(0); 3852 } 3853 3854 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3855 // Check to see if X is a loop variant variable value now. 3856 const SCEV *Idx = getSCEV(VarIdx); 3857 Idx = getSCEVAtScope(Idx, L); 3858 3859 // We can only recognize very limited forms of loop index expressions, in 3860 // particular, only affine AddRec's like {C1,+,C2}. 3861 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3862 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3863 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3864 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3865 return getCouldNotCompute(); 3866 3867 unsigned MaxSteps = MaxBruteForceIterations; 3868 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3869 ConstantInt *ItCst = ConstantInt::get( 3870 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3871 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3872 3873 // Form the GEP offset. 3874 Indexes[VarIdxNum] = Val; 3875 3876 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3877 if (Result == 0) break; // Cannot compute! 3878 3879 // Evaluate the condition for this iteration. 3880 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3881 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3882 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3883#if 0 3884 dbgs() << "\n***\n*** Computed loop count " << *ItCst 3885 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3886 << "***\n"; 3887#endif 3888 ++NumArrayLenItCounts; 3889 return getConstant(ItCst); // Found terminating iteration! 3890 } 3891 } 3892 return getCouldNotCompute(); 3893} 3894 3895 3896/// CanConstantFold - Return true if we can constant fold an instruction of the 3897/// specified type, assuming that all operands were constants. 3898static bool CanConstantFold(const Instruction *I) { 3899 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3900 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3901 return true; 3902 3903 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3904 if (const Function *F = CI->getCalledFunction()) 3905 return canConstantFoldCallTo(F); 3906 return false; 3907} 3908 3909/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3910/// in the loop that V is derived from. We allow arbitrary operations along the 3911/// way, but the operands of an operation must either be constants or a value 3912/// derived from a constant PHI. If this expression does not fit with these 3913/// constraints, return null. 3914static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3915 // If this is not an instruction, or if this is an instruction outside of the 3916 // loop, it can't be derived from a loop PHI. 3917 Instruction *I = dyn_cast<Instruction>(V); 3918 if (I == 0 || !L->contains(I)) return 0; 3919 3920 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3921 if (L->getHeader() == I->getParent()) 3922 return PN; 3923 else 3924 // We don't currently keep track of the control flow needed to evaluate 3925 // PHIs, so we cannot handle PHIs inside of loops. 3926 return 0; 3927 } 3928 3929 // If we won't be able to constant fold this expression even if the operands 3930 // are constants, return early. 3931 if (!CanConstantFold(I)) return 0; 3932 3933 // Otherwise, we can evaluate this instruction if all of its operands are 3934 // constant or derived from a PHI node themselves. 3935 PHINode *PHI = 0; 3936 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3937 if (!(isa<Constant>(I->getOperand(Op)) || 3938 isa<GlobalValue>(I->getOperand(Op)))) { 3939 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3940 if (P == 0) return 0; // Not evolving from PHI 3941 if (PHI == 0) 3942 PHI = P; 3943 else if (PHI != P) 3944 return 0; // Evolving from multiple different PHIs. 3945 } 3946 3947 // This is a expression evolving from a constant PHI! 3948 return PHI; 3949} 3950 3951/// EvaluateExpression - Given an expression that passes the 3952/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3953/// in the loop has the value PHIVal. If we can't fold this expression for some 3954/// reason, return null. 3955static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 3956 const TargetData *TD) { 3957 if (isa<PHINode>(V)) return PHIVal; 3958 if (Constant *C = dyn_cast<Constant>(V)) return C; 3959 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3960 Instruction *I = cast<Instruction>(V); 3961 3962 std::vector<Constant*> Operands; 3963 Operands.resize(I->getNumOperands()); 3964 3965 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3966 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 3967 if (Operands[i] == 0) return 0; 3968 } 3969 3970 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3971 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 3972 Operands[1], TD); 3973 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3974 &Operands[0], Operands.size(), TD); 3975} 3976 3977/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3978/// in the header of its containing loop, we know the loop executes a 3979/// constant number of times, and the PHI node is just a recurrence 3980/// involving constants, fold it. 3981Constant * 3982ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3983 const APInt &BEs, 3984 const Loop *L) { 3985 std::map<PHINode*, Constant*>::iterator I = 3986 ConstantEvolutionLoopExitValue.find(PN); 3987 if (I != ConstantEvolutionLoopExitValue.end()) 3988 return I->second; 3989 3990 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3991 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3992 3993 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3994 3995 // Since the loop is canonicalized, the PHI node must have two entries. One 3996 // entry must be a constant (coming in from outside of the loop), and the 3997 // second must be derived from the same PHI. 3998 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3999 Constant *StartCST = 4000 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4001 if (StartCST == 0) 4002 return RetVal = 0; // Must be a constant. 4003 4004 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4005 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4006 if (PN2 != PN) 4007 return RetVal = 0; // Not derived from same PHI. 4008 4009 // Execute the loop symbolically to determine the exit value. 4010 if (BEs.getActiveBits() >= 32) 4011 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4012 4013 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4014 unsigned IterationNum = 0; 4015 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4016 if (IterationNum == NumIterations) 4017 return RetVal = PHIVal; // Got exit value! 4018 4019 // Compute the value of the PHI node for the next iteration. 4020 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4021 if (NextPHI == PHIVal) 4022 return RetVal = NextPHI; // Stopped evolving! 4023 if (NextPHI == 0) 4024 return 0; // Couldn't evaluate! 4025 PHIVal = NextPHI; 4026 } 4027} 4028 4029/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4030/// constant number of times (the condition evolves only from constants), 4031/// try to evaluate a few iterations of the loop until we get the exit 4032/// condition gets a value of ExitWhen (true or false). If we cannot 4033/// evaluate the trip count of the loop, return getCouldNotCompute(). 