ScalarEvolution.cpp revision 4ee451de366474b9c228b4e5fa573795a715216d
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/LoopInfo.h" 70#include "llvm/Assembly/Writer.h" 71#include "llvm/Transforms/Scalar.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/InstIterator.h" 77#include "llvm/Support/ManagedStatic.h" 78#include "llvm/Support/MathExtras.h" 79#include "llvm/Support/Streams.h" 80#include "llvm/ADT/Statistic.h" 81#include <ostream> 82#include <algorithm> 83#include <cmath> 84using namespace llvm; 85 86STATISTIC(NumBruteForceEvaluations, 87 "Number of brute force evaluations needed to " 88 "calculate high-order polynomial exit values"); 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant derived loop"), 102 cl::init(100)); 103 104namespace { 105 RegisterPass<ScalarEvolution> 106 R("scalar-evolution", "Scalar Evolution Analysis"); 107} 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117SCEV::~SCEV() {} 118void SCEV::dump() const { 119 print(cerr); 120} 121 122/// getValueRange - Return the tightest constant bounds that this value is 123/// known to have. This method is only valid on integer SCEV objects. 124ConstantRange SCEV::getValueRange() const { 125 const Type *Ty = getType(); 126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 127 // Default to a full range if no better information is available. 128 return ConstantRange(getBitWidth()); 129} 130 131uint32_t SCEV::getBitWidth() const { 132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 133 return ITy->getBitWidth(); 134 return 0; 135} 136 137 138SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 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(std::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); 184 return R; 185} 186 187SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 188 return getConstant(ConstantInt::get(Val)); 189} 190 191ConstantRange SCEVConstant::getValueRange() const { 192 return ConstantRange(V->getValue()); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(std::ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 202// particular input. Don't use a SCEVHandle here, or else the object will 203// never be deleted! 204static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 205 SCEVTruncateExpr*> > SCEVTruncates; 206 207SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 208 : SCEV(scTruncate), Op(op), Ty(ty) { 209 assert(Op->getType()->isInteger() && Ty->isInteger() && 210 "Cannot truncate non-integer value!"); 211 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 212 && "This is not a truncating conversion!"); 213} 214 215SCEVTruncateExpr::~SCEVTruncateExpr() { 216 SCEVTruncates->erase(std::make_pair(Op, Ty)); 217} 218 219ConstantRange SCEVTruncateExpr::getValueRange() const { 220 return getOperand()->getValueRange().truncate(getBitWidth()); 221} 222 223void SCEVTruncateExpr::print(std::ostream &OS) const { 224 OS << "(truncate " << *Op << " to " << *Ty << ")"; 225} 226 227// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 228// particular input. Don't use a SCEVHandle here, or else the object will never 229// be deleted! 230static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 231 SCEVZeroExtendExpr*> > SCEVZeroExtends; 232 233SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 234 : SCEV(scZeroExtend), Op(op), Ty(ty) { 235 assert(Op->getType()->isInteger() && Ty->isInteger() && 236 "Cannot zero extend non-integer value!"); 237 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 238 && "This is not an extending conversion!"); 239} 240 241SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 242 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 243} 244 245ConstantRange SCEVZeroExtendExpr::getValueRange() const { 246 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 247} 248 249void SCEVZeroExtendExpr::print(std::ostream &OS) const { 250 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 251} 252 253// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 254// particular input. Don't use a SCEVHandle here, or else the object will never 255// be deleted! 256static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 257 SCEVSignExtendExpr*> > SCEVSignExtends; 258 259SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 260 : SCEV(scSignExtend), Op(op), Ty(ty) { 261 assert(Op->getType()->isInteger() && Ty->isInteger() && 262 "Cannot sign extend non-integer value!"); 263 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 264 && "This is not an extending conversion!"); 265} 266 267SCEVSignExtendExpr::~SCEVSignExtendExpr() { 268 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 269} 270 271ConstantRange SCEVSignExtendExpr::getValueRange() const { 272 return getOperand()->getValueRange().signExtend(getBitWidth()); 273} 274 275void SCEVSignExtendExpr::print(std::ostream &OS) const { 276 OS << "(signextend " << *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<SCEV*> >, 283 SCEVCommutativeExpr*> > SCEVCommExprs; 284 285SCEVCommutativeExpr::~SCEVCommutativeExpr() { 286 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 287 std::vector<SCEV*>(Operands.begin(), 288 Operands.end()))); 289} 290 291void SCEVCommutativeExpr::print(std::ostream &OS) const { 292 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 293 const char *OpStr = getOperationStr(); 294 OS << "(" << *Operands[0]; 295 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 296 OS << OpStr << *Operands[i]; 297 OS << ")"; 298} 299 300SCEVHandle SCEVCommutativeExpr:: 301replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 302 const SCEVHandle &Conc, 303 ScalarEvolution &SE) const { 304 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 305 SCEVHandle H = 306 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 307 if (H != getOperand(i)) { 308 std::vector<SCEVHandle> NewOps; 309 NewOps.reserve(getNumOperands()); 310 for (unsigned j = 0; j != i; ++j) 311 NewOps.push_back(getOperand(j)); 312 NewOps.push_back(H); 313 for (++i; i != e; ++i) 314 NewOps.push_back(getOperand(i)-> 315 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 316 317 if (isa<SCEVAddExpr>(this)) 318 return SE.getAddExpr(NewOps); 319 else if (isa<SCEVMulExpr>(this)) 320 return SE.getMulExpr(NewOps); 321 else if (isa<SCEVSMaxExpr>(this)) 322 return SE.getSMaxExpr(NewOps); 323 else 324 assert(0 && "Unknown commutative expr!"); 325 } 326 } 327 return this; 328} 329 330 331// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 332// input. Don't use a SCEVHandle here, or else the object will never be 333// deleted! 334static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 335 SCEVSDivExpr*> > SCEVSDivs; 336 337SCEVSDivExpr::~SCEVSDivExpr() { 338 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 339} 340 341void SCEVSDivExpr::print(std::ostream &OS) const { 342 OS << "(" << *LHS << " /s " << *RHS << ")"; 343} 344 345const Type *SCEVSDivExpr::getType() const { 346 return LHS->getType(); 347} 348 349// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 350// particular input. Don't use a SCEVHandle here, or else the object will never 351// be deleted! 352static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 353 SCEVAddRecExpr*> > SCEVAddRecExprs; 354 355SCEVAddRecExpr::~SCEVAddRecExpr() { 356 SCEVAddRecExprs->erase(std::make_pair(L, 357 std::vector<SCEV*>(Operands.begin(), 358 Operands.end()))); 359} 360 361SCEVHandle SCEVAddRecExpr:: 362replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 363 const SCEVHandle &Conc, 364 ScalarEvolution &SE) const { 365 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 366 SCEVHandle H = 367 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 368 if (H != getOperand(i)) { 369 std::vector<SCEVHandle> NewOps; 370 NewOps.reserve(getNumOperands()); 371 for (unsigned j = 0; j != i; ++j) 372 NewOps.push_back(getOperand(j)); 373 NewOps.push_back(H); 374 for (++i; i != e; ++i) 375 NewOps.push_back(getOperand(i)-> 376 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 377 378 return SE.getAddRecExpr(NewOps, L); 379 } 380 } 381 return this; 382} 383 384 385bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 386 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 387 // contain L and if the start is invariant. 388 return !QueryLoop->contains(L->getHeader()) && 389 getOperand(0)->isLoopInvariant(QueryLoop); 390} 391 392 393void SCEVAddRecExpr::print(std::ostream &OS) const { 394 OS << "{" << *Operands[0]; 395 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 396 OS << ",+," << *Operands[i]; 397 OS << "}<" << L->getHeader()->getName() + ">"; 398} 399 400// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 401// value. Don't use a SCEVHandle here, or else the object will never be 402// deleted! 403static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 404 405SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 406 407bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 408 // All non-instruction values are loop invariant. All instructions are loop 409 // invariant if they are not contained in the specified loop. 410 if (Instruction *I = dyn_cast<Instruction>(V)) 411 return !L->contains(I->getParent()); 412 return true; 413} 414 415const Type *SCEVUnknown::getType() const { 416 return V->getType(); 417} 418 419void SCEVUnknown::print(std::ostream &OS) const { 420 WriteAsOperand(OS, V, false); 421} 422 423//===----------------------------------------------------------------------===// 424// SCEV Utilities 425//===----------------------------------------------------------------------===// 426 427namespace { 428 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 429 /// than the complexity of the RHS. This comparator is used to canonicalize 430 /// expressions. 431 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 432 bool operator()(SCEV *LHS, SCEV *RHS) { 433 return LHS->getSCEVType() < RHS->getSCEVType(); 434 } 435 }; 436} 437 438/// GroupByComplexity - Given a list of SCEV objects, order them by their 439/// complexity, and group objects of the same complexity together by value. 440/// When this routine is finished, we know that any duplicates in the vector are 441/// consecutive and that complexity is monotonically increasing. 442/// 443/// Note that we go take special precautions to ensure that we get determinstic 444/// results from this routine. In other words, we don't want the results of 445/// this to depend on where the addresses of various SCEV objects happened to 446/// land in memory. 447/// 448static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 449 if (Ops.size() < 2) return; // Noop 450 if (Ops.size() == 2) { 451 // This is the common case, which also happens to be trivially simple. 452 // Special case it. 453 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 454 std::swap(Ops[0], Ops[1]); 455 return; 456 } 457 458 // Do the rough sort by complexity. 459 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 460 461 // Now that we are sorted by complexity, group elements of the same 462 // complexity. Note that this is, at worst, N^2, but the vector is likely to 463 // be extremely short in practice. Note that we take this approach because we 464 // do not want to depend on the addresses of the objects we are grouping. 465 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 466 SCEV *S = Ops[i]; 467 unsigned Complexity = S->getSCEVType(); 468 469 // If there are any objects of the same complexity and same value as this 470 // one, group them. 471 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 472 if (Ops[j] == S) { // Found a duplicate. 473 // Move it to immediately after i'th element. 474 std::swap(Ops[i+1], Ops[j]); 475 ++i; // no need to rescan it. 476 if (i == e-2) return; // Done! 477 } 478 } 479 } 480} 481 482 483 484//===----------------------------------------------------------------------===// 485// Simple SCEV method implementations 486//===----------------------------------------------------------------------===// 487 488/// getIntegerSCEV - Given an integer or FP type, create a constant for the 489/// specified signed integer value and return a SCEV for the constant. 490SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 491 Constant *C; 492 if (Val == 0) 493 C = Constant::getNullValue(Ty); 494 else if (Ty->isFloatingPoint()) 495 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 496 APFloat::IEEEdouble, Val)); 497 else 498 C = ConstantInt::get(Ty, Val); 499 return getUnknown(C); 500} 501 502/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 503/// input value to the specified type. If the type must be extended, it is zero 504/// extended. 