ScalarEvolution.cpp revision 4fe16d607d11e29d742208894909733f5ad01f8f
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} 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116SCEV::~SCEV() {} 117void SCEV::dump() const { 118 print(cerr); 119} 120 121/// getValueRange - Return the tightest constant bounds that this value is 122/// known to have. This method is only valid on integer SCEV objects. 123ConstantRange SCEV::getValueRange() const { 124 const Type *Ty = getType(); 125 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 126 // Default to a full range if no better information is available. 127 return ConstantRange(getType()); 128} 129 130 131SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 132 133bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 134 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 135 return false; 136} 137 138const Type *SCEVCouldNotCompute::getType() const { 139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 140 return 0; 141} 142 143bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 145 return false; 146} 147 148SCEVHandle SCEVCouldNotCompute:: 149replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 150 const SCEVHandle &Conc) const { 151 return this; 152} 153 154void SCEVCouldNotCompute::print(std::ostream &OS) const { 155 OS << "***COULDNOTCOMPUTE***"; 156} 157 158bool SCEVCouldNotCompute::classof(const SCEV *S) { 159 return S->getSCEVType() == scCouldNotCompute; 160} 161 162 163// SCEVConstants - Only allow the creation of one SCEVConstant for any 164// particular value. Don't use a SCEVHandle here, or else the object will 165// never be deleted! 166static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 167 168 169SCEVConstant::~SCEVConstant() { 170 SCEVConstants->erase(V); 171} 172 173SCEVHandle SCEVConstant::get(ConstantInt *V) { 174 SCEVConstant *&R = (*SCEVConstants)[V]; 175 if (R == 0) R = new SCEVConstant(V); 176 return R; 177} 178 179ConstantRange SCEVConstant::getValueRange() const { 180 return ConstantRange(V); 181} 182 183const Type *SCEVConstant::getType() const { return V->getType(); } 184 185void SCEVConstant::print(std::ostream &OS) const { 186 WriteAsOperand(OS, V, false); 187} 188 189// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 190// particular input. Don't use a SCEVHandle here, or else the object will 191// never be deleted! 192static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 193 SCEVTruncateExpr*> > SCEVTruncates; 194 195SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 196 : SCEV(scTruncate), Op(op), Ty(ty) { 197 assert(Op->getType()->isInteger() && Ty->isInteger() && 198 "Cannot truncate non-integer value!"); 199 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 200 && "This is not a truncating conversion!"); 201} 202 203SCEVTruncateExpr::~SCEVTruncateExpr() { 204 SCEVTruncates->erase(std::make_pair(Op, Ty)); 205} 206 207ConstantRange SCEVTruncateExpr::getValueRange() const { 208 return getOperand()->getValueRange().truncate(getType()); 209} 210 211void SCEVTruncateExpr::print(std::ostream &OS) const { 212 OS << "(truncate " << *Op << " to " << *Ty << ")"; 213} 214 215// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 216// particular input. Don't use a SCEVHandle here, or else the object will never 217// be deleted! 218static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 219 SCEVZeroExtendExpr*> > SCEVZeroExtends; 220 221SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 222 : SCEV(scZeroExtend), Op(op), Ty(ty) { 223 assert(Op->getType()->isInteger() && Ty->isInteger() && 224 "Cannot zero extend non-integer value!"); 225 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 226 && "This is not an extending conversion!"); 227} 228 229SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 230 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 231} 232 233ConstantRange SCEVZeroExtendExpr::getValueRange() const { 234 return getOperand()->getValueRange().zeroExtend(getType()); 235} 236 237void SCEVZeroExtendExpr::print(std::ostream &OS) const { 238 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 239} 240 241// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 242// particular input. Don't use a SCEVHandle here, or else the object will never 243// be deleted! 244static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 245 SCEVCommutativeExpr*> > SCEVCommExprs; 246 247SCEVCommutativeExpr::~SCEVCommutativeExpr() { 248 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 249 std::vector<SCEV*>(Operands.begin(), 250 Operands.end()))); 251} 252 253void SCEVCommutativeExpr::print(std::ostream &OS) const { 254 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 255 const char *OpStr = getOperationStr(); 256 OS << "(" << *Operands[0]; 257 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 258 OS << OpStr << *Operands[i]; 259 OS << ")"; 260} 261 262SCEVHandle SCEVCommutativeExpr:: 263replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 264 const SCEVHandle &Conc) const { 265 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 266 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 267 if (H != getOperand(i)) { 268 std::vector<SCEVHandle> NewOps; 269 NewOps.reserve(getNumOperands()); 270 for (unsigned j = 0; j != i; ++j) 271 NewOps.push_back(getOperand(j)); 272 NewOps.push_back(H); 273 for (++i; i != e; ++i) 274 NewOps.push_back(getOperand(i)-> 275 replaceSymbolicValuesWithConcrete(Sym, Conc)); 276 277 if (isa<SCEVAddExpr>(this)) 278 return SCEVAddExpr::get(NewOps); 279 else if (isa<SCEVMulExpr>(this)) 280 return SCEVMulExpr::get(NewOps); 281 else 282 assert(0 && "Unknown commutative expr!"); 283 } 284 } 285 return this; 286} 287 288 289// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 290// input. Don't use a SCEVHandle here, or else the object will never be 291// deleted! 292static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 293 SCEVSDivExpr*> > SCEVSDivs; 294 295SCEVSDivExpr::~SCEVSDivExpr() { 296 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 297} 298 299void SCEVSDivExpr::print(std::ostream &OS) const { 300 OS << "(" << *LHS << " /s " << *RHS << ")"; 301} 302 303const Type *SCEVSDivExpr::getType() const { 304 return LHS->getType(); 305} 306 307// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 308// particular input. Don't use a SCEVHandle here, or else the object will never 309// be deleted! 310static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 311 SCEVAddRecExpr*> > SCEVAddRecExprs; 312 313SCEVAddRecExpr::~SCEVAddRecExpr() { 314 SCEVAddRecExprs->erase(std::make_pair(L, 315 std::vector<SCEV*>(Operands.begin(), 316 Operands.end()))); 317} 318 319SCEVHandle SCEVAddRecExpr:: 320replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 321 const SCEVHandle &Conc) const { 322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 323 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 324 if (H != getOperand(i)) { 325 std::vector<SCEVHandle> NewOps; 326 NewOps.reserve(getNumOperands()); 327 for (unsigned j = 0; j != i; ++j) 328 NewOps.push_back(getOperand(j)); 329 NewOps.push_back(H); 330 for (++i; i != e; ++i) 331 NewOps.push_back(getOperand(i)-> 332 replaceSymbolicValuesWithConcrete(Sym, Conc)); 333 334 return get(NewOps, L); 335 } 336 } 337 return this; 338} 339 340 341bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 342 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 343 // contain L and if the start is invariant. 344 return !QueryLoop->contains(L->getHeader()) && 345 getOperand(0)->isLoopInvariant(QueryLoop); 346} 347 348 349void SCEVAddRecExpr::print(std::ostream &OS) const { 350 OS << "{" << *Operands[0]; 351 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 352 OS << ",+," << *Operands[i]; 353 OS << "}<" << L->getHeader()->getName() + ">"; 354} 355 356// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 357// value. Don't use a SCEVHandle here, or else the object will never be 358// deleted! 359static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 360 361SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 362 363bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 364 // All non-instruction values are loop invariant. All instructions are loop 365 // invariant if they are not contained in the specified loop. 366 if (Instruction *I = dyn_cast<Instruction>(V)) 367 return !L->contains(I->getParent()); 368 return true; 369} 370 371const Type *SCEVUnknown::getType() const { 372 return V->getType(); 373} 374 375void SCEVUnknown::print(std::ostream &OS) const { 376 WriteAsOperand(OS, V, false); 377} 378 379//===----------------------------------------------------------------------===// 380// SCEV Utilities 381//===----------------------------------------------------------------------===// 382 383namespace { 384 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 385 /// than the complexity of the RHS. This comparator is used to canonicalize 386 /// expressions. 387 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 388 bool operator()(SCEV *LHS, SCEV *RHS) { 389 return LHS->getSCEVType() < RHS->getSCEVType(); 390 } 391 }; 392} 393 394/// GroupByComplexity - Given a list of SCEV objects, order them by their 395/// complexity, and group objects of the same complexity together by value. 396/// When this routine is finished, we know that any duplicates in the vector are 397/// consecutive and that complexity is monotonically increasing. 398/// 399/// Note that we go take special precautions to ensure that we get determinstic 400/// results from this routine. In other words, we don't want the results of 401/// this to depend on where the addresses of various SCEV objects happened to 402/// land in memory. 403/// 404static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 405 if (Ops.size() < 2) return; // Noop 406 if (Ops.size() == 2) { 407 // This is the common case, which also happens to be trivially simple. 408 // Special case it. 409 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 410 std::swap(Ops[0], Ops[1]); 411 return; 412 } 413 414 // Do the rough sort by complexity. 415 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 416 417 // Now that we are sorted by complexity, group elements of the same 418 // complexity. Note that this is, at worst, N^2, but the vector is likely to 419 // be extremely short in practice. Note that we take this approach because we 420 // do not want to depend on the addresses of the objects we are grouping. 421 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 422 SCEV *S = Ops[i]; 423 unsigned Complexity = S->getSCEVType(); 424 425 // If there are any objects of the same complexity and same value as this 426 // one, group them. 427 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 428 if (Ops[j] == S) { // Found a duplicate. 429 // Move it to immediately after i'th element. 430 std::swap(Ops[i+1], Ops[j]); 431 ++i; // no need to rescan it. 432 if (i == e-2) return; // Done! 433 } 434 } 435 } 436} 437 438 439 440//===----------------------------------------------------------------------===// 441// Simple SCEV method implementations 442//===----------------------------------------------------------------------===// 443 444/// getIntegerSCEV - Given an integer or FP type, create a constant for the 445/// specified signed integer value and return a SCEV for the constant. 446SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 447 Constant *C; 448 if (Val == 0) 449 C = Constant::getNullValue(Ty); 450 else if (Ty->isFloatingPoint()) 451 C = ConstantFP::get(Ty, Val); 452 else 453 C = ConstantInt::get(Ty, Val); 454 return SCEVUnknown::get(C); 455} 456 457/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 458/// input value to the specified type. If the type must be extended, it is zero 459/// extended. 