ScalarEvolution.cpp revision 75de5ab9f58b84aa99c2a9133572ce1d997ec1a8
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#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/Instructions.h" 67#include "llvm/Analysis/ConstantFolding.h" 68#include "llvm/Analysis/LoopInfo.h" 69#include "llvm/Assembly/Writer.h" 70#include "llvm/Transforms/Scalar.h" 71#include "llvm/Support/CFG.h" 72#include "llvm/Support/CommandLine.h" 73#include "llvm/Support/Compiler.h" 74#include "llvm/Support/ConstantRange.h" 75#include "llvm/Support/InstIterator.h" 76#include "llvm/Support/ManagedStatic.h" 77#include "llvm/Support/MathExtras.h" 78#include "llvm/Support/Streams.h" 79#include "llvm/ADT/Statistic.h" 80#include <ostream> 81#include <algorithm> 82#include <cmath> 83using namespace llvm; 84 85namespace { 86 RegisterPass<ScalarEvolution> 87 R("scalar-evolution", "Scalar Evolution Analysis"); 88 89 Statistic 90 NumBruteForceEvaluations("scalar-evolution", 91 "Number of brute force evaluations needed to " 92 "calculate high-order polynomial exit values"); 93 Statistic 94 NumArrayLenItCounts("scalar-evolution", 95 "Number of trip counts computed with array length"); 96 Statistic 97 NumTripCountsComputed("scalar-evolution", 98 "Number of loops with predictable loop counts"); 99 Statistic 100 NumTripCountsNotComputed("scalar-evolution", 101 "Number of loops without predictable loop counts"); 102 Statistic 103 NumBruteForceTripCountsComputed("scalar-evolution", 104 "Number of loops with trip counts computed by force"); 105 106 cl::opt<unsigned> 107 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 108 cl::desc("Maximum number of iterations SCEV will " 109 "symbolically execute a constant derived loop"), 110 cl::init(100)); 111} 112 113//===----------------------------------------------------------------------===// 114// SCEV class definitions 115//===----------------------------------------------------------------------===// 116 117//===----------------------------------------------------------------------===// 118// Implementation of the SCEV class. 119// 120SCEV::~SCEV() {} 121void SCEV::dump() const { 122 print(cerr); 123} 124 125/// getValueRange - Return the tightest constant bounds that this value is 126/// known to have. This method is only valid on integer SCEV objects. 127ConstantRange SCEV::getValueRange() const { 128 const Type *Ty = getType(); 129 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 130 Ty = Ty->getUnsignedVersion(); 131 // Default to a full range if no better information is available. 132 return ConstantRange(getType()); 133} 134 135 136SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 137 138bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 140 return false; 141} 142 143const Type *SCEVCouldNotCompute::getType() const { 144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 145 return 0; 146} 147 148bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 149 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 150 return false; 151} 152 153SCEVHandle SCEVCouldNotCompute:: 154replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 155 const SCEVHandle &Conc) const { 156 return this; 157} 158 159void SCEVCouldNotCompute::print(std::ostream &OS) const { 160 OS << "***COULDNOTCOMPUTE***"; 161} 162 163bool SCEVCouldNotCompute::classof(const SCEV *S) { 164 return S->getSCEVType() == scCouldNotCompute; 165} 166 167 168// SCEVConstants - Only allow the creation of one SCEVConstant for any 169// particular value. Don't use a SCEVHandle here, or else the object will 170// never be deleted! 171static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 172 173 174SCEVConstant::~SCEVConstant() { 175 SCEVConstants->erase(V); 176} 177 178SCEVHandle SCEVConstant::get(ConstantInt *V) { 179 // Make sure that SCEVConstant instances are all unsigned. 180 if (V->getType()->isSigned()) { 181 const Type *NewTy = V->getType()->getUnsignedVersion(); 182 V = cast<ConstantInt>( 183 ConstantExpr::getBitCast(V, NewTy)); 184 } 185 186 SCEVConstant *&R = (*SCEVConstants)[V]; 187 if (R == 0) R = new SCEVConstant(V); 188 return R; 189} 190 191ConstantRange SCEVConstant::getValueRange() const { 192 return ConstantRange(V); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(std::ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 202// particular input. Don't use a SCEVHandle here, or else the object will 203// never be deleted! 204static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 205 SCEVTruncateExpr*> > SCEVTruncates; 206 207SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 208 : SCEV(scTruncate), Op(op), Ty(ty) { 209 assert(Op->getType()->isInteger() && Ty->isInteger() && 210 "Cannot truncate non-integer value!"); 211 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 212 "This is not a truncating conversion!"); 213} 214 215SCEVTruncateExpr::~SCEVTruncateExpr() { 216 SCEVTruncates->erase(std::make_pair(Op, Ty)); 217} 218 219ConstantRange SCEVTruncateExpr::getValueRange() const { 220 return getOperand()->getValueRange().truncate(getType()); 221} 222 223void SCEVTruncateExpr::print(std::ostream &OS) const { 224 OS << "(truncate " << *Op << " to " << *Ty << ")"; 225} 226 227// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 228// particular input. Don't use a SCEVHandle here, or else the object will never 229// be deleted! 230static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 231 SCEVZeroExtendExpr*> > SCEVZeroExtends; 232 233SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 234 : SCEV(scZeroExtend), Op(op), Ty(ty) { 235 assert(Op->getType()->isInteger() && Ty->isInteger() && 236 "Cannot zero extend non-integer value!"); 237 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 238 "This is not an extending conversion!"); 239} 240 241SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 242 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 243} 244 245ConstantRange SCEVZeroExtendExpr::getValueRange() const { 246 return getOperand()->getValueRange().zeroExtend(getType()); 247} 248 249void SCEVZeroExtendExpr::print(std::ostream &OS) const { 250 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 251} 252 253// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 254// particular input. Don't use a SCEVHandle here, or else the object will never 255// be deleted! 256static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 257 SCEVCommutativeExpr*> > SCEVCommExprs; 258 259SCEVCommutativeExpr::~SCEVCommutativeExpr() { 260 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 261 std::vector<SCEV*>(Operands.begin(), 262 Operands.end()))); 263} 264 265void SCEVCommutativeExpr::print(std::ostream &OS) const { 266 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 267 const char *OpStr = getOperationStr(); 268 OS << "(" << *Operands[0]; 269 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 270 OS << OpStr << *Operands[i]; 271 OS << ")"; 272} 273 274SCEVHandle SCEVCommutativeExpr:: 275replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 276 const SCEVHandle &Conc) const { 277 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 278 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 279 if (H != getOperand(i)) { 280 std::vector<SCEVHandle> NewOps; 281 NewOps.reserve(getNumOperands()); 282 for (unsigned j = 0; j != i; ++j) 283 NewOps.push_back(getOperand(j)); 284 NewOps.push_back(H); 285 for (++i; i != e; ++i) 286 NewOps.push_back(getOperand(i)-> 287 replaceSymbolicValuesWithConcrete(Sym, Conc)); 288 289 if (isa<SCEVAddExpr>(this)) 290 return SCEVAddExpr::get(NewOps); 291 else if (isa<SCEVMulExpr>(this)) 292 return SCEVMulExpr::get(NewOps); 293 else 294 assert(0 && "Unknown commutative expr!"); 295 } 296 } 297 return this; 298} 299 300 301// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 302// input. Don't use a SCEVHandle here, or else the object will never be 303// deleted! 304static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 305 SCEVSDivExpr*> > SCEVSDivs; 306 307SCEVSDivExpr::~SCEVSDivExpr() { 308 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 309} 310 311void SCEVSDivExpr::print(std::ostream &OS) const { 312 OS << "(" << *LHS << " /s " << *RHS << ")"; 313} 314 315const Type *SCEVSDivExpr::getType() const { 316 const Type *Ty = LHS->getType(); 317 if (Ty->isUnsigned()) Ty = Ty->getSignedVersion(); 318 return Ty; 319} 320 321// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 322// particular input. Don't use a SCEVHandle here, or else the object will never 323// be deleted! 324static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 325 SCEVAddRecExpr*> > SCEVAddRecExprs; 326 327SCEVAddRecExpr::~SCEVAddRecExpr() { 328 SCEVAddRecExprs->erase(std::make_pair(L, 329 std::vector<SCEV*>(Operands.begin(), 330 Operands.end()))); 331} 332 333SCEVHandle SCEVAddRecExpr:: 334replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 335 const SCEVHandle &Conc) const { 336 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 337 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 338 if (H != getOperand(i)) { 339 std::vector<SCEVHandle> NewOps; 340 NewOps.reserve(getNumOperands()); 341 for (unsigned j = 0; j != i; ++j) 342 NewOps.push_back(getOperand(j)); 343 NewOps.push_back(H); 344 for (++i; i != e; ++i) 345 NewOps.push_back(getOperand(i)-> 346 replaceSymbolicValuesWithConcrete(Sym, Conc)); 347 348 return get(NewOps, L); 349 } 350 } 351 return this; 352} 353 354 355bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 356 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 357 // contain L and if the start is invariant. 358 return !QueryLoop->contains(L->getHeader()) && 359 getOperand(0)->isLoopInvariant(QueryLoop); 360} 361 362 363void SCEVAddRecExpr::print(std::ostream &OS) const { 364 OS << "{" << *Operands[0]; 365 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 366 OS << ",+," << *Operands[i]; 367 OS << "}<" << L->getHeader()->getName() + ">"; 368} 369 370// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 371// value. Don't use a SCEVHandle here, or else the object will never be 372// deleted! 373static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 374 375SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 376 377bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 378 // All non-instruction values are loop invariant. All instructions are loop 379 // invariant if they are not contained in the specified loop. 380 if (Instruction *I = dyn_cast<Instruction>(V)) 381 return !L->contains(I->getParent()); 382 return true; 383} 384 385const Type *SCEVUnknown::getType() const { 386 return V->getType(); 387} 388 389void SCEVUnknown::print(std::ostream &OS) const { 390 WriteAsOperand(OS, V, false); 391} 392 393//===----------------------------------------------------------------------===// 394// SCEV Utilities 395//===----------------------------------------------------------------------===// 396 397namespace { 398 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 399 /// than the complexity of the RHS. This comparator is used to canonicalize 400 /// expressions. 401 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 402 bool operator()(SCEV *LHS, SCEV *RHS) { 403 return LHS->getSCEVType() < RHS->getSCEVType(); 404 } 405 }; 406} 407 408/// GroupByComplexity - Given a list of SCEV objects, order them by their 409/// complexity, and group objects of the same complexity together by value. 410/// When this routine is finished, we know that any duplicates in the vector are 411/// consecutive and that complexity is monotonically increasing. 412/// 413/// Note that we go take special precautions to ensure that we get determinstic 414/// results from this routine. In other words, we don't want the results of 415/// this to depend on where the addresses of various SCEV objects happened to 416/// land in memory. 417/// 418static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 419 if (Ops.size() < 2) return; // Noop 420 if (Ops.size() == 2) { 421 // This is the common case, which also happens to be trivially simple. 422 // Special case it. 423 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 424 std::swap(Ops[0], Ops[1]); 425 return; 426 } 427 428 // Do the rough sort by complexity. 