505static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty, 506 ScalarEvolution &SE) { 507 const Type *SrcTy = V->getType(); 508 assert(SrcTy->isInteger() && Ty->isInteger() && 509 "Cannot truncate or zero extend with non-integer arguments!"); 510 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 511 return V; // No conversion 512 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 513 return SE.getTruncateExpr(V, Ty); 514 return SE.getZeroExtendExpr(V, Ty); 515} 516 517/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 518/// 519SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 520 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 521 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 522 523 return getMulExpr(V, getIntegerSCEV(-1, V->getType())); 524} 525 526/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 527/// 528SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 529 const SCEVHandle &RHS) { 530 // X - Y --> X + -Y 531 return getAddExpr(LHS, getNegativeSCEV(RHS)); 532} 533 534 535/// PartialFact - Compute V!/(V-NumSteps)! 536static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps, 537 ScalarEvolution &SE) { 538 // Handle this case efficiently, it is common to have constant iteration 539 // counts while computing loop exit values. 540 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 541 const APInt& Val = SC->getValue()->getValue(); 542 APInt Result(Val.getBitWidth(), 1); 543 for (; NumSteps; --NumSteps) 544 Result *= Val-(NumSteps-1); 545 return SE.getConstant(Result); 546 } 547 548 const Type *Ty = V->getType(); 549 if (NumSteps == 0) 550 return SE.getIntegerSCEV(1, Ty); 551 552 SCEVHandle Result = V; 553 for (unsigned i = 1; i != NumSteps; ++i) 554 Result = SE.getMulExpr(Result, SE.getMinusSCEV(V, 555 SE.getIntegerSCEV(i, Ty))); 556 return Result; 557} 558 559 560/// evaluateAtIteration - Return the value of this chain of recurrences at 561/// the specified iteration number. We can evaluate this recurrence by 562/// multiplying each element in the chain by the binomial coefficient 563/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 564/// 565/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 566/// 567/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 568/// Is the binomial equation safe using modular arithmetic?? 569/// 570SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 571 ScalarEvolution &SE) const { 572 SCEVHandle Result = getStart(); 573 int Divisor = 1; 574 const Type *Ty = It->getType(); 575 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 576 SCEVHandle BC = PartialFact(It, i, SE); 577 Divisor *= i; 578 SCEVHandle Val = SE.getSDivExpr(SE.getMulExpr(BC, getOperand(i)), 579 SE.getIntegerSCEV(Divisor,Ty)); 580 Result = SE.getAddExpr(Result, Val); 581 } 582 return Result; 583} 584 585 586//===----------------------------------------------------------------------===// 587// SCEV Expression folder implementations 588//===----------------------------------------------------------------------===// 589 590SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 591 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 592 return getUnknown( 593 ConstantExpr::getTrunc(SC->getValue(), Ty)); 594 595 // If the input value is a chrec scev made out of constants, truncate 596 // all of the constants. 597 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 598 std::vector<SCEVHandle> Operands; 599 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 600 // FIXME: This should allow truncation of other expression types! 601 if (isa<SCEVConstant>(AddRec->getOperand(i))) 602 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 603 else 604 break; 605 if (Operands.size() == AddRec->getNumOperands()) 606 return getAddRecExpr(Operands, AddRec->getLoop()); 607 } 608 609 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 610 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 611 return Result; 612} 613 614SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 615 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 616 return getUnknown( 617 ConstantExpr::getZExt(SC->getValue(), Ty)); 618 619 // FIXME: If the input value is a chrec scev, and we can prove that the value 620 // did not overflow the old, smaller, value, we can zero extend all of the 621 // operands (often constants). This would allow analysis of something like 622 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 623 624 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 625 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 626 return Result; 627} 628 629SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 630 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 631 return getUnknown( 632 ConstantExpr::getSExt(SC->getValue(), Ty)); 633 634 // FIXME: If the input value is a chrec scev, and we can prove that the value 635 // did not overflow the old, smaller, value, we can sign extend all of the 636 // operands (often constants). This would allow analysis of something like 637 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 638 639 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 640 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 641 return Result; 642} 643 644// get - Get a canonical add expression, or something simpler if possible. 645SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 646 assert(!Ops.empty() && "Cannot get empty add!"); 647 if (Ops.size() == 1) return Ops[0]; 648 649 // Sort by complexity, this groups all similar expression types together. 650 GroupByComplexity(Ops); 651 652 // If there are any constants, fold them together. 653 unsigned Idx = 0; 654 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 655 ++Idx; 656 assert(Idx < Ops.size()); 657 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 658 // We found two constants, fold them together! 659 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 660 RHSC->getValue()->getValue()); 661 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 662 Ops[0] = getConstant(CI); 663 Ops.erase(Ops.begin()+1); // Erase the folded element 664 if (Ops.size() == 1) return Ops[0]; 665 LHSC = cast<SCEVConstant>(Ops[0]); 666 } else { 667 // If we couldn't fold the expression, move to the next constant. Note 668 // that this is impossible to happen in practice because we always 669 // constant fold constant ints to constant ints. 670 ++Idx; 671 } 672 } 673 674 // If we are left with a constant zero being added, strip it off. 675 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 676 Ops.erase(Ops.begin()); 677 --Idx; 678 } 679 } 680 681 if (Ops.size() == 1) return Ops[0]; 682 683 // Okay, check to see if the same value occurs in the operand list twice. If 684 // so, merge them together into an multiply expression. Since we sorted the 685 // list, these values are required to be adjacent. 686 const Type *Ty = Ops[0]->getType(); 687 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 688 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 689 // Found a match, merge the two values into a multiply, and add any 690 // remaining values to the result. 691 SCEVHandle Two = getIntegerSCEV(2, Ty); 692 SCEVHandle Mul = getMulExpr(Ops[i], Two); 693 if (Ops.size() == 2) 694 return Mul; 695 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 696 Ops.push_back(Mul); 697 return getAddExpr(Ops); 698 } 699 700 // Now we know the first non-constant operand. Skip past any cast SCEVs. 701 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 702 ++Idx; 703 704 // If there are add operands they would be next. 705 if (Idx < Ops.size()) { 706 bool DeletedAdd = false; 707 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 708 // If we have an add, expand the add operands onto the end of the operands 709 // list. 710 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 711 Ops.erase(Ops.begin()+Idx); 712 DeletedAdd = true; 713 } 714 715 // If we deleted at least one add, we added operands to the end of the list, 716 // and they are not necessarily sorted. Recurse to resort and resimplify 717 // any operands we just aquired. 718 if (DeletedAdd) 719 return getAddExpr(Ops); 720 } 721 722 // Skip over the add expression until we get to a multiply. 723 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 724 ++Idx; 725 726 // If we are adding something to a multiply expression, make sure the 727 // something is not already an operand of the multiply. If so, merge it into 728 // the multiply. 729 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 730 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 731 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 732 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 733 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 734 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 735 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 736 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 737 if (Mul->getNumOperands() != 2) { 738 // If the multiply has more than two operands, we must get the 739 // Y*Z term. 740 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 741 MulOps.erase(MulOps.begin()+MulOp); 742 InnerMul = getMulExpr(MulOps); 743 } 744 SCEVHandle One = getIntegerSCEV(1, Ty); 745 SCEVHandle AddOne = getAddExpr(InnerMul, One); 746 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 747 if (Ops.size() == 2) return OuterMul; 748 if (AddOp < Idx) { 749 Ops.erase(Ops.begin()+AddOp); 750 Ops.erase(Ops.begin()+Idx-1); 751 } else { 752 Ops.erase(Ops.begin()+Idx); 753 Ops.erase(Ops.begin()+AddOp-1); 754 } 755 Ops.push_back(OuterMul); 756 return getAddExpr(Ops); 757 } 758 759 // Check this multiply against other multiplies being added together. 760 for (unsigned OtherMulIdx = Idx+1; 761 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 762 ++OtherMulIdx) { 763 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 764 // If MulOp occurs in OtherMul, we can fold the two multiplies 765 // together. 766 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 767 OMulOp != e; ++OMulOp) 768 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 769 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 770 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 771 if (Mul->getNumOperands() != 2) { 772 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 773 MulOps.erase(MulOps.begin()+MulOp); 774 InnerMul1 = getMulExpr(MulOps); 775 } 776 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 777 if (OtherMul->getNumOperands() != 2) { 778 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 779 OtherMul->op_end()); 780 MulOps.erase(MulOps.begin()+OMulOp); 781 InnerMul2 = getMulExpr(MulOps); 782 } 783 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 784 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 785 if (Ops.size() == 2) return OuterMul; 786 Ops.erase(Ops.begin()+Idx); 787 Ops.erase(Ops.begin()+OtherMulIdx-1); 788 Ops.push_back(OuterMul); 789 return getAddExpr(Ops); 790 } 791 } 792 } 793 } 794 795 // If there are any add recurrences in the operands list, see if any other 796 // added values are loop invariant. If so, we can fold them into the 797 // recurrence. 798 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 799 ++Idx; 800 801 // Scan over all recurrences, trying to fold loop invariants into them. 802 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 803 // Scan all of the other operands to this add and add them to the vector if 804 // they are loop invariant w.r.t. the recurrence. 805 std::vector<SCEVHandle> LIOps; 806 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 807 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 808 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 809 LIOps.push_back(Ops[i]); 810 Ops.erase(Ops.begin()+i); 811 --i; --e; 812 } 813 814 // If we found some loop invariants, fold them into the recurrence. 815 if (!LIOps.empty()) { 816 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 817 LIOps.push_back(AddRec->getStart()); 818 819 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 820 AddRecOps[0] = getAddExpr(LIOps); 821 822 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 823 // If all of the other operands were loop invariant, we are done. 824 if (Ops.size() == 1) return NewRec; 825 826 // Otherwise, add the folded AddRec by the non-liv parts. 