ScalarEvolution.cpp revision 2e20d39493aa58dfe7b1f9e8890215f0dedc038f
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#define DEBUG_TYPE "scalar-evolution" 63#include "llvm/Analysis/ScalarEvolutionExpressions.h" 64#include "llvm/Constants.h" 65#include "llvm/DerivedTypes.h" 66#include "llvm/GlobalVariable.h" 67#include "llvm/Instructions.h" 68#include "llvm/Analysis/ConstantFolding.h" 69#include "llvm/Analysis/LoopInfo.h" 70#include "llvm/Assembly/Writer.h" 71#include "llvm/Transforms/Scalar.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/InstIterator.h" 77#include "llvm/Support/ManagedStatic.h" 78#include "llvm/Support/MathExtras.h" 79#include "llvm/Support/Streams.h" 80#include "llvm/ADT/Statistic.h" 81#include <ostream> 82#include <algorithm> 83#include <cmath> 84using namespace llvm; 85 86STATISTIC(NumBruteForceEvaluations, 87 "Number of brute force evaluations needed to " 88 "calculate high-order polynomial exit values"); 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant derived loop"), 102 cl::init(100)); 103 104namespace { 105 RegisterPass<ScalarEvolution> 106 R("scalar-evolution", "Scalar Evolution Analysis"); 107} 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116SCEV::~SCEV() {} 117void SCEV::dump() const { 118 print(cerr); 119} 120 121/// getValueRange - Return the tightest constant bounds that this value is 122/// known to have. This method is only valid on integer SCEV objects. 123ConstantRange SCEV::getValueRange() const { 124 const Type *Ty = getType(); 125 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 126 Ty = Ty->getUnsignedVersion(); 127 // Default to a full range if no better information is available. 128 return ConstantRange(getType()); 129} 130 131 132SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 133 134bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 135 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 136 return false; 137} 138 139const Type *SCEVCouldNotCompute::getType() const { 140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 141 return 0; 142} 143 144bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 146 return false; 147} 148 149SCEVHandle SCEVCouldNotCompute:: 150replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 151 const SCEVHandle &Conc) const { 152 return this; 153} 154 155void SCEVCouldNotCompute::print(std::ostream &OS) const { 156 OS << "***COULDNOTCOMPUTE***"; 157} 158 159bool SCEVCouldNotCompute::classof(const SCEV *S) { 160 return S->getSCEVType() == scCouldNotCompute; 161} 162 163 164// SCEVConstants - Only allow the creation of one SCEVConstant for any 165// particular value. Don't use a SCEVHandle here, or else the object will 166// never be deleted! 167static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 168 169 170SCEVConstant::~SCEVConstant() { 171 SCEVConstants->erase(V); 172} 173 174SCEVHandle SCEVConstant::get(ConstantInt *V) { 175 // Make sure that SCEVConstant instances are all unsigned. 176 // FIXME:Signless. This entire if statement can be removed when integer types 177 // are signless. There won't be a need to bitcast then. 178 if (V->getType()->isSigned()) { 179 const Type *NewTy = V->getType()->getUnsignedVersion(); 180 V = cast<ConstantInt>( 181 ConstantExpr::getBitCast(V, NewTy)); 182 } 183 184 SCEVConstant *&R = (*SCEVConstants)[V]; 185 if (R == 0) R = new SCEVConstant(V); 186 return R; 187} 188 189ConstantRange SCEVConstant::getValueRange() const { 190 return ConstantRange(V); 191} 192 193const Type *SCEVConstant::getType() const { return V->getType(); } 194 195void SCEVConstant::print(std::ostream &OS) const { 196 WriteAsOperand(OS, V, false); 197} 198 199// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 200// particular input. Don't use a SCEVHandle here, or else the object will 201// never be deleted! 202static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 203 SCEVTruncateExpr*> > SCEVTruncates; 204 205SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 206 : SCEV(scTruncate), Op(op), Ty(ty) { 207 assert(Op->getType()->isInteger() && Ty->isInteger() && 208 "Cannot truncate non-integer value!"); 209 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 210 "This is not a truncating conversion!"); 211} 212 213SCEVTruncateExpr::~SCEVTruncateExpr() { 214 SCEVTruncates->erase(std::make_pair(Op, Ty)); 215} 216 217ConstantRange SCEVTruncateExpr::getValueRange() const { 218 return getOperand()->getValueRange().truncate(getType()); 219} 220 221void SCEVTruncateExpr::print(std::ostream &OS) const { 222 OS << "(truncate " << *Op << " to " << *Ty << ")"; 223} 224 225// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 226// particular input. Don't use a SCEVHandle here, or else the object will never 227// be deleted! 228static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 229 SCEVZeroExtendExpr*> > SCEVZeroExtends; 230 231SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 232 : SCEV(scZeroExtend), Op(op), Ty(ty) { 233 assert(Op->getType()->isInteger() && Ty->isInteger() && 234 "Cannot zero extend non-integer value!"); 235 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 236 "This is not an extending conversion!"); 237} 238 239SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 240 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 241} 242 243ConstantRange SCEVZeroExtendExpr::getValueRange() const { 244 return getOperand()->getValueRange().zeroExtend(getType()); 245} 246 247void SCEVZeroExtendExpr::print(std::ostream &OS) const { 248 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 249} 250 251// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 252// particular input. Don't use a SCEVHandle here, or else the object will never 253// be deleted! 254static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 255 SCEVCommutativeExpr*> > SCEVCommExprs; 256 257SCEVCommutativeExpr::~SCEVCommutativeExpr() { 258 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 259 std::vector<SCEV*>(Operands.begin(), 260 Operands.end()))); 261} 262 263void SCEVCommutativeExpr::print(std::ostream &OS) const { 264 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 265 const char *OpStr = getOperationStr(); 266 OS << "(" << *Operands[0]; 267 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 268 OS << OpStr << *Operands[i]; 269 OS << ")"; 270} 271 272SCEVHandle SCEVCommutativeExpr:: 273replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 274 const SCEVHandle &Conc) const { 275 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 276 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 277 if (H != getOperand(i)) { 278 std::vector<SCEVHandle> NewOps; 279 NewOps.reserve(getNumOperands()); 280 for (unsigned j = 0; j != i; ++j) 281 NewOps.push_back(getOperand(j)); 282 NewOps.push_back(H); 283 for (++i; i != e; ++i) 284 NewOps.push_back(getOperand(i)-> 285 replaceSymbolicValuesWithConcrete(Sym, Conc)); 286 287 if (isa<SCEVAddExpr>(this)) 288 return SCEVAddExpr::get(NewOps); 289 else if (isa<SCEVMulExpr>(this)) 290 return SCEVMulExpr::get(NewOps); 291 else 292 assert(0 && "Unknown commutative expr!"); 293 } 294 } 295 return this; 296} 297 298 299// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 300// input. Don't use a SCEVHandle here, or else the object will never be 301// deleted! 302static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 303 SCEVSDivExpr*> > SCEVSDivs; 304 305SCEVSDivExpr::~SCEVSDivExpr() { 306 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 307} 308 309void SCEVSDivExpr::print(std::ostream &OS) const { 310 OS << "(" << *LHS << " /s " << *RHS << ")"; 311} 312 313const Type *SCEVSDivExpr::getType() const { 314 const Type *Ty = LHS->getType(); 315 if (Ty->isUnsigned()) Ty = Ty->getSignedVersion(); 316 return Ty; 317} 318 319// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 320// particular input. Don't use a SCEVHandle here, or else the object will never 321// be deleted! 322static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 323 SCEVAddRecExpr*> > SCEVAddRecExprs; 324 325SCEVAddRecExpr::~SCEVAddRecExpr() { 326 SCEVAddRecExprs->erase(std::make_pair(L, 327 std::vector<SCEV*>(Operands.begin(), 328 Operands.end()))); 329} 330 331SCEVHandle SCEVAddRecExpr:: 332replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 333 const SCEVHandle &Conc) const { 334 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 335 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 336 if (H != getOperand(i)) { 337 std::vector<SCEVHandle> NewOps; 338 NewOps.reserve(getNumOperands()); 339 for (unsigned j = 0; j != i; ++j) 340 NewOps.push_back(getOperand(j)); 341 NewOps.push_back(H); 342 for (++i; i != e; ++i) 343 NewOps.push_back(getOperand(i)-> 344 replaceSymbolicValuesWithConcrete(Sym, Conc)); 345 346 return get(NewOps, L); 347 } 348 } 349 return this; 350} 351 352 353bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 354 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 355 // contain L and if the start is invariant. 356 return !QueryLoop->contains(L->getHeader()) && 357 getOperand(0)->isLoopInvariant(QueryLoop); 358} 359 360 361void SCEVAddRecExpr::print(std::ostream &OS) const { 362 OS << "{" << *Operands[0]; 363 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 364 OS << ",+," << *Operands[i]; 365 OS << "}<" << L->getHeader()->getName() + ">"; 366} 367 368// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 369// value. Don't use a SCEVHandle here, or else the object will never be 370// deleted! 371static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 372 373SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 374 375bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 376 // All non-instruction values are loop invariant. All instructions are loop 377 // invariant if they are not contained in the specified loop. 378 if (Instruction *I = dyn_cast<Instruction>(V)) 379 return !L->contains(I->getParent()); 380 return true; 381} 382 383const Type *SCEVUnknown::getType() const { 384 return V->getType(); 385} 386 387void SCEVUnknown::print(std::ostream &OS) const { 388 WriteAsOperand(OS, V, false); 389} 390 391//===----------------------------------------------------------------------===// 392// SCEV Utilities 393//===----------------------------------------------------------------------===// 394 395namespace { 396 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 397 /// than the complexity of the RHS. This comparator is used to canonicalize 398 /// expressions. 399 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 400 bool operator()(SCEV *LHS, SCEV *RHS) { 401 return LHS->getSCEVType() < RHS->getSCEVType(); 402 } 403 }; 404} 405 406/// GroupByComplexity - Given a list of SCEV objects, order them by their 407/// complexity, and group objects of the same complexity together by value. 408/// When this routine is finished, we know that any duplicates in the vector are 409/// consecutive and that complexity is monotonically increasing. 410/// 411/// Note that we go take special precautions to ensure that we get determinstic 412/// results from this routine. In other words, we don't want the results of 413/// this to depend on where the addresses of various SCEV objects happened to 414/// land in memory. 415/// 416static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 417 if (Ops.size() < 2) return; // Noop 418 if (Ops.size() == 2) { 419 // This is the common case, which also happens to be trivially simple. 420 // Special case it. 421 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 422 std::swap(Ops[0], Ops[1]); 423 return; 424 } 425 426 // Do the rough sort by complexity. 427 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 428 429 // Now that we are sorted by complexity, group elements of the same 430 // complexity. Note that this is, at worst, N^2, but the vector is likely to 431 // be extremely short in practice. Note that we take this approach because we 432 // do not want to depend on the addresses of the objects we are grouping. 