429 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 430 431 // Now that we are sorted by complexity, group elements of the same 432 // complexity. Note that this is, at worst, N^2, but the vector is likely to 433 // be extremely short in practice. Note that we take this approach because we 434 // do not want to depend on the addresses of the objects we are grouping. 435 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 436 SCEV *S = Ops[i]; 437 unsigned Complexity = S->getSCEVType(); 438 439 // If there are any objects of the same complexity and same value as this 440 // one, group them. 441 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 442 if (Ops[j] == S) { // Found a duplicate. 443 // Move it to immediately after i'th element. 444 std::swap(Ops[i+1], Ops[j]); 445 ++i; // no need to rescan it. 446 if (i == e-2) return; // Done! 447 } 448 } 449 } 450} 451 452 453 454//===----------------------------------------------------------------------===// 455// Simple SCEV method implementations 456//===----------------------------------------------------------------------===// 457 458/// getIntegerSCEV - Given an integer or FP type, create a constant for the 459/// specified signed integer value and return a SCEV for the constant. 460SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 461 Constant *C; 462 if (Val == 0) 463 C = Constant::getNullValue(Ty); 464 else if (Ty->isFloatingPoint()) 465 C = ConstantFP::get(Ty, Val); 466 else if (Ty->isSigned()) 467 C = ConstantInt::get(Ty, Val); 468 else { 469 C = ConstantInt::get(Ty->getSignedVersion(), Val); 470 C = ConstantExpr::getBitCast(C, Ty); 471 } 472 return SCEVUnknown::get(C); 473} 474 475/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 476/// input value to the specified type. If the type must be extended, it is zero 477/// extended. 478static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 479 const Type *SrcTy = V->getType(); 480 assert(SrcTy->isInteger() && Ty->isInteger() && 481 "Cannot truncate or zero extend with non-integer arguments!"); 482 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 483 return V; // No conversion 484 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 485 return SCEVTruncateExpr::get(V, Ty); 486 return SCEVZeroExtendExpr::get(V, Ty); 487} 488 489/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 490/// 491SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 492 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 493 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 494 495 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 496} 497 498/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 499/// 500SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 501 // X - Y --> X + -Y 502 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 503} 504 505 506/// PartialFact - Compute V!/(V-NumSteps)! 507static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 508 // Handle this case efficiently, it is common to have constant iteration 509 // counts while computing loop exit values. 510 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 511 uint64_t Val = SC->getValue()->getZExtValue(); 512 uint64_t Result = 1; 513 for (; NumSteps; --NumSteps) 514 Result *= Val-(NumSteps-1); 515 Constant *Res = ConstantInt::get(Type::ULongTy, Result); 516 return SCEVUnknown::get( 517 ConstantExpr::getTruncOrBitCast(Res, V->getType())); 518 } 519 520 const Type *Ty = V->getType(); 521 if (NumSteps == 0) 522 return SCEVUnknown::getIntegerSCEV(1, Ty); 523 524 SCEVHandle Result = V; 525 for (unsigned i = 1; i != NumSteps; ++i) 526 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 527 SCEVUnknown::getIntegerSCEV(i, Ty))); 528 return Result; 529} 530 531 532/// evaluateAtIteration - Return the value of this chain of recurrences at 533/// the specified iteration number. We can evaluate this recurrence by 534/// multiplying each element in the chain by the binomial coefficient 535/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 536/// 537/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 538/// 539/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 540/// Is the binomial equation safe using modular arithmetic?? 541/// 542SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 543 SCEVHandle Result = getStart(); 544 int Divisor = 1; 545 const Type *Ty = It->getType(); 546 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 547 SCEVHandle BC = PartialFact(It, i); 548 Divisor *= i; 549 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 550 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 551 Result = SCEVAddExpr::get(Result, Val); 552 } 553 return Result; 554} 555 556 557//===----------------------------------------------------------------------===// 558// SCEV Expression folder implementations 559//===----------------------------------------------------------------------===// 560 561SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 562 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 563 return SCEVUnknown::get( 564 ConstantExpr::getTrunc(SC->getValue(), Ty)); 565 566 // If the input value is a chrec scev made out of constants, truncate 567 // all of the constants. 568 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 569 std::vector<SCEVHandle> Operands; 570 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 571 // FIXME: This should allow truncation of other expression types! 572 if (isa<SCEVConstant>(AddRec->getOperand(i))) 573 Operands.push_back(get(AddRec->getOperand(i), Ty)); 574 else 575 break; 576 if (Operands.size() == AddRec->getNumOperands()) 577 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 578 } 579 580 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 581 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 582 return Result; 583} 584 585SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 586 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 587 return SCEVUnknown::get( 588 ConstantExpr::getZExt(SC->getValue(), Ty)); 589 590 // FIXME: If the input value is a chrec scev, and we can prove that the value 591 // did not overflow the old, smaller, value, we can zero extend all of the 592 // operands (often constants). This would allow analysis of something like 593 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 594 595 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 596 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 597 return Result; 598} 599 600// get - Get a canonical add expression, or something simpler if possible. 601SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 602 assert(!Ops.empty() && "Cannot get empty add!"); 603 if (Ops.size() == 1) return Ops[0]; 604 605 // Sort by complexity, this groups all similar expression types together. 606 GroupByComplexity(Ops); 607 608 // If there are any constants, fold them together. 609 unsigned Idx = 0; 610 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 611 ++Idx; 612 assert(Idx < Ops.size()); 613 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 614 // We found two constants, fold them together! 615 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 616 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 617 Ops[0] = SCEVConstant::get(CI); 618 Ops.erase(Ops.begin()+1); // Erase the folded element 619 if (Ops.size() == 1) return Ops[0]; 620 LHSC = cast<SCEVConstant>(Ops[0]); 621 } else { 622 // If we couldn't fold the expression, move to the next constant. Note 623 // that this is impossible to happen in practice because we always 624 // constant fold constant ints to constant ints. 625 ++Idx; 626 } 627 } 628 629 // If we are left with a constant zero being added, strip it off. 630 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 631 Ops.erase(Ops.begin()); 632 --Idx; 633 } 634 } 635 636 if (Ops.size() == 1) return Ops[0]; 637 638 // Okay, check to see if the same value occurs in the operand list twice. If 639 // so, merge them together into an multiply expression. Since we sorted the 640 // list, these values are required to be adjacent. 641 const Type *Ty = Ops[0]->getType(); 642 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 643 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 644 // Found a match, merge the two values into a multiply, and add any 645 // remaining values to the result. 646 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 647 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 648 if (Ops.size() == 2) 649 return Mul; 650 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 651 Ops.push_back(Mul); 652 return SCEVAddExpr::get(Ops); 653 } 654 655 // Okay, now we know the first non-constant operand. If there are add 656 // operands they would be next. 657 if (Idx < Ops.size()) { 658 bool DeletedAdd = false; 659 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 660 // If we have an add, expand the add operands onto the end of the operands 661 // list. 662 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 663 Ops.erase(Ops.begin()+Idx); 664 DeletedAdd = true; 665 } 666 667 // If we deleted at least one add, we added operands to the end of the list, 668 // and they are not necessarily sorted. Recurse to resort and resimplify 669 // any operands we just aquired. 670 if (DeletedAdd) 671 return get(Ops); 672 } 673 674 // Skip over the add expression until we get to a multiply. 675 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 676 ++Idx; 677 678 // If we are adding something to a multiply expression, make sure the 679 // something is not already an operand of the multiply. If so, merge it into 680 // the multiply. 681 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 682 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 683 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 684 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 685 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 686 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 687 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 688 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 689 if (Mul->getNumOperands() != 2) { 690 // If the multiply has more than two operands, we must get the 691 // Y*Z term. 692 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 693 MulOps.erase(MulOps.begin()+MulOp); 694 InnerMul = SCEVMulExpr::get(MulOps); 695 } 696 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 697 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 698 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 699 if (Ops.size() == 2) return OuterMul; 700 if (AddOp < Idx) { 701 Ops.erase(Ops.begin()+AddOp); 702 Ops.erase(Ops.begin()+Idx-1); 703 } else { 704 Ops.erase(Ops.begin()+Idx); 705 Ops.erase(Ops.begin()+AddOp-1); 706 } 707 Ops.push_back(OuterMul); 708 return SCEVAddExpr::get(Ops); 709 } 710 711 // Check this multiply against other multiplies being added together. 712 for (unsigned OtherMulIdx = Idx+1; 713 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 714 ++OtherMulIdx) { 715 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 716 // If MulOp occurs in OtherMul, we can fold the two multiplies 717 // together. 718 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 719 OMulOp != e; ++OMulOp) 720 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 721 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 722 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 723 if (Mul->getNumOperands() != 2) { 724 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 725 MulOps.erase(MulOps.begin()+MulOp); 726 InnerMul1 = SCEVMulExpr::get(MulOps); 727 } 728 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 729 if (OtherMul->getNumOperands() != 2) { 730 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 731 OtherMul->op_end()); 732 MulOps.erase(MulOps.begin()+OMulOp); 733 InnerMul2 = SCEVMulExpr::get(MulOps); 734 } 735 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 736 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 737 if (Ops.size() == 2) return OuterMul; 738 Ops.erase(Ops.begin()+Idx); 739 Ops.erase(Ops.begin()+OtherMulIdx-1); 740 Ops.push_back(OuterMul); 741 return SCEVAddExpr::get(Ops); 742 } 743 } 744 } 745 } 746 747 // If there are any add recurrences in the operands list, see if any other 748 // added values are loop invariant. If so, we can fold them into the 749 // recurrence. 