460static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 461 const Type *SrcTy = V->getType(); 462 assert(SrcTy->isInteger() && Ty->isInteger() && 463 "Cannot truncate or zero extend with non-integer arguments!"); 464 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 465 return V; // No conversion 466 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 467 return SCEVTruncateExpr::get(V, Ty); 468 return SCEVZeroExtendExpr::get(V, Ty); 469} 470 471/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 472/// 473SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 474 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 475 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 476 477 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 478} 479 480/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 481/// 482SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 483 // X - Y --> X + -Y 484 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 485} 486 487 488/// PartialFact - Compute V!/(V-NumSteps)! 489static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 490 // Handle this case efficiently, it is common to have constant iteration 491 // counts while computing loop exit values. 492 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 493 uint64_t Val = SC->getValue()->getZExtValue(); 494 uint64_t Result = 1; 495 for (; NumSteps; --NumSteps) 496 Result *= Val-(NumSteps-1); 497 Constant *Res = ConstantInt::get(Type::Int64Ty, Result); 498 return SCEVUnknown::get(ConstantExpr::getTruncOrBitCast(Res, V->getType())); 499 } 500 501 const Type *Ty = V->getType(); 502 if (NumSteps == 0) 503 return SCEVUnknown::getIntegerSCEV(1, Ty); 504 505 SCEVHandle Result = V; 506 for (unsigned i = 1; i != NumSteps; ++i) 507 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 508 SCEVUnknown::getIntegerSCEV(i, Ty))); 509 return Result; 510} 511 512 513/// evaluateAtIteration - Return the value of this chain of recurrences at 514/// the specified iteration number. We can evaluate this recurrence by 515/// multiplying each element in the chain by the binomial coefficient 516/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 517/// 518/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 519/// 520/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 521/// Is the binomial equation safe using modular arithmetic?? 522/// 523SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 524 SCEVHandle Result = getStart(); 525 int Divisor = 1; 526 const Type *Ty = It->getType(); 527 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 528 SCEVHandle BC = PartialFact(It, i); 529 Divisor *= i; 530 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 531 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 532 Result = SCEVAddExpr::get(Result, Val); 533 } 534 return Result; 535} 536 537 538//===----------------------------------------------------------------------===// 539// SCEV Expression folder implementations 540//===----------------------------------------------------------------------===// 541 542SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 543 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 544 return SCEVUnknown::get( 545 ConstantExpr::getTrunc(SC->getValue(), Ty)); 546 547 // If the input value is a chrec scev made out of constants, truncate 548 // all of the constants. 549 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 550 std::vector<SCEVHandle> Operands; 551 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 552 // FIXME: This should allow truncation of other expression types! 553 if (isa<SCEVConstant>(AddRec->getOperand(i))) 554 Operands.push_back(get(AddRec->getOperand(i), Ty)); 555 else 556 break; 557 if (Operands.size() == AddRec->getNumOperands()) 558 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 559 } 560 561 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 562 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 563 return Result; 564} 565 566SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 567 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 568 return SCEVUnknown::get( 569 ConstantExpr::getZExt(SC->getValue(), Ty)); 570 571 // FIXME: If the input value is a chrec scev, and we can prove that the value 572 // did not overflow the old, smaller, value, we can zero extend all of the 573 // operands (often constants). This would allow analysis of something like 574 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 575 576 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 577 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 578 return Result; 579} 580 581// get - Get a canonical add expression, or something simpler if possible. 582SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 583 assert(!Ops.empty() && "Cannot get empty add!"); 584 if (Ops.size() == 1) return Ops[0]; 585 586 // Sort by complexity, this groups all similar expression types together. 587 GroupByComplexity(Ops); 588 589 // If there are any constants, fold them together. 590 unsigned Idx = 0; 591 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 592 ++Idx; 593 assert(Idx < Ops.size()); 594 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 595 // We found two constants, fold them together! 596 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 597 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 598 Ops[0] = SCEVConstant::get(CI); 599 Ops.erase(Ops.begin()+1); // Erase the folded element 600 if (Ops.size() == 1) return Ops[0]; 601 LHSC = cast<SCEVConstant>(Ops[0]); 602 } else { 603 // If we couldn't fold the expression, move to the next constant. Note 604 // that this is impossible to happen in practice because we always 605 // constant fold constant ints to constant ints. 606 ++Idx; 607 } 608 } 609 610 // If we are left with a constant zero being added, strip it off. 611 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 612 Ops.erase(Ops.begin()); 613 --Idx; 614 } 615 } 616 617 if (Ops.size() == 1) return Ops[0]; 618 619 // Okay, check to see if the same value occurs in the operand list twice. If 620 // so, merge them together into an multiply expression. Since we sorted the 621 // list, these values are required to be adjacent. 622 const Type *Ty = Ops[0]->getType(); 623 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 624 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 625 // Found a match, merge the two values into a multiply, and add any 626 // remaining values to the result. 627 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 628 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 629 if (Ops.size() == 2) 630 return Mul; 631 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 632 Ops.push_back(Mul); 633 return SCEVAddExpr::get(Ops); 634 } 635 636 // Okay, now we know the first non-constant operand. If there are add 637 // operands they would be next. 638 if (Idx < Ops.size()) { 639 bool DeletedAdd = false; 640 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 641 // If we have an add, expand the add operands onto the end of the operands 642 // list. 643 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 644 Ops.erase(Ops.begin()+Idx); 645 DeletedAdd = true; 646 } 647 648 // If we deleted at least one add, we added operands to the end of the list, 649 // and they are not necessarily sorted. Recurse to resort and resimplify 650 // any operands we just aquired. 651 if (DeletedAdd) 652 return get(Ops); 653 } 654 655 // Skip over the add expression until we get to a multiply. 656 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 657 ++Idx; 658 659 // If we are adding something to a multiply expression, make sure the 660 // something is not already an operand of the multiply. If so, merge it into 661 // the multiply. 662 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 663 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 664 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 665 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 666 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 667 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 668 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 669 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 670 if (Mul->getNumOperands() != 2) { 671 // If the multiply has more than two operands, we must get the 672 // Y*Z term. 673 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 674 MulOps.erase(MulOps.begin()+MulOp); 675 InnerMul = SCEVMulExpr::get(MulOps); 676 } 677 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 678 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 679 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 680 if (Ops.size() == 2) return OuterMul; 681 if (AddOp < Idx) { 682 Ops.erase(Ops.begin()+AddOp); 683 Ops.erase(Ops.begin()+Idx-1); 684 } else { 685 Ops.erase(Ops.begin()+Idx); 686 Ops.erase(Ops.begin()+AddOp-1); 687 } 688 Ops.push_back(OuterMul); 689 return SCEVAddExpr::get(Ops); 690 } 691 692 // Check this multiply against other multiplies being added together. 693 for (unsigned OtherMulIdx = Idx+1; 694 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 695 ++OtherMulIdx) { 696 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 697 // If MulOp occurs in OtherMul, we can fold the two multiplies 698 // together. 699 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 700 OMulOp != e; ++OMulOp) 701 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 702 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 703 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 704 if (Mul->getNumOperands() != 2) { 705 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 706 MulOps.erase(MulOps.begin()+MulOp); 707 InnerMul1 = SCEVMulExpr::get(MulOps); 708 } 709 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 710 if (OtherMul->getNumOperands() != 2) { 711 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 712 OtherMul->op_end()); 713 MulOps.erase(MulOps.begin()+OMulOp); 714 InnerMul2 = SCEVMulExpr::get(MulOps); 715 } 716 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 717 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 718 if (Ops.size() == 2) return OuterMul; 719 Ops.erase(Ops.begin()+Idx); 720 Ops.erase(Ops.begin()+OtherMulIdx-1); 721 Ops.push_back(OuterMul); 722 return SCEVAddExpr::get(Ops); 723 } 724 } 725 } 726 } 727 728 // If there are any add recurrences in the operands list, see if any other 729 // added values are loop invariant. If so, we can fold them into the 730 // recurrence. 731 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 732 ++Idx; 733 734 // Scan over all recurrences, trying to fold loop invariants into them. 735 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 736 // Scan all of the other operands to this add and add them to the vector if 737 // they are loop invariant w.r.t. the recurrence. 738 std::vector<SCEVHandle> LIOps; 739 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 740 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 741 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 742 LIOps.push_back(Ops[i]); 743 Ops.erase(Ops.begin()+i); 744 --i; --e; 745 } 746 747 // If we found some loop invariants, fold them into the recurrence. 748 if (!LIOps.empty()) { 749 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 750 LIOps.push_back(AddRec->getStart()); 751 752 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 753 AddRecOps[0] = SCEVAddExpr::get(LIOps); 754 755 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 756 // If all of the other operands were loop invariant, we are done. 757 if (Ops.size() == 1) return NewRec; 758 759 // Otherwise, add the folded AddRec by the non-liv parts. 