4034const SCEV * 4035ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4036 Value *Cond, 4037 bool ExitWhen) { 4038 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4039 if (PN == 0) return getCouldNotCompute(); 4040 4041 // Since the loop is canonicalized, the PHI node must have two entries. One 4042 // entry must be a constant (coming in from outside of the loop), and the 4043 // second must be derived from the same PHI. 4044 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4045 Constant *StartCST = 4046 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4047 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4048 4049 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4050 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4051 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 4052 4053 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4054 // the loop symbolically to determine when the condition gets a value of 4055 // "ExitWhen". 4056 unsigned IterationNum = 0; 4057 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4058 for (Constant *PHIVal = StartCST; 4059 IterationNum != MaxIterations; ++IterationNum) { 4060 ConstantInt *CondVal = 4061 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4062 4063 // Couldn't symbolically evaluate. 4064 if (!CondVal) return getCouldNotCompute(); 4065 4066 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4067 ++NumBruteForceTripCountsComputed; 4068 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4069 } 4070 4071 // Compute the value of the PHI node for the next iteration. 4072 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4073 if (NextPHI == 0 || NextPHI == PHIVal) 4074 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4075 PHIVal = NextPHI; 4076 } 4077 4078 // Too many iterations were needed to evaluate. 4079 return getCouldNotCompute(); 4080} 4081 4082/// getSCEVAtScope - Return a SCEV expression for the specified value 4083/// at the specified scope in the program. The L value specifies a loop 4084/// nest to evaluate the expression at, where null is the top-level or a 4085/// specified loop is immediately inside of the loop. 4086/// 4087/// This method can be used to compute the exit value for a variable defined 4088/// in a loop by querying what the value will hold in the parent loop. 4089/// 4090/// In the case that a relevant loop exit value cannot be computed, the 4091/// original value V is returned. 4092const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4093 // Check to see if we've folded this expression at this loop before. 4094 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4095 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4096 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4097 if (!Pair.second) 4098 return Pair.first->second ? Pair.first->second : V; 4099 4100 // Otherwise compute it. 4101 const SCEV *C = computeSCEVAtScope(V, L); 4102 ValuesAtScopes[V][L] = C; 4103 return C; 4104} 4105 4106const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4107 if (isa<SCEVConstant>(V)) return V; 4108 4109 // If this instruction is evolved from a constant-evolving PHI, compute the 4110 // exit value from the loop without using SCEVs. 4111 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4112 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4113 const Loop *LI = (*this->LI)[I->getParent()]; 4114 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4115 if (PHINode *PN = dyn_cast<PHINode>(I)) 4116 if (PN->getParent() == LI->getHeader()) { 4117 // Okay, there is no closed form solution for the PHI node. Check 4118 // to see if the loop that contains it has a known backedge-taken 4119 // count. If so, we may be able to force computation of the exit 4120 // value. 4121 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4122 if (const SCEVConstant *BTCC = 4123 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4124 // Okay, we know how many times the containing loop executes. If 4125 // this is a constant evolving PHI node, get the final value at 4126 // the specified iteration number. 4127 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4128 BTCC->getValue()->getValue(), 4129 LI); 4130 if (RV) return getSCEV(RV); 4131 } 4132 } 4133 4134 // Okay, this is an expression that we cannot symbolically evaluate 4135 // into a SCEV. Check to see if it's possible to symbolically evaluate 4136 // the arguments into constants, and if so, try to constant propagate the 4137 // result. This is particularly useful for computing loop exit values. 4138 if (CanConstantFold(I)) { 4139 std::vector<Constant*> Operands; 4140 Operands.reserve(I->getNumOperands()); 4141 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4142 Value *Op = I->getOperand(i); 4143 if (Constant *C = dyn_cast<Constant>(Op)) { 4144 Operands.push_back(C); 4145 } else { 4146 // If any of the operands is non-constant and if they are 4147 // non-integer and non-pointer, don't even try to analyze them 4148 // with scev techniques. 4149 if (!isSCEVable(Op->getType())) 4150 return V; 4151 4152 const SCEV *OpV = getSCEVAtScope(Op, L); 4153 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4154 Constant *C = SC->getValue(); 4155 if (C->getType() != Op->getType()) 4156 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4157 Op->getType(), 4158 false), 4159 C, Op->getType()); 4160 Operands.push_back(C); 4161 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4162 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4163 if (C->getType() != Op->getType()) 4164 C = 4165 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4166 Op->getType(), 4167 false), 4168 C, Op->getType()); 4169 Operands.push_back(C); 4170 } else 4171 return V; 4172 } else { 4173 return V; 4174 } 4175 } 4176 } 4177 4178 Constant *C; 4179 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4180 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4181 Operands[0], Operands[1], TD); 4182 else 4183 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4184 &Operands[0], Operands.size(), TD); 4185 return getSCEV(C); 4186 } 4187 } 4188 4189 // This is some other type of SCEVUnknown, just return it. 4190 return V; 4191 } 4192 4193 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4194 // Avoid performing the look-up in the common case where the specified 4195 // expression has no loop-variant portions. 4196 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4197 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4198 if (OpAtScope != Comm->getOperand(i)) { 4199 // Okay, at least one of these operands is loop variant but might be 4200 // foldable. Build a new instance of the folded commutative expression. 4201 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4202 Comm->op_begin()+i); 4203 NewOps.push_back(OpAtScope); 4204 4205 for (++i; i != e; ++i) { 4206 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4207 NewOps.push_back(OpAtScope); 4208 } 4209 if (isa<SCEVAddExpr>(Comm)) 4210 return getAddExpr(NewOps); 4211 if (isa<SCEVMulExpr>(Comm)) 4212 return getMulExpr(NewOps); 4213 if (isa<SCEVSMaxExpr>(Comm)) 4214 return getSMaxExpr(NewOps); 4215 if (isa<SCEVUMaxExpr>(Comm)) 4216 return getUMaxExpr(NewOps); 4217 llvm_unreachable("Unknown commutative SCEV type!"); 4218 } 4219 } 4220 // If we got here, all operands are loop invariant. 