433 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 434 SCEV *S = Ops[i]; 435 unsigned Complexity = S->getSCEVType(); 436 437 // If there are any objects of the same complexity and same value as this 438 // one, group them. 439 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 440 if (Ops[j] == S) { // Found a duplicate. 441 // Move it to immediately after i'th element. 442 std::swap(Ops[i+1], Ops[j]); 443 ++i; // no need to rescan it. 444 if (i == e-2) return; // Done! 445 } 446 } 447 } 448} 449 450 451 452//===----------------------------------------------------------------------===// 453// Simple SCEV method implementations 454//===----------------------------------------------------------------------===// 455 456/// getIntegerSCEV - Given an integer or FP type, create a constant for the 457/// specified signed integer value and return a SCEV for the constant. 458SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 459 Constant *C; 460 if (Val == 0) 461 C = Constant::getNullValue(Ty); 462 else if (Ty->isFloatingPoint()) 463 C = ConstantFP::get(Ty, Val); 464 /// FIXME:Signless. when integer types are signless, just change this to: 465 /// else 466 /// C = ConstantInt::get(Ty, Val); 467 else if (Ty->isSigned()) 468 C = ConstantInt::get(Ty, Val); 469 else { 470 C = ConstantInt::get(Ty->getSignedVersion(), Val); 471 C = ConstantExpr::getBitCast(C, Ty); 472 } 473 return SCEVUnknown::get(C); 474} 475 476/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 477/// input value to the specified type. If the type must be extended, it is zero 478/// extended. 479static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 480 const Type *SrcTy = V->getType(); 481 assert(SrcTy->isInteger() && Ty->isInteger() && 482 "Cannot truncate or zero extend with non-integer arguments!"); 483 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 484 return V; // No conversion 485 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 486 return SCEVTruncateExpr::get(V, Ty); 487 return SCEVZeroExtendExpr::get(V, Ty); 488} 489 490/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 491/// 492SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 493 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 494 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 495 496 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 497} 498 499/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 500/// 501SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 502 // X - Y --> X + -Y 503 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 504} 505 506 507/// PartialFact - Compute V!/(V-NumSteps)! 508static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 509 // Handle this case efficiently, it is common to have constant iteration 510 // counts while computing loop exit values. 511 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 512 uint64_t Val = SC->getValue()->getZExtValue(); 513 uint64_t Result = 1; 514 for (; NumSteps; --NumSteps) 515 Result *= Val-(NumSteps-1); 516 Constant *Res = ConstantInt::get(Type::ULongTy, Result); 517 return SCEVUnknown::get( 518 ConstantExpr::getTruncOrBitCast(Res, V->getType())); 519 } 520 521 const Type *Ty = V->getType(); 522 if (NumSteps == 0) 523 return SCEVUnknown::getIntegerSCEV(1, Ty); 524 525 SCEVHandle Result = V; 526 for (unsigned i = 1; i != NumSteps; ++i) 527 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 528 SCEVUnknown::getIntegerSCEV(i, Ty))); 529 return Result; 530} 531 532 533/// evaluateAtIteration - Return the value of this chain of recurrences at 534/// the specified iteration number. We can evaluate this recurrence by 535/// multiplying each element in the chain by the binomial coefficient 536/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 537/// 538/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 539/// 540/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 541/// Is the binomial equation safe using modular arithmetic?? 542/// 543SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 544 SCEVHandle Result = getStart(); 545 int Divisor = 1; 546 const Type *Ty = It->getType(); 547 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 548 SCEVHandle BC = PartialFact(It, i); 549 Divisor *= i; 550 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 551 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 552 Result = SCEVAddExpr::get(Result, Val); 553 } 554 return Result; 555} 556 557 558//===----------------------------------------------------------------------===// 559// SCEV Expression folder implementations 560//===----------------------------------------------------------------------===// 561 562SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 563 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 564 return SCEVUnknown::get( 565 ConstantExpr::getTrunc(SC->getValue(), Ty)); 566 567 // If the input value is a chrec scev made out of constants, truncate 568 // all of the constants. 569 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 570 std::vector<SCEVHandle> Operands; 571 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 572 // FIXME: This should allow truncation of other expression types! 573 if (isa<SCEVConstant>(AddRec->getOperand(i))) 574 Operands.push_back(get(AddRec->getOperand(i), Ty)); 575 else 576 break; 577 if (Operands.size() == AddRec->getNumOperands()) 578 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 579 } 580 581 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 582 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 583 return Result; 584} 585 586SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 587 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 588 return SCEVUnknown::get( 589 ConstantExpr::getZExt(SC->getValue(), Ty)); 590 591 // FIXME: If the input value is a chrec scev, and we can prove that the value 592 // did not overflow the old, smaller, value, we can zero extend all of the 593 // operands (often constants). This would allow analysis of something like 594 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 595 596 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 597 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 598 return Result; 599} 600 601// get - Get a canonical add expression, or something simpler if possible. 602SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 603 assert(!Ops.empty() && "Cannot get empty add!"); 604 if (Ops.size() == 1) return Ops[0]; 605 606 // Sort by complexity, this groups all similar expression types together. 607 GroupByComplexity(Ops); 608 609 // If there are any constants, fold them together. 610 unsigned Idx = 0; 611 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 612 ++Idx; 613 assert(Idx < Ops.size()); 614 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 615 // We found two constants, fold them together! 616 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 617 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 618 Ops[0] = SCEVConstant::get(CI); 619 Ops.erase(Ops.begin()+1); // Erase the folded element 620 if (Ops.size() == 1) return Ops[0]; 621 LHSC = cast<SCEVConstant>(Ops[0]); 622 } else { 623 // If we couldn't fold the expression, move to the next constant. Note 624 // that this is impossible to happen in practice because we always 625 // constant fold constant ints to constant ints. 626 ++Idx; 627 } 628 } 629 630 // If we are left with a constant zero being added, strip it off. 631 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 632 Ops.erase(Ops.begin()); 633 --Idx; 634 } 635 } 636 637 if (Ops.size() == 1) return Ops[0]; 638 639 // Okay, check to see if the same value occurs in the operand list twice. If 640 // so, merge them together into an multiply expression. Since we sorted the 641 // list, these values are required to be adjacent. 642 const Type *Ty = Ops[0]->getType(); 643 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 644 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 645 // Found a match, merge the two values into a multiply, and add any 646 // remaining values to the result. 647 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 648 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 649 if (Ops.size() == 2) 650 return Mul; 651 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 652 Ops.push_back(Mul); 653 return SCEVAddExpr::get(Ops); 654 } 655 656 // Okay, now we know the first non-constant operand. If there are add 657 // operands they would be next. 658 if (Idx < Ops.size()) { 659 bool DeletedAdd = false; 660 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 661 // If we have an add, expand the add operands onto the end of the operands 662 // list. 663 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 664 Ops.erase(Ops.begin()+Idx); 665 DeletedAdd = true; 666 } 667 668 // If we deleted at least one add, we added operands to the end of the list, 669 // and they are not necessarily sorted. Recurse to resort and resimplify 670 // any operands we just aquired. 671 if (DeletedAdd) 672 return get(Ops); 673 } 674 675 // Skip over the add expression until we get to a multiply. 676 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 677 ++Idx; 678 679 // If we are adding something to a multiply expression, make sure the 680 // something is not already an operand of the multiply. If so, merge it into 681 // the multiply. 682 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 683 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 684 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 685 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 686 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 687 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 688 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 689 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 690 if (Mul->getNumOperands() != 2) { 691 // If the multiply has more than two operands, we must get the 692 // Y*Z term. 693 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 694 MulOps.erase(MulOps.begin()+MulOp); 695 InnerMul = SCEVMulExpr::get(MulOps); 696 } 697 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 698 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 699 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 700 if (Ops.size() == 2) return OuterMul; 701 if (AddOp < Idx) { 702 Ops.erase(Ops.begin()+AddOp); 703 Ops.erase(Ops.begin()+Idx-1); 704 } else { 705 Ops.erase(Ops.begin()+Idx); 706 Ops.erase(Ops.begin()+AddOp-1); 707 } 708 Ops.push_back(OuterMul); 709 return SCEVAddExpr::get(Ops); 710 } 711 712 // Check this multiply against other multiplies being added together. 713 for (unsigned OtherMulIdx = Idx+1; 714 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 715 ++OtherMulIdx) { 716 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 717 // If MulOp occurs in OtherMul, we can fold the two multiplies 718 // together. 719 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 720 OMulOp != e; ++OMulOp) 721 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 722 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 723 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 724 if (Mul->getNumOperands() != 2) { 725 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 726 MulOps.erase(MulOps.begin()+MulOp); 727 InnerMul1 = SCEVMulExpr::get(MulOps); 728 } 729 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 730 if (OtherMul->getNumOperands() != 2) { 731 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 732 OtherMul->op_end()); 733 MulOps.erase(MulOps.begin()+OMulOp); 734 InnerMul2 = SCEVMulExpr::get(MulOps); 735 } 736 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 737 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 738 if (Ops.size() == 2) return OuterMul; 739 Ops.erase(Ops.begin()+Idx); 740 Ops.erase(Ops.begin()+OtherMulIdx-1); 741 Ops.push_back(OuterMul); 742 return SCEVAddExpr::get(Ops); 743 } 744 } 745 } 746 } 747 748 // If there are any add recurrences in the operands list, see if any other 749 // added values are loop invariant. If so, we can fold them into the 750 // recurrence. 