760 for (unsigned i = 0;; ++i) 761 if (Ops[i] == AddRec) { 762 Ops[i] = NewRec; 763 break; 764 } 765 return SCEVAddExpr::get(Ops); 766 } 767 768 // Okay, if there weren't any loop invariants to be folded, check to see if 769 // there are multiple AddRec's with the same loop induction variable being 770 // added together. If so, we can fold them. 771 for (unsigned OtherIdx = Idx+1; 772 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 773 if (OtherIdx != Idx) { 774 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 775 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 776 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 777 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 778 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 779 if (i >= NewOps.size()) { 780 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 781 OtherAddRec->op_end()); 782 break; 783 } 784 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 785 } 786 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 787 788 if (Ops.size() == 2) return NewAddRec; 789 790 Ops.erase(Ops.begin()+Idx); 791 Ops.erase(Ops.begin()+OtherIdx-1); 792 Ops.push_back(NewAddRec); 793 return SCEVAddExpr::get(Ops); 794 } 795 } 796 797 // Otherwise couldn't fold anything into this recurrence. Move onto the 798 // next one. 799 } 800 801 // Okay, it looks like we really DO need an add expr. Check to see if we 802 // already have one, otherwise create a new one. 803 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 804 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 805 SCEVOps)]; 806 if (Result == 0) Result = new SCEVAddExpr(Ops); 807 return Result; 808} 809 810 811SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 812 assert(!Ops.empty() && "Cannot get empty mul!"); 813 814 // Sort by complexity, this groups all similar expression types together. 815 GroupByComplexity(Ops); 816 817 // If there are any constants, fold them together. 818 unsigned Idx = 0; 819 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 820 821 // C1*(C2+V) -> C1*C2 + C1*V 822 if (Ops.size() == 2) 823 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 824 if (Add->getNumOperands() == 2 && 825 isa<SCEVConstant>(Add->getOperand(0))) 826 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 827 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 828 829 830 ++Idx; 831 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 832 // We found two constants, fold them together! 833 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 834 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 835 Ops[0] = SCEVConstant::get(CI); 836 Ops.erase(Ops.begin()+1); // Erase the folded element 837 if (Ops.size() == 1) return Ops[0]; 838 LHSC = cast<SCEVConstant>(Ops[0]); 839 } else { 840 // If we couldn't fold the expression, move to the next constant. Note 841 // that this is impossible to happen in practice because we always 842 // constant fold constant ints to constant ints. 843 ++Idx; 844 } 845 } 846 847 // If we are left with a constant one being multiplied, strip it off. 848 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 849 Ops.erase(Ops.begin()); 850 --Idx; 851 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 852 // If we have a multiply of zero, it will always be zero. 853 return Ops[0]; 854 } 855 } 856 857 // Skip over the add expression until we get to a multiply. 858 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 859 ++Idx; 860 861 if (Ops.size() == 1) 862 return Ops[0]; 863 864 // If there are mul operands inline them all into this expression. 865 if (Idx < Ops.size()) { 866 bool DeletedMul = false; 867 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 868 // If we have an mul, expand the mul operands onto the end of the operands 869 // list. 870 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 871 Ops.erase(Ops.begin()+Idx); 872 DeletedMul = true; 873 } 874 875 // If we deleted at least one mul, we added operands to the end of the list, 876 // and they are not necessarily sorted. Recurse to resort and resimplify 877 // any operands we just aquired. 878 if (DeletedMul) 879 return get(Ops); 880 } 881 882 // If there are any add recurrences in the operands list, see if any other 883 // added values are loop invariant. If so, we can fold them into the 884 // recurrence. 885 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 886 ++Idx; 887 888 // Scan over all recurrences, trying to fold loop invariants into them. 889 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 890 // Scan all of the other operands to this mul and add them to the vector if 891 // they are loop invariant w.r.t. the recurrence. 892 std::vector<SCEVHandle> LIOps; 893 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 894 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 895 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 896 LIOps.push_back(Ops[i]); 897 Ops.erase(Ops.begin()+i); 898 --i; --e; 899 } 900 901 // If we found some loop invariants, fold them into the recurrence. 902 if (!LIOps.empty()) { 903 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 904 std::vector<SCEVHandle> NewOps; 905 NewOps.reserve(AddRec->getNumOperands()); 906 if (LIOps.size() == 1) { 907 SCEV *Scale = LIOps[0]; 908 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 909 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 910 } else { 911 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 912 std::vector<SCEVHandle> MulOps(LIOps); 913 MulOps.push_back(AddRec->getOperand(i)); 914 NewOps.push_back(SCEVMulExpr::get(MulOps)); 915 } 916 } 917 918 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 919 920 // If all of the other operands were loop invariant, we are done. 921 if (Ops.size() == 1) return NewRec; 922 923 // Otherwise, multiply the folded AddRec by the non-liv parts. 924 for (unsigned i = 0;; ++i) 925 if (Ops[i] == AddRec) { 926 Ops[i] = NewRec; 927 break; 928 } 929 return SCEVMulExpr::get(Ops); 930 } 931 932 // Okay, if there weren't any loop invariants to be folded, check to see if 933 // there are multiple AddRec's with the same loop induction variable being 934 // multiplied together. If so, we can fold them. 935 for (unsigned OtherIdx = Idx+1; 936 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 937 if (OtherIdx != Idx) { 938 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 939 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 940 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 941 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 942 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 943 G->getStart()); 944 SCEVHandle B = F->getStepRecurrence(); 945 SCEVHandle D = G->getStepRecurrence(); 946 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 947 SCEVMulExpr::get(G, B), 948 SCEVMulExpr::get(B, D)); 949 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 950 F->getLoop()); 951 if (Ops.size() == 2) return NewAddRec; 952 953 Ops.erase(Ops.begin()+Idx); 954 Ops.erase(Ops.begin()+OtherIdx-1); 955 Ops.push_back(NewAddRec); 956 return SCEVMulExpr::get(Ops); 957 } 958 } 959 960 // Otherwise couldn't fold anything into this recurrence. Move onto the 961 // next one. 962 } 963 964 // Okay, it looks like we really DO need an mul expr. Check to see if we 965 // already have one, otherwise create a new one. 966 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 967 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 968 SCEVOps)]; 969 if (Result == 0) 970 Result = new SCEVMulExpr(Ops); 971 return Result; 972} 973 974SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 975 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 976 if (RHSC->getValue()->equalsInt(1)) 977 return LHS; // X sdiv 1 --> x 978 if (RHSC->getValue()->isAllOnesValue()) 979 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 980 981 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 982 Constant *LHSCV = LHSC->getValue(); 983 Constant *RHSCV = RHSC->getValue(); 984 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 985 } 986 } 987 988 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 989 990 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 991 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 992 return Result; 993} 994 995 996/// SCEVAddRecExpr::get - Get a add recurrence expression for the 997/// specified loop. Simplify the expression as much as possible. 998SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 999 const SCEVHandle &Step, const Loop *L) { 1000 std::vector<SCEVHandle> Operands; 1001 Operands.push_back(Start); 1002 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1003 if (StepChrec->getLoop() == L) { 1004 Operands.insert(Operands.end(), StepChrec->op_begin(), 1005 StepChrec->op_end()); 1006 return get(Operands, L); 1007 } 1008 1009 Operands.push_back(Step); 1010 return get(Operands, L); 1011} 1012 1013/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1014/// specified loop. Simplify the expression as much as possible. 1015SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1016 const Loop *L) { 1017 if (Operands.size() == 1) return Operands[0]; 1018 1019 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1020 if (StepC->getValue()->isNullValue()) { 1021 Operands.pop_back(); 1022 return get(Operands, L); // { X,+,0 } --> X 1023 } 1024 1025 SCEVAddRecExpr *&Result = 1026 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1027 Operands.end()))]; 1028 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1029 return Result; 1030} 1031 1032SCEVHandle SCEVUnknown::get(Value *V) { 1033 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1034 return SCEVConstant::get(CI); 1035 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1036 if (Result == 0) Result = new SCEVUnknown(V); 1037 return Result; 1038} 1039 1040 1041//===----------------------------------------------------------------------===// 1042// ScalarEvolutionsImpl Definition and Implementation 1043//===----------------------------------------------------------------------===// 1044// 1045/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1046/// evolution code. 1047/// 1048namespace { 1049 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1050 /// F - The function we are analyzing. 1051 /// 1052 Function &F; 1053 1054 /// LI - The loop information for the function we are currently analyzing. 1055 /// 1056 LoopInfo &LI; 1057 1058 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1059 /// things. 1060 SCEVHandle UnknownValue; 1061 1062 /// Scalars - This is a cache of the scalars we have analyzed so far. 1063 /// 1064 std::map<Value*, SCEVHandle> Scalars; 1065 1066 /// IterationCounts - Cache the iteration count of the loops for this 1067 /// function as they are computed. 1068 std::map<const Loop*, SCEVHandle> IterationCounts; 1069 1070 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1071 /// the PHI instructions that we attempt to compute constant evolutions for. 1072 /// This allows us to avoid potentially expensive recomputation of these 1073 /// properties. An instruction maps to null if we are unable to compute its 1074 /// exit value. 1075 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1076 1077 public: 1078 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1079 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1080 1081 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1082 /// expression and create a new one. 1083 SCEVHandle getSCEV(Value *V); 1084 1085 /// hasSCEV - Return true if the SCEV for this value has already been 1086 /// computed. 1087 bool hasSCEV(Value *V) const { 1088 return Scalars.count(V); 1089 } 1090 1091 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1092 /// the specified value. 1093 void setSCEV(Value *V, const SCEVHandle &H) { 1094 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1095 assert(isNew && "This entry already existed!"); 1096 } 1097 1098 1099 /// getSCEVAtScope - Compute the value of the specified expression within 1100 /// the indicated loop (which may be null to indicate in no loop). If the 1101 /// expression cannot be evaluated, return UnknownValue itself. 1102 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1103 1104 1105 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1106 /// an analyzable loop-invariant iteration count. 