ScalarEvolution.cpp revision e8019bb1fc46069109dadd5b1c48e86a912bf990
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#define DEBUG_TYPE "scalar-evolution" 63#include "llvm/Analysis/ScalarEvolutionExpressions.h" 64#include "llvm/Constants.h" 65#include "llvm/DerivedTypes.h" 66#include "llvm/GlobalVariable.h" 67#include "llvm/Instructions.h" 68#include "llvm/Analysis/ConstantFolding.h" 69#include "llvm/Analysis/LoopInfo.h" 70#include "llvm/Assembly/Writer.h" 71#include "llvm/Transforms/Scalar.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/InstIterator.h" 77#include "llvm/Support/ManagedStatic.h" 78#include "llvm/Support/MathExtras.h" 79#include "llvm/Support/Streams.h" 80#include "llvm/ADT/Statistic.h" 81#include <ostream> 82#include <algorithm> 83#include <cmath> 84using namespace llvm; 85 86STATISTIC(NumBruteForceEvaluations, 87 "Number of brute force evaluations needed to " 88 "calculate high-order polynomial exit values"); 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant derived loop"), 102 cl::init(100)); 103 104namespace { 105 RegisterPass<ScalarEvolution> 106 R("scalar-evolution", "Scalar Evolution Analysis"); 107} 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116SCEV::~SCEV() {} 117void SCEV::dump() const { 118 print(cerr); 119} 120 121/// getValueRange - Return the tightest constant bounds that this value is 122/// known to have. This method is only valid on integer SCEV objects. 123ConstantRange SCEV::getValueRange() const { 124 const Type *Ty = getType(); 125 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 126 // Default to a full range if no better information is available. 127 return ConstantRange(getBitWidth()); 128} 129 130uint32_t SCEV::getBitWidth() const { 131 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 132 return ITy->getBitWidth(); 133 return 0; 134} 135 136 137SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 138 139bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 141 return false; 142} 143 144const Type *SCEVCouldNotCompute::getType() const { 145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 146 return 0; 147} 148 149bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 151 return false; 152} 153 154SCEVHandle SCEVCouldNotCompute:: 155replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 156 const SCEVHandle &Conc) const { 157 return this; 158} 159 160void SCEVCouldNotCompute::print(std::ostream &OS) const { 161 OS << "***COULDNOTCOMPUTE***"; 162} 163 164bool SCEVCouldNotCompute::classof(const SCEV *S) { 165 return S->getSCEVType() == scCouldNotCompute; 166} 167 168 169// SCEVConstants - Only allow the creation of one SCEVConstant for any 170// particular value. Don't use a SCEVHandle here, or else the object will 171// never be deleted! 172static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 173 174 175SCEVConstant::~SCEVConstant() { 176 SCEVConstants->erase(V); 177} 178 179SCEVHandle SCEVConstant::get(ConstantInt *V) { 180 SCEVConstant *&R = (*SCEVConstants)[V]; 181 if (R == 0) R = new SCEVConstant(V); 182 return R; 183} 184 185ConstantRange SCEVConstant::getValueRange() const { 186 return ConstantRange(V->getValue()); 187} 188 189const Type *SCEVConstant::getType() const { return V->getType(); } 190 191void SCEVConstant::print(std::ostream &OS) const { 192 WriteAsOperand(OS, V, false); 193} 194 195// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 196// particular input. Don't use a SCEVHandle here, or else the object will 197// never be deleted! 198static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 199 SCEVTruncateExpr*> > SCEVTruncates; 200 201SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 202 : SCEV(scTruncate), Op(op), Ty(ty) { 203 assert(Op->getType()->isInteger() && Ty->isInteger() && 204 "Cannot truncate non-integer value!"); 205 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 206 && "This is not a truncating conversion!"); 207} 208 209SCEVTruncateExpr::~SCEVTruncateExpr() { 210 SCEVTruncates->erase(std::make_pair(Op, Ty)); 211} 212 213ConstantRange SCEVTruncateExpr::getValueRange() const { 214 return getOperand()->getValueRange().truncate(getBitWidth()); 215} 216 217void SCEVTruncateExpr::print(std::ostream &OS) const { 218 OS << "(truncate " << *Op << " to " << *Ty << ")"; 219} 220 221// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 222// particular input. Don't use a SCEVHandle here, or else the object will never 223// be deleted! 224static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 225 SCEVZeroExtendExpr*> > SCEVZeroExtends; 226 227SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 228 : SCEV(scZeroExtend), Op(op), Ty(ty) { 229 assert(Op->getType()->isInteger() && Ty->isInteger() && 230 "Cannot zero extend non-integer value!"); 231 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 232 && "This is not an extending conversion!"); 233} 234 235SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 236 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 237} 238 239ConstantRange SCEVZeroExtendExpr::getValueRange() const { 240 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 241} 242 243void SCEVZeroExtendExpr::print(std::ostream &OS) const { 244 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 245} 246 247// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 248// particular input. Don't use a SCEVHandle here, or else the object will never 249// be deleted! 250static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 251 SCEVCommutativeExpr*> > SCEVCommExprs; 252 253SCEVCommutativeExpr::~SCEVCommutativeExpr() { 254 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 255 std::vector<SCEV*>(Operands.begin(), 256 Operands.end()))); 257} 258 259void SCEVCommutativeExpr::print(std::ostream &OS) const { 260 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 261 const char *OpStr = getOperationStr(); 262 OS << "(" << *Operands[0]; 263 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 264 OS << OpStr << *Operands[i]; 265 OS << ")"; 266} 267 268SCEVHandle SCEVCommutativeExpr:: 269replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 270 const SCEVHandle &Conc) const { 271 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 272 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 273 if (H != getOperand(i)) { 274 std::vector<SCEVHandle> NewOps; 275 NewOps.reserve(getNumOperands()); 276 for (unsigned j = 0; j != i; ++j) 277 NewOps.push_back(getOperand(j)); 278 NewOps.push_back(H); 279 for (++i; i != e; ++i) 280 NewOps.push_back(getOperand(i)-> 281 replaceSymbolicValuesWithConcrete(Sym, Conc)); 282 283 if (isa<SCEVAddExpr>(this)) 284 return SCEVAddExpr::get(NewOps); 285 else if (isa<SCEVMulExpr>(this)) 286 return SCEVMulExpr::get(NewOps); 287 else 288 assert(0 && "Unknown commutative expr!"); 289 } 290 } 291 return this; 292} 293 294 295// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 296// input. Don't use a SCEVHandle here, or else the object will never be 297// deleted! 298static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 299 SCEVSDivExpr*> > SCEVSDivs; 300 301SCEVSDivExpr::~SCEVSDivExpr() { 302 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 303} 304 305void SCEVSDivExpr::print(std::ostream &OS) const { 306 OS << "(" << *LHS << " /s " << *RHS << ")"; 307} 308 309const Type *SCEVSDivExpr::getType() const { 310 return LHS->getType(); 311} 312 313// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 314// particular input. Don't use a SCEVHandle here, or else the object will never 315// be deleted! 316static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 317 SCEVAddRecExpr*> > SCEVAddRecExprs; 318 319SCEVAddRecExpr::~SCEVAddRecExpr() { 320 SCEVAddRecExprs->erase(std::make_pair(L, 321 std::vector<SCEV*>(Operands.begin(), 322 Operands.end()))); 323} 324 325SCEVHandle SCEVAddRecExpr:: 326replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 327 const SCEVHandle &Conc) const { 328 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 329 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 330 if (H != getOperand(i)) { 331 std::vector<SCEVHandle> NewOps; 332 NewOps.reserve(getNumOperands()); 333 for (unsigned j = 0; j != i; ++j) 334 NewOps.push_back(getOperand(j)); 335 NewOps.push_back(H); 336 for (++i; i != e; ++i) 337 NewOps.push_back(getOperand(i)-> 338 replaceSymbolicValuesWithConcrete(Sym, Conc)); 339 340 return get(NewOps, L); 341 } 342 } 343 return this; 344} 345 346 347bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 348 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 349 // contain L and if the start is invariant. 350 return !QueryLoop->contains(L->getHeader()) && 351 getOperand(0)->isLoopInvariant(QueryLoop); 352} 353 354 355void SCEVAddRecExpr::print(std::ostream &OS) const { 356 OS << "{" << *Operands[0]; 357 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 358 OS << ",+," << *Operands[i]; 359 OS << "}<" << L->getHeader()->getName() + ">"; 360} 361 362// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 363// value. Don't use a SCEVHandle here, or else the object will never be 364// deleted! 365static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 366 367SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 368 369bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 370 // All non-instruction values are loop invariant. All instructions are loop 371 // invariant if they are not contained in the specified loop. 372 if (Instruction *I = dyn_cast<Instruction>(V)) 373 return !L->contains(I->getParent()); 374 return true; 375} 376 377const Type *SCEVUnknown::getType() const { 378 return V->getType(); 379} 380 381void SCEVUnknown::print(std::ostream &OS) const { 382 WriteAsOperand(OS, V, false); 383} 384 385//===----------------------------------------------------------------------===// 386// SCEV Utilities 387//===----------------------------------------------------------------------===// 388 389namespace { 390 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 391 /// than the complexity of the RHS. This comparator is used to canonicalize 392 /// expressions. 393 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 394 bool operator()(SCEV *LHS, SCEV *RHS) { 395 return LHS->getSCEVType() < RHS->getSCEVType(); 396 } 397 }; 398} 399 400/// GroupByComplexity - Given a list of SCEV objects, order them by their 401/// complexity, and group objects of the same complexity together by value. 402/// When this routine is finished, we know that any duplicates in the vector are 403/// consecutive and that complexity is monotonically increasing. 404/// 405/// Note that we go take special precautions to ensure that we get determinstic 406/// results from this routine. In other words, we don't want the results of 407/// this to depend on where the addresses of various SCEV objects happened to 408/// land in memory. 409/// 410static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 411 if (Ops.size() < 2) return; // Noop 412 if (Ops.size() == 2) { 413 // This is the common case, which also happens to be trivially simple. 