ScalarEvolution.cpp revision 194612
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. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#define DEBUG_TYPE "scalar-evolution" 63#include "llvm/Analysis/ScalarEvolutionExpressions.h" 64#include "llvm/Constants.h" 65#include "llvm/DerivedTypes.h" 66#include "llvm/GlobalVariable.h" 67#include "llvm/Instructions.h" 68#include "llvm/Analysis/ConstantFolding.h" 69#include "llvm/Analysis/Dominators.h" 70#include "llvm/Analysis/LoopInfo.h" 71#include "llvm/Analysis/ValueTracking.h" 72#include "llvm/Assembly/Writer.h" 73#include "llvm/Target/TargetData.h" 74#include "llvm/Support/CommandLine.h" 75#include "llvm/Support/Compiler.h" 76#include "llvm/Support/ConstantRange.h" 77#include "llvm/Support/GetElementPtrTypeIterator.h" 78#include "llvm/Support/InstIterator.h" 79#include "llvm/Support/ManagedStatic.h" 80#include "llvm/Support/MathExtras.h" 81#include "llvm/Support/raw_ostream.h" 82#include "llvm/ADT/Statistic.h" 83#include "llvm/ADT/STLExtras.h" 84#include <algorithm> 85using namespace llvm; 86 87STATISTIC(NumArrayLenItCounts, 88 "Number of trip counts computed with array length"); 89STATISTIC(NumTripCountsComputed, 90 "Number of loops with predictable loop counts"); 91STATISTIC(NumTripCountsNotComputed, 92 "Number of loops without predictable loop counts"); 93STATISTIC(NumBruteForceTripCountsComputed, 94 "Number of loops with trip counts computed by force"); 95 96static cl::opt<unsigned> 97MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 98 cl::desc("Maximum number of iterations SCEV will " 99 "symbolically execute a constant derived loop"), 100 cl::init(100)); 101 102static RegisterPass<ScalarEvolution> 103R("scalar-evolution", "Scalar Evolution Analysis", false, true); 104char ScalarEvolution::ID = 0; 105 106//===----------------------------------------------------------------------===// 107// SCEV class definitions 108//===----------------------------------------------------------------------===// 109 110//===----------------------------------------------------------------------===// 111// Implementation of the SCEV class. 112// 113SCEV::~SCEV() {} 114void SCEV::dump() const { 115 print(errs()); 116 errs() << '\n'; 117} 118 119void SCEV::print(std::ostream &o) const { 120 raw_os_ostream OS(o); 121 print(OS); 122} 123 124bool SCEV::isZero() const { 125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 126 return SC->getValue()->isZero(); 127 return false; 128} 129 130bool SCEV::isOne() const { 131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 132 return SC->getValue()->isOne(); 133 return false; 134} 135 136SCEVCouldNotCompute::SCEVCouldNotCompute(const ScalarEvolution* p) : 137 SCEV(scCouldNotCompute, p) {} 138SCEVCouldNotCompute::~SCEVCouldNotCompute() {} 139 140bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return false; 143} 144 145const Type *SCEVCouldNotCompute::getType() const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return 0; 148} 149 150bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 152 return false; 153} 154 155SCEVHandle SCEVCouldNotCompute:: 156replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 157 const SCEVHandle &Conc, 158 ScalarEvolution &SE) const { 159 return this; 160} 161 162void SCEVCouldNotCompute::print(raw_ostream &OS) const { 163 OS << "***COULDNOTCOMPUTE***"; 164} 165 166bool SCEVCouldNotCompute::classof(const SCEV *S) { 167 return S->getSCEVType() == scCouldNotCompute; 168} 169 170 171// SCEVConstants - Only allow the creation of one SCEVConstant for any 172// particular value. Don't use a SCEVHandle here, or else the object will 173// never be deleted! 174static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 175 176 177SCEVConstant::~SCEVConstant() { 178 SCEVConstants->erase(V); 179} 180 181SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 182 SCEVConstant *&R = (*SCEVConstants)[V]; 183 if (R == 0) R = new SCEVConstant(V, this); 184 return R; 185} 186 187SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 188 return getConstant(ConstantInt::get(Val)); 189} 190 191SCEVHandle 192ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 193 return getConstant(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(unsigned SCEVTy, 203 const SCEVHandle &op, const Type *ty, 204 const ScalarEvolution* p) 205 : SCEV(SCEVTy, p), Op(op), Ty(ty) {} 206 207SCEVCastExpr::~SCEVCastExpr() {} 208 209bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->dominates(BB, DT); 211} 212 213// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 214// particular input. Don't use a SCEVHandle here, or else the object will 215// never be deleted! 216static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 217 SCEVTruncateExpr*> > SCEVTruncates; 218 219SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty, 220 const ScalarEvolution* p) 221 : SCEVCastExpr(scTruncate, op, ty, p) { 222 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 223 (Ty->isInteger() || isa<PointerType>(Ty)) && 224 "Cannot truncate non-integer value!"); 225} 226 227SCEVTruncateExpr::~SCEVTruncateExpr() { 228 SCEVTruncates->erase(std::make_pair(Op, Ty)); 229} 230 231void SCEVTruncateExpr::print(raw_ostream &OS) const { 232 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 233} 234 235// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 236// particular input. Don't use a SCEVHandle here, or else the object will never 237// be deleted! 238static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 239 SCEVZeroExtendExpr*> > SCEVZeroExtends; 240 241SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty, 242 const ScalarEvolution* p) 243 : SCEVCastExpr(scZeroExtend, op, ty, p) { 244 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 245 (Ty->isInteger() || isa<PointerType>(Ty)) && 246 "Cannot zero extend non-integer value!"); 247} 248 249SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 250 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 251} 252 253void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 254 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 255} 256 257// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 258// particular input. Don't use a SCEVHandle here, or else the object will never 259// be deleted! 260static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 261 SCEVSignExtendExpr*> > SCEVSignExtends; 262 263SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty, 264 const ScalarEvolution* p) 265 : SCEVCastExpr(scSignExtend, op, ty, p) { 266 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 267 (Ty->isInteger() || isa<PointerType>(Ty)) && 268 "Cannot sign extend non-integer value!"); 269} 270 271SCEVSignExtendExpr::~SCEVSignExtendExpr() { 272 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 273} 274 275void SCEVSignExtendExpr::print(raw_ostream &OS) const { 276 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 277} 278 279// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 280// particular input. Don't use a SCEVHandle here, or else the object will never 281// be deleted! 282static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >, 283 SCEVCommutativeExpr*> > SCEVCommExprs; 284 285SCEVCommutativeExpr::~SCEVCommutativeExpr() { 286 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 287 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps)); 288} 289 290void SCEVCommutativeExpr::print(raw_ostream &OS) const { 291 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 292 const char *OpStr = getOperationStr(); 293 OS << "(" << *Operands[0]; 294 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 295 OS << OpStr << *Operands[i]; 296 OS << ")"; 297} 298 299SCEVHandle SCEVCommutativeExpr:: 300replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 301 const SCEVHandle &Conc, 302 ScalarEvolution &SE) const { 303 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 304 SCEVHandle H = 305 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 306 if (H != getOperand(i)) { 307 SmallVector<SCEVHandle, 8> NewOps; 308 NewOps.reserve(getNumOperands()); 309 for (unsigned j = 0; j != i; ++j) 310 NewOps.push_back(getOperand(j)); 311 NewOps.push_back(H); 312 for (++i; i != e; ++i) 313 NewOps.push_back(getOperand(i)-> 314 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 315 316 if (isa<SCEVAddExpr>(this)) 317 return SE.getAddExpr(NewOps); 318 else if (isa<SCEVMulExpr>(this)) 319 return SE.getMulExpr(NewOps); 320 else if (isa<SCEVSMaxExpr>(this)) 321 return SE.getSMaxExpr(NewOps); 322 else if (isa<SCEVUMaxExpr>(this)) 323 return SE.getUMaxExpr(NewOps); 324 else 325 assert(0 && "Unknown commutative expr!"); 326 } 327 } 328 return this; 329} 330 331bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 332 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 333 if (!getOperand(i)->dominates(BB, DT)) 334 return false; 335 } 336 return true; 337} 338 339 340// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 341// input. Don't use a SCEVHandle here, or else the object will never be 342// deleted! 343static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>, 344 SCEVUDivExpr*> > SCEVUDivs; 345 346SCEVUDivExpr::~SCEVUDivExpr() { 347 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 348} 349 350bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 351 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 352} 353 354void SCEVUDivExpr::print(raw_ostream &OS) const { 355 OS << "(" << *LHS << " /u " << *RHS << ")"; 356} 357 358const Type *SCEVUDivExpr::getType() const { 359 // In most cases the types of LHS and RHS will be the same, but in some 360 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 361 // depend on the type for correctness, but handling types carefully can 362 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 363 // a pointer type than the RHS, so use the RHS' type here. 364 return RHS->getType(); 365} 366 367// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 368// particular input. Don't use a SCEVHandle here, or else the object will never 369// be deleted! 370static ManagedStatic<std::map<std::pair<const Loop *, 371 std::vector<const SCEV*> >, 372 SCEVAddRecExpr*> > SCEVAddRecExprs; 373 374SCEVAddRecExpr::~SCEVAddRecExpr() { 375 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 376 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps)); 377} 378 379SCEVHandle SCEVAddRecExpr:: 380replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 381 const SCEVHandle &Conc, 382 ScalarEvolution &SE) const { 383 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 384 SCEVHandle H = 385 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 386 if (H != getOperand(i)) { 387 SmallVector<SCEVHandle, 8> NewOps; 388 NewOps.reserve(getNumOperands()); 389 for (unsigned j = 0; j != i; ++j) 390 NewOps.push_back(getOperand(j)); 391 NewOps.push_back(H); 392 for (++i; i != e; ++i) 393 NewOps.push_back(getOperand(i)-> 394 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 395 396 return SE.getAddRecExpr(NewOps, L); 397 } 398 } 399 return this; 400} 401 402 403bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 404 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 405 // contain L and if the start is invariant. 406 // Add recurrences are never invariant in the function-body (null loop). 407 return QueryLoop && 408 !QueryLoop->contains(L->getHeader()) && 409 getOperand(0)->isLoopInvariant(QueryLoop); 410} 411 412 413void SCEVAddRecExpr::print(raw_ostream &OS) const { 414 OS << "{" << *Operands[0]; 415 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 416 OS << ",+," << *Operands[i]; 417 OS << "}<" << L->getHeader()->getName() + ">"; 418} 419 420// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 421// value. Don't use a SCEVHandle here, or else the object will never be 422// deleted! 423static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 424 425SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 426 427bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 428 // All non-instruction values are loop invariant. All instructions are loop 429 // invariant if they are not contained in the specified loop. 430 // Instructions are never considered invariant in the function body 431 // (null loop) because they are defined within the "loop". 432 if (Instruction *I = dyn_cast<Instruction>(V)) 433 return L && !L->contains(I->getParent()); 434 return true; 435} 436 437bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 438 if (Instruction *I = dyn_cast<Instruction>(getValue())) 439 return DT->dominates(I->getParent(), BB); 440 return true; 441} 442 443const Type *SCEVUnknown::getType() const { 444 return V->getType(); 445} 446 447void SCEVUnknown::print(raw_ostream &OS) const { 448 WriteAsOperand(OS, V, false); 449} 450 451//===----------------------------------------------------------------------===// 452// SCEV Utilities 453//===----------------------------------------------------------------------===// 454 455namespace { 456 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 457 /// than the complexity of the RHS. This comparator is used to canonicalize 458 /// expressions. 459 class VISIBILITY_HIDDEN SCEVComplexityCompare { 460 LoopInfo *LI; 461 public: 462 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 463 464 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 465 // Primarily, sort the SCEVs by their getSCEVType(). 466 if (LHS->getSCEVType() != RHS->getSCEVType()) 467 return LHS->getSCEVType() < RHS->getSCEVType(); 468 469 // Aside from the getSCEVType() ordering, the particular ordering 470 // isn't very important except that it's beneficial to be consistent, 471 // so that (a + b) and (b + a) don't end up as different expressions. 472 473 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 474 // not as complete as it could be. 475 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 476 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 477 478 // Order pointer values after integer values. This helps SCEVExpander 479 // form GEPs. 480 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 481 return false; 482 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 483 return true; 484 485 // Compare getValueID values. 486 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 487 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 488 489 // Sort arguments by their position. 490 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 491 const Argument *RA = cast<Argument>(RU->getValue()); 492 return LA->getArgNo() < RA->getArgNo(); 493 } 494 495 // For instructions, compare their loop depth, and their opcode. 496 // This is pretty loose. 497 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 498 Instruction *RV = cast<Instruction>(RU->getValue()); 499 500 // Compare loop depths. 501 if (LI->getLoopDepth(LV->getParent()) != 502 LI->getLoopDepth(RV->getParent())) 503 return LI->getLoopDepth(LV->getParent()) < 504 LI->getLoopDepth(RV->getParent()); 505 506 // Compare opcodes. 507 if (LV->getOpcode() != RV->getOpcode()) 508 return LV->getOpcode() < RV->getOpcode(); 509 510 // Compare the number of operands. 511 if (LV->getNumOperands() != RV->getNumOperands()) 512 return LV->getNumOperands() < RV->getNumOperands(); 513 } 514 515 return false; 516 } 517 518 // Compare constant values. 519 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 520 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 521 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 522 } 523 524 // Compare addrec loop depths. 525 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 526 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 527 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 528 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 529 } 530 531 // Lexicographically compare n-ary expressions. 532 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 533 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 534 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 535 if (i >= RC->getNumOperands()) 536 return false; 537 if (operator()(LC->getOperand(i), RC->getOperand(i))) 538 return true; 539 if (operator()(RC->getOperand(i), LC->getOperand(i))) 540 return false; 541 } 542 return LC->getNumOperands() < RC->getNumOperands(); 543 } 544 545 // Lexicographically compare udiv expressions. 546 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 547 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 548 if (operator()(LC->getLHS(), RC->getLHS())) 549 return true; 550 if (operator()(RC->getLHS(), LC->getLHS())) 551 return false; 552 if (operator()(LC->getRHS(), RC->getRHS())) 553 return true; 554 if (operator()(RC->getRHS(), LC->getRHS())) 555 return false; 556 return false; 557 } 558 559 // Compare cast expressions by operand. 560 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 561 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 562 return operator()(LC->getOperand(), RC->getOperand()); 563 } 564 565 assert(0 && "Unknown SCEV kind!"); 566 return false; 567 } 568 }; 569} 570 571/// GroupByComplexity - Given a list of SCEV objects, order them by their 572/// complexity, and group objects of the same complexity together by value. 573/// When this routine is finished, we know that any duplicates in the vector are 574/// consecutive and that complexity is monotonically increasing. 575/// 576/// Note that we go take special precautions to ensure that we get determinstic 577/// results from this routine. In other words, we don't want the results of 578/// this to depend on where the addresses of various SCEV objects happened to 579/// land in memory. 580/// 581static void GroupByComplexity(SmallVectorImpl<SCEVHandle> &Ops, 582 LoopInfo *LI) { 583 if (Ops.size() < 2) return; // Noop 584 if (Ops.size() == 2) { 585 // This is the common case, which also happens to be trivially simple. 586 // Special case it. 587 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 588 std::swap(Ops[0], Ops[1]); 589 return; 590 } 591 592 // Do the rough sort by complexity. 593 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 594 595 // Now that we are sorted by complexity, group elements of the same 596 // complexity. Note that this is, at worst, N^2, but the vector is likely to 597 // be extremely short in practice. Note that we take this approach because we 598 // do not want to depend on the addresses of the objects we are grouping. 599 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 600 const SCEV *S = Ops[i]; 601 unsigned Complexity = S->getSCEVType(); 602 603 // If there are any objects of the same complexity and same value as this 604 // one, group them. 605 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 606 if (Ops[j] == S) { // Found a duplicate. 607 // Move it to immediately after i'th element. 608 std::swap(Ops[i+1], Ops[j]); 609 ++i; // no need to rescan it. 610 if (i == e-2) return; // Done! 611 } 612 } 613 } 614} 615 616 617 618//===----------------------------------------------------------------------===// 619// Simple SCEV method implementations 620//===----------------------------------------------------------------------===// 621 622/// BinomialCoefficient - Compute BC(It, K). The result has width W. 623/// Assume, K > 0. 624static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 625 ScalarEvolution &SE, 626 const Type* ResultTy) { 627 // Handle the simplest case efficiently. 628 if (K == 1) 629 return SE.getTruncateOrZeroExtend(It, ResultTy); 630 631 // We are using the following formula for BC(It, K): 632 // 633 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 634 // 635 // Suppose, W is the bitwidth of the return value. We must be prepared for 636 // overflow. Hence, we must assure that the result of our computation is 637 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 638 // safe in modular arithmetic. 639 // 640 // However, this code doesn't use exactly that formula; the formula it uses 641 // is something like the following, where T is the number of factors of 2 in 642 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 643 // exponentiation: 644 // 645 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 646 // 647 // This formula is trivially equivalent to the previous formula. However, 648 // this formula can be implemented much more efficiently. The trick is that 649 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 650 // arithmetic. To do exact division in modular arithmetic, all we have 651 // to do is multiply by the inverse. Therefore, this step can be done at 652 // width W. 653 // 654 // The next issue is how to safely do the division by 2^T. The way this 655 // is done is by doing the multiplication step at a width of at least W + T 656 // bits. This way, the bottom W+T bits of the product are accurate. Then, 657 // when we perform the division by 2^T (which is equivalent to a right shift 658 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 659 // truncated out after the division by 2^T. 660 // 661 // In comparison to just directly using the first formula, this technique 662 // is much more efficient; using the first formula requires W * K bits, 663 // but this formula less than W + K bits. Also, the first formula requires 664 // a division step, whereas this formula only requires multiplies and shifts. 