1107 bool hasLoopInvariantIterationCount(const Loop *L); 1108 1109 /// getIterationCount - If the specified loop has a predictable iteration 1110 /// count, return it. Note that it is not valid to call this method on a 1111 /// loop without a loop-invariant iteration count. 1112 SCEVHandle getIterationCount(const Loop *L); 1113 1114 /// deleteInstructionFromRecords - This method should be called by the 1115 /// client before it removes an instruction from the program, to make sure 1116 /// that no dangling references are left around. 1117 void deleteInstructionFromRecords(Instruction *I); 1118 1119 private: 1120 /// createSCEV - We know that there is no SCEV for the specified value. 1121 /// Analyze the expression. 1122 SCEVHandle createSCEV(Value *V); 1123 1124 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1125 /// SCEVs. 1126 SCEVHandle createNodeForPHI(PHINode *PN); 1127 1128 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1129 /// for the specified instruction and replaces any references to the 1130 /// symbolic value SymName with the specified value. This is used during 1131 /// PHI resolution. 1132 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1133 const SCEVHandle &SymName, 1134 const SCEVHandle &NewVal); 1135 1136 /// ComputeIterationCount - Compute the number of times the specified loop 1137 /// will iterate. 1138 SCEVHandle ComputeIterationCount(const Loop *L); 1139 1140 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1141 /// 'setcc load X, cst', try to se if we can compute the trip count. 1142 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1143 Constant *RHS, 1144 const Loop *L, 1145 ICmpInst::Predicate p); 1146 1147 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1148 /// constant number of times (the condition evolves only from constants), 1149 /// try to evaluate a few iterations of the loop until we get the exit 1150 /// condition gets a value of ExitWhen (true or false). If we cannot 1151 /// evaluate the trip count of the loop, return UnknownValue. 1152 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1153 bool ExitWhen); 1154 1155 /// HowFarToZero - Return the number of times a backedge comparing the 1156 /// specified value to zero will execute. If not computable, return 1157 /// UnknownValue. 1158 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1159 1160 /// HowFarToNonZero - Return the number of times a backedge checking the 1161 /// specified value for nonzero will execute. If not computable, return 1162 /// UnknownValue. 1163 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1164 1165 /// HowManyLessThans - Return the number of times a backedge containing the 1166 /// specified less-than comparison will execute. If not computable, return 1167 /// UnknownValue. 1168 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L); 1169 1170 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1171 /// in the header of its containing loop, we know the loop executes a 1172 /// constant number of times, and the PHI node is just a recurrence 1173 /// involving constants, fold it. 1174 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1175 const Loop *L); 1176 }; 1177} 1178 1179//===----------------------------------------------------------------------===// 1180// Basic SCEV Analysis and PHI Idiom Recognition Code 1181// 1182 1183/// deleteInstructionFromRecords - This method should be called by the 1184/// client before it removes an instruction from the program, to make sure 1185/// that no dangling references are left around. 1186void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1187 Scalars.erase(I); 1188 if (PHINode *PN = dyn_cast<PHINode>(I)) 1189 ConstantEvolutionLoopExitValue.erase(PN); 1190} 1191 1192 1193/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1194/// expression and create a new one. 1195SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1196 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1197 1198 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1199 if (I != Scalars.end()) return I->second; 1200 SCEVHandle S = createSCEV(V); 1201 Scalars.insert(std::make_pair(V, S)); 1202 return S; 1203} 1204 1205/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1206/// the specified instruction and replaces any references to the symbolic value 1207/// SymName with the specified value. This is used during PHI resolution. 1208void ScalarEvolutionsImpl:: 1209ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1210 const SCEVHandle &NewVal) { 1211 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1212 if (SI == Scalars.end()) return; 1213 1214 SCEVHandle NV = 1215 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1216 if (NV == SI->second) return; // No change. 1217 1218 SI->second = NV; // Update the scalars map! 1219 1220 // Any instruction values that use this instruction might also need to be 1221 // updated! 1222 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1223 UI != E; ++UI) 1224 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1225} 1226 1227/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1228/// a loop header, making it a potential recurrence, or it doesn't. 1229/// 1230SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1231 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1232 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1233 if (L->getHeader() == PN->getParent()) { 1234 // If it lives in the loop header, it has two incoming values, one 1235 // from outside the loop, and one from inside. 1236 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1237 unsigned BackEdge = IncomingEdge^1; 1238 1239 // While we are analyzing this PHI node, handle its value symbolically. 1240 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1241 assert(Scalars.find(PN) == Scalars.end() && 1242 "PHI node already processed?"); 1243 Scalars.insert(std::make_pair(PN, SymbolicName)); 1244 1245 // Using this symbolic name for the PHI, analyze the value coming around 1246 // the back-edge. 1247 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1248 1249 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1250 // has a special value for the first iteration of the loop. 1251 1252 // If the value coming around the backedge is an add with the symbolic 1253 // value we just inserted, then we found a simple induction variable! 1254 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1255 // If there is a single occurrence of the symbolic value, replace it 1256 // with a recurrence. 1257 unsigned FoundIndex = Add->getNumOperands(); 1258 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1259 if (Add->getOperand(i) == SymbolicName) 1260 if (FoundIndex == e) { 1261 FoundIndex = i; 1262 break; 1263 } 1264 1265 if (FoundIndex != Add->getNumOperands()) { 1266 // Create an add with everything but the specified operand. 1267 std::vector<SCEVHandle> Ops; 1268 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1269 if (i != FoundIndex) 1270 Ops.push_back(Add->getOperand(i)); 1271 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1272 1273 // This is not a valid addrec if the step amount is varying each 1274 // loop iteration, but is not itself an addrec in this loop. 1275 if (Accum->isLoopInvariant(L) || 1276 (isa<SCEVAddRecExpr>(Accum) && 1277 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1278 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1279 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1280 1281 // Okay, for the entire analysis of this edge we assumed the PHI 1282 // to be symbolic. We now need to go back and update all of the 1283 // entries for the scalars that use the PHI (except for the PHI 1284 // itself) to use the new analyzed value instead of the "symbolic" 1285 // value. 1286 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1287 return PHISCEV; 1288 } 1289 } 1290 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1291 // Otherwise, this could be a loop like this: 1292 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1293 // In this case, j = {1,+,1} and BEValue is j. 1294 // Because the other in-value of i (0) fits the evolution of BEValue 1295 // i really is an addrec evolution. 1296 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1297 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1298 1299 // If StartVal = j.start - j.stride, we can use StartVal as the 1300 // initial step of the addrec evolution. 1301 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1302 AddRec->getOperand(1))) { 1303 SCEVHandle PHISCEV = 1304 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1305 1306 // Okay, for the entire analysis of this edge we assumed the PHI 1307 // to be symbolic. We now need to go back and update all of the 1308 // entries for the scalars that use the PHI (except for the PHI 1309 // itself) to use the new analyzed value instead of the "symbolic" 1310 // value. 1311 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1312 return PHISCEV; 1313 } 1314 } 1315 } 1316 1317 return SymbolicName; 1318 } 1319 1320 // If it's not a loop phi, we can't handle it yet. 1321 return SCEVUnknown::get(PN); 1322} 1323 1324/// GetConstantFactor - Determine the largest constant factor that S has. For 1325/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1326static uint64_t GetConstantFactor(SCEVHandle S) { 1327 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1328 if (uint64_t V = C->getValue()->getZExtValue()) 1329 return V; 1330 else // Zero is a multiple of everything. 1331 return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1); 1332 } 1333 1334 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1335 return GetConstantFactor(T->getOperand()) & 1336 T->getType()->getIntegralTypeMask(); 1337 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1338 return GetConstantFactor(E->getOperand()); 1339 1340 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1341 // The result is the min of all operands. 1342 uint64_t Res = GetConstantFactor(A->getOperand(0)); 1343 for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i) 1344 Res = std::min(Res, GetConstantFactor(A->getOperand(i))); 1345 return Res; 1346 } 1347 1348 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1349 // The result is the product of all the operands. 1350 uint64_t Res = GetConstantFactor(M->getOperand(0)); 1351 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) 1352 Res *= GetConstantFactor(M->getOperand(i)); 1353 return Res; 1354 } 1355 1356 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1357 // For now, we just handle linear expressions. 1358 if (A->getNumOperands() == 2) { 1359 // We want the GCD between the start and the stride value. 1360 uint64_t Start = GetConstantFactor(A->getOperand(0)); 1361 if (Start == 1) return 1; 1362 uint64_t Stride = GetConstantFactor(A->getOperand(1)); 1363 return GreatestCommonDivisor64(Start, Stride); 1364 } 1365 } 1366 1367 // SCEVSDivExpr, SCEVUnknown. 1368 return 1; 1369} 1370 1371/// createSCEV - We know that there is no SCEV for the specified value. 1372/// Analyze the expression. 1373/// 1374SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1375 if (Instruction *I = dyn_cast<Instruction>(V)) { 1376 switch (I->getOpcode()) { 1377 case Instruction::Add: 1378 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1379 getSCEV(I->getOperand(1))); 1380 case Instruction::Mul: 1381 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1382 getSCEV(I->getOperand(1))); 1383 case Instruction::SDiv: 1384 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1385 getSCEV(I->getOperand(1))); 1386 break; 1387 1388 case Instruction::Sub: 1389 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1390 getSCEV(I->getOperand(1))); 1391 case Instruction::Or: 1392 // If the RHS of the Or is a constant, we may have something like: 1393 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1394 // optimizations will transparently handle this case. 1395 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1396 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1397 uint64_t CommonFact = GetConstantFactor(LHS); 1398 assert(CommonFact && "Common factor should at least be 1!"); 1399 if (CommonFact > CI->getZExtValue()) { 1400 // If the LHS is a multiple that is larger than the RHS, use +. 