827 for (unsigned i = 0;; ++i) 828 if (Ops[i] == AddRec) { 829 Ops[i] = NewRec; 830 break; 831 } 832 return getAddExpr(Ops); 833 } 834 835 // Okay, if there weren't any loop invariants to be folded, check to see if 836 // there are multiple AddRec's with the same loop induction variable being 837 // added together. If so, we can fold them. 838 for (unsigned OtherIdx = Idx+1; 839 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 840 if (OtherIdx != Idx) { 841 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 842 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 843 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 844 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 845 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 846 if (i >= NewOps.size()) { 847 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 848 OtherAddRec->op_end()); 849 break; 850 } 851 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 852 } 853 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 854 855 if (Ops.size() == 2) return NewAddRec; 856 857 Ops.erase(Ops.begin()+Idx); 858 Ops.erase(Ops.begin()+OtherIdx-1); 859 Ops.push_back(NewAddRec); 860 return getAddExpr(Ops); 861 } 862 } 863 864 // Otherwise couldn't fold anything into this recurrence. Move onto the 865 // next one. 866 } 867 868 // Okay, it looks like we really DO need an add expr. Check to see if we 869 // already have one, otherwise create a new one. 870 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 871 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 872 SCEVOps)]; 873 if (Result == 0) Result = new SCEVAddExpr(Ops); 874 return Result; 875} 876 877 878SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 879 assert(!Ops.empty() && "Cannot get empty mul!"); 880 881 // Sort by complexity, this groups all similar expression types together. 882 GroupByComplexity(Ops); 883 884 // If there are any constants, fold them together. 885 unsigned Idx = 0; 886 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 887 888 // C1*(C2+V) -> C1*C2 + C1*V 889 if (Ops.size() == 2) 890 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 891 if (Add->getNumOperands() == 2 && 892 isa<SCEVConstant>(Add->getOperand(0))) 893 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 894 getMulExpr(LHSC, Add->getOperand(1))); 895 896 897 ++Idx; 898 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 899 // We found two constants, fold them together! 900 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 901 RHSC->getValue()->getValue()); 902 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 903 Ops[0] = getConstant(CI); 904 Ops.erase(Ops.begin()+1); // Erase the folded element 905 if (Ops.size() == 1) return Ops[0]; 906 LHSC = cast<SCEVConstant>(Ops[0]); 907 } else { 908 // If we couldn't fold the expression, move to the next constant. Note 909 // that this is impossible to happen in practice because we always 910 // constant fold constant ints to constant ints. 911 ++Idx; 912 } 913 } 914 915 // If we are left with a constant one being multiplied, strip it off. 916 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 917 Ops.erase(Ops.begin()); 918 --Idx; 919 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 920 // If we have a multiply of zero, it will always be zero. 921 return Ops[0]; 922 } 923 } 924 925 // Skip over the add expression until we get to a multiply. 926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 927 ++Idx; 928 929 if (Ops.size() == 1) 930 return Ops[0]; 931 932 // If there are mul operands inline them all into this expression. 933 if (Idx < Ops.size()) { 934 bool DeletedMul = false; 935 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 936 // If we have an mul, expand the mul operands onto the end of the operands 937 // list. 938 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 939 Ops.erase(Ops.begin()+Idx); 940 DeletedMul = true; 941 } 942 943 // If we deleted at least one mul, we added operands to the end of the list, 944 // and they are not necessarily sorted. Recurse to resort and resimplify 945 // any operands we just aquired. 946 if (DeletedMul) 947 return getMulExpr(Ops); 948 } 949 950 // If there are any add recurrences in the operands list, see if any other 951 // added values are loop invariant. If so, we can fold them into the 952 // recurrence. 953 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 954 ++Idx; 955 956 // Scan over all recurrences, trying to fold loop invariants into them. 957 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 958 // Scan all of the other operands to this mul and add them to the vector if 959 // they are loop invariant w.r.t. the recurrence. 960 std::vector<SCEVHandle> LIOps; 961 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 962 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 963 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 964 LIOps.push_back(Ops[i]); 965 Ops.erase(Ops.begin()+i); 966 --i; --e; 967 } 968 969 // If we found some loop invariants, fold them into the recurrence. 970 if (!LIOps.empty()) { 971 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 972 std::vector<SCEVHandle> NewOps; 973 NewOps.reserve(AddRec->getNumOperands()); 974 if (LIOps.size() == 1) { 975 SCEV *Scale = LIOps[0]; 976 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 977 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 978 } else { 979 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 980 std::vector<SCEVHandle> MulOps(LIOps); 981 MulOps.push_back(AddRec->getOperand(i)); 982 NewOps.push_back(getMulExpr(MulOps)); 983 } 984 } 985 986 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 987 988 // If all of the other operands were loop invariant, we are done. 989 if (Ops.size() == 1) return NewRec; 990 991 // Otherwise, multiply the folded AddRec by the non-liv parts. 992 for (unsigned i = 0;; ++i) 993 if (Ops[i] == AddRec) { 994 Ops[i] = NewRec; 995 break; 996 } 997 return getMulExpr(Ops); 998 } 999 1000 // Okay, if there weren't any loop invariants to be folded, check to see if 1001 // there are multiple AddRec's with the same loop induction variable being 1002 // multiplied together. If so, we can fold them. 1003 for (unsigned OtherIdx = Idx+1; 1004 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1005 if (OtherIdx != Idx) { 1006 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1007 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1008 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1009 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1010 SCEVHandle NewStart = getMulExpr(F->getStart(), 1011 G->getStart()); 1012 SCEVHandle B = F->getStepRecurrence(*this); 1013 SCEVHandle D = G->getStepRecurrence(*this); 1014 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1015 getMulExpr(G, B), 1016 getMulExpr(B, D)); 1017 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1018 F->getLoop()); 1019 if (Ops.size() == 2) return NewAddRec; 1020 1021 Ops.erase(Ops.begin()+Idx); 1022 Ops.erase(Ops.begin()+OtherIdx-1); 1023 Ops.push_back(NewAddRec); 1024 return getMulExpr(Ops); 1025 } 1026 } 1027 1028 // Otherwise couldn't fold anything into this recurrence. Move onto the 1029 // next one. 1030 } 1031 1032 // Okay, it looks like we really DO need an mul expr. Check to see if we 1033 // already have one, otherwise create a new one. 1034 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1035 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1036 SCEVOps)]; 1037 if (Result == 0) 1038 Result = new SCEVMulExpr(Ops); 1039 return Result; 1040} 1041 1042SCEVHandle ScalarEvolution::getSDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1043 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1044 if (RHSC->getValue()->equalsInt(1)) 1045 return LHS; // X sdiv 1 --> x 1046 if (RHSC->getValue()->isAllOnesValue()) 1047 return getNegativeSCEV(LHS); // X sdiv -1 --> -x 1048 1049 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1050 Constant *LHSCV = LHSC->getValue(); 1051 Constant *RHSCV = RHSC->getValue(); 1052 return getUnknown(ConstantExpr::getSDiv(LHSCV, RHSCV)); 1053 } 1054 } 1055 1056 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1057 1058 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 1059 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1060 return Result; 1061} 1062 1063 1064/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1065/// specified loop. Simplify the expression as much as possible. 1066SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1067 const SCEVHandle &Step, const Loop *L) { 1068 std::vector<SCEVHandle> Operands; 1069 Operands.push_back(Start); 1070 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1071 if (StepChrec->getLoop() == L) { 1072 Operands.insert(Operands.end(), StepChrec->op_begin(), 1073 StepChrec->op_end()); 1074 return getAddRecExpr(Operands, L); 1075 } 1076 1077 Operands.push_back(Step); 1078 return getAddRecExpr(Operands, L); 1079} 1080 1081/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1082/// specified loop. Simplify the expression as much as possible. 1083SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1084 const Loop *L) { 1085 if (Operands.size() == 1) return Operands[0]; 1086 1087 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1088 if (StepC->getValue()->isZero()) { 1089 Operands.pop_back(); 1090 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1091 } 1092 1093 SCEVAddRecExpr *&Result = 1094 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1095 Operands.end()))]; 1096 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1097 return Result; 1098} 1099 1100SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1101 const SCEVHandle &RHS) { 1102 std::vector<SCEVHandle> Ops; 1103 Ops.push_back(LHS); 1104 Ops.push_back(RHS); 1105 return getSMaxExpr(Ops); 1106} 1107 1108SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1109 assert(!Ops.empty() && "Cannot get empty smax!"); 1110 if (Ops.size() == 1) return Ops[0]; 1111 1112 // Sort by complexity, this groups all similar expression types together. 1113 GroupByComplexity(Ops); 1114 1115 // If there are any constants, fold them together. 1116 unsigned Idx = 0; 1117 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1118 ++Idx; 1119 assert(Idx < Ops.size()); 1120 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1121 // We found two constants, fold them together! 1122 Constant *Fold = ConstantInt::get( 1123 APIntOps::smax(LHSC->getValue()->getValue(), 1124 RHSC->getValue()->getValue())); 1125 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 1126 Ops[0] = getConstant(CI); 1127 Ops.erase(Ops.begin()+1); // Erase the folded element 1128 if (Ops.size() == 1) return Ops[0]; 1129 LHSC = cast<SCEVConstant>(Ops[0]); 1130 } else { 1131 // If we couldn't fold the expression, move to the next constant. Note 1132 // that this is impossible to happen in practice because we always 1133 // constant fold constant ints to constant ints. 1134 ++Idx; 1135 } 1136 } 1137 1138 // If we are left with a constant -inf, strip it off. 1139 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1140 Ops.erase(Ops.begin()); 1141 --Idx; 1142 } 1143 } 1144 1145 if (Ops.size() == 1) return Ops[0]; 1146 1147 // Find the first SMax 1148 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1149 ++Idx; 1150 1151 // Check to see if one of the operands is an SMax. If so, expand its operands 1152 // onto our operand list, and recurse to simplify. 1153 if (Idx < Ops.size()) { 1154 bool DeletedSMax = false; 1155 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1156 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1157 Ops.erase(Ops.begin()+Idx); 1158 DeletedSMax = true; 1159 } 1160 1161 if (DeletedSMax) 1162 return getSMaxExpr(Ops); 1163 } 1164 1165 // Okay, check to see if the same value occurs in the operand list twice. If 1166 // so, delete one. Since we sorted the list, these values are required to 1167 // be adjacent. 