ScalarEvolution.cpp revision 9a2f93121b31bf6345d1552bdc43037f89714d86
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source 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) const { 158 return this; 159} 160 161void SCEVCouldNotCompute::print(std::ostream &OS) const { 162 OS << "***COULDNOTCOMPUTE***"; 163} 164 165bool SCEVCouldNotCompute::classof(const SCEV *S) { 166 return S->getSCEVType() == scCouldNotCompute; 167} 168 169 170// SCEVConstants - Only allow the creation of one SCEVConstant for any 171// particular value. Don't use a SCEVHandle here, or else the object will 172// never be deleted! 173static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 174 175 176SCEVConstant::~SCEVConstant() { 177 SCEVConstants->erase(V); 178} 179 180SCEVHandle SCEVConstant::get(ConstantInt *V) { 181 SCEVConstant *&R = (*SCEVConstants)[V]; 182 if (R == 0) R = new SCEVConstant(V); 183 return R; 184} 185 186SCEVHandle SCEVConstant::get(const APInt& Val) { 187 return get(ConstantInt::get(Val)); 188} 189 190ConstantRange SCEVConstant::getValueRange() const { 191 return ConstantRange(V->getValue()); 192} 193 194const Type *SCEVConstant::getType() const { return V->getType(); } 195 196void SCEVConstant::print(std::ostream &OS) const { 197 WriteAsOperand(OS, V, false); 198} 199 200// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 201// particular input. Don't use a SCEVHandle here, or else the object will 202// never be deleted! 203static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 204 SCEVTruncateExpr*> > SCEVTruncates; 205 206SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 207 : SCEV(scTruncate), Op(op), Ty(ty) { 208 assert(Op->getType()->isInteger() && Ty->isInteger() && 209 "Cannot truncate non-integer value!"); 210 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 211 && "This is not a truncating conversion!"); 212} 213 214SCEVTruncateExpr::~SCEVTruncateExpr() { 215 SCEVTruncates->erase(std::make_pair(Op, Ty)); 216} 217 218ConstantRange SCEVTruncateExpr::getValueRange() const { 219 return getOperand()->getValueRange().truncate(getBitWidth()); 220} 221 222void SCEVTruncateExpr::print(std::ostream &OS) const { 223 OS << "(truncate " << *Op << " to " << *Ty << ")"; 224} 225 226// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 227// particular input. Don't use a SCEVHandle here, or else the object will never 228// be deleted! 229static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 230 SCEVZeroExtendExpr*> > SCEVZeroExtends; 231 232SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 233 : SCEV(scZeroExtend), Op(op), Ty(ty) { 234 assert(Op->getType()->isInteger() && Ty->isInteger() && 235 "Cannot zero extend non-integer value!"); 236 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 237 && "This is not an extending conversion!"); 238} 239 240SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 241 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 242} 243 244ConstantRange SCEVZeroExtendExpr::getValueRange() const { 245 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 246} 247 248void SCEVZeroExtendExpr::print(std::ostream &OS) const { 249 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 250} 251 252// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 253// particular input. Don't use a SCEVHandle here, or else the object will never 254// be deleted! 255static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 256 SCEVSignExtendExpr*> > SCEVSignExtends; 257 258SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 259 : SCEV(scSignExtend), Op(op), Ty(ty) { 260 assert(Op->getType()->isInteger() && Ty->isInteger() && 261 "Cannot sign extend non-integer value!"); 262 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 263 && "This is not an extending conversion!"); 264} 265 266SCEVSignExtendExpr::~SCEVSignExtendExpr() { 267 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 268} 269 270ConstantRange SCEVSignExtendExpr::getValueRange() const { 271 return getOperand()->getValueRange().signExtend(getBitWidth()); 272} 273 274void SCEVSignExtendExpr::print(std::ostream &OS) const { 275 OS << "(signextend " << *Op << " to " << *Ty << ")"; 276} 277 278// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 279// particular input. Don't use a SCEVHandle here, or else the object will never 280// be deleted! 281static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 282 SCEVCommutativeExpr*> > SCEVCommExprs; 283 284SCEVCommutativeExpr::~SCEVCommutativeExpr() { 285 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 286 std::vector<SCEV*>(Operands.begin(), 287 Operands.end()))); 288} 289 290void SCEVCommutativeExpr::print(std::ostream &OS) const { 291 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 292 const char *OpStr = getOperationStr(); 293 OS << "(" << *Operands[0]; 294 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 295 OS << OpStr << *Operands[i]; 296 OS << ")"; 297} 298 299SCEVHandle SCEVCommutativeExpr:: 300replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 301 const SCEVHandle &Conc) const { 302 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 303 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 304 if (H != getOperand(i)) { 305 std::vector<SCEVHandle> NewOps; 306 NewOps.reserve(getNumOperands()); 307 for (unsigned j = 0; j != i; ++j) 308 NewOps.push_back(getOperand(j)); 309 NewOps.push_back(H); 310 for (++i; i != e; ++i) 311 NewOps.push_back(getOperand(i)-> 312 replaceSymbolicValuesWithConcrete(Sym, Conc)); 313 314 if (isa<SCEVAddExpr>(this)) 315 return SCEVAddExpr::get(NewOps); 316 else if (isa<SCEVMulExpr>(this)) 317 return SCEVMulExpr::get(NewOps); 318 else 319 assert(0 && "Unknown commutative expr!"); 320 } 321 } 322 return this; 323} 324 325 326// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 327// input. Don't use a SCEVHandle here, or else the object will never be 328// deleted! 329static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 330 SCEVSDivExpr*> > SCEVSDivs; 331 332SCEVSDivExpr::~SCEVSDivExpr() { 333 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 334} 335 336void SCEVSDivExpr::print(std::ostream &OS) const { 337 OS << "(" << *LHS << " /s " << *RHS << ")"; 338} 339 340const Type *SCEVSDivExpr::getType() const { 341 return LHS->getType(); 342} 343 344// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 345// particular input. Don't use a SCEVHandle here, or else the object will never 346// be deleted! 347static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 348 SCEVAddRecExpr*> > SCEVAddRecExprs; 349 350SCEVAddRecExpr::~SCEVAddRecExpr() { 351 SCEVAddRecExprs->erase(std::make_pair(L, 352 std::vector<SCEV*>(Operands.begin(), 353 Operands.end()))); 354} 355 356SCEVHandle SCEVAddRecExpr:: 357replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 358 const SCEVHandle &Conc) const { 359 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 360 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 361 if (H != getOperand(i)) { 362 std::vector<SCEVHandle> NewOps; 363 NewOps.reserve(getNumOperands()); 364 for (unsigned j = 0; j != i; ++j) 365 NewOps.push_back(getOperand(j)); 366 NewOps.push_back(H); 367 for (++i; i != e; ++i) 368 NewOps.push_back(getOperand(i)-> 369 replaceSymbolicValuesWithConcrete(Sym, Conc)); 370 371 return get(NewOps, L); 372 } 373 } 374 return this; 375} 376 377 378bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 379 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 380 // contain L and if the start is invariant. 381 return !QueryLoop->contains(L->getHeader()) && 382 getOperand(0)->isLoopInvariant(QueryLoop); 383} 384 385 386void SCEVAddRecExpr::print(std::ostream &OS) const { 387 OS << "{" << *Operands[0]; 388 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 389 OS << ",+," << *Operands[i]; 390 OS << "}<" << L->getHeader()->getName() + ">"; 391} 392 393// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 394// value. Don't use a SCEVHandle here, or else the object will never be 395// deleted! 396static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 397 398SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 399 400bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 401 // All non-instruction values are loop invariant. All instructions are loop 402 // invariant if they are not contained in the specified loop. 403 if (Instruction *I = dyn_cast<Instruction>(V)) 404 return !L->contains(I->getParent()); 405 return true; 406} 407 408const Type *SCEVUnknown::getType() const { 409 return V->getType(); 410} 411 412void SCEVUnknown::print(std::ostream &OS) const { 413 WriteAsOperand(OS, V, false); 414} 415 416//===----------------------------------------------------------------------===// 417// SCEV Utilities 418//===----------------------------------------------------------------------===// 419 420namespace { 421 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 422 /// than the complexity of the RHS. This comparator is used to canonicalize 423 /// expressions. 424 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 425 bool operator()(SCEV *LHS, SCEV *RHS) { 426 return LHS->getSCEVType() < RHS->getSCEVType(); 427 } 428 }; 429} 430 431/// GroupByComplexity - Given a list of SCEV objects, order them by their 432/// complexity, and group objects of the same complexity together by value. 433/// When this routine is finished, we know that any duplicates in the vector are 434/// consecutive and that complexity is monotonically increasing. 435/// 436/// Note that we go take special precautions to ensure that we get determinstic 437/// results from this routine. In other words, we don't want the results of 438/// this to depend on where the addresses of various SCEV objects happened to 439/// land in memory. 440/// 441static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 442 if (Ops.size() < 2) return; // Noop 443 if (Ops.size() == 2) { 444 // This is the common case, which also happens to be trivially simple. 445 // Special case it. 446 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 447 std::swap(Ops[0], Ops[1]); 448 return; 449 } 450 451 // Do the rough sort by complexity. 452 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 453 454 // Now that we are sorted by complexity, group elements of the same 455 // complexity. Note that this is, at worst, N^2, but the vector is likely to 456 // be extremely short in practice. Note that we take this approach because we 457 // do not want to depend on the addresses of the objects we are grouping. 458 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 459 SCEV *S = Ops[i]; 460 unsigned Complexity = S->getSCEVType(); 461 462 // If there are any objects of the same complexity and same value as this 463 // one, group them. 464 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 465 if (Ops[j] == S) { // Found a duplicate. 466 // Move it to immediately after i'th element. 467 std::swap(Ops[i+1], Ops[j]); 468 ++i; // no need to rescan it. 469 if (i == e-2) return; // Done! 470 } 471 } 472 } 473} 474 475 476 477//===----------------------------------------------------------------------===// 478// Simple SCEV method implementations 479//===----------------------------------------------------------------------===// 480 481/// getIntegerSCEV - Given an integer or FP type, create a constant for the 482/// specified signed integer value and return a SCEV for the constant. 483SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 484 Constant *C; 485 if (Val == 0) 486 C = Constant::getNullValue(Ty); 487 else if (Ty->isFloatingPoint()) 488 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 489 APFloat::IEEEdouble, Val)); 490 else 491 C = ConstantInt::get(Ty, Val); 492 return SCEVUnknown::get(C); 493} 494 495/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 496/// input value to the specified type. If the type must be extended, it is zero 497/// extended. 