751 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 752 ++Idx; 753 754 // Scan over all recurrences, trying to fold loop invariants into them. 755 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 756 // Scan all of the other operands to this add and add them to the vector if 757 // they are loop invariant w.r.t. the recurrence. 758 std::vector<SCEVHandle> LIOps; 759 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 760 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 761 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 762 LIOps.push_back(Ops[i]); 763 Ops.erase(Ops.begin()+i); 764 --i; --e; 765 } 766 767 // If we found some loop invariants, fold them into the recurrence. 768 if (!LIOps.empty()) { 769 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 770 LIOps.push_back(AddRec->getStart()); 771 772 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 773 AddRecOps[0] = SCEVAddExpr::get(LIOps); 774 775 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 776 // If all of the other operands were loop invariant, we are done. 777 if (Ops.size() == 1) return NewRec; 778 779 // Otherwise, add the folded AddRec by the non-liv parts. 780 for (unsigned i = 0;; ++i) 781 if (Ops[i] == AddRec) { 782 Ops[i] = NewRec; 783 break; 784 } 785 return SCEVAddExpr::get(Ops); 786 } 787 788 // Okay, if there weren't any loop invariants to be folded, check to see if 789 // there are multiple AddRec's with the same loop induction variable being 790 // added together. If so, we can fold them. 791 for (unsigned OtherIdx = Idx+1; 792 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 793 if (OtherIdx != Idx) { 794 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 795 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 796 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 797 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 798 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 799 if (i >= NewOps.size()) { 800 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 801 OtherAddRec->op_end()); 802 break; 803 } 804 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 805 } 806 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 807 808 if (Ops.size() == 2) return NewAddRec; 809 810 Ops.erase(Ops.begin()+Idx); 811 Ops.erase(Ops.begin()+OtherIdx-1); 812 Ops.push_back(NewAddRec); 813 return SCEVAddExpr::get(Ops); 814 } 815 } 816 817 // Otherwise couldn't fold anything into this recurrence. Move onto the 818 // next one. 819 } 820 821 // Okay, it looks like we really DO need an add expr. Check to see if we 822 // already have one, otherwise create a new one. 823 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 824 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 825 SCEVOps)]; 826 if (Result == 0) Result = new SCEVAddExpr(Ops); 827 return Result; 828} 829 830 831SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 832 assert(!Ops.empty() && "Cannot get empty mul!"); 833 834 // Sort by complexity, this groups all similar expression types together. 835 GroupByComplexity(Ops); 836 837 // If there are any constants, fold them together. 838 unsigned Idx = 0; 839 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 840 841 // C1*(C2+V) -> C1*C2 + C1*V 842 if (Ops.size() == 2) 843 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 844 if (Add->getNumOperands() == 2 && 845 isa<SCEVConstant>(Add->getOperand(0))) 846 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 847 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 848 849 850 ++Idx; 851 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 852 // We found two constants, fold them together! 853 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 854 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 855 Ops[0] = SCEVConstant::get(CI); 856 Ops.erase(Ops.begin()+1); // Erase the folded element 857 if (Ops.size() == 1) return Ops[0]; 858 LHSC = cast<SCEVConstant>(Ops[0]); 859 } else { 860 // If we couldn't fold the expression, move to the next constant. Note 861 // that this is impossible to happen in practice because we always 862 // constant fold constant ints to constant ints. 863 ++Idx; 864 } 865 } 866 867 // If we are left with a constant one being multiplied, strip it off. 868 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 869 Ops.erase(Ops.begin()); 870 --Idx; 871 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 872 // If we have a multiply of zero, it will always be zero. 873 return Ops[0]; 874 } 875 } 876 877 // Skip over the add expression until we get to a multiply. 878 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 879 ++Idx; 880 881 if (Ops.size() == 1) 882 return Ops[0]; 883 884 // If there are mul operands inline them all into this expression. 885 if (Idx < Ops.size()) { 886 bool DeletedMul = false; 887 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 888 // If we have an mul, expand the mul operands onto the end of the operands 889 // list. 890 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 891 Ops.erase(Ops.begin()+Idx); 892 DeletedMul = true; 893 } 894 895 // If we deleted at least one mul, we added operands to the end of the list, 896 // and they are not necessarily sorted. Recurse to resort and resimplify 897 // any operands we just aquired. 898 if (DeletedMul) 899 return get(Ops); 900 } 901 902 // If there are any add recurrences in the operands list, see if any other 903 // added values are loop invariant. If so, we can fold them into the 904 // recurrence. 905 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 906 ++Idx; 907 908 // Scan over all recurrences, trying to fold loop invariants into them. 909 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 910 // Scan all of the other operands to this mul and add them to the vector if 911 // they are loop invariant w.r.t. the recurrence. 912 std::vector<SCEVHandle> LIOps; 913 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 914 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 915 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 916 LIOps.push_back(Ops[i]); 917 Ops.erase(Ops.begin()+i); 918 --i; --e; 919 } 920 921 // If we found some loop invariants, fold them into the recurrence. 922 if (!LIOps.empty()) { 923 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 924 std::vector<SCEVHandle> NewOps; 925 NewOps.reserve(AddRec->getNumOperands()); 926 if (LIOps.size() == 1) { 927 SCEV *Scale = LIOps[0]; 928 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 929 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 930 } else { 931 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 932 std::vector<SCEVHandle> MulOps(LIOps); 933 MulOps.push_back(AddRec->getOperand(i)); 934 NewOps.push_back(SCEVMulExpr::get(MulOps)); 935 } 936 } 937 938 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 939 940 // If all of the other operands were loop invariant, we are done. 941 if (Ops.size() == 1) return NewRec; 942 943 // Otherwise, multiply the folded AddRec by the non-liv parts. 944 for (unsigned i = 0;; ++i) 945 if (Ops[i] == AddRec) { 946 Ops[i] = NewRec; 947 break; 948 } 949 return SCEVMulExpr::get(Ops); 950 } 951 952 // Okay, if there weren't any loop invariants to be folded, check to see if 953 // there are multiple AddRec's with the same loop induction variable being 954 // multiplied together. If so, we can fold them. 955 for (unsigned OtherIdx = Idx+1; 956 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 957 if (OtherIdx != Idx) { 958 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 959 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 960 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 961 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 962 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 963 G->getStart()); 964 SCEVHandle B = F->getStepRecurrence(); 965 SCEVHandle D = G->getStepRecurrence(); 966 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 967 SCEVMulExpr::get(G, B), 968 SCEVMulExpr::get(B, D)); 969 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 970 F->getLoop()); 971 if (Ops.size() == 2) return NewAddRec; 972 973 Ops.erase(Ops.begin()+Idx); 974 Ops.erase(Ops.begin()+OtherIdx-1); 975 Ops.push_back(NewAddRec); 976 return SCEVMulExpr::get(Ops); 977 } 978 } 979 980 // Otherwise couldn't fold anything into this recurrence. Move onto the 981 // next one. 982 } 983 984 // Okay, it looks like we really DO need an mul expr. Check to see if we 985 // already have one, otherwise create a new one. 986 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 987 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 988 SCEVOps)]; 989 if (Result == 0) 990 Result = new SCEVMulExpr(Ops); 991 return Result; 992} 993 994SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 995 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 996 if (RHSC->getValue()->equalsInt(1)) 997 return LHS; // X sdiv 1 --> x 998 if (RHSC->getValue()->isAllOnesValue()) 999 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 1000 1001 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1002 Constant *LHSCV = LHSC->getValue(); 1003 Constant *RHSCV = RHSC->getValue(); 1004 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 1005 } 1006 } 1007 1008 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1009 1010 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 1011 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1012 return Result; 1013} 1014 1015 1016/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1017/// specified loop. Simplify the expression as much as possible. 1018SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1019 const SCEVHandle &Step, const Loop *L) { 1020 std::vector<SCEVHandle> Operands; 1021 Operands.push_back(Start); 1022 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1023 if (StepChrec->getLoop() == L) { 1024 Operands.insert(Operands.end(), StepChrec->op_begin(), 1025 StepChrec->op_end()); 1026 return get(Operands, L); 1027 } 1028 1029 Operands.push_back(Step); 1030 return get(Operands, L); 1031} 1032 1033/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1034/// specified loop. Simplify the expression as much as possible. 1035SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1036 const Loop *L) { 1037 if (Operands.size() == 1) return Operands[0]; 1038 1039 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1040 if (StepC->getValue()->isNullValue()) { 1041 Operands.pop_back(); 1042 return get(Operands, L); // { X,+,0 } --> X 1043 } 1044 1045 SCEVAddRecExpr *&Result = 1046 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1047 Operands.end()))]; 1048 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1049 return Result; 1050} 1051 1052SCEVHandle SCEVUnknown::get(Value *V) { 1053 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1054 return SCEVConstant::get(CI); 1055 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1056 if (Result == 0) Result = new SCEVUnknown(V); 1057 return Result; 1058} 1059 1060 1061//===----------------------------------------------------------------------===// 1062// ScalarEvolutionsImpl Definition and Implementation 1063//===----------------------------------------------------------------------===// 1064// 1065/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1066/// evolution code. 1067/// 1068namespace { 1069 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1070 /// F - The function we are analyzing. 1071 /// 1072 Function &F; 1073 1074 /// LI - The loop information for the function we are currently analyzing. 1075 /// 1076 LoopInfo &LI; 1077 1078 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1079 /// things. 1080 SCEVHandle UnknownValue; 1081 1082 /// Scalars - This is a cache of the scalars we have analyzed so far. 1083 /// 1084 std::map<Value*, SCEVHandle> Scalars; 1085 1086 /// IterationCounts - Cache the iteration count of the loops for this 1087 /// function as they are computed. 1088 std::map<const Loop*, SCEVHandle> IterationCounts; 1089 1090 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1091 /// the PHI instructions that we attempt to compute constant evolutions for. 1092 /// This allows us to avoid potentially expensive recomputation of these 1093 /// properties. An instruction maps to null if we are unable to compute its 1094 /// exit value. 