4221 return Comm; 4222 } 4223 4224 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4225 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4226 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4227 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4228 return Div; // must be loop invariant 4229 return getUDivExpr(LHS, RHS); 4230 } 4231 4232 // If this is a loop recurrence for a loop that does not contain L, then we 4233 // are dealing with the final value computed by the loop. 4234 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4235 if (!L || !AddRec->getLoop()->contains(L)) { 4236 // To evaluate this recurrence, we need to know how many times the AddRec 4237 // loop iterates. Compute this now. 4238 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4239 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4240 4241 // Then, evaluate the AddRec. 4242 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4243 } 4244 return AddRec; 4245 } 4246 4247 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4248 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4249 if (Op == Cast->getOperand()) 4250 return Cast; // must be loop invariant 4251 return getZeroExtendExpr(Op, Cast->getType()); 4252 } 4253 4254 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4255 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4256 if (Op == Cast->getOperand()) 4257 return Cast; // must be loop invariant 4258 return getSignExtendExpr(Op, Cast->getType()); 4259 } 4260 4261 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4262 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4263 if (Op == Cast->getOperand()) 4264 return Cast; // must be loop invariant 4265 return getTruncateExpr(Op, Cast->getType()); 4266 } 4267 4268 llvm_unreachable("Unknown SCEV type!"); 4269 return 0; 4270} 4271 4272/// getSCEVAtScope - This is a convenience function which does 4273/// getSCEVAtScope(getSCEV(V), L). 4274const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4275 return getSCEVAtScope(getSCEV(V), L); 4276} 4277 4278/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4279/// following equation: 4280/// 4281/// A * X = B (mod N) 4282/// 4283/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4284/// A and B isn't important. 4285/// 4286/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4287static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4288 ScalarEvolution &SE) { 4289 uint32_t BW = A.getBitWidth(); 4290 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4291 assert(A != 0 && "A must be non-zero."); 4292 4293 // 1. D = gcd(A, N) 4294 // 4295 // The gcd of A and N may have only one prime factor: 2. The number of 4296 // trailing zeros in A is its multiplicity 4297 uint32_t Mult2 = A.countTrailingZeros(); 4298 // D = 2^Mult2 4299 4300 // 2. Check if B is divisible by D. 4301 // 4302 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4303 // is not less than multiplicity of this prime factor for D. 4304 if (B.countTrailingZeros() < Mult2) 4305 return SE.getCouldNotCompute(); 4306 4307 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4308 // modulo (N / D). 4309 // 4310 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4311 // bit width during computations. 4312 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4313 APInt Mod(BW + 1, 0); 4314 Mod.set(BW - Mult2); // Mod = N / D 4315 APInt I = AD.multiplicativeInverse(Mod); 4316 4317 // 4. Compute the minimum unsigned root of the equation: 4318 // I * (B / D) mod (N / D) 4319 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4320 4321 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4322 // bits. 4323 return SE.getConstant(Result.trunc(BW)); 4324} 4325 4326/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4327/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4328/// might be the same) or two SCEVCouldNotCompute objects. 4329/// 4330static std::pair<const SCEV *,const SCEV *> 4331SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4332 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4333 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4334 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4335 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4336 4337 // We currently can only solve this if the coefficients are constants. 4338 if (!LC || !MC || !NC) { 4339 const SCEV *CNC = SE.getCouldNotCompute(); 4340 return std::make_pair(CNC, CNC); 4341 } 4342 4343 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4344 const APInt &L = LC->getValue()->getValue(); 4345 const APInt &M = MC->getValue()->getValue(); 4346 const APInt &N = NC->getValue()->getValue(); 4347 APInt Two(BitWidth, 2); 4348 APInt Four(BitWidth, 4); 4349 4350 { 4351 using namespace APIntOps; 4352 const APInt& C = L; 4353 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4354 // The B coefficient is M-N/2 4355 APInt B(M); 4356 B -= sdiv(N,Two); 4357 4358 // The A coefficient is N/2 4359 APInt A(N.sdiv(Two)); 4360 4361 // Compute the B^2-4ac term. 4362 APInt SqrtTerm(B); 4363 SqrtTerm *= B; 4364 SqrtTerm -= Four * (A * C); 4365 4366 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4367 // integer value or else APInt::sqrt() will assert. 4368 APInt SqrtVal(SqrtTerm.sqrt()); 4369 4370 // Compute the two solutions for the quadratic formula. 4371 // The divisions must be performed as signed divisions. 4372 APInt NegB(-B); 4373 APInt TwoA( A << 1 ); 4374 if (TwoA.isMinValue()) { 4375 const SCEV *CNC = SE.getCouldNotCompute(); 4376 return std::make_pair(CNC, CNC); 4377 } 4378 4379 LLVMContext &Context = SE.getContext(); 4380 4381 ConstantInt *Solution1 = 4382 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4383 ConstantInt *Solution2 = 4384 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4385 4386 return std::make_pair(SE.getConstant(Solution1), 4387 SE.getConstant(Solution2)); 4388 } // end APIntOps namespace 4389} 4390 4391/// HowFarToZero - Return the number of times a backedge comparing the specified 4392/// value to zero will execute. If not computable, return CouldNotCompute. 4393const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4394 // If the value is a constant 4395 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4396 // If the value is already zero, the branch will execute zero times. 4397 if (C->getValue()->isZero()) return C; 4398 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4399 } 4400 4401 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4402 if (!AddRec || AddRec->getLoop() != L) 4403 return getCouldNotCompute(); 4404 4405 if (AddRec->isAffine()) { 4406 // If this is an affine expression, the execution count of this branch is 4407 // the minimum unsigned root of the following equation: 4408 // 4409 // Start + Step*N = 0 (mod 2^BW) 4410 // 4411 // equivalent to: 4412 // 4413 // Step*N = -Start (mod 2^BW) 4414 // 4415 // where BW is the common bit width of Start and Step. 4416 4417 // Get the initial value for the loop. 4418 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4419 L->getParentLoop()); 4420 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4421 L->getParentLoop()); 4422 4423 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4424 // For now we handle only constant steps. 