498static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 499 const Type *SrcTy = V->getType(); 500 assert(SrcTy->isInteger() && Ty->isInteger() && 501 "Cannot truncate or zero extend with non-integer arguments!"); 502 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 503 return V; // No conversion 504 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 505 return SCEVTruncateExpr::get(V, Ty); 506 return SCEVZeroExtendExpr::get(V, Ty); 507} 508 509/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 510/// 511SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 512 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 513 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 514 515 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 516} 517 518/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 519/// 520SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 521 // X - Y --> X + -Y 522 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 523} 524 525 526/// PartialFact - Compute V!/(V-NumSteps)! 527static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 528 // Handle this case efficiently, it is common to have constant iteration 529 // counts while computing loop exit values. 530 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 531 const APInt& Val = SC->getValue()->getValue(); 532 APInt Result(Val.getBitWidth(), 1); 533 for (; NumSteps; --NumSteps) 534 Result *= Val-(NumSteps-1); 535 return SCEVConstant::get(Result); 536 } 537 538 const Type *Ty = V->getType(); 539 if (NumSteps == 0) 540 return SCEVUnknown::getIntegerSCEV(1, Ty); 541 542 SCEVHandle Result = V; 543 for (unsigned i = 1; i != NumSteps; ++i) 544 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 545 SCEVUnknown::getIntegerSCEV(i, Ty))); 546 return Result; 547} 548 549 550/// evaluateAtIteration - Return the value of this chain of recurrences at 551/// the specified iteration number. We can evaluate this recurrence by 552/// multiplying each element in the chain by the binomial coefficient 553/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 554/// 555/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 556/// 557/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 558/// Is the binomial equation safe using modular arithmetic?? 559/// 560SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 561 SCEVHandle Result = getStart(); 562 int Divisor = 1; 563 const Type *Ty = It->getType(); 564 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 565 SCEVHandle BC = PartialFact(It, i); 566 Divisor *= i; 567 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 568 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 569 Result = SCEVAddExpr::get(Result, Val); 570 } 571 return Result; 572} 573 574 575//===----------------------------------------------------------------------===// 576// SCEV Expression folder implementations 577//===----------------------------------------------------------------------===// 578 579SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 580 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 581 return SCEVUnknown::get( 582 ConstantExpr::getTrunc(SC->getValue(), Ty)); 583 584 // If the input value is a chrec scev made out of constants, truncate 585 // all of the constants. 586 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 587 std::vector<SCEVHandle> Operands; 588 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 589 // FIXME: This should allow truncation of other expression types! 590 if (isa<SCEVConstant>(AddRec->getOperand(i))) 591 Operands.push_back(get(AddRec->getOperand(i), Ty)); 592 else 593 break; 594 if (Operands.size() == AddRec->getNumOperands()) 595 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 596 } 597 598 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 599 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 600 return Result; 601} 602 603SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 604 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 605 return SCEVUnknown::get( 606 ConstantExpr::getZExt(SC->getValue(), Ty)); 607 608 // FIXME: If the input value is a chrec scev, and we can prove that the value 609 // did not overflow the old, smaller, value, we can zero extend all of the 610 // operands (often constants). This would allow analysis of something like 611 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 612 613 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 614 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 615 return Result; 616} 617 618SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 619 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 620 return SCEVUnknown::get( 621 ConstantExpr::getSExt(SC->getValue(), Ty)); 622 623 // FIXME: If the input value is a chrec scev, and we can prove that the value 624 // did not overflow the old, smaller, value, we can sign extend all of the 625 // operands (often constants). This would allow analysis of something like 626 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 627 628 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 629 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 630 return Result; 631} 632 633// get - Get a canonical add expression, or something simpler if possible. 634SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 635 assert(!Ops.empty() && "Cannot get empty add!"); 636 if (Ops.size() == 1) return Ops[0]; 637 638 // Sort by complexity, this groups all similar expression types together. 639 GroupByComplexity(Ops); 640 641 // If there are any constants, fold them together. 642 unsigned Idx = 0; 643 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 644 ++Idx; 645 assert(Idx < Ops.size()); 646 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 647 // We found two constants, fold them together! 648 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 649 RHSC->getValue()->getValue()); 650 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 651 Ops[0] = SCEVConstant::get(CI); 652 Ops.erase(Ops.begin()+1); // Erase the folded element 653 if (Ops.size() == 1) return Ops[0]; 654 LHSC = cast<SCEVConstant>(Ops[0]); 655 } else { 656 // If we couldn't fold the expression, move to the next constant. Note 657 // that this is impossible to happen in practice because we always 658 // constant fold constant ints to constant ints. 659 ++Idx; 660 } 661 } 662 663 // If we are left with a constant zero being added, strip it off. 664 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 665 Ops.erase(Ops.begin()); 666 --Idx; 667 } 668 } 669 670 if (Ops.size() == 1) return Ops[0]; 671 672 // Okay, check to see if the same value occurs in the operand list twice. If 673 // so, merge them together into an multiply expression. Since we sorted the 674 // list, these values are required to be adjacent. 675 const Type *Ty = Ops[0]->getType(); 676 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 677 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 678 // Found a match, merge the two values into a multiply, and add any 679 // remaining values to the result. 680 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 681 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 682 if (Ops.size() == 2) 683 return Mul; 684 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 685 Ops.push_back(Mul); 686 return SCEVAddExpr::get(Ops); 687 } 688 689 // Now we know the first non-constant operand. Skip past any cast SCEVs. 690 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 691 ++Idx; 692 693 // If there are add operands they would be next. 694 if (Idx < Ops.size()) { 695 bool DeletedAdd = false; 696 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 697 // If we have an add, expand the add operands onto the end of the operands 698 // list. 699 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 700 Ops.erase(Ops.begin()+Idx); 701 DeletedAdd = true; 702 } 703 704 // If we deleted at least one add, we added operands to the end of the list, 705 // and they are not necessarily sorted. Recurse to resort and resimplify 706 // any operands we just aquired. 707 if (DeletedAdd) 708 return get(Ops); 709 } 710 711 // Skip over the add expression until we get to a multiply. 712 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 713 ++Idx; 714 715 // If we are adding something to a multiply expression, make sure the 716 // something is not already an operand of the multiply. If so, merge it into 717 // the multiply. 718 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 719 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 720 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 721 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 722 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 723 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 724 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 725 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 726 if (Mul->getNumOperands() != 2) { 727 // If the multiply has more than two operands, we must get the 728 // Y*Z term. 729 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 730 MulOps.erase(MulOps.begin()+MulOp); 731 InnerMul = SCEVMulExpr::get(MulOps); 732 } 733 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 734 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 735 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 736 if (Ops.size() == 2) return OuterMul; 737 if (AddOp < Idx) { 738 Ops.erase(Ops.begin()+AddOp); 739 Ops.erase(Ops.begin()+Idx-1); 740 } else { 741 Ops.erase(Ops.begin()+Idx); 742 Ops.erase(Ops.begin()+AddOp-1); 743 } 744 Ops.push_back(OuterMul); 745 return SCEVAddExpr::get(Ops); 746 } 747 748 // Check this multiply against other multiplies being added together. 749 for (unsigned OtherMulIdx = Idx+1; 750 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 751 ++OtherMulIdx) { 752 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 753 // If MulOp occurs in OtherMul, we can fold the two multiplies 754 // together. 755 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 756 OMulOp != e; ++OMulOp) 757 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 758 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 759 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 760 if (Mul->getNumOperands() != 2) { 761 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 762 MulOps.erase(MulOps.begin()+MulOp); 763 InnerMul1 = SCEVMulExpr::get(MulOps); 764 } 765 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 766 if (OtherMul->getNumOperands() != 2) { 767 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 768 OtherMul->op_end()); 769 MulOps.erase(MulOps.begin()+OMulOp); 770 InnerMul2 = SCEVMulExpr::get(MulOps); 771 } 772 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 773 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 774 if (Ops.size() == 2) return OuterMul; 775 Ops.erase(Ops.begin()+Idx); 776 Ops.erase(Ops.begin()+OtherMulIdx-1); 777 Ops.push_back(OuterMul); 778 return SCEVAddExpr::get(Ops); 779 } 780 } 781 } 782 } 783 784 // If there are any add recurrences in the operands list, see if any other 785 // added values are loop invariant. If so, we can fold them into the 786 // recurrence. 787 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 788 ++Idx; 789 790 // Scan over all recurrences, trying to fold loop invariants into them. 791 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 792 // Scan all of the other operands to this add and add them to the vector if 793 // they are loop invariant w.r.t. the recurrence. 794 std::vector<SCEVHandle> LIOps; 795 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 796 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 797 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 798 LIOps.push_back(Ops[i]); 799 Ops.erase(Ops.begin()+i); 800 --i; --e; 801 } 802 803 // If we found some loop invariants, fold them into the recurrence. 804 if (!LIOps.empty()) { 805 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 806 LIOps.push_back(AddRec->getStart()); 807 808 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 809 AddRecOps[0] = SCEVAddExpr::get(LIOps); 810 811 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 812 // If all of the other operands were loop invariant, we are done. 813 if (Ops.size() == 1) return NewRec; 814 815 // Otherwise, add the folded AddRec by the non-liv parts. 