1401 return SCEVAddExpr::get(LHS, 1402 getSCEV(I->getOperand(1))); 1403 } 1404 } 1405 break; 1406 1407 case Instruction::Shl: 1408 // Turn shift left of a constant amount into a multiply. 1409 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1410 Constant *X = ConstantInt::get(V->getType(), 1); 1411 X = ConstantExpr::getShl(X, SA); 1412 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1413 } 1414 break; 1415 1416 case Instruction::Trunc: 1417 // We don't handle trunc to bool yet. 1418 if (I->getType()->isInteger()) 1419 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1420 break; 1421 1422 case Instruction::ZExt: 1423 // We don't handle zext from bool yet. 1424 if (I->getOperand(0)->getType()->isInteger()) 1425 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1426 break; 1427 1428 case Instruction::BitCast: 1429 // BitCasts are no-op casts so we just eliminate the cast. 1430 if (I->getType()->isInteger() && I->getOperand(0)->getType()->isInteger()) 1431 return getSCEV(I->getOperand(0)); 1432 break; 1433 1434 case Instruction::PHI: 1435 return createNodeForPHI(cast<PHINode>(I)); 1436 1437 default: // We cannot analyze this expression. 1438 break; 1439 } 1440 } 1441 1442 return SCEVUnknown::get(V); 1443} 1444 1445 1446 1447//===----------------------------------------------------------------------===// 1448// Iteration Count Computation Code 1449// 1450 1451/// getIterationCount - If the specified loop has a predictable iteration 1452/// count, return it. Note that it is not valid to call this method on a 1453/// loop without a loop-invariant iteration count. 1454SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1455 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1456 if (I == IterationCounts.end()) { 1457 SCEVHandle ItCount = ComputeIterationCount(L); 1458 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1459 if (ItCount != UnknownValue) { 1460 assert(ItCount->isLoopInvariant(L) && 1461 "Computed trip count isn't loop invariant for loop!"); 1462 ++NumTripCountsComputed; 1463 } else if (isa<PHINode>(L->getHeader()->begin())) { 1464 // Only count loops that have phi nodes as not being computable. 1465 ++NumTripCountsNotComputed; 1466 } 1467 } 1468 return I->second; 1469} 1470 1471/// ComputeIterationCount - Compute the number of times the specified loop 1472/// will iterate. 1473SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1474 // If the loop has a non-one exit block count, we can't analyze it. 1475 std::vector<BasicBlock*> ExitBlocks; 1476 L->getExitBlocks(ExitBlocks); 1477 if (ExitBlocks.size() != 1) return UnknownValue; 1478 1479 // Okay, there is one exit block. Try to find the condition that causes the 1480 // loop to be exited. 1481 BasicBlock *ExitBlock = ExitBlocks[0]; 1482 1483 BasicBlock *ExitingBlock = 0; 1484 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1485 PI != E; ++PI) 1486 if (L->contains(*PI)) { 1487 if (ExitingBlock == 0) 1488 ExitingBlock = *PI; 1489 else 1490 return UnknownValue; // More than one block exiting! 1491 } 1492 assert(ExitingBlock && "No exits from loop, something is broken!"); 1493 1494 // Okay, we've computed the exiting block. See what condition causes us to 1495 // exit. 1496 // 1497 // FIXME: we should be able to handle switch instructions (with a single exit) 1498 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1499 if (ExitBr == 0) return UnknownValue; 1500 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1501 1502 // At this point, we know we have a conditional branch that determines whether 1503 // the loop is exited. However, we don't know if the branch is executed each 1504 // time through the loop. If not, then the execution count of the branch will 1505 // not be equal to the trip count of the loop. 1506 // 1507 // Currently we check for this by checking to see if the Exit branch goes to 1508 // the loop header. If so, we know it will always execute the same number of 1509 // times as the loop. More extensive analysis could be done to handle more 1510 // cases here. 1511 if (ExitBr->getSuccessor(0) != L->getHeader() && 1512 ExitBr->getSuccessor(1) != L->getHeader()) 1513 return UnknownValue; 1514 1515 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1516 1517 // If its not an integer comparison then compute it the hard way. 1518 // Note that ICmpInst deals with pointer comparisons too so we must check 1519 // the type of the operand. 1520 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1521 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1522 ExitBr->getSuccessor(0) == ExitBlock); 1523 1524 // If the condition was exit on true, convert the condition to exit on false 1525 ICmpInst::Predicate Cond; 1526 if (ExitBr->getSuccessor(1) == ExitBlock) 1527 Cond = ExitCond->getPredicate(); 1528 else 1529 Cond = ExitCond->getInversePredicate(); 1530 1531 // Handle common loops like: for (X = "string"; *X; ++X) 1532 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1533 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1534 SCEVHandle ItCnt = 1535 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1536 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1537 } 1538 1539 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1540 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1541 1542 // Try to evaluate any dependencies out of the loop. 1543 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1544 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1545 Tmp = getSCEVAtScope(RHS, L); 1546 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1547 1548 // At this point, we would like to compute how many iterations of the 1549 // loop the predicate will return true for these inputs. 1550 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1551 // If there is a constant, force it into the RHS. 1552 std::swap(LHS, RHS); 1553 Cond = ICmpInst::getSwappedPredicate(Cond); 1554 } 1555 1556 // FIXME: think about handling pointer comparisons! i.e.: 1557 // while (P != P+100) ++P; 1558 1559 // If we have a comparison of a chrec against a constant, try to use value 1560 // ranges to answer this query. 1561 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1562 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1563 if (AddRec->getLoop() == L) { 1564 // Form the comparison range using the constant of the correct type so 1565 // that the ConstantRange class knows to do a signed or unsigned 1566 // comparison. 1567 ConstantInt *CompVal = RHSC->getValue(); 1568 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1569 CompVal = dyn_cast<ConstantInt>( 1570 ConstantExpr::getBitCast(CompVal, RealTy)); 1571 if (CompVal) { 1572 // Form the constant range. 1573 ConstantRange CompRange(Cond, CompVal); 1574 1575 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, 1576 false /*Always treat as unsigned range*/); 1577 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1578 } 1579 } 1580 1581 switch (Cond) { 1582 case ICmpInst::ICMP_NE: { // while (X != Y) 1583 // Convert to: while (X-Y != 0) 1584 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1585 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1586 break; 1587 } 1588 case ICmpInst::ICMP_EQ: { 1589 // Convert to: while (X-Y == 0) // while (X == Y) 1590 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1591 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1592 break; 1593 } 1594 case ICmpInst::ICMP_SLT: { 1595 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1596 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1597 break; 1598 } 1599 case ICmpInst::ICMP_SGT: { 1600 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1601 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1602 break; 1603 } 1604 default: 1605#if 0 1606 cerr << "ComputeIterationCount "; 1607 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1608 cerr << "[unsigned] "; 1609 cerr << *LHS << " " 1610 << Instruction::getOpcodeName(Instruction::ICmp) 1611 << " " << *RHS << "\n"; 1612#endif 1613 break; 1614 } 1615 return ComputeIterationCountExhaustively(L, ExitCond, 1616 ExitBr->getSuccessor(0) == ExitBlock); 1617} 1618 1619static ConstantInt * 1620EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1621 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1622 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1623 assert(isa<SCEVConstant>(Val) && 1624 "Evaluation of SCEV at constant didn't fold correctly?"); 1625 return cast<SCEVConstant>(Val)->getValue(); 1626} 1627 1628/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1629/// and a GEP expression (missing the pointer index) indexing into it, return 1630/// the addressed element of the initializer or null if the index expression is 1631/// invalid. 1632static Constant * 1633GetAddressedElementFromGlobal(GlobalVariable *GV, 1634 const std::vector<ConstantInt*> &Indices) { 1635 Constant *Init = GV->getInitializer(); 1636 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1637 uint64_t Idx = Indices[i]->getZExtValue(); 1638 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1639 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1640 Init = cast<Constant>(CS->getOperand(Idx)); 1641 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1642 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1643 Init = cast<Constant>(CA->getOperand(Idx)); 1644 } else if (isa<ConstantAggregateZero>(Init)) { 1645 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1646 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1647 Init = Constant::getNullValue(STy->getElementType(Idx)); 1648 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1649 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1650 Init = Constant::getNullValue(ATy->getElementType()); 1651 } else { 1652 assert(0 && "Unknown constant aggregate type!"); 1653 } 1654 return 0; 1655 } else { 1656 return 0; // Unknown initializer type 1657 } 1658 } 1659 return Init; 1660} 1661 1662/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1663/// 'setcc load X, cst', try to se if we can compute the trip count. 1664SCEVHandle ScalarEvolutionsImpl:: 1665ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1666 const Loop *L, 1667 ICmpInst::Predicate predicate) { 1668 if (LI->isVolatile()) return UnknownValue; 1669 1670 // Check to see if the loaded pointer is a getelementptr of a global. 1671 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1672 if (!GEP) return UnknownValue; 1673 1674 // Make sure that it is really a constant global we are gepping, with an 1675 // initializer, and make sure the first IDX is really 0. 1676 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1677 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1678 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1679 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1680 return UnknownValue; 1681 1682 // Okay, we allow one non-constant index into the GEP instruction. 1683 Value *VarIdx = 0; 1684 std::vector<ConstantInt*> Indexes; 1685 unsigned VarIdxNum = 0; 1686 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1687 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1688 Indexes.push_back(CI); 1689 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1690 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1691 VarIdx = GEP->getOperand(i); 1692 VarIdxNum = i-2; 1693 Indexes.push_back(0); 1694 } 1695 1696 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1697 // Check to see if X is a loop variant variable value now. 1698 SCEVHandle Idx = getSCEV(VarIdx); 1699 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1700 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1701 1702 // We can only recognize very limited forms of loop index expressions, in 1703 // particular, only affine AddRec's like {C1,+,C2}. 