4425 4426 // First, handle unitary steps. 4427 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4428 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4429 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4430 return Start; // N = Start (as unsigned) 4431 4432 // Then, try to solve the above equation provided that Start is constant. 4433 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4434 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4435 -StartC->getValue()->getValue(), 4436 *this); 4437 } 4438 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4439 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4440 // the quadratic equation to solve it. 4441 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4442 *this); 4443 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4444 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4445 if (R1) { 4446#if 0 4447 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4448 << " sol#2: " << *R2 << "\n"; 4449#endif 4450 // Pick the smallest positive root value. 4451 if (ConstantInt *CB = 4452 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4453 R1->getValue(), R2->getValue()))) { 4454 if (CB->getZExtValue() == false) 4455 std::swap(R1, R2); // R1 is the minimum root now. 4456 4457 // We can only use this value if the chrec ends up with an exact zero 4458 // value at this index. When solving for "X*X != 5", for example, we 4459 // should not accept a root of 2. 4460 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4461 if (Val->isZero()) 4462 return R1; // We found a quadratic root! 4463 } 4464 } 4465 } 4466 4467 return getCouldNotCompute(); 4468} 4469 4470/// HowFarToNonZero - Return the number of times a backedge checking the 4471/// specified value for nonzero will execute. If not computable, return 4472/// CouldNotCompute 4473const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4474 // Loops that look like: while (X == 0) are very strange indeed. We don't 4475 // handle them yet except for the trivial case. This could be expanded in the 4476 // future as needed. 4477 4478 // If the value is a constant, check to see if it is known to be non-zero 4479 // already. If so, the backedge will execute zero times. 4480 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4481 if (!C->getValue()->isNullValue()) 4482 return getIntegerSCEV(0, C->getType()); 4483 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4484 } 4485 4486 // We could implement others, but I really doubt anyone writes loops like 4487 // this, and if they did, they would already be constant folded. 4488 return getCouldNotCompute(); 4489} 4490 4491/// getLoopPredecessor - If the given loop's header has exactly one unique 4492/// predecessor outside the loop, return it. Otherwise return null. 4493/// 4494BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4495 BasicBlock *Header = L->getHeader(); 4496 BasicBlock *Pred = 0; 4497 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4498 PI != E; ++PI) 4499 if (!L->contains(*PI)) { 4500 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4501 Pred = *PI; 4502 } 4503 return Pred; 4504} 4505 4506/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4507/// (which may not be an immediate predecessor) which has exactly one 4508/// successor from which BB is reachable, or null if no such block is 4509/// found. 4510/// 4511BasicBlock * 4512ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4513 // If the block has a unique predecessor, then there is no path from the 4514 // predecessor to the block that does not go through the direct edge 4515 // from the predecessor to the block. 4516 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4517 return Pred; 4518 4519 // A loop's header is defined to be a block that dominates the loop. 4520 // If the header has a unique predecessor outside the loop, it must be 4521 // a block that has exactly one successor that can reach the loop. 4522 if (Loop *L = LI->getLoopFor(BB)) 4523 return getLoopPredecessor(L); 4524 4525 return 0; 4526} 4527 4528/// HasSameValue - SCEV structural equivalence is usually sufficient for 4529/// testing whether two expressions are equal, however for the purposes of 4530/// looking for a condition guarding a loop, it can be useful to be a little 4531/// more general, since a front-end may have replicated the controlling 4532/// expression. 4533/// 4534static bool HasSameValue(const SCEV *A, const SCEV *B) { 4535 // Quick check to see if they are the same SCEV. 4536 if (A == B) return true; 4537 4538 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4539 // two different instructions with the same value. Check for this case. 4540 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4541 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4542 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4543 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4544 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4545 return true; 4546 4547 // Otherwise assume they may have a different value. 4548 return false; 4549} 4550 4551bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4552 return getSignedRange(S).getSignedMax().isNegative(); 4553} 4554 4555bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4556 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4557} 4558 4559bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4560 return !getSignedRange(S).getSignedMin().isNegative(); 4561} 4562 4563bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4564 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4565} 4566 4567bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4568 return isKnownNegative(S) || isKnownPositive(S); 4569} 4570 4571bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4572 const SCEV *LHS, const SCEV *RHS) { 4573 4574 if (HasSameValue(LHS, RHS)) 4575 return ICmpInst::isTrueWhenEqual(Pred); 4576 4577 switch (Pred) { 4578 default: 4579 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4580 break; 4581 case ICmpInst::ICMP_SGT: 4582 Pred = ICmpInst::ICMP_SLT; 4583 std::swap(LHS, RHS); 4584 case ICmpInst::ICMP_SLT: { 4585 ConstantRange LHSRange = getSignedRange(LHS); 4586 ConstantRange RHSRange = getSignedRange(RHS); 4587 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4588 return true; 4589 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4590 return false; 4591 break; 4592 } 4593 case ICmpInst::ICMP_SGE: 4594 Pred = ICmpInst::ICMP_SLE; 4595 std::swap(LHS, RHS); 4596 case ICmpInst::ICMP_SLE: { 4597 ConstantRange LHSRange = getSignedRange(LHS); 4598 ConstantRange RHSRange = getSignedRange(RHS); 4599 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4600 return true; 4601 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4602 return false; 4603 break; 4604 } 4605 case ICmpInst::ICMP_UGT: 4606 Pred = ICmpInst::ICMP_ULT; 4607 std::swap(LHS, RHS); 4608 case ICmpInst::ICMP_ULT: { 4609 