ScalarEvolution.cpp revision 9525528a7dc5462b6374d38c81ba5c07b11741fe
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/Instructions.h" 67#include "llvm/Analysis/ConstantFolding.h" 68#include "llvm/Analysis/LoopInfo.h" 69#include "llvm/Assembly/Writer.h" 70#include "llvm/Transforms/Scalar.h" 71#include "llvm/Support/CFG.h" 72#include "llvm/Support/CommandLine.h" 73#include "llvm/Support/ConstantRange.h" 74#include "llvm/Support/InstIterator.h" 75#include "llvm/Support/Visibility.h" 76#include "llvm/ADT/Statistic.h" 77#include <cmath> 78#include <iostream> 79#include <algorithm> 80using namespace llvm; 81 82namespace { 83 RegisterAnalysis<ScalarEvolution> 84 R("scalar-evolution", "Scalar Evolution Analysis"); 85 86 Statistic<> 87 NumBruteForceEvaluations("scalar-evolution", 88 "Number of brute force evaluations needed to " 89 "calculate high-order polynomial exit values"); 90 Statistic<> 91 NumArrayLenItCounts("scalar-evolution", 92 "Number of trip counts computed with array length"); 93 Statistic<> 94 NumTripCountsComputed("scalar-evolution", 95 "Number of loops with predictable loop counts"); 96 Statistic<> 97 NumTripCountsNotComputed("scalar-evolution", 98 "Number of loops without predictable loop counts"); 99 Statistic<> 100 NumBruteForceTripCountsComputed("scalar-evolution", 101 "Number of loops with trip counts computed by force"); 102 103 cl::opt<unsigned> 104 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 105 cl::desc("Maximum number of iterations SCEV will " 106 "symbolically execute a constant derived loop"), 107 cl::init(100)); 108} 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117SCEV::~SCEV() {} 118void SCEV::dump() const { 119 print(std::cerr); 120} 121 122/// getValueRange - Return the tightest constant bounds that this value is 123/// known to have. This method is only valid on integer SCEV objects. 124ConstantRange SCEV::getValueRange() const { 125 const Type *Ty = getType(); 126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 127 Ty = Ty->getUnsignedVersion(); 128 // Default to a full range if no better information is available. 129 return ConstantRange(getType()); 130} 131 132 133SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 134 135bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 136 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 137 return false; 138} 139 140const Type *SCEVCouldNotCompute::getType() const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return 0; 143} 144 145bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return false; 148} 149 150SCEVHandle SCEVCouldNotCompute:: 151replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 152 const SCEVHandle &Conc) const { 153 return this; 154} 155 156void SCEVCouldNotCompute::print(std::ostream &OS) const { 157 OS << "***COULDNOTCOMPUTE***"; 158} 159 160bool SCEVCouldNotCompute::classof(const SCEV *S) { 161 return S->getSCEVType() == scCouldNotCompute; 162} 163 164 165// SCEVConstants - Only allow the creation of one SCEVConstant for any 166// particular value. Don't use a SCEVHandle here, or else the object will 167// never be deleted! 168static std::map<ConstantInt*, SCEVConstant*> SCEVConstants; 169 170 171SCEVConstant::~SCEVConstant() { 172 SCEVConstants.erase(V); 173} 174 175SCEVHandle SCEVConstant::get(ConstantInt *V) { 176 // Make sure that SCEVConstant instances are all unsigned. 177 if (V->getType()->isSigned()) { 178 const Type *NewTy = V->getType()->getUnsignedVersion(); 179 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy)); 180 } 181 182 SCEVConstant *&R = SCEVConstants[V]; 183 if (R == 0) R = new SCEVConstant(V); 184 return R; 185} 186 187ConstantRange SCEVConstant::getValueRange() const { 188 return ConstantRange(V); 189} 190 191const Type *SCEVConstant::getType() const { return V->getType(); } 192 193void SCEVConstant::print(std::ostream &OS) const { 194 WriteAsOperand(OS, V, false); 195} 196 197// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 198// particular input. Don't use a SCEVHandle here, or else the object will 199// never be deleted! 200static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates; 201 202SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 203 : SCEV(scTruncate), Op(op), Ty(ty) { 204 assert(Op->getType()->isInteger() && Ty->isInteger() && 205 Ty->isUnsigned() && 206 "Cannot truncate non-integer value!"); 207 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 208 "This is not a truncating conversion!"); 209} 210 211SCEVTruncateExpr::~SCEVTruncateExpr() { 212 SCEVTruncates.erase(std::make_pair(Op, Ty)); 213} 214 215ConstantRange SCEVTruncateExpr::getValueRange() const { 216 return getOperand()->getValueRange().truncate(getType()); 217} 218 219void SCEVTruncateExpr::print(std::ostream &OS) const { 220 OS << "(truncate " << *Op << " to " << *Ty << ")"; 221} 222 223// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 224// particular input. Don't use a SCEVHandle here, or else the object will never 225// be deleted! 226static std::map<std::pair<SCEV*, const Type*>, 227 SCEVZeroExtendExpr*> SCEVZeroExtends; 228 229SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 230 : SCEV(scTruncate), Op(op), Ty(ty) { 231 assert(Op->getType()->isInteger() && Ty->isInteger() && 232 Ty->isUnsigned() && 233 "Cannot zero extend non-integer value!"); 234 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 235 "This is not an extending conversion!"); 236} 237 238SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 239 SCEVZeroExtends.erase(std::make_pair(Op, Ty)); 240} 241 242ConstantRange SCEVZeroExtendExpr::getValueRange() const { 243 return getOperand()->getValueRange().zeroExtend(getType()); 244} 245 246void SCEVZeroExtendExpr::print(std::ostream &OS) const { 247 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 248} 249 250// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 251// particular input. Don't use a SCEVHandle here, or else the object will never 252// be deleted! 253static std::map<std::pair<unsigned, std::vector<SCEV*> >, 254 SCEVCommutativeExpr*> SCEVCommExprs; 255 256SCEVCommutativeExpr::~SCEVCommutativeExpr() { 257 SCEVCommExprs.erase(std::make_pair(getSCEVType(), 258 std::vector<SCEV*>(Operands.begin(), 259 Operands.end()))); 260} 261 262void SCEVCommutativeExpr::print(std::ostream &OS) const { 263 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 264 const char *OpStr = getOperationStr(); 265 OS << "(" << *Operands[0]; 266 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 267 OS << OpStr << *Operands[i]; 268 OS << ")"; 269} 270 271SCEVHandle SCEVCommutativeExpr:: 272replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 273 const SCEVHandle &Conc) const { 274 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 275 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 276 if (H != getOperand(i)) { 277 std::vector<SCEVHandle> NewOps; 278 NewOps.reserve(getNumOperands()); 279 for (unsigned j = 0; j != i; ++j) 280 NewOps.push_back(getOperand(j)); 281 NewOps.push_back(H); 282 for (++i; i != e; ++i) 283 NewOps.push_back(getOperand(i)-> 284 replaceSymbolicValuesWithConcrete(Sym, Conc)); 285 286 if (isa<SCEVAddExpr>(this)) 287 return SCEVAddExpr::get(NewOps); 288 else if (isa<SCEVMulExpr>(this)) 289 return SCEVMulExpr::get(NewOps); 290 else 291 assert(0 && "Unknown commutative expr!"); 292 } 293 } 294 return this; 295} 296 297 298// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 299// input. Don't use a SCEVHandle here, or else the object will never be 300// deleted! 301static std::map<std::pair<SCEV*, SCEV*>, SCEVSDivExpr*> SCEVSDivs; 302 303SCEVSDivExpr::~SCEVSDivExpr() { 304 SCEVSDivs.erase(std::make_pair(LHS, RHS)); 305} 306 307void SCEVSDivExpr::print(std::ostream &OS) const { 308 OS << "(" << *LHS << " /s " << *RHS << ")"; 309} 310 311const Type *SCEVSDivExpr::getType() const { 312 const Type *Ty = LHS->getType(); 313 if (Ty->isUnsigned()) Ty = Ty->getSignedVersion(); 314 return Ty; 315} 316 317// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 318// particular input. Don't use a SCEVHandle here, or else the object will never 319// be deleted! 320static std::map<std::pair<const Loop *, std::vector<SCEV*> >, 321 SCEVAddRecExpr*> SCEVAddRecExprs; 322 323SCEVAddRecExpr::~SCEVAddRecExpr() { 324 SCEVAddRecExprs.erase(std::make_pair(L, 325 std::vector<SCEV*>(Operands.begin(), 326 Operands.end()))); 327} 328 329SCEVHandle SCEVAddRecExpr:: 330replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 331 const SCEVHandle &Conc) const { 332 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 333 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 334 if (H != getOperand(i)) { 335 std::vector<SCEVHandle> NewOps; 336 NewOps.reserve(getNumOperands()); 337 for (unsigned j = 0; j != i; ++j) 338 NewOps.push_back(getOperand(j)); 339 NewOps.push_back(H); 340 for (++i; i != e; ++i) 341 NewOps.push_back(getOperand(i)-> 342 replaceSymbolicValuesWithConcrete(Sym, Conc)); 343 344 return get(NewOps, L); 345 } 346 } 347 return this; 348} 349 350 351bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 352 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 353 // contain L and if the start is invariant. 354 return !QueryLoop->contains(L->getHeader()) && 355 getOperand(0)->isLoopInvariant(QueryLoop); 356} 357 358 359void SCEVAddRecExpr::print(std::ostream &OS) const { 360 OS << "{" << *Operands[0]; 361 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 362 OS << ",+," << *Operands[i]; 363 OS << "}<" << L->getHeader()->getName() + ">"; 364} 365 366// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 367// value. Don't use a SCEVHandle here, or else the object will never be 368// deleted! 369static std::map<Value*, SCEVUnknown*> SCEVUnknowns; 370 371SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); } 372 373bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 374 // All non-instruction values are loop invariant. All instructions are loop 375 // invariant if they are not contained in the specified loop. 376 if (Instruction *I = dyn_cast<Instruction>(V)) 377 return !L->contains(I->getParent()); 378 return true; 379} 380 381const Type *SCEVUnknown::getType() const { 382 return V->getType(); 383} 384 385void SCEVUnknown::print(std::ostream &OS) const { 386 WriteAsOperand(OS, V, false); 387} 388 389//===----------------------------------------------------------------------===// 390// SCEV Utilities 391//===----------------------------------------------------------------------===// 392 393namespace { 394 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 395 /// than the complexity of the RHS. This comparator is used to canonicalize 396 /// expressions. 397 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 398 bool operator()(SCEV *LHS, SCEV *RHS) { 399 return LHS->getSCEVType() < RHS->getSCEVType(); 400 } 401 }; 402} 403 404/// GroupByComplexity - Given a list of SCEV objects, order them by their 405/// complexity, and group objects of the same complexity together by value. 406/// When this routine is finished, we know that any duplicates in the vector are 407/// consecutive and that complexity is monotonically increasing. 408/// 409/// Note that we go take special precautions to ensure that we get determinstic 410/// results from this routine. In other words, we don't want the results of 411/// this to depend on where the addresses of various SCEV objects happened to 412/// land in memory. 413/// 414static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 415 if (Ops.size() < 2) return; // Noop 416 if (Ops.size() == 2) { 417 // This is the common case, which also happens to be trivially simple. 418 // Special case it. 419 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 420 std::swap(Ops[0], Ops[1]); 421 return; 422 } 423 424 // Do the rough sort by complexity. 