665 // 666 // It doesn't matter whether the subtraction step is done in the calculation 667 // width or the input iteration count's width; if the subtraction overflows, 668 // the result must be zero anyway. We prefer here to do it in the width of 669 // the induction variable because it helps a lot for certain cases; CodeGen 670 // isn't smart enough to ignore the overflow, which leads to much less 671 // efficient code if the width of the subtraction is wider than the native 672 // register width. 673 // 674 // (It's possible to not widen at all by pulling out factors of 2 before 675 // the multiplication; for example, K=2 can be calculated as 676 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 677 // extra arithmetic, so it's not an obvious win, and it gets 678 // much more complicated for K > 3.) 679 680 // Protection from insane SCEVs; this bound is conservative, 681 // but it probably doesn't matter. 682 if (K > 1000) 683 return SE.getCouldNotCompute(); 684 685 unsigned W = SE.getTypeSizeInBits(ResultTy); 686 687 // Calculate K! / 2^T and T; we divide out the factors of two before 688 // multiplying for calculating K! / 2^T to avoid overflow. 689 // Other overflow doesn't matter because we only care about the bottom 690 // W bits of the result. 691 APInt OddFactorial(W, 1); 692 unsigned T = 1; 693 for (unsigned i = 3; i <= K; ++i) { 694 APInt Mult(W, i); 695 unsigned TwoFactors = Mult.countTrailingZeros(); 696 T += TwoFactors; 697 Mult = Mult.lshr(TwoFactors); 698 OddFactorial *= Mult; 699 } 700 701 // We need at least W + T bits for the multiplication step 702 unsigned CalculationBits = W + T; 703 704 // Calcuate 2^T, at width T+W. 705 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 706 707 // Calculate the multiplicative inverse of K! / 2^T; 708 // this multiplication factor will perform the exact division by 709 // K! / 2^T. 710 APInt Mod = APInt::getSignedMinValue(W+1); 711 APInt MultiplyFactor = OddFactorial.zext(W+1); 712 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 713 MultiplyFactor = MultiplyFactor.trunc(W); 714 715 // Calculate the product, at width T+W 716 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 717 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 718 for (unsigned i = 1; i != K; ++i) { 719 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 720 Dividend = SE.getMulExpr(Dividend, 721 SE.getTruncateOrZeroExtend(S, CalculationTy)); 722 } 723 724 // Divide by 2^T 725 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 726 727 // Truncate the result, and divide by K! / 2^T. 728 729 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 730 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 731} 732 733/// evaluateAtIteration - Return the value of this chain of recurrences at 734/// the specified iteration number. We can evaluate this recurrence by 735/// multiplying each element in the chain by the binomial coefficient 736/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 737/// 738/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 739/// 740/// where BC(It, k) stands for binomial coefficient. 741/// 742SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 743 ScalarEvolution &SE) const { 744 SCEVHandle Result = getStart(); 745 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 746 // The computation is correct in the face of overflow provided that the 747 // multiplication is performed _after_ the evaluation of the binomial 748 // coefficient. 749 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType()); 750 if (isa<SCEVCouldNotCompute>(Coeff)) 751 return Coeff; 752 753 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 754 } 755 return Result; 756} 757 758//===----------------------------------------------------------------------===// 759// SCEV Expression folder implementations 760//===----------------------------------------------------------------------===// 761 762SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, 763 const Type *Ty) { 764 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 765 "This is not a truncating conversion!"); 766 assert(isSCEVable(Ty) && 767 "This is not a conversion to a SCEVable type!"); 768 Ty = getEffectiveSCEVType(Ty); 769 770 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 771 return getUnknown( 772 ConstantExpr::getTrunc(SC->getValue(), Ty)); 773 774 // trunc(trunc(x)) --> trunc(x) 775 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 776 return getTruncateExpr(ST->getOperand(), Ty); 777 778 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 779 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 780 return getTruncateOrSignExtend(SS->getOperand(), Ty); 781 782 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 783 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 784 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 785 786 // If the input value is a chrec scev, truncate the chrec's operands. 787 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 788 SmallVector<SCEVHandle, 4> Operands; 789 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 790 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 791 return getAddRecExpr(Operands, AddRec->getLoop()); 792 } 793 794 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 795 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty, this); 796 return Result; 797} 798 799SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 800 const Type *Ty) { 801 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 802 "This is not an extending conversion!"); 803 assert(isSCEVable(Ty) && 804 "This is not a conversion to a SCEVable type!"); 805 Ty = getEffectiveSCEVType(Ty); 806 807 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 808 const Type *IntTy = getEffectiveSCEVType(Ty); 809 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 810 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 811 return getUnknown(C); 812 } 813 814 // zext(zext(x)) --> zext(x) 815 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 816 return getZeroExtendExpr(SZ->getOperand(), Ty); 817 818 // If the input value is a chrec scev, and we can prove that the value 819 // did not overflow the old, smaller, value, we can zero extend all of the 820 // operands (often constants). This allows analysis of something like 821 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 822 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 823 if (AR->isAffine()) { 824 // Check whether the backedge-taken count is SCEVCouldNotCompute. 825 // Note that this serves two purposes: It filters out loops that are 826 // simply not analyzable, and it covers the case where this code is 827 // being called from within backedge-taken count analysis, such that 828 // attempting to ask for the backedge-taken count would likely result 829 // in infinite recursion. In the later case, the analysis code will 830 // cope with a conservative value, and it will take care to purge 831 // that value once it has finished. 832 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 833 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 834 // Manually compute the final value for AR, checking for 835 // overflow. 836 SCEVHandle Start = AR->getStart(); 837 SCEVHandle Step = AR->getStepRecurrence(*this); 838 839 // Check whether the backedge-taken count can be losslessly casted to 840 // the addrec's type. The count is always unsigned. 841 SCEVHandle CastedMaxBECount = 842 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 843 SCEVHandle RecastedMaxBECount = 844 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 845 if (MaxBECount == RecastedMaxBECount) { 846 const Type *WideTy = 847 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 848 // Check whether Start+Step*MaxBECount has no unsigned overflow. 849 SCEVHandle ZMul = 850 getMulExpr(CastedMaxBECount, 851 getTruncateOrZeroExtend(Step, Start->getType())); 852 SCEVHandle Add = getAddExpr(Start, ZMul); 853 SCEVHandle OperandExtendedAdd = 854 getAddExpr(getZeroExtendExpr(Start, WideTy), 855 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 856 getZeroExtendExpr(Step, WideTy))); 857 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 858 // Return the expression with the addrec on the outside. 859 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 860 getZeroExtendExpr(Step, Ty), 861 AR->getLoop()); 862 863 // Similar to above, only this time treat the step value as signed. 864 // This covers loops that count down. 865 SCEVHandle SMul = 866 getMulExpr(CastedMaxBECount, 867 getTruncateOrSignExtend(Step, Start->getType())); 868 Add = getAddExpr(Start, SMul); 869 OperandExtendedAdd = 870 getAddExpr(getZeroExtendExpr(Start, WideTy), 871 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 872 getSignExtendExpr(Step, WideTy))); 873 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 874 // Return the expression with the addrec on the outside. 875 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 876 getSignExtendExpr(Step, Ty), 877 AR->getLoop()); 878 } 879 } 880 } 881 882 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 883 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty, this); 884 return Result; 885} 886 887SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, 888 const Type *Ty) { 889 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 890 "This is not an extending conversion!"); 891 assert(isSCEVable(Ty) && 892 "This is not a conversion to a SCEVable type!"); 893 Ty = getEffectiveSCEVType(Ty); 894 895 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 896 const Type *IntTy = getEffectiveSCEVType(Ty); 897 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 898 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 899 return getUnknown(C); 900 } 901 902 // sext(sext(x)) --> sext(x) 903 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 904 return getSignExtendExpr(SS->getOperand(), Ty); 905 906 // If the input value is a chrec scev, and we can prove that the value 907 // did not overflow the old, smaller, value, we can sign extend all of the 908 // operands (often constants). This allows analysis of something like 909 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 910 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 911 if (AR->isAffine()) { 912 // Check whether the backedge-taken count is SCEVCouldNotCompute. 913 // Note that this serves two purposes: It filters out loops that are 914 // simply not analyzable, and it covers the case where this code is 915 // being called from within backedge-taken count analysis, such that 916 // attempting to ask for the backedge-taken count would likely result 917 // in infinite recursion. In the later case, the analysis code will 918 // cope with a conservative value, and it will take care to purge 919 // that value once it has finished. 920 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 921 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 922 // Manually compute the final value for AR, checking for 923 // overflow. 924 SCEVHandle Start = AR->getStart(); 925 SCEVHandle Step = AR->getStepRecurrence(*this); 926 927 // Check whether the backedge-taken count can be losslessly casted to 928 // the addrec's type. The count is always unsigned. 929 SCEVHandle CastedMaxBECount = 930 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 931 SCEVHandle RecastedMaxBECount = 932 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 933 if (MaxBECount == RecastedMaxBECount) { 934 const Type *WideTy = 935 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 936 // Check whether Start+Step*MaxBECount has no signed overflow. 937 SCEVHandle SMul = 938 getMulExpr(CastedMaxBECount, 939 getTruncateOrSignExtend(Step, Start->getType())); 940 SCEVHandle Add = getAddExpr(Start, SMul); 941 SCEVHandle OperandExtendedAdd = 942 getAddExpr(getSignExtendExpr(Start, WideTy), 943 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 944 getSignExtendExpr(Step, WideTy))); 945 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 946 // Return the expression with the addrec on the outside. 947 return getAddRecExpr(getSignExtendExpr(Start, Ty), 948 getSignExtendExpr(Step, Ty), 949 AR->getLoop()); 950 } 951 } 952 } 953 954 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 955 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty, this); 956 return Result; 957} 958 959/// getAnyExtendExpr - Return a SCEV for the given operand extended with 960/// unspecified bits out to the given type. 961/// 962SCEVHandle ScalarEvolution::getAnyExtendExpr(const SCEVHandle &Op, 963 const Type *Ty) { 964 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 965 "This is not an extending conversion!"); 966 assert(isSCEVable(Ty) && 967 "This is not a conversion to a SCEVable type!"); 968 Ty = getEffectiveSCEVType(Ty); 969 970 // Sign-extend negative constants. 971 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 972 if (SC->getValue()->getValue().isNegative()) 973 return getSignExtendExpr(Op, Ty); 974 975 // Peel off a truncate cast. 976 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 977 SCEVHandle NewOp = T->getOperand(); 978 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 979 return getAnyExtendExpr(NewOp, Ty); 980 return getTruncateOrNoop(NewOp, Ty); 981 } 982 983 // Next try a zext cast. If the cast is folded, use it. 984 SCEVHandle ZExt = getZeroExtendExpr(Op, Ty); 985 if (!isa<SCEVZeroExtendExpr>(ZExt)) 986 return ZExt; 987 988 // Next try a sext cast. If the cast is folded, use it. 989 SCEVHandle SExt = getSignExtendExpr(Op, Ty); 990 if (!isa<SCEVSignExtendExpr>(SExt)) 991 return SExt; 992 993 // If the expression is obviously signed, use the sext cast value. 994 if (isa<SCEVSMaxExpr>(Op)) 995 return SExt; 996 997 // Absent any other information, use the zext cast value. 998 return ZExt; 999} 1000 1001/// CollectAddOperandsWithScales - Process the given Ops list, which is 1002/// a list of operands to be added under the given scale, update the given 1003/// map. This is a helper function for getAddRecExpr. As an example of 1004/// what it does, given a sequence of operands that would form an add 1005/// expression like this: 1006/// 1007/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1008/// 1009/// where A and B are constants, update the map with these values: 1010/// 1011/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1012/// 1013/// and add 13 + A*B*29 to AccumulatedConstant. 1014/// This will allow getAddRecExpr to produce this: 1015/// 1016/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1017/// 1018/// This form often exposes folding opportunities that are hidden in 1019/// the original operand list. 1020/// 1021/// Return true iff it appears that any interesting folding opportunities 1022/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1023/// the common case where no interesting opportunities are present, and 1024/// is also used as a check to avoid infinite recursion. 1025/// 1026static bool 1027CollectAddOperandsWithScales(DenseMap<SCEVHandle, APInt> &M, 1028 SmallVector<SCEVHandle, 8> &NewOps, 1029 APInt &AccumulatedConstant, 1030 const SmallVectorImpl<SCEVHandle> &Ops, 1031 const APInt &Scale, 1032 ScalarEvolution &SE) { 1033 bool Interesting = false; 1034 1035 // Iterate over the add operands. 1036 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1037 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1038 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1039 APInt NewScale = 1040 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1041 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1042 // A multiplication of a constant with another add; recurse. 1043 Interesting |= 1044 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1045 cast<SCEVAddExpr>(Mul->getOperand(1)) 1046 ->getOperands(), 1047 NewScale, SE); 1048 } else { 1049 // A multiplication of a constant with some other value. Update 1050 // the map. 1051 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1052 SCEVHandle Key = SE.getMulExpr(MulOps); 1053 std::pair<DenseMap<SCEVHandle, APInt>::iterator, bool> Pair = 1054 M.insert(std::make_pair(Key, APInt())); 1055 if (Pair.second) { 1056 Pair.first->second = NewScale; 1057 NewOps.push_back(Pair.first->first); 1058 } else { 1059 Pair.first->second += NewScale; 1060 // The map already had an entry for this value, which may indicate 1061 // a folding opportunity. 1062 Interesting = true; 1063 } 1064 } 1065 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1066 // Pull a buried constant out to the outside. 1067 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1068 Interesting = true; 1069 AccumulatedConstant += Scale * C->getValue()->getValue(); 1070 } else { 1071 // An ordinary operand. Update the map. 1072 std::pair<DenseMap<SCEVHandle, APInt>::iterator, bool> Pair = 1073 M.insert(std::make_pair(Ops[i], APInt())); 1074 if (Pair.second) { 1075 Pair.first->second = Scale; 1076 NewOps.push_back(Pair.first->first); 1077 } else { 1078 Pair.first->second += Scale; 1079 // The map already had an entry for this value, which may indicate 1080 // a folding opportunity. 1081 Interesting = true; 1082 } 1083 } 1084 } 1085 1086 return Interesting; 1087} 1088 1089namespace { 1090 struct APIntCompare { 1091 bool operator()(const APInt &LHS, const APInt &RHS) const { 1092 return LHS.ult(RHS); 1093 } 1094 }; 1095} 1096 1097/// getAddExpr - Get a canonical add expression, or something simpler if 1098/// possible. 1099SCEVHandle ScalarEvolution::getAddExpr(SmallVectorImpl<SCEVHandle> &Ops) { 1100 assert(!Ops.empty() && "Cannot get empty add!"); 1101 if (Ops.size() == 1) return Ops[0]; 1102#ifndef NDEBUG 1103 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1104 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1105 getEffectiveSCEVType(Ops[0]->getType()) && 1106 "SCEVAddExpr operand types don't match!"); 1107#endif 1108 1109 // Sort by complexity, this groups all similar expression types together. 1110 GroupByComplexity(Ops, LI); 1111 1112 // If there are any constants, fold them together. 1113 unsigned Idx = 0; 1114 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1115 ++Idx; 1116 assert(Idx < Ops.size()); 1117 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1118 // We found two constants, fold them together! 1119 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1120 RHSC->getValue()->getValue()); 1121 if (Ops.size() == 2) return Ops[0]; 1122 Ops.erase(Ops.begin()+1); // Erase the folded element 1123 LHSC = cast<SCEVConstant>(Ops[0]); 1124 } 1125 1126 // If we are left with a constant zero being added, strip it off. 1127 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1128 Ops.erase(Ops.begin()); 1129 --Idx; 1130 } 1131 } 1132 1133 if (Ops.size() == 1) return Ops[0]; 1134 1135 // Okay, check to see if the same value occurs in the operand list twice. If 1136 // so, merge them together into an multiply expression. Since we sorted the 1137 // list, these values are required to be adjacent. 1138 const Type *Ty = Ops[0]->getType(); 1139 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1140 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1141 // Found a match, merge the two values into a multiply, and add any 1142 // remaining values to the result. 1143 SCEVHandle Two = getIntegerSCEV(2, Ty); 1144 SCEVHandle Mul = getMulExpr(Ops[i], Two); 1145 if (Ops.size() == 2) 1146 return Mul; 1147 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1148 Ops.push_back(Mul); 1149 return getAddExpr(Ops); 1150 } 1151 1152 // Check for truncates. If all the operands are truncated from the same 1153 // type, see if factoring out the truncate would permit the result to be 1154 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1155 // if the contents of the resulting outer trunc fold to something simple. 1156 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1157 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1158 const Type *DstType = Trunc->getType(); 1159 const Type *SrcType = Trunc->getOperand()->getType(); 1160 SmallVector<SCEVHandle, 8> LargeOps; 1161 bool Ok = true; 1162 // Check all the operands to see if they can be represented in the 1163 // source type of the truncate. 