414 // Special case it. 415 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 416 std::swap(Ops[0], Ops[1]); 417 return; 418 } 419 420 // Do the rough sort by complexity. 421 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 422 423 // Now that we are sorted by complexity, group elements of the same 424 // complexity. Note that this is, at worst, N^2, but the vector is likely to 425 // be extremely short in practice. Note that we take this approach because we 426 // do not want to depend on the addresses of the objects we are grouping. 427 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 428 SCEV *S = Ops[i]; 429 unsigned Complexity = S->getSCEVType(); 430 431 // If there are any objects of the same complexity and same value as this 432 // one, group them. 433 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 434 if (Ops[j] == S) { // Found a duplicate. 435 // Move it to immediately after i'th element. 436 std::swap(Ops[i+1], Ops[j]); 437 ++i; // no need to rescan it. 438 if (i == e-2) return; // Done! 439 } 440 } 441 } 442} 443 444 445 446//===----------------------------------------------------------------------===// 447// Simple SCEV method implementations 448//===----------------------------------------------------------------------===// 449 450/// getIntegerSCEV - Given an integer or FP type, create a constant for the 451/// specified signed integer value and return a SCEV for the constant. 452SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 453 Constant *C; 454 if (Val == 0) 455 C = Constant::getNullValue(Ty); 456 else if (Ty->isFloatingPoint()) 457 C = ConstantFP::get(Ty, Val); 458 else 459 C = ConstantInt::get(Ty, Val); 460 return SCEVUnknown::get(C); 461} 462 463/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 464/// input value to the specified type. If the type must be extended, it is zero 465/// extended. 466static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 467 const Type *SrcTy = V->getType(); 468 assert(SrcTy->isInteger() && Ty->isInteger() && 469 "Cannot truncate or zero extend with non-integer arguments!"); 470 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 471 return V; // No conversion 472 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 473 return SCEVTruncateExpr::get(V, Ty); 474 return SCEVZeroExtendExpr::get(V, Ty); 475} 476 477/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 478/// 479SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 480 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 481 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 482 483 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 484} 485 486/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 487/// 488SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 489 // X - Y --> X + -Y 490 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 491} 492 493 494/// PartialFact - Compute V!/(V-NumSteps)! 495static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 496 // Handle this case efficiently, it is common to have constant iteration 497 // counts while computing loop exit values. 498 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 499 APInt Val = SC->getValue()->getValue(); 500 APInt Result(Val.getBitWidth(), 1); 501 for (; NumSteps; --NumSteps) 502 Result *= Val-(NumSteps-1); 503 return SCEVUnknown::get(ConstantInt::get(V->getType(), Result)); 504 } 505 506 const Type *Ty = V->getType(); 507 if (NumSteps == 0) 508 return SCEVUnknown::getIntegerSCEV(1, Ty); 509 510 SCEVHandle Result = V; 511 for (unsigned i = 1; i != NumSteps; ++i) 512 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 513 SCEVUnknown::getIntegerSCEV(i, Ty))); 514 return Result; 515} 516 517 518/// evaluateAtIteration - Return the value of this chain of recurrences at 519/// the specified iteration number. We can evaluate this recurrence by 520/// multiplying each element in the chain by the binomial coefficient 521/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 522/// 523/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 524/// 525/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 526/// Is the binomial equation safe using modular arithmetic?? 527/// 528SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 529 SCEVHandle Result = getStart(); 530 int Divisor = 1; 531 const Type *Ty = It->getType(); 532 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 533 SCEVHandle BC = PartialFact(It, i); 534 Divisor *= i; 535 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 536 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 537 Result = SCEVAddExpr::get(Result, Val); 538 } 539 return Result; 540} 541 542 543//===----------------------------------------------------------------------===// 544// SCEV Expression folder implementations 545//===----------------------------------------------------------------------===// 546 547SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 548 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 549 return SCEVUnknown::get( 550 ConstantExpr::getTrunc(SC->getValue(), Ty)); 551 552 // If the input value is a chrec scev made out of constants, truncate 553 // all of the constants. 554 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 555 std::vector<SCEVHandle> Operands; 556 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 557 // FIXME: This should allow truncation of other expression types! 558 if (isa<SCEVConstant>(AddRec->getOperand(i))) 559 Operands.push_back(get(AddRec->getOperand(i), Ty)); 560 else 561 break; 562 if (Operands.size() == AddRec->getNumOperands()) 563 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 564 } 565 566 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 567 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 568 return Result; 569} 570 571SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 572 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 573 return SCEVUnknown::get( 574 ConstantExpr::getZExt(SC->getValue(), Ty)); 575 576 // FIXME: If the input value is a chrec scev, and we can prove that the value 577 // did not overflow the old, smaller, value, we can zero extend all of the 578 // operands (often constants). This would allow analysis of something like 579 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 580 581 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 582 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 583 return Result; 584} 585 586// get - Get a canonical add expression, or something simpler if possible. 587SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 588 assert(!Ops.empty() && "Cannot get empty add!"); 589 if (Ops.size() == 1) return Ops[0]; 590 591 // Sort by complexity, this groups all similar expression types together. 592 GroupByComplexity(Ops); 593 594 // If there are any constants, fold them together. 595 unsigned Idx = 0; 596 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 597 ++Idx; 598 assert(Idx < Ops.size()); 599 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 600 // We found two constants, fold them together! 601 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 602 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 603 Ops[0] = SCEVConstant::get(CI); 604 Ops.erase(Ops.begin()+1); // Erase the folded element 605 if (Ops.size() == 1) return Ops[0]; 606 LHSC = cast<SCEVConstant>(Ops[0]); 607 } else { 608 // If we couldn't fold the expression, move to the next constant. Note 609 // that this is impossible to happen in practice because we always 610 // constant fold constant ints to constant ints. 611 ++Idx; 612 } 613 } 614 615 // If we are left with a constant zero being added, strip it off. 616 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 617 Ops.erase(Ops.begin()); 618 --Idx; 619 } 620 } 621 622 if (Ops.size() == 1) return Ops[0]; 623 624 // Okay, check to see if the same value occurs in the operand list twice. If 625 // so, merge them together into an multiply expression. Since we sorted the 626 // list, these values are required to be adjacent. 627 const Type *Ty = Ops[0]->getType(); 628 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 629 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 630 // Found a match, merge the two values into a multiply, and add any 631 // remaining values to the result. 632 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 633 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 634 if (Ops.size() == 2) 635 return Mul; 636 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 637 Ops.push_back(Mul); 638 return SCEVAddExpr::get(Ops); 639 } 640 641 // Okay, now we know the first non-constant operand. If there are add 642 // operands they would be next. 643 if (Idx < Ops.size()) { 644 bool DeletedAdd = false; 645 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 646 // If we have an add, expand the add operands onto the end of the operands 647 // list. 648 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 649 Ops.erase(Ops.begin()+Idx); 650 DeletedAdd = true; 651 } 652 653 // If we deleted at least one add, we added operands to the end of the list, 654 // and they are not necessarily sorted. Recurse to resort and resimplify 655 // any operands we just aquired. 656 if (DeletedAdd) 657 return get(Ops); 658 } 659 660 // Skip over the add expression until we get to a multiply. 661 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 662 ++Idx; 663 664 // If we are adding something to a multiply expression, make sure the 665 // something is not already an operand of the multiply. If so, merge it into 666 // the multiply. 667 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 668 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 669 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 670 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 671 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 672 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 673 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 674 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 675 if (Mul->getNumOperands() != 2) { 676 // If the multiply has more than two operands, we must get the 677 // Y*Z term. 678 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 679 MulOps.erase(MulOps.begin()+MulOp); 680 InnerMul = SCEVMulExpr::get(MulOps); 681 } 682 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 683 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 684 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 685 if (Ops.size() == 2) return OuterMul; 686 if (AddOp < Idx) { 687 Ops.erase(Ops.begin()+AddOp); 688 Ops.erase(Ops.begin()+Idx-1); 689 } else { 690 Ops.erase(Ops.begin()+Idx); 691 Ops.erase(Ops.begin()+AddOp-1); 692 } 693 Ops.push_back(OuterMul); 694 return SCEVAddExpr::get(Ops); 695 } 696 697 // Check this multiply against other multiplies being added together. 