816 for (unsigned i = 0;; ++i) 817 if (Ops[i] == AddRec) { 818 Ops[i] = NewRec; 819 break; 820 } 821 return SCEVAddExpr::get(Ops); 822 } 823 824 // Okay, if there weren't any loop invariants to be folded, check to see if 825 // there are multiple AddRec's with the same loop induction variable being 826 // added together. If so, we can fold them. 827 for (unsigned OtherIdx = Idx+1; 828 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 829 if (OtherIdx != Idx) { 830 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 831 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 832 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 833 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 834 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 835 if (i >= NewOps.size()) { 836 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 837 OtherAddRec->op_end()); 838 break; 839 } 840 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 841 } 842 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 843 844 if (Ops.size() == 2) return NewAddRec; 845 846 Ops.erase(Ops.begin()+Idx); 847 Ops.erase(Ops.begin()+OtherIdx-1); 848 Ops.push_back(NewAddRec); 849 return SCEVAddExpr::get(Ops); 850 } 851 } 852 853 // Otherwise couldn't fold anything into this recurrence. Move onto the 854 // next one. 855 } 856 857 // Okay, it looks like we really DO need an add expr. Check to see if we 858 // already have one, otherwise create a new one. 859 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 860 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 861 SCEVOps)]; 862 if (Result == 0) Result = new SCEVAddExpr(Ops); 863 return Result; 864} 865 866 867SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 868 assert(!Ops.empty() && "Cannot get empty mul!"); 869 870 // Sort by complexity, this groups all similar expression types together. 871 GroupByComplexity(Ops); 872 873 // If there are any constants, fold them together. 874 unsigned Idx = 0; 875 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 876 877 // C1*(C2+V) -> C1*C2 + C1*V 878 if (Ops.size() == 2) 879 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 880 if (Add->getNumOperands() == 2 && 881 isa<SCEVConstant>(Add->getOperand(0))) 882 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 883 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 884 885 886 ++Idx; 887 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 888 // We found two constants, fold them together! 889 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 890 RHSC->getValue()->getValue()); 891 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 892 Ops[0] = SCEVConstant::get(CI); 893 Ops.erase(Ops.begin()+1); // Erase the folded element 894 if (Ops.size() == 1) return Ops[0]; 895 LHSC = cast<SCEVConstant>(Ops[0]); 896 } else { 897 // If we couldn't fold the expression, move to the next constant. Note 898 // that this is impossible to happen in practice because we always 899 // constant fold constant ints to constant ints. 900 ++Idx; 901 } 902 } 903 904 // If we are left with a constant one being multiplied, strip it off. 905 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 906 Ops.erase(Ops.begin()); 907 --Idx; 908 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 909 // If we have a multiply of zero, it will always be zero. 910 return Ops[0]; 911 } 912 } 913 914 // Skip over the add expression until we get to a multiply. 915 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 916 ++Idx; 917 918 if (Ops.size() == 1) 919 return Ops[0]; 920 921 // If there are mul operands inline them all into this expression. 922 if (Idx < Ops.size()) { 923 bool DeletedMul = false; 924 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 925 // If we have an mul, expand the mul operands onto the end of the operands 926 // list. 927 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 928 Ops.erase(Ops.begin()+Idx); 929 DeletedMul = true; 930 } 931 932 // If we deleted at least one mul, we added operands to the end of the list, 933 // and they are not necessarily sorted. Recurse to resort and resimplify 934 // any operands we just aquired. 935 if (DeletedMul) 936 return get(Ops); 937 } 938 939 // If there are any add recurrences in the operands list, see if any other 940 // added values are loop invariant. If so, we can fold them into the 941 // recurrence. 942 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 943 ++Idx; 944 945 // Scan over all recurrences, trying to fold loop invariants into them. 946 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 947 // Scan all of the other operands to this mul and add them to the vector if 948 // they are loop invariant w.r.t. the recurrence. 949 std::vector<SCEVHandle> LIOps; 950 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 951 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 952 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 953 LIOps.push_back(Ops[i]); 954 Ops.erase(Ops.begin()+i); 955 --i; --e; 956 } 957 958 // If we found some loop invariants, fold them into the recurrence. 959 if (!LIOps.empty()) { 960 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 961 std::vector<SCEVHandle> NewOps; 962 NewOps.reserve(AddRec->getNumOperands()); 963 if (LIOps.size() == 1) { 964 SCEV *Scale = LIOps[0]; 965 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 966 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 967 } else { 968 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 969 std::vector<SCEVHandle> MulOps(LIOps); 970 MulOps.push_back(AddRec->getOperand(i)); 971 NewOps.push_back(SCEVMulExpr::get(MulOps)); 972 } 973 } 974 975 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 976 977 // If all of the other operands were loop invariant, we are done. 978 if (Ops.size() == 1) return NewRec; 979 980 // Otherwise, multiply the folded AddRec by the non-liv parts. 981 for (unsigned i = 0;; ++i) 982 if (Ops[i] == AddRec) { 983 Ops[i] = NewRec; 984 break; 985 } 986 return SCEVMulExpr::get(Ops); 987 } 988 989 // Okay, if there weren't any loop invariants to be folded, check to see if 990 // there are multiple AddRec's with the same loop induction variable being 991 // multiplied together. If so, we can fold them. 992 for (unsigned OtherIdx = Idx+1; 993 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 994 if (OtherIdx != Idx) { 995 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 996 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 997 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 998 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 999 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 1000 G->getStart()); 1001 SCEVHandle B = F->getStepRecurrence(); 1002 SCEVHandle D = G->getStepRecurrence(); 1003 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 1004 SCEVMulExpr::get(G, B), 1005 SCEVMulExpr::get(B, D)); 1006 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 1007 F->getLoop()); 1008 if (Ops.size() == 2) return NewAddRec; 1009 1010 Ops.erase(Ops.begin()+Idx); 1011 Ops.erase(Ops.begin()+OtherIdx-1); 1012 Ops.push_back(NewAddRec); 1013 return SCEVMulExpr::get(Ops); 1014 } 1015 } 1016 1017 // Otherwise couldn't fold anything into this recurrence. Move onto the 1018 // next one. 1019 } 1020 1021 // Okay, it looks like we really DO need an mul expr. Check to see if we 1022 // already have one, otherwise create a new one. 1023 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1024 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1025 SCEVOps)]; 1026 if (Result == 0) 1027 Result = new SCEVMulExpr(Ops); 1028 return Result; 1029} 1030 1031SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1032 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1033 if (RHSC->getValue()->equalsInt(1)) 1034 return LHS; // X sdiv 1 --> x 1035 if (RHSC->getValue()->isAllOnesValue()) 1036 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 1037 1038 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1039 Constant *LHSCV = LHSC->getValue(); 1040 Constant *RHSCV = RHSC->getValue(); 1041 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 1042 } 1043 } 1044 1045 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1046 1047 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 1048 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1049 return Result; 1050} 1051 1052 1053/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1054/// specified loop. Simplify the expression as much as possible. 1055SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1056 const SCEVHandle &Step, const Loop *L) { 1057 std::vector<SCEVHandle> Operands; 1058 Operands.push_back(Start); 1059 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1060 if (StepChrec->getLoop() == L) { 1061 Operands.insert(Operands.end(), StepChrec->op_begin(), 1062 StepChrec->op_end()); 1063 return get(Operands, L); 1064 } 1065 1066 Operands.push_back(Step); 1067 return get(Operands, L); 1068} 1069 1070/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1071/// specified loop. Simplify the expression as much as possible. 1072SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1073 const Loop *L) { 1074 if (Operands.size() == 1) return Operands[0]; 1075 1076 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1077 if (StepC->getValue()->isZero()) { 1078 Operands.pop_back(); 1079 return get(Operands, L); // { X,+,0 } --> X 1080 } 1081 1082 SCEVAddRecExpr *&Result = 1083 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1084 Operands.end()))]; 1085 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1086 return Result; 1087} 1088 1089SCEVHandle SCEVUnknown::get(Value *V) { 1090 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1091 return SCEVConstant::get(CI); 1092 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1093 if (Result == 0) Result = new SCEVUnknown(V); 1094 return Result; 1095} 1096 1097 1098//===----------------------------------------------------------------------===// 1099// ScalarEvolutionsImpl Definition and Implementation 1100//===----------------------------------------------------------------------===// 1101// 1102/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1103/// evolution code. 1104/// 1105namespace { 1106 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1107 /// F - The function we are analyzing. 1108 /// 1109 Function &F; 1110 1111 /// LI - The loop information for the function we are currently analyzing. 1112 /// 1113 LoopInfo &LI; 1114 1115 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1116 /// things. 1117 SCEVHandle UnknownValue; 1118 1119 /// Scalars - This is a cache of the scalars we have analyzed so far. 1120 /// 1121 std::map<Value*, SCEVHandle> Scalars; 1122 1123 /// IterationCounts - Cache the iteration count of the loops for this 1124 /// function as they are computed. 1125 std::map<const Loop*, SCEVHandle> IterationCounts; 1126 1127 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1128 /// the PHI instructions that we attempt to compute constant evolutions for. 1129 /// This allows us to avoid potentially expensive recomputation of these 1130 /// properties. An instruction maps to null if we are unable to compute its 1131 /// exit value. 1132 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1133 1134 public: 1135 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1136 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1137 1138 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1139 /// expression and create a new one. 1140 SCEVHandle getSCEV(Value *V); 1141 1142 /// hasSCEV - Return true if the SCEV for this value has already been 1143 /// computed. 1144 bool hasSCEV(Value *V) const { 1145 return Scalars.count(V); 1146 } 1147 1148 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1149 /// the specified value. 