1704 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1705 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1706 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1707 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1708 return UnknownValue; 1709 1710 unsigned MaxSteps = MaxBruteForceIterations; 1711 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1712 ConstantInt *ItCst = 1713 ConstantInt::get(IdxExpr->getType(), IterationNum); 1714 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1715 1716 // Form the GEP offset. 1717 Indexes[VarIdxNum] = Val; 1718 1719 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1720 if (Result == 0) break; // Cannot compute! 1721 1722 // Evaluate the condition for this iteration. 1723 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1724 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1725 if (cast<ConstantInt>(Result)->getBoolValue() == false) { 1726#if 0 1727 cerr << "\n***\n*** Computed loop count " << *ItCst 1728 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1729 << "***\n"; 1730#endif 1731 ++NumArrayLenItCounts; 1732 return SCEVConstant::get(ItCst); // Found terminating iteration! 1733 } 1734 } 1735 return UnknownValue; 1736} 1737 1738 1739/// CanConstantFold - Return true if we can constant fold an instruction of the 1740/// specified type, assuming that all operands were constants. 1741static bool CanConstantFold(const Instruction *I) { 1742 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || isa<CmpInst>(I) || 1743 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1744 return true; 1745 1746 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1747 if (const Function *F = CI->getCalledFunction()) 1748 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1749 return false; 1750} 1751 1752/// ConstantFold - Constant fold an instruction of the specified type with the 1753/// specified constant operands. This function may modify the operands vector. 1754static Constant *ConstantFold(const Instruction *I, 1755 std::vector<Constant*> &Operands) { 1756 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1757 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1758 1759 if (isa<CastInst>(I)) 1760 return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType()); 1761 1762 switch (I->getOpcode()) { 1763 case Instruction::Select: 1764 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1765 case Instruction::Call: 1766 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1767 Operands.erase(Operands.begin()); 1768 return ConstantFoldCall(cast<Function>(GV), Operands); 1769 } 1770 return 0; 1771 case Instruction::GetElementPtr: { 1772 Constant *Base = Operands[0]; 1773 Operands.erase(Operands.begin()); 1774 return ConstantExpr::getGetElementPtr(Base, Operands); 1775 } 1776 case Instruction::ICmp: 1777 return ConstantExpr::getICmp( 1778 cast<ICmpInst>(I)->getPredicate(), Operands[0], Operands[1]); 1779 case Instruction::FCmp: 1780 return ConstantExpr::getFCmp( 1781 cast<FCmpInst>(I)->getPredicate(), Operands[0], Operands[1]); 1782 } 1783 return 0; 1784} 1785 1786 1787/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1788/// in the loop that V is derived from. We allow arbitrary operations along the 1789/// way, but the operands of an operation must either be constants or a value 1790/// derived from a constant PHI. If this expression does not fit with these 1791/// constraints, return null. 1792static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1793 // If this is not an instruction, or if this is an instruction outside of the 1794 // loop, it can't be derived from a loop PHI. 1795 Instruction *I = dyn_cast<Instruction>(V); 1796 if (I == 0 || !L->contains(I->getParent())) return 0; 1797 1798 if (PHINode *PN = dyn_cast<PHINode>(I)) 1799 if (L->getHeader() == I->getParent()) 1800 return PN; 1801 else 1802 // We don't currently keep track of the control flow needed to evaluate 1803 // PHIs, so we cannot handle PHIs inside of loops. 1804 return 0; 1805 1806 // If we won't be able to constant fold this expression even if the operands 1807 // are constants, return early. 1808 if (!CanConstantFold(I)) return 0; 1809 1810 // Otherwise, we can evaluate this instruction if all of its operands are 1811 // constant or derived from a PHI node themselves. 1812 PHINode *PHI = 0; 1813 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1814 if (!(isa<Constant>(I->getOperand(Op)) || 1815 isa<GlobalValue>(I->getOperand(Op)))) { 1816 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1817 if (P == 0) return 0; // Not evolving from PHI 1818 if (PHI == 0) 1819 PHI = P; 1820 else if (PHI != P) 1821 return 0; // Evolving from multiple different PHIs. 1822 } 1823 1824 // This is a expression evolving from a constant PHI! 1825 return PHI; 1826} 1827 1828/// EvaluateExpression - Given an expression that passes the 1829/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1830/// in the loop has the value PHIVal. If we can't fold this expression for some 1831/// reason, return null. 1832static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1833 if (isa<PHINode>(V)) return PHIVal; 1834 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1835 return GV; 1836 if (Constant *C = dyn_cast<Constant>(V)) return C; 1837 Instruction *I = cast<Instruction>(V); 1838 1839 std::vector<Constant*> Operands; 1840 Operands.resize(I->getNumOperands()); 1841 1842 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1843 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1844 if (Operands[i] == 0) return 0; 1845 } 1846 1847 return ConstantFold(I, Operands); 1848} 1849 1850/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1851/// in the header of its containing loop, we know the loop executes a 1852/// constant number of times, and the PHI node is just a recurrence 1853/// involving constants, fold it. 1854Constant *ScalarEvolutionsImpl:: 1855getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1856 std::map<PHINode*, Constant*>::iterator I = 1857 ConstantEvolutionLoopExitValue.find(PN); 1858 if (I != ConstantEvolutionLoopExitValue.end()) 1859 return I->second; 1860 1861 if (Its > MaxBruteForceIterations) 1862 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1863 1864 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1865 1866 // Since the loop is canonicalized, the PHI node must have two entries. One 1867 // entry must be a constant (coming in from outside of the loop), and the 1868 // second must be derived from the same PHI. 1869 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1870 Constant *StartCST = 1871 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1872 if (StartCST == 0) 1873 return RetVal = 0; // Must be a constant. 1874 1875 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1876 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1877 if (PN2 != PN) 1878 return RetVal = 0; // Not derived from same PHI. 1879 1880 // Execute the loop symbolically to determine the exit value. 1881 unsigned IterationNum = 0; 1882 unsigned NumIterations = Its; 1883 if (NumIterations != Its) 1884 return RetVal = 0; // More than 2^32 iterations?? 1885 1886 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1887 if (IterationNum == NumIterations) 1888 return RetVal = PHIVal; // Got exit value! 1889 1890 // Compute the value of the PHI node for the next iteration. 1891 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1892 if (NextPHI == PHIVal) 1893 return RetVal = NextPHI; // Stopped evolving! 1894 if (NextPHI == 0) 1895 return 0; // Couldn't evaluate! 1896 PHIVal = NextPHI; 1897 } 1898} 1899 1900/// ComputeIterationCountExhaustively - If the trip is known to execute a 1901/// constant number of times (the condition evolves only from constants), 1902/// try to evaluate a few iterations of the loop until we get the exit 1903/// condition gets a value of ExitWhen (true or false). If we cannot 1904/// evaluate the trip count of the loop, return UnknownValue. 1905SCEVHandle ScalarEvolutionsImpl:: 1906ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1907 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1908 if (PN == 0) return UnknownValue; 1909 1910 // Since the loop is canonicalized, the PHI node must have two entries. One 1911 // entry must be a constant (coming in from outside of the loop), and the 1912 // second must be derived from the same PHI. 1913 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1914 Constant *StartCST = 1915 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1916 if (StartCST == 0) return UnknownValue; // Must be a constant. 1917 1918 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1919 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1920 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1921 1922 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1923 // the loop symbolically to determine when the condition gets a value of 1924 // "ExitWhen". 1925 unsigned IterationNum = 0; 1926 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1927 for (Constant *PHIVal = StartCST; 1928 IterationNum != MaxIterations; ++IterationNum) { 1929 ConstantInt *CondVal = 1930 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 1931 1932 // Couldn't symbolically evaluate. 1933 if (!CondVal || CondVal->getType() != Type::Int1Ty) return UnknownValue; 1934 1935 if (CondVal->getBoolValue() == ExitWhen) { 1936 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1937 ++NumBruteForceTripCountsComputed; 1938 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum)); 1939 } 1940 1941 // Compute the value of the PHI node for the next iteration. 1942 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1943 if (NextPHI == 0 || NextPHI == PHIVal) 1944 return UnknownValue; // Couldn't evaluate or not making progress... 1945 PHIVal = NextPHI; 1946 } 1947 1948 // Too many iterations were needed to evaluate. 1949 return UnknownValue; 1950} 1951 1952/// getSCEVAtScope - Compute the value of the specified expression within the 1953/// indicated loop (which may be null to indicate in no loop). If the 1954/// expression cannot be evaluated, return UnknownValue. 1955SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1956 // FIXME: this should be turned into a virtual method on SCEV! 1957 1958 if (isa<SCEVConstant>(V)) return V; 1959 1960 // If this instruction is evolves from a constant-evolving PHI, compute the 1961 // exit value from the loop without using SCEVs. 1962 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1963 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1964 const Loop *LI = this->LI[I->getParent()]; 1965 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1966 if (PHINode *PN = dyn_cast<PHINode>(I)) 1967 if (PN->getParent() == LI->getHeader()) { 1968 // Okay, there is no closed form solution for the PHI node. Check 1969 // to see if the loop that contains it has a known iteration count. 1970 // If so, we may be able to force computation of the exit value. 1971 SCEVHandle IterationCount = getIterationCount(LI); 1972 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1973 // Okay, we know how many times the containing loop executes. If 1974 // this is a constant evolving PHI node, get the final value at 1975 // the specified iteration number. 1976 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1977 ICC->getValue()->getZExtValue(), 1978 LI); 1979 if (RV) return SCEVUnknown::get(RV); 1980 } 1981 } 1982 1983 // Okay, this is an expression that we cannot symbolically evaluate 1984 // into a SCEV. Check to see if it's possible to symbolically evaluate 1985 // the arguments into constants, and if so, try to constant propagate the 1986 // result. This is particularly useful for computing loop exit values. 