698 for (unsigned OtherMulIdx = Idx+1; 699 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 700 ++OtherMulIdx) { 701 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 702 // If MulOp occurs in OtherMul, we can fold the two multiplies 703 // together. 704 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 705 OMulOp != e; ++OMulOp) 706 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 707 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 708 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 709 if (Mul->getNumOperands() != 2) { 710 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 711 MulOps.erase(MulOps.begin()+MulOp); 712 InnerMul1 = SCEVMulExpr::get(MulOps); 713 } 714 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 715 if (OtherMul->getNumOperands() != 2) { 716 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 717 OtherMul->op_end()); 718 MulOps.erase(MulOps.begin()+OMulOp); 719 InnerMul2 = SCEVMulExpr::get(MulOps); 720 } 721 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 722 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 723 if (Ops.size() == 2) return OuterMul; 724 Ops.erase(Ops.begin()+Idx); 725 Ops.erase(Ops.begin()+OtherMulIdx-1); 726 Ops.push_back(OuterMul); 727 return SCEVAddExpr::get(Ops); 728 } 729 } 730 } 731 } 732 733 // If there are any add recurrences in the operands list, see if any other 734 // added values are loop invariant. If so, we can fold them into the 735 // recurrence. 736 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 737 ++Idx; 738 739 // Scan over all recurrences, trying to fold loop invariants into them. 740 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 741 // Scan all of the other operands to this add and add them to the vector if 742 // they are loop invariant w.r.t. the recurrence. 743 std::vector<SCEVHandle> LIOps; 744 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 745 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 746 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 747 LIOps.push_back(Ops[i]); 748 Ops.erase(Ops.begin()+i); 749 --i; --e; 750 } 751 752 // If we found some loop invariants, fold them into the recurrence. 753 if (!LIOps.empty()) { 754 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 755 LIOps.push_back(AddRec->getStart()); 756 757 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 758 AddRecOps[0] = SCEVAddExpr::get(LIOps); 759 760 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 761 // If all of the other operands were loop invariant, we are done. 762 if (Ops.size() == 1) return NewRec; 763 764 // Otherwise, add the folded AddRec by the non-liv parts. 765 for (unsigned i = 0;; ++i) 766 if (Ops[i] == AddRec) { 767 Ops[i] = NewRec; 768 break; 769 } 770 return SCEVAddExpr::get(Ops); 771 } 772 773 // Okay, if there weren't any loop invariants to be folded, check to see if 774 // there are multiple AddRec's with the same loop induction variable being 775 // added together. If so, we can fold them. 776 for (unsigned OtherIdx = Idx+1; 777 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 778 if (OtherIdx != Idx) { 779 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 780 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 781 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 782 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 783 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 784 if (i >= NewOps.size()) { 785 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 786 OtherAddRec->op_end()); 787 break; 788 } 789 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 790 } 791 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 792 793 if (Ops.size() == 2) return NewAddRec; 794 795 Ops.erase(Ops.begin()+Idx); 796 Ops.erase(Ops.begin()+OtherIdx-1); 797 Ops.push_back(NewAddRec); 798 return SCEVAddExpr::get(Ops); 799 } 800 } 801 802 // Otherwise couldn't fold anything into this recurrence. Move onto the 803 // next one. 804 } 805 806 // Okay, it looks like we really DO need an add expr. Check to see if we 807 // already have one, otherwise create a new one. 808 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 809 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 810 SCEVOps)]; 811 if (Result == 0) Result = new SCEVAddExpr(Ops); 812 return Result; 813} 814 815 816SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 817 assert(!Ops.empty() && "Cannot get empty mul!"); 818 819 // Sort by complexity, this groups all similar expression types together. 820 GroupByComplexity(Ops); 821 822 // If there are any constants, fold them together. 823 unsigned Idx = 0; 824 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 825 826 // C1*(C2+V) -> C1*C2 + C1*V 827 if (Ops.size() == 2) 828 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 829 if (Add->getNumOperands() == 2 && 830 isa<SCEVConstant>(Add->getOperand(0))) 831 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 832 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 833 834 835 ++Idx; 836 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 837 // We found two constants, fold them together! 838 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 839 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 840 Ops[0] = SCEVConstant::get(CI); 841 Ops.erase(Ops.begin()+1); // Erase the folded element 842 if (Ops.size() == 1) return Ops[0]; 843 LHSC = cast<SCEVConstant>(Ops[0]); 844 } else { 845 // If we couldn't fold the expression, move to the next constant. Note 846 // that this is impossible to happen in practice because we always 847 // constant fold constant ints to constant ints. 848 ++Idx; 849 } 850 } 851 852 // If we are left with a constant one being multiplied, strip it off. 853 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 854 Ops.erase(Ops.begin()); 855 --Idx; 856 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 857 // If we have a multiply of zero, it will always be zero. 858 return Ops[0]; 859 } 860 } 861 862 // Skip over the add expression until we get to a multiply. 863 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 864 ++Idx; 865 866 if (Ops.size() == 1) 867 return Ops[0]; 868 869 // If there are mul operands inline them all into this expression. 870 if (Idx < Ops.size()) { 871 bool DeletedMul = false; 872 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 873 // If we have an mul, expand the mul operands onto the end of the operands 874 // list. 875 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 876 Ops.erase(Ops.begin()+Idx); 877 DeletedMul = true; 878 } 879 880 // If we deleted at least one mul, we added operands to the end of the list, 881 // and they are not necessarily sorted. Recurse to resort and resimplify 882 // any operands we just aquired. 883 if (DeletedMul) 884 return get(Ops); 885 } 886 887 // If there are any add recurrences in the operands list, see if any other 888 // added values are loop invariant. If so, we can fold them into the 889 // recurrence. 890 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 891 ++Idx; 892 893 // Scan over all recurrences, trying to fold loop invariants into them. 894 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 895 // Scan all of the other operands to this mul and add them to the vector if 896 // they are loop invariant w.r.t. the recurrence. 897 std::vector<SCEVHandle> LIOps; 898 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 899 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 900 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 901 LIOps.push_back(Ops[i]); 902 Ops.erase(Ops.begin()+i); 903 --i; --e; 904 } 905 906 // If we found some loop invariants, fold them into the recurrence. 907 if (!LIOps.empty()) { 908 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 909 std::vector<SCEVHandle> NewOps; 910 NewOps.reserve(AddRec->getNumOperands()); 911 if (LIOps.size() == 1) { 912 SCEV *Scale = LIOps[0]; 913 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 914 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 915 } else { 916 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 917 std::vector<SCEVHandle> MulOps(LIOps); 918 MulOps.push_back(AddRec->getOperand(i)); 919 NewOps.push_back(SCEVMulExpr::get(MulOps)); 920 } 921 } 922 923 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 924 925 // If all of the other operands were loop invariant, we are done. 926 if (Ops.size() == 1) return NewRec; 927 928 // Otherwise, multiply the folded AddRec by the non-liv parts. 929 for (unsigned i = 0;; ++i) 930 if (Ops[i] == AddRec) { 931 Ops[i] = NewRec; 932 break; 933 } 934 return SCEVMulExpr::get(Ops); 935 } 936 937 // Okay, if there weren't any loop invariants to be folded, check to see if 938 // there are multiple AddRec's with the same loop induction variable being 939 // multiplied together. If so, we can fold them. 940 for (unsigned OtherIdx = Idx+1; 941 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 942 if (OtherIdx != Idx) { 943 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 944 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 945 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 946 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 947 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 948 G->getStart()); 949 SCEVHandle B = F->getStepRecurrence(); 950 SCEVHandle D = G->getStepRecurrence(); 951 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 952 SCEVMulExpr::get(G, B), 953 SCEVMulExpr::get(B, D)); 954 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 955 F->getLoop()); 956 if (Ops.size() == 2) return NewAddRec; 957 958 Ops.erase(Ops.begin()+Idx); 959 Ops.erase(Ops.begin()+OtherIdx-1); 960 Ops.push_back(NewAddRec); 961 return SCEVMulExpr::get(Ops); 962 } 963 } 964 965 // Otherwise couldn't fold anything into this recurrence. Move onto the 966 // next one. 967 } 968 969 // Okay, it looks like we really DO need an mul expr. Check to see if we 970 // already have one, otherwise create a new one. 971 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 972 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 973 SCEVOps)]; 974 if (Result == 0) 975 Result = new SCEVMulExpr(Ops); 976 return Result; 977} 978 979SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 980 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 981 if (RHSC->getValue()->equalsInt(1)) 982 return LHS; // X sdiv 1 --> x 983 if (RHSC->getValue()->isAllOnesValue()) 984 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 985 986 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 987 Constant *LHSCV = LHSC->getValue(); 988 Constant *RHSCV = RHSC->getValue(); 989 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 990 } 991 } 992 993 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 994 995 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 996 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 997 return Result; 998} 999 1000 1001/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1002/// specified loop. Simplify the expression as much as possible. 