1164 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1165 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1166 if (T->getOperand()->getType() != SrcType) { 1167 Ok = false; 1168 break; 1169 } 1170 LargeOps.push_back(T->getOperand()); 1171 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1172 // This could be either sign or zero extension, but sign extension 1173 // is much more likely to be foldable here. 1174 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1175 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1176 SmallVector<SCEVHandle, 8> LargeMulOps; 1177 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1178 if (const SCEVTruncateExpr *T = 1179 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1180 if (T->getOperand()->getType() != SrcType) { 1181 Ok = false; 1182 break; 1183 } 1184 LargeMulOps.push_back(T->getOperand()); 1185 } else if (const SCEVConstant *C = 1186 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1187 // This could be either sign or zero extension, but sign extension 1188 // is much more likely to be foldable here. 1189 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1190 } else { 1191 Ok = false; 1192 break; 1193 } 1194 } 1195 if (Ok) 1196 LargeOps.push_back(getMulExpr(LargeMulOps)); 1197 } else { 1198 Ok = false; 1199 break; 1200 } 1201 } 1202 if (Ok) { 1203 // Evaluate the expression in the larger type. 1204 SCEVHandle Fold = getAddExpr(LargeOps); 1205 // If it folds to something simple, use it. Otherwise, don't. 1206 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1207 return getTruncateExpr(Fold, DstType); 1208 } 1209 } 1210 1211 // Skip past any other cast SCEVs. 1212 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1213 ++Idx; 1214 1215 // If there are add operands they would be next. 1216 if (Idx < Ops.size()) { 1217 bool DeletedAdd = false; 1218 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1219 // If we have an add, expand the add operands onto the end of the operands 1220 // list. 1221 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1222 Ops.erase(Ops.begin()+Idx); 1223 DeletedAdd = true; 1224 } 1225 1226 // If we deleted at least one add, we added operands to the end of the list, 1227 // and they are not necessarily sorted. Recurse to resort and resimplify 1228 // any operands we just aquired. 1229 if (DeletedAdd) 1230 return getAddExpr(Ops); 1231 } 1232 1233 // Skip over the add expression until we get to a multiply. 1234 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1235 ++Idx; 1236 1237 // Check to see if there are any folding opportunities present with 1238 // operands multiplied by constant values. 1239 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1240 uint64_t BitWidth = getTypeSizeInBits(Ty); 1241 DenseMap<SCEVHandle, APInt> M; 1242 SmallVector<SCEVHandle, 8> NewOps; 1243 APInt AccumulatedConstant(BitWidth, 0); 1244 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1245 Ops, APInt(BitWidth, 1), *this)) { 1246 // Some interesting folding opportunity is present, so its worthwhile to 1247 // re-generate the operands list. Group the operands by constant scale, 1248 // to avoid multiplying by the same constant scale multiple times. 1249 std::map<APInt, SmallVector<SCEVHandle, 4>, APIntCompare> MulOpLists; 1250 for (SmallVector<SCEVHandle, 8>::iterator I = NewOps.begin(), 1251 E = NewOps.end(); I != E; ++I) 1252 MulOpLists[M.find(*I)->second].push_back(*I); 1253 // Re-generate the operands list. 1254 Ops.clear(); 1255 if (AccumulatedConstant != 0) 1256 Ops.push_back(getConstant(AccumulatedConstant)); 1257 for (std::map<APInt, SmallVector<SCEVHandle, 4>, APIntCompare>::iterator I = 1258 MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1259 if (I->first != 0) 1260 Ops.push_back(getMulExpr(getConstant(I->first), getAddExpr(I->second))); 1261 if (Ops.empty()) 1262 return getIntegerSCEV(0, Ty); 1263 if (Ops.size() == 1) 1264 return Ops[0]; 1265 return getAddExpr(Ops); 1266 } 1267 } 1268 1269 // If we are adding something to a multiply expression, make sure the 1270 // something is not already an operand of the multiply. If so, merge it into 1271 // the multiply. 1272 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1273 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1274 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1275 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1276 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1277 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1278 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1279 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 1280 if (Mul->getNumOperands() != 2) { 1281 // If the multiply has more than two operands, we must get the 1282 // Y*Z term. 1283 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1284 MulOps.erase(MulOps.begin()+MulOp); 1285 InnerMul = getMulExpr(MulOps); 1286 } 1287 SCEVHandle One = getIntegerSCEV(1, Ty); 1288 SCEVHandle AddOne = getAddExpr(InnerMul, One); 1289 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1290 if (Ops.size() == 2) return OuterMul; 1291 if (AddOp < Idx) { 1292 Ops.erase(Ops.begin()+AddOp); 1293 Ops.erase(Ops.begin()+Idx-1); 1294 } else { 1295 Ops.erase(Ops.begin()+Idx); 1296 Ops.erase(Ops.begin()+AddOp-1); 1297 } 1298 Ops.push_back(OuterMul); 1299 return getAddExpr(Ops); 1300 } 1301 1302 // Check this multiply against other multiplies being added together. 1303 for (unsigned OtherMulIdx = Idx+1; 1304 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1305 ++OtherMulIdx) { 1306 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1307 // If MulOp occurs in OtherMul, we can fold the two multiplies 1308 // together. 1309 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1310 OMulOp != e; ++OMulOp) 1311 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1312 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1313 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 1314 if (Mul->getNumOperands() != 2) { 1315 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1316 MulOps.erase(MulOps.begin()+MulOp); 1317 InnerMul1 = getMulExpr(MulOps); 1318 } 1319 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1320 if (OtherMul->getNumOperands() != 2) { 1321 SmallVector<SCEVHandle, 4> MulOps(OtherMul->op_begin(), 1322 OtherMul->op_end()); 1323 MulOps.erase(MulOps.begin()+OMulOp); 1324 InnerMul2 = getMulExpr(MulOps); 1325 } 1326 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1327 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1328 if (Ops.size() == 2) return OuterMul; 1329 Ops.erase(Ops.begin()+Idx); 1330 Ops.erase(Ops.begin()+OtherMulIdx-1); 1331 Ops.push_back(OuterMul); 1332 return getAddExpr(Ops); 1333 } 1334 } 1335 } 1336 } 1337 1338 // If there are any add recurrences in the operands list, see if any other 1339 // added values are loop invariant. If so, we can fold them into the 1340 // recurrence. 1341 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1342 ++Idx; 1343 1344 // Scan over all recurrences, trying to fold loop invariants into them. 1345 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1346 // Scan all of the other operands to this add and add them to the vector if 1347 // they are loop invariant w.r.t. the recurrence. 1348 SmallVector<SCEVHandle, 8> LIOps; 1349 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1350 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1351 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1352 LIOps.push_back(Ops[i]); 1353 Ops.erase(Ops.begin()+i); 1354 --i; --e; 1355 } 1356 1357 // If we found some loop invariants, fold them into the recurrence. 1358 if (!LIOps.empty()) { 1359 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1360 LIOps.push_back(AddRec->getStart()); 1361 1362 SmallVector<SCEVHandle, 4> AddRecOps(AddRec->op_begin(), 1363 AddRec->op_end()); 1364 AddRecOps[0] = getAddExpr(LIOps); 1365 1366 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1367 // If all of the other operands were loop invariant, we are done. 1368 if (Ops.size() == 1) return NewRec; 1369 1370 // Otherwise, add the folded AddRec by the non-liv parts. 1371 for (unsigned i = 0;; ++i) 1372 if (Ops[i] == AddRec) { 1373 Ops[i] = NewRec; 1374 break; 1375 } 1376 return getAddExpr(Ops); 1377 } 1378 1379 // Okay, if there weren't any loop invariants to be folded, check to see if 1380 // there are multiple AddRec's with the same loop induction variable being 1381 // added together. If so, we can fold them. 1382 for (unsigned OtherIdx = Idx+1; 1383 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1384 if (OtherIdx != Idx) { 1385 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1386 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1387 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1388 SmallVector<SCEVHandle, 4> NewOps(AddRec->op_begin(), AddRec->op_end()); 1389 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1390 if (i >= NewOps.size()) { 1391 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1392 OtherAddRec->op_end()); 1393 break; 1394 } 1395 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1396 } 1397 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1398 1399 if (Ops.size() == 2) return NewAddRec; 1400 1401 Ops.erase(Ops.begin()+Idx); 1402 Ops.erase(Ops.begin()+OtherIdx-1); 1403 Ops.push_back(NewAddRec); 1404 return getAddExpr(Ops); 1405 } 1406 } 1407 1408 // Otherwise couldn't fold anything into this recurrence. Move onto the 1409 // next one. 1410 } 1411 1412 // Okay, it looks like we really DO need an add expr. Check to see if we 1413 // already have one, otherwise create a new one. 1414 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1415 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 1416 SCEVOps)]; 1417 if (Result == 0) Result = new SCEVAddExpr(Ops, this); 1418 return Result; 1419} 1420 1421 1422/// getMulExpr - Get a canonical multiply expression, or something simpler if 1423/// possible. 1424SCEVHandle ScalarEvolution::getMulExpr(SmallVectorImpl<SCEVHandle> &Ops) { 1425 assert(!Ops.empty() && "Cannot get empty mul!"); 1426#ifndef NDEBUG 1427 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1428 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1429 getEffectiveSCEVType(Ops[0]->getType()) && 1430 "SCEVMulExpr operand types don't match!"); 1431#endif 1432 1433 // Sort by complexity, this groups all similar expression types together. 1434 GroupByComplexity(Ops, LI); 1435 1436 // If there are any constants, fold them together. 1437 unsigned Idx = 0; 1438 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1439 1440 // C1*(C2+V) -> C1*C2 + C1*V 1441 if (Ops.size() == 2) 1442 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1443 if (Add->getNumOperands() == 2 && 1444 isa<SCEVConstant>(Add->getOperand(0))) 1445 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1446 getMulExpr(LHSC, Add->getOperand(1))); 1447 1448 1449 ++Idx; 1450 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1451 // We found two constants, fold them together! 1452 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1453 RHSC->getValue()->getValue()); 1454 Ops[0] = getConstant(Fold); 1455 Ops.erase(Ops.begin()+1); // Erase the folded element 1456 if (Ops.size() == 1) return Ops[0]; 1457 LHSC = cast<SCEVConstant>(Ops[0]); 1458 } 1459 1460 // If we are left with a constant one being multiplied, strip it off. 1461 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1462 Ops.erase(Ops.begin()); 1463 --Idx; 1464 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1465 // If we have a multiply of zero, it will always be zero. 1466 return Ops[0]; 1467 } 1468 } 1469 1470 // Skip over the add expression until we get to a multiply. 1471 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1472 ++Idx; 1473 1474 if (Ops.size() == 1) 1475 return Ops[0]; 1476 1477 // If there are mul operands inline them all into this expression. 1478 if (Idx < Ops.size()) { 1479 bool DeletedMul = false; 1480 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1481 // If we have an mul, expand the mul operands onto the end of the operands 1482 // list. 1483 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1484 Ops.erase(Ops.begin()+Idx); 1485 DeletedMul = true; 1486 } 1487 1488 // If we deleted at least one mul, we added operands to the end of the list, 1489 // and they are not necessarily sorted. Recurse to resort and resimplify 1490 // any operands we just aquired. 1491 if (DeletedMul) 1492 return getMulExpr(Ops); 1493 } 1494 1495 // If there are any add recurrences in the operands list, see if any other 1496 // added values are loop invariant. If so, we can fold them into the 1497 // recurrence. 1498 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1499 ++Idx; 1500 1501 // Scan over all recurrences, trying to fold loop invariants into them. 1502 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1503 // Scan all of the other operands to this mul and add them to the vector if 1504 // they are loop invariant w.r.t. the recurrence. 1505 SmallVector<SCEVHandle, 8> LIOps; 1506 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1507 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1508 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1509 LIOps.push_back(Ops[i]); 1510 Ops.erase(Ops.begin()+i); 1511 --i; --e; 1512 } 1513 1514 // If we found some loop invariants, fold them into the recurrence. 1515 if (!LIOps.empty()) { 1516 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1517 SmallVector<SCEVHandle, 4> NewOps; 1518 NewOps.reserve(AddRec->getNumOperands()); 1519 if (LIOps.size() == 1) { 1520 const SCEV *Scale = LIOps[0]; 1521 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1522 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1523 } else { 1524 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1525 SmallVector<SCEVHandle, 4> MulOps(LIOps.begin(), LIOps.end()); 1526 MulOps.push_back(AddRec->getOperand(i)); 1527 NewOps.push_back(getMulExpr(MulOps)); 1528 } 1529 } 1530 1531 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1532 1533 // If all of the other operands were loop invariant, we are done. 1534 if (Ops.size() == 1) return NewRec; 1535 1536 // Otherwise, multiply the folded AddRec by the non-liv parts. 1537 for (unsigned i = 0;; ++i) 1538 if (Ops[i] == AddRec) { 1539 Ops[i] = NewRec; 1540 break; 1541 } 1542 return getMulExpr(Ops); 1543 } 1544 1545 // Okay, if there weren't any loop invariants to be folded, check to see if 1546 // there are multiple AddRec's with the same loop induction variable being 1547 // multiplied together. If so, we can fold them. 1548 for (unsigned OtherIdx = Idx+1; 1549 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1550 if (OtherIdx != Idx) { 1551 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1552 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1553 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1554 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1555 SCEVHandle NewStart = getMulExpr(F->getStart(), 1556 G->getStart()); 1557 SCEVHandle B = F->getStepRecurrence(*this); 1558 SCEVHandle D = G->getStepRecurrence(*this); 1559 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1560 getMulExpr(G, B), 1561 getMulExpr(B, D)); 1562 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1563 F->getLoop()); 1564 if (Ops.size() == 2) return NewAddRec; 1565 1566 Ops.erase(Ops.begin()+Idx); 1567 Ops.erase(Ops.begin()+OtherIdx-1); 1568 Ops.push_back(NewAddRec); 1569 return getMulExpr(Ops); 1570 } 1571 } 1572 1573 // Otherwise couldn't fold anything into this recurrence. Move onto the 1574 // next one. 1575 } 1576 1577 // Okay, it looks like we really DO need an mul expr. Check to see if we 1578 // already have one, otherwise create a new one. 1579 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1580 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1581 SCEVOps)]; 1582 if (Result == 0) 1583 Result = new SCEVMulExpr(Ops, this); 1584 return Result; 1585} 1586 1587/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1588/// possible. 1589SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, 1590 const SCEVHandle &RHS) { 1591 assert(getEffectiveSCEVType(LHS->getType()) == 1592 getEffectiveSCEVType(RHS->getType()) && 1593 "SCEVUDivExpr operand types don't match!"); 1594 1595 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1596 if (RHSC->getValue()->equalsInt(1)) 1597 return LHS; // X udiv 1 --> x 1598 if (RHSC->isZero()) 1599 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1600 1601 // Determine if the division can be folded into the operands of 1602 // its operands. 1603 // TODO: Generalize this to non-constants by using known-bits information. 1604 const Type *Ty = LHS->getType(); 1605 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1606 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1607 // For non-power-of-two values, effectively round the value up to the 1608 // nearest power of two. 1609 if (!RHSC->getValue()->getValue().isPowerOf2()) 1610 ++MaxShiftAmt; 1611 const IntegerType *ExtTy = 1612 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1613 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1614 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1615 if (const SCEVConstant *Step = 1616 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1617 if (!Step->getValue()->getValue() 1618 .urem(RHSC->getValue()->getValue()) && 1619 getZeroExtendExpr(AR, ExtTy) == 1620 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1621 getZeroExtendExpr(Step, ExtTy), 1622 AR->getLoop())) { 1623 SmallVector<SCEVHandle, 4> Operands; 1624 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1625 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1626 return getAddRecExpr(Operands, AR->getLoop()); 1627 } 1628 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1629 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1630 SmallVector<SCEVHandle, 4> Operands; 1631 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1632 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1633 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1634 // Find an operand that's safely divisible. 1635 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1636 SCEVHandle Op = M->getOperand(i); 1637 SCEVHandle Div = getUDivExpr(Op, RHSC); 1638 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1639 const SmallVectorImpl<SCEVHandle> &MOperands = M->getOperands(); 1640 Operands = SmallVector<SCEVHandle, 4>(MOperands.begin(), 1641 MOperands.end()); 1642 Operands[i] = Div; 1643 return getMulExpr(Operands); 1644 } 1645 } 1646 } 1647 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1648 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1649 SmallVector<SCEVHandle, 4> Operands; 1650 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1651 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1652 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1653 Operands.clear(); 1654 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1655 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS); 1656 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1657 break; 1658 Operands.push_back(Op); 1659 } 1660 if (Operands.size() == A->getNumOperands()) 1661 return getAddExpr(Operands); 1662 } 1663 } 1664 1665 // Fold if both operands are constant. 1666 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1667 Constant *LHSCV = LHSC->getValue(); 1668 Constant *RHSCV = RHSC->getValue(); 1669 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1670 } 1671 } 1672 1673 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1674 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS, this); 1675 return Result; 1676} 1677 1678 1679/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1680/// Simplify the expression as much as possible. 1681SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1682 const SCEVHandle &Step, const Loop *L) { 1683 SmallVector<SCEVHandle, 4> Operands; 1684 Operands.push_back(Start); 1685 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1686 if (StepChrec->getLoop() == L) { 1687 Operands.insert(Operands.end(), StepChrec->op_begin(), 1688 StepChrec->op_end()); 1689 return getAddRecExpr(Operands, L); 1690 } 1691 1692 Operands.push_back(Step); 1693 return getAddRecExpr(Operands, L); 1694} 1695 1696/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1697/// Simplify the expression as much as possible. 