ConstantRange LHSRange = getUnsignedRange(LHS); 4610 ConstantRange RHSRange = getUnsignedRange(RHS); 4611 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4612 return true; 4613 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4614 return false; 4615 break; 4616 } 4617 case ICmpInst::ICMP_UGE: 4618 Pred = ICmpInst::ICMP_ULE; 4619 std::swap(LHS, RHS); 4620 case ICmpInst::ICMP_ULE: { 4621 ConstantRange LHSRange = getUnsignedRange(LHS); 4622 ConstantRange RHSRange = getUnsignedRange(RHS); 4623 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4624 return true; 4625 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4626 return false; 4627 break; 4628 } 4629 case ICmpInst::ICMP_NE: { 4630 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4631 return true; 4632 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4633 return true; 4634 4635 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4636 if (isKnownNonZero(Diff)) 4637 return true; 4638 break; 4639 } 4640 case ICmpInst::ICMP_EQ: 4641 // The check at the top of the function catches the case where 4642 // the values are known to be equal. 4643 break; 4644 } 4645 return false; 4646} 4647 4648/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4649/// protected by a conditional between LHS and RHS. This is used to 4650/// to eliminate casts. 4651bool 4652ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4653 ICmpInst::Predicate Pred, 4654 const SCEV *LHS, const SCEV *RHS) { 4655 // Interpret a null as meaning no loop, where there is obviously no guard 4656 // (interprocedural conditions notwithstanding). 4657 if (!L) return true; 4658 4659 BasicBlock *Latch = L->getLoopLatch(); 4660 if (!Latch) 4661 return false; 4662 4663 BranchInst *LoopContinuePredicate = 4664 dyn_cast<BranchInst>(Latch->getTerminator()); 4665 if (!LoopContinuePredicate || 4666 LoopContinuePredicate->isUnconditional()) 4667 return false; 4668 4669 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4670 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4671} 4672 4673/// isLoopGuardedByCond - Test whether entry to the loop is protected 4674/// by a conditional between LHS and RHS. This is used to help avoid max 4675/// expressions in loop trip counts, and to eliminate casts. 4676bool 4677ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4678 ICmpInst::Predicate Pred, 4679 const SCEV *LHS, const SCEV *RHS) { 4680 // Interpret a null as meaning no loop, where there is obviously no guard 4681 // (interprocedural conditions notwithstanding). 4682 if (!L) return false; 4683 4684 BasicBlock *Predecessor = getLoopPredecessor(L); 4685 BasicBlock *PredecessorDest = L->getHeader(); 4686 4687 // Starting at the loop predecessor, climb up the predecessor chain, as long 4688 // as there are predecessors that can be found that have unique successors 4689 // leading to the original header. 4690 for (; Predecessor; 4691 PredecessorDest = Predecessor, 4692 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4693 4694 BranchInst *LoopEntryPredicate = 4695 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4696 if (!LoopEntryPredicate || 4697 LoopEntryPredicate->isUnconditional()) 4698 continue; 4699 4700 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4701 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4702 return true; 4703 } 4704 4705 return false; 4706} 4707 4708/// isImpliedCond - Test whether the condition described by Pred, LHS, 4709/// and RHS is true whenever the given Cond value evaluates to true. 4710bool ScalarEvolution::isImpliedCond(Value *CondValue, 4711 ICmpInst::Predicate Pred, 4712 const SCEV *LHS, const SCEV *RHS, 4713 bool Inverse) { 4714 // Recursivly handle And and Or conditions. 4715 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4716 if (BO->getOpcode() == Instruction::And) { 4717 if (!Inverse) 4718 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4719 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4720 } else if (BO->getOpcode() == Instruction::Or) { 4721 if (Inverse) 4722 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4723 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4724 } 4725 } 4726 4727 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4728 if (!ICI) return false; 4729 4730 // Bail if the ICmp's operands' types are wider than the needed type 4731 // before attempting to call getSCEV on them. This avoids infinite 4732 // recursion, since the analysis of widening casts can require loop 4733 // exit condition information for overflow checking, which would 4734 // lead back here. 4735 if (getTypeSizeInBits(LHS->getType()) < 4736 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4737 return false; 4738 4739 // Now that we found a conditional branch that dominates the loop, check to 4740 // see if it is the comparison we are looking for. 4741 ICmpInst::Predicate FoundPred; 4742 if (Inverse) 4743 FoundPred = ICI->getInversePredicate(); 4744 else 4745 FoundPred = ICI->getPredicate(); 4746 4747 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4748 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4749 4750 // Balance the types. The case where FoundLHS' type is wider than 4751 // LHS' type is checked for above. 4752 if (getTypeSizeInBits(LHS->getType()) > 4753 getTypeSizeInBits(FoundLHS->getType())) { 4754 if (CmpInst::isSigned(Pred)) { 4755 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4756 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4757 } else { 4758 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4759 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4760 } 4761 } 4762 4763 // Canonicalize the query to match the way instcombine will have 4764 // canonicalized the comparison. 4765 // First, put a constant operand on the right. 4766 if (isa<SCEVConstant>(LHS)) { 4767 std::swap(LHS, RHS); 4768 Pred = ICmpInst::getSwappedPredicate(Pred); 4769 } 4770 // Then, canonicalize comparisons with boundary cases. 4771 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4772 const APInt &RA = RC->getValue()->getValue(); 4773 switch (Pred) { 4774 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4775 case ICmpInst::ICMP_EQ: 4776 case ICmpInst::ICMP_NE: 4777 break; 4778 case ICmpInst::ICMP_UGE: 4779 if ((RA - 1).isMinValue()) { 4780 Pred = ICmpInst::ICMP_NE; 4781 RHS = getConstant(RA - 1); 4782 break; 4783 } 4784 if (RA.isMaxValue()) { 4785 Pred = ICmpInst::ICMP_EQ; 4786 break; 4787 } 4788 if (RA.isMinValue()) return true; 4789 break; 4790 case ICmpInst::ICMP_ULE: 4791 if ((RA + 1).isMaxValue()) { 4792 Pred = ICmpInst::ICMP_NE; 4793 RHS = getConstant(RA + 1); 4794 break; 4795 } 4796 if (RA.isMinValue()) { 4797 Pred = ICmpInst::ICMP_EQ; 4798 break; 4799 } 4800 if (RA.isMaxValue()) return true; 4801 break; 4802 case ICmpInst::ICMP_SGE: 4803 if ((RA - 1).isMinSignedValue()) { 4804 Pred = ICmpInst::ICMP_NE; 4805 RHS = getConstant(RA - 1); 4806 break; 4807 } 4808 if (RA.isMaxSignedValue()) { 4809 Pred = ICmpInst::ICMP_EQ; 4810 break; 4811 } 4812 if (RA.isMinSignedValue()) return true; 4813 break; 4814 case ICmpInst::ICMP_SLE: 4815 if ((RA + 1).isMaxSignedValue()) { 4816 Pred = ICmpInst::ICMP_NE; 4817 RHS = getConstant(RA + 1); 4818 break; 4819 } 