1003SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1004 const SCEVHandle &Step, const Loop *L) { 1005 std::vector<SCEVHandle> Operands; 1006 Operands.push_back(Start); 1007 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1008 if (StepChrec->getLoop() == L) { 1009 Operands.insert(Operands.end(), StepChrec->op_begin(), 1010 StepChrec->op_end()); 1011 return get(Operands, L); 1012 } 1013 1014 Operands.push_back(Step); 1015 return get(Operands, L); 1016} 1017 1018/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1019/// specified loop. Simplify the expression as much as possible. 1020SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1021 const Loop *L) { 1022 if (Operands.size() == 1) return Operands[0]; 1023 1024 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1025 if (StepC->getValue()->isNullValue()) { 1026 Operands.pop_back(); 1027 return get(Operands, L); // { X,+,0 } --> X 1028 } 1029 1030 SCEVAddRecExpr *&Result = 1031 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1032 Operands.end()))]; 1033 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1034 return Result; 1035} 1036 1037SCEVHandle SCEVUnknown::get(Value *V) { 1038 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1039 return SCEVConstant::get(CI); 1040 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1041 if (Result == 0) Result = new SCEVUnknown(V); 1042 return Result; 1043} 1044 1045 1046//===----------------------------------------------------------------------===// 1047// ScalarEvolutionsImpl Definition and Implementation 1048//===----------------------------------------------------------------------===// 1049// 1050/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1051/// evolution code. 1052/// 1053namespace { 1054 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1055 /// F - The function we are analyzing. 1056 /// 1057 Function &F; 1058 1059 /// LI - The loop information for the function we are currently analyzing. 1060 /// 1061 LoopInfo &LI; 1062 1063 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1064 /// things. 1065 SCEVHandle UnknownValue; 1066 1067 /// Scalars - This is a cache of the scalars we have analyzed so far. 1068 /// 1069 std::map<Value*, SCEVHandle> Scalars; 1070 1071 /// IterationCounts - Cache the iteration count of the loops for this 1072 /// function as they are computed. 1073 std::map<const Loop*, SCEVHandle> IterationCounts; 1074 1075 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1076 /// the PHI instructions that we attempt to compute constant evolutions for. 1077 /// This allows us to avoid potentially expensive recomputation of these 1078 /// properties. An instruction maps to null if we are unable to compute its 1079 /// exit value. 1080 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1081 1082 public: 1083 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1084 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1085 1086 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1087 /// expression and create a new one. 1088 SCEVHandle getSCEV(Value *V); 1089 1090 /// hasSCEV - Return true if the SCEV for this value has already been 1091 /// computed. 1092 bool hasSCEV(Value *V) const { 1093 return Scalars.count(V); 1094 } 1095 1096 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1097 /// the specified value. 1098 void setSCEV(Value *V, const SCEVHandle &H) { 1099 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1100 assert(isNew && "This entry already existed!"); 1101 } 1102 1103 1104 /// getSCEVAtScope - Compute the value of the specified expression within 1105 /// the indicated loop (which may be null to indicate in no loop). If the 1106 /// expression cannot be evaluated, return UnknownValue itself. 1107 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1108 1109 1110 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1111 /// an analyzable loop-invariant iteration count. 1112 bool hasLoopInvariantIterationCount(const Loop *L); 1113 1114 /// getIterationCount - If the specified loop has a predictable iteration 1115 /// count, return it. Note that it is not valid to call this method on a 1116 /// loop without a loop-invariant iteration count. 1117 SCEVHandle getIterationCount(const Loop *L); 1118 1119 /// deleteInstructionFromRecords - This method should be called by the 1120 /// client before it removes an instruction from the program, to make sure 1121 /// that no dangling references are left around. 1122 void deleteInstructionFromRecords(Instruction *I); 1123 1124 private: 1125 /// createSCEV - We know that there is no SCEV for the specified value. 1126 /// Analyze the expression. 1127 SCEVHandle createSCEV(Value *V); 1128 1129 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1130 /// SCEVs. 1131 SCEVHandle createNodeForPHI(PHINode *PN); 1132 1133 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1134 /// for the specified instruction and replaces any references to the 1135 /// symbolic value SymName with the specified value. This is used during 1136 /// PHI resolution. 1137 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1138 const SCEVHandle &SymName, 1139 const SCEVHandle &NewVal); 1140 1141 /// ComputeIterationCount - Compute the number of times the specified loop 1142 /// will iterate. 1143 SCEVHandle ComputeIterationCount(const Loop *L); 1144 1145 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1146 /// 'setcc load X, cst', try to se if we can compute the trip count. 1147 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1148 Constant *RHS, 1149 const Loop *L, 1150 ICmpInst::Predicate p); 1151 1152 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1153 /// constant number of times (the condition evolves only from constants), 1154 /// try to evaluate a few iterations of the loop until we get the exit 1155 /// condition gets a value of ExitWhen (true or false). If we cannot 1156 /// evaluate the trip count of the loop, return UnknownValue. 1157 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1158 bool ExitWhen); 1159 1160 /// HowFarToZero - Return the number of times a backedge comparing the 1161 /// specified value to zero will execute. If not computable, return 1162 /// UnknownValue. 1163 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1164 1165 /// HowFarToNonZero - Return the number of times a backedge checking the 1166 /// specified value for nonzero will execute. If not computable, return 1167 /// UnknownValue. 1168 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1169 1170 /// HowManyLessThans - Return the number of times a backedge containing the 1171 /// specified less-than comparison will execute. If not computable, return 1172 /// UnknownValue. 1173 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L); 1174 1175 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1176 /// in the header of its containing loop, we know the loop executes a 1177 /// constant number of times, and the PHI node is just a recurrence 1178 /// involving constants, fold it. 1179 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1180 const Loop *L); 1181 }; 1182} 1183 1184//===----------------------------------------------------------------------===// 1185// Basic SCEV Analysis and PHI Idiom Recognition Code 1186// 1187 1188/// deleteInstructionFromRecords - This method should be called by the 1189/// client before it removes an instruction from the program, to make sure 1190/// that no dangling references are left around. 1191void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1192 Scalars.erase(I); 1193 if (PHINode *PN = dyn_cast<PHINode>(I)) 1194 ConstantEvolutionLoopExitValue.erase(PN); 1195} 1196 1197 1198/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1199/// expression and create a new one. 1200SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1201 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1202 1203 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1204 if (I != Scalars.end()) return I->second; 1205 SCEVHandle S = createSCEV(V); 1206 Scalars.insert(std::make_pair(V, S)); 1207 return S; 1208} 1209 1210/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1211/// the specified instruction and replaces any references to the symbolic value 1212/// SymName with the specified value. This is used during PHI resolution. 1213void ScalarEvolutionsImpl:: 1214ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1215 const SCEVHandle &NewVal) { 1216 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1217 if (SI == Scalars.end()) return; 1218 1219 SCEVHandle NV = 1220 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1221 if (NV == SI->second) return; // No change. 1222 1223 SI->second = NV; // Update the scalars map! 1224 1225 // Any instruction values that use this instruction might also need to be 1226 // updated! 1227 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1228 UI != E; ++UI) 1229 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1230} 1231 1232/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1233/// a loop header, making it a potential recurrence, or it doesn't. 1234/// 1235SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1236 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1237 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1238 if (L->getHeader() == PN->getParent()) { 1239 // If it lives in the loop header, it has two incoming values, one 1240 // from outside the loop, and one from inside. 1241 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1242 unsigned BackEdge = IncomingEdge^1; 1243 1244 // While we are analyzing this PHI node, handle its value symbolically. 1245 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1246 assert(Scalars.find(PN) == Scalars.end() && 1247 "PHI node already processed?"); 1248 Scalars.insert(std::make_pair(PN, SymbolicName)); 1249 1250 // Using this symbolic name for the PHI, analyze the value coming around 1251 // the back-edge. 1252 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1253 1254 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1255 // has a special value for the first iteration of the loop. 1256 1257 // If the value coming around the backedge is an add with the symbolic 1258 // value we just inserted, then we found a simple induction variable! 1259 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1260 // If there is a single occurrence of the symbolic value, replace it 1261 // with a recurrence. 1262 unsigned FoundIndex = Add->getNumOperands(); 1263 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1264 if (Add->getOperand(i) == SymbolicName) 1265 if (FoundIndex == e) { 1266 FoundIndex = i; 1267 break; 1268 } 1269 1270 if (FoundIndex != Add->getNumOperands()) { 1271 // Create an add with everything but the specified operand. 