1698SCEVHandle ScalarEvolution::getAddRecExpr(SmallVectorImpl<SCEVHandle> &Operands, 1699 const Loop *L) { 1700 if (Operands.size() == 1) return Operands[0]; 1701#ifndef NDEBUG 1702 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1703 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1704 getEffectiveSCEVType(Operands[0]->getType()) && 1705 "SCEVAddRecExpr operand types don't match!"); 1706#endif 1707 1708 if (Operands.back()->isZero()) { 1709 Operands.pop_back(); 1710 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1711 } 1712 1713 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1714 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1715 const Loop* NestedLoop = NestedAR->getLoop(); 1716 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1717 SmallVector<SCEVHandle, 4> NestedOperands(NestedAR->op_begin(), 1718 NestedAR->op_end()); 1719 SCEVHandle NestedARHandle(NestedAR); 1720 Operands[0] = NestedAR->getStart(); 1721 NestedOperands[0] = getAddRecExpr(Operands, L); 1722 return getAddRecExpr(NestedOperands, NestedLoop); 1723 } 1724 } 1725 1726 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 1727 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)]; 1728 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L, this); 1729 return Result; 1730} 1731 1732SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1733 const SCEVHandle &RHS) { 1734 SmallVector<SCEVHandle, 2> Ops; 1735 Ops.push_back(LHS); 1736 Ops.push_back(RHS); 1737 return getSMaxExpr(Ops); 1738} 1739 1740SCEVHandle 1741ScalarEvolution::getSMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) { 1742 assert(!Ops.empty() && "Cannot get empty smax!"); 1743 if (Ops.size() == 1) return Ops[0]; 1744#ifndef NDEBUG 1745 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1746 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1747 getEffectiveSCEVType(Ops[0]->getType()) && 1748 "SCEVSMaxExpr operand types don't match!"); 1749#endif 1750 1751 // Sort by complexity, this groups all similar expression types together. 1752 GroupByComplexity(Ops, LI); 1753 1754 // If there are any constants, fold them together. 1755 unsigned Idx = 0; 1756 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1757 ++Idx; 1758 assert(Idx < Ops.size()); 1759 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1760 // We found two constants, fold them together! 1761 ConstantInt *Fold = ConstantInt::get( 1762 APIntOps::smax(LHSC->getValue()->getValue(), 1763 RHSC->getValue()->getValue())); 1764 Ops[0] = getConstant(Fold); 1765 Ops.erase(Ops.begin()+1); // Erase the folded element 1766 if (Ops.size() == 1) return Ops[0]; 1767 LHSC = cast<SCEVConstant>(Ops[0]); 1768 } 1769 1770 // If we are left with a constant -inf, strip it off. 1771 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1772 Ops.erase(Ops.begin()); 1773 --Idx; 1774 } 1775 } 1776 1777 if (Ops.size() == 1) return Ops[0]; 1778 1779 // Find the first SMax 1780 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1781 ++Idx; 1782 1783 // Check to see if one of the operands is an SMax. If so, expand its operands 1784 // onto our operand list, and recurse to simplify. 1785 if (Idx < Ops.size()) { 1786 bool DeletedSMax = false; 1787 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1788 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1789 Ops.erase(Ops.begin()+Idx); 1790 DeletedSMax = true; 1791 } 1792 1793 if (DeletedSMax) 1794 return getSMaxExpr(Ops); 1795 } 1796 1797 // Okay, check to see if the same value occurs in the operand list twice. If 1798 // so, delete one. Since we sorted the list, these values are required to 1799 // be adjacent. 1800 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1801 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1802 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1803 --i; --e; 1804 } 1805 1806 if (Ops.size() == 1) return Ops[0]; 1807 1808 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1809 1810 // Okay, it looks like we really DO need an smax expr. Check to see if we 1811 // already have one, otherwise create a new one. 1812 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1813 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1814 SCEVOps)]; 1815 if (Result == 0) Result = new SCEVSMaxExpr(Ops, this); 1816 return Result; 1817} 1818 1819SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1820 const SCEVHandle &RHS) { 1821 SmallVector<SCEVHandle, 2> Ops; 1822 Ops.push_back(LHS); 1823 Ops.push_back(RHS); 1824 return getUMaxExpr(Ops); 1825} 1826 1827SCEVHandle 1828ScalarEvolution::getUMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) { 1829 assert(!Ops.empty() && "Cannot get empty umax!"); 1830 if (Ops.size() == 1) return Ops[0]; 1831#ifndef NDEBUG 1832 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1833 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1834 getEffectiveSCEVType(Ops[0]->getType()) && 1835 "SCEVUMaxExpr operand types don't match!"); 1836#endif 1837 1838 // Sort by complexity, this groups all similar expression types together. 1839 GroupByComplexity(Ops, LI); 1840 1841 // If there are any constants, fold them together. 1842 unsigned Idx = 0; 1843 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1844 ++Idx; 1845 assert(Idx < Ops.size()); 1846 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1847 // We found two constants, fold them together! 1848 ConstantInt *Fold = ConstantInt::get( 1849 APIntOps::umax(LHSC->getValue()->getValue(), 1850 RHSC->getValue()->getValue())); 1851 Ops[0] = getConstant(Fold); 1852 Ops.erase(Ops.begin()+1); // Erase the folded element 1853 if (Ops.size() == 1) return Ops[0]; 1854 LHSC = cast<SCEVConstant>(Ops[0]); 1855 } 1856 1857 // If we are left with a constant zero, strip it off. 1858 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1859 Ops.erase(Ops.begin()); 1860 --Idx; 1861 } 1862 } 1863 1864 if (Ops.size() == 1) return Ops[0]; 1865 1866 // Find the first UMax 1867 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1868 ++Idx; 1869 1870 // Check to see if one of the operands is a UMax. If so, expand its operands 1871 // onto our operand list, and recurse to simplify. 1872 if (Idx < Ops.size()) { 1873 bool DeletedUMax = false; 1874 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1875 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1876 Ops.erase(Ops.begin()+Idx); 1877 DeletedUMax = true; 1878 } 1879 1880 if (DeletedUMax) 1881 return getUMaxExpr(Ops); 1882 } 1883 1884 // Okay, check to see if the same value occurs in the operand list twice. If 1885 // so, delete one. Since we sorted the list, these values are required to 1886 // be adjacent. 1887 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1888 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1889 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1890 --i; --e; 1891 } 1892 1893 if (Ops.size() == 1) return Ops[0]; 1894 1895 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1896 1897 // Okay, it looks like we really DO need a umax expr. Check to see if we 1898 // already have one, otherwise create a new one. 1899 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1900 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1901 SCEVOps)]; 1902 if (Result == 0) Result = new SCEVUMaxExpr(Ops, this); 1903 return Result; 1904} 1905 1906SCEVHandle ScalarEvolution::getSMinExpr(const SCEVHandle &LHS, 1907 const SCEVHandle &RHS) { 1908 // ~smax(~x, ~y) == smin(x, y). 1909 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1910} 1911 1912SCEVHandle ScalarEvolution::getUMinExpr(const SCEVHandle &LHS, 1913 const SCEVHandle &RHS) { 1914 // ~umax(~x, ~y) == umin(x, y) 1915 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1916} 1917 1918SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1919 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1920 return getConstant(CI); 1921 if (isa<ConstantPointerNull>(V)) 1922 return getIntegerSCEV(0, V->getType()); 1923 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1924 if (Result == 0) Result = new SCEVUnknown(V, this); 1925 return Result; 1926} 1927 1928//===----------------------------------------------------------------------===// 1929// Basic SCEV Analysis and PHI Idiom Recognition Code 1930// 1931 1932/// isSCEVable - Test if values of the given type are analyzable within 1933/// the SCEV framework. This primarily includes integer types, and it 1934/// can optionally include pointer types if the ScalarEvolution class 1935/// has access to target-specific information. 1936bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1937 // Integers are always SCEVable. 1938 if (Ty->isInteger()) 1939 return true; 1940 1941 // Pointers are SCEVable if TargetData information is available 1942 // to provide pointer size information. 1943 if (isa<PointerType>(Ty)) 1944 return TD != NULL; 1945 1946 // Otherwise it's not SCEVable. 1947 return false; 1948} 1949 1950/// getTypeSizeInBits - Return the size in bits of the specified type, 1951/// for which isSCEVable must return true. 1952uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1953 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1954 1955 // If we have a TargetData, use it! 1956 if (TD) 1957 return TD->getTypeSizeInBits(Ty); 1958 1959 // Otherwise, we support only integer types. 1960 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1961 return Ty->getPrimitiveSizeInBits(); 1962} 1963 1964/// getEffectiveSCEVType - Return a type with the same bitwidth as 1965/// the given type and which represents how SCEV will treat the given 1966/// type, for which isSCEVable must return true. For pointer types, 1967/// this is the pointer-sized integer type. 1968const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1969 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1970 1971 if (Ty->isInteger()) 1972 return Ty; 1973 1974 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1975 return TD->getIntPtrType(); 1976} 1977 1978SCEVHandle ScalarEvolution::getCouldNotCompute() { 1979 return CouldNotCompute; 1980} 1981 1982/// hasSCEV - Return true if the SCEV for this value has already been 1983/// computed. 1984bool ScalarEvolution::hasSCEV(Value *V) const { 1985 return Scalars.count(V); 1986} 1987 1988/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1989/// expression and create a new one. 1990SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1991 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1992 1993 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V); 1994 if (I != Scalars.end()) return I->second; 1995 SCEVHandle S = createSCEV(V); 1996 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 1997 return S; 1998} 1999 2000/// getIntegerSCEV - Given an integer or FP type, create a constant for the 2001/// specified signed integer value and return a SCEV for the constant. 2002SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2003 Ty = getEffectiveSCEVType(Ty); 2004 Constant *C; 2005 if (Val == 0) 2006 C = Constant::getNullValue(Ty); 2007 else if (Ty->isFloatingPoint()) 2008 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 2009 APFloat::IEEEdouble, Val)); 2010 else 2011 C = ConstantInt::get(Ty, Val); 2012 return getUnknown(C); 2013} 2014 2015/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2016/// 2017SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 2018 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2019 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 2020 2021 const Type *Ty = V->getType(); 2022 Ty = getEffectiveSCEVType(Ty); 2023 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 2024} 2025 2026/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2027SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 2028 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2029 return getUnknown(ConstantExpr::getNot(VC->getValue())); 2030 2031 const Type *Ty = V->getType(); 2032 Ty = getEffectiveSCEVType(Ty); 2033 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 2034 return getMinusSCEV(AllOnes, V); 2035} 2036 2037/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2038/// 2039SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 2040 const SCEVHandle &RHS) { 2041 // X - Y --> X + -Y 2042 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2043} 2044 2045/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2046/// input value to the specified type. If the type must be extended, it is zero 2047/// extended. 2048SCEVHandle 2049ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 2050 const Type *Ty) { 2051 const Type *SrcTy = V->getType(); 2052 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2053 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2054 "Cannot truncate or zero extend with non-integer arguments!"); 2055 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2056 return V; // No conversion 2057 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2058 return getTruncateExpr(V, Ty); 2059 return getZeroExtendExpr(V, Ty); 2060} 2061 2062/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2063/// input value to the specified type. If the type must be extended, it is sign 2064/// extended. 2065SCEVHandle 2066ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 2067 const Type *Ty) { 2068 const Type *SrcTy = V->getType(); 2069 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2070 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2071 "Cannot truncate or zero extend with non-integer arguments!"); 2072 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2073 return V; // No conversion 2074 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2075 return getTruncateExpr(V, Ty); 2076 return getSignExtendExpr(V, Ty); 2077} 2078 2079/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2080/// input value to the specified type. If the type must be extended, it is zero 2081/// extended. The conversion must not be narrowing. 2082SCEVHandle 2083ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 2084 const Type *SrcTy = V->getType(); 2085 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2086 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2087 "Cannot noop or zero extend with non-integer arguments!"); 2088 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2089 "getNoopOrZeroExtend cannot truncate!"); 2090 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2091 return V; // No conversion 2092 return getZeroExtendExpr(V, Ty); 2093} 2094 2095/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2096/// input value to the specified type. If the type must be extended, it is sign 2097/// extended. The conversion must not be narrowing. 2098SCEVHandle 2099ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) { 2100 const Type *SrcTy = V->getType(); 2101 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2102 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2103 "Cannot noop or sign extend with non-integer arguments!"); 2104 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2105 "getNoopOrSignExtend cannot truncate!"); 2106 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2107 return V; // No conversion 2108 return getSignExtendExpr(V, Ty); 2109} 2110 2111/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2112/// the input value to the specified type. If the type must be extended, 2113/// it is extended with unspecified bits. The conversion must not be 2114/// narrowing. 2115SCEVHandle 2116ScalarEvolution::getNoopOrAnyExtend(const SCEVHandle &V, const Type *Ty) { 2117 const Type *SrcTy = V->getType(); 2118 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2119 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2120 "Cannot noop or any extend with non-integer arguments!"); 2121 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2122 "getNoopOrAnyExtend cannot truncate!"); 2123 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2124 return V; // No conversion 2125 return getAnyExtendExpr(V, Ty); 2126} 2127 2128/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2129/// input value to the specified type. The conversion must not be widening. 2130SCEVHandle 2131ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) { 2132 const Type *SrcTy = V->getType(); 2133 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2134 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2135 "Cannot truncate or noop with non-integer arguments!"); 2136 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2137 "getTruncateOrNoop cannot extend!"); 2138 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2139 return V; // No conversion 2140 return getTruncateExpr(V, Ty); 2141} 2142 2143/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2144/// the types using zero-extension, and then perform a umax operation 2145/// with them. 2146SCEVHandle ScalarEvolution::getUMaxFromMismatchedTypes(const SCEVHandle &LHS, 2147 const SCEVHandle &RHS) { 2148 SCEVHandle PromotedLHS = LHS; 2149 SCEVHandle PromotedRHS = RHS; 2150 2151 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2152 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2153 else 2154 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2155 2156 return getUMaxExpr(PromotedLHS, PromotedRHS); 2157} 2158 2159/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2160/// the specified instruction and replaces any references to the symbolic value 2161/// SymName with the specified value. This is used during PHI resolution. 2162void ScalarEvolution:: 2163ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 2164 const SCEVHandle &NewVal) { 2165 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI = 2166 Scalars.find(SCEVCallbackVH(I, this)); 2167 if (SI == Scalars.end()) return; 2168 2169 SCEVHandle NV = 2170 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2171 if (NV == SI->second) return; // No change. 2172 2173 SI->second = NV; // Update the scalars map! 2174 2175 // Any instruction values that use this instruction might also need to be 2176 // updated! 2177 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2178 UI != E; ++UI) 2179 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2180} 2181 2182/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2183/// a loop header, making it a potential recurrence, or it doesn't. 2184/// 2185SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 2186 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2187 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2188 if (L->getHeader() == PN->getParent()) { 2189 // If it lives in the loop header, it has two incoming values, one 2190 // from outside the loop, and one from inside. 2191 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2192 unsigned BackEdge = IncomingEdge^1; 2193 2194 // While we are analyzing this PHI node, handle its value symbolically. 2195 SCEVHandle SymbolicName = getUnknown(PN); 2196 assert(Scalars.find(PN) == Scalars.end() && 2197 "PHI node already processed?"); 2198 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2199 2200 // Using this symbolic name for the PHI, analyze the value coming around 2201 // the back-edge. 2202 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2203 2204 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2205 // has a special value for the first iteration of the loop. 2206 2207 // If the value coming around the backedge is an add with the symbolic 2208 // value we just inserted, then we found a simple induction variable! 2209 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2210 // If there is a single occurrence of the symbolic value, replace it 2211 // with a recurrence. 2212 unsigned FoundIndex = Add->getNumOperands(); 2213 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2214 if (Add->getOperand(i) == SymbolicName) 2215 if (FoundIndex == e) { 2216 FoundIndex = i; 2217 break; 2218 } 2219 2220 if (FoundIndex != Add->getNumOperands()) { 2221 // Create an add with everything but the specified operand. 2222 SmallVector<SCEVHandle, 8> Ops; 2223 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2224 if (i != FoundIndex) 2225 Ops.push_back(Add->getOperand(i)); 2226 SCEVHandle Accum = getAddExpr(Ops); 2227 2228 // This is not a valid addrec if the step amount is varying each 2229 // loop iteration, but is not itself an addrec in this loop. 2230 if (Accum->isLoopInvariant(L) || 2231 (isa<SCEVAddRecExpr>(Accum) && 2232 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2233 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2234 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 2235 2236 // Okay, for the entire analysis of this edge we assumed the PHI 2237 // to be symbolic. We now need to go back and update all of the 2238 // entries for the scalars that use the PHI (except for the PHI 2239 // itself) to use the new analyzed value instead of the "symbolic" 2240 // value. 2241 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2242 return PHISCEV; 2243 } 2244 } 2245 } else if (const SCEVAddRecExpr *AddRec = 2246 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2247 // Otherwise, this could be a loop like this: 2248 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2249 // In this case, j = {1,+,1} and BEValue is j. 2250 // Because the other in-value of i (0) fits the evolution of BEValue 2251 // i really is an addrec evolution. 