1150 void setSCEV(Value *V, const SCEVHandle &H) { 1151 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1152 assert(isNew && "This entry already existed!"); 1153 } 1154 1155 1156 /// getSCEVAtScope - Compute the value of the specified expression within 1157 /// the indicated loop (which may be null to indicate in no loop). If the 1158 /// expression cannot be evaluated, return UnknownValue itself. 1159 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1160 1161 1162 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1163 /// an analyzable loop-invariant iteration count. 1164 bool hasLoopInvariantIterationCount(const Loop *L); 1165 1166 /// getIterationCount - If the specified loop has a predictable iteration 1167 /// count, return it. Note that it is not valid to call this method on a 1168 /// loop without a loop-invariant iteration count. 1169 SCEVHandle getIterationCount(const Loop *L); 1170 1171 /// deleteValueFromRecords - This method should be called by the 1172 /// client before it removes a value from the program, to make sure 1173 /// that no dangling references are left around. 1174 void deleteValueFromRecords(Value *V); 1175 1176 private: 1177 /// createSCEV - We know that there is no SCEV for the specified value. 1178 /// Analyze the expression. 1179 SCEVHandle createSCEV(Value *V); 1180 1181 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1182 /// SCEVs. 1183 SCEVHandle createNodeForPHI(PHINode *PN); 1184 1185 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1186 /// for the specified instruction and replaces any references to the 1187 /// symbolic value SymName with the specified value. This is used during 1188 /// PHI resolution. 1189 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1190 const SCEVHandle &SymName, 1191 const SCEVHandle &NewVal); 1192 1193 /// ComputeIterationCount - Compute the number of times the specified loop 1194 /// will iterate. 1195 SCEVHandle ComputeIterationCount(const Loop *L); 1196 1197 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1198 /// 'setcc load X, cst', try to see if we can compute the trip count. 1199 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1200 Constant *RHS, 1201 const Loop *L, 1202 ICmpInst::Predicate p); 1203 1204 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1205 /// constant number of times (the condition evolves only from constants), 1206 /// try to evaluate a few iterations of the loop until we get the exit 1207 /// condition gets a value of ExitWhen (true or false). If we cannot 1208 /// evaluate the trip count of the loop, return UnknownValue. 1209 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1210 bool ExitWhen); 1211 1212 /// HowFarToZero - Return the number of times a backedge comparing the 1213 /// specified value to zero will execute. If not computable, return 1214 /// UnknownValue. 1215 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1216 1217 /// HowFarToNonZero - Return the number of times a backedge checking the 1218 /// specified value for nonzero will execute. If not computable, return 1219 /// UnknownValue. 1220 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1221 1222 /// HowManyLessThans - Return the number of times a backedge containing the 1223 /// specified less-than comparison will execute. If not computable, return 1224 /// UnknownValue. isSigned specifies whether the less-than is signed. 1225 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1226 bool isSigned); 1227 1228 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1229 /// in the header of its containing loop, we know the loop executes a 1230 /// constant number of times, and the PHI node is just a recurrence 1231 /// involving constants, fold it. 1232 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1233 const Loop *L); 1234 }; 1235} 1236 1237//===----------------------------------------------------------------------===// 1238// Basic SCEV Analysis and PHI Idiom Recognition Code 1239// 1240 1241/// deleteValueFromRecords - This method should be called by the 1242/// client before it removes an instruction from the program, to make sure 1243/// that no dangling references are left around. 1244void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1245 SmallVector<Value *, 16> Worklist; 1246 1247 if (Scalars.erase(V)) { 1248 if (PHINode *PN = dyn_cast<PHINode>(V)) 1249 ConstantEvolutionLoopExitValue.erase(PN); 1250 Worklist.push_back(V); 1251 } 1252 1253 while (!Worklist.empty()) { 1254 Value *VV = Worklist.back(); 1255 Worklist.pop_back(); 1256 1257 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1258 UI != UE; ++UI) { 1259 Instruction *Inst = cast<Instruction>(*UI); 1260 if (Scalars.erase(Inst)) { 1261 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1262 ConstantEvolutionLoopExitValue.erase(PN); 1263 Worklist.push_back(Inst); 1264 } 1265 } 1266 } 1267} 1268 1269 1270/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1271/// expression and create a new one. 1272SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1273 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1274 1275 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1276 if (I != Scalars.end()) return I->second; 1277 SCEVHandle S = createSCEV(V); 1278 Scalars.insert(std::make_pair(V, S)); 1279 return S; 1280} 1281 1282/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1283/// the specified instruction and replaces any references to the symbolic value 1284/// SymName with the specified value. This is used during PHI resolution. 1285void ScalarEvolutionsImpl:: 1286ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1287 const SCEVHandle &NewVal) { 1288 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1289 if (SI == Scalars.end()) return; 1290 1291 SCEVHandle NV = 1292 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1293 if (NV == SI->second) return; // No change. 1294 1295 SI->second = NV; // Update the scalars map! 1296 1297 // Any instruction values that use this instruction might also need to be 1298 // updated! 1299 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1300 UI != E; ++UI) 1301 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1302} 1303 1304/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1305/// a loop header, making it a potential recurrence, or it doesn't. 1306/// 1307SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1308 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1309 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1310 if (L->getHeader() == PN->getParent()) { 1311 // If it lives in the loop header, it has two incoming values, one 1312 // from outside the loop, and one from inside. 1313 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1314 unsigned BackEdge = IncomingEdge^1; 1315 1316 // While we are analyzing this PHI node, handle its value symbolically. 1317 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1318 assert(Scalars.find(PN) == Scalars.end() && 1319 "PHI node already processed?"); 1320 Scalars.insert(std::make_pair(PN, SymbolicName)); 1321 1322 // Using this symbolic name for the PHI, analyze the value coming around 1323 // the back-edge. 1324 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1325 1326 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1327 // has a special value for the first iteration of the loop. 1328 1329 // If the value coming around the backedge is an add with the symbolic 1330 // value we just inserted, then we found a simple induction variable! 1331 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1332 // If there is a single occurrence of the symbolic value, replace it 1333 // with a recurrence. 1334 unsigned FoundIndex = Add->getNumOperands(); 1335 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1336 if (Add->getOperand(i) == SymbolicName) 1337 if (FoundIndex == e) { 1338 FoundIndex = i; 1339 break; 1340 } 1341 1342 if (FoundIndex != Add->getNumOperands()) { 1343 // Create an add with everything but the specified operand. 1344 std::vector<SCEVHandle> Ops; 1345 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1346 if (i != FoundIndex) 1347 Ops.push_back(Add->getOperand(i)); 1348 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1349 1350 // This is not a valid addrec if the step amount is varying each 1351 // loop iteration, but is not itself an addrec in this loop. 1352 if (Accum->isLoopInvariant(L) || 1353 (isa<SCEVAddRecExpr>(Accum) && 1354 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1355 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1356 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1357 1358 // Okay, for the entire analysis of this edge we assumed the PHI 1359 // to be symbolic. We now need to go back and update all of the 1360 // entries for the scalars that use the PHI (except for the PHI 1361 // itself) to use the new analyzed value instead of the "symbolic" 1362 // value. 1363 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1364 return PHISCEV; 1365 } 1366 } 1367 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1368 // Otherwise, this could be a loop like this: 1369 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1370 // In this case, j = {1,+,1} and BEValue is j. 1371 // Because the other in-value of i (0) fits the evolution of BEValue 1372 // i really is an addrec evolution. 1373 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1374 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1375 1376 // If StartVal = j.start - j.stride, we can use StartVal as the 1377 // initial step of the addrec evolution. 1378 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1379 AddRec->getOperand(1))) { 1380 SCEVHandle PHISCEV = 1381 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1382 1383 // Okay, for the entire analysis of this edge we assumed the PHI 1384 // to be symbolic. We now need to go back and update all of the 1385 // entries for the scalars that use the PHI (except for the PHI 1386 // itself) to use the new analyzed value instead of the "symbolic" 1387 // value. 1388 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1389 return PHISCEV; 1390 } 1391 } 1392 } 1393 1394 return SymbolicName; 1395 } 1396 1397 // If it's not a loop phi, we can't handle it yet. 1398 return SCEVUnknown::get(PN); 1399} 1400 1401/// GetConstantFactor - Determine the largest constant factor that S has. For 1402/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1403static APInt GetConstantFactor(SCEVHandle S) { 1404 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1405 const APInt& V = C->getValue()->getValue(); 1406 if (!V.isMinValue()) 1407 return V; 1408 else // Zero is a multiple of everything. 1409 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1); 1410 } 1411 1412 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) { 1413 return GetConstantFactor(T->getOperand()).trunc( 1414 cast<IntegerType>(T->getType())->getBitWidth()); 1415 } 1416 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1417 return GetConstantFactor(E->getOperand()).zext( 1418 cast<IntegerType>(E->getType())->getBitWidth()); 1419 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) 1420 return GetConstantFactor(E->getOperand()).sext( 1421 cast<IntegerType>(E->getType())->getBitWidth()); 1422 1423 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1424 // The result is the min of all operands. 1425 APInt Res(GetConstantFactor(A->getOperand(0))); 1426 for (unsigned i = 1, e = A->getNumOperands(); 1427 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) { 1428 APInt Tmp(GetConstantFactor(A->getOperand(i))); 1429 Res = APIntOps::umin(Res, Tmp); 1430 } 1431 return Res; 1432 } 1433 1434 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1435 // The result is the product of all the operands. 1436 APInt Res(GetConstantFactor(M->getOperand(0))); 1437 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) { 1438 APInt Tmp(GetConstantFactor(M->getOperand(i))); 1439 Res *= Tmp; 1440 } 1441 return Res; 1442 } 1443 1444 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1445 // For now, we just handle linear expressions. 