1272 std::vector<SCEVHandle> Ops; 1273 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1274 if (i != FoundIndex) 1275 Ops.push_back(Add->getOperand(i)); 1276 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1277 1278 // This is not a valid addrec if the step amount is varying each 1279 // loop iteration, but is not itself an addrec in this loop. 1280 if (Accum->isLoopInvariant(L) || 1281 (isa<SCEVAddRecExpr>(Accum) && 1282 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1283 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1284 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1285 1286 // Okay, for the entire analysis of this edge we assumed the PHI 1287 // to be symbolic. We now need to go back and update all of the 1288 // entries for the scalars that use the PHI (except for the PHI 1289 // itself) to use the new analyzed value instead of the "symbolic" 1290 // value. 1291 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1292 return PHISCEV; 1293 } 1294 } 1295 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1296 // Otherwise, this could be a loop like this: 1297 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1298 // In this case, j = {1,+,1} and BEValue is j. 1299 // Because the other in-value of i (0) fits the evolution of BEValue 1300 // i really is an addrec evolution. 1301 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1302 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1303 1304 // If StartVal = j.start - j.stride, we can use StartVal as the 1305 // initial step of the addrec evolution. 1306 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1307 AddRec->getOperand(1))) { 1308 SCEVHandle PHISCEV = 1309 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1310 1311 // Okay, for the entire analysis of this edge we assumed the PHI 1312 // to be symbolic. We now need to go back and update all of the 1313 // entries for the scalars that use the PHI (except for the PHI 1314 // itself) to use the new analyzed value instead of the "symbolic" 1315 // value. 1316 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1317 return PHISCEV; 1318 } 1319 } 1320 } 1321 1322 return SymbolicName; 1323 } 1324 1325 // If it's not a loop phi, we can't handle it yet. 1326 return SCEVUnknown::get(PN); 1327} 1328 1329/// GetConstantFactor - Determine the largest constant factor that S has. For 1330/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1331static APInt GetConstantFactor(SCEVHandle S) { 1332 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1333 APInt V = C->getValue()->getValue(); 1334 if (!V.isMinValue()) 1335 return V; 1336 else // Zero is a multiple of everything. 1337 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1); 1338 } 1339 1340 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1341 return GetConstantFactor(T->getOperand()) & 1342 cast<IntegerType>(T->getType())->getMask(); 1343 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1344 return GetConstantFactor(E->getOperand()); 1345 1346 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1347 // The result is the min of all operands. 1348 APInt Res = GetConstantFactor(A->getOperand(0)); 1349 for (unsigned i = 1, e = A->getNumOperands(); 1350 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) 1351 Res = APIntOps::umin(Res, GetConstantFactor(A->getOperand(i))); 1352 return Res; 1353 } 1354 1355 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1356 // The result is the product of all the operands. 1357 APInt Res = GetConstantFactor(M->getOperand(0)); 1358 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) 1359 Res *= GetConstantFactor(M->getOperand(i)); 1360 return Res; 1361 } 1362 1363 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1364 // For now, we just handle linear expressions. 1365 if (A->getNumOperands() == 2) { 1366 // We want the GCD between the start and the stride value. 1367 APInt Start = GetConstantFactor(A->getOperand(0)); 1368 if (Start == 1) 1369 return APInt(A->getBitWidth(),1); 1370 APInt Stride = GetConstantFactor(A->getOperand(1)); 1371 return APIntOps::GreatestCommonDivisor(Start, Stride); 1372 } 1373 } 1374 1375 // SCEVSDivExpr, SCEVUnknown. 1376 return APInt(S->getBitWidth(), 1); 1377} 1378 1379/// createSCEV - We know that there is no SCEV for the specified value. 1380/// Analyze the expression. 1381/// 1382SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1383 if (Instruction *I = dyn_cast<Instruction>(V)) { 1384 switch (I->getOpcode()) { 1385 case Instruction::Add: 1386 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1387 getSCEV(I->getOperand(1))); 1388 case Instruction::Mul: 1389 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1390 getSCEV(I->getOperand(1))); 1391 case Instruction::SDiv: 1392 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1393 getSCEV(I->getOperand(1))); 1394 break; 1395 1396 case Instruction::Sub: 1397 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1398 getSCEV(I->getOperand(1))); 1399 case Instruction::Or: 1400 // If the RHS of the Or is a constant, we may have something like: 1401 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1402 // optimizations will transparently handle this case. 1403 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1404 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1405 APInt CommonFact = GetConstantFactor(LHS); 1406 assert(!CommonFact.isMinValue() && 1407 "Common factor should at least be 1!"); 1408 if (CommonFact.ugt(CI->getValue())) { 1409 // If the LHS is a multiple that is larger than the RHS, use +. 1410 return SCEVAddExpr::get(LHS, 1411 getSCEV(I->getOperand(1))); 1412 } 1413 } 1414 break; 1415 1416 case Instruction::Shl: 1417 // Turn shift left of a constant amount into a multiply. 1418 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1419 Constant *X = ConstantInt::get(V->getType(), 1); 1420 X = ConstantExpr::getShl(X, SA); 1421 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1422 } 1423 break; 1424 1425 case Instruction::Trunc: 1426 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1427 1428 case Instruction::ZExt: 1429 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1430 1431 case Instruction::BitCast: 1432 // BitCasts are no-op casts so we just eliminate the cast. 1433 if (I->getType()->isInteger() && 1434 I->getOperand(0)->getType()->isInteger()) 1435 return getSCEV(I->getOperand(0)); 1436 break; 1437 1438 case Instruction::PHI: 1439 return createNodeForPHI(cast<PHINode>(I)); 1440 1441 default: // We cannot analyze this expression. 1442 break; 1443 } 1444 } 1445 1446 return SCEVUnknown::get(V); 1447} 1448 1449 1450 1451//===----------------------------------------------------------------------===// 1452// Iteration Count Computation Code 1453// 1454 1455/// getIterationCount - If the specified loop has a predictable iteration 1456/// count, return it. Note that it is not valid to call this method on a 1457/// loop without a loop-invariant iteration count. 1458SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1459 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1460 if (I == IterationCounts.end()) { 1461 SCEVHandle ItCount = ComputeIterationCount(L); 1462 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1463 if (ItCount != UnknownValue) { 1464 assert(ItCount->isLoopInvariant(L) && 1465 "Computed trip count isn't loop invariant for loop!"); 1466 ++NumTripCountsComputed; 1467 } else if (isa<PHINode>(L->getHeader()->begin())) { 1468 // Only count loops that have phi nodes as not being computable. 1469 ++NumTripCountsNotComputed; 1470 } 1471 } 1472 return I->second; 1473} 1474 1475/// ComputeIterationCount - Compute the number of times the specified loop 1476/// will iterate. 1477SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1478 // If the loop has a non-one exit block count, we can't analyze it. 1479 std::vector<BasicBlock*> ExitBlocks; 1480 L->getExitBlocks(ExitBlocks); 1481 if (ExitBlocks.size() != 1) return UnknownValue; 1482 1483 // Okay, there is one exit block. Try to find the condition that causes the 1484 // loop to be exited. 1485 BasicBlock *ExitBlock = ExitBlocks[0]; 1486 1487 BasicBlock *ExitingBlock = 0; 1488 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1489 PI != E; ++PI) 1490 if (L->contains(*PI)) { 1491 if (ExitingBlock == 0) 1492 ExitingBlock = *PI; 1493 else 1494 return UnknownValue; // More than one block exiting! 1495 } 1496 assert(ExitingBlock && "No exits from loop, something is broken!"); 1497 1498 // Okay, we've computed the exiting block. See what condition causes us to 1499 // exit. 1500 // 1501 // FIXME: we should be able to handle switch instructions (with a single exit) 1502 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1503 if (ExitBr == 0) return UnknownValue; 1504 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1505 1506 // At this point, we know we have a conditional branch that determines whether 1507 // the loop is exited. However, we don't know if the branch is executed each 1508 // time through the loop. If not, then the execution count of the branch will 1509 // not be equal to the trip count of the loop. 1510 // 1511 // Currently we check for this by checking to see if the Exit branch goes to 1512 // the loop header. If so, we know it will always execute the same number of 1513 // times as the loop. We also handle the case where the exit block *is* the 1514 // loop header. This is common for un-rotated loops. More extensive analysis 1515 // could be done to handle more cases here. 1516 if (ExitBr->getSuccessor(0) != L->getHeader() && 1517 ExitBr->getSuccessor(1) != L->getHeader() && 1518 ExitBr->getParent() != L->getHeader()) 1519 return UnknownValue; 1520 1521 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1522 1523 // If its not an integer comparison then compute it the hard way. 1524 // Note that ICmpInst deals with pointer comparisons too so we must check 1525 // the type of the operand. 1526 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1527 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1528 ExitBr->getSuccessor(0) == ExitBlock); 1529 1530 // If the condition was exit on true, convert the condition to exit on false 1531 ICmpInst::Predicate Cond; 1532 if (ExitBr->getSuccessor(1) == ExitBlock) 1533 Cond = ExitCond->getPredicate(); 1534 else 1535 Cond = ExitCond->getInversePredicate(); 1536 1537 // Handle common loops like: for (X = "string"; *X; ++X) 1538 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1539 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1540 SCEVHandle ItCnt = 1541 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1542 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1543 } 1544 1545 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1546 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1547 1548 // Try to evaluate any dependencies out of the loop. 1549 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1550 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1551 Tmp = getSCEVAtScope(RHS, L); 1552 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1553 1554 // At this point, we would like to compute how many iterations of the 1555 // loop the predicate will return true for these inputs. 