2252 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2253 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2254 2255 // If StartVal = j.start - j.stride, we can use StartVal as the 2256 // initial step of the addrec evolution. 2257 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2258 AddRec->getOperand(1))) { 2259 SCEVHandle PHISCEV = 2260 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2261 2262 // Okay, for the entire analysis of this edge we assumed the PHI 2263 // to be symbolic. We now need to go back and update all of the 2264 // entries for the scalars that use the PHI (except for the PHI 2265 // itself) to use the new analyzed value instead of the "symbolic" 2266 // value. 2267 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2268 return PHISCEV; 2269 } 2270 } 2271 } 2272 2273 return SymbolicName; 2274 } 2275 2276 // If it's not a loop phi, we can't handle it yet. 2277 return getUnknown(PN); 2278} 2279 2280/// createNodeForGEP - Expand GEP instructions into add and multiply 2281/// operations. This allows them to be analyzed by regular SCEV code. 2282/// 2283SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) { 2284 2285 const Type *IntPtrTy = TD->getIntPtrType(); 2286 Value *Base = GEP->getOperand(0); 2287 // Don't attempt to analyze GEPs over unsized objects. 2288 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2289 return getUnknown(GEP); 2290 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 2291 gep_type_iterator GTI = gep_type_begin(GEP); 2292 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2293 E = GEP->op_end(); 2294 I != E; ++I) { 2295 Value *Index = *I; 2296 // Compute the (potentially symbolic) offset in bytes for this index. 2297 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2298 // For a struct, add the member offset. 2299 const StructLayout &SL = *TD->getStructLayout(STy); 2300 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2301 uint64_t Offset = SL.getElementOffset(FieldNo); 2302 TotalOffset = getAddExpr(TotalOffset, 2303 getIntegerSCEV(Offset, IntPtrTy)); 2304 } else { 2305 // For an array, add the element offset, explicitly scaled. 2306 SCEVHandle LocalOffset = getSCEV(Index); 2307 if (!isa<PointerType>(LocalOffset->getType())) 2308 // Getelementptr indicies are signed. 2309 LocalOffset = getTruncateOrSignExtend(LocalOffset, 2310 IntPtrTy); 2311 LocalOffset = 2312 getMulExpr(LocalOffset, 2313 getIntegerSCEV(TD->getTypeAllocSize(*GTI), 2314 IntPtrTy)); 2315 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2316 } 2317 } 2318 return getAddExpr(getSCEV(Base), TotalOffset); 2319} 2320 2321/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2322/// guaranteed to end in (at every loop iteration). It is, at the same time, 2323/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2324/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2325uint32_t 2326ScalarEvolution::GetMinTrailingZeros(const SCEVHandle &S) { 2327 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2328 return C->getValue()->getValue().countTrailingZeros(); 2329 2330 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2331 return std::min(GetMinTrailingZeros(T->getOperand()), 2332 (uint32_t)getTypeSizeInBits(T->getType())); 2333 2334 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2335 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2336 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2337 getTypeSizeInBits(E->getType()) : OpRes; 2338 } 2339 2340 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2341 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2342 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2343 getTypeSizeInBits(E->getType()) : OpRes; 2344 } 2345 2346 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2347 // The result is the min of all operands results. 2348 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2349 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2350 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2351 return MinOpRes; 2352 } 2353 2354 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2355 // The result is the sum of all operands results. 2356 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2357 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2358 for (unsigned i = 1, e = M->getNumOperands(); 2359 SumOpRes != BitWidth && i != e; ++i) 2360 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2361 BitWidth); 2362 return SumOpRes; 2363 } 2364 2365 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2366 // The result is the min of all operands results. 2367 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2368 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2369 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2370 return MinOpRes; 2371 } 2372 2373 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2374 // The result is the min of all operands results. 2375 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2376 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2377 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2378 return MinOpRes; 2379 } 2380 2381 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2382 // The result is the min of all operands results. 2383 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2384 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2385 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2386 return MinOpRes; 2387 } 2388 2389 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2390 // For a SCEVUnknown, ask ValueTracking. 2391 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2392 APInt Mask = APInt::getAllOnesValue(BitWidth); 2393 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2394 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2395 return Zeros.countTrailingOnes(); 2396 } 2397 2398 // SCEVUDivExpr 2399 return 0; 2400} 2401 2402uint32_t 2403ScalarEvolution::GetMinLeadingZeros(const SCEVHandle &S) { 2404 // TODO: Handle other SCEV expression types here. 2405 2406 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2407 return C->getValue()->getValue().countLeadingZeros(); 2408 2409 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) { 2410 // A zero-extension cast adds zero bits. 2411 return GetMinLeadingZeros(C->getOperand()) + 2412 (getTypeSizeInBits(C->getType()) - 2413 getTypeSizeInBits(C->getOperand()->getType())); 2414 } 2415 2416 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2417 // For a SCEVUnknown, ask ValueTracking. 2418 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2419 APInt Mask = APInt::getAllOnesValue(BitWidth); 2420 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2421 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2422 return Zeros.countLeadingOnes(); 2423 } 2424 2425 return 1; 2426} 2427 2428uint32_t 2429ScalarEvolution::GetMinSignBits(const SCEVHandle &S) { 2430 // TODO: Handle other SCEV expression types here. 2431 2432 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 2433 const APInt &A = C->getValue()->getValue(); 2434 return A.isNegative() ? A.countLeadingOnes() : 2435 A.countLeadingZeros(); 2436 } 2437 2438 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) { 2439 // A sign-extension cast adds sign bits. 2440 return GetMinSignBits(C->getOperand()) + 2441 (getTypeSizeInBits(C->getType()) - 2442 getTypeSizeInBits(C->getOperand()->getType())); 2443 } 2444 2445 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2446 // For a SCEVUnknown, ask ValueTracking. 2447 return ComputeNumSignBits(U->getValue(), TD); 2448 } 2449 2450 return 1; 2451} 2452 2453/// createSCEV - We know that there is no SCEV for the specified value. 2454/// Analyze the expression. 2455/// 2456SCEVHandle ScalarEvolution::createSCEV(Value *V) { 2457 if (!isSCEVable(V->getType())) 2458 return getUnknown(V); 2459 2460 unsigned Opcode = Instruction::UserOp1; 2461 if (Instruction *I = dyn_cast<Instruction>(V)) 2462 Opcode = I->getOpcode(); 2463 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2464 Opcode = CE->getOpcode(); 2465 else 2466 return getUnknown(V); 2467 2468 User *U = cast<User>(V); 2469 switch (Opcode) { 2470 case Instruction::Add: 2471 return getAddExpr(getSCEV(U->getOperand(0)), 2472 getSCEV(U->getOperand(1))); 2473 case Instruction::Mul: 2474 return getMulExpr(getSCEV(U->getOperand(0)), 2475 getSCEV(U->getOperand(1))); 2476 case Instruction::UDiv: 2477 return getUDivExpr(getSCEV(U->getOperand(0)), 2478 getSCEV(U->getOperand(1))); 2479 case Instruction::Sub: 2480 return getMinusSCEV(getSCEV(U->getOperand(0)), 2481 getSCEV(U->getOperand(1))); 2482 case Instruction::And: 2483 // For an expression like x&255 that merely masks off the high bits, 2484 // use zext(trunc(x)) as the SCEV expression. 2485 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2486 if (CI->isNullValue()) 2487 return getSCEV(U->getOperand(1)); 2488 if (CI->isAllOnesValue()) 2489 return getSCEV(U->getOperand(0)); 2490 const APInt &A = CI->getValue(); 2491 2492 // Instcombine's ShrinkDemandedConstant may strip bits out of 2493 // constants, obscuring what would otherwise be a low-bits mask. 2494 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2495 // knew about to reconstruct a low-bits mask value. 2496 unsigned LZ = A.countLeadingZeros(); 2497 unsigned BitWidth = A.getBitWidth(); 2498 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2499 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2500 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2501 2502 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2503 2504 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2505 return 2506 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2507 IntegerType::get(BitWidth - LZ)), 2508 U->getType()); 2509 } 2510 break; 2511 2512 case Instruction::Or: 2513 // If the RHS of the Or is a constant, we may have something like: 2514 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2515 // optimizations will transparently handle this case. 2516 // 2517 // In order for this transformation to be safe, the LHS must be of the 2518 // form X*(2^n) and the Or constant must be less than 2^n. 2519 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2520 SCEVHandle LHS = getSCEV(U->getOperand(0)); 2521 const APInt &CIVal = CI->getValue(); 2522 if (GetMinTrailingZeros(LHS) >= 2523 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2524 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2525 } 2526 break; 2527 case Instruction::Xor: 2528 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2529 // If the RHS of the xor is a signbit, then this is just an add. 2530 // Instcombine turns add of signbit into xor as a strength reduction step. 2531 if (CI->getValue().isSignBit()) 2532 return getAddExpr(getSCEV(U->getOperand(0)), 2533 getSCEV(U->getOperand(1))); 2534 2535 // If the RHS of xor is -1, then this is a not operation. 2536 if (CI->isAllOnesValue()) 2537 return getNotSCEV(getSCEV(U->getOperand(0))); 2538 2539 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2540 // This is a variant of the check for xor with -1, and it handles 2541 // the case where instcombine has trimmed non-demanded bits out 2542 // of an xor with -1. 2543 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2544 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2545 if (BO->getOpcode() == Instruction::And && 2546 LCI->getValue() == CI->getValue()) 2547 if (const SCEVZeroExtendExpr *Z = 2548 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2549 const Type *UTy = U->getType(); 2550 SCEVHandle Z0 = Z->getOperand(); 2551 const Type *Z0Ty = Z0->getType(); 2552 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2553 2554 // If C is a low-bits mask, the zero extend is zerving to 2555 // mask off the high bits. Complement the operand and 2556 // re-apply the zext. 2557 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2558 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2559 2560 // If C is a single bit, it may be in the sign-bit position 2561 // before the zero-extend. In this case, represent the xor 2562 // using an add, which is equivalent, and re-apply the zext. 2563 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2564 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2565 Trunc.isSignBit()) 2566 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2567 UTy); 2568 } 2569 } 2570 break; 2571 2572 case Instruction::Shl: 2573 // Turn shift left of a constant amount into a multiply. 2574 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2575 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2576 Constant *X = ConstantInt::get( 2577 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2578 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2579 } 2580 break; 2581 2582 case Instruction::LShr: 2583 // Turn logical shift right of a constant into a unsigned divide. 2584 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2585 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2586 Constant *X = ConstantInt::get( 2587 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2588 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2589 } 2590 break; 2591 2592 case Instruction::AShr: 2593 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2594 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2595 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2596 if (L->getOpcode() == Instruction::Shl && 2597 L->getOperand(1) == U->getOperand(1)) { 2598 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2599 uint64_t Amt = BitWidth - CI->getZExtValue(); 2600 if (Amt == BitWidth) 2601 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2602 if (Amt > BitWidth) 2603 return getIntegerSCEV(0, U->getType()); // value is undefined 2604 return 2605 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2606 IntegerType::get(Amt)), 2607 U->getType()); 2608 } 2609 break; 2610 2611 case Instruction::Trunc: 2612 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2613 2614 case Instruction::ZExt: 2615 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2616 2617 case Instruction::SExt: 2618 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2619 2620 case Instruction::BitCast: 2621 // BitCasts are no-op casts so we just eliminate the cast. 2622 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2623 return getSCEV(U->getOperand(0)); 2624 break; 2625 2626 case Instruction::IntToPtr: 2627 if (!TD) break; // Without TD we can't analyze pointers. 2628 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2629 TD->getIntPtrType()); 2630 2631 case Instruction::PtrToInt: 2632 if (!TD) break; // Without TD we can't analyze pointers. 2633 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2634 U->getType()); 2635 2636 case Instruction::GetElementPtr: 2637 if (!TD) break; // Without TD we can't analyze pointers. 2638 return createNodeForGEP(U); 2639 2640 case Instruction::PHI: 2641 return createNodeForPHI(cast<PHINode>(U)); 2642 2643 case Instruction::Select: 2644 // This could be a smax or umax that was lowered earlier. 2645 // Try to recover it. 2646 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2647 Value *LHS = ICI->getOperand(0); 2648 Value *RHS = ICI->getOperand(1); 2649 switch (ICI->getPredicate()) { 2650 case ICmpInst::ICMP_SLT: 2651 case ICmpInst::ICMP_SLE: 2652 std::swap(LHS, RHS); 2653 // fall through 2654 case ICmpInst::ICMP_SGT: 2655 case ICmpInst::ICMP_SGE: 2656 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2657 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2658 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2659 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2660 break; 2661 case ICmpInst::ICMP_ULT: 2662 case ICmpInst::ICMP_ULE: 2663 std::swap(LHS, RHS); 2664 // fall through 2665 case ICmpInst::ICMP_UGT: 2666 case ICmpInst::ICMP_UGE: 2667 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2668 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2669 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2670 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2671 break; 2672 case ICmpInst::ICMP_NE: 2673 // n != 0 ? n : 1 -> umax(n, 1) 2674 if (LHS == U->getOperand(1) && 2675 isa<ConstantInt>(U->getOperand(2)) && 2676 cast<ConstantInt>(U->getOperand(2))->isOne() && 2677 isa<ConstantInt>(RHS) && 2678 cast<ConstantInt>(RHS)->isZero()) 2679 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2680 break; 2681 case ICmpInst::ICMP_EQ: 2682 // n == 0 ? 1 : n -> umax(n, 1) 2683 if (LHS == U->getOperand(2) && 2684 isa<ConstantInt>(U->getOperand(1)) && 2685 cast<ConstantInt>(U->getOperand(1))->isOne() && 2686 isa<ConstantInt>(RHS) && 2687 cast<ConstantInt>(RHS)->isZero()) 2688 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 2689 break; 2690 default: 2691 break; 2692 } 2693 } 2694 2695 default: // We cannot analyze this expression. 2696 break; 2697 } 2698 2699 return getUnknown(V); 2700} 2701 2702 2703 2704//===----------------------------------------------------------------------===// 2705// Iteration Count Computation Code 2706// 2707 2708/// getBackedgeTakenCount - If the specified loop has a predictable 2709/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2710/// object. The backedge-taken count is the number of times the loop header 2711/// will be branched to from within the loop. This is one less than the 2712/// trip count of the loop, since it doesn't count the first iteration, 2713/// when the header is branched to from outside the loop. 2714/// 2715/// Note that it is not valid to call this method on a loop without a 2716/// loop-invariant backedge-taken count (see 2717/// hasLoopInvariantBackedgeTakenCount). 2718/// 2719SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2720 return getBackedgeTakenInfo(L).Exact; 2721} 2722 2723/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2724/// return the least SCEV value that is known never to be less than the 2725/// actual backedge taken count. 2726SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2727 return getBackedgeTakenInfo(L).Max; 2728} 2729 2730const ScalarEvolution::BackedgeTakenInfo & 2731ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2732 // Initially insert a CouldNotCompute for this loop. If the insertion 2733 // succeeds, procede to actually compute a backedge-taken count and 2734 // update the value. The temporary CouldNotCompute value tells SCEV 2735 // code elsewhere that it shouldn't attempt to request a new 2736 // backedge-taken count, which could result in infinite recursion. 2737 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2738 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2739 if (Pair.second) { 2740 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2741 if (ItCount.Exact != CouldNotCompute) { 2742 assert(ItCount.Exact->isLoopInvariant(L) && 2743 ItCount.Max->isLoopInvariant(L) && 2744 "Computed trip count isn't loop invariant for loop!"); 2745 ++NumTripCountsComputed; 2746 2747 // Update the value in the map. 2748 Pair.first->second = ItCount; 2749 } else { 2750 if (ItCount.Max != CouldNotCompute) 2751 // Update the value in the map. 2752 Pair.first->second = ItCount; 2753 if (isa<PHINode>(L->getHeader()->begin())) 2754 // Only count loops that have phi nodes as not being computable. 2755 ++NumTripCountsNotComputed; 2756 } 2757 2758 // Now that we know more about the trip count for this loop, forget any 2759 // existing SCEV values for PHI nodes in this loop since they are only 2760 // conservative estimates made without the benefit 2761 // of trip count information. 2762 if (ItCount.hasAnyInfo()) 2763 forgetLoopPHIs(L); 2764 } 2765 return Pair.first->second; 2766} 2767 2768/// forgetLoopBackedgeTakenCount - This method should be called by the 2769/// client when it has changed a loop in a way that may effect 2770/// ScalarEvolution's ability to compute a trip count, or if the loop 2771/// is deleted. 2772void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2773 BackedgeTakenCounts.erase(L); 2774 forgetLoopPHIs(L); 2775} 2776 2777/// forgetLoopPHIs - Delete the memoized SCEVs associated with the 2778/// PHI nodes in the given loop. This is used when the trip count of 2779/// the loop may have changed. 2780void ScalarEvolution::forgetLoopPHIs(const Loop *L) { 2781 BasicBlock *Header = L->getHeader(); 2782 2783 // Push all Loop-header PHIs onto the Worklist stack, except those 2784 // that are presently represented via a SCEVUnknown. SCEVUnknown for 2785 // a PHI either means that it has an unrecognized structure, or it's 2786 // a PHI that's in the progress of being computed by createNodeForPHI. 2787 // In the former case, additional loop trip count information isn't 2788 // going to change anything. In the later case, createNodeForPHI will 2789 // perform the necessary updates on its own when it gets to that point. 