750 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 751 ++Idx; 752 753 // Scan over all recurrences, trying to fold loop invariants into them. 754 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 755 // Scan all of the other operands to this add and add them to the vector if 756 // they are loop invariant w.r.t. the recurrence. 757 std::vector<SCEVHandle> LIOps; 758 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 759 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 760 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 761 LIOps.push_back(Ops[i]); 762 Ops.erase(Ops.begin()+i); 763 --i; --e; 764 } 765 766 // If we found some loop invariants, fold them into the recurrence. 767 if (!LIOps.empty()) { 768 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 769 LIOps.push_back(AddRec->getStart()); 770 771 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 772 AddRecOps[0] = SCEVAddExpr::get(LIOps); 773 774 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 775 // If all of the other operands were loop invariant, we are done. 776 if (Ops.size() == 1) return NewRec; 777 778 // Otherwise, add the folded AddRec by the non-liv parts. 779 for (unsigned i = 0;; ++i) 780 if (Ops[i] == AddRec) { 781 Ops[i] = NewRec; 782 break; 783 } 784 return SCEVAddExpr::get(Ops); 785 } 786 787 // Okay, if there weren't any loop invariants to be folded, check to see if 788 // there are multiple AddRec's with the same loop induction variable being 789 // added together. If so, we can fold them. 790 for (unsigned OtherIdx = Idx+1; 791 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 792 if (OtherIdx != Idx) { 793 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 794 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 795 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 796 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 797 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 798 if (i >= NewOps.size()) { 799 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 800 OtherAddRec->op_end()); 801 break; 802 } 803 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 804 } 805 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 806 807 if (Ops.size() == 2) return NewAddRec; 808 809 Ops.erase(Ops.begin()+Idx); 810 Ops.erase(Ops.begin()+OtherIdx-1); 811 Ops.push_back(NewAddRec); 812 return SCEVAddExpr::get(Ops); 813 } 814 } 815 816 // Otherwise couldn't fold anything into this recurrence. Move onto the 817 // next one. 818 } 819 820 // Okay, it looks like we really DO need an add expr. Check to see if we 821 // already have one, otherwise create a new one. 822 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 823 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 824 SCEVOps)]; 825 if (Result == 0) Result = new SCEVAddExpr(Ops); 826 return Result; 827} 828 829 830SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 831 assert(!Ops.empty() && "Cannot get empty mul!"); 832 833 // Sort by complexity, this groups all similar expression types together. 834 GroupByComplexity(Ops); 835 836 // If there are any constants, fold them together. 837 unsigned Idx = 0; 838 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 839 840 // C1*(C2+V) -> C1*C2 + C1*V 841 if (Ops.size() == 2) 842 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 843 if (Add->getNumOperands() == 2 && 844 isa<SCEVConstant>(Add->getOperand(0))) 845 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 846 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 847 848 849 ++Idx; 850 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 851 // We found two constants, fold them together! 852 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 853 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 854 Ops[0] = SCEVConstant::get(CI); 855 Ops.erase(Ops.begin()+1); // Erase the folded element 856 if (Ops.size() == 1) return Ops[0]; 857 LHSC = cast<SCEVConstant>(Ops[0]); 858 } else { 859 // If we couldn't fold the expression, move to the next constant. Note 860 // that this is impossible to happen in practice because we always 861 // constant fold constant ints to constant ints. 862 ++Idx; 863 } 864 } 865 866 // If we are left with a constant one being multiplied, strip it off. 867 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 868 Ops.erase(Ops.begin()); 869 --Idx; 870 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 871 // If we have a multiply of zero, it will always be zero. 872 return Ops[0]; 873 } 874 } 875 876 // Skip over the add expression until we get to a multiply. 877 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 878 ++Idx; 879 880 if (Ops.size() == 1) 881 return Ops[0]; 882 883 // If there are mul operands inline them all into this expression. 884 if (Idx < Ops.size()) { 885 bool DeletedMul = false; 886 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 887 // If we have an mul, expand the mul operands onto the end of the operands 888 // list. 889 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 890 Ops.erase(Ops.begin()+Idx); 891 DeletedMul = true; 892 } 893 894 // If we deleted at least one mul, we added operands to the end of the list, 895 // and they are not necessarily sorted. Recurse to resort and resimplify 896 // any operands we just aquired. 897 if (DeletedMul) 898 return get(Ops); 899 } 900 901 // If there are any add recurrences in the operands list, see if any other 902 // added values are loop invariant. If so, we can fold them into the 903 // recurrence. 904 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 905 ++Idx; 906 907 // Scan over all recurrences, trying to fold loop invariants into them. 908 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 909 // Scan all of the other operands to this mul and add them to the vector if 910 // they are loop invariant w.r.t. the recurrence. 911 std::vector<SCEVHandle> LIOps; 912 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 913 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 914 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 915 LIOps.push_back(Ops[i]); 916 Ops.erase(Ops.begin()+i); 917 --i; --e; 918 } 919 920 // If we found some loop invariants, fold them into the recurrence. 921 if (!LIOps.empty()) { 922 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 923 std::vector<SCEVHandle> NewOps; 924 NewOps.reserve(AddRec->getNumOperands()); 925 if (LIOps.size() == 1) { 926 SCEV *Scale = LIOps[0]; 927 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 928 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 929 } else { 930 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 931 std::vector<SCEVHandle> MulOps(LIOps); 932 MulOps.push_back(AddRec->getOperand(i)); 933 NewOps.push_back(SCEVMulExpr::get(MulOps)); 934 } 935 } 936 937 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 938 939 // If all of the other operands were loop invariant, we are done. 940 if (Ops.size() == 1) return NewRec; 941 942 // Otherwise, multiply the folded AddRec by the non-liv parts. 943 for (unsigned i = 0;; ++i) 944 if (Ops[i] == AddRec) { 945 Ops[i] = NewRec; 946 break; 947 } 948 return SCEVMulExpr::get(Ops); 949 } 950 951 // Okay, if there weren't any loop invariants to be folded, check to see if 952 // there are multiple AddRec's with the same loop induction variable being 953 // multiplied together. If so, we can fold them. 954 for (unsigned OtherIdx = Idx+1; 955 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 956 if (OtherIdx != Idx) { 957 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 958 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 959 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 960 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 961 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 962 G->getStart()); 963 SCEVHandle B = F->getStepRecurrence(); 964 SCEVHandle D = G->getStepRecurrence(); 965 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 966 SCEVMulExpr::get(G, B), 967 SCEVMulExpr::get(B, D)); 968 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 969 F->getLoop()); 970 if (Ops.size() == 2) return NewAddRec; 971 972 Ops.erase(Ops.begin()+Idx); 973 Ops.erase(Ops.begin()+OtherIdx-1); 974 Ops.push_back(NewAddRec); 975 return SCEVMulExpr::get(Ops); 976 } 977 } 978 979 // Otherwise couldn't fold anything into this recurrence. Move onto the 980 // next one. 981 } 982 983 // Okay, it looks like we really DO need an mul expr. Check to see if we 984 // already have one, otherwise create a new one. 985 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 986 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 987 SCEVOps)]; 988 if (Result == 0) 989 Result = new SCEVMulExpr(Ops); 990 return Result; 991} 992 993SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 994 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 995 if (RHSC->getValue()->equalsInt(1)) 996 return LHS; // X sdiv 1 --> x 997 if (RHSC->getValue()->isAllOnesValue()) 998 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 999 1000 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1001 Constant *LHSCV = LHSC->getValue(); 1002 Constant *RHSCV = RHSC->getValue(); 1003 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 1004 } 1005 } 1006 1007 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1008 1009 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 1010 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1011 return Result; 1012} 1013 1014 1015/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1016/// specified loop. Simplify the expression as much as possible. 1017SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1018 const SCEVHandle &Step, const Loop *L) { 1019 std::vector<SCEVHandle> Operands; 1020 Operands.push_back(Start); 1021 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1022 if (StepChrec->getLoop() == L) { 1023 Operands.insert(Operands.end(), StepChrec->op_begin(), 1024 StepChrec->op_end()); 1025 return get(Operands, L); 1026 } 1027 1028 Operands.push_back(Step); 1029 return get(Operands, L); 1030} 1031 1032/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1033/// specified loop. Simplify the expression as much as possible. 1034SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1035 const Loop *L) { 1036 if (Operands.size() == 1) return Operands[0]; 1037 1038 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1039 if (StepC->getValue()->isNullValue()) { 1040 Operands.pop_back(); 1041 return get(Operands, L); // { X,+,0 } --> X 1042 } 1043 1044 SCEVAddRecExpr *&Result = 1045 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1046 Operands.end()))]; 1047 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1048 return Result; 1049} 1050 1051SCEVHandle SCEVUnknown::get(Value *V) { 1052 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1053 return SCEVConstant::get(CI); 1054 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1055 if (Result == 0) Result = new SCEVUnknown(V); 1056 return Result; 1057} 1058 1059 1060//===----------------------------------------------------------------------===// 1061// ScalarEvolutionsImpl Definition and Implementation 1062//===----------------------------------------------------------------------===// 1063// 1064/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1065/// evolution code. 1066/// 1067namespace { 1068 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1069 /// F - The function we are analyzing. 1070 /// 1071 Function &F; 1072 1073 /// LI - The loop information for the function we are currently analyzing. 1074 /// 1075 LoopInfo &LI; 1076 1077 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1078 /// things. 1079 SCEVHandle UnknownValue; 1080 1081 /// Scalars - This is a cache of the scalars we have analyzed so far. 1082 /// 1083 std::map<Value*, SCEVHandle> Scalars; 1084 1085 /// IterationCounts - Cache the iteration count of the loops for this 1086 /// function as they are computed. 