1987 if (CanConstantFold(I)) { 1988 std::vector<Constant*> Operands; 1989 Operands.reserve(I->getNumOperands()); 1990 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1991 Value *Op = I->getOperand(i); 1992 if (Constant *C = dyn_cast<Constant>(Op)) { 1993 Operands.push_back(C); 1994 } else { 1995 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1996 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1997 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 1998 Op->getType(), 1999 false)); 2000 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2001 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2002 Operands.push_back(ConstantExpr::getIntegerCast(C, 2003 Op->getType(), 2004 false)); 2005 else 2006 return V; 2007 } else { 2008 return V; 2009 } 2010 } 2011 } 2012 return SCEVUnknown::get(ConstantFold(I, Operands)); 2013 } 2014 } 2015 2016 // This is some other type of SCEVUnknown, just return it. 2017 return V; 2018 } 2019 2020 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2021 // Avoid performing the look-up in the common case where the specified 2022 // expression has no loop-variant portions. 2023 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2024 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2025 if (OpAtScope != Comm->getOperand(i)) { 2026 if (OpAtScope == UnknownValue) return UnknownValue; 2027 // Okay, at least one of these operands is loop variant but might be 2028 // foldable. Build a new instance of the folded commutative expression. 2029 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2030 NewOps.push_back(OpAtScope); 2031 2032 for (++i; i != e; ++i) { 2033 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2034 if (OpAtScope == UnknownValue) return UnknownValue; 2035 NewOps.push_back(OpAtScope); 2036 } 2037 if (isa<SCEVAddExpr>(Comm)) 2038 return SCEVAddExpr::get(NewOps); 2039 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2040 return SCEVMulExpr::get(NewOps); 2041 } 2042 } 2043 // If we got here, all operands are loop invariant. 2044 return Comm; 2045 } 2046 2047 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2048 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2049 if (LHS == UnknownValue) return LHS; 2050 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2051 if (RHS == UnknownValue) return RHS; 2052 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2053 return Div; // must be loop invariant 2054 return SCEVSDivExpr::get(LHS, RHS); 2055 } 2056 2057 // If this is a loop recurrence for a loop that does not contain L, then we 2058 // are dealing with the final value computed by the loop. 2059 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2060 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2061 // To evaluate this recurrence, we need to know how many times the AddRec 2062 // loop iterates. Compute this now. 2063 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2064 if (IterationCount == UnknownValue) return UnknownValue; 2065 IterationCount = getTruncateOrZeroExtend(IterationCount, 2066 AddRec->getType()); 2067 2068 // If the value is affine, simplify the expression evaluation to just 2069 // Start + Step*IterationCount. 2070 if (AddRec->isAffine()) 2071 return SCEVAddExpr::get(AddRec->getStart(), 2072 SCEVMulExpr::get(IterationCount, 2073 AddRec->getOperand(1))); 2074 2075 // Otherwise, evaluate it the hard way. 2076 return AddRec->evaluateAtIteration(IterationCount); 2077 } 2078 return UnknownValue; 2079 } 2080 2081 //assert(0 && "Unknown SCEV type!"); 2082 return UnknownValue; 2083} 2084 2085 2086/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2087/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2088/// might be the same) or two SCEVCouldNotCompute objects. 2089/// 2090static std::pair<SCEVHandle,SCEVHandle> 2091SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2092 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2093 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2094 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2095 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2096 2097 // We currently can only solve this if the coefficients are constants. 2098 if (!L || !M || !N) { 2099 SCEV *CNC = new SCEVCouldNotCompute(); 2100 return std::make_pair(CNC, CNC); 2101 } 2102 2103 Constant *C = L->getValue(); 2104 Constant *Two = ConstantInt::get(C->getType(), 2); 2105 2106 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2107 // The B coefficient is M-N/2 2108 Constant *B = ConstantExpr::getSub(M->getValue(), 2109 ConstantExpr::getSDiv(N->getValue(), 2110 Two)); 2111 // The A coefficient is N/2 2112 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two); 2113 2114 // Compute the B^2-4ac term. 2115 Constant *SqrtTerm = 2116 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2117 ConstantExpr::getMul(A, C)); 2118 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2119 2120 // Compute floor(sqrt(B^2-4ac)) 2121 uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue(); 2122 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2123 // The square root might not be precise for arbitrary 64-bit integer 2124 // values. Do some sanity checks to ensure it's correct. 2125 if (SqrtValV2*SqrtValV2 > SqrtValV || 2126 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2127 SCEV *CNC = new SCEVCouldNotCompute(); 2128 return std::make_pair(CNC, CNC); 2129 } 2130 2131 ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2); 2132 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType()); 2133 2134 Constant *NegB = ConstantExpr::getNeg(B); 2135 Constant *TwoA = ConstantExpr::getMul(A, Two); 2136 2137 // The divisions must be performed as signed divisions. 2138 Constant *Solution1 = 2139 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2140 Constant *Solution2 = 2141 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2142 return std::make_pair(SCEVUnknown::get(Solution1), 2143 SCEVUnknown::get(Solution2)); 2144} 2145 2146/// HowFarToZero - Return the number of times a backedge comparing the specified 2147/// value to zero will execute. If not computable, return UnknownValue 2148SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2149 // If the value is a constant 2150 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2151 // If the value is already zero, the branch will execute zero times. 2152 if (C->getValue()->isNullValue()) return C; 2153 return UnknownValue; // Otherwise it will loop infinitely. 2154 } 2155 2156 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2157 if (!AddRec || AddRec->getLoop() != L) 2158 return UnknownValue; 2159 2160 if (AddRec->isAffine()) { 2161 // If this is an affine expression the execution count of this branch is 2162 // equal to: 2163 // 2164 // (0 - Start/Step) iff Start % Step == 0 2165 // 2166 // Get the initial value for the loop. 2167 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2168 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2169 SCEVHandle Step = AddRec->getOperand(1); 2170 2171 Step = getSCEVAtScope(Step, L->getParentLoop()); 2172 2173 // Figure out if Start % Step == 0. 2174 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2175 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2176 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2177 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2178 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2179 return Start; // 0 - Start/-1 == Start 2180 2181 // Check to see if Start is divisible by SC with no remainder. 2182 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2183 ConstantInt *StartCC = StartC->getValue(); 2184 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2185 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2186 if (Rem->isNullValue()) { 2187 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2188 return SCEVUnknown::get(Result); 2189 } 2190 } 2191 } 2192 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2193 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2194 // the quadratic equation to solve it. 2195 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2196 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2197 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2198 if (R1) { 2199#if 0 2200 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2201 << " sol#2: " << *R2 << "\n"; 2202#endif 2203 // Pick the smallest positive root value. 2204 if (ConstantInt *CB = 2205 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2206 R1->getValue(), R2->getValue()))) { 2207 if (CB->getBoolValue() == false) 2208 std::swap(R1, R2); // R1 is the minimum root now. 2209 2210 // We can only use this value if the chrec ends up with an exact zero 2211 // value at this index. When solving for "X*X != 5", for example, we 2212 // should not accept a root of 2. 2213 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2214 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2215 if (EvalVal->getValue()->isNullValue()) 2216 return R1; // We found a quadratic root! 2217 } 2218 } 2219 } 2220 2221 return UnknownValue; 2222} 2223 2224/// HowFarToNonZero - Return the number of times a backedge checking the 2225/// specified value for nonzero will execute. If not computable, return 2226/// UnknownValue 2227SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2228 // Loops that look like: while (X == 0) are very strange indeed. We don't 2229 // handle them yet except for the trivial case. This could be expanded in the 2230 // future as needed. 2231 2232 // If the value is a constant, check to see if it is known to be non-zero 2233 // already. If so, the backedge will execute zero times. 2234 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2235 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2236 Constant *NonZero = 2237 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2238 if (NonZero == ConstantInt::getTrue()) 2239 return getSCEV(Zero); 2240 return UnknownValue; // Otherwise it will loop infinitely. 2241 } 2242 2243 // We could implement others, but I really doubt anyone writes loops like 2244 // this, and if they did, they would already be constant folded. 2245 return UnknownValue; 2246} 2247 2248/// HowManyLessThans - Return the number of times a backedge containing the 2249/// specified less-than comparison will execute. If not computable, return 2250/// UnknownValue. 2251SCEVHandle ScalarEvolutionsImpl:: 2252HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2253 // Only handle: "ADDREC < LoopInvariant". 2254 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2255 2256 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2257 if (!AddRec || AddRec->getLoop() != L) 2258 return UnknownValue; 2259 2260 if (AddRec->isAffine()) { 2261 // FORNOW: We only support unit strides. 2262 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2263 if (AddRec->getOperand(1) != One) 2264 return UnknownValue; 2265 2266 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2267 // know that m is >= n on input to the loop. If it is, the condition return 2268 // true zero times. What we really should return, for full generality, is 2269 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2270 // canonical loop form: most do-loops will have a check that dominates the 2271 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2272 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2273 2274 // Search for the check. 2275 BasicBlock *Preheader = L->getLoopPreheader(); 2276 BasicBlock *PreheaderDest = L->getHeader(); 2277 if (Preheader == 0) return UnknownValue; 2278 2279 BranchInst *LoopEntryPredicate = 2280 dyn_cast<BranchInst>(Preheader->getTerminator()); 2281 if (!LoopEntryPredicate) return UnknownValue; 2282 2283 // This might be a critical edge broken out. If the loop preheader ends in 2284 // an unconditional branch to the loop, check to see if the preheader has a 2285 // single predecessor, and if so, look for its terminator. 