1446 if (A->getNumOperands() == 2) { 1447 // We want the GCD between the start and the stride value. 1448 APInt Start(GetConstantFactor(A->getOperand(0))); 1449 if (Start == 1) 1450 return Start; 1451 APInt Stride(GetConstantFactor(A->getOperand(1))); 1452 return APIntOps::GreatestCommonDivisor(Start, Stride); 1453 } 1454 } 1455 1456 // SCEVSDivExpr, SCEVUnknown. 1457 return APInt(S->getBitWidth(), 1); 1458} 1459 1460/// createSCEV - We know that there is no SCEV for the specified value. 1461/// Analyze the expression. 1462/// 1463SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1464 if (Instruction *I = dyn_cast<Instruction>(V)) { 1465 switch (I->getOpcode()) { 1466 case Instruction::Add: 1467 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1468 getSCEV(I->getOperand(1))); 1469 case Instruction::Mul: 1470 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1471 getSCEV(I->getOperand(1))); 1472 case Instruction::SDiv: 1473 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1474 getSCEV(I->getOperand(1))); 1475 break; 1476 1477 case Instruction::Sub: 1478 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1479 getSCEV(I->getOperand(1))); 1480 case Instruction::Or: 1481 // If the RHS of the Or is a constant, we may have something like: 1482 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1483 // optimizations will transparently handle this case. 1484 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1485 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1486 APInt CommonFact(GetConstantFactor(LHS)); 1487 assert(!CommonFact.isMinValue() && 1488 "Common factor should at least be 1!"); 1489 if (CommonFact.ugt(CI->getValue())) { 1490 // If the LHS is a multiple that is larger than the RHS, use +. 1491 return SCEVAddExpr::get(LHS, 1492 getSCEV(I->getOperand(1))); 1493 } 1494 } 1495 break; 1496 case Instruction::Xor: 1497 // If the RHS of the xor is a signbit, then this is just an add. 1498 // Instcombine turns add of signbit into xor as a strength reduction step. 1499 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1500 if (CI->getValue().isSignBit()) 1501 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1502 getSCEV(I->getOperand(1))); 1503 } 1504 break; 1505 1506 case Instruction::Shl: 1507 // Turn shift left of a constant amount into a multiply. 1508 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1509 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1510 Constant *X = ConstantInt::get( 1511 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1512 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1513 } 1514 break; 1515 1516 case Instruction::Trunc: 1517 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1518 1519 case Instruction::ZExt: 1520 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1521 1522 case Instruction::SExt: 1523 return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1524 1525 case Instruction::BitCast: 1526 // BitCasts are no-op casts so we just eliminate the cast. 1527 if (I->getType()->isInteger() && 1528 I->getOperand(0)->getType()->isInteger()) 1529 return getSCEV(I->getOperand(0)); 1530 break; 1531 1532 case Instruction::PHI: 1533 return createNodeForPHI(cast<PHINode>(I)); 1534 1535 default: // We cannot analyze this expression. 1536 break; 1537 } 1538 } 1539 1540 return SCEVUnknown::get(V); 1541} 1542 1543 1544 1545//===----------------------------------------------------------------------===// 1546// Iteration Count Computation Code 1547// 1548 1549/// getIterationCount - If the specified loop has a predictable iteration 1550/// count, return it. Note that it is not valid to call this method on a 1551/// loop without a loop-invariant iteration count. 1552SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1553 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1554 if (I == IterationCounts.end()) { 1555 SCEVHandle ItCount = ComputeIterationCount(L); 1556 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1557 if (ItCount != UnknownValue) { 1558 assert(ItCount->isLoopInvariant(L) && 1559 "Computed trip count isn't loop invariant for loop!"); 1560 ++NumTripCountsComputed; 1561 } else if (isa<PHINode>(L->getHeader()->begin())) { 1562 // Only count loops that have phi nodes as not being computable. 1563 ++NumTripCountsNotComputed; 1564 } 1565 } 1566 return I->second; 1567} 1568 1569/// ComputeIterationCount - Compute the number of times the specified loop 1570/// will iterate. 1571SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1572 // If the loop has a non-one exit block count, we can't analyze it. 1573 SmallVector<BasicBlock*, 8> ExitBlocks; 1574 L->getExitBlocks(ExitBlocks); 1575 if (ExitBlocks.size() != 1) return UnknownValue; 1576 1577 // Okay, there is one exit block. Try to find the condition that causes the 1578 // loop to be exited. 1579 BasicBlock *ExitBlock = ExitBlocks[0]; 1580 1581 BasicBlock *ExitingBlock = 0; 1582 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1583 PI != E; ++PI) 1584 if (L->contains(*PI)) { 1585 if (ExitingBlock == 0) 1586 ExitingBlock = *PI; 1587 else 1588 return UnknownValue; // More than one block exiting! 1589 } 1590 assert(ExitingBlock && "No exits from loop, something is broken!"); 1591 1592 // Okay, we've computed the exiting block. See what condition causes us to 1593 // exit. 1594 // 1595 // FIXME: we should be able to handle switch instructions (with a single exit) 1596 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1597 if (ExitBr == 0) return UnknownValue; 1598 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1599 1600 // At this point, we know we have a conditional branch that determines whether 1601 // the loop is exited. However, we don't know if the branch is executed each 1602 // time through the loop. If not, then the execution count of the branch will 1603 // not be equal to the trip count of the loop. 1604 // 1605 // Currently we check for this by checking to see if the Exit branch goes to 1606 // the loop header. If so, we know it will always execute the same number of 1607 // times as the loop. We also handle the case where the exit block *is* the 1608 // loop header. This is common for un-rotated loops. More extensive analysis 1609 // could be done to handle more cases here. 1610 if (ExitBr->getSuccessor(0) != L->getHeader() && 1611 ExitBr->getSuccessor(1) != L->getHeader() && 1612 ExitBr->getParent() != L->getHeader()) 1613 return UnknownValue; 1614 1615 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1616 1617 // If its not an integer comparison then compute it the hard way. 1618 // Note that ICmpInst deals with pointer comparisons too so we must check 1619 // the type of the operand. 1620 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1621 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1622 ExitBr->getSuccessor(0) == ExitBlock); 1623 1624 // If the condition was exit on true, convert the condition to exit on false 1625 ICmpInst::Predicate Cond; 1626 if (ExitBr->getSuccessor(1) == ExitBlock) 1627 Cond = ExitCond->getPredicate(); 1628 else 1629 Cond = ExitCond->getInversePredicate(); 1630 1631 // Handle common loops like: for (X = "string"; *X; ++X) 1632 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1633 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1634 SCEVHandle ItCnt = 1635 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1636 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1637 } 1638 1639 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1640 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1641 1642 // Try to evaluate any dependencies out of the loop. 1643 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1644 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1645 Tmp = getSCEVAtScope(RHS, L); 1646 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1647 1648 // At this point, we would like to compute how many iterations of the 1649 // loop the predicate will return true for these inputs. 1650 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1651 // If there is a constant, force it into the RHS. 1652 std::swap(LHS, RHS); 1653 Cond = ICmpInst::getSwappedPredicate(Cond); 1654 } 1655 1656 // FIXME: think about handling pointer comparisons! i.e.: 1657 // while (P != P+100) ++P; 1658 1659 // If we have a comparison of a chrec against a constant, try to use value 1660 // ranges to answer this query. 1661 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1662 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1663 if (AddRec->getLoop() == L) { 1664 // Form the comparison range using the constant of the correct type so 1665 // that the ConstantRange class knows to do a signed or unsigned 1666 // comparison. 1667 ConstantInt *CompVal = RHSC->getValue(); 1668 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1669 CompVal = dyn_cast<ConstantInt>( 1670 ConstantExpr::getBitCast(CompVal, RealTy)); 1671 if (CompVal) { 1672 // Form the constant range. 1673 ConstantRange CompRange( 1674 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1675 1676 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1677 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1678 } 1679 } 1680 1681 switch (Cond) { 1682 case ICmpInst::ICMP_NE: { // while (X != Y) 1683 // Convert to: while (X-Y != 0) 1684 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1685 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1686 break; 1687 } 1688 case ICmpInst::ICMP_EQ: { 1689 // Convert to: while (X-Y == 0) // while (X == Y) 1690 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1691 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1692 break; 1693 } 1694 case ICmpInst::ICMP_SLT: { 1695 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1696 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1697 break; 1698 } 1699 case ICmpInst::ICMP_SGT: { 1700 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS), 1701 SCEV::getNegativeSCEV(RHS), L, true); 1702 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1703 break; 1704 } 1705 case ICmpInst::ICMP_ULT: { 1706 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1707 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1708 break; 1709 } 1710 case ICmpInst::ICMP_UGT: { 1711 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS), 1712 SCEV::getNegativeSCEV(RHS), L, false); 1713 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1714 break; 1715 } 1716 default: 1717#if 0 1718 cerr << "ComputeIterationCount "; 1719 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1720 cerr << "[unsigned] "; 1721 cerr << *LHS << " " 1722 << Instruction::getOpcodeName(Instruction::ICmp) 1723 << " " << *RHS << "\n"; 1724#endif 1725 break; 1726 } 1727 return ComputeIterationCountExhaustively(L, ExitCond, 1728 ExitBr->getSuccessor(0) == ExitBlock); 1729} 1730 1731static ConstantInt * 1732EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C) { 1733 SCEVHandle InVal = SCEVConstant::get(C); 1734 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1735 assert(isa<SCEVConstant>(Val) && 1736 "Evaluation of SCEV at constant didn't fold correctly?"); 1737 return cast<SCEVConstant>(Val)->getValue(); 1738} 1739 1740/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1741/// and a GEP expression (missing the pointer index) indexing into it, return 1742/// the addressed element of the initializer or null if the index expression is 1743/// invalid. 1744static Constant * 1745GetAddressedElementFromGlobal(GlobalVariable *GV, 1746 const std::vector<ConstantInt*> &Indices) { 1747 Constant *Init = GV->getInitializer(); 1748 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1749 uint64_t Idx = Indices[i]->getZExtValue(); 1750 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1751 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1752 Init = cast<Constant>(CS->getOperand(Idx)); 1753 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1754 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1755 Init = cast<Constant>(CA->getOperand(Idx)); 1756 } else if (isa<ConstantAggregateZero>(Init)) { 1757 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1758 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1759 Init = Constant::getNullValue(STy->getElementType(Idx)); 1760 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1761 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1762 Init = Constant::getNullValue(ATy->getElementType()); 1763 } else { 1764 assert(0 && "Unknown constant aggregate type!"); 1765 } 1766 return 0; 1767 } else { 1768 return 0; // Unknown initializer type 1769 } 1770 } 1771 return Init; 1772} 1773 1774/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1775/// 'setcc load X, cst', try to se if we can compute the trip count. 