1168 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1169 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1170 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1171 --i; --e; 1172 } 1173 1174 if (Ops.size() == 1) return Ops[0]; 1175 1176 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1177 1178 // Okay, it looks like we really DO need an add expr. Check to see if we 1179 // already have one, otherwise create a new one. 1180 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1181 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1182 SCEVOps)]; 1183 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1184 return Result; 1185} 1186 1187SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1188 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1189 return getConstant(CI); 1190 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1191 if (Result == 0) Result = new SCEVUnknown(V); 1192 return Result; 1193} 1194 1195 1196//===----------------------------------------------------------------------===// 1197// ScalarEvolutionsImpl Definition and Implementation 1198//===----------------------------------------------------------------------===// 1199// 1200/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1201/// evolution code. 1202/// 1203namespace { 1204 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1205 /// SE - A reference to the public ScalarEvolution object. 1206 ScalarEvolution &SE; 1207 1208 /// F - The function we are analyzing. 1209 /// 1210 Function &F; 1211 1212 /// LI - The loop information for the function we are currently analyzing. 1213 /// 1214 LoopInfo &LI; 1215 1216 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1217 /// things. 1218 SCEVHandle UnknownValue; 1219 1220 /// Scalars - This is a cache of the scalars we have analyzed so far. 1221 /// 1222 std::map<Value*, SCEVHandle> Scalars; 1223 1224 /// IterationCounts - Cache the iteration count of the loops for this 1225 /// function as they are computed. 1226 std::map<const Loop*, SCEVHandle> IterationCounts; 1227 1228 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1229 /// the PHI instructions that we attempt to compute constant evolutions for. 1230 /// This allows us to avoid potentially expensive recomputation of these 1231 /// properties. An instruction maps to null if we are unable to compute its 1232 /// exit value. 1233 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1234 1235 public: 1236 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1237 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1238 1239 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1240 /// expression and create a new one. 1241 SCEVHandle getSCEV(Value *V); 1242 1243 /// hasSCEV - Return true if the SCEV for this value has already been 1244 /// computed. 1245 bool hasSCEV(Value *V) const { 1246 return Scalars.count(V); 1247 } 1248 1249 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1250 /// the specified value. 1251 void setSCEV(Value *V, const SCEVHandle &H) { 1252 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1253 assert(isNew && "This entry already existed!"); 1254 } 1255 1256 1257 /// getSCEVAtScope - Compute the value of the specified expression within 1258 /// the indicated loop (which may be null to indicate in no loop). If the 1259 /// expression cannot be evaluated, return UnknownValue itself. 1260 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1261 1262 1263 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1264 /// an analyzable loop-invariant iteration count. 1265 bool hasLoopInvariantIterationCount(const Loop *L); 1266 1267 /// getIterationCount - If the specified loop has a predictable iteration 1268 /// count, return it. Note that it is not valid to call this method on a 1269 /// loop without a loop-invariant iteration count. 1270 SCEVHandle getIterationCount(const Loop *L); 1271 1272 /// deleteValueFromRecords - This method should be called by the 1273 /// client before it removes a value from the program, to make sure 1274 /// that no dangling references are left around. 1275 void deleteValueFromRecords(Value *V); 1276 1277 private: 1278 /// createSCEV - We know that there is no SCEV for the specified value. 1279 /// Analyze the expression. 1280 SCEVHandle createSCEV(Value *V); 1281 1282 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1283 /// SCEVs. 1284 SCEVHandle createNodeForPHI(PHINode *PN); 1285 1286 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1287 /// for the specified instruction and replaces any references to the 1288 /// symbolic value SymName with the specified value. This is used during 1289 /// PHI resolution. 1290 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1291 const SCEVHandle &SymName, 1292 const SCEVHandle &NewVal); 1293 1294 /// ComputeIterationCount - Compute the number of times the specified loop 1295 /// will iterate. 1296 SCEVHandle ComputeIterationCount(const Loop *L); 1297 1298 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1299 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1300 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1301 Constant *RHS, 1302 const Loop *L, 1303 ICmpInst::Predicate p); 1304 1305 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1306 /// constant number of times (the condition evolves only from constants), 1307 /// try to evaluate a few iterations of the loop until we get the exit 1308 /// condition gets a value of ExitWhen (true or false). If we cannot 1309 /// evaluate the trip count of the loop, return UnknownValue. 1310 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1311 bool ExitWhen); 1312 1313 /// HowFarToZero - Return the number of times a backedge comparing the 1314 /// specified value to zero will execute. If not computable, return 1315 /// UnknownValue. 1316 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1317 1318 /// HowFarToNonZero - Return the number of times a backedge checking the 1319 /// specified value for nonzero will execute. If not computable, return 1320 /// UnknownValue. 1321 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1322 1323 /// HowManyLessThans - Return the number of times a backedge containing the 1324 /// specified less-than comparison will execute. If not computable, return 1325 /// UnknownValue. isSigned specifies whether the less-than is signed. 1326 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1327 bool isSigned); 1328 1329 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1330 /// in the header of its containing loop, we know the loop executes a 1331 /// constant number of times, and the PHI node is just a recurrence 1332 /// involving constants, fold it. 1333 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1334 const Loop *L); 1335 }; 1336} 1337 1338//===----------------------------------------------------------------------===// 1339// Basic SCEV Analysis and PHI Idiom Recognition Code 1340// 1341 1342/// deleteValueFromRecords - This method should be called by the 1343/// client before it removes an instruction from the program, to make sure 1344/// that no dangling references are left around. 1345void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1346 SmallVector<Value *, 16> Worklist; 1347 1348 if (Scalars.erase(V)) { 1349 if (PHINode *PN = dyn_cast<PHINode>(V)) 1350 ConstantEvolutionLoopExitValue.erase(PN); 1351 Worklist.push_back(V); 1352 } 1353 1354 while (!Worklist.empty()) { 1355 Value *VV = Worklist.back(); 1356 Worklist.pop_back(); 1357 1358 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1359 UI != UE; ++UI) { 1360 Instruction *Inst = cast<Instruction>(*UI); 1361 if (Scalars.erase(Inst)) { 1362 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1363 ConstantEvolutionLoopExitValue.erase(PN); 1364 Worklist.push_back(Inst); 1365 } 1366 } 1367 } 1368} 1369 1370 1371/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1372/// expression and create a new one. 1373SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1374 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1375 1376 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1377 if (I != Scalars.end()) return I->second; 1378 SCEVHandle S = createSCEV(V); 1379 Scalars.insert(std::make_pair(V, S)); 1380 return S; 1381} 1382 1383/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1384/// the specified instruction and replaces any references to the symbolic value 1385/// SymName with the specified value. This is used during PHI resolution. 1386void ScalarEvolutionsImpl:: 1387ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1388 const SCEVHandle &NewVal) { 1389 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1390 if (SI == Scalars.end()) return; 1391 1392 SCEVHandle NV = 1393 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1394 if (NV == SI->second) return; // No change. 1395 1396 SI->second = NV; // Update the scalars map! 1397 1398 // Any instruction values that use this instruction might also need to be 1399 // updated! 1400 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1401 UI != E; ++UI) 1402 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1403} 1404 1405/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1406/// a loop header, making it a potential recurrence, or it doesn't. 1407/// 1408SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1409 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1410 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1411 if (L->getHeader() == PN->getParent()) { 1412 // If it lives in the loop header, it has two incoming values, one 1413 // from outside the loop, and one from inside. 1414 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1415 unsigned BackEdge = IncomingEdge^1; 1416 1417 // While we are analyzing this PHI node, handle its value symbolically. 1418 SCEVHandle SymbolicName = SE.getUnknown(PN); 1419 assert(Scalars.find(PN) == Scalars.end() && 1420 "PHI node already processed?"); 1421 Scalars.insert(std::make_pair(PN, SymbolicName)); 1422 1423 // Using this symbolic name for the PHI, analyze the value coming around 1424 // the back-edge. 1425 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1426 1427 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1428 // has a special value for the first iteration of the loop. 1429 1430 // If the value coming around the backedge is an add with the symbolic 1431 // value we just inserted, then we found a simple induction variable! 1432 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1433 // If there is a single occurrence of the symbolic value, replace it 1434 // with a recurrence. 1435 unsigned FoundIndex = Add->getNumOperands(); 1436 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1437 if (Add->getOperand(i) == SymbolicName) 1438 if (FoundIndex == e) { 1439 FoundIndex = i; 1440 break; 1441 } 1442 1443 if (FoundIndex != Add->getNumOperands()) { 1444 // Create an add with everything but the specified operand. 1445 std::vector<SCEVHandle> Ops; 1446 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1447 if (i != FoundIndex) 1448 Ops.push_back(Add->getOperand(i)); 1449 SCEVHandle Accum = SE.getAddExpr(Ops); 1450 1451 // This is not a valid addrec if the step amount is varying each 1452 // loop iteration, but is not itself an addrec in this loop. 1453 if (Accum->isLoopInvariant(L) || 1454 (isa<SCEVAddRecExpr>(Accum) && 1455 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1456 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1457 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1458 1459 // Okay, for the entire analysis of this edge we assumed the PHI 1460 // to be symbolic. We now need to go back and update all of the 1461 // entries for the scalars that use the PHI (except for the PHI 1462 // itself) to use the new analyzed value instead of the "symbolic" 1463 // value. 1464 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1465 return PHISCEV; 1466 } 1467 } 1468 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1469 // Otherwise, this could be a loop like this: 1470 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1471 // In this case, j = {1,+,1} and BEValue is j. 1472 // Because the other in-value of i (0) fits the evolution of BEValue 1473 // i really is an addrec evolution. 1474 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1475 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1476 1477 // If StartVal = j.start - j.stride, we can use StartVal as the 1478 // initial step of the addrec evolution. 