1087 std::map<const Loop*, SCEVHandle> IterationCounts; 1088 1089 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1090 /// the PHI instructions that we attempt to compute constant evolutions for. 1091 /// This allows us to avoid potentially expensive recomputation of these 1092 /// properties. An instruction maps to null if we are unable to compute its 1093 /// exit value. 1094 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1095 1096 public: 1097 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1098 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1099 1100 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1101 /// expression and create a new one. 1102 SCEVHandle getSCEV(Value *V); 1103 1104 /// hasSCEV - Return true if the SCEV for this value has already been 1105 /// computed. 1106 bool hasSCEV(Value *V) const { 1107 return Scalars.count(V); 1108 } 1109 1110 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1111 /// the specified value. 1112 void setSCEV(Value *V, const SCEVHandle &H) { 1113 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1114 assert(isNew && "This entry already existed!"); 1115 } 1116 1117 1118 /// getSCEVAtScope - Compute the value of the specified expression within 1119 /// the indicated loop (which may be null to indicate in no loop). If the 1120 /// expression cannot be evaluated, return UnknownValue itself. 1121 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1122 1123 1124 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1125 /// an analyzable loop-invariant iteration count. 1126 bool hasLoopInvariantIterationCount(const Loop *L); 1127 1128 /// getIterationCount - If the specified loop has a predictable iteration 1129 /// count, return it. Note that it is not valid to call this method on a 1130 /// loop without a loop-invariant iteration count. 1131 SCEVHandle getIterationCount(const Loop *L); 1132 1133 /// deleteInstructionFromRecords - This method should be called by the 1134 /// client before it removes an instruction from the program, to make sure 1135 /// that no dangling references are left around. 1136 void deleteInstructionFromRecords(Instruction *I); 1137 1138 private: 1139 /// createSCEV - We know that there is no SCEV for the specified value. 1140 /// Analyze the expression. 1141 SCEVHandle createSCEV(Value *V); 1142 1143 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1144 /// SCEVs. 1145 SCEVHandle createNodeForPHI(PHINode *PN); 1146 1147 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1148 /// for the specified instruction and replaces any references to the 1149 /// symbolic value SymName with the specified value. This is used during 1150 /// PHI resolution. 1151 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1152 const SCEVHandle &SymName, 1153 const SCEVHandle &NewVal); 1154 1155 /// ComputeIterationCount - Compute the number of times the specified loop 1156 /// will iterate. 1157 SCEVHandle ComputeIterationCount(const Loop *L); 1158 1159 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1160 /// 'setcc load X, cst', try to se if we can compute the trip count. 1161 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1162 Constant *RHS, 1163 const Loop *L, 1164 unsigned SetCCOpcode); 1165 1166 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1167 /// constant number of times (the condition evolves only from constants), 1168 /// try to evaluate a few iterations of the loop until we get the exit 1169 /// condition gets a value of ExitWhen (true or false). If we cannot 1170 /// evaluate the trip count of the loop, return UnknownValue. 1171 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1172 bool ExitWhen); 1173 1174 /// HowFarToZero - Return the number of times a backedge comparing the 1175 /// specified value to zero will execute. If not computable, return 1176 /// UnknownValue. 1177 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1178 1179 /// HowFarToNonZero - Return the number of times a backedge checking the 1180 /// specified value for nonzero will execute. If not computable, return 1181 /// UnknownValue. 1182 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1183 1184 /// HowManyLessThans - Return the number of times a backedge containing the 1185 /// specified less-than comparison will execute. If not computable, return 1186 /// UnknownValue. 1187 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L); 1188 1189 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1190 /// in the header of its containing loop, we know the loop executes a 1191 /// constant number of times, and the PHI node is just a recurrence 1192 /// involving constants, fold it. 1193 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1194 const Loop *L); 1195 }; 1196} 1197 1198//===----------------------------------------------------------------------===// 1199// Basic SCEV Analysis and PHI Idiom Recognition Code 1200// 1201 1202/// deleteInstructionFromRecords - This method should be called by the 1203/// client before it removes an instruction from the program, to make sure 1204/// that no dangling references are left around. 1205void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1206 Scalars.erase(I); 1207 if (PHINode *PN = dyn_cast<PHINode>(I)) 1208 ConstantEvolutionLoopExitValue.erase(PN); 1209} 1210 1211 1212/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1213/// expression and create a new one. 1214SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1215 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1216 1217 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1218 if (I != Scalars.end()) return I->second; 1219 SCEVHandle S = createSCEV(V); 1220 Scalars.insert(std::make_pair(V, S)); 1221 return S; 1222} 1223 1224/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1225/// the specified instruction and replaces any references to the symbolic value 1226/// SymName with the specified value. This is used during PHI resolution. 1227void ScalarEvolutionsImpl:: 1228ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1229 const SCEVHandle &NewVal) { 1230 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1231 if (SI == Scalars.end()) return; 1232 1233 SCEVHandle NV = 1234 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1235 if (NV == SI->second) return; // No change. 1236 1237 SI->second = NV; // Update the scalars map! 1238 1239 // Any instruction values that use this instruction might also need to be 1240 // updated! 1241 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1242 UI != E; ++UI) 1243 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1244} 1245 1246/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1247/// a loop header, making it a potential recurrence, or it doesn't. 1248/// 1249SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1250 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1251 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1252 if (L->getHeader() == PN->getParent()) { 1253 // If it lives in the loop header, it has two incoming values, one 1254 // from outside the loop, and one from inside. 1255 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1256 unsigned BackEdge = IncomingEdge^1; 1257 1258 // While we are analyzing this PHI node, handle its value symbolically. 1259 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1260 assert(Scalars.find(PN) == Scalars.end() && 1261 "PHI node already processed?"); 1262 Scalars.insert(std::make_pair(PN, SymbolicName)); 1263 1264 // Using this symbolic name for the PHI, analyze the value coming around 1265 // the back-edge. 1266 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1267 1268 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1269 // has a special value for the first iteration of the loop. 1270 1271 // If the value coming around the backedge is an add with the symbolic 1272 // value we just inserted, then we found a simple induction variable! 1273 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1274 // If there is a single occurrence of the symbolic value, replace it 1275 // with a recurrence. 1276 unsigned FoundIndex = Add->getNumOperands(); 1277 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1278 if (Add->getOperand(i) == SymbolicName) 1279 if (FoundIndex == e) { 1280 FoundIndex = i; 1281 break; 1282 } 1283 1284 if (FoundIndex != Add->getNumOperands()) { 1285 // Create an add with everything but the specified operand. 1286 std::vector<SCEVHandle> Ops; 1287 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1288 if (i != FoundIndex) 1289 Ops.push_back(Add->getOperand(i)); 1290 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1291 1292 // This is not a valid addrec if the step amount is varying each 1293 // loop iteration, but is not itself an addrec in this loop. 1294 if (Accum->isLoopInvariant(L) || 1295 (isa<SCEVAddRecExpr>(Accum) && 1296 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1297 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1298 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1299 1300 // Okay, for the entire analysis of this edge we assumed the PHI 1301 // to be symbolic. We now need to go back and update all of the 1302 // entries for the scalars that use the PHI (except for the PHI 1303 // itself) to use the new analyzed value instead of the "symbolic" 1304 // value. 1305 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1306 return PHISCEV; 1307 } 1308 } 1309 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1310 // Otherwise, this could be a loop like this: 1311 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1312 // In this case, j = {1,+,1} and BEValue is j. 1313 // Because the other in-value of i (0) fits the evolution of BEValue 1314 // i really is an addrec evolution. 1315 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1316 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1317 1318 // If StartVal = j.start - j.stride, we can use StartVal as the 1319 // initial step of the addrec evolution. 1320 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1321 AddRec->getOperand(1))) { 1322 SCEVHandle PHISCEV = 1323 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1324 1325 // Okay, for the entire analysis of this edge we assumed the PHI 1326 // to be symbolic. We now need to go back and update all of the 1327 // entries for the scalars that use the PHI (except for the PHI 1328 // itself) to use the new analyzed value instead of the "symbolic" 1329 // value. 1330 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1331 return PHISCEV; 1332 } 1333 } 1334 } 1335 1336 return SymbolicName; 1337 } 1338 1339 // If it's not a loop phi, we can't handle it yet. 1340 return SCEVUnknown::get(PN); 1341} 1342 1343/// GetConstantFactor - Determine the largest constant factor that S has. For 1344/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1345static uint64_t GetConstantFactor(SCEVHandle S) { 1346 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1347 if (uint64_t V = C->getValue()->getZExtValue()) 1348 return V; 1349 else // Zero is a multiple of everything. 1350 return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1); 1351 } 1352 1353 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1354 return GetConstantFactor(T->getOperand()) & 1355 T->getType()->getIntegralTypeMask(); 1356 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1357 return GetConstantFactor(E->getOperand()); 1358 1359 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1360 // The result is the min of all operands. 1361 uint64_t Res = GetConstantFactor(A->getOperand(0)); 1362 for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i) 1363 Res = std::min(Res, GetConstantFactor(A->getOperand(i))); 1364 return Res; 1365 } 1366 1367 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1368 // The result is the product of all the operands. 1369 uint64_t Res = GetConstantFactor(M->getOperand(0)); 1370 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) 1371 Res *= GetConstantFactor(M->getOperand(i)); 1372 return Res; 1373 } 1374 1375 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1376 // For now, we just handle linear expressions. 