1776SCEVHandle ScalarEvolutionsImpl:: 1777ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1778 const Loop *L, 1779 ICmpInst::Predicate predicate) { 1780 if (LI->isVolatile()) return UnknownValue; 1781 1782 // Check to see if the loaded pointer is a getelementptr of a global. 1783 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1784 if (!GEP) return UnknownValue; 1785 1786 // Make sure that it is really a constant global we are gepping, with an 1787 // initializer, and make sure the first IDX is really 0. 1788 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1789 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1790 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1791 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1792 return UnknownValue; 1793 1794 // Okay, we allow one non-constant index into the GEP instruction. 1795 Value *VarIdx = 0; 1796 std::vector<ConstantInt*> Indexes; 1797 unsigned VarIdxNum = 0; 1798 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1799 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1800 Indexes.push_back(CI); 1801 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1802 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1803 VarIdx = GEP->getOperand(i); 1804 VarIdxNum = i-2; 1805 Indexes.push_back(0); 1806 } 1807 1808 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1809 // Check to see if X is a loop variant variable value now. 1810 SCEVHandle Idx = getSCEV(VarIdx); 1811 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1812 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1813 1814 // We can only recognize very limited forms of loop index expressions, in 1815 // particular, only affine AddRec's like {C1,+,C2}. 1816 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1817 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1818 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1819 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1820 return UnknownValue; 1821 1822 unsigned MaxSteps = MaxBruteForceIterations; 1823 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1824 ConstantInt *ItCst = 1825 ConstantInt::get(IdxExpr->getType(), IterationNum); 1826 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1827 1828 // Form the GEP offset. 1829 Indexes[VarIdxNum] = Val; 1830 1831 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1832 if (Result == 0) break; // Cannot compute! 1833 1834 // Evaluate the condition for this iteration. 1835 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1836 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1837 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 1838#if 0 1839 cerr << "\n***\n*** Computed loop count " << *ItCst 1840 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1841 << "***\n"; 1842#endif 1843 ++NumArrayLenItCounts; 1844 return SCEVConstant::get(ItCst); // Found terminating iteration! 1845 } 1846 } 1847 return UnknownValue; 1848} 1849 1850 1851/// CanConstantFold - Return true if we can constant fold an instruction of the 1852/// specified type, assuming that all operands were constants. 1853static bool CanConstantFold(const Instruction *I) { 1854 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 1855 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1856 return true; 1857 1858 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1859 if (const Function *F = CI->getCalledFunction()) 1860 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1861 return false; 1862} 1863 1864/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1865/// in the loop that V is derived from. We allow arbitrary operations along the 1866/// way, but the operands of an operation must either be constants or a value 1867/// derived from a constant PHI. If this expression does not fit with these 1868/// constraints, return null. 1869static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1870 // If this is not an instruction, or if this is an instruction outside of the 1871 // loop, it can't be derived from a loop PHI. 1872 Instruction *I = dyn_cast<Instruction>(V); 1873 if (I == 0 || !L->contains(I->getParent())) return 0; 1874 1875 if (PHINode *PN = dyn_cast<PHINode>(I)) 1876 if (L->getHeader() == I->getParent()) 1877 return PN; 1878 else 1879 // We don't currently keep track of the control flow needed to evaluate 1880 // PHIs, so we cannot handle PHIs inside of loops. 1881 return 0; 1882 1883 // If we won't be able to constant fold this expression even if the operands 1884 // are constants, return early. 1885 if (!CanConstantFold(I)) return 0; 1886 1887 // Otherwise, we can evaluate this instruction if all of its operands are 1888 // constant or derived from a PHI node themselves. 1889 PHINode *PHI = 0; 1890 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1891 if (!(isa<Constant>(I->getOperand(Op)) || 1892 isa<GlobalValue>(I->getOperand(Op)))) { 1893 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1894 if (P == 0) return 0; // Not evolving from PHI 1895 if (PHI == 0) 1896 PHI = P; 1897 else if (PHI != P) 1898 return 0; // Evolving from multiple different PHIs. 1899 } 1900 1901 // This is a expression evolving from a constant PHI! 1902 return PHI; 1903} 1904 1905/// EvaluateExpression - Given an expression that passes the 1906/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1907/// in the loop has the value PHIVal. If we can't fold this expression for some 1908/// reason, return null. 1909static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1910 if (isa<PHINode>(V)) return PHIVal; 1911 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1912 return GV; 1913 if (Constant *C = dyn_cast<Constant>(V)) return C; 1914 Instruction *I = cast<Instruction>(V); 1915 1916 std::vector<Constant*> Operands; 1917 Operands.resize(I->getNumOperands()); 1918 1919 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1920 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1921 if (Operands[i] == 0) return 0; 1922 } 1923 1924 return ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1925} 1926 1927/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1928/// in the header of its containing loop, we know the loop executes a 1929/// constant number of times, and the PHI node is just a recurrence 1930/// involving constants, fold it. 1931Constant *ScalarEvolutionsImpl:: 1932getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 1933 std::map<PHINode*, Constant*>::iterator I = 1934 ConstantEvolutionLoopExitValue.find(PN); 1935 if (I != ConstantEvolutionLoopExitValue.end()) 1936 return I->second; 1937 1938 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 1939 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1940 1941 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1942 1943 // Since the loop is canonicalized, the PHI node must have two entries. One 1944 // entry must be a constant (coming in from outside of the loop), and the 1945 // second must be derived from the same PHI. 1946 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1947 Constant *StartCST = 1948 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1949 if (StartCST == 0) 1950 return RetVal = 0; // Must be a constant. 1951 1952 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1953 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1954 if (PN2 != PN) 1955 return RetVal = 0; // Not derived from same PHI. 1956 1957 // Execute the loop symbolically to determine the exit value. 1958 if (Its.getActiveBits() >= 32) 1959 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 1960 1961 unsigned NumIterations = Its.getZExtValue(); // must be in range 1962 unsigned IterationNum = 0; 1963 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1964 if (IterationNum == NumIterations) 1965 return RetVal = PHIVal; // Got exit value! 1966 1967 // Compute the value of the PHI node for the next iteration. 1968 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1969 if (NextPHI == PHIVal) 1970 return RetVal = NextPHI; // Stopped evolving! 1971 if (NextPHI == 0) 1972 return 0; // Couldn't evaluate! 1973 PHIVal = NextPHI; 1974 } 1975} 1976 1977/// ComputeIterationCountExhaustively - If the trip is known to execute a 1978/// constant number of times (the condition evolves only from constants), 1979/// try to evaluate a few iterations of the loop until we get the exit 1980/// condition gets a value of ExitWhen (true or false). If we cannot 1981/// evaluate the trip count of the loop, return UnknownValue. 1982SCEVHandle ScalarEvolutionsImpl:: 1983ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1984 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1985 if (PN == 0) return UnknownValue; 1986 1987 // Since the loop is canonicalized, the PHI node must have two entries. One 1988 // entry must be a constant (coming in from outside of the loop), and the 1989 // second must be derived from the same PHI. 1990 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1991 Constant *StartCST = 1992 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1993 if (StartCST == 0) return UnknownValue; // Must be a constant. 1994 1995 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1996 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1997 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1998 1999 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2000 // the loop symbolically to determine when the condition gets a value of 2001 // "ExitWhen". 2002 unsigned IterationNum = 0; 2003 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2004 for (Constant *PHIVal = StartCST; 2005 IterationNum != MaxIterations; ++IterationNum) { 2006 ConstantInt *CondVal = 2007 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2008 2009 // Couldn't symbolically evaluate. 2010 if (!CondVal) return UnknownValue; 2011 2012 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2013 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2014 ++NumBruteForceTripCountsComputed; 2015 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum)); 2016 } 2017 2018 // Compute the value of the PHI node for the next iteration. 2019 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2020 if (NextPHI == 0 || NextPHI == PHIVal) 2021 return UnknownValue; // Couldn't evaluate or not making progress... 2022 PHIVal = NextPHI; 2023 } 2024 2025 // Too many iterations were needed to evaluate. 2026 return UnknownValue; 2027} 2028 2029/// getSCEVAtScope - Compute the value of the specified expression within the 2030/// indicated loop (which may be null to indicate in no loop). If the 2031/// expression cannot be evaluated, return UnknownValue. 2032SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2033 // FIXME: this should be turned into a virtual method on SCEV! 2034 2035 if (isa<SCEVConstant>(V)) return V; 2036 2037 // If this instruction is evolves from a constant-evolving PHI, compute the 2038 // exit value from the loop without using SCEVs. 2039 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2040 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2041 const Loop *LI = this->LI[I->getParent()]; 2042 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2043 if (PHINode *PN = dyn_cast<PHINode>(I)) 2044 if (PN->getParent() == LI->getHeader()) { 2045 // Okay, there is no closed form solution for the PHI node. Check 2046 // to see if the loop that contains it has a known iteration count. 