425 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 426 427 // Now that we are sorted by complexity, group elements of the same 428 // complexity. Note that this is, at worst, N^2, but the vector is likely to 429 // be extremely short in practice. Note that we take this approach because we 430 // do not want to depend on the addresses of the objects we are grouping. 431 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 432 SCEV *S = Ops[i]; 433 unsigned Complexity = S->getSCEVType(); 434 435 // If there are any objects of the same complexity and same value as this 436 // one, group them. 437 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 438 if (Ops[j] == S) { // Found a duplicate. 439 // Move it to immediately after i'th element. 440 std::swap(Ops[i+1], Ops[j]); 441 ++i; // no need to rescan it. 442 if (i == e-2) return; // Done! 443 } 444 } 445 } 446} 447 448 449 450//===----------------------------------------------------------------------===// 451// Simple SCEV method implementations 452//===----------------------------------------------------------------------===// 453 454/// getIntegerSCEV - Given an integer or FP type, create a constant for the 455/// specified signed integer value and return a SCEV for the constant. 456SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 457 Constant *C; 458 if (Val == 0) 459 C = Constant::getNullValue(Ty); 460 else if (Ty->isFloatingPoint()) 461 C = ConstantFP::get(Ty, Val); 462 else if (Ty->isSigned()) 463 C = ConstantSInt::get(Ty, Val); 464 else { 465 C = ConstantSInt::get(Ty->getSignedVersion(), Val); 466 C = ConstantExpr::getCast(C, Ty); 467 } 468 return SCEVUnknown::get(C); 469} 470 471/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 472/// input value to the specified type. If the type must be extended, it is zero 473/// extended. 474static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 475 const Type *SrcTy = V->getType(); 476 assert(SrcTy->isInteger() && Ty->isInteger() && 477 "Cannot truncate or zero extend with non-integer arguments!"); 478 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 479 return V; // No conversion 480 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 481 return SCEVTruncateExpr::get(V, Ty); 482 return SCEVZeroExtendExpr::get(V, Ty); 483} 484 485/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 486/// 487SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 488 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 489 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 490 491 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 492} 493 494/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 495/// 496SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 497 // X - Y --> X + -Y 498 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 499} 500 501 502/// PartialFact - Compute V!/(V-NumSteps)! 503static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 504 // Handle this case efficiently, it is common to have constant iteration 505 // counts while computing loop exit values. 506 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 507 uint64_t Val = SC->getValue()->getRawValue(); 508 uint64_t Result = 1; 509 for (; NumSteps; --NumSteps) 510 Result *= Val-(NumSteps-1); 511 Constant *Res = ConstantUInt::get(Type::ULongTy, Result); 512 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType())); 513 } 514 515 const Type *Ty = V->getType(); 516 if (NumSteps == 0) 517 return SCEVUnknown::getIntegerSCEV(1, Ty); 518 519 SCEVHandle Result = V; 520 for (unsigned i = 1; i != NumSteps; ++i) 521 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 522 SCEVUnknown::getIntegerSCEV(i, Ty))); 523 return Result; 524} 525 526 527/// evaluateAtIteration - Return the value of this chain of recurrences at 528/// the specified iteration number. We can evaluate this recurrence by 529/// multiplying each element in the chain by the binomial coefficient 530/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 531/// 532/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 533/// 534/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 535/// Is the binomial equation safe using modular arithmetic?? 536/// 537SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 538 SCEVHandle Result = getStart(); 539 int Divisor = 1; 540 const Type *Ty = It->getType(); 541 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 542 SCEVHandle BC = PartialFact(It, i); 543 Divisor *= i; 544 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 545 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 546 Result = SCEVAddExpr::get(Result, Val); 547 } 548 return Result; 549} 550 551 552//===----------------------------------------------------------------------===// 553// SCEV Expression folder implementations 554//===----------------------------------------------------------------------===// 555 556SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 557 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 558 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 559 560 // If the input value is a chrec scev made out of constants, truncate 561 // all of the constants. 562 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 563 std::vector<SCEVHandle> Operands; 564 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 565 // FIXME: This should allow truncation of other expression types! 566 if (isa<SCEVConstant>(AddRec->getOperand(i))) 567 Operands.push_back(get(AddRec->getOperand(i), Ty)); 568 else 569 break; 570 if (Operands.size() == AddRec->getNumOperands()) 571 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 572 } 573 574 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)]; 575 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 576 return Result; 577} 578 579SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 580 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 581 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 582 583 // FIXME: If the input value is a chrec scev, and we can prove that the value 584 // did not overflow the old, smaller, value, we can zero extend all of the 585 // operands (often constants). This would allow analysis of something like 586 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 587 588 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)]; 589 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 590 return Result; 591} 592 593// get - Get a canonical add expression, or something simpler if possible. 594SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 595 assert(!Ops.empty() && "Cannot get empty add!"); 596 if (Ops.size() == 1) return Ops[0]; 597 598 // Sort by complexity, this groups all similar expression types together. 599 GroupByComplexity(Ops); 600 601 // If there are any constants, fold them together. 602 unsigned Idx = 0; 603 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 604 ++Idx; 605 assert(Idx < Ops.size()); 606 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 607 // We found two constants, fold them together! 608 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 609 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 610 Ops[0] = SCEVConstant::get(CI); 611 Ops.erase(Ops.begin()+1); // Erase the folded element 612 if (Ops.size() == 1) return Ops[0]; 613 LHSC = cast<SCEVConstant>(Ops[0]); 614 } else { 615 // If we couldn't fold the expression, move to the next constant. Note 616 // that this is impossible to happen in practice because we always 617 // constant fold constant ints to constant ints. 618 ++Idx; 619 } 620 } 621 622 // If we are left with a constant zero being added, strip it off. 623 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 624 Ops.erase(Ops.begin()); 625 --Idx; 626 } 627 } 628 629 if (Ops.size() == 1) return Ops[0]; 630 631 // Okay, check to see if the same value occurs in the operand list twice. If 632 // so, merge them together into an multiply expression. Since we sorted the 633 // list, these values are required to be adjacent. 634 const Type *Ty = Ops[0]->getType(); 635 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 636 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 637 // Found a match, merge the two values into a multiply, and add any 638 // remaining values to the result. 639 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 640 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 641 if (Ops.size() == 2) 642 return Mul; 643 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 644 Ops.push_back(Mul); 645 return SCEVAddExpr::get(Ops); 646 } 647 648 // Okay, now we know the first non-constant operand. If there are add 649 // operands they would be next. 650 if (Idx < Ops.size()) { 651 bool DeletedAdd = false; 652 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 653 // If we have an add, expand the add operands onto the end of the operands 654 // list. 655 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 656 Ops.erase(Ops.begin()+Idx); 657 DeletedAdd = true; 658 } 659 660 // If we deleted at least one add, we added operands to the end of the list, 661 // and they are not necessarily sorted. Recurse to resort and resimplify 662 // any operands we just aquired. 663 if (DeletedAdd) 664 return get(Ops); 665 } 666 667 // Skip over the add expression until we get to a multiply. 668 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 669 ++Idx; 670 671 // If we are adding something to a multiply expression, make sure the 672 // something is not already an operand of the multiply. If so, merge it into 673 // the multiply. 674 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 675 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 676 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 677 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 678 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 679 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 680 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 681 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 682 if (Mul->getNumOperands() != 2) { 683 // If the multiply has more than two operands, we must get the 684 // Y*Z term. 685 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 686 MulOps.erase(MulOps.begin()+MulOp); 687 InnerMul = SCEVMulExpr::get(MulOps); 688 } 689 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 690 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 691 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 692 if (Ops.size() == 2) return OuterMul; 693 if (AddOp < Idx) { 694 Ops.erase(Ops.begin()+AddOp); 695 Ops.erase(Ops.begin()+Idx-1); 696 } else { 697 Ops.erase(Ops.begin()+Idx); 698 Ops.erase(Ops.begin()+AddOp-1); 699 } 700 Ops.push_back(OuterMul); 701 return SCEVAddExpr::get(Ops); 702 } 703 704 // Check this multiply against other multiplies being added together. 705 for (unsigned OtherMulIdx = Idx+1; 706 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 707 ++OtherMulIdx) { 708 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 709 // If MulOp occurs in OtherMul, we can fold the two multiplies 710 // together. 711 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 712 OMulOp != e; ++OMulOp) 713 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 714 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 715 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 716 if (Mul->getNumOperands() != 2) { 717 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 718 MulOps.erase(MulOps.begin()+MulOp); 719 InnerMul1 = SCEVMulExpr::get(MulOps); 720 } 721 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 722 if (OtherMul->getNumOperands() != 2) { 723 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 724 OtherMul->op_end()); 725 MulOps.erase(MulOps.begin()+OMulOp); 726 InnerMul2 = SCEVMulExpr::get(MulOps); 727 } 728 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 729 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 730 if (Ops.size() == 2) return OuterMul; 731 Ops.erase(Ops.begin()+Idx); 732 Ops.erase(Ops.begin()+OtherMulIdx-1); 733 Ops.push_back(OuterMul); 734 return SCEVAddExpr::get(Ops); 735 } 736 } 737 } 738 } 739 740 // If there are any add recurrences in the operands list, see if any other 741 // added values are loop invariant. If so, we can fold them into the 742 // recurrence. 