2790 SmallVector<Instruction *, 16> Worklist; 2791 for (BasicBlock::iterator I = Header->begin(); 2792 PHINode *PN = dyn_cast<PHINode>(I); ++I) { 2793 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I); 2794 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second)) 2795 Worklist.push_back(PN); 2796 } 2797 2798 while (!Worklist.empty()) { 2799 Instruction *I = Worklist.pop_back_val(); 2800 if (Scalars.erase(I)) 2801 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2802 UI != UE; ++UI) 2803 Worklist.push_back(cast<Instruction>(UI)); 2804 } 2805} 2806 2807/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2808/// of the specified loop will execute. 2809ScalarEvolution::BackedgeTakenInfo 2810ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2811 SmallVector<BasicBlock*, 8> ExitingBlocks; 2812 L->getExitingBlocks(ExitingBlocks); 2813 2814 // Examine all exits and pick the most conservative values. 2815 SCEVHandle BECount = CouldNotCompute; 2816 SCEVHandle MaxBECount = CouldNotCompute; 2817 bool CouldNotComputeBECount = false; 2818 bool CouldNotComputeMaxBECount = false; 2819 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 2820 BackedgeTakenInfo NewBTI = 2821 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 2822 2823 if (NewBTI.Exact == CouldNotCompute) { 2824 // We couldn't compute an exact value for this exit, so 2825 // we don't be able to compute an exact value for the loop. 2826 CouldNotComputeBECount = true; 2827 BECount = CouldNotCompute; 2828 } else if (!CouldNotComputeBECount) { 2829 if (BECount == CouldNotCompute) 2830 BECount = NewBTI.Exact; 2831 else { 2832 // TODO: More analysis could be done here. For example, a 2833 // loop with a short-circuiting && operator has an exact count 2834 // of the min of both sides. 2835 CouldNotComputeBECount = true; 2836 BECount = CouldNotCompute; 2837 } 2838 } 2839 if (NewBTI.Max == CouldNotCompute) { 2840 // We couldn't compute an maximum value for this exit, so 2841 // we don't be able to compute an maximum value for the loop. 2842 CouldNotComputeMaxBECount = true; 2843 MaxBECount = CouldNotCompute; 2844 } else if (!CouldNotComputeMaxBECount) { 2845 if (MaxBECount == CouldNotCompute) 2846 MaxBECount = NewBTI.Max; 2847 else 2848 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, NewBTI.Max); 2849 } 2850 } 2851 2852 return BackedgeTakenInfo(BECount, MaxBECount); 2853} 2854 2855/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 2856/// of the specified loop will execute if it exits via the specified block. 2857ScalarEvolution::BackedgeTakenInfo 2858ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 2859 BasicBlock *ExitingBlock) { 2860 2861 // Okay, we've chosen an exiting block. See what condition causes us to 2862 // exit at this block. 2863 // 2864 // FIXME: we should be able to handle switch instructions (with a single exit) 2865 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2866 if (ExitBr == 0) return CouldNotCompute; 2867 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2868 2869 // At this point, we know we have a conditional branch that determines whether 2870 // the loop is exited. However, we don't know if the branch is executed each 2871 // time through the loop. If not, then the execution count of the branch will 2872 // not be equal to the trip count of the loop. 2873 // 2874 // Currently we check for this by checking to see if the Exit branch goes to 2875 // the loop header. If so, we know it will always execute the same number of 2876 // times as the loop. We also handle the case where the exit block *is* the 2877 // loop header. This is common for un-rotated loops. 2878 // 2879 // If both of those tests fail, walk up the unique predecessor chain to the 2880 // header, stopping if there is an edge that doesn't exit the loop. If the 2881 // header is reached, the execution count of the branch will be equal to the 2882 // trip count of the loop. 2883 // 2884 // More extensive analysis could be done to handle more cases here. 2885 // 2886 if (ExitBr->getSuccessor(0) != L->getHeader() && 2887 ExitBr->getSuccessor(1) != L->getHeader() && 2888 ExitBr->getParent() != L->getHeader()) { 2889 // The simple checks failed, try climbing the unique predecessor chain 2890 // up to the header. 2891 bool Ok = false; 2892 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 2893 BasicBlock *Pred = BB->getUniquePredecessor(); 2894 if (!Pred) 2895 return CouldNotCompute; 2896 TerminatorInst *PredTerm = Pred->getTerminator(); 2897 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 2898 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 2899 if (PredSucc == BB) 2900 continue; 2901 // If the predecessor has a successor that isn't BB and isn't 2902 // outside the loop, assume the worst. 2903 if (L->contains(PredSucc)) 2904 return CouldNotCompute; 2905 } 2906 if (Pred == L->getHeader()) { 2907 Ok = true; 2908 break; 2909 } 2910 BB = Pred; 2911 } 2912 if (!Ok) 2913 return CouldNotCompute; 2914 } 2915 2916 // Procede to the next level to examine the exit condition expression. 2917 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 2918 ExitBr->getSuccessor(0), 2919 ExitBr->getSuccessor(1)); 2920} 2921 2922/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 2923/// backedge of the specified loop will execute if its exit condition 2924/// were a conditional branch of ExitCond, TBB, and FBB. 2925ScalarEvolution::BackedgeTakenInfo 2926ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 2927 Value *ExitCond, 2928 BasicBlock *TBB, 2929 BasicBlock *FBB) { 2930 // Check if the controlling expression for this loop is an and or or. In 2931 // such cases, an exact backedge-taken count may be infeasible, but a 2932 // maximum count may still be feasible. 2933 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 2934 if (BO->getOpcode() == Instruction::And) { 2935 // Recurse on the operands of the and. 2936 BackedgeTakenInfo BTI0 = 2937 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 2938 BackedgeTakenInfo BTI1 = 2939 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 2940 SCEVHandle BECount = CouldNotCompute; 2941 SCEVHandle MaxBECount = CouldNotCompute; 2942 if (L->contains(TBB)) { 2943 // Both conditions must be true for the loop to continue executing. 2944 // Choose the less conservative count. 2945 // TODO: Take the minimum of the exact counts. 2946 if (BTI0.Exact == BTI1.Exact) 2947 BECount = BTI0.Exact; 2948 // TODO: Take the minimum of the maximum counts. 2949 if (BTI0.Max == CouldNotCompute) 2950 MaxBECount = BTI1.Max; 2951 else if (BTI1.Max == CouldNotCompute) 2952 MaxBECount = BTI0.Max; 2953 else if (const SCEVConstant *C0 = dyn_cast<SCEVConstant>(BTI0.Max)) 2954 if (const SCEVConstant *C1 = dyn_cast<SCEVConstant>(BTI1.Max)) 2955 MaxBECount = getConstant(APIntOps::umin(C0->getValue()->getValue(), 2956 C1->getValue()->getValue())); 2957 } else { 2958 // Both conditions must be true for the loop to exit. 2959 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 2960 if (BTI0.Exact != CouldNotCompute && BTI1.Exact != CouldNotCompute) 2961 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 2962 if (BTI0.Max != CouldNotCompute && BTI1.Max != CouldNotCompute) 2963 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 2964 } 2965 2966 return BackedgeTakenInfo(BECount, MaxBECount); 2967 } 2968 if (BO->getOpcode() == Instruction::Or) { 2969 // Recurse on the operands of the or. 2970 BackedgeTakenInfo BTI0 = 2971 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 2972 BackedgeTakenInfo BTI1 = 2973 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 2974 SCEVHandle BECount = CouldNotCompute; 2975 SCEVHandle MaxBECount = CouldNotCompute; 2976 if (L->contains(FBB)) { 2977 // Both conditions must be false for the loop to continue executing. 2978 // Choose the less conservative count. 2979 // TODO: Take the minimum of the exact counts. 2980 if (BTI0.Exact == BTI1.Exact) 2981 BECount = BTI0.Exact; 2982 // TODO: Take the minimum of the maximum counts. 2983 if (BTI0.Max == CouldNotCompute) 2984 MaxBECount = BTI1.Max; 2985 else if (BTI1.Max == CouldNotCompute) 2986 MaxBECount = BTI0.Max; 2987 else if (const SCEVConstant *C0 = dyn_cast<SCEVConstant>(BTI0.Max)) 2988 if (const SCEVConstant *C1 = dyn_cast<SCEVConstant>(BTI1.Max)) 2989 MaxBECount = getConstant(APIntOps::umin(C0->getValue()->getValue(), 2990 C1->getValue()->getValue())); 2991 } else { 2992 // Both conditions must be false for the loop to exit. 2993 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 2994 if (BTI0.Exact != CouldNotCompute && BTI1.Exact != CouldNotCompute) 2995 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 2996 if (BTI0.Max != CouldNotCompute && BTI1.Max != CouldNotCompute) 2997 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 2998 } 2999 3000 return BackedgeTakenInfo(BECount, MaxBECount); 3001 } 3002 } 3003 3004 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3005 // Procede to the next level to examine the icmp. 3006 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3007 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3008 3009 // If it's not an integer or pointer comparison then compute it the hard way. 3010 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3011} 3012 3013/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3014/// backedge of the specified loop will execute if its exit condition 3015/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3016ScalarEvolution::BackedgeTakenInfo 3017ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3018 ICmpInst *ExitCond, 3019 BasicBlock *TBB, 3020 BasicBlock *FBB) { 3021 3022 // If the condition was exit on true, convert the condition to exit on false 3023 ICmpInst::Predicate Cond; 3024 if (!L->contains(FBB)) 3025 Cond = ExitCond->getPredicate(); 3026 else 3027 Cond = ExitCond->getInversePredicate(); 3028 3029 // Handle common loops like: for (X = "string"; *X; ++X) 3030 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3031 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3032 SCEVHandle ItCnt = 3033 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3034 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3035 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3036 return BackedgeTakenInfo(ItCnt, 3037 isa<SCEVConstant>(ItCnt) ? ItCnt : 3038 getConstant(APInt::getMaxValue(BitWidth)-1)); 3039 } 3040 } 3041 3042 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 3043 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 3044 3045 // Try to evaluate any dependencies out of the loop. 3046 LHS = getSCEVAtScope(LHS, L); 3047 RHS = getSCEVAtScope(RHS, L); 3048 3049 // At this point, we would like to compute how many iterations of the 3050 // loop the predicate will return true for these inputs. 3051 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3052 // If there is a loop-invariant, force it into the RHS. 3053 std::swap(LHS, RHS); 3054 Cond = ICmpInst::getSwappedPredicate(Cond); 3055 } 3056 3057 // If we have a comparison of a chrec against a constant, try to use value 3058 // ranges to answer this query. 3059 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3060 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3061 if (AddRec->getLoop() == L) { 3062 // Form the constant range. 3063 ConstantRange CompRange( 3064 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3065 3066 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3067 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3068 } 3069 3070 switch (Cond) { 3071 case ICmpInst::ICMP_NE: { // while (X != Y) 3072 // Convert to: while (X-Y != 0) 3073 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3074 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3075 break; 3076 } 3077 case ICmpInst::ICMP_EQ: { 3078 // Convert to: while (X-Y == 0) // while (X == Y) 3079 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3080 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3081 break; 3082 } 3083 case ICmpInst::ICMP_SLT: { 3084 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3085 if (BTI.hasAnyInfo()) return BTI; 3086 break; 3087 } 3088 case ICmpInst::ICMP_SGT: { 3089 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3090 getNotSCEV(RHS), L, true); 3091 if (BTI.hasAnyInfo()) return BTI; 3092 break; 3093 } 3094 case ICmpInst::ICMP_ULT: { 3095 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3096 if (BTI.hasAnyInfo()) return BTI; 3097 break; 3098 } 3099 case ICmpInst::ICMP_UGT: { 3100 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3101 getNotSCEV(RHS), L, false); 3102 if (BTI.hasAnyInfo()) return BTI; 3103 break; 3104 } 3105 default: 3106#if 0 3107 errs() << "ComputeBackedgeTakenCount "; 3108 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3109 errs() << "[unsigned] "; 3110 errs() << *LHS << " " 3111 << Instruction::getOpcodeName(Instruction::ICmp) 3112 << " " << *RHS << "\n"; 3113#endif 3114 break; 3115 } 3116 return 3117 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3118} 3119 3120static ConstantInt * 3121EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3122 ScalarEvolution &SE) { 3123 SCEVHandle InVal = SE.getConstant(C); 3124 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 3125 assert(isa<SCEVConstant>(Val) && 3126 "Evaluation of SCEV at constant didn't fold correctly?"); 3127 return cast<SCEVConstant>(Val)->getValue(); 3128} 3129 3130/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3131/// and a GEP expression (missing the pointer index) indexing into it, return 3132/// the addressed element of the initializer or null if the index expression is 3133/// invalid. 3134static Constant * 3135GetAddressedElementFromGlobal(GlobalVariable *GV, 3136 const std::vector<ConstantInt*> &Indices) { 3137 Constant *Init = GV->getInitializer(); 3138 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3139 uint64_t Idx = Indices[i]->getZExtValue(); 3140 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3141 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3142 Init = cast<Constant>(CS->getOperand(Idx)); 3143 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3144 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3145 Init = cast<Constant>(CA->getOperand(Idx)); 3146 } else if (isa<ConstantAggregateZero>(Init)) { 3147 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3148 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3149 Init = Constant::getNullValue(STy->getElementType(Idx)); 3150 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3151 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3152 Init = Constant::getNullValue(ATy->getElementType()); 3153 } else { 3154 assert(0 && "Unknown constant aggregate type!"); 3155 } 3156 return 0; 3157 } else { 3158 return 0; // Unknown initializer type 3159 } 3160 } 3161 return Init; 3162} 3163 3164/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3165/// 'icmp op load X, cst', try to see if we can compute the backedge 3166/// execution count. 3167SCEVHandle ScalarEvolution:: 3168ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 3169 const Loop *L, 3170 ICmpInst::Predicate predicate) { 3171 if (LI->isVolatile()) return CouldNotCompute; 3172 3173 // Check to see if the loaded pointer is a getelementptr of a global. 3174 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3175 if (!GEP) return CouldNotCompute; 3176 3177 // Make sure that it is really a constant global we are gepping, with an 3178 // initializer, and make sure the first IDX is really 0. 3179 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3180 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3181 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3182 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3183 return CouldNotCompute; 3184 3185 // Okay, we allow one non-constant index into the GEP instruction. 3186 Value *VarIdx = 0; 3187 std::vector<ConstantInt*> Indexes; 3188 unsigned VarIdxNum = 0; 3189 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3190 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3191 Indexes.push_back(CI); 3192 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3193 if (VarIdx) return CouldNotCompute; // Multiple non-constant idx's. 3194 VarIdx = GEP->getOperand(i); 3195 VarIdxNum = i-2; 3196 Indexes.push_back(0); 3197 } 3198 3199 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3200 // Check to see if X is a loop variant variable value now. 3201 SCEVHandle Idx = getSCEV(VarIdx); 3202 Idx = getSCEVAtScope(Idx, L); 3203 3204 // We can only recognize very limited forms of loop index expressions, in 3205 // particular, only affine AddRec's like {C1,+,C2}. 3206 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3207 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3208 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3209 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3210 return CouldNotCompute; 3211 3212 unsigned MaxSteps = MaxBruteForceIterations; 3213 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3214 ConstantInt *ItCst = 3215 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3216 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3217 3218 // Form the GEP offset. 3219 Indexes[VarIdxNum] = Val; 3220 3221 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3222 if (Result == 0) break; // Cannot compute! 3223 3224 // Evaluate the condition for this iteration. 3225 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3226 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3227 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3228#if 0 3229 errs() << "\n***\n*** Computed loop count " << *ItCst 3230 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3231 << "***\n"; 3232#endif 3233 ++NumArrayLenItCounts; 3234 return getConstant(ItCst); // Found terminating iteration! 3235 } 3236 } 3237 return CouldNotCompute; 3238} 3239 3240 3241/// CanConstantFold - Return true if we can constant fold an instruction of the 3242/// specified type, assuming that all operands were constants. 3243static bool CanConstantFold(const Instruction *I) { 3244 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3245 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3246 return true; 3247 3248 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3249 if (const Function *F = CI->getCalledFunction()) 3250 return canConstantFoldCallTo(F); 3251 return false; 3252} 3253 3254/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3255/// in the loop that V is derived from. We allow arbitrary operations along the 3256/// way, but the operands of an operation must either be constants or a value 3257/// derived from a constant PHI. If this expression does not fit with these 3258/// constraints, return null. 3259static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3260 // If this is not an instruction, or if this is an instruction outside of the 3261 // loop, it can't be derived from a loop PHI. 3262 Instruction *I = dyn_cast<Instruction>(V); 3263 if (I == 0 || !L->contains(I->getParent())) return 0; 3264 3265 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3266 if (L->getHeader() == I->getParent()) 3267 return PN; 3268 else 3269 // We don't currently keep track of the control flow needed to evaluate 3270 // PHIs, so we cannot handle PHIs inside of loops. 3271 return 0; 3272 } 3273 3274 // If we won't be able to constant fold this expression even if the operands 3275 // are constants, return early. 3276 if (!CanConstantFold(I)) return 0; 3277 3278 // Otherwise, we can evaluate this instruction if all of its operands are 3279 // constant or derived from a PHI node themselves. 3280 PHINode *PHI = 0; 3281 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3282 if (!