2047 // If so, we may be able to force computation of the exit value. 2048 SCEVHandle IterationCount = getIterationCount(LI); 2049 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2050 // Okay, we know how many times the containing loop executes. If 2051 // this is a constant evolving PHI node, get the final value at 2052 // the specified iteration number. 2053 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2054 ICC->getValue()->getValue(), 2055 LI); 2056 if (RV) return SCEVUnknown::get(RV); 2057 } 2058 } 2059 2060 // Okay, this is an expression that we cannot symbolically evaluate 2061 // into a SCEV. Check to see if it's possible to symbolically evaluate 2062 // the arguments into constants, and if so, try to constant propagate the 2063 // result. This is particularly useful for computing loop exit values. 2064 if (CanConstantFold(I)) { 2065 std::vector<Constant*> Operands; 2066 Operands.reserve(I->getNumOperands()); 2067 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2068 Value *Op = I->getOperand(i); 2069 if (Constant *C = dyn_cast<Constant>(Op)) { 2070 Operands.push_back(C); 2071 } else { 2072 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2073 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2074 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2075 Op->getType(), 2076 false)); 2077 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2078 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2079 Operands.push_back(ConstantExpr::getIntegerCast(C, 2080 Op->getType(), 2081 false)); 2082 else 2083 return V; 2084 } else { 2085 return V; 2086 } 2087 } 2088 } 2089 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 2090 return SCEVUnknown::get(C); 2091 } 2092 } 2093 2094 // This is some other type of SCEVUnknown, just return it. 2095 return V; 2096 } 2097 2098 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2099 // Avoid performing the look-up in the common case where the specified 2100 // expression has no loop-variant portions. 2101 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2102 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2103 if (OpAtScope != Comm->getOperand(i)) { 2104 if (OpAtScope == UnknownValue) return UnknownValue; 2105 // Okay, at least one of these operands is loop variant but might be 2106 // foldable. Build a new instance of the folded commutative expression. 2107 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2108 NewOps.push_back(OpAtScope); 2109 2110 for (++i; i != e; ++i) { 2111 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2112 if (OpAtScope == UnknownValue) return UnknownValue; 2113 NewOps.push_back(OpAtScope); 2114 } 2115 if (isa<SCEVAddExpr>(Comm)) 2116 return SCEVAddExpr::get(NewOps); 2117 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2118 return SCEVMulExpr::get(NewOps); 2119 } 2120 } 2121 // If we got here, all operands are loop invariant. 2122 return Comm; 2123 } 2124 2125 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2126 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2127 if (LHS == UnknownValue) return LHS; 2128 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2129 if (RHS == UnknownValue) return RHS; 2130 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2131 return Div; // must be loop invariant 2132 return SCEVSDivExpr::get(LHS, RHS); 2133 } 2134 2135 // If this is a loop recurrence for a loop that does not contain L, then we 2136 // are dealing with the final value computed by the loop. 2137 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2138 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2139 // To evaluate this recurrence, we need to know how many times the AddRec 2140 // loop iterates. Compute this now. 2141 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2142 if (IterationCount == UnknownValue) return UnknownValue; 2143 IterationCount = getTruncateOrZeroExtend(IterationCount, 2144 AddRec->getType()); 2145 2146 // If the value is affine, simplify the expression evaluation to just 2147 // Start + Step*IterationCount. 2148 if (AddRec->isAffine()) 2149 return SCEVAddExpr::get(AddRec->getStart(), 2150 SCEVMulExpr::get(IterationCount, 2151 AddRec->getOperand(1))); 2152 2153 // Otherwise, evaluate it the hard way. 2154 return AddRec->evaluateAtIteration(IterationCount); 2155 } 2156 return UnknownValue; 2157 } 2158 2159 //assert(0 && "Unknown SCEV type!"); 2160 return UnknownValue; 2161} 2162 2163 2164/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2165/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2166/// might be the same) or two SCEVCouldNotCompute objects. 2167/// 2168static std::pair<SCEVHandle,SCEVHandle> 2169SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2170 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2171 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2172 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2173 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2174 2175 // We currently can only solve this if the coefficients are constants. 2176 if (!LC || !MC || !NC) { 2177 SCEV *CNC = new SCEVCouldNotCompute(); 2178 return std::make_pair(CNC, CNC); 2179 } 2180 2181 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2182 const APInt &L = LC->getValue()->getValue(); 2183 const APInt &M = MC->getValue()->getValue(); 2184 const APInt &N = NC->getValue()->getValue(); 2185 APInt Two(BitWidth, 2); 2186 APInt Four(BitWidth, 4); 2187 2188 { 2189 using namespace APIntOps; 2190 const APInt& C = L; 2191 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2192 // The B coefficient is M-N/2 2193 APInt B(M); 2194 B -= sdiv(N,Two); 2195 2196 // The A coefficient is N/2 2197 APInt A(N.sdiv(Two)); 2198 2199 // Compute the B^2-4ac term. 2200 APInt SqrtTerm(B); 2201 SqrtTerm *= B; 2202 SqrtTerm -= Four * (A * C); 2203 2204 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2205 // integer value or else APInt::sqrt() will assert. 2206 APInt SqrtVal(SqrtTerm.sqrt()); 2207 2208 // Compute the two solutions for the quadratic formula. 2209 // The divisions must be performed as signed divisions. 2210 APInt NegB(-B); 2211 APInt TwoA( A << 1 ); 2212 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2213 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2214 2215 return std::make_pair(SCEVConstant::get(Solution1), 2216 SCEVConstant::get(Solution2)); 2217 } // end APIntOps namespace 2218} 2219 2220/// HowFarToZero - Return the number of times a backedge comparing the specified 2221/// value to zero will execute. If not computable, return UnknownValue 2222SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2223 // If the value is a constant 2224 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2225 // If the value is already zero, the branch will execute zero times. 2226 if (C->getValue()->isZero()) return C; 2227 return UnknownValue; // Otherwise it will loop infinitely. 2228 } 2229 2230 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2231 if (!AddRec || AddRec->getLoop() != L) 2232 return UnknownValue; 2233 2234 if (AddRec->isAffine()) { 2235 // If this is an affine expression the execution count of this branch is 2236 // equal to: 2237 // 2238 // (0 - Start/Step) iff Start % Step == 0 2239 // 2240 // Get the initial value for the loop. 2241 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2242 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2243 SCEVHandle Step = AddRec->getOperand(1); 2244 2245 Step = getSCEVAtScope(Step, L->getParentLoop()); 2246 2247 // Figure out if Start % Step == 0. 2248 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2249 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2250 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2251 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2252 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2253 return Start; // 0 - Start/-1 == Start 2254 2255 // Check to see if Start is divisible by SC with no remainder. 2256 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2257 ConstantInt *StartCC = StartC->getValue(); 2258 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2259 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2260 if (Rem->isNullValue()) { 2261 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2262 return SCEVUnknown::get(Result); 2263 } 2264 } 2265 } 2266 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2267 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2268 // the quadratic equation to solve it. 2269 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2270 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2271 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2272 if (R1) { 2273#if 0 2274 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2275 << " sol#2: " << *R2 << "\n"; 2276#endif 2277 // Pick the smallest positive root value. 2278 if (ConstantInt *CB = 2279 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2280 R1->getValue(), R2->getValue()))) { 2281 if (CB->getZExtValue() == false) 2282 std::swap(R1, R2); // R1 is the minimum root now. 2283 2284 // We can only use this value if the chrec ends up with an exact zero 2285 // value at this index. When solving for "X*X != 5", for example, we 2286 // should not accept a root of 2. 2287 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2288 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2289 if (EvalVal->getValue()->isZero()) 2290 return R1; // We found a quadratic root! 2291 } 2292 } 2293 } 2294 2295 return UnknownValue; 2296} 2297 2298/// HowFarToNonZero - Return the number of times a backedge checking the 2299/// specified value for nonzero will execute. If not computable, return 2300/// UnknownValue 2301SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2302 // Loops that look like: while (X == 0) are very strange indeed. We don't 2303 // handle them yet except for the trivial case. This could be expanded in the 2304 // future as needed. 2305 2306 // If the value is a constant, check to see if it is known to be non-zero 2307 // already. If so, the backedge will execute zero times. 2308 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2309 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2310 Constant *NonZero = 2311 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2312 if (NonZero == ConstantInt::getTrue()) 2313 return getSCEV(Zero); 2314 return UnknownValue; // Otherwise it will loop infinitely. 2315 } 2316 2317 // We could implement others, but I really doubt anyone writes loops like 2318 // this, and if they did, they would already be constant folded. 2319 return UnknownValue; 2320} 2321 2322/// HowManyLessThans - Return the number of times a backedge containing the 2323/// specified less-than comparison will execute. If not computable, return 2324/// UnknownValue. 2325SCEVHandle ScalarEvolutionsImpl:: 2326HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2327 // Only handle: "ADDREC < LoopInvariant". 2328 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2329 2330 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2331 if (!AddRec || AddRec->getLoop() != L) 2332 return UnknownValue; 2333 2334 if (AddRec->isAffine()) { 2335 // FORNOW: We only support unit strides. 2336 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2337 if (AddRec->getOperand(1) != One) 2338 return UnknownValue; 2339 2340 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2341 // know that m is >= n on input to the loop. If it is, the condition return 2342 // true zero times. What we really should return, for full generality, is 2343 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2344 // canonical loop form: most do-loops will have a check that dominates the 2345 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2346 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2347 2348 // Search for the check. 