1556 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1557 // If there is a constant, force it into the RHS. 1558 std::swap(LHS, RHS); 1559 Cond = ICmpInst::getSwappedPredicate(Cond); 1560 } 1561 1562 // FIXME: think about handling pointer comparisons! i.e.: 1563 // while (P != P+100) ++P; 1564 1565 // If we have a comparison of a chrec against a constant, try to use value 1566 // ranges to answer this query. 1567 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1568 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1569 if (AddRec->getLoop() == L) { 1570 // Form the comparison range using the constant of the correct type so 1571 // that the ConstantRange class knows to do a signed or unsigned 1572 // comparison. 1573 ConstantInt *CompVal = RHSC->getValue(); 1574 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1575 CompVal = dyn_cast<ConstantInt>( 1576 ConstantExpr::getBitCast(CompVal, RealTy)); 1577 if (CompVal) { 1578 // Form the constant range. 1579 ConstantRange CompRange( 1580 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1581 1582 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, 1583 false /*Always treat as unsigned range*/); 1584 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1585 } 1586 } 1587 1588 switch (Cond) { 1589 case ICmpInst::ICMP_NE: { // while (X != Y) 1590 // Convert to: while (X-Y != 0) 1591 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1592 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1593 break; 1594 } 1595 case ICmpInst::ICMP_EQ: { 1596 // Convert to: while (X-Y == 0) // while (X == Y) 1597 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1598 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1599 break; 1600 } 1601 case ICmpInst::ICMP_SLT: { 1602 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1603 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1604 break; 1605 } 1606 case ICmpInst::ICMP_SGT: { 1607 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1608 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1609 break; 1610 } 1611 default: 1612#if 0 1613 cerr << "ComputeIterationCount "; 1614 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1615 cerr << "[unsigned] "; 1616 cerr << *LHS << " " 1617 << Instruction::getOpcodeName(Instruction::ICmp) 1618 << " " << *RHS << "\n"; 1619#endif 1620 break; 1621 } 1622 return ComputeIterationCountExhaustively(L, ExitCond, 1623 ExitBr->getSuccessor(0) == ExitBlock); 1624} 1625 1626static ConstantInt * 1627EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1628 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1629 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1630 assert(isa<SCEVConstant>(Val) && 1631 "Evaluation of SCEV at constant didn't fold correctly?"); 1632 return cast<SCEVConstant>(Val)->getValue(); 1633} 1634 1635/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1636/// and a GEP expression (missing the pointer index) indexing into it, return 1637/// the addressed element of the initializer or null if the index expression is 1638/// invalid. 1639static Constant * 1640GetAddressedElementFromGlobal(GlobalVariable *GV, 1641 const std::vector<ConstantInt*> &Indices) { 1642 Constant *Init = GV->getInitializer(); 1643 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1644 uint64_t Idx = Indices[i]->getZExtValue(); 1645 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1646 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1647 Init = cast<Constant>(CS->getOperand(Idx)); 1648 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1649 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1650 Init = cast<Constant>(CA->getOperand(Idx)); 1651 } else if (isa<ConstantAggregateZero>(Init)) { 1652 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1653 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1654 Init = Constant::getNullValue(STy->getElementType(Idx)); 1655 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1656 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1657 Init = Constant::getNullValue(ATy->getElementType()); 1658 } else { 1659 assert(0 && "Unknown constant aggregate type!"); 1660 } 1661 return 0; 1662 } else { 1663 return 0; // Unknown initializer type 1664 } 1665 } 1666 return Init; 1667} 1668 1669/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1670/// 'setcc load X, cst', try to se if we can compute the trip count. 1671SCEVHandle ScalarEvolutionsImpl:: 1672ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1673 const Loop *L, 1674 ICmpInst::Predicate predicate) { 1675 if (LI->isVolatile()) return UnknownValue; 1676 1677 // Check to see if the loaded pointer is a getelementptr of a global. 1678 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1679 if (!GEP) return UnknownValue; 1680 1681 // Make sure that it is really a constant global we are gepping, with an 1682 // initializer, and make sure the first IDX is really 0. 1683 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1684 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1685 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1686 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1687 return UnknownValue; 1688 1689 // Okay, we allow one non-constant index into the GEP instruction. 1690 Value *VarIdx = 0; 1691 std::vector<ConstantInt*> Indexes; 1692 unsigned VarIdxNum = 0; 1693 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1694 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1695 Indexes.push_back(CI); 1696 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1697 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1698 VarIdx = GEP->getOperand(i); 1699 VarIdxNum = i-2; 1700 Indexes.push_back(0); 1701 } 1702 1703 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1704 // Check to see if X is a loop variant variable value now. 1705 SCEVHandle Idx = getSCEV(VarIdx); 1706 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1707 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1708 1709 // We can only recognize very limited forms of loop index expressions, in 1710 // particular, only affine AddRec's like {C1,+,C2}. 1711 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1712 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1713 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1714 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1715 return UnknownValue; 1716 1717 unsigned MaxSteps = MaxBruteForceIterations; 1718 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1719 ConstantInt *ItCst = 1720 ConstantInt::get(IdxExpr->getType(), IterationNum); 1721 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1722 1723 // Form the GEP offset. 1724 Indexes[VarIdxNum] = Val; 1725 1726 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1727 if (Result == 0) break; // Cannot compute! 1728 1729 // Evaluate the condition for this iteration. 1730 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1731 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1732 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 1733#if 0 1734 cerr << "\n***\n*** Computed loop count " << *ItCst 1735 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1736 << "***\n"; 1737#endif 1738 ++NumArrayLenItCounts; 1739 return SCEVConstant::get(ItCst); // Found terminating iteration! 1740 } 1741 } 1742 return UnknownValue; 1743} 1744 1745 1746/// CanConstantFold - Return true if we can constant fold an instruction of the 1747/// specified type, assuming that all operands were constants. 1748static bool CanConstantFold(const Instruction *I) { 1749 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 1750 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1751 return true; 1752 1753 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1754 if (const Function *F = CI->getCalledFunction()) 1755 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1756 return false; 1757} 1758 1759/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1760/// in the loop that V is derived from. We allow arbitrary operations along the 1761/// way, but the operands of an operation must either be constants or a value 1762/// derived from a constant PHI. If this expression does not fit with these 1763/// constraints, return null. 1764static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1765 // If this is not an instruction, or if this is an instruction outside of the 1766 // loop, it can't be derived from a loop PHI. 1767 Instruction *I = dyn_cast<Instruction>(V); 1768 if (I == 0 || !L->contains(I->getParent())) return 0; 1769 1770 if (PHINode *PN = dyn_cast<PHINode>(I)) 1771 if (L->getHeader() == I->getParent()) 1772 return PN; 1773 else 1774 // We don't currently keep track of the control flow needed to evaluate 1775 // PHIs, so we cannot handle PHIs inside of loops. 1776 return 0; 1777 1778 // If we won't be able to constant fold this expression even if the operands 1779 // are constants, return early. 1780 if (!CanConstantFold(I)) return 0; 1781 1782 // Otherwise, we can evaluate this instruction if all of its operands are 1783 // constant or derived from a PHI node themselves. 1784 PHINode *PHI = 0; 1785 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1786 if (!(isa<Constant>(I->getOperand(Op)) || 1787 isa<GlobalValue>(I->getOperand(Op)))) { 1788 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1789 if (P == 0) return 0; // Not evolving from PHI 1790 if (PHI == 0) 1791 PHI = P; 1792 else if (PHI != P) 1793 return 0; // Evolving from multiple different PHIs. 1794 } 1795 1796 // This is a expression evolving from a constant PHI! 1797 return PHI; 1798} 1799 1800/// EvaluateExpression - Given an expression that passes the 1801/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1802/// in the loop has the value PHIVal. If we can't fold this expression for some 1803/// reason, return null. 1804static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1805 if (isa<PHINode>(V)) return PHIVal; 1806 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1807 return GV; 1808 if (Constant *C = dyn_cast<Constant>(V)) return C; 1809 Instruction *I = cast<Instruction>(V); 1810 1811 std::vector<Constant*> Operands; 1812 Operands.resize(I->getNumOperands()); 1813 1814 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1815 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1816 if (Operands[i] == 0) return 0; 1817 } 1818 1819 return ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1820} 1821 1822/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1823/// in the header of its containing loop, we know the loop executes a 1824/// constant number of times, and the PHI node is just a recurrence 1825/// involving constants, fold it. 1826Constant *ScalarEvolutionsImpl:: 1827getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 1828 std::map<PHINode*, Constant*>::iterator I = 1829 ConstantEvolutionLoopExitValue.find(PN); 1830 if (I != ConstantEvolutionLoopExitValue.end()) 1831 return I->second; 1832 1833 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 1834 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1835 1836 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1837 1838 // Since the loop is canonicalized, the PHI node must have two entries. One 1839 // entry must be a constant (coming in from outside of the loop), and the 1840 // second must be derived from the same PHI. 1841 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1842 Constant *StartCST = 1843 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1844 if (StartCST == 0) 1845 return RetVal = 0; // Must be a constant. 