1377 if (A->getNumOperands() == 2) { 1378 // We want the GCD between the start and the stride value. 1379 uint64_t Start = GetConstantFactor(A->getOperand(0)); 1380 if (Start == 1) return 1; 1381 uint64_t Stride = GetConstantFactor(A->getOperand(1)); 1382 return GreatestCommonDivisor64(Start, Stride); 1383 } 1384 } 1385 1386 // SCEVSDivExpr, SCEVUnknown. 1387 return 1; 1388} 1389 1390/// createSCEV - We know that there is no SCEV for the specified value. 1391/// Analyze the expression. 1392/// 1393SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1394 if (Instruction *I = dyn_cast<Instruction>(V)) { 1395 switch (I->getOpcode()) { 1396 case Instruction::Add: 1397 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1398 getSCEV(I->getOperand(1))); 1399 case Instruction::Mul: 1400 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1401 getSCEV(I->getOperand(1))); 1402 case Instruction::SDiv: 1403 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1404 getSCEV(I->getOperand(1))); 1405 break; 1406 1407 case Instruction::Sub: 1408 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1409 getSCEV(I->getOperand(1))); 1410 case Instruction::Or: 1411 // If the RHS of the Or is a constant, we may have something like: 1412 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1413 // optimizations will transparently handle this case. 1414 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1415 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1416 uint64_t CommonFact = GetConstantFactor(LHS); 1417 assert(CommonFact && "Common factor should at least be 1!"); 1418 if (CommonFact > CI->getZExtValue()) { 1419 // If the LHS is a multiple that is larger than the RHS, use +. 1420 return SCEVAddExpr::get(LHS, 1421 getSCEV(I->getOperand(1))); 1422 } 1423 } 1424 break; 1425 1426 case Instruction::Shl: 1427 // Turn shift left of a constant amount into a multiply. 1428 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1429 Constant *X = ConstantInt::get(V->getType(), 1); 1430 X = ConstantExpr::getShl(X, SA); 1431 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1432 } 1433 break; 1434 1435 case Instruction::Trunc: 1436 // We don't handle trunc to bool yet. 1437 if (I->getType()->isInteger()) 1438 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), 1439 I->getType()->getUnsignedVersion()); 1440 break; 1441 1442 case Instruction::ZExt: 1443 // We don't handle zext from bool yet. 1444 if (I->getOperand(0)->getType()->isInteger()) 1445 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), 1446 I->getType()->getUnsignedVersion()); 1447 break; 1448 1449 case Instruction::BitCast: 1450 // BitCasts are no-op casts so we just eliminate the cast. 1451 if (I->getType()->isInteger() && I->getOperand(0)->getType()->isInteger()) 1452 return getSCEV(I->getOperand(0)); 1453 break; 1454 1455 case Instruction::PHI: 1456 return createNodeForPHI(cast<PHINode>(I)); 1457 1458 default: // We cannot analyze this expression. 1459 break; 1460 } 1461 } 1462 1463 return SCEVUnknown::get(V); 1464} 1465 1466 1467 1468//===----------------------------------------------------------------------===// 1469// Iteration Count Computation Code 1470// 1471 1472/// getIterationCount - If the specified loop has a predictable iteration 1473/// count, return it. Note that it is not valid to call this method on a 1474/// loop without a loop-invariant iteration count. 1475SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1476 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1477 if (I == IterationCounts.end()) { 1478 SCEVHandle ItCount = ComputeIterationCount(L); 1479 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1480 if (ItCount != UnknownValue) { 1481 assert(ItCount->isLoopInvariant(L) && 1482 "Computed trip count isn't loop invariant for loop!"); 1483 ++NumTripCountsComputed; 1484 } else if (isa<PHINode>(L->getHeader()->begin())) { 1485 // Only count loops that have phi nodes as not being computable. 1486 ++NumTripCountsNotComputed; 1487 } 1488 } 1489 return I->second; 1490} 1491 1492/// ComputeIterationCount - Compute the number of times the specified loop 1493/// will iterate. 1494SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1495 // If the loop has a non-one exit block count, we can't analyze it. 1496 std::vector<BasicBlock*> ExitBlocks; 1497 L->getExitBlocks(ExitBlocks); 1498 if (ExitBlocks.size() != 1) return UnknownValue; 1499 1500 // Okay, there is one exit block. Try to find the condition that causes the 1501 // loop to be exited. 1502 BasicBlock *ExitBlock = ExitBlocks[0]; 1503 1504 BasicBlock *ExitingBlock = 0; 1505 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1506 PI != E; ++PI) 1507 if (L->contains(*PI)) { 1508 if (ExitingBlock == 0) 1509 ExitingBlock = *PI; 1510 else 1511 return UnknownValue; // More than one block exiting! 1512 } 1513 assert(ExitingBlock && "No exits from loop, something is broken!"); 1514 1515 // Okay, we've computed the exiting block. See what condition causes us to 1516 // exit. 1517 // 1518 // FIXME: we should be able to handle switch instructions (with a single exit) 1519 // FIXME: We should handle cast of int to bool as well 1520 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1521 if (ExitBr == 0) return UnknownValue; 1522 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1523 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1524 if (ExitCond == 0) // Not a setcc 1525 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1526 ExitBr->getSuccessor(0) == ExitBlock); 1527 1528 // If the condition was exit on true, convert the condition to exit on false. 1529 Instruction::BinaryOps Cond; 1530 if (ExitBr->getSuccessor(1) == ExitBlock) 1531 Cond = ExitCond->getOpcode(); 1532 else 1533 Cond = ExitCond->getInverseCondition(); 1534 1535 // Handle common loops like: for (X = "string"; *X; ++X) 1536 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1537 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1538 SCEVHandle ItCnt = 1539 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1540 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1541 } 1542 1543 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1544 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1545 1546 // Try to evaluate any dependencies out of the loop. 1547 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1548 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1549 Tmp = getSCEVAtScope(RHS, L); 1550 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1551 1552 // At this point, we would like to compute how many iterations of the loop the 1553 // predicate will return true for these inputs. 1554 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1555 // If there is a constant, force it into the RHS. 1556 std::swap(LHS, RHS); 1557 Cond = SetCondInst::getSwappedCondition(Cond); 1558 } 1559 1560 // FIXME: think about handling pointer comparisons! i.e.: 1561 // while (P != P+100) ++P; 1562 1563 // If we have a comparison of a chrec against a constant, try to use value 1564 // ranges to answer this query. 1565 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1566 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1567 if (AddRec->getLoop() == L) { 1568 // Form the comparison range using the constant of the correct type so 1569 // that the ConstantRange class knows to do a signed or unsigned 1570 // comparison. 1571 ConstantInt *CompVal = RHSC->getValue(); 1572 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1573 CompVal = dyn_cast<ConstantInt>( 1574 ConstantExpr::getBitCast(CompVal, RealTy)); 1575 if (CompVal) { 1576 // Form the constant range. 1577 ConstantRange CompRange(Cond, CompVal); 1578 1579 // Now that we have it, if it's signed, convert it to an unsigned 1580 // range. 1581 if (CompRange.getLower()->getType()->isSigned()) { 1582 const Type *NewTy = RHSC->getValue()->getType(); 1583 Constant *NewL = ConstantExpr::getBitCast(CompRange.getLower(), 1584 NewTy); 1585 Constant *NewU = ConstantExpr::getBitCast(CompRange.getUpper(), 1586 NewTy); 1587 CompRange = ConstantRange(NewL, NewU); 1588 } 1589 1590 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1591 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1592 } 1593 } 1594 1595 switch (Cond) { 1596 case Instruction::SetNE: // while (X != Y) 1597 // Convert to: while (X-Y != 0) 1598 if (LHS->getType()->isInteger()) { 1599 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1600 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1601 } 1602 break; 1603 case Instruction::SetEQ: 1604 // Convert to: while (X-Y == 0) // while (X == Y) 1605 if (LHS->getType()->isInteger()) { 1606 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1607 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1608 } 1609 break; 1610 case Instruction::SetLT: 1611 if (LHS->getType()->isInteger() && 1612 ExitCond->getOperand(0)->getType()->isSigned()) { 1613 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1614 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1615 } 1616 break; 1617 case Instruction::SetGT: 1618 if (LHS->getType()->isInteger() && 1619 ExitCond->getOperand(0)->getType()->isSigned()) { 1620 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1621 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1622 } 1623 break; 1624 default: 1625#if 0 1626 cerr << "ComputeIterationCount "; 1627 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1628 cerr << "[unsigned] "; 1629 cerr << *LHS << " " 1630 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1631#endif 1632 break; 1633 } 1634 1635 return ComputeIterationCountExhaustively(L, ExitCond, 1636 ExitBr->getSuccessor(0) == ExitBlock); 1637} 1638 1639static ConstantInt * 1640EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1641 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1642 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1643 assert(isa<SCEVConstant>(Val) && 1644 "Evaluation of SCEV at constant didn't fold correctly?"); 1645 return cast<SCEVConstant>(Val)->getValue(); 1646} 1647 1648/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1649/// and a GEP expression (missing the pointer index) indexing into it, return 1650/// the addressed element of the initializer or null if the index expression is 1651/// invalid. 1652static Constant * 1653GetAddressedElementFromGlobal(GlobalVariable *GV, 1654 const std::vector<ConstantInt*> &Indices) { 1655 Constant *Init = GV->getInitializer(); 1656 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1657 uint64_t Idx = Indices[i]->getZExtValue(); 1658 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1659 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1660 Init = cast<Constant>(CS->getOperand(Idx)); 1661 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1662 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1663 Init = cast<Constant>(CA->getOperand(Idx)); 1664 } else if (isa<ConstantAggregateZero>(Init)) { 1665 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1666 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1667 Init = Constant::getNullValue(STy->getElementType(Idx)); 1668 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1669 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1670 Init = Constant::getNullValue(ATy->getElementType()); 1671 } else { 1672 assert(0 && "Unknown constant aggregate type!"); 1673 } 1674 return 0; 1675 } else { 1676 return 0; // Unknown initializer type 1677 } 1678 } 1679 return Init; 1680} 1681 1682/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1683/// 'setcc load X, cst', try to se if we can compute the trip count. 1684SCEVHandle ScalarEvolutionsImpl:: 1685ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1686 const Loop *L, unsigned SetCCOpcode) { 1687 if (LI->isVolatile()) return UnknownValue; 1688 1689 // Check to see if the loaded pointer is a getelementptr of a global. 1690 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1691 if (!GEP) return UnknownValue; 1692 1693 // Make sure that it is really a constant global we are gepping, with an 1694 // initializer, and make sure the first IDX is really 0. 