743 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 744 ++Idx; 745 746 // Scan over all recurrences, trying to fold loop invariants into them. 747 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 748 // Scan all of the other operands to this add and add them to the vector if 749 // they are loop invariant w.r.t. the recurrence. 750 std::vector<SCEVHandle> LIOps; 751 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 752 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 753 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 754 LIOps.push_back(Ops[i]); 755 Ops.erase(Ops.begin()+i); 756 --i; --e; 757 } 758 759 // If we found some loop invariants, fold them into the recurrence. 760 if (!LIOps.empty()) { 761 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 762 LIOps.push_back(AddRec->getStart()); 763 764 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 765 AddRecOps[0] = SCEVAddExpr::get(LIOps); 766 767 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 768 // If all of the other operands were loop invariant, we are done. 769 if (Ops.size() == 1) return NewRec; 770 771 // Otherwise, add the folded AddRec by the non-liv parts. 772 for (unsigned i = 0;; ++i) 773 if (Ops[i] == AddRec) { 774 Ops[i] = NewRec; 775 break; 776 } 777 return SCEVAddExpr::get(Ops); 778 } 779 780 // Okay, if there weren't any loop invariants to be folded, check to see if 781 // there are multiple AddRec's with the same loop induction variable being 782 // added together. If so, we can fold them. 783 for (unsigned OtherIdx = Idx+1; 784 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 785 if (OtherIdx != Idx) { 786 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 787 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 788 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 789 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 790 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 791 if (i >= NewOps.size()) { 792 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 793 OtherAddRec->op_end()); 794 break; 795 } 796 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 797 } 798 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 799 800 if (Ops.size() == 2) return NewAddRec; 801 802 Ops.erase(Ops.begin()+Idx); 803 Ops.erase(Ops.begin()+OtherIdx-1); 804 Ops.push_back(NewAddRec); 805 return SCEVAddExpr::get(Ops); 806 } 807 } 808 809 // Otherwise couldn't fold anything into this recurrence. Move onto the 810 // next one. 811 } 812 813 // Okay, it looks like we really DO need an add expr. Check to see if we 814 // already have one, otherwise create a new one. 815 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 816 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 817 SCEVOps)]; 818 if (Result == 0) Result = new SCEVAddExpr(Ops); 819 return Result; 820} 821 822 823SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 824 assert(!Ops.empty() && "Cannot get empty mul!"); 825 826 // Sort by complexity, this groups all similar expression types together. 827 GroupByComplexity(Ops); 828 829 // If there are any constants, fold them together. 830 unsigned Idx = 0; 831 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 832 833 // C1*(C2+V) -> C1*C2 + C1*V 834 if (Ops.size() == 2) 835 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 836 if (Add->getNumOperands() == 2 && 837 isa<SCEVConstant>(Add->getOperand(0))) 838 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 839 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 840 841 842 ++Idx; 843 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 844 // We found two constants, fold them together! 845 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 846 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 847 Ops[0] = SCEVConstant::get(CI); 848 Ops.erase(Ops.begin()+1); // Erase the folded element 849 if (Ops.size() == 1) return Ops[0]; 850 LHSC = cast<SCEVConstant>(Ops[0]); 851 } else { 852 // If we couldn't fold the expression, move to the next constant. Note 853 // that this is impossible to happen in practice because we always 854 // constant fold constant ints to constant ints. 855 ++Idx; 856 } 857 } 858 859 // If we are left with a constant one being multiplied, strip it off. 860 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 861 Ops.erase(Ops.begin()); 862 --Idx; 863 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 864 // If we have a multiply of zero, it will always be zero. 865 return Ops[0]; 866 } 867 } 868 869 // Skip over the add expression until we get to a multiply. 870 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 871 ++Idx; 872 873 if (Ops.size() == 1) 874 return Ops[0]; 875 876 // If there are mul operands inline them all into this expression. 877 if (Idx < Ops.size()) { 878 bool DeletedMul = false; 879 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 880 // If we have an mul, expand the mul operands onto the end of the operands 881 // list. 882 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 883 Ops.erase(Ops.begin()+Idx); 884 DeletedMul = true; 885 } 886 887 // If we deleted at least one mul, we added operands to the end of the list, 888 // and they are not necessarily sorted. Recurse to resort and resimplify 889 // any operands we just aquired. 890 if (DeletedMul) 891 return get(Ops); 892 } 893 894 // If there are any add recurrences in the operands list, see if any other 895 // added values are loop invariant. If so, we can fold them into the 896 // recurrence. 897 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 898 ++Idx; 899 900 // Scan over all recurrences, trying to fold loop invariants into them. 901 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 902 // Scan all of the other operands to this mul and add them to the vector if 903 // they are loop invariant w.r.t. the recurrence. 904 std::vector<SCEVHandle> LIOps; 905 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 906 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 907 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 908 LIOps.push_back(Ops[i]); 909 Ops.erase(Ops.begin()+i); 910 --i; --e; 911 } 912 913 // If we found some loop invariants, fold them into the recurrence. 914 if (!LIOps.empty()) { 915 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 916 std::vector<SCEVHandle> NewOps; 917 NewOps.reserve(AddRec->getNumOperands()); 918 if (LIOps.size() == 1) { 919 SCEV *Scale = LIOps[0]; 920 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 921 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 922 } else { 923 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 924 std::vector<SCEVHandle> MulOps(LIOps); 925 MulOps.push_back(AddRec->getOperand(i)); 926 NewOps.push_back(SCEVMulExpr::get(MulOps)); 927 } 928 } 929 930 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 931 932 // If all of the other operands were loop invariant, we are done. 933 if (Ops.size() == 1) return NewRec; 934 935 // Otherwise, multiply the folded AddRec by the non-liv parts. 936 for (unsigned i = 0;; ++i) 937 if (Ops[i] == AddRec) { 938 Ops[i] = NewRec; 939 break; 940 } 941 return SCEVMulExpr::get(Ops); 942 } 943 944 // Okay, if there weren't any loop invariants to be folded, check to see if 945 // there are multiple AddRec's with the same loop induction variable being 946 // multiplied together. If so, we can fold them. 947 for (unsigned OtherIdx = Idx+1; 948 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 949 if (OtherIdx != Idx) { 950 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 951 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 952 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 953 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 954 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 955 G->getStart()); 956 SCEVHandle B = F->getStepRecurrence(); 957 SCEVHandle D = G->getStepRecurrence(); 958 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 959 SCEVMulExpr::get(G, B), 960 SCEVMulExpr::get(B, D)); 961 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 962 F->getLoop()); 963 if (Ops.size() == 2) return NewAddRec; 964 965 Ops.erase(Ops.begin()+Idx); 966 Ops.erase(Ops.begin()+OtherIdx-1); 967 Ops.push_back(NewAddRec); 968 return SCEVMulExpr::get(Ops); 969 } 970 } 971 972 // Otherwise couldn't fold anything into this recurrence. Move onto the 973 // next one. 974 } 975 976 // Okay, it looks like we really DO need an mul expr. Check to see if we 977 // already have one, otherwise create a new one. 978 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 979 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 980 SCEVOps)]; 981 if (Result == 0) 982 Result = new SCEVMulExpr(Ops); 983 return Result; 984} 985 986SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 987 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 988 if (RHSC->getValue()->equalsInt(1)) 989 return LHS; // X /s 1 --> x 990 if (RHSC->getValue()->isAllOnesValue()) 991 return SCEV::getNegativeSCEV(LHS); // X /s -1 --> -x 992 993 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 994 Constant *LHSCV = LHSC->getValue(); 995 Constant *RHSCV = RHSC->getValue(); 996 if (LHSCV->getType()->isUnsigned()) 997 LHSCV = ConstantExpr::getCast(LHSCV, 998 LHSCV->getType()->getSignedVersion()); 999 if (RHSCV->getType()->isUnsigned()) 1000 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 1001 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 1002 } 1003 } 1004 1005 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1006 1007 SCEVSDivExpr *&Result = SCEVSDivs[std::make_pair(LHS, RHS)]; 1008 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1009 return Result; 1010} 1011 1012 1013/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1014/// specified loop. Simplify the expression as much as possible. 1015SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1016 const SCEVHandle &Step, const Loop *L) { 1017 std::vector<SCEVHandle> Operands; 1018 Operands.push_back(Start); 1019 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1020 if (StepChrec->getLoop() == L) { 1021 Operands.insert(Operands.end(), StepChrec->op_begin(), 1022 StepChrec->op_end()); 1023 return get(Operands, L); 1024 } 1025 1026 Operands.push_back(Step); 1027 return get(Operands, L); 1028} 1029 1030/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1031/// specified loop. Simplify the expression as much as possible. 1032SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1033 const Loop *L) { 1034 if (Operands.size() == 1) return Operands[0]; 1035 1036 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1037 if (StepC->getValue()->isNullValue()) { 1038 Operands.pop_back(); 1039 return get(Operands, L); // { X,+,0 } --> X 1040 } 1041 1042 SCEVAddRecExpr *&Result = 1043 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1044 Operands.end()))]; 1045 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1046 return Result; 1047} 1048 1049SCEVHandle SCEVUnknown::get(Value *V) { 1050 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1051 return SCEVConstant::get(CI); 1052 SCEVUnknown *&Result = SCEVUnknowns[V]; 1053 if (Result == 0) Result = new SCEVUnknown(V); 1054 return Result; 1055} 1056 1057 1058//===----------------------------------------------------------------------===// 1059// ScalarEvolutionsImpl Definition and Implementation 1060//===----------------------------------------------------------------------===// 1061// 1062/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1063/// evolution code. 1064/// 1065namespace { 1066 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1067 /// F - The function we are analyzing. 