1846 1847 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1848 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1849 if (PN2 != PN) 1850 return RetVal = 0; // Not derived from same PHI. 1851 1852 // Execute the loop symbolically to determine the exit value. 1853 if (Its.getActiveBits() >= 32) 1854 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 1855 1856 unsigned NumIterations = Its.getZExtValue(); // must be in range 1857 unsigned IterationNum = 0; 1858 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1859 if (IterationNum == NumIterations) 1860 return RetVal = PHIVal; // Got exit value! 1861 1862 // Compute the value of the PHI node for the next iteration. 1863 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1864 if (NextPHI == PHIVal) 1865 return RetVal = NextPHI; // Stopped evolving! 1866 if (NextPHI == 0) 1867 return 0; // Couldn't evaluate! 1868 PHIVal = NextPHI; 1869 } 1870} 1871 1872/// ComputeIterationCountExhaustively - If the trip is known to execute a 1873/// constant number of times (the condition evolves only from constants), 1874/// try to evaluate a few iterations of the loop until we get the exit 1875/// condition gets a value of ExitWhen (true or false). If we cannot 1876/// evaluate the trip count of the loop, return UnknownValue. 1877SCEVHandle ScalarEvolutionsImpl:: 1878ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1879 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1880 if (PN == 0) return UnknownValue; 1881 1882 // Since the loop is canonicalized, the PHI node must have two entries. One 1883 // entry must be a constant (coming in from outside of the loop), and the 1884 // second must be derived from the same PHI. 1885 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1886 Constant *StartCST = 1887 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1888 if (StartCST == 0) return UnknownValue; // Must be a constant. 1889 1890 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1891 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1892 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1893 1894 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1895 // the loop symbolically to determine when the condition gets a value of 1896 // "ExitWhen". 1897 unsigned IterationNum = 0; 1898 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1899 for (Constant *PHIVal = StartCST; 1900 IterationNum != MaxIterations; ++IterationNum) { 1901 ConstantInt *CondVal = 1902 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 1903 1904 // Couldn't symbolically evaluate. 1905 if (!CondVal) return UnknownValue; 1906 1907 if (CondVal->getValue() == uint64_t(ExitWhen)) { 1908 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1909 ++NumBruteForceTripCountsComputed; 1910 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum)); 1911 } 1912 1913 // Compute the value of the PHI node for the next iteration. 1914 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1915 if (NextPHI == 0 || NextPHI == PHIVal) 1916 return UnknownValue; // Couldn't evaluate or not making progress... 1917 PHIVal = NextPHI; 1918 } 1919 1920 // Too many iterations were needed to evaluate. 1921 return UnknownValue; 1922} 1923 1924/// getSCEVAtScope - Compute the value of the specified expression within the 1925/// indicated loop (which may be null to indicate in no loop). If the 1926/// expression cannot be evaluated, return UnknownValue. 1927SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1928 // FIXME: this should be turned into a virtual method on SCEV! 1929 1930 if (isa<SCEVConstant>(V)) return V; 1931 1932 // If this instruction is evolves from a constant-evolving PHI, compute the 1933 // exit value from the loop without using SCEVs. 1934 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1935 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1936 const Loop *LI = this->LI[I->getParent()]; 1937 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1938 if (PHINode *PN = dyn_cast<PHINode>(I)) 1939 if (PN->getParent() == LI->getHeader()) { 1940 // Okay, there is no closed form solution for the PHI node. Check 1941 // to see if the loop that contains it has a known iteration count. 1942 // If so, we may be able to force computation of the exit value. 1943 SCEVHandle IterationCount = getIterationCount(LI); 1944 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1945 // Okay, we know how many times the containing loop executes. If 1946 // this is a constant evolving PHI node, get the final value at 1947 // the specified iteration number. 1948 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1949 ICC->getValue()->getValue(), 1950 LI); 1951 if (RV) return SCEVUnknown::get(RV); 1952 } 1953 } 1954 1955 // Okay, this is an expression that we cannot symbolically evaluate 1956 // into a SCEV. Check to see if it's possible to symbolically evaluate 1957 // the arguments into constants, and if so, try to constant propagate the 1958 // result. This is particularly useful for computing loop exit values. 1959 if (CanConstantFold(I)) { 1960 std::vector<Constant*> Operands; 1961 Operands.reserve(I->getNumOperands()); 1962 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1963 Value *Op = I->getOperand(i); 1964 if (Constant *C = dyn_cast<Constant>(Op)) { 1965 Operands.push_back(C); 1966 } else { 1967 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1968 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1969 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 1970 Op->getType(), 1971 false)); 1972 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1973 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1974 Operands.push_back(ConstantExpr::getIntegerCast(C, 1975 Op->getType(), 1976 false)); 1977 else 1978 return V; 1979 } else { 1980 return V; 1981 } 1982 } 1983 } 1984 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1985 return SCEVUnknown::get(C); 1986 } 1987 } 1988 1989 // This is some other type of SCEVUnknown, just return it. 1990 return V; 1991 } 1992 1993 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1994 // Avoid performing the look-up in the common case where the specified 1995 // expression has no loop-variant portions. 1996 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1997 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1998 if (OpAtScope != Comm->getOperand(i)) { 1999 if (OpAtScope == UnknownValue) return UnknownValue; 2000 // Okay, at least one of these operands is loop variant but might be 2001 // foldable. Build a new instance of the folded commutative expression. 2002 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2003 NewOps.push_back(OpAtScope); 2004 2005 for (++i; i != e; ++i) { 2006 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2007 if (OpAtScope == UnknownValue) return UnknownValue; 2008 NewOps.push_back(OpAtScope); 2009 } 2010 if (isa<SCEVAddExpr>(Comm)) 2011 return SCEVAddExpr::get(NewOps); 2012 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2013 return SCEVMulExpr::get(NewOps); 2014 } 2015 } 2016 // If we got here, all operands are loop invariant. 2017 return Comm; 2018 } 2019 2020 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2021 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2022 if (LHS == UnknownValue) return LHS; 2023 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2024 if (RHS == UnknownValue) return RHS; 2025 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2026 return Div; // must be loop invariant 2027 return SCEVSDivExpr::get(LHS, RHS); 2028 } 2029 2030 // If this is a loop recurrence for a loop that does not contain L, then we 2031 // are dealing with the final value computed by the loop. 2032 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2033 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2034 // To evaluate this recurrence, we need to know how many times the AddRec 2035 // loop iterates. Compute this now. 2036 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2037 if (IterationCount == UnknownValue) return UnknownValue; 2038 IterationCount = getTruncateOrZeroExtend(IterationCount, 2039 AddRec->getType()); 2040 2041 // If the value is affine, simplify the expression evaluation to just 2042 // Start + Step*IterationCount. 2043 if (AddRec->isAffine()) 2044 return SCEVAddExpr::get(AddRec->getStart(), 2045 SCEVMulExpr::get(IterationCount, 2046 AddRec->getOperand(1))); 2047 2048 // Otherwise, evaluate it the hard way. 2049 return AddRec->evaluateAtIteration(IterationCount); 2050 } 2051 return UnknownValue; 2052 } 2053 2054 //assert(0 && "Unknown SCEV type!"); 2055 return UnknownValue; 2056} 2057 2058 2059/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2060/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2061/// might be the same) or two SCEVCouldNotCompute objects. 2062/// 2063static std::pair<SCEVHandle,SCEVHandle> 2064SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2065 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2066 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2067 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2068 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2069 2070 // We currently can only solve this if the coefficients are constants. 2071 if (!LC || !MC || !NC) { 2072 SCEV *CNC = new SCEVCouldNotCompute(); 2073 return std::make_pair(CNC, CNC); 2074 } 2075 2076 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2077 APInt L(LC->getValue()->getValue()); 2078 APInt M(MC->getValue()->getValue()); 2079 APInt N(MC->getValue()->getValue()); 2080 APInt Two(BitWidth, 2); 2081 APInt Four(BitWidth, 4); 2082 2083 { 2084 using namespace APIntOps; 2085 APInt C(L); 2086 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2087 // The B coefficient is M-N/2 2088 APInt B(M); 2089 B -= sdiv(N,Two); 2090 2091 // The A coefficient is N/2 2092 APInt A(N); 2093 A = A.sdiv(Two); 2094 2095 // Compute the B^2-4ac term. 2096 APInt SqrtTerm(B); 2097 SqrtTerm *= B; 2098 SqrtTerm -= Four * (A * C); 2099 2100 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2101 // integer value or else APInt::sqrt() will assert. 2102 APInt SqrtVal(SqrtTerm.sqrt()); 2103 2104 // Compute the two solutions for the quadratic formula. 2105 // The divisions must be performed as signed divisions. 