1695 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1696 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1697 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1698 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1699 return UnknownValue; 1700 1701 // Okay, we allow one non-constant index into the GEP instruction. 1702 Value *VarIdx = 0; 1703 std::vector<ConstantInt*> Indexes; 1704 unsigned VarIdxNum = 0; 1705 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1706 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1707 Indexes.push_back(CI); 1708 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1709 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1710 VarIdx = GEP->getOperand(i); 1711 VarIdxNum = i-2; 1712 Indexes.push_back(0); 1713 } 1714 1715 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1716 // Check to see if X is a loop variant variable value now. 1717 SCEVHandle Idx = getSCEV(VarIdx); 1718 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1719 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1720 1721 // We can only recognize very limited forms of loop index expressions, in 1722 // particular, only affine AddRec's like {C1,+,C2}. 1723 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1724 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1725 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1726 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1727 return UnknownValue; 1728 1729 unsigned MaxSteps = MaxBruteForceIterations; 1730 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1731 ConstantInt *ItCst = 1732 ConstantInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 1733 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1734 1735 // Form the GEP offset. 1736 Indexes[VarIdxNum] = Val; 1737 1738 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1739 if (Result == 0) break; // Cannot compute! 1740 1741 // Evaluate the condition for this iteration. 1742 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 1743 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 1744 if (cast<ConstantBool>(Result)->getValue() == false) { 1745#if 0 1746 cerr << "\n***\n*** Computed loop count " << *ItCst 1747 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1748 << "***\n"; 1749#endif 1750 ++NumArrayLenItCounts; 1751 return SCEVConstant::get(ItCst); // Found terminating iteration! 1752 } 1753 } 1754 return UnknownValue; 1755} 1756 1757 1758/// CanConstantFold - Return true if we can constant fold an instruction of the 1759/// specified type, assuming that all operands were constants. 1760static bool CanConstantFold(const Instruction *I) { 1761 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1762 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1763 return true; 1764 1765 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1766 if (const Function *F = CI->getCalledFunction()) 1767 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1768 return false; 1769} 1770 1771/// ConstantFold - Constant fold an instruction of the specified type with the 1772/// specified constant operands. This function may modify the operands vector. 1773static Constant *ConstantFold(const Instruction *I, 1774 std::vector<Constant*> &Operands) { 1775 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1776 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1777 1778 if (isa<CastInst>(I)) 1779 return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType()); 1780 1781 switch (I->getOpcode()) { 1782 case Instruction::Select: 1783 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1784 case Instruction::Call: 1785 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1786 Operands.erase(Operands.begin()); 1787 return ConstantFoldCall(cast<Function>(GV), Operands); 1788 } 1789 return 0; 1790 case Instruction::GetElementPtr: 1791 Constant *Base = Operands[0]; 1792 Operands.erase(Operands.begin()); 1793 return ConstantExpr::getGetElementPtr(Base, Operands); 1794 } 1795 return 0; 1796} 1797 1798 1799/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1800/// in the loop that V is derived from. We allow arbitrary operations along the 1801/// way, but the operands of an operation must either be constants or a value 1802/// derived from a constant PHI. If this expression does not fit with these 1803/// constraints, return null. 1804static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1805 // If this is not an instruction, or if this is an instruction outside of the 1806 // loop, it can't be derived from a loop PHI. 1807 Instruction *I = dyn_cast<Instruction>(V); 1808 if (I == 0 || !L->contains(I->getParent())) return 0; 1809 1810 if (PHINode *PN = dyn_cast<PHINode>(I)) 1811 if (L->getHeader() == I->getParent()) 1812 return PN; 1813 else 1814 // We don't currently keep track of the control flow needed to evaluate 1815 // PHIs, so we cannot handle PHIs inside of loops. 1816 return 0; 1817 1818 // If we won't be able to constant fold this expression even if the operands 1819 // are constants, return early. 1820 if (!CanConstantFold(I)) return 0; 1821 1822 // Otherwise, we can evaluate this instruction if all of its operands are 1823 // constant or derived from a PHI node themselves. 1824 PHINode *PHI = 0; 1825 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1826 if (!(isa<Constant>(I->getOperand(Op)) || 1827 isa<GlobalValue>(I->getOperand(Op)))) { 1828 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1829 if (P == 0) return 0; // Not evolving from PHI 1830 if (PHI == 0) 1831 PHI = P; 1832 else if (PHI != P) 1833 return 0; // Evolving from multiple different PHIs. 1834 } 1835 1836 // This is a expression evolving from a constant PHI! 1837 return PHI; 1838} 1839 1840/// EvaluateExpression - Given an expression that passes the 1841/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1842/// in the loop has the value PHIVal. If we can't fold this expression for some 1843/// reason, return null. 1844static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1845 if (isa<PHINode>(V)) return PHIVal; 1846 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1847 return GV; 1848 if (Constant *C = dyn_cast<Constant>(V)) return C; 1849 Instruction *I = cast<Instruction>(V); 1850 1851 std::vector<Constant*> Operands; 1852 Operands.resize(I->getNumOperands()); 1853 1854 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1855 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1856 if (Operands[i] == 0) return 0; 1857 } 1858 1859 return ConstantFold(I, Operands); 1860} 1861 1862/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1863/// in the header of its containing loop, we know the loop executes a 1864/// constant number of times, and the PHI node is just a recurrence 1865/// involving constants, fold it. 1866Constant *ScalarEvolutionsImpl:: 1867getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1868 std::map<PHINode*, Constant*>::iterator I = 1869 ConstantEvolutionLoopExitValue.find(PN); 1870 if (I != ConstantEvolutionLoopExitValue.end()) 1871 return I->second; 1872 1873 if (Its > MaxBruteForceIterations) 1874 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1875 1876 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1877 1878 // Since the loop is canonicalized, the PHI node must have two entries. One 1879 // entry must be a constant (coming in from outside of the loop), and the 1880 // second must be derived from the same PHI. 1881 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1882 Constant *StartCST = 1883 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1884 if (StartCST == 0) 1885 return RetVal = 0; // Must be a constant. 1886 1887 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1888 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1889 if (PN2 != PN) 1890 return RetVal = 0; // Not derived from same PHI. 1891 1892 // Execute the loop symbolically to determine the exit value. 1893 unsigned IterationNum = 0; 1894 unsigned NumIterations = Its; 1895 if (NumIterations != Its) 1896 return RetVal = 0; // More than 2^32 iterations?? 1897 1898 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1899 if (IterationNum == NumIterations) 1900 return RetVal = PHIVal; // Got exit value! 1901 1902 // Compute the value of the PHI node for the next iteration. 1903 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1904 if (NextPHI == PHIVal) 1905 return RetVal = NextPHI; // Stopped evolving! 1906 if (NextPHI == 0) 1907 return 0; // Couldn't evaluate! 1908 PHIVal = NextPHI; 1909 } 1910} 1911 1912/// ComputeIterationCountExhaustively - If the trip is known to execute a 1913/// constant number of times (the condition evolves only from constants), 1914/// try to evaluate a few iterations of the loop until we get the exit 1915/// condition gets a value of ExitWhen (true or false). If we cannot 1916/// evaluate the trip count of the loop, return UnknownValue. 1917SCEVHandle ScalarEvolutionsImpl:: 1918ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1919 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1920 if (PN == 0) return UnknownValue; 1921 1922 // Since the loop is canonicalized, the PHI node must have two entries. One 1923 // entry must be a constant (coming in from outside of the loop), and the 1924 // second must be derived from the same PHI. 1925 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1926 Constant *StartCST = 1927 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1928 if (StartCST == 0) return UnknownValue; // Must be a constant. 1929 1930 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1931 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1932 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1933 1934 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1935 // the loop symbolically to determine when the condition gets a value of 1936 // "ExitWhen". 1937 unsigned IterationNum = 0; 1938 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1939 for (Constant *PHIVal = StartCST; 1940 IterationNum != MaxIterations; ++IterationNum) { 1941 ConstantBool *CondVal = 1942 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1943 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1944 1945 if (CondVal->getValue() == ExitWhen) { 1946 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1947 ++NumBruteForceTripCountsComputed; 1948 return SCEVConstant::get(ConstantInt::get(Type::UIntTy, IterationNum)); 1949 } 1950 1951 // Compute the value of the PHI node for the next iteration. 1952 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1953 if (NextPHI == 0 || NextPHI == PHIVal) 1954 return UnknownValue; // Couldn't evaluate or not making progress... 1955 PHIVal = NextPHI; 1956 } 1957 1958 // Too many iterations were needed to evaluate. 1959 return UnknownValue; 1960} 1961 1962/// getSCEVAtScope - Compute the value of the specified expression within the 1963/// indicated loop (which may be null to indicate in no loop). If the 1964/// expression cannot be evaluated, return UnknownValue. 1965SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1966 // FIXME: this should be turned into a virtual method on SCEV! 1967 1968 if (isa<SCEVConstant>(V)) return V; 1969 1970 // If this instruction is evolves from a constant-evolving PHI, compute the 1971 // exit value from the loop without using SCEVs. 1972 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1973 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1974 const Loop *LI = this->LI[I->getParent()]; 1975 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1976 if (PHINode *PN = dyn_cast<PHINode>(I)) 1977 if (PN->getParent() == LI->getHeader()) { 1978 // Okay, there is no closed form solution for the PHI node. Check 1979 // to see if the loop that contains it has a known iteration count. 1980 // If so, we may be able to force computation of the exit value. 1981 SCEVHandle IterationCount = getIterationCount(LI); 1982 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1983 // Okay, we know how many times the containing loop executes. If 1984 // this is a constant evolving PHI node, get the final value at 1985 // the specified iteration number. 