1068 /// 1069 Function &F; 1070 1071 /// LI - The loop information for the function we are currently analyzing. 1072 /// 1073 LoopInfo &LI; 1074 1075 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1076 /// things. 1077 SCEVHandle UnknownValue; 1078 1079 /// Scalars - This is a cache of the scalars we have analyzed so far. 1080 /// 1081 std::map<Value*, SCEVHandle> Scalars; 1082 1083 /// IterationCounts - Cache the iteration count of the loops for this 1084 /// function as they are computed. 1085 std::map<const Loop*, SCEVHandle> IterationCounts; 1086 1087 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1088 /// the PHI instructions that we attempt to compute constant evolutions for. 1089 /// This allows us to avoid potentially expensive recomputation of these 1090 /// properties. An instruction maps to null if we are unable to compute its 1091 /// exit value. 1092 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1093 1094 public: 1095 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1096 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1097 1098 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1099 /// expression and create a new one. 1100 SCEVHandle getSCEV(Value *V); 1101 1102 /// hasSCEV - Return true if the SCEV for this value has already been 1103 /// computed. 1104 bool hasSCEV(Value *V) const { 1105 return Scalars.count(V); 1106 } 1107 1108 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1109 /// the specified value. 1110 void setSCEV(Value *V, const SCEVHandle &H) { 1111 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1112 assert(isNew && "This entry already existed!"); 1113 } 1114 1115 1116 /// getSCEVAtScope - Compute the value of the specified expression within 1117 /// the indicated loop (which may be null to indicate in no loop). If the 1118 /// expression cannot be evaluated, return UnknownValue itself. 1119 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1120 1121 1122 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1123 /// an analyzable loop-invariant iteration count. 1124 bool hasLoopInvariantIterationCount(const Loop *L); 1125 1126 /// getIterationCount - If the specified loop has a predictable iteration 1127 /// count, return it. Note that it is not valid to call this method on a 1128 /// loop without a loop-invariant iteration count. 1129 SCEVHandle getIterationCount(const Loop *L); 1130 1131 /// deleteInstructionFromRecords - This method should be called by the 1132 /// client before it removes an instruction from the program, to make sure 1133 /// that no dangling references are left around. 1134 void deleteInstructionFromRecords(Instruction *I); 1135 1136 private: 1137 /// createSCEV - We know that there is no SCEV for the specified value. 1138 /// Analyze the expression. 1139 SCEVHandle createSCEV(Value *V); 1140 SCEVHandle createNodeForCast(CastInst *CI); 1141 1142 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1143 /// SCEVs. 1144 SCEVHandle createNodeForPHI(PHINode *PN); 1145 1146 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1147 /// for the specified instruction and replaces any references to the 1148 /// symbolic value SymName with the specified value. This is used during 1149 /// PHI resolution. 1150 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1151 const SCEVHandle &SymName, 1152 const SCEVHandle &NewVal); 1153 1154 /// ComputeIterationCount - Compute the number of times the specified loop 1155 /// will iterate. 1156 SCEVHandle ComputeIterationCount(const Loop *L); 1157 1158 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1159 /// 'setcc load X, cst', try to se if we can compute the trip count. 1160 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1161 Constant *RHS, 1162 const Loop *L, 1163 unsigned SetCCOpcode); 1164 1165 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1166 /// constant number of times (the condition evolves only from constants), 1167 /// try to evaluate a few iterations of the loop until we get the exit 1168 /// condition gets a value of ExitWhen (true or false). If we cannot 1169 /// evaluate the trip count of the loop, return UnknownValue. 1170 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1171 bool ExitWhen); 1172 1173 /// HowFarToZero - Return the number of times a backedge comparing the 1174 /// specified value to zero will execute. If not computable, return 1175 /// UnknownValue. 1176 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1177 1178 /// HowFarToNonZero - Return the number of times a backedge checking the 1179 /// specified value for nonzero will execute. If not computable, return 1180 /// UnknownValue. 1181 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1182 1183 /// HowManyLessThans - Return the number of times a backedge containing the 1184 /// specified less-than comparison will execute. If not computable, return 1185 /// UnknownValue. 1186 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L); 1187 1188 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1189 /// in the header of its containing loop, we know the loop executes a 1190 /// constant number of times, and the PHI node is just a recurrence 1191 /// involving constants, fold it. 1192 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1193 const Loop *L); 1194 }; 1195} 1196 1197//===----------------------------------------------------------------------===// 1198// Basic SCEV Analysis and PHI Idiom Recognition Code 1199// 1200 1201/// deleteInstructionFromRecords - This method should be called by the 1202/// client before it removes an instruction from the program, to make sure 1203/// that no dangling references are left around. 1204void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1205 Scalars.erase(I); 1206 if (PHINode *PN = dyn_cast<PHINode>(I)) 1207 ConstantEvolutionLoopExitValue.erase(PN); 1208} 1209 1210 1211/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1212/// expression and create a new one. 1213SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1214 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1215 1216 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1217 if (I != Scalars.end()) return I->second; 1218 SCEVHandle S = createSCEV(V); 1219 Scalars.insert(std::make_pair(V, S)); 1220 return S; 1221} 1222 1223/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1224/// the specified instruction and replaces any references to the symbolic value 1225/// SymName with the specified value. This is used during PHI resolution. 1226void ScalarEvolutionsImpl:: 1227ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1228 const SCEVHandle &NewVal) { 1229 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1230 if (SI == Scalars.end()) return; 1231 1232 SCEVHandle NV = 1233 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1234 if (NV == SI->second) return; // No change. 1235 1236 SI->second = NV; // Update the scalars map! 1237 1238 // Any instruction values that use this instruction might also need to be 1239 // updated! 1240 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1241 UI != E; ++UI) 1242 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1243} 1244 1245/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1246/// a loop header, making it a potential recurrence, or it doesn't. 1247/// 1248SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1249 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1250 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1251 if (L->getHeader() == PN->getParent()) { 1252 // If it lives in the loop header, it has two incoming values, one 1253 // from outside the loop, and one from inside. 1254 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1255 unsigned BackEdge = IncomingEdge^1; 1256 1257 // While we are analyzing this PHI node, handle its value symbolically. 1258 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1259 assert(Scalars.find(PN) == Scalars.end() && 1260 "PHI node already processed?"); 1261 Scalars.insert(std::make_pair(PN, SymbolicName)); 1262 1263 // Using this symbolic name for the PHI, analyze the value coming around 1264 // the back-edge. 1265 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1266 1267 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1268 // has a special value for the first iteration of the loop. 1269 1270 // If the value coming around the backedge is an add with the symbolic 1271 // value we just inserted, then we found a simple induction variable! 1272 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1273 // If there is a single occurrence of the symbolic value, replace it 1274 // with a recurrence. 1275 unsigned FoundIndex = Add->getNumOperands(); 1276 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1277 if (Add->getOperand(i) == SymbolicName) 1278 if (FoundIndex == e) { 1279 FoundIndex = i; 1280 break; 1281 } 1282 1283 if (FoundIndex != Add->getNumOperands()) { 1284 // Create an add with everything but the specified operand. 1285 std::vector<SCEVHandle> Ops; 1286 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1287 if (i != FoundIndex) 1288 Ops.push_back(Add->getOperand(i)); 1289 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1290 1291 // This is not a valid addrec if the step amount is varying each 1292 // loop iteration, but is not itself an addrec in this loop. 1293 if (Accum->isLoopInvariant(L) || 1294 (isa<SCEVAddRecExpr>(Accum) && 1295 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1296 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1297 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1298 1299 // Okay, for the entire analysis of this edge we assumed the PHI 1300 // to be symbolic. We now need to go back and update all of the 1301 // entries for the scalars that use the PHI (except for the PHI 1302 // itself) to use the new analyzed value instead of the "symbolic" 1303 // value. 1304 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1305 return PHISCEV; 1306 } 1307 } 1308 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1309 // Otherwise, this could be a loop like this: 1310 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1311 // In this case, j = {1,+,1} and BEValue is j. 1312 // Because the other in-value of i (0) fits the evolution of BEValue 1313 // i really is an addrec evolution. 1314 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1315 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1316 1317 // If StartVal = j.start - j.stride, we can use StartVal as the 1318 // initial step of the addrec evolution. 1319 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1320 AddRec->getOperand(1))) { 1321 SCEVHandle PHISCEV = 1322 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1323 1324 // Okay, for the entire analysis of this edge we assumed the PHI 1325 // to be symbolic. We now need to go back and update all of the 1326 // entries for the scalars that use the PHI (except for the PHI 1327 // itself) to use the new analyzed value instead of the "symbolic" 1328 // value. 1329 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1330 return PHISCEV; 1331 } 1332 } 1333 } 1334 1335 return SymbolicName; 1336 } 1337 1338 // If it's not a loop phi, we can't handle it yet. 1339 return SCEVUnknown::get(PN); 1340} 1341 1342/// createNodeForCast - Handle the various forms of casts that we support. 1343/// 1344SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 1345 const Type *SrcTy = CI->getOperand(0)->getType(); 1346 const Type *DestTy = CI->getType(); 1347 1348 // If this is a noop cast (ie, conversion from int to uint), ignore it. 1349 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 1350 return getSCEV(CI->getOperand(0)); 1351 1352 if (SrcTy->isInteger() && DestTy->isInteger()) { 1353 // Otherwise, if this is a truncating integer cast, we can represent this 1354 // cast. 1355 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1356 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 1357 CI->getType()->getUnsignedVersion()); 1358 if (SrcTy->isUnsigned() && 1359 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1360 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 1361 CI->getType()->getUnsignedVersion()); 1362 } 1363 1364 // If this is an sign or zero extending cast and we can prove that the value 1365 // will never overflow, we could do similar transformations. 