4820 if (RA.isMinSignedValue()) { 4821 Pred = ICmpInst::ICMP_EQ; 4822 break; 4823 } 4824 if (RA.isMaxSignedValue()) return true; 4825 break; 4826 case ICmpInst::ICMP_UGT: 4827 if (RA.isMinValue()) { 4828 Pred = ICmpInst::ICMP_NE; 4829 break; 4830 } 4831 if ((RA + 1).isMaxValue()) { 4832 Pred = ICmpInst::ICMP_EQ; 4833 RHS = getConstant(RA + 1); 4834 break; 4835 } 4836 if (RA.isMaxValue()) return false; 4837 break; 4838 case ICmpInst::ICMP_ULT: 4839 if (RA.isMaxValue()) { 4840 Pred = ICmpInst::ICMP_NE; 4841 break; 4842 } 4843 if ((RA - 1).isMinValue()) { 4844 Pred = ICmpInst::ICMP_EQ; 4845 RHS = getConstant(RA - 1); 4846 break; 4847 } 4848 if (RA.isMinValue()) return false; 4849 break; 4850 case ICmpInst::ICMP_SGT: 4851 if (RA.isMinSignedValue()) { 4852 Pred = ICmpInst::ICMP_NE; 4853 break; 4854 } 4855 if ((RA + 1).isMaxSignedValue()) { 4856 Pred = ICmpInst::ICMP_EQ; 4857 RHS = getConstant(RA + 1); 4858 break; 4859 } 4860 if (RA.isMaxSignedValue()) return false; 4861 break; 4862 case ICmpInst::ICMP_SLT: 4863 if (RA.isMaxSignedValue()) { 4864 Pred = ICmpInst::ICMP_NE; 4865 break; 4866 } 4867 if ((RA - 1).isMinSignedValue()) { 4868 Pred = ICmpInst::ICMP_EQ; 4869 RHS = getConstant(RA - 1); 4870 break; 4871 } 4872 if (RA.isMinSignedValue()) return false; 4873 break; 4874 } 4875 } 4876 4877 // Check to see if we can make the LHS or RHS match. 4878 if (LHS == FoundRHS || RHS == FoundLHS) { 4879 if (isa<SCEVConstant>(RHS)) { 4880 std::swap(FoundLHS, FoundRHS); 4881 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4882 } else { 4883 std::swap(LHS, RHS); 4884 Pred = ICmpInst::getSwappedPredicate(Pred); 4885 } 4886 } 4887 4888 // Check whether the found predicate is the same as the desired predicate. 4889 if (FoundPred == Pred) 4890 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4891 4892 // Check whether swapping the found predicate makes it the same as the 4893 // desired predicate. 4894 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4895 if (isa<SCEVConstant>(RHS)) 4896 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4897 else 4898 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4899 RHS, LHS, FoundLHS, FoundRHS); 4900 } 4901 4902 // Check whether the actual condition is beyond sufficient. 4903 if (FoundPred == ICmpInst::ICMP_EQ) 4904 if (ICmpInst::isTrueWhenEqual(Pred)) 4905 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4906 return true; 4907 if (Pred == ICmpInst::ICMP_NE) 4908 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4909 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4910 return true; 4911 4912 // Otherwise assume the worst. 4913 return false; 4914} 4915 4916/// isImpliedCondOperands - Test whether the condition described by Pred, 4917/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4918/// and FoundRHS is true. 4919bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4920 const SCEV *LHS, const SCEV *RHS, 4921 const SCEV *FoundLHS, 4922 const SCEV *FoundRHS) { 4923 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4924 FoundLHS, FoundRHS) || 4925 // ~x < ~y --> x > y 4926 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4927 getNotSCEV(FoundRHS), 4928 getNotSCEV(FoundLHS)); 4929} 4930 4931/// isImpliedCondOperandsHelper - Test whether the condition described by 4932/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4933/// FoundLHS, and FoundRHS is true. 4934bool 4935ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4936 const SCEV *LHS, const SCEV *RHS, 4937 const SCEV *FoundLHS, 4938 const SCEV *FoundRHS) { 4939 switch (Pred) { 4940 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4941 case ICmpInst::ICMP_EQ: 4942 case ICmpInst::ICMP_NE: 4943 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4944 return true; 4945 break; 4946 case ICmpInst::ICMP_SLT: 4947 case ICmpInst::ICMP_SLE: 4948 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4949 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4950 return true; 4951 break; 4952 case ICmpInst::ICMP_SGT: 4953 case ICmpInst::ICMP_SGE: 4954 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4955 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4956 return true; 4957 break; 4958 case ICmpInst::ICMP_ULT: 4959 case ICmpInst::ICMP_ULE: 4960 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4961 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4962 return true; 4963 break; 4964 case ICmpInst::ICMP_UGT: 4965 case ICmpInst::ICMP_UGE: 4966 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4967 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4968 return true; 4969 break; 4970 } 4971 4972 return false; 4973} 4974 4975/// getBECount - Subtract the end and start values and divide by the step, 4976/// rounding up, to get the number of times the backedge is executed. Return 4977/// CouldNotCompute if an intermediate computation overflows. 4978const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4979 const SCEV *End, 4980 const SCEV *Step, 4981 bool NoWrap) { 4982 assert(!isKnownNegative(Step) && 4983 "This code doesn't handle negative strides yet!"); 4984 4985 const Type *Ty = Start->getType(); 4986 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4987 const SCEV *Diff = getMinusSCEV(End, Start); 4988 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4989 4990 // Add an adjustment to the difference between End and Start so that 4991 // the division will effectively round up. 4992 const SCEV *Add = getAddExpr(Diff, RoundUp); 4993 4994 if (!NoWrap) { 4995 // Check Add for unsigned overflow. 4996 // TODO: More sophisticated things could be done here. 4997 const Type *WideTy = IntegerType::get(getContext(), 4998 getTypeSizeInBits(Ty) + 1); 4999 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5000 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5001 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5002 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5003 return getCouldNotCompute(); 5004 } 5005 5006 return getUDivExpr(Add, Step); 5007} 5008 5009/// HowManyLessThans - Return the number of times a backedge containing the 5010/// specified less-than comparison will execute. If not computable, return 5011/// CouldNotCompute. 5012ScalarEvolution::BackedgeTakenInfo 5013ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5014 const Loop *L, bool isSigned) { 5015 // Only handle: "ADDREC < LoopInvariant". 5016 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5017 5018 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5019 if (!AddRec || AddRec->getLoop() != L) 5020 return getCouldNotCompute(); 5021 5022 // Check to see if we have a flag which makes analysis easy. 5023 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5024 AddRec->hasNoUnsignedWrap(); 5025 5026 if (AddRec->isAffine()) { 5027 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5028 const SCEV *Step = AddRec->getStepRecurrence(*this); 5029 5030 if (Step->isZero()) 5031 return getCouldNotCompute(); 5032 if (Step->isOne()) { 5033 // With unit stride, the iteration never steps past the limit value. 