1986 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1987 ICC->getValue()->getZExtValue(), 1988 LI); 1989 if (RV) return SCEVUnknown::get(RV); 1990 } 1991 } 1992 1993 // Okay, this is an expression that we cannot symbolically evaluate 1994 // into a SCEV. Check to see if it's possible to symbolically evaluate 1995 // the arguments into constants, and if so, try to constant propagate the 1996 // result. This is particularly useful for computing loop exit values. 1997 if (CanConstantFold(I)) { 1998 std::vector<Constant*> Operands; 1999 Operands.reserve(I->getNumOperands()); 2000 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2001 Value *Op = I->getOperand(i); 2002 if (Constant *C = dyn_cast<Constant>(Op)) { 2003 Operands.push_back(C); 2004 } else { 2005 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2006 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2007 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2008 Op->getType(), 2009 false)); 2010 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2011 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2012 Operands.push_back(ConstantExpr::getIntegerCast(C, 2013 Op->getType(), 2014 false)); 2015 else 2016 return V; 2017 } else { 2018 return V; 2019 } 2020 } 2021 } 2022 return SCEVUnknown::get(ConstantFold(I, Operands)); 2023 } 2024 } 2025 2026 // This is some other type of SCEVUnknown, just return it. 2027 return V; 2028 } 2029 2030 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2031 // Avoid performing the look-up in the common case where the specified 2032 // expression has no loop-variant portions. 2033 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2034 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2035 if (OpAtScope != Comm->getOperand(i)) { 2036 if (OpAtScope == UnknownValue) return UnknownValue; 2037 // Okay, at least one of these operands is loop variant but might be 2038 // foldable. Build a new instance of the folded commutative expression. 2039 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2040 NewOps.push_back(OpAtScope); 2041 2042 for (++i; i != e; ++i) { 2043 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2044 if (OpAtScope == UnknownValue) return UnknownValue; 2045 NewOps.push_back(OpAtScope); 2046 } 2047 if (isa<SCEVAddExpr>(Comm)) 2048 return SCEVAddExpr::get(NewOps); 2049 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2050 return SCEVMulExpr::get(NewOps); 2051 } 2052 } 2053 // If we got here, all operands are loop invariant. 2054 return Comm; 2055 } 2056 2057 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2058 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2059 if (LHS == UnknownValue) return LHS; 2060 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2061 if (RHS == UnknownValue) return RHS; 2062 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2063 return Div; // must be loop invariant 2064 return SCEVSDivExpr::get(LHS, RHS); 2065 } 2066 2067 // If this is a loop recurrence for a loop that does not contain L, then we 2068 // are dealing with the final value computed by the loop. 2069 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2070 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2071 // To evaluate this recurrence, we need to know how many times the AddRec 2072 // loop iterates. Compute this now. 2073 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2074 if (IterationCount == UnknownValue) return UnknownValue; 2075 IterationCount = getTruncateOrZeroExtend(IterationCount, 2076 AddRec->getType()); 2077 2078 // If the value is affine, simplify the expression evaluation to just 2079 // Start + Step*IterationCount. 2080 if (AddRec->isAffine()) 2081 return SCEVAddExpr::get(AddRec->getStart(), 2082 SCEVMulExpr::get(IterationCount, 2083 AddRec->getOperand(1))); 2084 2085 // Otherwise, evaluate it the hard way. 2086 return AddRec->evaluateAtIteration(IterationCount); 2087 } 2088 return UnknownValue; 2089 } 2090 2091 //assert(0 && "Unknown SCEV type!"); 2092 return UnknownValue; 2093} 2094 2095 2096/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2097/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2098/// might be the same) or two SCEVCouldNotCompute objects. 2099/// 2100static std::pair<SCEVHandle,SCEVHandle> 2101SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2102 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2103 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2104 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2105 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2106 2107 // We currently can only solve this if the coefficients are constants. 2108 if (!L || !M || !N) { 2109 SCEV *CNC = new SCEVCouldNotCompute(); 2110 return std::make_pair(CNC, CNC); 2111 } 2112 2113 Constant *C = L->getValue(); 2114 Constant *Two = ConstantInt::get(C->getType(), 2); 2115 2116 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2117 // The B coefficient is M-N/2 2118 Constant *B = ConstantExpr::getSub(M->getValue(), 2119 ConstantExpr::getSDiv(N->getValue(), 2120 Two)); 2121 // The A coefficient is N/2 2122 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two); 2123 2124 // Compute the B^2-4ac term. 2125 Constant *SqrtTerm = 2126 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2127 ConstantExpr::getMul(A, C)); 2128 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2129 2130 // Compute floor(sqrt(B^2-4ac)) 2131 ConstantInt *SqrtVal = 2132 cast<ConstantInt>(ConstantExpr::getBitCast(SqrtTerm, 2133 SqrtTerm->getType()->getUnsignedVersion())); 2134 uint64_t SqrtValV = SqrtVal->getZExtValue(); 2135 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2136 // The square root might not be precise for arbitrary 64-bit integer 2137 // values. Do some sanity checks to ensure it's correct. 2138 if (SqrtValV2*SqrtValV2 > SqrtValV || 2139 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2140 SCEV *CNC = new SCEVCouldNotCompute(); 2141 return std::make_pair(CNC, CNC); 2142 } 2143 2144 SqrtVal = ConstantInt::get(Type::ULongTy, SqrtValV2); 2145 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType()); 2146 2147 Constant *NegB = ConstantExpr::getNeg(B); 2148 Constant *TwoA = ConstantExpr::getMul(A, Two); 2149 2150 // The divisions must be performed as signed divisions. 2151 const Type *SignedTy = NegB->getType()->getSignedVersion(); 2152 NegB = ConstantExpr::getBitCast(NegB, SignedTy); 2153 TwoA = ConstantExpr::getBitCast(TwoA, SignedTy); 2154 SqrtTerm = ConstantExpr::getBitCast(SqrtTerm, SignedTy); 2155 2156 Constant *Solution1 = 2157 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2158 Constant *Solution2 = 2159 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2160 return std::make_pair(SCEVUnknown::get(Solution1), 2161 SCEVUnknown::get(Solution2)); 2162} 2163 2164/// HowFarToZero - Return the number of times a backedge comparing the specified 2165/// value to zero will execute. If not computable, return UnknownValue 2166SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2167 // If the value is a constant 2168 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2169 // If the value is already zero, the branch will execute zero times. 2170 if (C->getValue()->isNullValue()) return C; 2171 return UnknownValue; // Otherwise it will loop infinitely. 2172 } 2173 2174 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2175 if (!AddRec || AddRec->getLoop() != L) 2176 return UnknownValue; 2177 2178 if (AddRec->isAffine()) { 2179 // If this is an affine expression the execution count of this branch is 2180 // equal to: 2181 // 2182 // (0 - Start/Step) iff Start % Step == 0 2183 // 2184 // Get the initial value for the loop. 2185 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2186 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2187 SCEVHandle Step = AddRec->getOperand(1); 2188 2189 Step = getSCEVAtScope(Step, L->getParentLoop()); 2190 2191 // Figure out if Start % Step == 0. 2192 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2193 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2194 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2195 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2196 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2197 return Start; // 0 - Start/-1 == Start 2198 2199 // Check to see if Start is divisible by SC with no remainder. 2200 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2201 ConstantInt *StartCC = StartC->getValue(); 2202 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2203 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2204 if (Rem->isNullValue()) { 2205 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2206 return SCEVUnknown::get(Result); 2207 } 2208 } 2209 } 2210 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2211 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2212 // the quadratic equation to solve it. 2213 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2214 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2215 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2216 if (R1) { 2217#if 0 2218 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2219 << " sol#2: " << *R2 << "\n"; 2220#endif 2221 // Pick the smallest positive root value. 2222 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 2223 if (ConstantBool *CB = 2224 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2225 R2->getValue()))) { 2226 if (CB->getValue() == false) 2227 std::swap(R1, R2); // R1 is the minimum root now. 2228 2229 // We can only use this value if the chrec ends up with an exact zero 2230 // value at this index. When solving for "X*X != 5", for example, we 2231 // should not accept a root of 2. 2232 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2233 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2234 if (EvalVal->getValue()->isNullValue()) 2235 return R1; // We found a quadratic root! 2236 } 2237 } 2238 } 2239 2240 return UnknownValue; 2241} 2242 2243/// HowFarToNonZero - Return the number of times a backedge checking the 2244/// specified value for nonzero will execute. If not computable, return 2245/// UnknownValue 2246SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2247 // Loops that look like: while (X == 0) are very strange indeed. We don't 2248 // handle them yet except for the trivial case. This could be expanded in the 2249 // future as needed. 2250 2251 // If the value is a constant, check to see if it is known to be non-zero 2252 // already. If so, the backedge will execute zero times. 2253 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2254 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2255 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 2256 if (NonZero == ConstantBool::getTrue()) 2257 return getSCEV(Zero); 2258 return UnknownValue; // Otherwise it will loop infinitely. 2259 } 2260 2261 // We could implement others, but I really doubt anyone writes loops like 2262 // this, and if they did, they would already be constant folded. 2263 return UnknownValue; 2264} 2265 2266/// HowManyLessThans - Return the number of times a backedge containing the 2267/// specified less-than comparison will execute. If not computable, return 2268/// UnknownValue. 2269SCEVHandle ScalarEvolutionsImpl:: 2270HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2271 // Only handle: "ADDREC < LoopInvariant". 2272 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2273 2274 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2275 if (!AddRec || AddRec->getLoop() != L) 2276 return UnknownValue; 2277 2278 if (AddRec->isAffine()) { 2279 // FORNOW: We only support unit strides. 2280 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2281 if (AddRec->getOperand(1) != One) 2282 return UnknownValue; 2283 2284 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2285 // know that m is >= n on input to the loop. If it is, the condition return 2286 // true zero times. What we really should return, for full generality, is 2287 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2288 // canonical loop form: most do-loops will have a check that dominates the 2289 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2290 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2291 2292 // Search for the check. 