1366 1367 // Otherwise, we can't handle this cast! 1368 return SCEVUnknown::get(CI); 1369} 1370 1371 1372/// createSCEV - We know that there is no SCEV for the specified value. 1373/// Analyze the expression. 1374/// 1375SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1376 if (Instruction *I = dyn_cast<Instruction>(V)) { 1377 switch (I->getOpcode()) { 1378 case Instruction::Add: 1379 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1380 getSCEV(I->getOperand(1))); 1381 case Instruction::Mul: 1382 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1383 getSCEV(I->getOperand(1))); 1384 case Instruction::Div: 1385 if (V->getType()->isInteger() && V->getType()->isSigned()) 1386 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1387 getSCEV(I->getOperand(1))); 1388 break; 1389 1390 case Instruction::Sub: 1391 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1392 getSCEV(I->getOperand(1))); 1393 1394 case Instruction::Shl: 1395 // Turn shift left of a constant amount into a multiply. 1396 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1397 Constant *X = ConstantInt::get(V->getType(), 1); 1398 X = ConstantExpr::getShl(X, SA); 1399 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1400 } 1401 break; 1402 1403 case Instruction::Cast: 1404 return createNodeForCast(cast<CastInst>(I)); 1405 1406 case Instruction::PHI: 1407 return createNodeForPHI(cast<PHINode>(I)); 1408 1409 default: // We cannot analyze this expression. 1410 break; 1411 } 1412 } 1413 1414 return SCEVUnknown::get(V); 1415} 1416 1417 1418 1419//===----------------------------------------------------------------------===// 1420// Iteration Count Computation Code 1421// 1422 1423/// getIterationCount - If the specified loop has a predictable iteration 1424/// count, return it. Note that it is not valid to call this method on a 1425/// loop without a loop-invariant iteration count. 1426SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1427 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1428 if (I == IterationCounts.end()) { 1429 SCEVHandle ItCount = ComputeIterationCount(L); 1430 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1431 if (ItCount != UnknownValue) { 1432 assert(ItCount->isLoopInvariant(L) && 1433 "Computed trip count isn't loop invariant for loop!"); 1434 ++NumTripCountsComputed; 1435 } else if (isa<PHINode>(L->getHeader()->begin())) { 1436 // Only count loops that have phi nodes as not being computable. 1437 ++NumTripCountsNotComputed; 1438 } 1439 } 1440 return I->second; 1441} 1442 1443/// ComputeIterationCount - Compute the number of times the specified loop 1444/// will iterate. 1445SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1446 // If the loop has a non-one exit block count, we can't analyze it. 1447 std::vector<BasicBlock*> ExitBlocks; 1448 L->getExitBlocks(ExitBlocks); 1449 if (ExitBlocks.size() != 1) return UnknownValue; 1450 1451 // Okay, there is one exit block. Try to find the condition that causes the 1452 // loop to be exited. 1453 BasicBlock *ExitBlock = ExitBlocks[0]; 1454 1455 BasicBlock *ExitingBlock = 0; 1456 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1457 PI != E; ++PI) 1458 if (L->contains(*PI)) { 1459 if (ExitingBlock == 0) 1460 ExitingBlock = *PI; 1461 else 1462 return UnknownValue; // More than one block exiting! 1463 } 1464 assert(ExitingBlock && "No exits from loop, something is broken!"); 1465 1466 // Okay, we've computed the exiting block. See what condition causes us to 1467 // exit. 1468 // 1469 // FIXME: we should be able to handle switch instructions (with a single exit) 1470 // FIXME: We should handle cast of int to bool as well 1471 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1472 if (ExitBr == 0) return UnknownValue; 1473 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1474 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1475 if (ExitCond == 0) // Not a setcc 1476 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1477 ExitBr->getSuccessor(0) == ExitBlock); 1478 1479 // If the condition was exit on true, convert the condition to exit on false. 1480 Instruction::BinaryOps Cond; 1481 if (ExitBr->getSuccessor(1) == ExitBlock) 1482 Cond = ExitCond->getOpcode(); 1483 else 1484 Cond = ExitCond->getInverseCondition(); 1485 1486 // Handle common loops like: for (X = "string"; *X; ++X) 1487 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1488 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1489 SCEVHandle ItCnt = 1490 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1491 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1492 } 1493 1494 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1495 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1496 1497 // Try to evaluate any dependencies out of the loop. 1498 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1499 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1500 Tmp = getSCEVAtScope(RHS, L); 1501 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1502 1503 // At this point, we would like to compute how many iterations of the loop the 1504 // predicate will return true for these inputs. 1505 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1506 // If there is a constant, force it into the RHS. 1507 std::swap(LHS, RHS); 1508 Cond = SetCondInst::getSwappedCondition(Cond); 1509 } 1510 1511 // FIXME: think about handling pointer comparisons! i.e.: 1512 // while (P != P+100) ++P; 1513 1514 // If we have a comparison of a chrec against a constant, try to use value 1515 // ranges to answer this query. 1516 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1517 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1518 if (AddRec->getLoop() == L) { 1519 // Form the comparison range using the constant of the correct type so 1520 // that the ConstantRange class knows to do a signed or unsigned 1521 // comparison. 1522 ConstantInt *CompVal = RHSC->getValue(); 1523 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1524 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 1525 if (CompVal) { 1526 // Form the constant range. 1527 ConstantRange CompRange(Cond, CompVal); 1528 1529 // Now that we have it, if it's signed, convert it to an unsigned 1530 // range. 1531 if (CompRange.getLower()->getType()->isSigned()) { 1532 const Type *NewTy = RHSC->getValue()->getType(); 1533 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 1534 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 1535 CompRange = ConstantRange(NewL, NewU); 1536 } 1537 1538 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1539 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1540 } 1541 } 1542 1543 switch (Cond) { 1544 case Instruction::SetNE: // while (X != Y) 1545 // Convert to: while (X-Y != 0) 1546 if (LHS->getType()->isInteger()) { 1547 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1548 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1549 } 1550 break; 1551 case Instruction::SetEQ: 1552 // Convert to: while (X-Y == 0) // while (X == Y) 1553 if (LHS->getType()->isInteger()) { 1554 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1555 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1556 } 1557 break; 1558 case Instruction::SetLT: 1559 if (LHS->getType()->isInteger() && 1560 ExitCond->getOperand(0)->getType()->isSigned()) { 1561 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1562 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1563 } 1564 break; 1565 case Instruction::SetGT: 1566 if (LHS->getType()->isInteger() && 1567 ExitCond->getOperand(0)->getType()->isSigned()) { 1568 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1569 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1570 } 1571 break; 1572 default: 1573#if 0 1574 std::cerr << "ComputeIterationCount "; 1575 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1576 std::cerr << "[unsigned] "; 1577 std::cerr << *LHS << " " 1578 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1579#endif 1580 break; 1581 } 1582 1583 return ComputeIterationCountExhaustively(L, ExitCond, 1584 ExitBr->getSuccessor(0) == ExitBlock); 1585} 1586 1587static ConstantInt * 1588EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1589 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1590 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1591 assert(isa<SCEVConstant>(Val) && 1592 "Evaluation of SCEV at constant didn't fold correctly?"); 1593 return cast<SCEVConstant>(Val)->getValue(); 1594} 1595 1596/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1597/// and a GEP expression (missing the pointer index) indexing into it, return 1598/// the addressed element of the initializer or null if the index expression is 1599/// invalid. 1600static Constant * 1601GetAddressedElementFromGlobal(GlobalVariable *GV, 1602 const std::vector<ConstantInt*> &Indices) { 1603 Constant *Init = GV->getInitializer(); 1604 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1605 uint64_t Idx = Indices[i]->getRawValue(); 1606 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1607 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1608 Init = cast<Constant>(CS->getOperand(Idx)); 1609 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1610 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1611 Init = cast<Constant>(CA->getOperand(Idx)); 1612 } else if (isa<ConstantAggregateZero>(Init)) { 1613 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1614 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1615 Init = Constant::getNullValue(STy->getElementType(Idx)); 1616 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1617 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1618 Init = Constant::getNullValue(ATy->getElementType()); 1619 } else { 1620 assert(0 && "Unknown constant aggregate type!"); 1621 } 1622 return 0; 1623 } else { 1624 return 0; // Unknown initializer type 1625 } 1626 } 1627 return Init; 1628} 1629 1630/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1631/// 'setcc load X, cst', try to se if we can compute the trip count. 1632SCEVHandle ScalarEvolutionsImpl:: 1633ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1634 const Loop *L, unsigned SetCCOpcode) { 1635 if (LI->isVolatile()) return UnknownValue; 1636 1637 // Check to see if the loaded pointer is a getelementptr of a global. 1638 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1639 if (!GEP) return UnknownValue; 1640 1641 // Make sure that it is really a constant global we are gepping, with an 1642 // initializer, and make sure the first IDX is really 0. 1643 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1644 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1645 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1646 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1647 return UnknownValue; 1648 1649 // Okay, we allow one non-constant index into the GEP instruction. 1650 Value *VarIdx = 0; 1651 std::vector<ConstantInt*> Indexes; 1652 unsigned VarIdxNum = 0; 1653 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1654 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1655 Indexes.push_back(CI); 1656 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1657 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1658 VarIdx = GEP->getOperand(i); 1659 VarIdxNum = i-2; 1660 Indexes.push_back(0); 1661 } 1662 1663 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1664 // Check to see if X is a loop variant variable value now. 1665 SCEVHandle Idx = getSCEV(VarIdx); 1666 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1667 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1668 1669 // We can only recognize very limited forms of loop index expressions, in 1670 // particular, only affine AddRec's like {C1,+,C2}. 