5034 } else if (isKnownPositive(Step)) { 5035 // Test whether a positive iteration iteration can step past the limit 5036 // value and past the maximum value for its type in a single step. 5037 // Note that it's not sufficient to check NoWrap here, because even 5038 // though the value after a wrap is undefined, it's not undefined 5039 // behavior, so if wrap does occur, the loop could either terminate or 5040 // loop infinitely, but in either case, the loop is guaranteed to 5041 // iterate at least until the iteration where the wrapping occurs. 5042 const SCEV *One = getIntegerSCEV(1, Step->getType()); 5043 if (isSigned) { 5044 APInt Max = APInt::getSignedMaxValue(BitWidth); 5045 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5046 .slt(getSignedRange(RHS).getSignedMax())) 5047 return getCouldNotCompute(); 5048 } else { 5049 APInt Max = APInt::getMaxValue(BitWidth); 5050 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5051 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5052 return getCouldNotCompute(); 5053 } 5054 } else 5055 // TODO: Handle negative strides here and below. 5056 return getCouldNotCompute(); 5057 5058 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5059 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5060 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5061 // treat m-n as signed nor unsigned due to overflow possibility. 5062 5063 // First, we get the value of the LHS in the first iteration: n 5064 const SCEV *Start = AddRec->getOperand(0); 5065 5066 // Determine the minimum constant start value. 5067 const SCEV *MinStart = getConstant(isSigned ? 5068 getSignedRange(Start).getSignedMin() : 5069 getUnsignedRange(Start).getUnsignedMin()); 5070 5071 // If we know that the condition is true in order to enter the loop, 5072 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5073 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5074 // the division must round up. 5075 const SCEV *End = RHS; 5076 if (!isLoopGuardedByCond(L, 5077 isSigned ? ICmpInst::ICMP_SLT : 5078 ICmpInst::ICMP_ULT, 5079 getMinusSCEV(Start, Step), RHS)) 5080 End = isSigned ? getSMaxExpr(RHS, Start) 5081 : getUMaxExpr(RHS, Start); 5082 5083 // Determine the maximum constant end value. 5084 const SCEV *MaxEnd = getConstant(isSigned ? 5085 getSignedRange(End).getSignedMax() : 5086 getUnsignedRange(End).getUnsignedMax()); 5087 5088 // If MaxEnd is within a step of the maximum integer value in its type, 5089 // adjust it down to the minimum value which would produce the same effect. 5090 // This allows the subsequent ceiling divison of (N+(step-1))/step to 5091 // compute the correct value. 5092 const SCEV *StepMinusOne = getMinusSCEV(Step, 5093 getIntegerSCEV(1, Step->getType())); 5094 MaxEnd = isSigned ? 5095 getSMinExpr(MaxEnd, 5096 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5097 StepMinusOne)) : 5098 getUMinExpr(MaxEnd, 5099 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5100 StepMinusOne)); 5101 5102 // Finally, we subtract these two values and divide, rounding up, to get 5103 // the number of times the backedge is executed. 5104 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5105 5106 // The maximum backedge count is similar, except using the minimum start 5107 // value and the maximum end value. 5108 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5109 5110 return BackedgeTakenInfo(BECount, MaxBECount); 5111 } 5112 5113 return getCouldNotCompute(); 5114} 5115 5116/// getNumIterationsInRange - Return the number of iterations of this loop that 5117/// produce values in the specified constant range. Another way of looking at 5118/// this is that it returns the first iteration number where the value is not in 5119/// the condition, thus computing the exit count. If the iteration count can't 5120/// be computed, an instance of SCEVCouldNotCompute is returned. 5121const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5122 ScalarEvolution &SE) const { 5123 if (Range.isFullSet()) // Infinite loop. 5124 return SE.getCouldNotCompute(); 5125 5126 // If the start is a non-zero constant, shift the range to simplify things. 5127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5128 if (!SC->getValue()->isZero()) { 5129 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5130 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 5131 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5132 if (const SCEVAddRecExpr *ShiftedAddRec = 5133 dyn_cast<SCEVAddRecExpr>(Shifted)) 5134 return ShiftedAddRec->getNumIterationsInRange( 5135 Range.subtract(SC->getValue()->getValue()), SE); 5136 // This is strange and shouldn't happen. 5137 return SE.getCouldNotCompute(); 5138 } 5139 5140 // The only time we can solve this is when we have all constant indices. 5141 // Otherwise, we cannot determine the overflow conditions. 5142 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5143 if (!isa<SCEVConstant>(getOperand(i))) 5144 return SE.getCouldNotCompute(); 5145 5146 5147 // Okay at this point we know that all elements of the chrec are constants and 5148 // that the start element is zero. 5149 5150 // First check to see if the range contains zero. If not, the first 5151 // iteration exits. 5152 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5153 if (!Range.contains(APInt(BitWidth, 0))) 5154 return SE.getIntegerSCEV(0, getType()); 5155 5156 if (isAffine()) { 5157 // If this is an affine expression then we have this situation: 5158 // Solve {0,+,A} in Range === Ax in Range 5159 5160 // We know that zero is in the range. If A is positive then we know that 5161 // the upper value of the range must be the first possible exit value. 5162 // If A is negative then the lower of the range is the last possible loop 5163 // value. Also note that we already checked for a full range. 5164 APInt One(BitWidth,1); 5165 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5166 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5167 5168 // The exit value should be (End+A)/A. 5169 APInt ExitVal = (End + A).udiv(A); 5170 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5171 5172 // Evaluate at the exit value. If we really did fall out of the valid 5173 // range, then we computed our trip count, otherwise wrap around or other 5174 // things must have happened. 5175 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5176 if (Range.contains(Val->getValue())) 5177 return SE.getCouldNotCompute(); // Something strange happened 5178 5179 // Ensure that the previous value is in the range. This is a sanity check. 5180 assert(Range.contains( 5181 EvaluateConstantChrecAtConstant(this, 5182 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5183 "Linear scev computation is off in a bad way!"); 5184 return SE.getConstant(ExitValue); 5185 } else if (isQuadratic()) { 5186 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5187 // quadratic equation to solve it. To do this, we must frame our problem in 5188 // terms of figuring out when zero is crossed, instead of when 5189 // Range.getUpper() is crossed. 5190 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5191 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5192 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5193 5194 // Next, solve the constructed addrec 5195 std::pair<const SCEV *,const SCEV *> Roots = 5196 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5197 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5198 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5199 if (R1) { 5200 // Pick the smallest positive root value. 