1479 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1480 AddRec->getOperand(1))) { 1481 SCEVHandle PHISCEV = 1482 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1483 1484 // Okay, for the entire analysis of this edge we assumed the PHI 1485 // to be symbolic. We now need to go back and update all of the 1486 // entries for the scalars that use the PHI (except for the PHI 1487 // itself) to use the new analyzed value instead of the "symbolic" 1488 // value. 1489 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1490 return PHISCEV; 1491 } 1492 } 1493 } 1494 1495 return SymbolicName; 1496 } 1497 1498 // If it's not a loop phi, we can't handle it yet. 1499 return SE.getUnknown(PN); 1500} 1501 1502/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1503/// guaranteed to end in (at every loop iteration). It is, at the same time, 1504/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1505/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1506static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1507 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1508 return C->getValue()->getValue().countTrailingZeros(); 1509 1510 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1511 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1512 1513 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1514 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1515 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1516 } 1517 1518 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1519 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1520 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1521 } 1522 1523 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1524 // The result is the min of all operands results. 1525 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1526 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1527 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1528 return MinOpRes; 1529 } 1530 1531 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1532 // The result is the sum of all operands results. 1533 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1534 uint32_t BitWidth = M->getBitWidth(); 1535 for (unsigned i = 1, e = M->getNumOperands(); 1536 SumOpRes != BitWidth && i != e; ++i) 1537 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1538 BitWidth); 1539 return SumOpRes; 1540 } 1541 1542 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1543 // The result is the min of all operands results. 1544 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1545 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1546 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1547 return MinOpRes; 1548 } 1549 1550 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1551 // The result is the min of all operands results. 1552 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1553 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1554 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1555 return MinOpRes; 1556 } 1557 1558 // SCEVSDivExpr, SCEVUnknown 1559 return 0; 1560} 1561 1562/// createSCEV - We know that there is no SCEV for the specified value. 1563/// Analyze the expression. 1564/// 1565SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1566 if (!isa<IntegerType>(V->getType())) 1567 return SE.getUnknown(V); 1568 1569 if (Instruction *I = dyn_cast<Instruction>(V)) { 1570 switch (I->getOpcode()) { 1571 case Instruction::Add: 1572 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1573 getSCEV(I->getOperand(1))); 1574 case Instruction::Mul: 1575 return SE.getMulExpr(getSCEV(I->getOperand(0)), 1576 getSCEV(I->getOperand(1))); 1577 case Instruction::SDiv: 1578 return SE.getSDivExpr(getSCEV(I->getOperand(0)), 1579 getSCEV(I->getOperand(1))); 1580 case Instruction::Sub: 1581 return SE.getMinusSCEV(getSCEV(I->getOperand(0)), 1582 getSCEV(I->getOperand(1))); 1583 case Instruction::Or: 1584 // If the RHS of the Or is a constant, we may have something like: 1585 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1586 // optimizations will transparently handle this case. 1587 // 1588 // In order for this transformation to be safe, the LHS must be of the 1589 // form X*(2^n) and the Or constant must be less than 2^n. 1590 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1591 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1592 const APInt &CIVal = CI->getValue(); 1593 if (GetMinTrailingZeros(LHS) >= 1594 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1595 return SE.getAddExpr(LHS, getSCEV(I->getOperand(1))); 1596 } 1597 break; 1598 case Instruction::Xor: 1599 // If the RHS of the xor is a signbit, then this is just an add. 1600 // Instcombine turns add of signbit into xor as a strength reduction step. 1601 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1602 if (CI->getValue().isSignBit()) 1603 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1604 getSCEV(I->getOperand(1))); 1605 } 1606 break; 1607 1608 case Instruction::Shl: 1609 // Turn shift left of a constant amount into a multiply. 1610 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1611 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1612 Constant *X = ConstantInt::get( 1613 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1614 return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X)); 1615 } 1616 break; 1617 1618 case Instruction::Trunc: 1619 return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType()); 1620 1621 case Instruction::ZExt: 1622 return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1623 1624 case Instruction::SExt: 1625 return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1626 1627 case Instruction::BitCast: 1628 // BitCasts are no-op casts so we just eliminate the cast. 1629 if (I->getType()->isInteger() && 1630 I->getOperand(0)->getType()->isInteger()) 1631 return getSCEV(I->getOperand(0)); 1632 break; 1633 1634 case Instruction::PHI: 1635 return createNodeForPHI(cast<PHINode>(I)); 1636 1637 case Instruction::Select: 1638 // This could be an SCEVSMax that was lowered earlier. Try to recover it. 1639 if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) { 1640 Value *LHS = ICI->getOperand(0); 1641 Value *RHS = ICI->getOperand(1); 1642 switch (ICI->getPredicate()) { 1643 case ICmpInst::ICMP_SLT: 1644 case ICmpInst::ICMP_SLE: 1645 std::swap(LHS, RHS); 1646 // fall through 1647 case ICmpInst::ICMP_SGT: 1648 case ICmpInst::ICMP_SGE: 1649 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1650 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1651 default: 1652 break; 1653 } 1654 } 1655 1656 default: // We cannot analyze this expression. 1657 break; 1658 } 1659 } 1660 1661 return SE.getUnknown(V); 1662} 1663 1664 1665 1666//===----------------------------------------------------------------------===// 1667// Iteration Count Computation Code 1668// 1669 1670/// getIterationCount - If the specified loop has a predictable iteration 1671/// count, return it. Note that it is not valid to call this method on a 1672/// loop without a loop-invariant iteration count. 1673SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1674 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1675 if (I == IterationCounts.end()) { 1676 SCEVHandle ItCount = ComputeIterationCount(L); 1677 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1678 if (ItCount != UnknownValue) { 1679 assert(ItCount->isLoopInvariant(L) && 1680 "Computed trip count isn't loop invariant for loop!"); 1681 ++NumTripCountsComputed; 1682 } else if (isa<PHINode>(L->getHeader()->begin())) { 1683 // Only count loops that have phi nodes as not being computable. 1684 ++NumTripCountsNotComputed; 1685 } 1686 } 1687 return I->second; 1688} 1689 1690/// ComputeIterationCount - Compute the number of times the specified loop 1691/// will iterate. 1692SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1693 // If the loop has a non-one exit block count, we can't analyze it. 1694 SmallVector<BasicBlock*, 8> ExitBlocks; 1695 L->getExitBlocks(ExitBlocks); 1696 if (ExitBlocks.size() != 1) return UnknownValue; 1697 1698 // Okay, there is one exit block. Try to find the condition that causes the 1699 // loop to be exited. 1700 BasicBlock *ExitBlock = ExitBlocks[0]; 1701 1702 BasicBlock *ExitingBlock = 0; 1703 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1704 PI != E; ++PI) 1705 if (L->contains(*PI)) { 1706 if (ExitingBlock == 0) 1707 ExitingBlock = *PI; 1708 else 1709 return UnknownValue; // More than one block exiting! 1710 } 1711 assert(ExitingBlock && "No exits from loop, something is broken!"); 1712 1713 // Okay, we've computed the exiting block. See what condition causes us to 1714 // exit. 1715 // 1716 // FIXME: we should be able to handle switch instructions (with a single exit) 1717 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1718 if (ExitBr == 0) return UnknownValue; 1719 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1720 1721 // At this point, we know we have a conditional branch that determines whether 1722 // the loop is exited. However, we don't know if the branch is executed each 1723 // time through the loop. If not, then the execution count of the branch will 1724 // not be equal to the trip count of the loop. 1725 // 1726 // Currently we check for this by checking to see if the Exit branch goes to 1727 // the loop header. If so, we know it will always execute the same number of 1728 // times as the loop. We also handle the case where the exit block *is* the 1729 // loop header. This is common for un-rotated loops. More extensive analysis 1730 // could be done to handle more cases here. 1731 if (ExitBr->getSuccessor(0) != L->getHeader() && 1732 ExitBr->getSuccessor(1) != L->getHeader() && 1733 ExitBr->getParent() != L->getHeader()) 1734 return UnknownValue; 1735 1736 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1737 1738 // If its not an integer comparison then compute it the hard way. 1739 // Note that ICmpInst deals with pointer comparisons too so we must check 1740 // the type of the operand. 1741 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1742 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1743 ExitBr->getSuccessor(0) == ExitBlock); 1744 1745 // If the condition was exit on true, convert the condition to exit on false 1746 ICmpInst::Predicate Cond; 1747 if (ExitBr->getSuccessor(1) == ExitBlock) 1748 Cond = ExitCond->getPredicate(); 1749 else 1750 Cond = ExitCond->getInversePredicate(); 1751 1752 // Handle common loops like: for (X = "string"; *X; ++X) 1753 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1754 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1755 SCEVHandle ItCnt = 1756 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1757 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1758 } 1759 1760 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1761 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1762 1763 // Try to evaluate any dependencies out of the loop. 1764 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1765 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1766 Tmp = getSCEVAtScope(RHS, L); 1767 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1768 1769 // At this point, we would like to compute how many iterations of the 1770 // loop the predicate will return true for these inputs. 1771 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1772 // If there is a constant, force it into the RHS. 1773 std::swap(LHS, RHS); 1774 Cond = ICmpInst::getSwappedPredicate(Cond); 1775 } 1776 1777 // FIXME: think about handling pointer comparisons! i.e.: 1778 // while (P != P+100) ++P; 1779 1780 // If we have a comparison of a chrec against a constant, try to use value 1781 // ranges to answer this query. 1782 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1783 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1784 if (AddRec->getLoop() == L) { 1785 // Form the comparison range using the constant of the correct type so 1786 // that the ConstantRange class knows to do a signed or unsigned 1787 // comparison. 1788 ConstantInt *CompVal = RHSC->getValue(); 1789 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1790 CompVal = dyn_cast<ConstantInt>( 1791 ConstantExpr::getBitCast(CompVal, RealTy)); 1792 if (CompVal) { 1793 // Form the constant range. 