1095 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1096 1097 public: 1098 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1099 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1100 1101 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1102 /// expression and create a new one. 1103 SCEVHandle getSCEV(Value *V); 1104 1105 /// hasSCEV - Return true if the SCEV for this value has already been 1106 /// computed. 1107 bool hasSCEV(Value *V) const { 1108 return Scalars.count(V); 1109 } 1110 1111 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1112 /// the specified value. 1113 void setSCEV(Value *V, const SCEVHandle &H) { 1114 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1115 assert(isNew && "This entry already existed!"); 1116 } 1117 1118 1119 /// getSCEVAtScope - Compute the value of the specified expression within 1120 /// the indicated loop (which may be null to indicate in no loop). If the 1121 /// expression cannot be evaluated, return UnknownValue itself. 1122 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1123 1124 1125 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1126 /// an analyzable loop-invariant iteration count. 1127 bool hasLoopInvariantIterationCount(const Loop *L); 1128 1129 /// getIterationCount - If the specified loop has a predictable iteration 1130 /// count, return it. Note that it is not valid to call this method on a 1131 /// loop without a loop-invariant iteration count. 1132 SCEVHandle getIterationCount(const Loop *L); 1133 1134 /// deleteInstructionFromRecords - This method should be called by the 1135 /// client before it removes an instruction from the program, to make sure 1136 /// that no dangling references are left around. 1137 void deleteInstructionFromRecords(Instruction *I); 1138 1139 private: 1140 /// createSCEV - We know that there is no SCEV for the specified value. 1141 /// Analyze the expression. 1142 SCEVHandle createSCEV(Value *V); 1143 1144 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1145 /// SCEVs. 1146 SCEVHandle createNodeForPHI(PHINode *PN); 1147 1148 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1149 /// for the specified instruction and replaces any references to the 1150 /// symbolic value SymName with the specified value. This is used during 1151 /// PHI resolution. 1152 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1153 const SCEVHandle &SymName, 1154 const SCEVHandle &NewVal); 1155 1156 /// ComputeIterationCount - Compute the number of times the specified loop 1157 /// will iterate. 1158 SCEVHandle ComputeIterationCount(const Loop *L); 1159 1160 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1161 /// 'setcc load X, cst', try to se if we can compute the trip count. 1162 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1163 Constant *RHS, 1164 const Loop *L, 1165 unsigned SetCCOpcode); 1166 1167 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1168 /// constant number of times (the condition evolves only from constants), 1169 /// try to evaluate a few iterations of the loop until we get the exit 1170 /// condition gets a value of ExitWhen (true or false). If we cannot 1171 /// evaluate the trip count of the loop, return UnknownValue. 1172 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1173 bool ExitWhen); 1174 1175 /// HowFarToZero - Return the number of times a backedge comparing the 1176 /// specified value to zero will execute. If not computable, return 1177 /// UnknownValue. 1178 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1179 1180 /// HowFarToNonZero - Return the number of times a backedge checking the 1181 /// specified value for nonzero will execute. If not computable, return 1182 /// UnknownValue. 1183 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1184 1185 /// HowManyLessThans - Return the number of times a backedge containing the 1186 /// specified less-than comparison will execute. If not computable, return 1187 /// UnknownValue. 1188 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L); 1189 1190 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1191 /// in the header of its containing loop, we know the loop executes a 1192 /// constant number of times, and the PHI node is just a recurrence 1193 /// involving constants, fold it. 1194 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1195 const Loop *L); 1196 }; 1197} 1198 1199//===----------------------------------------------------------------------===// 1200// Basic SCEV Analysis and PHI Idiom Recognition Code 1201// 1202 1203/// deleteInstructionFromRecords - This method should be called by the 1204/// client before it removes an instruction from the program, to make sure 1205/// that no dangling references are left around. 1206void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1207 Scalars.erase(I); 1208 if (PHINode *PN = dyn_cast<PHINode>(I)) 1209 ConstantEvolutionLoopExitValue.erase(PN); 1210} 1211 1212 1213/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1214/// expression and create a new one. 1215SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1216 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1217 1218 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1219 if (I != Scalars.end()) return I->second; 1220 SCEVHandle S = createSCEV(V); 1221 Scalars.insert(std::make_pair(V, S)); 1222 return S; 1223} 1224 1225/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1226/// the specified instruction and replaces any references to the symbolic value 1227/// SymName with the specified value. This is used during PHI resolution. 1228void ScalarEvolutionsImpl:: 1229ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1230 const SCEVHandle &NewVal) { 1231 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1232 if (SI == Scalars.end()) return; 1233 1234 SCEVHandle NV = 1235 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1236 if (NV == SI->second) return; // No change. 1237 1238 SI->second = NV; // Update the scalars map! 1239 1240 // Any instruction values that use this instruction might also need to be 1241 // updated! 1242 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1243 UI != E; ++UI) 1244 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1245} 1246 1247/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1248/// a loop header, making it a potential recurrence, or it doesn't. 1249/// 1250SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1251 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1252 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1253 if (L->getHeader() == PN->getParent()) { 1254 // If it lives in the loop header, it has two incoming values, one 1255 // from outside the loop, and one from inside. 1256 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1257 unsigned BackEdge = IncomingEdge^1; 1258 1259 // While we are analyzing this PHI node, handle its value symbolically. 1260 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1261 assert(Scalars.find(PN) == Scalars.end() && 1262 "PHI node already processed?"); 1263 Scalars.insert(std::make_pair(PN, SymbolicName)); 1264 1265 // Using this symbolic name for the PHI, analyze the value coming around 1266 // the back-edge. 1267 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1268 1269 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1270 // has a special value for the first iteration of the loop. 1271 1272 // If the value coming around the backedge is an add with the symbolic 1273 // value we just inserted, then we found a simple induction variable! 1274 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1275 // If there is a single occurrence of the symbolic value, replace it 1276 // with a recurrence. 1277 unsigned FoundIndex = Add->getNumOperands(); 1278 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1279 if (Add->getOperand(i) == SymbolicName) 1280 if (FoundIndex == e) { 1281 FoundIndex = i; 1282 break; 1283 } 1284 1285 if (FoundIndex != Add->getNumOperands()) { 1286 // Create an add with everything but the specified operand. 1287 std::vector<SCEVHandle> Ops; 1288 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1289 if (i != FoundIndex) 1290 Ops.push_back(Add->getOperand(i)); 1291 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1292 1293 // This is not a valid addrec if the step amount is varying each 1294 // loop iteration, but is not itself an addrec in this loop. 1295 if (Accum->isLoopInvariant(L) || 1296 (isa<SCEVAddRecExpr>(Accum) && 1297 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1298 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1299 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1300 1301 // Okay, for the entire analysis of this edge we assumed the PHI 1302 // to be symbolic. We now need to go back and update all of the 1303 // entries for the scalars that use the PHI (except for the PHI 1304 // itself) to use the new analyzed value instead of the "symbolic" 1305 // value. 1306 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1307 return PHISCEV; 1308 } 1309 } 1310 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1311 // Otherwise, this could be a loop like this: 1312 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1313 // In this case, j = {1,+,1} and BEValue is j. 1314 // Because the other in-value of i (0) fits the evolution of BEValue 1315 // i really is an addrec evolution. 1316 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1317 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1318 1319 // If StartVal = j.start - j.stride, we can use StartVal as the 1320 // initial step of the addrec evolution. 1321 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1322 AddRec->getOperand(1))) { 1323 SCEVHandle PHISCEV = 1324 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1325 1326 // Okay, for the entire analysis of this edge we assumed the PHI 1327 // to be symbolic. We now need to go back and update all of the 1328 // entries for the scalars that use the PHI (except for the PHI 1329 // itself) to use the new analyzed value instead of the "symbolic" 1330 // value. 1331 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1332 return PHISCEV; 1333 } 1334 } 1335 } 1336 1337 return SymbolicName; 1338 } 1339 1340 // If it's not a loop phi, we can't handle it yet. 1341 return SCEVUnknown::get(PN); 1342} 1343 1344/// GetConstantFactor - Determine the largest constant factor that S has. For 1345/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1346static uint64_t GetConstantFactor(SCEVHandle S) { 1347 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1348 if (uint64_t V = C->getValue()->getZExtValue()) 1349 return V; 1350 else // Zero is a multiple of everything. 1351 return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1); 1352 } 1353 1354 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1355 return GetConstantFactor(T->getOperand()) & 1356 T->getType()->getIntegralTypeMask(); 1357 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1358 return GetConstantFactor(E->getOperand()); 1359 1360 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1361 // The result is the min of all operands. 1362 uint64_t Res = GetConstantFactor(A->getOperand(0)); 1363 for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i) 1364 Res = std::min(Res, GetConstantFactor(A->getOperand(i))); 1365 return Res; 1366 } 1367 1368 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1369 // The result is the product of all the operands. 1370 uint64_t Res = GetConstantFactor(M->getOperand(0)); 1371 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) 1372 Res *= GetConstantFactor(M->getOperand(i)); 1373 return Res; 1374 } 1375 1376 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1377 // For now, we just handle linear expressions. 1378 if (A->getNumOperands() == 2) { 1379 // We want the GCD between the start and the stride value. 1380 uint64_t Start = GetConstantFactor(A->getOperand(0)); 1381 if (Start == 1) return 1; 1382 uint64_t Stride = GetConstantFactor(A->getOperand(1)); 1383 return GreatestCommonDivisor64(Start, Stride); 1384 } 1385 } 1386 1387 // SCEVSDivExpr, SCEVUnknown. 