5201 if (ConstantInt *CB = 5202 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5203 R1->getValue(), R2->getValue()))) { 5204 if (CB->getZExtValue() == false) 5205 std::swap(R1, R2); // R1 is the minimum root now. 5206 5207 // Make sure the root is not off by one. The returned iteration should 5208 // not be in the range, but the previous one should be. When solving 5209 // for "X*X < 5", for example, we should not return a root of 2. 5210 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5211 R1->getValue(), 5212 SE); 5213 if (Range.contains(R1Val->getValue())) { 5214 // The next iteration must be out of the range... 5215 ConstantInt *NextVal = 5216 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5217 5218 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5219 if (!Range.contains(R1Val->getValue())) 5220 return SE.getConstant(NextVal); 5221 return SE.getCouldNotCompute(); // Something strange happened 5222 } 5223 5224 // If R1 was not in the range, then it is a good return value. Make 5225 // sure that R1-1 WAS in the range though, just in case. 5226 ConstantInt *NextVal = 5227 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5228 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5229 if (Range.contains(R1Val->getValue())) 5230 return R1; 5231 return SE.getCouldNotCompute(); // Something strange happened 5232 } 5233 } 5234 } 5235 5236 return SE.getCouldNotCompute(); 5237} 5238 5239 5240 5241//===----------------------------------------------------------------------===// 5242// SCEVCallbackVH Class Implementation 5243//===----------------------------------------------------------------------===// 5244 5245void ScalarEvolution::SCEVCallbackVH::deleted() { 5246 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5247 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5248 SE->ConstantEvolutionLoopExitValue.erase(PN); 5249 SE->Scalars.erase(getValPtr()); 5250 // this now dangles! 5251} 5252 5253void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5254 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5255 5256 // Forget all the expressions associated with users of the old value, 5257 // so that future queries will recompute the expressions using the new 5258 // value. 5259 SmallVector<User *, 16> Worklist; 5260 SmallPtrSet<User *, 8> Visited; 5261 Value *Old = getValPtr(); 5262 bool DeleteOld = false; 5263 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5264 UI != UE; ++UI) 5265 Worklist.push_back(*UI); 5266 while (!Worklist.empty()) { 5267 User *U = Worklist.pop_back_val(); 5268 // Deleting the Old value will cause this to dangle. Postpone 5269 // that until everything else is done. 5270 if (U == Old) { 5271 DeleteOld = true; 5272 continue; 5273 } 5274 if (!Visited.insert(U)) 5275 continue; 5276 if (PHINode *PN = dyn_cast<PHINode>(U)) 5277 SE->ConstantEvolutionLoopExitValue.erase(PN); 5278 SE->Scalars.erase(U); 5279 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5280 UI != UE; ++UI) 5281 Worklist.push_back(*UI); 5282 } 5283 // Delete the Old value if it (indirectly) references itself. 5284 if (DeleteOld) { 5285 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5286 SE->ConstantEvolutionLoopExitValue.erase(PN); 5287 SE->Scalars.erase(Old); 5288 // this now dangles! 5289 } 5290 // this may dangle! 5291} 5292 5293ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5294 : CallbackVH(V), SE(se) {} 5295 5296//===----------------------------------------------------------------------===// 5297// ScalarEvolution Class Implementation 5298//===----------------------------------------------------------------------===// 5299 5300ScalarEvolution::ScalarEvolution() 5301 : FunctionPass(&ID) { 5302} 5303 5304bool ScalarEvolution::runOnFunction(Function &F) { 5305 this->F = &F; 5306 LI = &getAnalysis<LoopInfo>(); 5307 DT = &getAnalysis<DominatorTree>(); 5308 TD = getAnalysisIfAvailable<TargetData>(); 5309 return false; 5310} 5311 5312void ScalarEvolution::releaseMemory() { 5313 Scalars.clear(); 5314 BackedgeTakenCounts.clear(); 5315 ConstantEvolutionLoopExitValue.clear(); 5316 ValuesAtScopes.clear(); 5317 UniqueSCEVs.clear(); 5318 SCEVAllocator.Reset(); 5319} 5320 5321void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5322 AU.setPreservesAll(); 5323 AU.addRequiredTransitive<LoopInfo>(); 5324 AU.addRequiredTransitive<DominatorTree>(); 5325} 5326 5327bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5328 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5329} 5330 5331static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5332 const Loop *L) { 5333 // Print all inner loops first 5334 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5335 PrintLoopInfo(OS, SE, *I); 5336 5337 OS << "Loop "; 5338 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5339 OS << ": "; 5340 5341 SmallVector<BasicBlock *, 8> ExitBlocks; 5342 L->getExitBlocks(ExitBlocks); 5343 if (ExitBlocks.size() != 1) 5344 OS << "<multiple exits> "; 5345 5346 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5347 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5348 } else { 5349 OS << "Unpredictable backedge-taken count. "; 5350 } 5351 5352 OS << "\n" 5353 "Loop "; 5354 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5355 OS << ": "; 5356 5357 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5358 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5359 } else { 5360 OS << "Unpredictable max backedge-taken count. "; 5361 } 5362 5363 OS << "\n"; 5364} 5365 5366void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5367 // ScalarEvolution's implementaiton of the print method is to print 5368 // out SCEV values of all instructions that are interesting. Doing 5369 // this potentially causes it to create new SCEV objects though, 5370 // which technically conflicts with the const qualifier. This isn't 5371 // observable from outside the class though, so casting away the 5372 // const isn't dangerous. 5373 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5374 5375 OS << "Classifying expressions for: "; 5376 WriteAsOperand(OS, F, /*PrintType=*/false); 5377 OS << "\n"; 5378 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5379 if (isSCEVable(I->getType())) { 5380 OS << *I << '\n'; 5381 OS << " --> "; 5382 const SCEV *SV = SE.getSCEV(&*I); 5383 SV->print(OS); 5384 5385 const Loop *L = LI->getLoopFor((*I).getParent()); 5386 5387 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5388 if (AtUse != SV) { 5389 OS << " --> "; 5390 AtUse->print(OS); 5391 } 5392 5393 if (L) { 5394 OS << "\t\t" "Exits: "; 5395 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5396 if (!ExitValue->isLoopInvariant(L)) { 5397 OS << "<<Unknown>>"; 5398 } else { 5399 OS << *ExitValue; 5400 } 5401 } 5402 5403 OS << "\n"; 5404 } 5405 5406 OS << "Determining loop execution counts for: "; 5407 WriteAsOperand(OS, F, /*PrintType=*/false); 5408 OS << "\n"; 5409 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5410 PrintLoopInfo(OS, &SE, *I); 5411} 5412 5413