1794 ConstantRange CompRange( 1795 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1796 1797 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1798 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1799 } 1800 } 1801 1802 switch (Cond) { 1803 case ICmpInst::ICMP_NE: { // while (X != Y) 1804 // Convert to: while (X-Y != 0) 1805 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1806 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1807 break; 1808 } 1809 case ICmpInst::ICMP_EQ: { 1810 // Convert to: while (X-Y == 0) // while (X == Y) 1811 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1812 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1813 break; 1814 } 1815 case ICmpInst::ICMP_SLT: { 1816 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1817 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1818 break; 1819 } 1820 case ICmpInst::ICMP_SGT: { 1821 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1822 SE.getNegativeSCEV(RHS), L, true); 1823 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1824 break; 1825 } 1826 case ICmpInst::ICMP_ULT: { 1827 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1828 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1829 break; 1830 } 1831 case ICmpInst::ICMP_UGT: { 1832 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1833 SE.getNegativeSCEV(RHS), L, false); 1834 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1835 break; 1836 } 1837 default: 1838#if 0 1839 cerr << "ComputeIterationCount "; 1840 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1841 cerr << "[unsigned] "; 1842 cerr << *LHS << " " 1843 << Instruction::getOpcodeName(Instruction::ICmp) 1844 << " " << *RHS << "\n"; 1845#endif 1846 break; 1847 } 1848 return ComputeIterationCountExhaustively(L, ExitCond, 1849 ExitBr->getSuccessor(0) == ExitBlock); 1850} 1851 1852static ConstantInt * 1853EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 1854 ScalarEvolution &SE) { 1855 SCEVHandle InVal = SE.getConstant(C); 1856 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 1857 assert(isa<SCEVConstant>(Val) && 1858 "Evaluation of SCEV at constant didn't fold correctly?"); 1859 return cast<SCEVConstant>(Val)->getValue(); 1860} 1861 1862/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1863/// and a GEP expression (missing the pointer index) indexing into it, return 1864/// the addressed element of the initializer or null if the index expression is 1865/// invalid. 1866static Constant * 1867GetAddressedElementFromGlobal(GlobalVariable *GV, 1868 const std::vector<ConstantInt*> &Indices) { 1869 Constant *Init = GV->getInitializer(); 1870 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1871 uint64_t Idx = Indices[i]->getZExtValue(); 1872 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1873 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1874 Init = cast<Constant>(CS->getOperand(Idx)); 1875 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1876 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1877 Init = cast<Constant>(CA->getOperand(Idx)); 1878 } else if (isa<ConstantAggregateZero>(Init)) { 1879 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1880 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1881 Init = Constant::getNullValue(STy->getElementType(Idx)); 1882 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1883 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1884 Init = Constant::getNullValue(ATy->getElementType()); 1885 } else { 1886 assert(0 && "Unknown constant aggregate type!"); 1887 } 1888 return 0; 1889 } else { 1890 return 0; // Unknown initializer type 1891 } 1892 } 1893 return Init; 1894} 1895 1896/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1897/// 'icmp op load X, cst', try to se if we can compute the trip count. 1898SCEVHandle ScalarEvolutionsImpl:: 1899ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1900 const Loop *L, 1901 ICmpInst::Predicate predicate) { 1902 if (LI->isVolatile()) return UnknownValue; 1903 1904 // Check to see if the loaded pointer is a getelementptr of a global. 1905 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1906 if (!GEP) return UnknownValue; 1907 1908 // Make sure that it is really a constant global we are gepping, with an 1909 // initializer, and make sure the first IDX is really 0. 1910 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1911 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1912 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1913 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1914 return UnknownValue; 1915 1916 // Okay, we allow one non-constant index into the GEP instruction. 1917 Value *VarIdx = 0; 1918 std::vector<ConstantInt*> Indexes; 1919 unsigned VarIdxNum = 0; 1920 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1921 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1922 Indexes.push_back(CI); 1923 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1924 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1925 VarIdx = GEP->getOperand(i); 1926 VarIdxNum = i-2; 1927 Indexes.push_back(0); 1928 } 1929 1930 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1931 // Check to see if X is a loop variant variable value now. 1932 SCEVHandle Idx = getSCEV(VarIdx); 1933 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1934 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1935 1936 // We can only recognize very limited forms of loop index expressions, in 1937 // particular, only affine AddRec's like {C1,+,C2}. 1938 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1939 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1940 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1941 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1942 return UnknownValue; 1943 1944 unsigned MaxSteps = MaxBruteForceIterations; 1945 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1946 ConstantInt *ItCst = 1947 ConstantInt::get(IdxExpr->getType(), IterationNum); 1948 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 1949 1950 // Form the GEP offset. 1951 Indexes[VarIdxNum] = Val; 1952 1953 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1954 if (Result == 0) break; // Cannot compute! 1955 1956 // Evaluate the condition for this iteration. 1957 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1958 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1959 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 1960#if 0 1961 cerr << "\n***\n*** Computed loop count " << *ItCst 1962 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1963 << "***\n"; 1964#endif 1965 ++NumArrayLenItCounts; 1966 return SE.getConstant(ItCst); // Found terminating iteration! 1967 } 1968 } 1969 return UnknownValue; 1970} 1971 1972 1973/// CanConstantFold - Return true if we can constant fold an instruction of the 1974/// specified type, assuming that all operands were constants. 1975static bool CanConstantFold(const Instruction *I) { 1976 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 1977 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1978 return true; 1979 1980 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1981 if (const Function *F = CI->getCalledFunction()) 1982 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1983 return false; 1984} 1985 1986/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1987/// in the loop that V is derived from. We allow arbitrary operations along the 1988/// way, but the operands of an operation must either be constants or a value 1989/// derived from a constant PHI. If this expression does not fit with these 1990/// constraints, return null. 1991static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1992 // If this is not an instruction, or if this is an instruction outside of the 1993 // loop, it can't be derived from a loop PHI. 1994 Instruction *I = dyn_cast<Instruction>(V); 1995 if (I == 0 || !L->contains(I->getParent())) return 0; 1996 1997 if (PHINode *PN = dyn_cast<PHINode>(I)) 1998 if (L->getHeader() == I->getParent()) 1999 return PN; 2000 else 2001 // We don't currently keep track of the control flow needed to evaluate 2002 // PHIs, so we cannot handle PHIs inside of loops. 2003 return 0; 2004 2005 // If we won't be able to constant fold this expression even if the operands 2006 // are constants, return early. 2007 if (!CanConstantFold(I)) return 0; 2008 2009 // Otherwise, we can evaluate this instruction if all of its operands are 2010 // constant or derived from a PHI node themselves. 2011 PHINode *PHI = 0; 2012 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2013 if (!(isa<Constant>(I->getOperand(Op)) || 2014 isa<GlobalValue>(I->getOperand(Op)))) { 2015 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2016 if (P == 0) return 0; // Not evolving from PHI 2017 if (PHI == 0) 2018 PHI = P; 2019 else if (PHI != P) 2020 return 0; // Evolving from multiple different PHIs. 2021 } 2022 2023 // This is a expression evolving from a constant PHI! 2024 return PHI; 2025} 2026 2027/// EvaluateExpression - Given an expression that passes the 2028/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2029/// in the loop has the value PHIVal. If we can't fold this expression for some 2030/// reason, return null. 2031static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2032 if (isa<PHINode>(V)) return PHIVal; 2033 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 2034 return GV; 2035 if (Constant *C = dyn_cast<Constant>(V)) return C; 2036 Instruction *I = cast<Instruction>(V); 2037 2038 std::vector<Constant*> Operands; 2039 Operands.resize(I->getNumOperands()); 2040 2041 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2042 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2043 if (Operands[i] == 0) return 0; 2044 } 2045 2046 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2047 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2048 &Operands[0], Operands.size()); 2049 else 2050 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2051 &Operands[0], Operands.size()); 2052} 2053 2054/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2055/// in the header of its containing loop, we know the loop executes a 2056/// constant number of times, and the PHI node is just a recurrence 2057/// involving constants, fold it. 2058Constant *ScalarEvolutionsImpl:: 2059getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2060 std::map<PHINode*, Constant*>::iterator I = 2061 ConstantEvolutionLoopExitValue.find(PN); 2062 if (I != ConstantEvolutionLoopExitValue.end()) 2063 return I->second; 2064 2065 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2066 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2067 2068 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2069 2070 // Since the loop is canonicalized, the PHI node must have two entries. One 2071 // entry must be a constant (coming in from outside of the loop), and the 2072 // second must be derived from the same PHI. 2073 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2074 Constant *StartCST = 2075 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2076 if (StartCST == 0) 2077 return RetVal = 0; // Must be a constant. 2078 2079 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2080 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2081 if (PN2 != PN) 2082 return RetVal = 0; // Not derived from same PHI. 2083 2084 // Execute the loop symbolically to determine the exit value. 2085 if (Its.getActiveBits() >= 32) 2086 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2087 2088 unsigned NumIterations = Its.getZExtValue(); // must be in range 2089 unsigned IterationNum = 0; 2090 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2091 if (IterationNum == NumIterations) 2092 return RetVal = PHIVal; // Got exit value! 2093 2094 // Compute the value of the PHI node for the next iteration. 2095 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2096 if (NextPHI == PHIVal) 2097 return RetVal = NextPHI; // Stopped evolving! 2098 if (NextPHI == 0) 2099 return 0; // Couldn't evaluate! 2100 PHIVal = NextPHI; 2101 } 2102} 2103 2104/// ComputeIterationCountExhaustively - If the trip is known to execute a 2105/// constant number of times (the condition evolves only from constants), 2106/// try to evaluate a few iterations of the loop until we get the exit 2107/// condition gets a value of ExitWhen (true or false). If we cannot 2108/// evaluate the trip count of the loop, return UnknownValue. 