1388 return 1; 1389} 1390 1391/// createSCEV - We know that there is no SCEV for the specified value. 1392/// Analyze the expression. 1393/// 1394SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1395 if (Instruction *I = dyn_cast<Instruction>(V)) { 1396 switch (I->getOpcode()) { 1397 case Instruction::Add: 1398 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1399 getSCEV(I->getOperand(1))); 1400 case Instruction::Mul: 1401 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1402 getSCEV(I->getOperand(1))); 1403 case Instruction::SDiv: 1404 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1405 getSCEV(I->getOperand(1))); 1406 break; 1407 1408 case Instruction::Sub: 1409 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1410 getSCEV(I->getOperand(1))); 1411 case Instruction::Or: 1412 // If the RHS of the Or is a constant, we may have something like: 1413 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1414 // optimizations will transparently handle this case. 1415 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1416 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1417 uint64_t CommonFact = GetConstantFactor(LHS); 1418 assert(CommonFact && "Common factor should at least be 1!"); 1419 if (CommonFact > CI->getZExtValue()) { 1420 // If the LHS is a multiple that is larger than the RHS, use +. 1421 return SCEVAddExpr::get(LHS, 1422 getSCEV(I->getOperand(1))); 1423 } 1424 } 1425 break; 1426 1427 case Instruction::Shl: 1428 // Turn shift left of a constant amount into a multiply. 1429 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1430 Constant *X = ConstantInt::get(V->getType(), 1); 1431 X = ConstantExpr::getShl(X, SA); 1432 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1433 } 1434 break; 1435 1436 case Instruction::Trunc: 1437 // We don't handle trunc to bool yet. 1438 if (I->getType()->isInteger()) 1439 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), 1440 I->getType()->getUnsignedVersion()); 1441 break; 1442 1443 case Instruction::ZExt: 1444 // We don't handle zext from bool yet. 1445 if (I->getOperand(0)->getType()->isInteger()) 1446 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), 1447 I->getType()->getUnsignedVersion()); 1448 break; 1449 1450 case Instruction::BitCast: 1451 // BitCasts are no-op casts so we just eliminate the cast. 1452 if (I->getType()->isInteger() && I->getOperand(0)->getType()->isInteger()) 1453 return getSCEV(I->getOperand(0)); 1454 break; 1455 1456 case Instruction::PHI: 1457 return createNodeForPHI(cast<PHINode>(I)); 1458 1459 default: // We cannot analyze this expression. 1460 break; 1461 } 1462 } 1463 1464 return SCEVUnknown::get(V); 1465} 1466 1467 1468 1469//===----------------------------------------------------------------------===// 1470// Iteration Count Computation Code 1471// 1472 1473/// getIterationCount - If the specified loop has a predictable iteration 1474/// count, return it. Note that it is not valid to call this method on a 1475/// loop without a loop-invariant iteration count. 1476SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1477 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1478 if (I == IterationCounts.end()) { 1479 SCEVHandle ItCount = ComputeIterationCount(L); 1480 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1481 if (ItCount != UnknownValue) { 1482 assert(ItCount->isLoopInvariant(L) && 1483 "Computed trip count isn't loop invariant for loop!"); 1484 ++NumTripCountsComputed; 1485 } else if (isa<PHINode>(L->getHeader()->begin())) { 1486 // Only count loops that have phi nodes as not being computable. 1487 ++NumTripCountsNotComputed; 1488 } 1489 } 1490 return I->second; 1491} 1492 1493/// ComputeIterationCount - Compute the number of times the specified loop 1494/// will iterate. 1495SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1496 // If the loop has a non-one exit block count, we can't analyze it. 1497 std::vector<BasicBlock*> ExitBlocks; 1498 L->getExitBlocks(ExitBlocks); 1499 if (ExitBlocks.size() != 1) return UnknownValue; 1500 1501 // Okay, there is one exit block. Try to find the condition that causes the 1502 // loop to be exited. 1503 BasicBlock *ExitBlock = ExitBlocks[0]; 1504 1505 BasicBlock *ExitingBlock = 0; 1506 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1507 PI != E; ++PI) 1508 if (L->contains(*PI)) { 1509 if (ExitingBlock == 0) 1510 ExitingBlock = *PI; 1511 else 1512 return UnknownValue; // More than one block exiting! 1513 } 1514 assert(ExitingBlock && "No exits from loop, something is broken!"); 1515 1516 // Okay, we've computed the exiting block. See what condition causes us to 1517 // exit. 1518 // 1519 // FIXME: we should be able to handle switch instructions (with a single exit) 1520 // FIXME: We should handle cast of int to bool as well 1521 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1522 if (ExitBr == 0) return UnknownValue; 1523 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1524 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1525 if (ExitCond == 0) // Not a setcc 1526 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1527 ExitBr->getSuccessor(0) == ExitBlock); 1528 1529 // If the condition was exit on true, convert the condition to exit on false. 1530 Instruction::BinaryOps Cond; 1531 if (ExitBr->getSuccessor(1) == ExitBlock) 1532 Cond = ExitCond->getOpcode(); 1533 else 1534 Cond = ExitCond->getInverseCondition(); 1535 1536 // Handle common loops like: for (X = "string"; *X; ++X) 1537 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1538 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1539 SCEVHandle ItCnt = 1540 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1541 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1542 } 1543 1544 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1545 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1546 1547 // Try to evaluate any dependencies out of the loop. 1548 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1549 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1550 Tmp = getSCEVAtScope(RHS, L); 1551 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1552 1553 // At this point, we would like to compute how many iterations of the loop the 1554 // predicate will return true for these inputs. 1555 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1556 // If there is a constant, force it into the RHS. 1557 std::swap(LHS, RHS); 1558 Cond = SetCondInst::getSwappedCondition(Cond); 1559 } 1560 1561 // FIXME: think about handling pointer comparisons! i.e.: 1562 // while (P != P+100) ++P; 1563 1564 // If we have a comparison of a chrec against a constant, try to use value 1565 // ranges to answer this query. 1566 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1567 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1568 if (AddRec->getLoop() == L) { 1569 // Form the comparison range using the constant of the correct type so 1570 // that the ConstantRange class knows to do a signed or unsigned 1571 // comparison. 1572 ConstantInt *CompVal = RHSC->getValue(); 1573 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1574 CompVal = dyn_cast<ConstantInt>( 1575 ConstantExpr::getBitCast(CompVal, RealTy)); 1576 if (CompVal) { 1577 // Form the constant range. 1578 ConstantRange CompRange(Cond, CompVal); 1579 1580 // Now that we have it, if it's signed, convert it to an unsigned 1581 // range. 1582 // FIXME:Signless. This entire if statement can go away when 1583 // integers are signless. ConstantRange is already signless. 1584 if (CompRange.getLower()->getType()->isSigned()) { 1585 const Type *NewTy = RHSC->getValue()->getType(); 1586 Constant *NewL = ConstantExpr::getBitCast(CompRange.getLower(), 1587 NewTy); 1588 Constant *NewU = ConstantExpr::getBitCast(CompRange.getUpper(), 1589 NewTy); 1590 CompRange = ConstantRange(NewL, NewU); 1591 } 1592 1593 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1594 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1595 } 1596 } 1597 1598 switch (Cond) { 1599 case Instruction::SetNE: // while (X != Y) 1600 // Convert to: while (X-Y != 0) 1601 if (LHS->getType()->isInteger()) { 1602 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1603 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1604 } 1605 break; 1606 case Instruction::SetEQ: 1607 // Convert to: while (X-Y == 0) // while (X == Y) 1608 if (LHS->getType()->isInteger()) { 1609 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1610 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1611 } 1612 break; 1613 case Instruction::SetLT: 1614 if (LHS->getType()->isInteger() && 1615 ExitCond->getOperand(0)->getType()->isSigned()) { 1616 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1617 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1618 } 1619 break; 1620 case Instruction::SetGT: 1621 if (LHS->getType()->isInteger() && 1622 ExitCond->getOperand(0)->getType()->isSigned()) { 1623 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1624 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1625 } 1626 break; 1627 default: 1628#if 0 1629 cerr << "ComputeIterationCount "; 1630 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1631 cerr << "[unsigned] "; 1632 cerr << *LHS << " " 1633 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1634#endif 1635 break; 1636 } 1637 1638 return ComputeIterationCountExhaustively(L, ExitCond, 1639 ExitBr->getSuccessor(0) == ExitBlock); 1640} 1641 1642static ConstantInt * 1643EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1644 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1645 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1646 assert(isa<SCEVConstant>(Val) && 1647 "Evaluation of SCEV at constant didn't fold correctly?"); 1648 return cast<SCEVConstant>(Val)->getValue(); 1649} 1650 1651/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1652/// and a GEP expression (missing the pointer index) indexing into it, return 1653/// the addressed element of the initializer or null if the index expression is 1654/// invalid. 1655static Constant * 1656GetAddressedElementFromGlobal(GlobalVariable *GV, 1657 const std::vector<ConstantInt*> &Indices) { 1658 Constant *Init = GV->getInitializer(); 1659 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1660 uint64_t Idx = Indices[i]->getZExtValue(); 1661 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1662 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1663 Init = cast<Constant>(CS->getOperand(Idx)); 1664 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1665 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1666 Init = cast<Constant>(CA->getOperand(Idx)); 1667 } else if (isa<ConstantAggregateZero>(Init)) { 1668 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1669 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1670 Init = Constant::getNullValue(STy->getElementType(Idx)); 1671 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1672 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1673 Init = Constant::getNullValue(ATy->getElementType()); 1674 } else { 1675 assert(0 && "Unknown constant aggregate type!"); 1676 } 1677 return 0; 1678 } else { 1679 return 0; // Unknown initializer type 1680 } 1681 } 1682 return Init; 1683} 1684 1685/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1686/// 'setcc load X, cst', try to se if we can compute the trip count. 1687SCEVHandle ScalarEvolutionsImpl:: 1688ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1689 const Loop *L, unsigned SetCCOpcode) { 1690 if (LI->isVolatile()) return UnknownValue; 1691 1692 // Check to see if the loaded pointer is a getelementptr of a global. 1693 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1694 if (!GEP) return UnknownValue; 1695 1696 // Make sure that it is really a constant global we are gepping, with an 1697 // initializer, and make sure the first IDX is really 0. 1698 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1699 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1700 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1701 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1702 return UnknownValue; 1703 1704 // Okay, we allow one non-constant index into the GEP instruction. 