2286 while (LoopEntryPredicate->isUnconditional()) { 2287 PreheaderDest = Preheader; 2288 Preheader = Preheader->getSinglePredecessor(); 2289 if (!Preheader) return UnknownValue; // Multiple preds. 2290 2291 LoopEntryPredicate = 2292 dyn_cast<BranchInst>(Preheader->getTerminator()); 2293 if (!LoopEntryPredicate) return UnknownValue; 2294 } 2295 2296 // Now that we found a conditional branch that dominates the loop, check to 2297 // see if it is the comparison we are looking for. 2298 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){ 2299 Value *PreCondLHS = ICI->getOperand(0); 2300 Value *PreCondRHS = ICI->getOperand(1); 2301 ICmpInst::Predicate Cond; 2302 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2303 Cond = ICI->getPredicate(); 2304 else 2305 Cond = ICI->getInversePredicate(); 2306 2307 switch (Cond) { 2308 case ICmpInst::ICMP_UGT: 2309 std::swap(PreCondLHS, PreCondRHS); 2310 Cond = ICmpInst::ICMP_ULT; 2311 break; 2312 case ICmpInst::ICMP_SGT: 2313 std::swap(PreCondLHS, PreCondRHS); 2314 Cond = ICmpInst::ICMP_SLT; 2315 break; 2316 default: break; 2317 } 2318 2319 if (Cond == ICmpInst::ICMP_SLT) { 2320 if (PreCondLHS->getType()->isInteger()) { 2321 if (RHS != getSCEV(PreCondRHS)) 2322 return UnknownValue; // Not a comparison against 'm'. 2323 2324 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2325 != getSCEV(PreCondLHS)) 2326 return UnknownValue; // Not a comparison against 'n-1'. 2327 } 2328 else return UnknownValue; 2329 } else if (Cond == ICmpInst::ICMP_ULT) 2330 return UnknownValue; 2331 2332 // cerr << "Computed Loop Trip Count as: " 2333 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2334 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2335 } 2336 else 2337 return UnknownValue; 2338 } 2339 2340 return UnknownValue; 2341} 2342 2343/// getNumIterationsInRange - Return the number of iterations of this loop that 2344/// produce values in the specified constant range. Another way of looking at 2345/// this is that it returns the first iteration number where the value is not in 2346/// the condition, thus computing the exit count. If the iteration count can't 2347/// be computed, an instance of SCEVCouldNotCompute is returned. 2348SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2349 bool isSigned) const { 2350 if (Range.isFullSet()) // Infinite loop. 2351 return new SCEVCouldNotCompute(); 2352 2353 // If the start is a non-zero constant, shift the range to simplify things. 2354 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2355 if (!SC->getValue()->isNullValue()) { 2356 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2357 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2358 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2359 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2360 return ShiftedAddRec->getNumIterationsInRange( 2361 Range.subtract(SC->getValue()),isSigned); 2362 // This is strange and shouldn't happen. 2363 return new SCEVCouldNotCompute(); 2364 } 2365 2366 // The only time we can solve this is when we have all constant indices. 2367 // Otherwise, we cannot determine the overflow conditions. 2368 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2369 if (!isa<SCEVConstant>(getOperand(i))) 2370 return new SCEVCouldNotCompute(); 2371 2372 2373 // Okay at this point we know that all elements of the chrec are constants and 2374 // that the start element is zero. 2375 2376 // First check to see if the range contains zero. If not, the first 2377 // iteration exits. 2378 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2379 if (!Range.contains(Zero, isSigned)) return SCEVConstant::get(Zero); 2380 2381 if (isAffine()) { 2382 // If this is an affine expression then we have this situation: 2383 // Solve {0,+,A} in Range === Ax in Range 2384 2385 // Since we know that zero is in the range, we know that the upper value of 2386 // the range must be the first possible exit value. Also note that we 2387 // already checked for a full range. 2388 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2389 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2390 ConstantInt *One = ConstantInt::get(getType(), 1); 2391 2392 // The exit value should be (Upper+A-1)/A. 2393 Constant *ExitValue = Upper; 2394 if (A != One) { 2395 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2396 ExitValue = ConstantExpr::getSDiv(ExitValue, A); 2397 } 2398 assert(isa<ConstantInt>(ExitValue) && 2399 "Constant folding of integers not implemented?"); 2400 2401 // Evaluate at the exit value. If we really did fall out of the valid 2402 // range, then we computed our trip count, otherwise wrap around or other 2403 // things must have happened. 2404 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2405 if (Range.contains(Val, isSigned)) 2406 return new SCEVCouldNotCompute(); // Something strange happened 2407 2408 // Ensure that the previous value is in the range. This is a sanity check. 2409 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2410 ConstantExpr::getSub(ExitValue, One)), isSigned) && 2411 "Linear scev computation is off in a bad way!"); 2412 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2413 } else if (isQuadratic()) { 2414 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2415 // quadratic equation to solve it. To do this, we must frame our problem in 2416 // terms of figuring out when zero is crossed, instead of when 2417 // Range.getUpper() is crossed. 2418 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2419 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2420 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2421 2422 // Next, solve the constructed addrec 2423 std::pair<SCEVHandle,SCEVHandle> Roots = 2424 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2425 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2426 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2427 if (R1) { 2428 // Pick the smallest positive root value. 2429 if (ConstantInt *CB = 2430 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2431 R1->getValue(), R2->getValue()))) { 2432 if (CB->getBoolValue() == false) 2433 std::swap(R1, R2); // R1 is the minimum root now. 2434 2435 // Make sure the root is not off by one. The returned iteration should 2436 // not be in the range, but the previous one should be. When solving 2437 // for "X*X < 5", for example, we should not return a root of 2. 2438 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2439 R1->getValue()); 2440 if (Range.contains(R1Val, isSigned)) { 2441 // The next iteration must be out of the range... 2442 Constant *NextVal = 2443 ConstantExpr::getAdd(R1->getValue(), 2444 ConstantInt::get(R1->getType(), 1)); 2445 2446 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2447 if (!Range.contains(R1Val, isSigned)) 2448 return SCEVUnknown::get(NextVal); 2449 return new SCEVCouldNotCompute(); // Something strange happened 2450 } 2451 2452 // If R1 was not in the range, then it is a good return value. Make 2453 // sure that R1-1 WAS in the range though, just in case. 2454 Constant *NextVal = 2455 ConstantExpr::getSub(R1->getValue(), 2456 ConstantInt::get(R1->getType(), 1)); 2457 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2458 if (Range.contains(R1Val, isSigned)) 2459 return R1; 2460 return new SCEVCouldNotCompute(); // Something strange happened 2461 } 2462 } 2463 } 2464 2465 // Fallback, if this is a general polynomial, figure out the progression 2466 // through brute force: evaluate until we find an iteration that fails the 2467 // test. This is likely to be slow, but getting an accurate trip count is 2468 // incredibly important, we will be able to simplify the exit test a lot, and 2469 // we are almost guaranteed to get a trip count in this case. 2470 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2471 ConstantInt *One = ConstantInt::get(getType(), 1); 2472 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2473 do { 2474 ++NumBruteForceEvaluations; 2475 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2476 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2477 return new SCEVCouldNotCompute(); 2478 2479 // Check to see if we found the value! 2480 if (!Range.contains(cast<SCEVConstant>(Val)->getValue(), isSigned)) 2481 return SCEVConstant::get(TestVal); 2482 2483 // Increment to test the next index. 2484 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2485 } while (TestVal != EndVal); 2486 2487 return new SCEVCouldNotCompute(); 2488} 2489 2490 2491 2492//===----------------------------------------------------------------------===// 2493// ScalarEvolution Class Implementation 2494//===----------------------------------------------------------------------===// 2495 2496bool ScalarEvolution::runOnFunction(Function &F) { 2497 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2498 return false; 2499} 2500 2501void ScalarEvolution::releaseMemory() { 2502 delete (ScalarEvolutionsImpl*)Impl; 2503 Impl = 0; 2504} 2505 2506void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2507 AU.setPreservesAll(); 2508 AU.addRequiredTransitive<LoopInfo>(); 2509} 2510 2511SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2512 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2513} 2514 2515/// hasSCEV - Return true if the SCEV for this value has already been 2516/// computed. 2517bool ScalarEvolution::hasSCEV(Value *V) const { 2518 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2519} 2520 2521 2522/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2523/// the specified value. 2524void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2525 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2526} 2527 2528 2529SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2530 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2531} 2532 2533bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2534 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2535} 2536 2537SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2538 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2539} 2540 2541void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2542 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2543} 2544 2545static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2546 const Loop *L) { 2547 // Print all inner loops first 2548 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2549 PrintLoopInfo(OS, SE, *I); 2550 2551 cerr << "Loop " << L->getHeader()->getName() << ": "; 2552 2553 std::vector<BasicBlock*> ExitBlocks; 2554 L->getExitBlocks(ExitBlocks); 2555 if (ExitBlocks.size() != 1) 2556 cerr << "<multiple exits> "; 2557 2558 if (SE->hasLoopInvariantIterationCount(L)) { 2559 cerr << *SE->getIterationCount(L) << " iterations! "; 2560 } else { 2561 cerr << "Unpredictable iteration count. "; 2562 } 2563 2564 cerr << "\n"; 2565} 2566 2567void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2568 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2569 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2570 2571 OS << "Classifying expressions for: " << F.getName() << "\n"; 2572 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2573 if (I->getType()->isInteger()) { 2574 OS << *I; 2575 OS << " --> "; 2576 SCEVHandle SV = getSCEV(&*I); 2577 SV->print(OS); 2578 OS << "\t\t"; 2579 2580 if ((*I).getType()->isIntegral()) { 2581 ConstantRange Bounds = SV->getValueRange(); 2582 if (!Bounds.isFullSet()) 2583 OS << "Bounds: " << Bounds << " "; 2584 } 2585 2586 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2587 OS << "Exits: "; 2588 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2589 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2590 OS << "<<Unknown>>"; 2591 } else { 2592 OS << *ExitValue; 2593 } 2594 } 2595 2596 2597 OS << "\n"; 2598 } 2599 2600 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2601 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2602 PrintLoopInfo(OS, this, *I); 2603} 2604 2605