2109SCEVHandle ScalarEvolutionsImpl:: 2110ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2111 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2112 if (PN == 0) return UnknownValue; 2113 2114 // Since the loop is canonicalized, the PHI node must have two entries. One 2115 // entry must be a constant (coming in from outside of the loop), and the 2116 // second must be derived from the same PHI. 2117 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2118 Constant *StartCST = 2119 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2120 if (StartCST == 0) return UnknownValue; // Must be a constant. 2121 2122 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2123 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2124 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2125 2126 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2127 // the loop symbolically to determine when the condition gets a value of 2128 // "ExitWhen". 2129 unsigned IterationNum = 0; 2130 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2131 for (Constant *PHIVal = StartCST; 2132 IterationNum != MaxIterations; ++IterationNum) { 2133 ConstantInt *CondVal = 2134 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2135 2136 // Couldn't symbolically evaluate. 2137 if (!CondVal) return UnknownValue; 2138 2139 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2140 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2141 ++NumBruteForceTripCountsComputed; 2142 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2143 } 2144 2145 // Compute the value of the PHI node for the next iteration. 2146 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2147 if (NextPHI == 0 || NextPHI == PHIVal) 2148 return UnknownValue; // Couldn't evaluate or not making progress... 2149 PHIVal = NextPHI; 2150 } 2151 2152 // Too many iterations were needed to evaluate. 2153 return UnknownValue; 2154} 2155 2156/// getSCEVAtScope - Compute the value of the specified expression within the 2157/// indicated loop (which may be null to indicate in no loop). If the 2158/// expression cannot be evaluated, return UnknownValue. 2159SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2160 // FIXME: this should be turned into a virtual method on SCEV! 2161 2162 if (isa<SCEVConstant>(V)) return V; 2163 2164 // If this instruction is evolves from a constant-evolving PHI, compute the 2165 // exit value from the loop without using SCEVs. 2166 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2167 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2168 const Loop *LI = this->LI[I->getParent()]; 2169 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2170 if (PHINode *PN = dyn_cast<PHINode>(I)) 2171 if (PN->getParent() == LI->getHeader()) { 2172 // Okay, there is no closed form solution for the PHI node. Check 2173 // to see if the loop that contains it has a known iteration count. 2174 // If so, we may be able to force computation of the exit value. 2175 SCEVHandle IterationCount = getIterationCount(LI); 2176 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2177 // Okay, we know how many times the containing loop executes. If 2178 // this is a constant evolving PHI node, get the final value at 2179 // the specified iteration number. 2180 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2181 ICC->getValue()->getValue(), 2182 LI); 2183 if (RV) return SE.getUnknown(RV); 2184 } 2185 } 2186 2187 // Okay, this is an expression that we cannot symbolically evaluate 2188 // into a SCEV. Check to see if it's possible to symbolically evaluate 2189 // the arguments into constants, and if so, try to constant propagate the 2190 // result. This is particularly useful for computing loop exit values. 2191 if (CanConstantFold(I)) { 2192 std::vector<Constant*> Operands; 2193 Operands.reserve(I->getNumOperands()); 2194 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2195 Value *Op = I->getOperand(i); 2196 if (Constant *C = dyn_cast<Constant>(Op)) { 2197 Operands.push_back(C); 2198 } else { 2199 // If any of the operands is non-constant and if they are 2200 // non-integer, don't even try to analyze them with scev techniques. 2201 if (!isa<IntegerType>(Op->getType())) 2202 return V; 2203 2204 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2205 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2206 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2207 Op->getType(), 2208 false)); 2209 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2210 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2211 Operands.push_back(ConstantExpr::getIntegerCast(C, 2212 Op->getType(), 2213 false)); 2214 else 2215 return V; 2216 } else { 2217 return V; 2218 } 2219 } 2220 } 2221 2222 Constant *C; 2223 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2224 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2225 &Operands[0], Operands.size()); 2226 else 2227 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2228 &Operands[0], Operands.size()); 2229 return SE.getUnknown(C); 2230 } 2231 } 2232 2233 // This is some other type of SCEVUnknown, just return it. 2234 return V; 2235 } 2236 2237 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2238 // Avoid performing the look-up in the common case where the specified 2239 // expression has no loop-variant portions. 2240 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2241 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2242 if (OpAtScope != Comm->getOperand(i)) { 2243 if (OpAtScope == UnknownValue) return UnknownValue; 2244 // Okay, at least one of these operands is loop variant but might be 2245 // foldable. Build a new instance of the folded commutative expression. 2246 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2247 NewOps.push_back(OpAtScope); 2248 2249 for (++i; i != e; ++i) { 2250 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2251 if (OpAtScope == UnknownValue) return UnknownValue; 2252 NewOps.push_back(OpAtScope); 2253 } 2254 if (isa<SCEVAddExpr>(Comm)) 2255 return SE.getAddExpr(NewOps); 2256 if (isa<SCEVMulExpr>(Comm)) 2257 return SE.getMulExpr(NewOps); 2258 if (isa<SCEVSMaxExpr>(Comm)) 2259 return SE.getSMaxExpr(NewOps); 2260 assert(0 && "Unknown commutative SCEV type!"); 2261 } 2262 } 2263 // If we got here, all operands are loop invariant. 2264 return Comm; 2265 } 2266 2267 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2268 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2269 if (LHS == UnknownValue) return LHS; 2270 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2271 if (RHS == UnknownValue) return RHS; 2272 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2273 return Div; // must be loop invariant 2274 return SE.getSDivExpr(LHS, RHS); 2275 } 2276 2277 // If this is a loop recurrence for a loop that does not contain L, then we 2278 // are dealing with the final value computed by the loop. 2279 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2280 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2281 // To evaluate this recurrence, we need to know how many times the AddRec 2282 // loop iterates. Compute this now. 2283 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2284 if (IterationCount == UnknownValue) return UnknownValue; 2285 IterationCount = getTruncateOrZeroExtend(IterationCount, 2286 AddRec->getType(), SE); 2287 2288 // If the value is affine, simplify the expression evaluation to just 2289 // Start + Step*IterationCount. 2290 if (AddRec->isAffine()) 2291 return SE.getAddExpr(AddRec->getStart(), 2292 SE.getMulExpr(IterationCount, 2293 AddRec->getOperand(1))); 2294 2295 // Otherwise, evaluate it the hard way. 2296 return AddRec->evaluateAtIteration(IterationCount, SE); 2297 } 2298 return UnknownValue; 2299 } 2300 2301 //assert(0 && "Unknown SCEV type!"); 2302 return UnknownValue; 2303} 2304 2305 2306/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2307/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2308/// might be the same) or two SCEVCouldNotCompute objects. 2309/// 2310static std::pair<SCEVHandle,SCEVHandle> 2311SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2312 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2313 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2314 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2315 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2316 2317 // We currently can only solve this if the coefficients are constants. 2318 if (!LC || !MC || !NC) { 2319 SCEV *CNC = new SCEVCouldNotCompute(); 2320 return std::make_pair(CNC, CNC); 2321 } 2322 2323 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2324 const APInt &L = LC->getValue()->getValue(); 2325 const APInt &M = MC->getValue()->getValue(); 2326 const APInt &N = NC->getValue()->getValue(); 2327 APInt Two(BitWidth, 2); 2328 APInt Four(BitWidth, 4); 2329 2330 { 2331 using namespace APIntOps; 2332 const APInt& C = L; 2333 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2334 // The B coefficient is M-N/2 2335 APInt B(M); 2336 B -= sdiv(N,Two); 2337 2338 // The A coefficient is N/2 2339 APInt A(N.sdiv(Two)); 2340 2341 // Compute the B^2-4ac term. 2342 APInt SqrtTerm(B); 2343 SqrtTerm *= B; 2344 SqrtTerm -= Four * (A * C); 2345 2346 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2347 // integer value or else APInt::sqrt() will assert. 2348 APInt SqrtVal(SqrtTerm.sqrt()); 2349 2350 // Compute the two solutions for the quadratic formula. 2351 // The divisions must be performed as signed divisions. 2352 APInt NegB(-B); 2353 APInt TwoA( A << 1 ); 2354 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2355 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2356 2357 return std::make_pair(SE.getConstant(Solution1), 2358 SE.getConstant(Solution2)); 2359 } // end APIntOps namespace 2360} 2361 2362/// HowFarToZero - Return the number of times a backedge comparing the specified 2363/// value to zero will execute. If not computable, return UnknownValue 2364SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2365 // If the value is a constant 2366 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2367 // If the value is already zero, the branch will execute zero times. 2368 if (C->getValue()->isZero()) return C; 2369 return UnknownValue; // Otherwise it will loop infinitely. 2370 } 2371 2372 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2373 if (!AddRec || AddRec->getLoop() != L) 2374 return UnknownValue; 2375 2376 if (AddRec->isAffine()) { 2377 // If this is an affine expression the execution count of this branch is 2378 // equal to: 2379 // 2380 // (0 - Start/Step) iff Start % Step == 0 2381 // 2382 // Get the initial value for the loop. 2383 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2384 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2385 SCEVHandle Step = AddRec->getOperand(1); 2386 2387 Step = getSCEVAtScope(Step, L->getParentLoop()); 2388 2389 // Figure out if Start % Step == 0. 2390 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2391 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2392 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2393 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start 2394 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2395 return Start; // 0 - Start/-1 == Start 2396 2397 // Check to see if Start is divisible by SC with no remainder. 2398 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2399 ConstantInt *StartCC = StartC->getValue(); 2400 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2401 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2402 if (Rem->isNullValue()) { 2403 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2404 return SE.getUnknown(Result); 2405 } 2406 } 2407 } 2408 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2409 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2410 // the quadratic equation to solve it. 2411 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2412 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2413 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2414 if (R1) { 2415#if 0 2416 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2417 << " sol#2: " << *R2 << "\n"; 2418#endif 2419 // Pick the smallest positive root value. 2420 if (ConstantInt *CB = 2421 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2422 R1->getValue(), R2->getValue()))) { 2423 if (CB->getZExtValue() == false) 2424 std::swap(R1, R2); // R1 is the minimum root now. 2425 2426 // We can only use this value if the chrec ends up with an exact zero 2427 // value at this index. When solving for "X*X != 5", for example, we 2428 // should not accept a root of 2. 