1705 Value *VarIdx = 0; 1706 std::vector<ConstantInt*> Indexes; 1707 unsigned VarIdxNum = 0; 1708 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1709 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1710 Indexes.push_back(CI); 1711 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1712 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1713 VarIdx = GEP->getOperand(i); 1714 VarIdxNum = i-2; 1715 Indexes.push_back(0); 1716 } 1717 1718 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1719 // Check to see if X is a loop variant variable value now. 1720 SCEVHandle Idx = getSCEV(VarIdx); 1721 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1722 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1723 1724 // We can only recognize very limited forms of loop index expressions, in 1725 // particular, only affine AddRec's like {C1,+,C2}. 1726 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1727 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1728 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1729 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1730 return UnknownValue; 1731 1732 unsigned MaxSteps = MaxBruteForceIterations; 1733 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1734 ConstantInt *ItCst = 1735 ConstantInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 1736 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1737 1738 // Form the GEP offset. 1739 Indexes[VarIdxNum] = Val; 1740 1741 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1742 if (Result == 0) break; // Cannot compute! 1743 1744 // Evaluate the condition for this iteration. 1745 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 1746 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 1747 if (cast<ConstantBool>(Result)->getValue() == false) { 1748#if 0 1749 cerr << "\n***\n*** Computed loop count " << *ItCst 1750 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1751 << "***\n"; 1752#endif 1753 ++NumArrayLenItCounts; 1754 return SCEVConstant::get(ItCst); // Found terminating iteration! 1755 } 1756 } 1757 return UnknownValue; 1758} 1759 1760 1761/// CanConstantFold - Return true if we can constant fold an instruction of the 1762/// specified type, assuming that all operands were constants. 1763static bool CanConstantFold(const Instruction *I) { 1764 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1765 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1766 return true; 1767 1768 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1769 if (const Function *F = CI->getCalledFunction()) 1770 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1771 return false; 1772} 1773 1774/// ConstantFold - Constant fold an instruction of the specified type with the 1775/// specified constant operands. This function may modify the operands vector. 1776static Constant *ConstantFold(const Instruction *I, 1777 std::vector<Constant*> &Operands) { 1778 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1779 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1780 1781 if (isa<CastInst>(I)) 1782 return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType()); 1783 1784 switch (I->getOpcode()) { 1785 case Instruction::Select: 1786 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1787 case Instruction::Call: 1788 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1789 Operands.erase(Operands.begin()); 1790 return ConstantFoldCall(cast<Function>(GV), Operands); 1791 } 1792 return 0; 1793 case Instruction::GetElementPtr: 1794 Constant *Base = Operands[0]; 1795 Operands.erase(Operands.begin()); 1796 return ConstantExpr::getGetElementPtr(Base, Operands); 1797 } 1798 return 0; 1799} 1800 1801 1802/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1803/// in the loop that V is derived from. We allow arbitrary operations along the 1804/// way, but the operands of an operation must either be constants or a value 1805/// derived from a constant PHI. If this expression does not fit with these 1806/// constraints, return null. 1807static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1808 // If this is not an instruction, or if this is an instruction outside of the 1809 // loop, it can't be derived from a loop PHI. 1810 Instruction *I = dyn_cast<Instruction>(V); 1811 if (I == 0 || !L->contains(I->getParent())) return 0; 1812 1813 if (PHINode *PN = dyn_cast<PHINode>(I)) 1814 if (L->getHeader() == I->getParent()) 1815 return PN; 1816 else 1817 // We don't currently keep track of the control flow needed to evaluate 1818 // PHIs, so we cannot handle PHIs inside of loops. 1819 return 0; 1820 1821 // If we won't be able to constant fold this expression even if the operands 1822 // are constants, return early. 1823 if (!CanConstantFold(I)) return 0; 1824 1825 // Otherwise, we can evaluate this instruction if all of its operands are 1826 // constant or derived from a PHI node themselves. 1827 PHINode *PHI = 0; 1828 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1829 if (!(isa<Constant>(I->getOperand(Op)) || 1830 isa<GlobalValue>(I->getOperand(Op)))) { 1831 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1832 if (P == 0) return 0; // Not evolving from PHI 1833 if (PHI == 0) 1834 PHI = P; 1835 else if (PHI != P) 1836 return 0; // Evolving from multiple different PHIs. 1837 } 1838 1839 // This is a expression evolving from a constant PHI! 1840 return PHI; 1841} 1842 1843/// EvaluateExpression - Given an expression that passes the 1844/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1845/// in the loop has the value PHIVal. If we can't fold this expression for some 1846/// reason, return null. 1847static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1848 if (isa<PHINode>(V)) return PHIVal; 1849 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1850 return GV; 1851 if (Constant *C = dyn_cast<Constant>(V)) return C; 1852 Instruction *I = cast<Instruction>(V); 1853 1854 std::vector<Constant*> Operands; 1855 Operands.resize(I->getNumOperands()); 1856 1857 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1858 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1859 if (Operands[i] == 0) return 0; 1860 } 1861 1862 return ConstantFold(I, Operands); 1863} 1864 1865/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1866/// in the header of its containing loop, we know the loop executes a 1867/// constant number of times, and the PHI node is just a recurrence 1868/// involving constants, fold it. 1869Constant *ScalarEvolutionsImpl:: 1870getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1871 std::map<PHINode*, Constant*>::iterator I = 1872 ConstantEvolutionLoopExitValue.find(PN); 1873 if (I != ConstantEvolutionLoopExitValue.end()) 1874 return I->second; 1875 1876 if (Its > MaxBruteForceIterations) 1877 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1878 1879 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1880 1881 // Since the loop is canonicalized, the PHI node must have two entries. One 1882 // entry must be a constant (coming in from outside of the loop), and the 1883 // second must be derived from the same PHI. 1884 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1885 Constant *StartCST = 1886 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1887 if (StartCST == 0) 1888 return RetVal = 0; // Must be a constant. 1889 1890 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1891 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1892 if (PN2 != PN) 1893 return RetVal = 0; // Not derived from same PHI. 1894 1895 // Execute the loop symbolically to determine the exit value. 1896 unsigned IterationNum = 0; 1897 unsigned NumIterations = Its; 1898 if (NumIterations != Its) 1899 return RetVal = 0; // More than 2^32 iterations?? 1900 1901 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1902 if (IterationNum == NumIterations) 1903 return RetVal = PHIVal; // Got exit value! 1904 1905 // Compute the value of the PHI node for the next iteration. 1906 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1907 if (NextPHI == PHIVal) 1908 return RetVal = NextPHI; // Stopped evolving! 1909 if (NextPHI == 0) 1910 return 0; // Couldn't evaluate! 1911 PHIVal = NextPHI; 1912 } 1913} 1914 1915/// ComputeIterationCountExhaustively - If the trip is known to execute a 1916/// constant number of times (the condition evolves only from constants), 1917/// try to evaluate a few iterations of the loop until we get the exit 1918/// condition gets a value of ExitWhen (true or false). If we cannot 1919/// evaluate the trip count of the loop, return UnknownValue. 1920SCEVHandle ScalarEvolutionsImpl:: 1921ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1922 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1923 if (PN == 0) return UnknownValue; 1924 1925 // Since the loop is canonicalized, the PHI node must have two entries. One 1926 // entry must be a constant (coming in from outside of the loop), and the 1927 // second must be derived from the same PHI. 1928 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1929 Constant *StartCST = 1930 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1931 if (StartCST == 0) return UnknownValue; // Must be a constant. 1932 1933 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1934 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1935 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1936 1937 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1938 // the loop symbolically to determine when the condition gets a value of 1939 // "ExitWhen". 1940 unsigned IterationNum = 0; 1941 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1942 for (Constant *PHIVal = StartCST; 1943 IterationNum != MaxIterations; ++IterationNum) { 1944 ConstantBool *CondVal = 1945 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1946 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1947 1948 if (CondVal->getValue() == ExitWhen) { 1949 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1950 ++NumBruteForceTripCountsComputed; 1951 return SCEVConstant::get(ConstantInt::get(Type::UIntTy, IterationNum)); 1952 } 1953 1954 // Compute the value of the PHI node for the next iteration. 1955 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1956 if (NextPHI == 0 || NextPHI == PHIVal) 1957 return UnknownValue; // Couldn't evaluate or not making progress... 1958 PHIVal = NextPHI; 1959 } 1960 1961 // Too many iterations were needed to evaluate. 1962 return UnknownValue; 1963} 1964 1965/// getSCEVAtScope - Compute the value of the specified expression within the 1966/// indicated loop (which may be null to indicate in no loop). If the 1967/// expression cannot be evaluated, return UnknownValue. 1968SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1969 // FIXME: this should be turned into a virtual method on SCEV! 1970 1971 if (isa<SCEVConstant>(V)) return V; 1972 1973 // If this instruction is evolves from a constant-evolving PHI, compute the 1974 // exit value from the loop without using SCEVs. 1975 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1976 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1977 const Loop *LI = this->LI[I->getParent()]; 1978 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1979 if (PHINode *PN = dyn_cast<PHINode>(I)) 1980 if (PN->getParent() == LI->getHeader()) { 1981 // Okay, there is no closed form solution for the PHI node. Check 1982 // to see if the loop that contains it has a known iteration count. 1983 // If so, we may be able to force computation of the exit value. 1984 SCEVHandle IterationCount = getIterationCount(LI); 1985 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1986 // Okay, we know how many times the containing loop executes. If 1987 // this is a constant evolving PHI node, get the final value at 1988 // the specified iteration number. 