1671 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1672 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1673 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1674 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1675 return UnknownValue; 1676 1677 unsigned MaxSteps = MaxBruteForceIterations; 1678 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1679 ConstantUInt *ItCst = 1680 ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 1681 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1682 1683 // Form the GEP offset. 1684 Indexes[VarIdxNum] = Val; 1685 1686 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1687 if (Result == 0) break; // Cannot compute! 1688 1689 // Evaluate the condition for this iteration. 1690 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 1691 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 1692 if (Result == ConstantBool::False) { 1693#if 0 1694 std::cerr << "\n***\n*** Computed loop count " << *ItCst 1695 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1696 << "***\n"; 1697#endif 1698 ++NumArrayLenItCounts; 1699 return SCEVConstant::get(ItCst); // Found terminating iteration! 1700 } 1701 } 1702 return UnknownValue; 1703} 1704 1705 1706/// CanConstantFold - Return true if we can constant fold an instruction of the 1707/// specified type, assuming that all operands were constants. 1708static bool CanConstantFold(const Instruction *I) { 1709 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1710 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1711 return true; 1712 1713 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1714 if (const Function *F = CI->getCalledFunction()) 1715 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1716 return false; 1717} 1718 1719/// ConstantFold - Constant fold an instruction of the specified type with the 1720/// specified constant operands. This function may modify the operands vector. 1721static Constant *ConstantFold(const Instruction *I, 1722 std::vector<Constant*> &Operands) { 1723 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1724 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1725 1726 switch (I->getOpcode()) { 1727 case Instruction::Cast: 1728 return ConstantExpr::getCast(Operands[0], I->getType()); 1729 case Instruction::Select: 1730 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1731 case Instruction::Call: 1732 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1733 Operands.erase(Operands.begin()); 1734 return ConstantFoldCall(cast<Function>(GV), Operands); 1735 } 1736 1737 return 0; 1738 case Instruction::GetElementPtr: 1739 Constant *Base = Operands[0]; 1740 Operands.erase(Operands.begin()); 1741 return ConstantExpr::getGetElementPtr(Base, Operands); 1742 } 1743 return 0; 1744} 1745 1746 1747/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1748/// in the loop that V is derived from. We allow arbitrary operations along the 1749/// way, but the operands of an operation must either be constants or a value 1750/// derived from a constant PHI. If this expression does not fit with these 1751/// constraints, return null. 1752static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1753 // If this is not an instruction, or if this is an instruction outside of the 1754 // loop, it can't be derived from a loop PHI. 1755 Instruction *I = dyn_cast<Instruction>(V); 1756 if (I == 0 || !L->contains(I->getParent())) return 0; 1757 1758 if (PHINode *PN = dyn_cast<PHINode>(I)) 1759 if (L->getHeader() == I->getParent()) 1760 return PN; 1761 else 1762 // We don't currently keep track of the control flow needed to evaluate 1763 // PHIs, so we cannot handle PHIs inside of loops. 1764 return 0; 1765 1766 // If we won't be able to constant fold this expression even if the operands 1767 // are constants, return early. 1768 if (!CanConstantFold(I)) return 0; 1769 1770 // Otherwise, we can evaluate this instruction if all of its operands are 1771 // constant or derived from a PHI node themselves. 1772 PHINode *PHI = 0; 1773 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1774 if (!(isa<Constant>(I->getOperand(Op)) || 1775 isa<GlobalValue>(I->getOperand(Op)))) { 1776 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1777 if (P == 0) return 0; // Not evolving from PHI 1778 if (PHI == 0) 1779 PHI = P; 1780 else if (PHI != P) 1781 return 0; // Evolving from multiple different PHIs. 1782 } 1783 1784 // This is a expression evolving from a constant PHI! 1785 return PHI; 1786} 1787 1788/// EvaluateExpression - Given an expression that passes the 1789/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1790/// in the loop has the value PHIVal. If we can't fold this expression for some 1791/// reason, return null. 1792static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1793 if (isa<PHINode>(V)) return PHIVal; 1794 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1795 return GV; 1796 if (Constant *C = dyn_cast<Constant>(V)) return C; 1797 Instruction *I = cast<Instruction>(V); 1798 1799 std::vector<Constant*> Operands; 1800 Operands.resize(I->getNumOperands()); 1801 1802 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1803 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1804 if (Operands[i] == 0) return 0; 1805 } 1806 1807 return ConstantFold(I, Operands); 1808} 1809 1810/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1811/// in the header of its containing loop, we know the loop executes a 1812/// constant number of times, and the PHI node is just a recurrence 1813/// involving constants, fold it. 1814Constant *ScalarEvolutionsImpl:: 1815getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1816 std::map<PHINode*, Constant*>::iterator I = 1817 ConstantEvolutionLoopExitValue.find(PN); 1818 if (I != ConstantEvolutionLoopExitValue.end()) 1819 return I->second; 1820 1821 if (Its > MaxBruteForceIterations) 1822 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1823 1824 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1825 1826 // Since the loop is canonicalized, the PHI node must have two entries. One 1827 // entry must be a constant (coming in from outside of the loop), and the 1828 // second must be derived from the same PHI. 1829 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1830 Constant *StartCST = 1831 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1832 if (StartCST == 0) 1833 return RetVal = 0; // Must be a constant. 1834 1835 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1836 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1837 if (PN2 != PN) 1838 return RetVal = 0; // Not derived from same PHI. 1839 1840 // Execute the loop symbolically to determine the exit value. 1841 unsigned IterationNum = 0; 1842 unsigned NumIterations = Its; 1843 if (NumIterations != Its) 1844 return RetVal = 0; // More than 2^32 iterations?? 1845 1846 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1847 if (IterationNum == NumIterations) 1848 return RetVal = PHIVal; // Got exit value! 1849 1850 // Compute the value of the PHI node for the next iteration. 1851 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1852 if (NextPHI == PHIVal) 1853 return RetVal = NextPHI; // Stopped evolving! 1854 if (NextPHI == 0) 1855 return 0; // Couldn't evaluate! 1856 PHIVal = NextPHI; 1857 } 1858} 1859 1860/// ComputeIterationCountExhaustively - If the trip is known to execute a 1861/// constant number of times (the condition evolves only from constants), 1862/// try to evaluate a few iterations of the loop until we get the exit 1863/// condition gets a value of ExitWhen (true or false). If we cannot 1864/// evaluate the trip count of the loop, return UnknownValue. 1865SCEVHandle ScalarEvolutionsImpl:: 1866ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1867 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1868 if (PN == 0) return UnknownValue; 1869 1870 // Since the loop is canonicalized, the PHI node must have two entries. One 1871 // entry must be a constant (coming in from outside of the loop), and the 1872 // second must be derived from the same PHI. 1873 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1874 Constant *StartCST = 1875 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1876 if (StartCST == 0) return UnknownValue; // Must be a constant. 1877 1878 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1879 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1880 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1881 1882 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1883 // the loop symbolically to determine when the condition gets a value of 1884 // "ExitWhen". 1885 unsigned IterationNum = 0; 1886 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1887 for (Constant *PHIVal = StartCST; 1888 IterationNum != MaxIterations; ++IterationNum) { 1889 ConstantBool *CondVal = 1890 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1891 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1892 1893 if (CondVal->getValue() == ExitWhen) { 1894 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1895 ++NumBruteForceTripCountsComputed; 1896 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 1897 } 1898 1899 // Compute the value of the PHI node for the next iteration. 1900 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1901 if (NextPHI == 0 || NextPHI == PHIVal) 1902 return UnknownValue; // Couldn't evaluate or not making progress... 1903 PHIVal = NextPHI; 1904 } 1905 1906 // Too many iterations were needed to evaluate. 1907 return UnknownValue; 1908} 1909 1910/// getSCEVAtScope - Compute the value of the specified expression within the 1911/// indicated loop (which may be null to indicate in no loop). If the 1912/// expression cannot be evaluated, return UnknownValue. 1913SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1914 // FIXME: this should be turned into a virtual method on SCEV! 1915 1916 if (isa<SCEVConstant>(V)) return V; 1917 1918 // If this instruction is evolves from a constant-evolving PHI, compute the 1919 // exit value from the loop without using SCEVs. 1920 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1921 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1922 const Loop *LI = this->LI[I->getParent()]; 1923 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1924 if (PHINode *PN = dyn_cast<PHINode>(I)) 1925 if (PN->getParent() == LI->getHeader()) { 1926 // Okay, there is no closed form solution for the PHI node. Check 1927 // to see if the loop that contains it has a known iteration count. 1928 // If so, we may be able to force computation of the exit value. 1929 SCEVHandle IterationCount = getIterationCount(LI); 1930 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1931 // Okay, we know how many times the containing loop executes. If 1932 // this is a constant evolving PHI node, get the final value at 1933 // the specified iteration number. 1934 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1935 ICC->getValue()->getRawValue(), 1936 LI); 1937 if (RV) return SCEVUnknown::get(RV); 1938 } 1939 } 1940 1941 // Okay, this is a some expression that we cannot symbolically evaluate 1942 // into a SCEV. Check to see if it's possible to symbolically evaluate 1943 // the arguments into constants, and if see, try to constant propagate the 1944 // result. This is particularly useful for computing loop exit values. 