2349 BasicBlock *Preheader = L->getLoopPreheader(); 2350 BasicBlock *PreheaderDest = L->getHeader(); 2351 if (Preheader == 0) return UnknownValue; 2352 2353 BranchInst *LoopEntryPredicate = 2354 dyn_cast<BranchInst>(Preheader->getTerminator()); 2355 if (!LoopEntryPredicate) return UnknownValue; 2356 2357 // This might be a critical edge broken out. If the loop preheader ends in 2358 // an unconditional branch to the loop, check to see if the preheader has a 2359 // single predecessor, and if so, look for its terminator. 2360 while (LoopEntryPredicate->isUnconditional()) { 2361 PreheaderDest = Preheader; 2362 Preheader = Preheader->getSinglePredecessor(); 2363 if (!Preheader) return UnknownValue; // Multiple preds. 2364 2365 LoopEntryPredicate = 2366 dyn_cast<BranchInst>(Preheader->getTerminator()); 2367 if (!LoopEntryPredicate) return UnknownValue; 2368 } 2369 2370 // Now that we found a conditional branch that dominates the loop, check to 2371 // see if it is the comparison we are looking for. 2372 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){ 2373 Value *PreCondLHS = ICI->getOperand(0); 2374 Value *PreCondRHS = ICI->getOperand(1); 2375 ICmpInst::Predicate Cond; 2376 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2377 Cond = ICI->getPredicate(); 2378 else 2379 Cond = ICI->getInversePredicate(); 2380 2381 switch (Cond) { 2382 case ICmpInst::ICMP_UGT: 2383 if (isSigned) return UnknownValue; 2384 std::swap(PreCondLHS, PreCondRHS); 2385 Cond = ICmpInst::ICMP_ULT; 2386 break; 2387 case ICmpInst::ICMP_SGT: 2388 if (!isSigned) return UnknownValue; 2389 std::swap(PreCondLHS, PreCondRHS); 2390 Cond = ICmpInst::ICMP_SLT; 2391 break; 2392 case ICmpInst::ICMP_ULT: 2393 if (isSigned) return UnknownValue; 2394 break; 2395 case ICmpInst::ICMP_SLT: 2396 if (!isSigned) return UnknownValue; 2397 break; 2398 default: 2399 return UnknownValue; 2400 } 2401 2402 if (PreCondLHS->getType()->isInteger()) { 2403 if (RHS != getSCEV(PreCondRHS)) 2404 return UnknownValue; // Not a comparison against 'm'. 2405 2406 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2407 != getSCEV(PreCondLHS)) 2408 return UnknownValue; // Not a comparison against 'n-1'. 2409 } 2410 else return UnknownValue; 2411 2412 // cerr << "Computed Loop Trip Count as: " 2413 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2414 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2415 } 2416 else 2417 return UnknownValue; 2418 } 2419 2420 return UnknownValue; 2421} 2422 2423/// getNumIterationsInRange - Return the number of iterations of this loop that 2424/// produce values in the specified constant range. Another way of looking at 2425/// this is that it returns the first iteration number where the value is not in 2426/// the condition, thus computing the exit count. If the iteration count can't 2427/// be computed, an instance of SCEVCouldNotCompute is returned. 2428SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2429 if (Range.isFullSet()) // Infinite loop. 2430 return new SCEVCouldNotCompute(); 2431 2432 // If the start is a non-zero constant, shift the range to simplify things. 2433 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2434 if (!SC->getValue()->isZero()) { 2435 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2436 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2437 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2438 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2439 return ShiftedAddRec->getNumIterationsInRange( 2440 Range.subtract(SC->getValue()->getValue())); 2441 // This is strange and shouldn't happen. 2442 return new SCEVCouldNotCompute(); 2443 } 2444 2445 // The only time we can solve this is when we have all constant indices. 2446 // Otherwise, we cannot determine the overflow conditions. 2447 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2448 if (!isa<SCEVConstant>(getOperand(i))) 2449 return new SCEVCouldNotCompute(); 2450 2451 2452 // Okay at this point we know that all elements of the chrec are constants and 2453 // that the start element is zero. 2454 2455 // First check to see if the range contains zero. If not, the first 2456 // iteration exits. 2457 if (!Range.contains(APInt(getBitWidth(),0))) 2458 return SCEVConstant::get(ConstantInt::get(getType(),0)); 2459 2460 if (isAffine()) { 2461 // If this is an affine expression then we have this situation: 2462 // Solve {0,+,A} in Range === Ax in Range 2463 2464 // We know that zero is in the range. If A is positive then we know that 2465 // the upper value of the range must be the first possible exit value. 2466 // If A is negative then the lower of the range is the last possible loop 2467 // value. Also note that we already checked for a full range. 2468 APInt One(getBitWidth(),1); 2469 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2470 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2471 2472 // The exit value should be (End+A)/A. 2473 APInt ExitVal = (End + A).udiv(A); 2474 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2475 2476 // Evaluate at the exit value. If we really did fall out of the valid 2477 // range, then we computed our trip count, otherwise wrap around or other 2478 // things must have happened. 2479 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2480 if (Range.contains(Val->getValue())) 2481 return new SCEVCouldNotCompute(); // Something strange happened 2482 2483 // Ensure that the previous value is in the range. This is a sanity check. 2484 assert(Range.contains( 2485 EvaluateConstantChrecAtConstant(this, 2486 ConstantInt::get(ExitVal - One))->getValue()) && 2487 "Linear scev computation is off in a bad way!"); 2488 return SCEVConstant::get(ExitValue); 2489 } else if (isQuadratic()) { 2490 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2491 // quadratic equation to solve it. To do this, we must frame our problem in 2492 // terms of figuring out when zero is crossed, instead of when 2493 // Range.getUpper() is crossed. 2494 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2495 NewOps[0] = SCEV::getNegativeSCEV(SCEVConstant::get(Range.getUpper())); 2496 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2497 2498 // Next, solve the constructed addrec 2499 std::pair<SCEVHandle,SCEVHandle> Roots = 2500 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2501 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2502 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2503 if (R1) { 2504 // Pick the smallest positive root value. 2505 if (ConstantInt *CB = 2506 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2507 R1->getValue(), R2->getValue()))) { 2508 if (CB->getZExtValue() == false) 2509 std::swap(R1, R2); // R1 is the minimum root now. 2510 2511 // Make sure the root is not off by one. The returned iteration should 2512 // not be in the range, but the previous one should be. When solving 2513 // for "X*X < 5", for example, we should not return a root of 2. 2514 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2515 R1->getValue()); 2516 if (Range.contains(R1Val->getValue())) { 2517 // The next iteration must be out of the range... 2518 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2519 2520 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2521 if (!Range.contains(R1Val->getValue())) 2522 return SCEVConstant::get(NextVal); 2523 return new SCEVCouldNotCompute(); // Something strange happened 2524 } 2525 2526 // If R1 was not in the range, then it is a good return value. Make 2527 // sure that R1-1 WAS in the range though, just in case. 2528 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2529 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2530 if (Range.contains(R1Val->getValue())) 2531 return R1; 2532 return new SCEVCouldNotCompute(); // Something strange happened 2533 } 2534 } 2535 } 2536 2537 // Fallback, if this is a general polynomial, figure out the progression 2538 // through brute force: evaluate until we find an iteration that fails the 2539 // test. This is likely to be slow, but getting an accurate trip count is 2540 // incredibly important, we will be able to simplify the exit test a lot, and 2541 // we are almost guaranteed to get a trip count in this case. 2542 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2543 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2544 do { 2545 ++NumBruteForceEvaluations; 2546 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2547 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2548 return new SCEVCouldNotCompute(); 2549 2550 // Check to see if we found the value! 2551 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2552 return SCEVConstant::get(TestVal); 2553 2554 // Increment to test the next index. 2555 TestVal = ConstantInt::get(TestVal->getValue()+1); 2556 } while (TestVal != EndVal); 2557 2558 return new SCEVCouldNotCompute(); 2559} 2560 2561 2562 2563//===----------------------------------------------------------------------===// 2564// ScalarEvolution Class Implementation 2565//===----------------------------------------------------------------------===// 2566 2567bool ScalarEvolution::runOnFunction(Function &F) { 2568 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2569 return false; 2570} 2571 2572void ScalarEvolution::releaseMemory() { 2573 delete (ScalarEvolutionsImpl*)Impl; 2574 Impl = 0; 2575} 2576 2577void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2578 AU.setPreservesAll(); 2579 AU.addRequiredTransitive<LoopInfo>(); 2580} 2581 2582SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2583 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2584} 2585 2586/// hasSCEV - Return true if the SCEV for this value has already been 2587/// computed. 2588bool ScalarEvolution::hasSCEV(Value *V) const { 2589 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2590} 2591 2592 2593/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2594/// the specified value. 2595void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2596 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2597} 2598 2599 2600SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2601 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2602} 2603 2604bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2605 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2606} 2607 2608SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2609 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2610} 2611 2612void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2613 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2614} 2615 2616static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2617 const Loop *L) { 2618 // Print all inner loops first 2619 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2620 PrintLoopInfo(OS, SE, *I); 2621 2622 cerr << "Loop " << L->getHeader()->getName() << ": "; 2623 2624 SmallVector<BasicBlock*, 8> ExitBlocks; 2625 L->getExitBlocks(ExitBlocks); 2626 if (ExitBlocks.size() != 1) 2627 cerr << "<multiple exits> "; 2628 2629 if (SE->hasLoopInvariantIterationCount(L)) { 2630 cerr << *SE->getIterationCount(L) << " iterations! "; 2631 } else { 2632 cerr << "Unpredictable iteration count. "; 2633 } 2634 2635 cerr << "\n"; 2636} 2637 2638void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2639 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2640 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2641 2642 OS << "Classifying expressions for: " << F.getName() << "\n"; 2643 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2644 if (I->getType()->isInteger()) { 2645 OS << *I; 2646 OS << " --> "; 2647 SCEVHandle SV = getSCEV(&*I); 2648 SV->print(OS); 2649 OS << "\t\t"; 2650 2651 if ((*I).getType()->isInteger()) { 2652 ConstantRange Bounds = SV->getValueRange(); 2653 if (!Bounds.isFullSet()) 2654 OS << "Bounds: " << Bounds << " "; 2655 } 2656 2657 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2658 OS << "Exits: "; 2659 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2660 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2661 OS << "<<Unknown>>"; 2662 } else { 2663 OS << *ExitValue; 2664 } 2665 } 2666 2667 2668 OS << "\n"; 2669 } 2670 2671 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2672 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2673 PrintLoopInfo(OS, this, *I); 2674} 2675 2676