2293 BasicBlock *Preheader = L->getLoopPreheader(); 2294 BasicBlock *PreheaderDest = L->getHeader(); 2295 if (Preheader == 0) return UnknownValue; 2296 2297 BranchInst *LoopEntryPredicate = 2298 dyn_cast<BranchInst>(Preheader->getTerminator()); 2299 if (!LoopEntryPredicate) return UnknownValue; 2300 2301 // This might be a critical edge broken out. If the loop preheader ends in 2302 // an unconditional branch to the loop, check to see if the preheader has a 2303 // single predecessor, and if so, look for its terminator. 2304 while (LoopEntryPredicate->isUnconditional()) { 2305 PreheaderDest = Preheader; 2306 Preheader = Preheader->getSinglePredecessor(); 2307 if (!Preheader) return UnknownValue; // Multiple preds. 2308 2309 LoopEntryPredicate = 2310 dyn_cast<BranchInst>(Preheader->getTerminator()); 2311 if (!LoopEntryPredicate) return UnknownValue; 2312 } 2313 2314 // Now that we found a conditional branch that dominates the loop, check to 2315 // see if it is the comparison we are looking for. 2316 SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition()); 2317 if (!SCI) return UnknownValue; 2318 Value *PreCondLHS = SCI->getOperand(0); 2319 Value *PreCondRHS = SCI->getOperand(1); 2320 Instruction::BinaryOps Cond; 2321 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2322 Cond = SCI->getOpcode(); 2323 else 2324 Cond = SCI->getInverseCondition(); 2325 2326 switch (Cond) { 2327 case Instruction::SetGT: 2328 std::swap(PreCondLHS, PreCondRHS); 2329 Cond = Instruction::SetLT; 2330 // Fall Through. 2331 case Instruction::SetLT: 2332 if (PreCondLHS->getType()->isInteger() && 2333 PreCondLHS->getType()->isSigned()) { 2334 if (RHS != getSCEV(PreCondRHS)) 2335 return UnknownValue; // Not a comparison against 'm'. 2336 2337 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2338 != getSCEV(PreCondLHS)) 2339 return UnknownValue; // Not a comparison against 'n-1'. 2340 break; 2341 } else { 2342 return UnknownValue; 2343 } 2344 default: break; 2345 } 2346 2347 //cerr << "Computed Loop Trip Count as: " 2348 // << *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2349 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2350 } 2351 2352 return UnknownValue; 2353} 2354 2355/// getNumIterationsInRange - Return the number of iterations of this loop that 2356/// produce values in the specified constant range. Another way of looking at 2357/// this is that it returns the first iteration number where the value is not in 2358/// the condition, thus computing the exit count. If the iteration count can't 2359/// be computed, an instance of SCEVCouldNotCompute is returned. 2360SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2361 if (Range.isFullSet()) // Infinite loop. 2362 return new SCEVCouldNotCompute(); 2363 2364 // If the start is a non-zero constant, shift the range to simplify things. 2365 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2366 if (!SC->getValue()->isNullValue()) { 2367 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2368 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2369 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2370 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2371 return ShiftedAddRec->getNumIterationsInRange( 2372 Range.subtract(SC->getValue())); 2373 // This is strange and shouldn't happen. 2374 return new SCEVCouldNotCompute(); 2375 } 2376 2377 // The only time we can solve this is when we have all constant indices. 2378 // Otherwise, we cannot determine the overflow conditions. 2379 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2380 if (!isa<SCEVConstant>(getOperand(i))) 2381 return new SCEVCouldNotCompute(); 2382 2383 2384 // Okay at this point we know that all elements of the chrec are constants and 2385 // that the start element is zero. 2386 2387 // First check to see if the range contains zero. If not, the first 2388 // iteration exits. 2389 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2390 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2391 2392 if (isAffine()) { 2393 // If this is an affine expression then we have this situation: 2394 // Solve {0,+,A} in Range === Ax in Range 2395 2396 // Since we know that zero is in the range, we know that the upper value of 2397 // the range must be the first possible exit value. Also note that we 2398 // already checked for a full range. 2399 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2400 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2401 ConstantInt *One = ConstantInt::get(getType(), 1); 2402 2403 // The exit value should be (Upper+A-1)/A. 2404 Constant *ExitValue = Upper; 2405 if (A != One) { 2406 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2407 ExitValue = ConstantExpr::getSDiv(ExitValue, A); 2408 } 2409 assert(isa<ConstantInt>(ExitValue) && 2410 "Constant folding of integers not implemented?"); 2411 2412 // Evaluate at the exit value. If we really did fall out of the valid 2413 // range, then we computed our trip count, otherwise wrap around or other 2414 // things must have happened. 2415 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2416 if (Range.contains(Val)) 2417 return new SCEVCouldNotCompute(); // Something strange happened 2418 2419 // Ensure that the previous value is in the range. This is a sanity check. 2420 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2421 ConstantExpr::getSub(ExitValue, One))) && 2422 "Linear scev computation is off in a bad way!"); 2423 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2424 } else if (isQuadratic()) { 2425 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2426 // quadratic equation to solve it. To do this, we must frame our problem in 2427 // terms of figuring out when zero is crossed, instead of when 2428 // Range.getUpper() is crossed. 2429 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2430 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2431 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2432 2433 // Next, solve the constructed addrec 2434 std::pair<SCEVHandle,SCEVHandle> Roots = 2435 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2436 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2437 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2438 if (R1) { 2439 // Pick the smallest positive root value. 2440 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2441 if (ConstantBool *CB = 2442 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2443 R2->getValue()))) { 2444 if (CB->getValue() == false) 2445 std::swap(R1, R2); // R1 is the minimum root now. 2446 2447 // Make sure the root is not off by one. The returned iteration should 2448 // not be in the range, but the previous one should be. When solving 2449 // for "X*X < 5", for example, we should not return a root of 2. 2450 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2451 R1->getValue()); 2452 if (Range.contains(R1Val)) { 2453 // The next iteration must be out of the range... 2454 Constant *NextVal = 2455 ConstantExpr::getAdd(R1->getValue(), 2456 ConstantInt::get(R1->getType(), 1)); 2457 2458 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2459 if (!Range.contains(R1Val)) 2460 return SCEVUnknown::get(NextVal); 2461 return new SCEVCouldNotCompute(); // Something strange happened 2462 } 2463 2464 // If R1 was not in the range, then it is a good return value. Make 2465 // sure that R1-1 WAS in the range though, just in case. 2466 Constant *NextVal = 2467 ConstantExpr::getSub(R1->getValue(), 2468 ConstantInt::get(R1->getType(), 1)); 2469 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2470 if (Range.contains(R1Val)) 2471 return R1; 2472 return new SCEVCouldNotCompute(); // Something strange happened 2473 } 2474 } 2475 } 2476 2477 // Fallback, if this is a general polynomial, figure out the progression 2478 // through brute force: evaluate until we find an iteration that fails the 2479 // test. This is likely to be slow, but getting an accurate trip count is 2480 // incredibly important, we will be able to simplify the exit test a lot, and 2481 // we are almost guaranteed to get a trip count in this case. 2482 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2483 ConstantInt *One = ConstantInt::get(getType(), 1); 2484 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2485 do { 2486 ++NumBruteForceEvaluations; 2487 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2488 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2489 return new SCEVCouldNotCompute(); 2490 2491 // Check to see if we found the value! 2492 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2493 return SCEVConstant::get(TestVal); 2494 2495 // Increment to test the next index. 2496 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2497 } while (TestVal != EndVal); 2498 2499 return new SCEVCouldNotCompute(); 2500} 2501 2502 2503 2504//===----------------------------------------------------------------------===// 2505// ScalarEvolution Class Implementation 2506//===----------------------------------------------------------------------===// 2507 2508bool ScalarEvolution::runOnFunction(Function &F) { 2509 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2510 return false; 2511} 2512 2513void ScalarEvolution::releaseMemory() { 2514 delete (ScalarEvolutionsImpl*)Impl; 2515 Impl = 0; 2516} 2517 2518void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2519 AU.setPreservesAll(); 2520 AU.addRequiredTransitive<LoopInfo>(); 2521} 2522 2523SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2524 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2525} 2526 2527/// hasSCEV - Return true if the SCEV for this value has already been 2528/// computed. 2529bool ScalarEvolution::hasSCEV(Value *V) const { 2530 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2531} 2532 2533 2534/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2535/// the specified value. 2536void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2537 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2538} 2539 2540 2541SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2542 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2543} 2544 2545bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2546 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2547} 2548 2549SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2550 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2551} 2552 2553void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2554 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2555} 2556 2557static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2558 const Loop *L) { 2559 // Print all inner loops first 2560 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2561 PrintLoopInfo(OS, SE, *I); 2562 2563 cerr << "Loop " << L->getHeader()->getName() << ": "; 2564 2565 std::vector<BasicBlock*> ExitBlocks; 2566 L->getExitBlocks(ExitBlocks); 2567 if (ExitBlocks.size() != 1) 2568 cerr << "<multiple exits> "; 2569 2570 if (SE->hasLoopInvariantIterationCount(L)) { 2571 cerr << *SE->getIterationCount(L) << " iterations! "; 2572 } else { 2573 cerr << "Unpredictable iteration count. "; 2574 } 2575 2576 cerr << "\n"; 2577} 2578 2579void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2580 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2581 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2582 2583 OS << "Classifying expressions for: " << F.getName() << "\n"; 2584 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2585 if (I->getType()->isInteger()) { 2586 OS << *I; 2587 OS << " --> "; 2588 SCEVHandle SV = getSCEV(&*I); 2589 SV->print(OS); 2590 OS << "\t\t"; 2591 2592 if ((*I).getType()->isIntegral()) { 2593 ConstantRange Bounds = SV->getValueRange(); 2594 if (!Bounds.isFullSet()) 2595 OS << "Bounds: " << Bounds << " "; 2596 } 2597 2598 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2599 OS << "Exits: "; 2600 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2601 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2602 OS << "<<Unknown>>"; 2603 } else { 2604 OS << *ExitValue; 2605 } 2606 } 2607 2608 2609 OS << "\n"; 2610 } 2611 2612 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2613 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2614 PrintLoopInfo(OS, this, *I); 2615} 2616 2617