2429 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2430 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2431 if (EvalVal->getValue()->isZero()) 2432 return R1; // We found a quadratic root! 2433 } 2434 } 2435 } 2436 2437 return UnknownValue; 2438} 2439 2440/// HowFarToNonZero - Return the number of times a backedge checking the 2441/// specified value for nonzero will execute. If not computable, return 2442/// UnknownValue 2443SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2444 // Loops that look like: while (X == 0) are very strange indeed. We don't 2445 // handle them yet except for the trivial case. This could be expanded in the 2446 // future as needed. 2447 2448 // If the value is a constant, check to see if it is known to be non-zero 2449 // already. If so, the backedge will execute zero times. 2450 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2451 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2452 Constant *NonZero = 2453 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2454 if (NonZero == ConstantInt::getTrue()) 2455 return getSCEV(Zero); 2456 return UnknownValue; // Otherwise it will loop infinitely. 2457 } 2458 2459 // We could implement others, but I really doubt anyone writes loops like 2460 // this, and if they did, they would already be constant folded. 2461 return UnknownValue; 2462} 2463 2464/// HowManyLessThans - Return the number of times a backedge containing the 2465/// specified less-than comparison will execute. If not computable, return 2466/// UnknownValue. 2467SCEVHandle ScalarEvolutionsImpl:: 2468HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2469 // Only handle: "ADDREC < LoopInvariant". 2470 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2471 2472 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2473 if (!AddRec || AddRec->getLoop() != L) 2474 return UnknownValue; 2475 2476 if (AddRec->isAffine()) { 2477 // The number of iterations for "{n,+,1} < m", is m-n. However, we don't 2478 // know that m is >= n on input to the loop. If it is, the condition 2479 // returns true zero times. To handle both cases, we return SMAX(0, m-n). 2480 2481 // FORNOW: We only support unit strides. 2482 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2483 if (AddRec->getOperand(1) != One) 2484 return UnknownValue; 2485 2486 SCEVHandle Iters = SE.getMinusSCEV(RHS, AddRec->getOperand(0)); 2487 2488 if (isSigned) 2489 return SE.getSMaxExpr(SE.getIntegerSCEV(0, RHS->getType()), Iters); 2490 else 2491 return Iters; 2492 } 2493 2494 return UnknownValue; 2495} 2496 2497/// getNumIterationsInRange - Return the number of iterations of this loop that 2498/// produce values in the specified constant range. Another way of looking at 2499/// this is that it returns the first iteration number where the value is not in 2500/// the condition, thus computing the exit count. If the iteration count can't 2501/// be computed, an instance of SCEVCouldNotCompute is returned. 2502SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2503 ScalarEvolution &SE) const { 2504 if (Range.isFullSet()) // Infinite loop. 2505 return new SCEVCouldNotCompute(); 2506 2507 // If the start is a non-zero constant, shift the range to simplify things. 2508 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2509 if (!SC->getValue()->isZero()) { 2510 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2511 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2512 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2513 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2514 return ShiftedAddRec->getNumIterationsInRange( 2515 Range.subtract(SC->getValue()->getValue()), SE); 2516 // This is strange and shouldn't happen. 2517 return new SCEVCouldNotCompute(); 2518 } 2519 2520 // The only time we can solve this is when we have all constant indices. 2521 // Otherwise, we cannot determine the overflow conditions. 2522 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2523 if (!isa<SCEVConstant>(getOperand(i))) 2524 return new SCEVCouldNotCompute(); 2525 2526 2527 // Okay at this point we know that all elements of the chrec are constants and 2528 // that the start element is zero. 2529 2530 // First check to see if the range contains zero. If not, the first 2531 // iteration exits. 2532 if (!Range.contains(APInt(getBitWidth(),0))) 2533 return SE.getConstant(ConstantInt::get(getType(),0)); 2534 2535 if (isAffine()) { 2536 // If this is an affine expression then we have this situation: 2537 // Solve {0,+,A} in Range === Ax in Range 2538 2539 // We know that zero is in the range. If A is positive then we know that 2540 // the upper value of the range must be the first possible exit value. 2541 // If A is negative then the lower of the range is the last possible loop 2542 // value. Also note that we already checked for a full range. 2543 APInt One(getBitWidth(),1); 2544 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2545 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2546 2547 // The exit value should be (End+A)/A. 2548 APInt ExitVal = (End + A).udiv(A); 2549 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2550 2551 // Evaluate at the exit value. If we really did fall out of the valid 2552 // range, then we computed our trip count, otherwise wrap around or other 2553 // things must have happened. 2554 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2555 if (Range.contains(Val->getValue())) 2556 return new SCEVCouldNotCompute(); // Something strange happened 2557 2558 // Ensure that the previous value is in the range. This is a sanity check. 2559 assert(Range.contains( 2560 EvaluateConstantChrecAtConstant(this, 2561 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2562 "Linear scev computation is off in a bad way!"); 2563 return SE.getConstant(ExitValue); 2564 } else if (isQuadratic()) { 2565 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2566 // quadratic equation to solve it. To do this, we must frame our problem in 2567 // terms of figuring out when zero is crossed, instead of when 2568 // Range.getUpper() is crossed. 2569 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2570 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2571 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2572 2573 // Next, solve the constructed addrec 2574 std::pair<SCEVHandle,SCEVHandle> Roots = 2575 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2576 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2577 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2578 if (R1) { 2579 // Pick the smallest positive root value. 2580 if (ConstantInt *CB = 2581 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2582 R1->getValue(), R2->getValue()))) { 2583 if (CB->getZExtValue() == false) 2584 std::swap(R1, R2); // R1 is the minimum root now. 2585 2586 // Make sure the root is not off by one. The returned iteration should 2587 // not be in the range, but the previous one should be. When solving 2588 // for "X*X < 5", for example, we should not return a root of 2. 2589 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2590 R1->getValue(), 2591 SE); 2592 if (Range.contains(R1Val->getValue())) { 2593 // The next iteration must be out of the range... 2594 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2595 2596 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2597 if (!Range.contains(R1Val->getValue())) 2598 return SE.getConstant(NextVal); 2599 return new SCEVCouldNotCompute(); // Something strange happened 2600 } 2601 2602 // If R1 was not in the range, then it is a good return value. Make 2603 // sure that R1-1 WAS in the range though, just in case. 2604 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2605 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2606 if (Range.contains(R1Val->getValue())) 2607 return R1; 2608 return new SCEVCouldNotCompute(); // Something strange happened 2609 } 2610 } 2611 } 2612 2613 // Fallback, if this is a general polynomial, figure out the progression 2614 // through brute force: evaluate until we find an iteration that fails the 2615 // test. This is likely to be slow, but getting an accurate trip count is 2616 // incredibly important, we will be able to simplify the exit test a lot, and 2617 // we are almost guaranteed to get a trip count in this case. 2618 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2619 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2620 do { 2621 ++NumBruteForceEvaluations; 2622 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2623 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2624 return new SCEVCouldNotCompute(); 2625 2626 // Check to see if we found the value! 2627 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2628 return SE.getConstant(TestVal); 2629 2630 // Increment to test the next index. 2631 TestVal = ConstantInt::get(TestVal->getValue()+1); 2632 } while (TestVal != EndVal); 2633 2634 return new SCEVCouldNotCompute(); 2635} 2636 2637 2638 2639//===----------------------------------------------------------------------===// 2640// ScalarEvolution Class Implementation 2641//===----------------------------------------------------------------------===// 2642 2643bool ScalarEvolution::runOnFunction(Function &F) { 2644 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2645 return false; 2646} 2647 2648void ScalarEvolution::releaseMemory() { 2649 delete (ScalarEvolutionsImpl*)Impl; 2650 Impl = 0; 2651} 2652 2653void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2654 AU.setPreservesAll(); 2655 AU.addRequiredTransitive<LoopInfo>(); 2656} 2657 2658SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2659 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2660} 2661 2662/// hasSCEV - Return true if the SCEV for this value has already been 2663/// computed. 2664bool ScalarEvolution::hasSCEV(Value *V) const { 2665 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2666} 2667 2668 2669/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2670/// the specified value. 2671void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2672 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2673} 2674 2675 2676SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2677 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2678} 2679 2680bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2681 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2682} 2683 2684SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2685 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2686} 2687 2688void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2689 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2690} 2691 2692static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2693 const Loop *L) { 2694 // Print all inner loops first 2695 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2696 PrintLoopInfo(OS, SE, *I); 2697 2698 cerr << "Loop " << L->getHeader()->getName() << ": "; 2699 2700 SmallVector<BasicBlock*, 8> ExitBlocks; 2701 L->getExitBlocks(ExitBlocks); 2702 if (ExitBlocks.size() != 1) 2703 cerr << "<multiple exits> "; 2704 2705 if (SE->hasLoopInvariantIterationCount(L)) { 2706 cerr << *SE->getIterationCount(L) << " iterations! "; 2707 } else { 2708 cerr << "Unpredictable iteration count. "; 2709 } 2710 2711 cerr << "\n"; 2712} 2713 2714void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2715 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2716 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2717 2718 OS << "Classifying expressions for: " << F.getName() << "\n"; 2719 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2720 if (I->getType()->isInteger()) { 2721 OS << *I; 2722 OS << " --> "; 2723 SCEVHandle SV = getSCEV(&*I); 2724 SV->print(OS); 2725 OS << "\t\t"; 2726 2727 if ((*I).getType()->isInteger()) { 2728 ConstantRange Bounds = SV->getValueRange(); 2729 if (!Bounds.isFullSet()) 2730 OS << "Bounds: " << Bounds << " "; 2731 } 2732 2733 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2734 OS << "Exits: "; 2735 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2736 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2737 OS << "<<Unknown>>"; 2738 } else { 2739 OS << *ExitValue; 2740 } 2741 } 2742 2743 2744 OS << "\n"; 2745 } 2746 2747 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2748 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2749 PrintLoopInfo(OS, this, *I); 2750} 2751