(isa<Constant>(I->getOperand(Op)) || 3283 isa<GlobalValue>(I->getOperand(Op)))) { 3284 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3285 if (P == 0) return 0; // Not evolving from PHI 3286 if (PHI == 0) 3287 PHI = P; 3288 else if (PHI != P) 3289 return 0; // Evolving from multiple different PHIs. 3290 } 3291 3292 // This is a expression evolving from a constant PHI! 3293 return PHI; 3294} 3295 3296/// EvaluateExpression - Given an expression that passes the 3297/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3298/// in the loop has the value PHIVal. If we can't fold this expression for some 3299/// reason, return null. 3300static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3301 if (isa<PHINode>(V)) return PHIVal; 3302 if (Constant *C = dyn_cast<Constant>(V)) return C; 3303 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3304 Instruction *I = cast<Instruction>(V); 3305 3306 std::vector<Constant*> Operands; 3307 Operands.resize(I->getNumOperands()); 3308 3309 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3310 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3311 if (Operands[i] == 0) return 0; 3312 } 3313 3314 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3315 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3316 &Operands[0], Operands.size()); 3317 else 3318 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3319 &Operands[0], Operands.size()); 3320} 3321 3322/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3323/// in the header of its containing loop, we know the loop executes a 3324/// constant number of times, and the PHI node is just a recurrence 3325/// involving constants, fold it. 3326Constant *ScalarEvolution:: 3327getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 3328 std::map<PHINode*, Constant*>::iterator I = 3329 ConstantEvolutionLoopExitValue.find(PN); 3330 if (I != ConstantEvolutionLoopExitValue.end()) 3331 return I->second; 3332 3333 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3334 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3335 3336 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3337 3338 // Since the loop is canonicalized, the PHI node must have two entries. One 3339 // entry must be a constant (coming in from outside of the loop), and the 3340 // second must be derived from the same PHI. 3341 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3342 Constant *StartCST = 3343 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3344 if (StartCST == 0) 3345 return RetVal = 0; // Must be a constant. 3346 3347 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3348 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3349 if (PN2 != PN) 3350 return RetVal = 0; // Not derived from same PHI. 3351 3352 // Execute the loop symbolically to determine the exit value. 3353 if (BEs.getActiveBits() >= 32) 3354 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3355 3356 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3357 unsigned IterationNum = 0; 3358 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3359 if (IterationNum == NumIterations) 3360 return RetVal = PHIVal; // Got exit value! 3361 3362 // Compute the value of the PHI node for the next iteration. 3363 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3364 if (NextPHI == PHIVal) 3365 return RetVal = NextPHI; // Stopped evolving! 3366 if (NextPHI == 0) 3367 return 0; // Couldn't evaluate! 3368 PHIVal = NextPHI; 3369 } 3370} 3371 3372/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3373/// constant number of times (the condition evolves only from constants), 3374/// try to evaluate a few iterations of the loop until we get the exit 3375/// condition gets a value of ExitWhen (true or false). If we cannot 3376/// evaluate the trip count of the loop, return CouldNotCompute. 3377SCEVHandle ScalarEvolution:: 3378ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 3379 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3380 if (PN == 0) return CouldNotCompute; 3381 3382 // Since the loop is canonicalized, the PHI node must have two entries. One 3383 // entry must be a constant (coming in from outside of the loop), and the 3384 // second must be derived from the same PHI. 3385 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3386 Constant *StartCST = 3387 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3388 if (StartCST == 0) return CouldNotCompute; // Must be a constant. 3389 3390 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3391 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3392 if (PN2 != PN) return CouldNotCompute; // Not derived from same PHI. 3393 3394 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3395 // the loop symbolically to determine when the condition gets a value of 3396 // "ExitWhen". 3397 unsigned IterationNum = 0; 3398 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3399 for (Constant *PHIVal = StartCST; 3400 IterationNum != MaxIterations; ++IterationNum) { 3401 ConstantInt *CondVal = 3402 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3403 3404 // Couldn't symbolically evaluate. 3405 if (!CondVal) return CouldNotCompute; 3406 3407 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3408 ConstantEvolutionLoopExitValue[PN] = PHIVal; 3409 ++NumBruteForceTripCountsComputed; 3410 return getConstant(Type::Int32Ty, IterationNum); 3411 } 3412 3413 // Compute the value of the PHI node for the next iteration. 3414 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3415 if (NextPHI == 0 || NextPHI == PHIVal) 3416 return CouldNotCompute; // Couldn't evaluate or not making progress... 3417 PHIVal = NextPHI; 3418 } 3419 3420 // Too many iterations were needed to evaluate. 3421 return CouldNotCompute; 3422} 3423 3424/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3425/// at the specified scope in the program. The L value specifies a loop 3426/// nest to evaluate the expression at, where null is the top-level or a 3427/// specified loop is immediately inside of the loop. 3428/// 3429/// This method can be used to compute the exit value for a variable defined 3430/// in a loop by querying what the value will hold in the parent loop. 3431/// 3432/// In the case that a relevant loop exit value cannot be computed, the 3433/// original value V is returned. 3434SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3435 // FIXME: this should be turned into a virtual method on SCEV! 3436 3437 if (isa<SCEVConstant>(V)) return V; 3438 3439 // If this instruction is evolved from a constant-evolving PHI, compute the 3440 // exit value from the loop without using SCEVs. 3441 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3442 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3443 const Loop *LI = (*this->LI)[I->getParent()]; 3444 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3445 if (PHINode *PN = dyn_cast<PHINode>(I)) 3446 if (PN->getParent() == LI->getHeader()) { 3447 // Okay, there is no closed form solution for the PHI node. Check 3448 // to see if the loop that contains it has a known backedge-taken 3449 // count. If so, we may be able to force computation of the exit 3450 // value. 3451 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 3452 if (const SCEVConstant *BTCC = 3453 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3454 // Okay, we know how many times the containing loop executes. If 3455 // this is a constant evolving PHI node, get the final value at 3456 // the specified iteration number. 3457 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3458 BTCC->getValue()->getValue(), 3459 LI); 3460 if (RV) return getUnknown(RV); 3461 } 3462 } 3463 3464 // Okay, this is an expression that we cannot symbolically evaluate 3465 // into a SCEV. Check to see if it's possible to symbolically evaluate 3466 // the arguments into constants, and if so, try to constant propagate the 3467 // result. This is particularly useful for computing loop exit values. 3468 if (CanConstantFold(I)) { 3469 // Check to see if we've folded this instruction at this loop before. 3470 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3471 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3472 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3473 if (!Pair.second) 3474 return Pair.first->second ? &*getUnknown(Pair.first->second) : V; 3475 3476 std::vector<Constant*> Operands; 3477 Operands.reserve(I->getNumOperands()); 3478 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3479 Value *Op = I->getOperand(i); 3480 if (Constant *C = dyn_cast<Constant>(Op)) { 3481 Operands.push_back(C); 3482 } else { 3483 // If any of the operands is non-constant and if they are 3484 // non-integer and non-pointer, don't even try to analyze them 3485 // with scev techniques. 3486 if (!isSCEVable(Op->getType())) 3487 return V; 3488 3489 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 3490 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3491 Constant *C = SC->getValue(); 3492 if (C->getType() != Op->getType()) 3493 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3494 Op->getType(), 3495 false), 3496 C, Op->getType()); 3497 Operands.push_back(C); 3498 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3499 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3500 if (C->getType() != Op->getType()) 3501 C = 3502 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3503 Op->getType(), 3504 false), 3505 C, Op->getType()); 3506 Operands.push_back(C); 3507 } else 3508 return V; 3509 } else { 3510 return V; 3511 } 3512 } 3513 } 3514 3515 Constant *C; 3516 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3517 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3518 &Operands[0], Operands.size()); 3519 else 3520 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3521 &Operands[0], Operands.size()); 3522 Pair.first->second = C; 3523 return getUnknown(C); 3524 } 3525 } 3526 3527 // This is some other type of SCEVUnknown, just return it. 3528 return V; 3529 } 3530 3531 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3532 // Avoid performing the look-up in the common case where the specified 3533 // expression has no loop-variant portions. 3534 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3535 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3536 if (OpAtScope != Comm->getOperand(i)) { 3537 // Okay, at least one of these operands is loop variant but might be 3538 // foldable. Build a new instance of the folded commutative expression. 3539 SmallVector<SCEVHandle, 8> NewOps(Comm->op_begin(), Comm->op_begin()+i); 3540 NewOps.push_back(OpAtScope); 3541 3542 for (++i; i != e; ++i) { 3543 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3544 NewOps.push_back(OpAtScope); 3545 } 3546 if (isa<SCEVAddExpr>(Comm)) 3547 return getAddExpr(NewOps); 3548 if (isa<SCEVMulExpr>(Comm)) 3549 return getMulExpr(NewOps); 3550 if (isa<SCEVSMaxExpr>(Comm)) 3551 return getSMaxExpr(NewOps); 3552 if (isa<SCEVUMaxExpr>(Comm)) 3553 return getUMaxExpr(NewOps); 3554 assert(0 && "Unknown commutative SCEV type!"); 3555 } 3556 } 3557 // If we got here, all operands are loop invariant. 3558 return Comm; 3559 } 3560 3561 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3562 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 3563 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 3564 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3565 return Div; // must be loop invariant 3566 return getUDivExpr(LHS, RHS); 3567 } 3568 3569 // If this is a loop recurrence for a loop that does not contain L, then we 3570 // are dealing with the final value computed by the loop. 3571 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3572 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3573 // To evaluate this recurrence, we need to know how many times the AddRec 3574 // loop iterates. Compute this now. 3575 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3576 if (BackedgeTakenCount == CouldNotCompute) return AddRec; 3577 3578 // Then, evaluate the AddRec. 3579 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3580 } 3581 return AddRec; 3582 } 3583 3584 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3585 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 3586 if (Op == Cast->getOperand()) 3587 return Cast; // must be loop invariant 3588 return getZeroExtendExpr(Op, Cast->getType()); 3589 } 3590 3591 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3592 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 3593 if (Op == Cast->getOperand()) 3594 return Cast; // must be loop invariant 3595 return getSignExtendExpr(Op, Cast->getType()); 3596 } 3597 3598 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3599 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 3600 if (Op == Cast->getOperand()) 3601 return Cast; // must be loop invariant 3602 return getTruncateExpr(Op, Cast->getType()); 3603 } 3604 3605 assert(0 && "Unknown SCEV type!"); 3606 return 0; 3607} 3608 3609/// getSCEVAtScope - This is a convenience function which does 3610/// getSCEVAtScope(getSCEV(V), L). 3611SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3612 return getSCEVAtScope(getSCEV(V), L); 3613} 3614 3615/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3616/// following equation: 3617/// 3618/// A * X = B (mod N) 3619/// 3620/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3621/// A and B isn't important. 3622/// 3623/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3624static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3625 ScalarEvolution &SE) { 3626 uint32_t BW = A.getBitWidth(); 3627 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3628 assert(A != 0 && "A must be non-zero."); 3629 3630 // 1. D = gcd(A, N) 3631 // 3632 // The gcd of A and N may have only one prime factor: 2. The number of 3633 // trailing zeros in A is its multiplicity 3634 uint32_t Mult2 = A.countTrailingZeros(); 3635 // D = 2^Mult2 3636 3637 // 2. Check if B is divisible by D. 3638 // 3639 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3640 // is not less than multiplicity of this prime factor for D. 3641 if (B.countTrailingZeros() < Mult2) 3642 return SE.getCouldNotCompute(); 3643 3644 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3645 // modulo (N / D). 3646 // 3647 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3648 // bit width during computations. 3649 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3650 APInt Mod(BW + 1, 0); 3651 Mod.set(BW - Mult2); // Mod = N / D 3652 APInt I = AD.multiplicativeInverse(Mod); 3653 3654 // 4. Compute the minimum unsigned root of the equation: 3655 // I * (B / D) mod (N / D) 3656 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 3657 3658 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 3659 // bits. 3660 return SE.getConstant(Result.trunc(BW)); 3661} 3662 3663/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 3664/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 3665/// might be the same) or two SCEVCouldNotCompute objects. 3666/// 3667static std::pair<SCEVHandle,SCEVHandle> 3668SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 3669 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 3670 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 3671 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 3672 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 3673 3674 // We currently can only solve this if the coefficients are constants. 3675 if (!LC || !MC || !NC) { 3676 const SCEV *CNC = SE.getCouldNotCompute(); 3677 return std::make_pair(CNC, CNC); 3678 } 3679 3680 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 3681 const APInt &L = LC->getValue()->getValue(); 3682 const APInt &M = MC->getValue()->getValue(); 3683 const APInt &N = NC->getValue()->getValue(); 3684 APInt Two(BitWidth, 2); 3685 APInt Four(BitWidth, 4); 3686 3687 { 3688 using namespace APIntOps; 3689 const APInt& C = L; 3690 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 3691 // The B coefficient is M-N/2 3692 APInt B(M); 3693 B -= sdiv(N,Two); 3694 3695 // The A coefficient is N/2 3696 APInt A(N.sdiv(Two)); 3697 3698 // Compute the B^2-4ac term. 3699 APInt SqrtTerm(B); 3700 SqrtTerm *= B; 3701 SqrtTerm -= Four * (A * C); 3702 3703 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 3704 // integer value or else APInt::sqrt() will assert. 3705 APInt SqrtVal(SqrtTerm.sqrt()); 3706 3707 // Compute the two solutions for the quadratic formula. 3708 // The divisions must be performed as signed divisions. 3709 APInt NegB(-B); 3710 APInt TwoA( A << 1 ); 3711 if (TwoA.isMinValue()) { 3712 const SCEV *CNC = SE.getCouldNotCompute(); 3713 return std::make_pair(CNC, CNC); 3714 } 3715 3716 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 3717 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 3718 3719 return std::make_pair(SE.getConstant(Solution1), 3720 SE.getConstant(Solution2)); 3721 } // end APIntOps namespace 3722} 3723 3724/// HowFarToZero - Return the number of times a backedge comparing the specified 3725/// value to zero will execute. If not computable, return CouldNotCompute. 3726SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 3727 // If the value is a constant 3728 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3729 // If the value is already zero, the branch will execute zero times. 3730 if (C->getValue()->isZero()) return C; 3731 return CouldNotCompute; // Otherwise it will loop infinitely. 3732 } 3733 3734 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 3735 if (!AddRec || AddRec->getLoop() != L) 3736 return CouldNotCompute; 3737 3738 if (AddRec->isAffine()) { 3739 // If this is an affine expression, the execution count of this branch is 3740 // the minimum unsigned root of the following equation: 3741 // 3742 // Start + Step*N = 0 (mod 2^BW) 3743 // 3744 // equivalent to: 3745 // 3746 // Step*N = -Start (mod 2^BW) 3747 // 3748 // where BW is the common bit width of Start and Step. 3749 3750 // Get the initial value for the loop. 3751 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 3752 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 3753 3754 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 3755 // For now we handle only constant steps. 3756 3757 // First, handle unitary steps. 3758 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 3759 return getNegativeSCEV(Start); // N = -Start (as unsigned) 3760 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 3761 return Start; // N = Start (as unsigned) 3762 3763 // Then, try to solve the above equation provided that Start is constant. 3764 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 3765 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 3766 -StartC->getValue()->getValue(), 3767 *this); 3768 } 3769 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 3770 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 3771 // the quadratic equation to solve it. 3772 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 3773 *this); 3774 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3775 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3776 if (R1) { 3777#if 0 3778 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 3779 << " sol#2: " << *R2 << "\n"; 3780#endif 3781 // Pick the smallest positive root value. 3782 if (ConstantInt *CB = 3783 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3784 R1->getValue(), R2->getValue()))) { 3785 if (CB->getZExtValue() == false) 3786 std::swap(R1, R2); // R1 is the minimum root now. 3787 3788 // We can only use this value if the chrec ends up with an exact zero 3789 // value at this index. When solving for "X*X != 5", for example, we 3790 // should not accept a root of 2. 3791 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 3792 if (Val->isZero()) 3793 return R1; // We found a quadratic root! 3794 } 3795 } 3796 } 3797 3798 return CouldNotCompute; 3799} 3800 3801/// HowFarToNonZero - Return the number of times a backedge checking the 3802/// specified value for nonzero will execute. If not computable, return 3803/// CouldNotCompute 3804SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 3805 // Loops that look like: while (X == 0) are very strange indeed. We don't 3806 // handle them yet except for the trivial case. This could be expanded in the 3807 // future as needed. 3808 3809 // If the value is a constant, check to see if it is known to be non-zero 3810 // already. If so, the backedge will execute zero times. 3811 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3812 if (!C->getValue()->isNullValue()) 3813 return getIntegerSCEV(0, C->getType()); 3814 return CouldNotCompute; // Otherwise it will loop infinitely. 3815 } 3816 3817 // We could implement others, but I really doubt anyone writes loops like 3818 // this, and if they did, they would already be constant folded. 3819 return CouldNotCompute; 3820} 3821 3822/// getLoopPredecessor - If the given loop's header has exactly one unique 3823/// predecessor outside the loop, return it. Otherwise return null. 3824/// 3825BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 3826 BasicBlock *Header = L->getHeader(); 3827 BasicBlock *Pred = 0; 3828 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 3829 PI != E; ++PI) 3830 if (!L->contains(*PI)) { 3831 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 3832 Pred = *PI; 3833 } 3834 return Pred; 3835} 3836 3837/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 3838/// (which may not be an immediate predecessor) which has exactly one 3839/// successor from which BB is reachable, or null if no such block is 3840/// found. 3841/// 3842BasicBlock * 3843ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 3844 // If the block has a unique predecessor, then there is no path from the 3845 // predecessor to the block that does not go through the direct edge 3846 // from the predecessor to the block. 