1945 if (CanConstantFold(I)) { 1946 std::vector<Constant*> Operands; 1947 Operands.reserve(I->getNumOperands()); 1948 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1949 Value *Op = I->getOperand(i); 1950 if (Constant *C = dyn_cast<Constant>(Op)) { 1951 Operands.push_back(C); 1952 } else { 1953 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1954 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1955 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 1956 Op->getType())); 1957 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1958 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1959 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 1960 else 1961 return V; 1962 } else { 1963 return V; 1964 } 1965 } 1966 } 1967 return SCEVUnknown::get(ConstantFold(I, Operands)); 1968 } 1969 } 1970 1971 // This is some other type of SCEVUnknown, just return it. 1972 return V; 1973 } 1974 1975 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1976 // Avoid performing the look-up in the common case where the specified 1977 // expression has no loop-variant portions. 1978 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1979 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1980 if (OpAtScope != Comm->getOperand(i)) { 1981 if (OpAtScope == UnknownValue) return UnknownValue; 1982 // Okay, at least one of these operands is loop variant but might be 1983 // foldable. Build a new instance of the folded commutative expression. 1984 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1985 NewOps.push_back(OpAtScope); 1986 1987 for (++i; i != e; ++i) { 1988 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1989 if (OpAtScope == UnknownValue) return UnknownValue; 1990 NewOps.push_back(OpAtScope); 1991 } 1992 if (isa<SCEVAddExpr>(Comm)) 1993 return SCEVAddExpr::get(NewOps); 1994 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 1995 return SCEVMulExpr::get(NewOps); 1996 } 1997 } 1998 // If we got here, all operands are loop invariant. 1999 return Comm; 2000 } 2001 2002 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2003 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2004 if (LHS == UnknownValue) return LHS; 2005 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2006 if (RHS == UnknownValue) return RHS; 2007 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2008 return Div; // must be loop invariant 2009 return SCEVSDivExpr::get(LHS, RHS); 2010 } 2011 2012 // If this is a loop recurrence for a loop that does not contain L, then we 2013 // are dealing with the final value computed by the loop. 2014 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2015 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2016 // To evaluate this recurrence, we need to know how many times the AddRec 2017 // loop iterates. Compute this now. 2018 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2019 if (IterationCount == UnknownValue) return UnknownValue; 2020 IterationCount = getTruncateOrZeroExtend(IterationCount, 2021 AddRec->getType()); 2022 2023 // If the value is affine, simplify the expression evaluation to just 2024 // Start + Step*IterationCount. 2025 if (AddRec->isAffine()) 2026 return SCEVAddExpr::get(AddRec->getStart(), 2027 SCEVMulExpr::get(IterationCount, 2028 AddRec->getOperand(1))); 2029 2030 // Otherwise, evaluate it the hard way. 2031 return AddRec->evaluateAtIteration(IterationCount); 2032 } 2033 return UnknownValue; 2034 } 2035 2036 //assert(0 && "Unknown SCEV type!"); 2037 return UnknownValue; 2038} 2039 2040 2041/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2042/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2043/// might be the same) or two SCEVCouldNotCompute objects. 2044/// 2045static std::pair<SCEVHandle,SCEVHandle> 2046SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2047 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2048 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2049 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2050 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2051 2052 // We currently can only solve this if the coefficients are constants. 2053 if (!L || !M || !N) { 2054 SCEV *CNC = new SCEVCouldNotCompute(); 2055 return std::make_pair(CNC, CNC); 2056 } 2057 2058 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 2059 2060 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2061 Constant *C = L->getValue(); 2062 // The B coefficient is M-N/2 2063 Constant *B = ConstantExpr::getSub(M->getValue(), 2064 ConstantExpr::getDiv(N->getValue(), 2065 Two)); 2066 // The A coefficient is N/2 2067 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 2068 2069 // Compute the B^2-4ac term. 2070 Constant *SqrtTerm = 2071 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2072 ConstantExpr::getMul(A, C)); 2073 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2074 2075 // Compute floor(sqrt(B^2-4ac)) 2076 ConstantUInt *SqrtVal = 2077 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 2078 SqrtTerm->getType()->getUnsignedVersion())); 2079 uint64_t SqrtValV = SqrtVal->getValue(); 2080 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2081 // The square root might not be precise for arbitrary 64-bit integer 2082 // values. Do some sanity checks to ensure it's correct. 2083 if (SqrtValV2*SqrtValV2 > SqrtValV || 2084 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2085 SCEV *CNC = new SCEVCouldNotCompute(); 2086 return std::make_pair(CNC, CNC); 2087 } 2088 2089 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 2090 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 2091 2092 Constant *NegB = ConstantExpr::getNeg(B); 2093 Constant *TwoA = ConstantExpr::getMul(A, Two); 2094 2095 // The divisions must be performed as signed divisions. 2096 const Type *SignedTy = NegB->getType()->getSignedVersion(); 2097 NegB = ConstantExpr::getCast(NegB, SignedTy); 2098 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 2099 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 2100 2101 Constant *Solution1 = 2102 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2103 Constant *Solution2 = 2104 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2105 return std::make_pair(SCEVUnknown::get(Solution1), 2106 SCEVUnknown::get(Solution2)); 2107} 2108 2109/// HowFarToZero - Return the number of times a backedge comparing the specified 2110/// value to zero will execute. If not computable, return UnknownValue 2111SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2112 // If the value is a constant 2113 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2114 // If the value is already zero, the branch will execute zero times. 2115 if (C->getValue()->isNullValue()) return C; 2116 return UnknownValue; // Otherwise it will loop infinitely. 2117 } 2118 2119 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2120 if (!AddRec || AddRec->getLoop() != L) 2121 return UnknownValue; 2122 2123 if (AddRec->isAffine()) { 2124 // If this is an affine expression the execution count of this branch is 2125 // equal to: 2126 // 2127 // (0 - Start/Step) iff Start % Step == 0 2128 // 2129 // Get the initial value for the loop. 2130 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2131 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2132 SCEVHandle Step = AddRec->getOperand(1); 2133 2134 Step = getSCEVAtScope(Step, L->getParentLoop()); 2135 2136 // Figure out if Start % Step == 0. 2137 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2138 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2139 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2140 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2141 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2142 return Start; // 0 - Start/-1 == Start 2143 2144 // Check to see if Start is divisible by SC with no remainder. 2145 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2146 ConstantInt *StartCC = StartC->getValue(); 2147 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2148 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 2149 if (Rem->isNullValue()) { 2150 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 2151 return SCEVUnknown::get(Result); 2152 } 2153 } 2154 } 2155 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2156 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2157 // the quadratic equation to solve it. 2158 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2159 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2160 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2161 if (R1) { 2162#if 0 2163 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2164 << " sol#2: " << *R2 << "\n"; 2165#endif 2166 // Pick the smallest positive root value. 2167 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 2168 if (ConstantBool *CB = 2169 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2170 R2->getValue()))) { 2171 if (CB != ConstantBool::True) 2172 std::swap(R1, R2); // R1 is the minimum root now. 2173 2174 // We can only use this value if the chrec ends up with an exact zero 2175 // value at this index. When solving for "X*X != 5", for example, we 2176 // should not accept a root of 2. 2177 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2178 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2179 if (EvalVal->getValue()->isNullValue()) 2180 return R1; // We found a quadratic root! 2181 } 2182 } 2183 } 2184 2185 return UnknownValue; 2186} 2187 2188/// HowFarToNonZero - Return the number of times a backedge checking the 2189/// specified value for nonzero will execute. If not computable, return 2190/// UnknownValue 2191SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2192 // Loops that look like: while (X == 0) are very strange indeed. We don't 2193 // handle them yet except for the trivial case. This could be expanded in the 2194 // future as needed. 2195 2196 // If the value is a constant, check to see if it is known to be non-zero 2197 // already. If so, the backedge will execute zero times. 2198 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2199 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2200 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 2201 if (NonZero == ConstantBool::True) 2202 return getSCEV(Zero); 2203 return UnknownValue; // Otherwise it will loop infinitely. 2204 } 2205 2206 // We could implement others, but I really doubt anyone writes loops like 2207 // this, and if they did, they would already be constant folded. 2208 return UnknownValue; 2209} 2210 2211/// HowManyLessThans - Return the number of times a backedge containing the 2212/// specified less-than comparison will execute. If not computable, return 2213/// UnknownValue. 2214SCEVHandle ScalarEvolutionsImpl:: 2215HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2216 // Only handle: "ADDREC < LoopInvariant". 2217 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2218 2219 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2220 if (!AddRec || AddRec->getLoop() != L) 2221 return UnknownValue; 2222 2223 if (AddRec->isAffine()) { 2224 // FORNOW: We only support unit strides. 2225 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2226 if (AddRec->getOperand(1) != One) 2227 return UnknownValue; 2228 2229 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2230 // know that m is >= n on input to the loop. If it is, the condition return 2231 // true zero times. What we really should return, for full generality, is 2232 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2233 // canonical loop form: most do-loops will have a check that dominates the 2234 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2235 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2236 2237 // Search for the check. 2238 BasicBlock *Preheader = L->getLoopPreheader(); 2239 BasicBlock *PreheaderDest = L->getHeader(); 2240 if (Preheader == 0) return UnknownValue; 2241 2242 BranchInst *LoopEntryPredicate = 2243 dyn_cast<BranchInst>(Preheader->getTerminator()); 2244 if (!LoopEntryPredicate) return UnknownValue; 2245 2246 // This might be a critical edge broken out. If the loop preheader ends in 2247 // an unconditional branch to the loop, check to see if the preheader has a 2248 // single predecessor, and if so, look for its terminator. 