1989 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1990 ICC->getValue()->getZExtValue(), 1991 LI); 1992 if (RV) return SCEVUnknown::get(RV); 1993 } 1994 } 1995 1996 // Okay, this is an expression that we cannot symbolically evaluate 1997 // into a SCEV. Check to see if it's possible to symbolically evaluate 1998 // the arguments into constants, and if so, try to constant propagate the 1999 // result. This is particularly useful for computing loop exit values. 2000 if (CanConstantFold(I)) { 2001 std::vector<Constant*> Operands; 2002 Operands.reserve(I->getNumOperands()); 2003 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2004 Value *Op = I->getOperand(i); 2005 if (Constant *C = dyn_cast<Constant>(Op)) { 2006 Operands.push_back(C); 2007 } else { 2008 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2009 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2010 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2011 Op->getType(), 2012 false)); 2013 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2014 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2015 Operands.push_back(ConstantExpr::getIntegerCast(C, 2016 Op->getType(), 2017 false)); 2018 else 2019 return V; 2020 } else { 2021 return V; 2022 } 2023 } 2024 } 2025 return SCEVUnknown::get(ConstantFold(I, Operands)); 2026 } 2027 } 2028 2029 // This is some other type of SCEVUnknown, just return it. 2030 return V; 2031 } 2032 2033 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2034 // Avoid performing the look-up in the common case where the specified 2035 // expression has no loop-variant portions. 2036 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2037 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2038 if (OpAtScope != Comm->getOperand(i)) { 2039 if (OpAtScope == UnknownValue) return UnknownValue; 2040 // Okay, at least one of these operands is loop variant but might be 2041 // foldable. Build a new instance of the folded commutative expression. 2042 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2043 NewOps.push_back(OpAtScope); 2044 2045 for (++i; i != e; ++i) { 2046 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2047 if (OpAtScope == UnknownValue) return UnknownValue; 2048 NewOps.push_back(OpAtScope); 2049 } 2050 if (isa<SCEVAddExpr>(Comm)) 2051 return SCEVAddExpr::get(NewOps); 2052 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2053 return SCEVMulExpr::get(NewOps); 2054 } 2055 } 2056 // If we got here, all operands are loop invariant. 2057 return Comm; 2058 } 2059 2060 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2061 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2062 if (LHS == UnknownValue) return LHS; 2063 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2064 if (RHS == UnknownValue) return RHS; 2065 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2066 return Div; // must be loop invariant 2067 return SCEVSDivExpr::get(LHS, RHS); 2068 } 2069 2070 // If this is a loop recurrence for a loop that does not contain L, then we 2071 // are dealing with the final value computed by the loop. 2072 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2073 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2074 // To evaluate this recurrence, we need to know how many times the AddRec 2075 // loop iterates. Compute this now. 2076 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2077 if (IterationCount == UnknownValue) return UnknownValue; 2078 IterationCount = getTruncateOrZeroExtend(IterationCount, 2079 AddRec->getType()); 2080 2081 // If the value is affine, simplify the expression evaluation to just 2082 // Start + Step*IterationCount. 2083 if (AddRec->isAffine()) 2084 return SCEVAddExpr::get(AddRec->getStart(), 2085 SCEVMulExpr::get(IterationCount, 2086 AddRec->getOperand(1))); 2087 2088 // Otherwise, evaluate it the hard way. 2089 return AddRec->evaluateAtIteration(IterationCount); 2090 } 2091 return UnknownValue; 2092 } 2093 2094 //assert(0 && "Unknown SCEV type!"); 2095 return UnknownValue; 2096} 2097 2098 2099/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2100/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2101/// might be the same) or two SCEVCouldNotCompute objects. 2102/// 2103static std::pair<SCEVHandle,SCEVHandle> 2104SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2105 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2106 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2107 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2108 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2109 2110 // We currently can only solve this if the coefficients are constants. 2111 if (!L || !M || !N) { 2112 SCEV *CNC = new SCEVCouldNotCompute(); 2113 return std::make_pair(CNC, CNC); 2114 } 2115 2116 Constant *C = L->getValue(); 2117 Constant *Two = ConstantInt::get(C->getType(), 2); 2118 2119 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2120 // The B coefficient is M-N/2 2121 Constant *B = ConstantExpr::getSub(M->getValue(), 2122 ConstantExpr::getSDiv(N->getValue(), 2123 Two)); 2124 // The A coefficient is N/2 2125 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two); 2126 2127 // Compute the B^2-4ac term. 2128 Constant *SqrtTerm = 2129 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2130 ConstantExpr::getMul(A, C)); 2131 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2132 2133 // Compute floor(sqrt(B^2-4ac)) 2134 ConstantInt *SqrtVal = 2135 cast<ConstantInt>(ConstantExpr::getBitCast(SqrtTerm, 2136 SqrtTerm->getType()->getUnsignedVersion())); 2137 uint64_t SqrtValV = SqrtVal->getZExtValue(); 2138 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2139 // The square root might not be precise for arbitrary 64-bit integer 2140 // values. Do some sanity checks to ensure it's correct. 2141 if (SqrtValV2*SqrtValV2 > SqrtValV || 2142 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2143 SCEV *CNC = new SCEVCouldNotCompute(); 2144 return std::make_pair(CNC, CNC); 2145 } 2146 2147 SqrtVal = ConstantInt::get(Type::ULongTy, SqrtValV2); 2148 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType()); 2149 2150 Constant *NegB = ConstantExpr::getNeg(B); 2151 Constant *TwoA = ConstantExpr::getMul(A, Two); 2152 2153 // The divisions must be performed as signed divisions. 2154 const Type *SignedTy = NegB->getType()->getSignedVersion(); 2155 NegB = ConstantExpr::getBitCast(NegB, SignedTy); 2156 TwoA = ConstantExpr::getBitCast(TwoA, SignedTy); 2157 SqrtTerm = ConstantExpr::getBitCast(SqrtTerm, SignedTy); 2158 2159 Constant *Solution1 = 2160 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2161 Constant *Solution2 = 2162 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2163 return std::make_pair(SCEVUnknown::get(Solution1), 2164 SCEVUnknown::get(Solution2)); 2165} 2166 2167/// HowFarToZero - Return the number of times a backedge comparing the specified 2168/// value to zero will execute. If not computable, return UnknownValue 2169SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2170 // If the value is a constant 2171 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2172 // If the value is already zero, the branch will execute zero times. 2173 if (C->getValue()->isNullValue()) return C; 2174 return UnknownValue; // Otherwise it will loop infinitely. 2175 } 2176 2177 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2178 if (!AddRec || AddRec->getLoop() != L) 2179 return UnknownValue; 2180 2181 if (AddRec->isAffine()) { 2182 // If this is an affine expression the execution count of this branch is 2183 // equal to: 2184 // 2185 // (0 - Start/Step) iff Start % Step == 0 2186 // 2187 // Get the initial value for the loop. 2188 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2189 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2190 SCEVHandle Step = AddRec->getOperand(1); 2191 2192 Step = getSCEVAtScope(Step, L->getParentLoop()); 2193 2194 // Figure out if Start % Step == 0. 2195 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2196 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2197 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2198 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2199 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2200 return Start; // 0 - Start/-1 == Start 2201 2202 // Check to see if Start is divisible by SC with no remainder. 2203 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2204 ConstantInt *StartCC = StartC->getValue(); 2205 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2206 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2207 if (Rem->isNullValue()) { 2208 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2209 return SCEVUnknown::get(Result); 2210 } 2211 } 2212 } 2213 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2214 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2215 // the quadratic equation to solve it. 2216 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2217 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2218 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2219 if (R1) { 2220#if 0 2221 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2222 << " sol#2: " << *R2 << "\n"; 2223#endif 2224 // Pick the smallest positive root value. 2225 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 2226 if (ConstantBool *CB = 2227 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2228 R2->getValue()))) { 2229 if (CB->getValue() == false) 2230 std::swap(R1, R2); // R1 is the minimum root now. 2231 2232 // We can only use this value if the chrec ends up with an exact zero 2233 // value at this index. When solving for "X*X != 5", for example, we 2234 // should not accept a root of 2. 2235 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2236 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2237 if (EvalVal->getValue()->isNullValue()) 2238 return R1; // We found a quadratic root! 2239 } 2240 } 2241 } 2242 2243 return UnknownValue; 2244} 2245 2246/// HowFarToNonZero - Return the number of times a backedge checking the 2247/// specified value for nonzero will execute. If not computable, return 2248/// UnknownValue 2249SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2250 // Loops that look like: while (X == 0) are very strange indeed. We don't 2251 // handle them yet except for the trivial case. This could be expanded in the 2252 // future as needed. 2253 2254 // If the value is a constant, check to see if it is known to be non-zero 2255 // already. If so, the backedge will execute zero times. 2256 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2257 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2258 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 2259 if (NonZero == ConstantBool::getTrue()) 2260 return getSCEV(Zero); 2261 return UnknownValue; // Otherwise it will loop infinitely. 2262 } 2263 2264 // We could implement others, but I really doubt anyone writes loops like 2265 // this, and if they did, they would already be constant folded. 2266 return UnknownValue; 2267} 2268 2269/// HowManyLessThans - Return the number of times a backedge containing the 2270/// specified less-than comparison will execute. If not computable, return 2271/// UnknownValue. 2272SCEVHandle ScalarEvolutionsImpl:: 2273HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2274 // Only handle: "ADDREC < LoopInvariant". 2275 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2276 2277 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2278 if (!AddRec || AddRec->getLoop() != L) 2279 return UnknownValue; 2280 2281 if (AddRec->isAffine()) { 2282 // FORNOW: We only support unit strides. 2283 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2284 if (AddRec->getOperand(1) != One) 2285 return UnknownValue; 2286 2287 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2288 // know that m is >= n on input to the loop. If it is, the condition return 2289 // true zero times. What we really should return, for full generality, is 2290 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2291 // canonical loop form: most do-loops will have a check that dominates the 2292 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2293 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2294 2295 // Search for the check. 