3847 if (BasicBlock *Pred = BB->getSinglePredecessor()) 3848 return Pred; 3849 3850 // A loop's header is defined to be a block that dominates the loop. 3851 // If the header has a unique predecessor outside the loop, it must be 3852 // a block that has exactly one successor that can reach the loop. 3853 if (Loop *L = LI->getLoopFor(BB)) 3854 return getLoopPredecessor(L); 3855 3856 return 0; 3857} 3858 3859/// HasSameValue - SCEV structural equivalence is usually sufficient for 3860/// testing whether two expressions are equal, however for the purposes of 3861/// looking for a condition guarding a loop, it can be useful to be a little 3862/// more general, since a front-end may have replicated the controlling 3863/// expression. 3864/// 3865static bool HasSameValue(const SCEVHandle &A, const SCEVHandle &B) { 3866 // Quick check to see if they are the same SCEV. 3867 if (A == B) return true; 3868 3869 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 3870 // two different instructions with the same value. Check for this case. 3871 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 3872 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 3873 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 3874 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 3875 if (AI->isIdenticalTo(BI)) 3876 return true; 3877 3878 // Otherwise assume they may have a different value. 3879 return false; 3880} 3881 3882/// isLoopGuardedByCond - Test whether entry to the loop is protected by 3883/// a conditional between LHS and RHS. This is used to help avoid max 3884/// expressions in loop trip counts. 3885bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 3886 ICmpInst::Predicate Pred, 3887 const SCEV *LHS, const SCEV *RHS) { 3888 // Interpret a null as meaning no loop, where there is obviously no guard 3889 // (interprocedural conditions notwithstanding). 3890 if (!L) return false; 3891 3892 BasicBlock *Predecessor = getLoopPredecessor(L); 3893 BasicBlock *PredecessorDest = L->getHeader(); 3894 3895 // Starting at the loop predecessor, climb up the predecessor chain, as long 3896 // as there are predecessors that can be found that have unique successors 3897 // leading to the original header. 3898 for (; Predecessor; 3899 PredecessorDest = Predecessor, 3900 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 3901 3902 BranchInst *LoopEntryPredicate = 3903 dyn_cast<BranchInst>(Predecessor->getTerminator()); 3904 if (!LoopEntryPredicate || 3905 LoopEntryPredicate->isUnconditional()) 3906 continue; 3907 3908 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 3909 if (!ICI) continue; 3910 3911 // Now that we found a conditional branch that dominates the loop, check to 3912 // see if it is the comparison we are looking for. 3913 Value *PreCondLHS = ICI->getOperand(0); 3914 Value *PreCondRHS = ICI->getOperand(1); 3915 ICmpInst::Predicate Cond; 3916 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest) 3917 Cond = ICI->getPredicate(); 3918 else 3919 Cond = ICI->getInversePredicate(); 3920 3921 if (Cond == Pred) 3922 ; // An exact match. 3923 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 3924 ; // The actual condition is beyond sufficient. 3925 else 3926 // Check a few special cases. 3927 switch (Cond) { 3928 case ICmpInst::ICMP_UGT: 3929 if (Pred == ICmpInst::ICMP_ULT) { 3930 std::swap(PreCondLHS, PreCondRHS); 3931 Cond = ICmpInst::ICMP_ULT; 3932 break; 3933 } 3934 continue; 3935 case ICmpInst::ICMP_SGT: 3936 if (Pred == ICmpInst::ICMP_SLT) { 3937 std::swap(PreCondLHS, PreCondRHS); 3938 Cond = ICmpInst::ICMP_SLT; 3939 break; 3940 } 3941 continue; 3942 case ICmpInst::ICMP_NE: 3943 // Expressions like (x >u 0) are often canonicalized to (x != 0), 3944 // so check for this case by checking if the NE is comparing against 3945 // a minimum or maximum constant. 3946 if (!ICmpInst::isTrueWhenEqual(Pred)) 3947 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 3948 const APInt &A = CI->getValue(); 3949 switch (Pred) { 3950 case ICmpInst::ICMP_SLT: 3951 if (A.isMaxSignedValue()) break; 3952 continue; 3953 case ICmpInst::ICMP_SGT: 3954 if (A.isMinSignedValue()) break; 3955 continue; 3956 case ICmpInst::ICMP_ULT: 3957 if (A.isMaxValue()) break; 3958 continue; 3959 case ICmpInst::ICMP_UGT: 3960 if (A.isMinValue()) break; 3961 continue; 3962 default: 3963 continue; 3964 } 3965 Cond = ICmpInst::ICMP_NE; 3966 // NE is symmetric but the original comparison may not be. Swap 3967 // the operands if necessary so that they match below. 3968 if (isa<SCEVConstant>(LHS)) 3969 std::swap(PreCondLHS, PreCondRHS); 3970 break; 3971 } 3972 continue; 3973 default: 3974 // We weren't able to reconcile the condition. 3975 continue; 3976 } 3977 3978 if (!PreCondLHS->getType()->isInteger()) continue; 3979 3980 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 3981 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 3982 if ((HasSameValue(LHS, PreCondLHSSCEV) && 3983 HasSameValue(RHS, PreCondRHSSCEV)) || 3984 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) && 3985 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV)))) 3986 return true; 3987 } 3988 3989 return false; 3990} 3991 3992/// getBECount - Subtract the end and start values and divide by the step, 3993/// rounding up, to get the number of times the backedge is executed. Return 3994/// CouldNotCompute if an intermediate computation overflows. 3995SCEVHandle ScalarEvolution::getBECount(const SCEVHandle &Start, 3996 const SCEVHandle &End, 3997 const SCEVHandle &Step) { 3998 const Type *Ty = Start->getType(); 3999 SCEVHandle NegOne = getIntegerSCEV(-1, Ty); 4000 SCEVHandle Diff = getMinusSCEV(End, Start); 4001 SCEVHandle RoundUp = getAddExpr(Step, NegOne); 4002 4003 // Add an adjustment to the difference between End and Start so that 4004 // the division will effectively round up. 4005 SCEVHandle Add = getAddExpr(Diff, RoundUp); 4006 4007 // Check Add for unsigned overflow. 4008 // TODO: More sophisticated things could be done here. 4009 const Type *WideTy = IntegerType::get(getTypeSizeInBits(Ty) + 1); 4010 SCEVHandle OperandExtendedAdd = 4011 getAddExpr(getZeroExtendExpr(Diff, WideTy), 4012 getZeroExtendExpr(RoundUp, WideTy)); 4013 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4014 return CouldNotCompute; 4015 4016 return getUDivExpr(Add, Step); 4017} 4018 4019/// HowManyLessThans - Return the number of times a backedge containing the 4020/// specified less-than comparison will execute. If not computable, return 4021/// CouldNotCompute. 4022ScalarEvolution::BackedgeTakenInfo ScalarEvolution:: 4023HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4024 const Loop *L, bool isSigned) { 4025 // Only handle: "ADDREC < LoopInvariant". 4026 if (!RHS->isLoopInvariant(L)) return CouldNotCompute; 4027 4028 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4029 if (!AddRec || AddRec->getLoop() != L) 4030 return CouldNotCompute; 4031 4032 if (AddRec->isAffine()) { 4033 // FORNOW: We only support unit strides. 4034 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4035 SCEVHandle Step = AddRec->getStepRecurrence(*this); 4036 4037 // TODO: handle non-constant strides. 4038 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4039 if (!CStep || CStep->isZero()) 4040 return CouldNotCompute; 4041 if (CStep->isOne()) { 4042 // With unit stride, the iteration never steps past the limit value. 4043 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4044 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4045 // Test whether a positive iteration iteration can step past the limit 4046 // value and past the maximum value for its type in a single step. 4047 if (isSigned) { 4048 APInt Max = APInt::getSignedMaxValue(BitWidth); 4049 if ((Max - CStep->getValue()->getValue()) 4050 .slt(CLimit->getValue()->getValue())) 4051 return CouldNotCompute; 4052 } else { 4053 APInt Max = APInt::getMaxValue(BitWidth); 4054 if ((Max - CStep->getValue()->getValue()) 4055 .ult(CLimit->getValue()->getValue())) 4056 return CouldNotCompute; 4057 } 4058 } else 4059 // TODO: handle non-constant limit values below. 4060 return CouldNotCompute; 4061 } else 4062 // TODO: handle negative strides below. 4063 return CouldNotCompute; 4064 4065 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4066 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4067 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4068 // treat m-n as signed nor unsigned due to overflow possibility. 4069 4070 // First, we get the value of the LHS in the first iteration: n 4071 SCEVHandle Start = AddRec->getOperand(0); 4072 4073 // Determine the minimum constant start value. 4074 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start : 4075 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 4076 APInt::getMinValue(BitWidth)); 4077 4078 // If we know that the condition is true in order to enter the loop, 4079 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4080 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4081 // the division must round up. 4082 SCEVHandle End = RHS; 4083 if (!isLoopGuardedByCond(L, 4084 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 4085 getMinusSCEV(Start, Step), RHS)) 4086 End = isSigned ? getSMaxExpr(RHS, Start) 4087 : getUMaxExpr(RHS, Start); 4088 4089 // Determine the maximum constant end value. 4090 SCEVHandle MaxEnd = 4091 isa<SCEVConstant>(End) ? End : 4092 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) 4093 .ashr(GetMinSignBits(End) - 1) : 4094 APInt::getMaxValue(BitWidth) 4095 .lshr(GetMinLeadingZeros(End))); 4096 4097 // Finally, we subtract these two values and divide, rounding up, to get 4098 // the number of times the backedge is executed. 4099 SCEVHandle BECount = getBECount(Start, End, Step); 4100 4101 // The maximum backedge count is similar, except using the minimum start 4102 // value and the maximum end value. 4103 SCEVHandle MaxBECount = getBECount(MinStart, MaxEnd, Step);; 4104 4105 return BackedgeTakenInfo(BECount, MaxBECount); 4106 } 4107 4108 return CouldNotCompute; 4109} 4110 4111/// getNumIterationsInRange - Return the number of iterations of this loop that 4112/// produce values in the specified constant range. Another way of looking at 4113/// this is that it returns the first iteration number where the value is not in 4114/// the condition, thus computing the exit count. If the iteration count can't 4115/// be computed, an instance of SCEVCouldNotCompute is returned. 4116SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4117 ScalarEvolution &SE) const { 4118 if (Range.isFullSet()) // Infinite loop. 4119 return SE.getCouldNotCompute(); 4120 4121 // If the start is a non-zero constant, shift the range to simplify things. 4122 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4123 if (!SC->getValue()->isZero()) { 4124 SmallVector<SCEVHandle, 4> Operands(op_begin(), op_end()); 4125 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4126 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 4127 if (const SCEVAddRecExpr *ShiftedAddRec = 4128 dyn_cast<SCEVAddRecExpr>(Shifted)) 4129 return ShiftedAddRec->getNumIterationsInRange( 4130 Range.subtract(SC->getValue()->getValue()), SE); 4131 // This is strange and shouldn't happen. 4132 return SE.getCouldNotCompute(); 4133 } 4134 4135 // The only time we can solve this is when we have all constant indices. 4136 // Otherwise, we cannot determine the overflow conditions. 4137 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4138 if (!isa<SCEVConstant>(getOperand(i))) 4139 return SE.getCouldNotCompute(); 4140 4141 4142 // Okay at this point we know that all elements of the chrec are constants and 4143 // that the start element is zero. 4144 4145 // First check to see if the range contains zero. If not, the first 4146 // iteration exits. 4147 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4148 if (!Range.contains(APInt(BitWidth, 0))) 4149 return SE.getIntegerSCEV(0, getType()); 4150 4151 if (isAffine()) { 4152 // If this is an affine expression then we have this situation: 4153 // Solve {0,+,A} in Range === Ax in Range 4154 4155 // We know that zero is in the range. If A is positive then we know that 4156 // the upper value of the range must be the first possible exit value. 4157 // If A is negative then the lower of the range is the last possible loop 4158 // value. Also note that we already checked for a full range. 4159 APInt One(BitWidth,1); 4160 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4161 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4162 4163 // The exit value should be (End+A)/A. 4164 APInt ExitVal = (End + A).udiv(A); 4165 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 4166 4167 // Evaluate at the exit value. If we really did fall out of the valid 4168 // range, then we computed our trip count, otherwise wrap around or other 4169 // things must have happened. 4170 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4171 if (Range.contains(Val->getValue())) 4172 return SE.getCouldNotCompute(); // Something strange happened 4173 4174 // Ensure that the previous value is in the range. This is a sanity check. 4175 assert(Range.contains( 4176 EvaluateConstantChrecAtConstant(this, 4177 ConstantInt::get(ExitVal - One), SE)->getValue()) && 4178 "Linear scev computation is off in a bad way!"); 4179 return SE.getConstant(ExitValue); 4180 } else if (isQuadratic()) { 4181 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4182 // quadratic equation to solve it. To do this, we must frame our problem in 4183 // terms of figuring out when zero is crossed, instead of when 4184 // Range.getUpper() is crossed. 4185 SmallVector<SCEVHandle, 4> NewOps(op_begin(), op_end()); 4186 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4187 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4188 4189 // Next, solve the constructed addrec 4190 std::pair<SCEVHandle,SCEVHandle> Roots = 4191 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4192 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4193 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4194 if (R1) { 4195 // Pick the smallest positive root value. 4196 if (ConstantInt *CB = 4197 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4198 R1->getValue(), R2->getValue()))) { 4199 if (CB->getZExtValue() == false) 4200 std::swap(R1, R2); // R1 is the minimum root now. 4201 4202 // Make sure the root is not off by one. The returned iteration should 4203 // not be in the range, but the previous one should be. When solving 4204 // for "X*X < 5", for example, we should not return a root of 2. 4205 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4206 R1->getValue(), 4207 SE); 4208 if (Range.contains(R1Val->getValue())) { 4209 // The next iteration must be out of the range... 4210 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 4211 4212 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4213 if (!Range.contains(R1Val->getValue())) 4214 return SE.getConstant(NextVal); 4215 return SE.getCouldNotCompute(); // Something strange happened 4216 } 4217 4218 // If R1 was not in the range, then it is a good return value. Make 4219 // sure that R1-1 WAS in the range though, just in case. 4220 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 4221 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4222 if (Range.contains(R1Val->getValue())) 4223 return R1; 4224 return SE.getCouldNotCompute(); // Something strange happened 4225 } 4226 } 4227 } 4228 4229 return SE.getCouldNotCompute(); 4230} 4231 4232 4233 4234//===----------------------------------------------------------------------===// 4235// SCEVCallbackVH Class Implementation 4236//===----------------------------------------------------------------------===// 4237 4238void ScalarEvolution::SCEVCallbackVH::deleted() { 4239 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4240 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4241 SE->ConstantEvolutionLoopExitValue.erase(PN); 4242 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4243 SE->ValuesAtScopes.erase(I); 4244 SE->Scalars.erase(getValPtr()); 4245 // this now dangles! 4246} 4247 4248void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4249 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4250 4251 // Forget all the expressions associated with users of the old value, 4252 // so that future queries will recompute the expressions using the new 4253 // value. 4254 SmallVector<User *, 16> Worklist; 4255 Value *Old = getValPtr(); 4256 bool DeleteOld = false; 4257 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4258 UI != UE; ++UI) 4259 Worklist.push_back(*UI); 4260 while (!Worklist.empty()) { 4261 User *U = Worklist.pop_back_val(); 4262 // Deleting the Old value will cause this to dangle. Postpone 4263 // that until everything else is done. 4264 if (U == Old) { 4265 DeleteOld = true; 4266 continue; 4267 } 4268 if (PHINode *PN = dyn_cast<PHINode>(U)) 4269 SE->ConstantEvolutionLoopExitValue.erase(PN); 4270 if (Instruction *I = dyn_cast<Instruction>(U)) 4271 SE->ValuesAtScopes.erase(I); 4272 if (SE->Scalars.erase(U)) 4273 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4274 UI != UE; ++UI) 4275 Worklist.push_back(*UI); 4276 } 4277 if (DeleteOld) { 4278 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4279 SE->ConstantEvolutionLoopExitValue.erase(PN); 4280 if (Instruction *I = dyn_cast<Instruction>(Old)) 4281 SE->ValuesAtScopes.erase(I); 4282 SE->Scalars.erase(Old); 4283 // this now dangles! 4284 } 4285 // this may dangle! 4286} 4287 4288ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4289 : CallbackVH(V), SE(se) {} 4290 4291//===----------------------------------------------------------------------===// 4292// ScalarEvolution Class Implementation 4293//===----------------------------------------------------------------------===// 4294 4295ScalarEvolution::ScalarEvolution() 4296 : FunctionPass(&ID), CouldNotCompute(new SCEVCouldNotCompute(0)) { 4297} 4298 4299bool ScalarEvolution::runOnFunction(Function &F) { 4300 this->F = &F; 4301 LI = &getAnalysis<LoopInfo>(); 4302 TD = getAnalysisIfAvailable<TargetData>(); 4303 return false; 4304} 4305 4306void ScalarEvolution::releaseMemory() { 4307 Scalars.clear(); 4308 BackedgeTakenCounts.clear(); 4309 ConstantEvolutionLoopExitValue.clear(); 4310 ValuesAtScopes.clear(); 4311} 4312 4313void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4314 AU.setPreservesAll(); 4315 AU.addRequiredTransitive<LoopInfo>(); 4316} 4317 4318bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4319 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4320} 4321 4322static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4323 const Loop *L) { 4324 // Print all inner loops first 4325 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4326 PrintLoopInfo(OS, SE, *I); 4327 4328 OS << "Loop " << L->getHeader()->getName() << ": "; 4329 4330 SmallVector<BasicBlock*, 8> ExitBlocks; 4331 L->getExitBlocks(ExitBlocks); 4332 if (ExitBlocks.size() != 1) 4333 OS << "<multiple exits> "; 4334 4335 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4336 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4337 } else { 4338 OS << "Unpredictable backedge-taken count. "; 4339 } 4340 4341 OS << "\n"; 4342} 4343 4344void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4345 // ScalarEvolution's implementaiton of the print method is to print 4346 // out SCEV values of all instructions that are interesting. Doing 4347 // this potentially causes it to create new SCEV objects though, 4348 // which technically conflicts with the const qualifier. This isn't 4349 // observable from outside the class though (the hasSCEV function 4350 // notwithstanding), so casting away the const isn't dangerous. 4351 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4352 4353 OS << "Classifying expressions for: " << F->getName() << "\n"; 4354 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4355 if (isSCEVable(I->getType())) { 4356 OS << *I; 4357 OS << " --> "; 4358 SCEVHandle SV = SE.getSCEV(&*I); 4359 SV->print(OS); 4360 4361 const Loop *L = LI->getLoopFor((*I).getParent()); 4362 4363 SCEVHandle AtUse = SE.getSCEVAtScope(SV, L); 4364 if (AtUse != SV) { 4365 OS << " --> "; 4366 AtUse->print(OS); 4367 } 4368 4369 if (L) { 4370 OS << "\t\t" "Exits: "; 4371 SCEVHandle ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4372 if (!ExitValue->isLoopInvariant(L)) { 4373 OS << "<<Unknown>>"; 4374 } else { 4375 OS << *ExitValue; 4376 } 4377 } 4378 4379 OS << "\n"; 4380 } 4381 4382 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 4383 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 4384 PrintLoopInfo(OS, &SE, *I); 4385} 4386 4387void ScalarEvolution::print(std::ostream &o, const Module *M) const { 4388 raw_os_ostream OS(o); 4389 print(OS, M); 4390} 4391