2249 while (LoopEntryPredicate->isUnconditional()) { 2250 PreheaderDest = Preheader; 2251 Preheader = Preheader->getSinglePredecessor(); 2252 if (!Preheader) return UnknownValue; // Multiple preds. 2253 2254 LoopEntryPredicate = 2255 dyn_cast<BranchInst>(Preheader->getTerminator()); 2256 if (!LoopEntryPredicate) return UnknownValue; 2257 } 2258 2259 // Now that we found a conditional branch that dominates the loop, check to 2260 // see if it is the comparison we are looking for. 2261 SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition()); 2262 if (!SCI) return UnknownValue; 2263 Value *PreCondLHS = SCI->getOperand(0); 2264 Value *PreCondRHS = SCI->getOperand(1); 2265 Instruction::BinaryOps Cond; 2266 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2267 Cond = SCI->getOpcode(); 2268 else 2269 Cond = SCI->getInverseCondition(); 2270 2271 switch (Cond) { 2272 case Instruction::SetGT: 2273 std::swap(PreCondLHS, PreCondRHS); 2274 Cond = Instruction::SetLT; 2275 // Fall Through. 2276 case Instruction::SetLT: 2277 if (PreCondLHS->getType()->isInteger() && 2278 PreCondLHS->getType()->isSigned()) { 2279 if (RHS != getSCEV(PreCondRHS)) 2280 return UnknownValue; // Not a comparison against 'm'. 2281 2282 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2283 != getSCEV(PreCondLHS)) 2284 return UnknownValue; // Not a comparison against 'n-1'. 2285 break; 2286 } else { 2287 return UnknownValue; 2288 } 2289 default: break; 2290 } 2291 2292 //std::cerr << "Computed Loop Trip Count as: " << 2293 // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2294 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2295 } 2296 2297 return UnknownValue; 2298} 2299 2300/// getNumIterationsInRange - Return the number of iterations of this loop that 2301/// produce values in the specified constant range. Another way of looking at 2302/// this is that it returns the first iteration number where the value is not in 2303/// the condition, thus computing the exit count. If the iteration count can't 2304/// be computed, an instance of SCEVCouldNotCompute is returned. 2305SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2306 if (Range.isFullSet()) // Infinite loop. 2307 return new SCEVCouldNotCompute(); 2308 2309 // If the start is a non-zero constant, shift the range to simplify things. 2310 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2311 if (!SC->getValue()->isNullValue()) { 2312 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2313 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2314 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2315 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2316 return ShiftedAddRec->getNumIterationsInRange( 2317 Range.subtract(SC->getValue())); 2318 // This is strange and shouldn't happen. 2319 return new SCEVCouldNotCompute(); 2320 } 2321 2322 // The only time we can solve this is when we have all constant indices. 2323 // Otherwise, we cannot determine the overflow conditions. 2324 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2325 if (!isa<SCEVConstant>(getOperand(i))) 2326 return new SCEVCouldNotCompute(); 2327 2328 2329 // Okay at this point we know that all elements of the chrec are constants and 2330 // that the start element is zero. 2331 2332 // First check to see if the range contains zero. If not, the first 2333 // iteration exits. 2334 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2335 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2336 2337 if (isAffine()) { 2338 // If this is an affine expression then we have this situation: 2339 // Solve {0,+,A} in Range === Ax in Range 2340 2341 // Since we know that zero is in the range, we know that the upper value of 2342 // the range must be the first possible exit value. Also note that we 2343 // already checked for a full range. 2344 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2345 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2346 ConstantInt *One = ConstantInt::get(getType(), 1); 2347 2348 // The exit value should be (Upper+A-1)/A. 2349 Constant *ExitValue = Upper; 2350 if (A != One) { 2351 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2352 ExitValue = ConstantExpr::getDiv(ExitValue, A); 2353 } 2354 assert(isa<ConstantInt>(ExitValue) && 2355 "Constant folding of integers not implemented?"); 2356 2357 // Evaluate at the exit value. If we really did fall out of the valid 2358 // range, then we computed our trip count, otherwise wrap around or other 2359 // things must have happened. 2360 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2361 if (Range.contains(Val)) 2362 return new SCEVCouldNotCompute(); // Something strange happened 2363 2364 // Ensure that the previous value is in the range. This is a sanity check. 2365 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2366 ConstantExpr::getSub(ExitValue, One))) && 2367 "Linear scev computation is off in a bad way!"); 2368 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2369 } else if (isQuadratic()) { 2370 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2371 // quadratic equation to solve it. To do this, we must frame our problem in 2372 // terms of figuring out when zero is crossed, instead of when 2373 // Range.getUpper() is crossed. 2374 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2375 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2376 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2377 2378 // Next, solve the constructed addrec 2379 std::pair<SCEVHandle,SCEVHandle> Roots = 2380 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2381 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2382 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2383 if (R1) { 2384 // Pick the smallest positive root value. 2385 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2386 if (ConstantBool *CB = 2387 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2388 R2->getValue()))) { 2389 if (CB != ConstantBool::True) 2390 std::swap(R1, R2); // R1 is the minimum root now. 2391 2392 // Make sure the root is not off by one. The returned iteration should 2393 // not be in the range, but the previous one should be. When solving 2394 // for "X*X < 5", for example, we should not return a root of 2. 2395 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2396 R1->getValue()); 2397 if (Range.contains(R1Val)) { 2398 // The next iteration must be out of the range... 2399 Constant *NextVal = 2400 ConstantExpr::getAdd(R1->getValue(), 2401 ConstantInt::get(R1->getType(), 1)); 2402 2403 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2404 if (!Range.contains(R1Val)) 2405 return SCEVUnknown::get(NextVal); 2406 return new SCEVCouldNotCompute(); // Something strange happened 2407 } 2408 2409 // If R1 was not in the range, then it is a good return value. Make 2410 // sure that R1-1 WAS in the range though, just in case. 2411 Constant *NextVal = 2412 ConstantExpr::getSub(R1->getValue(), 2413 ConstantInt::get(R1->getType(), 1)); 2414 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2415 if (Range.contains(R1Val)) 2416 return R1; 2417 return new SCEVCouldNotCompute(); // Something strange happened 2418 } 2419 } 2420 } 2421 2422 // Fallback, if this is a general polynomial, figure out the progression 2423 // through brute force: evaluate until we find an iteration that fails the 2424 // test. This is likely to be slow, but getting an accurate trip count is 2425 // incredibly important, we will be able to simplify the exit test a lot, and 2426 // we are almost guaranteed to get a trip count in this case. 2427 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2428 ConstantInt *One = ConstantInt::get(getType(), 1); 2429 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2430 do { 2431 ++NumBruteForceEvaluations; 2432 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2433 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2434 return new SCEVCouldNotCompute(); 2435 2436 // Check to see if we found the value! 2437 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2438 return SCEVConstant::get(TestVal); 2439 2440 // Increment to test the next index. 2441 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2442 } while (TestVal != EndVal); 2443 2444 return new SCEVCouldNotCompute(); 2445} 2446 2447 2448 2449//===----------------------------------------------------------------------===// 2450// ScalarEvolution Class Implementation 2451//===----------------------------------------------------------------------===// 2452 2453bool ScalarEvolution::runOnFunction(Function &F) { 2454 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2455 return false; 2456} 2457 2458void ScalarEvolution::releaseMemory() { 2459 delete (ScalarEvolutionsImpl*)Impl; 2460 Impl = 0; 2461} 2462 2463void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2464 AU.setPreservesAll(); 2465 AU.addRequiredTransitive<LoopInfo>(); 2466} 2467 2468SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2469 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2470} 2471 2472/// hasSCEV - Return true if the SCEV for this value has already been 2473/// computed. 2474bool ScalarEvolution::hasSCEV(Value *V) const { 2475 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2476} 2477 2478 2479/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2480/// the specified value. 2481void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2482 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2483} 2484 2485 2486SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2487 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2488} 2489 2490bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2491 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2492} 2493 2494SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2495 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2496} 2497 2498void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2499 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2500} 2501 2502static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2503 const Loop *L) { 2504 // Print all inner loops first 2505 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2506 PrintLoopInfo(OS, SE, *I); 2507 2508 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 2509 2510 std::vector<BasicBlock*> ExitBlocks; 2511 L->getExitBlocks(ExitBlocks); 2512 if (ExitBlocks.size() != 1) 2513 std::cerr << "<multiple exits> "; 2514 2515 if (SE->hasLoopInvariantIterationCount(L)) { 2516 std::cerr << *SE->getIterationCount(L) << " iterations! "; 2517 } else { 2518 std::cerr << "Unpredictable iteration count. "; 2519 } 2520 2521 std::cerr << "\n"; 2522} 2523 2524void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2525 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2526 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2527 2528 OS << "Classifying expressions for: " << F.getName() << "\n"; 2529 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2530 if (I->getType()->isInteger()) { 2531 OS << *I; 2532 OS << " --> "; 2533 SCEVHandle SV = getSCEV(&*I); 2534 SV->print(OS); 2535 OS << "\t\t"; 2536 2537 if ((*I).getType()->isIntegral()) { 2538 ConstantRange Bounds = SV->getValueRange(); 2539 if (!Bounds.isFullSet()) 2540 OS << "Bounds: " << Bounds << " "; 2541 } 2542 2543 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2544 OS << "Exits: "; 2545 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2546 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2547 OS << "<<Unknown>>"; 2548 } else { 2549 OS << *ExitValue; 2550 } 2551 } 2552 2553 2554 OS << "\n"; 2555 } 2556 2557 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2558 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2559 PrintLoopInfo(OS, this, *I); 2560} 2561 2562