2296 BasicBlock *Preheader = L->getLoopPreheader(); 2297 BasicBlock *PreheaderDest = L->getHeader(); 2298 if (Preheader == 0) return UnknownValue; 2299 2300 BranchInst *LoopEntryPredicate = 2301 dyn_cast<BranchInst>(Preheader->getTerminator()); 2302 if (!LoopEntryPredicate) return UnknownValue; 2303 2304 // This might be a critical edge broken out. If the loop preheader ends in 2305 // an unconditional branch to the loop, check to see if the preheader has a 2306 // single predecessor, and if so, look for its terminator. 2307 while (LoopEntryPredicate->isUnconditional()) { 2308 PreheaderDest = Preheader; 2309 Preheader = Preheader->getSinglePredecessor(); 2310 if (!Preheader) return UnknownValue; // Multiple preds. 2311 2312 LoopEntryPredicate = 2313 dyn_cast<BranchInst>(Preheader->getTerminator()); 2314 if (!LoopEntryPredicate) return UnknownValue; 2315 } 2316 2317 // Now that we found a conditional branch that dominates the loop, check to 2318 // see if it is the comparison we are looking for. 2319 SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition()); 2320 if (!SCI) return UnknownValue; 2321 Value *PreCondLHS = SCI->getOperand(0); 2322 Value *PreCondRHS = SCI->getOperand(1); 2323 Instruction::BinaryOps Cond; 2324 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2325 Cond = SCI->getOpcode(); 2326 else 2327 Cond = SCI->getInverseCondition(); 2328 2329 switch (Cond) { 2330 case Instruction::SetGT: 2331 std::swap(PreCondLHS, PreCondRHS); 2332 Cond = Instruction::SetLT; 2333 // Fall Through. 2334 case Instruction::SetLT: 2335 if (PreCondLHS->getType()->isInteger() && 2336 PreCondLHS->getType()->isSigned()) { 2337 if (RHS != getSCEV(PreCondRHS)) 2338 return UnknownValue; // Not a comparison against 'm'. 2339 2340 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2341 != getSCEV(PreCondLHS)) 2342 return UnknownValue; // Not a comparison against 'n-1'. 2343 break; 2344 } else { 2345 return UnknownValue; 2346 } 2347 default: break; 2348 } 2349 2350 //cerr << "Computed Loop Trip Count as: " 2351 // << *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2352 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2353 } 2354 2355 return UnknownValue; 2356} 2357 2358/// getNumIterationsInRange - Return the number of iterations of this loop that 2359/// produce values in the specified constant range. Another way of looking at 2360/// this is that it returns the first iteration number where the value is not in 2361/// the condition, thus computing the exit count. If the iteration count can't 2362/// be computed, an instance of SCEVCouldNotCompute is returned. 2363SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2364 if (Range.isFullSet()) // Infinite loop. 2365 return new SCEVCouldNotCompute(); 2366 2367 // If the start is a non-zero constant, shift the range to simplify things. 2368 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2369 if (!SC->getValue()->isNullValue()) { 2370 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2371 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2372 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2373 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2374 return ShiftedAddRec->getNumIterationsInRange( 2375 Range.subtract(SC->getValue())); 2376 // This is strange and shouldn't happen. 2377 return new SCEVCouldNotCompute(); 2378 } 2379 2380 // The only time we can solve this is when we have all constant indices. 2381 // Otherwise, we cannot determine the overflow conditions. 2382 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2383 if (!isa<SCEVConstant>(getOperand(i))) 2384 return new SCEVCouldNotCompute(); 2385 2386 2387 // Okay at this point we know that all elements of the chrec are constants and 2388 // that the start element is zero. 2389 2390 // First check to see if the range contains zero. If not, the first 2391 // iteration exits. 2392 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2393 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2394 2395 if (isAffine()) { 2396 // If this is an affine expression then we have this situation: 2397 // Solve {0,+,A} in Range === Ax in Range 2398 2399 // Since we know that zero is in the range, we know that the upper value of 2400 // the range must be the first possible exit value. Also note that we 2401 // already checked for a full range. 2402 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2403 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2404 ConstantInt *One = ConstantInt::get(getType(), 1); 2405 2406 // The exit value should be (Upper+A-1)/A. 2407 Constant *ExitValue = Upper; 2408 if (A != One) { 2409 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2410 ExitValue = ConstantExpr::getSDiv(ExitValue, A); 2411 } 2412 assert(isa<ConstantInt>(ExitValue) && 2413 "Constant folding of integers not implemented?"); 2414 2415 // Evaluate at the exit value. If we really did fall out of the valid 2416 // range, then we computed our trip count, otherwise wrap around or other 2417 // things must have happened. 2418 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2419 if (Range.contains(Val)) 2420 return new SCEVCouldNotCompute(); // Something strange happened 2421 2422 // Ensure that the previous value is in the range. This is a sanity check. 2423 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2424 ConstantExpr::getSub(ExitValue, One))) && 2425 "Linear scev computation is off in a bad way!"); 2426 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2427 } else if (isQuadratic()) { 2428 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2429 // quadratic equation to solve it. To do this, we must frame our problem in 2430 // terms of figuring out when zero is crossed, instead of when 2431 // Range.getUpper() is crossed. 2432 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2433 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2434 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2435 2436 // Next, solve the constructed addrec 2437 std::pair<SCEVHandle,SCEVHandle> Roots = 2438 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2439 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2440 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2441 if (R1) { 2442 // Pick the smallest positive root value. 2443 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2444 if (ConstantBool *CB = 2445 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2446 R2->getValue()))) { 2447 if (CB->getValue() == false) 2448 std::swap(R1, R2); // R1 is the minimum root now. 2449 2450 // Make sure the root is not off by one. The returned iteration should 2451 // not be in the range, but the previous one should be. When solving 2452 // for "X*X < 5", for example, we should not return a root of 2. 2453 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2454 R1->getValue()); 2455 if (Range.contains(R1Val)) { 2456 // The next iteration must be out of the range... 2457 Constant *NextVal = 2458 ConstantExpr::getAdd(R1->getValue(), 2459 ConstantInt::get(R1->getType(), 1)); 2460 2461 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2462 if (!Range.contains(R1Val)) 2463 return SCEVUnknown::get(NextVal); 2464 return new SCEVCouldNotCompute(); // Something strange happened 2465 } 2466 2467 // If R1 was not in the range, then it is a good return value. Make 2468 // sure that R1-1 WAS in the range though, just in case. 2469 Constant *NextVal = 2470 ConstantExpr::getSub(R1->getValue(), 2471 ConstantInt::get(R1->getType(), 1)); 2472 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2473 if (Range.contains(R1Val)) 2474 return R1; 2475 return new SCEVCouldNotCompute(); // Something strange happened 2476 } 2477 } 2478 } 2479 2480 // Fallback, if this is a general polynomial, figure out the progression 2481 // through brute force: evaluate until we find an iteration that fails the 2482 // test. This is likely to be slow, but getting an accurate trip count is 2483 // incredibly important, we will be able to simplify the exit test a lot, and 2484 // we are almost guaranteed to get a trip count in this case. 2485 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2486 ConstantInt *One = ConstantInt::get(getType(), 1); 2487 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2488 do { 2489 ++NumBruteForceEvaluations; 2490 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2491 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2492 return new SCEVCouldNotCompute(); 2493 2494 // Check to see if we found the value! 2495 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2496 return SCEVConstant::get(TestVal); 2497 2498 // Increment to test the next index. 2499 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2500 } while (TestVal != EndVal); 2501 2502 return new SCEVCouldNotCompute(); 2503} 2504 2505 2506 2507//===----------------------------------------------------------------------===// 2508// ScalarEvolution Class Implementation 2509//===----------------------------------------------------------------------===// 2510 2511bool ScalarEvolution::runOnFunction(Function &F) { 2512 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2513 return false; 2514} 2515 2516void ScalarEvolution::releaseMemory() { 2517 delete (ScalarEvolutionsImpl*)Impl; 2518 Impl = 0; 2519} 2520 2521void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2522 AU.setPreservesAll(); 2523 AU.addRequiredTransitive<LoopInfo>(); 2524} 2525 2526SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2527 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2528} 2529 2530/// hasSCEV - Return true if the SCEV for this value has already been 2531/// computed. 2532bool ScalarEvolution::hasSCEV(Value *V) const { 2533 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2534} 2535 2536 2537/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2538/// the specified value. 2539void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2540 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2541} 2542 2543 2544SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2545 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2546} 2547 2548bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2549 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2550} 2551 2552SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2553 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2554} 2555 2556void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2557 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2558} 2559 2560static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2561 const Loop *L) { 2562 // Print all inner loops first 2563 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2564 PrintLoopInfo(OS, SE, *I); 2565 2566 cerr << "Loop " << L->getHeader()->getName() << ": "; 2567 2568 std::vector<BasicBlock*> ExitBlocks; 2569 L->getExitBlocks(ExitBlocks); 2570 if (ExitBlocks.size() != 1) 2571 cerr << "<multiple exits> "; 2572 2573 if (SE->hasLoopInvariantIterationCount(L)) { 2574 cerr << *SE->getIterationCount(L) << " iterations! "; 2575 } else { 2576 cerr << "Unpredictable iteration count. "; 2577 } 2578 2579 cerr << "\n"; 2580} 2581 2582void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2583 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2584 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2585 2586 OS << "Classifying expressions for: " << F.getName() << "\n"; 2587 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2588 if (I->getType()->isInteger()) { 2589 OS << *I; 2590 OS << " --> "; 2591 SCEVHandle SV = getSCEV(&*I); 2592 SV->print(OS); 2593 OS << "\t\t"; 2594 2595 if ((*I).getType()->isIntegral()) { 2596 ConstantRange Bounds = SV->getValueRange(); 2597 if (!Bounds.isFullSet()) 2598 OS << "Bounds: " << Bounds << " "; 2599 } 2600 2601 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2602 OS << "Exits: "; 2603 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2604 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2605 OS << "<<Unknown>>"; 2606 } else { 2607 OS << *ExitValue; 2608 } 2609 } 2610 2611 2612 OS << "\n"; 2613 } 2614 2615 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2616 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2617 PrintLoopInfo(OS, this, *I); 2618} 2619 2620