2106 APInt NegB(-B); 2107 APInt TwoA( A * Two ); 2108 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2109 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2110 2111 return std::make_pair(SCEVUnknown::get(Solution1), 2112 SCEVUnknown::get(Solution2)); 2113 } // end APIntOps namespace 2114} 2115 2116/// HowFarToZero - Return the number of times a backedge comparing the specified 2117/// value to zero will execute. If not computable, return UnknownValue 2118SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2119 // If the value is a constant 2120 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2121 // If the value is already zero, the branch will execute zero times. 2122 if (C->getValue()->isNullValue()) return C; 2123 return UnknownValue; // Otherwise it will loop infinitely. 2124 } 2125 2126 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2127 if (!AddRec || AddRec->getLoop() != L) 2128 return UnknownValue; 2129 2130 if (AddRec->isAffine()) { 2131 // If this is an affine expression the execution count of this branch is 2132 // equal to: 2133 // 2134 // (0 - Start/Step) iff Start % Step == 0 2135 // 2136 // Get the initial value for the loop. 2137 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2138 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2139 SCEVHandle Step = AddRec->getOperand(1); 2140 2141 Step = getSCEVAtScope(Step, L->getParentLoop()); 2142 2143 // Figure out if Start % Step == 0. 2144 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2145 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2146 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2147 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2148 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2149 return Start; // 0 - Start/-1 == Start 2150 2151 // Check to see if Start is divisible by SC with no remainder. 2152 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2153 ConstantInt *StartCC = StartC->getValue(); 2154 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2155 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2156 if (Rem->isNullValue()) { 2157 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2158 return SCEVUnknown::get(Result); 2159 } 2160 } 2161 } 2162 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2163 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2164 // the quadratic equation to solve it. 2165 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2166 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2167 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2168 if (R1) { 2169#if 0 2170 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2171 << " sol#2: " << *R2 << "\n"; 2172#endif 2173 // Pick the smallest positive root value. 2174 if (ConstantInt *CB = 2175 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2176 R1->getValue(), R2->getValue()))) { 2177 if (CB->getZExtValue() == false) 2178 std::swap(R1, R2); // R1 is the minimum root now. 2179 2180 // We can only use this value if the chrec ends up with an exact zero 2181 // value at this index. When solving for "X*X != 5", for example, we 2182 // should not accept a root of 2. 2183 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2184 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2185 if (EvalVal->getValue()->isNullValue()) 2186 return R1; // We found a quadratic root! 2187 } 2188 } 2189 } 2190 2191 return UnknownValue; 2192} 2193 2194/// HowFarToNonZero - Return the number of times a backedge checking the 2195/// specified value for nonzero will execute. If not computable, return 2196/// UnknownValue 2197SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2198 // Loops that look like: while (X == 0) are very strange indeed. We don't 2199 // handle them yet except for the trivial case. This could be expanded in the 2200 // future as needed. 2201 2202 // If the value is a constant, check to see if it is known to be non-zero 2203 // already. If so, the backedge will execute zero times. 2204 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2205 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2206 Constant *NonZero = 2207 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2208 if (NonZero == ConstantInt::getTrue()) 2209 return getSCEV(Zero); 2210 return UnknownValue; // Otherwise it will loop infinitely. 2211 } 2212 2213 // We could implement others, but I really doubt anyone writes loops like 2214 // this, and if they did, they would already be constant folded. 2215 return UnknownValue; 2216} 2217 2218/// HowManyLessThans - Return the number of times a backedge containing the 2219/// specified less-than comparison will execute. If not computable, return 2220/// UnknownValue. 2221SCEVHandle ScalarEvolutionsImpl:: 2222HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2223 // Only handle: "ADDREC < LoopInvariant". 2224 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2225 2226 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2227 if (!AddRec || AddRec->getLoop() != L) 2228 return UnknownValue; 2229 2230 if (AddRec->isAffine()) { 2231 // FORNOW: We only support unit strides. 2232 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2233 if (AddRec->getOperand(1) != One) 2234 return UnknownValue; 2235 2236 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2237 // know that m is >= n on input to the loop. If it is, the condition return 2238 // true zero times. What we really should return, for full generality, is 2239 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2240 // canonical loop form: most do-loops will have a check that dominates the 2241 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2242 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2243 2244 // Search for the check. 2245 BasicBlock *Preheader = L->getLoopPreheader(); 2246 BasicBlock *PreheaderDest = L->getHeader(); 2247 if (Preheader == 0) return UnknownValue; 2248 2249 BranchInst *LoopEntryPredicate = 2250 dyn_cast<BranchInst>(Preheader->getTerminator()); 2251 if (!LoopEntryPredicate) return UnknownValue; 2252 2253 // This might be a critical edge broken out. If the loop preheader ends in 2254 // an unconditional branch to the loop, check to see if the preheader has a 2255 // single predecessor, and if so, look for its terminator. 2256 while (LoopEntryPredicate->isUnconditional()) { 2257 PreheaderDest = Preheader; 2258 Preheader = Preheader->getSinglePredecessor(); 2259 if (!Preheader) return UnknownValue; // Multiple preds. 2260 2261 LoopEntryPredicate = 2262 dyn_cast<BranchInst>(Preheader->getTerminator()); 2263 if (!LoopEntryPredicate) return UnknownValue; 2264 } 2265 2266 // Now that we found a conditional branch that dominates the loop, check to 2267 // see if it is the comparison we are looking for. 2268 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){ 2269 Value *PreCondLHS = ICI->getOperand(0); 2270 Value *PreCondRHS = ICI->getOperand(1); 2271 ICmpInst::Predicate Cond; 2272 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2273 Cond = ICI->getPredicate(); 2274 else 2275 Cond = ICI->getInversePredicate(); 2276 2277 switch (Cond) { 2278 case ICmpInst::ICMP_UGT: 2279 std::swap(PreCondLHS, PreCondRHS); 2280 Cond = ICmpInst::ICMP_ULT; 2281 break; 2282 case ICmpInst::ICMP_SGT: 2283 std::swap(PreCondLHS, PreCondRHS); 2284 Cond = ICmpInst::ICMP_SLT; 2285 break; 2286 default: break; 2287 } 2288 2289 if (Cond == ICmpInst::ICMP_SLT) { 2290 if (PreCondLHS->getType()->isInteger()) { 2291 if (RHS != getSCEV(PreCondRHS)) 2292 return UnknownValue; // Not a comparison against 'm'. 2293 2294 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2295 != getSCEV(PreCondLHS)) 2296 return UnknownValue; // Not a comparison against 'n-1'. 2297 } 2298 else return UnknownValue; 2299 } else if (Cond == ICmpInst::ICMP_ULT) 2300 return UnknownValue; 2301 2302 // cerr << "Computed Loop Trip Count as: " 2303 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2304 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2305 } 2306 else 2307 return UnknownValue; 2308 } 2309 2310 return UnknownValue; 2311} 2312 2313/// getNumIterationsInRange - Return the number of iterations of this loop that 2314/// produce values in the specified constant range. Another way of looking at 2315/// this is that it returns the first iteration number where the value is not in 2316/// the condition, thus computing the exit count. If the iteration count can't 2317/// be computed, an instance of SCEVCouldNotCompute is returned. 2318SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2319 bool isSigned) const { 2320 if (Range.isFullSet()) // Infinite loop. 2321 return new SCEVCouldNotCompute(); 2322 2323 // If the start is a non-zero constant, shift the range to simplify things. 2324 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2325 if (!SC->getValue()->isNullValue()) { 2326 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2327 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2328 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2329 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2330 return ShiftedAddRec->getNumIterationsInRange( 2331 Range.subtract(SC->getValue()->getValue()),isSigned); 2332 // This is strange and shouldn't happen. 2333 return new SCEVCouldNotCompute(); 2334 } 2335 2336 // The only time we can solve this is when we have all constant indices. 2337 // Otherwise, we cannot determine the overflow conditions. 2338 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2339 if (!isa<SCEVConstant>(getOperand(i))) 2340 return new SCEVCouldNotCompute(); 2341 2342 2343 // Okay at this point we know that all elements of the chrec are constants and 2344 // that the start element is zero. 2345 2346 // First check to see if the range contains zero. If not, the first 2347 // iteration exits. 2348 if (!Range.contains(APInt(getBitWidth(),0), isSigned)) 2349 return SCEVConstant::get(ConstantInt::get(getType(),0)); 2350 2351 if (isAffine()) { 2352 // If this is an affine expression then we have this situation: 2353 // Solve {0,+,A} in Range === Ax in Range 2354 2355 // Since we know that zero is in the range, we know that the upper value of 2356 // the range must be the first possible exit value. Also note that we 2357 // already checked for a full range. 2358 const APInt &Upper = Range.getUpper(); 2359 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2360 APInt One(getBitWidth(),1); 2361 2362 // The exit value should be (Upper+A-1)/A. 2363 APInt ExitVal(Upper); 2364 if (A != One) 2365 ExitVal = (Upper + A - One).sdiv(A); 2366 ConstantInt *ExitValue = ConstantInt::get(getType(), ExitVal); 2367 2368 // Evaluate at the exit value. If we really did fall out of the valid 2369 // range, then we computed our trip count, otherwise wrap around or other 2370 // things must have happened. 2371 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2372 if (Range.contains(Val->getValue(), isSigned)) 2373 return new SCEVCouldNotCompute(); // Something strange happened 2374 2375 // Ensure that the previous value is in the range. This is a sanity check. 2376 assert(Range.contains( 2377 EvaluateConstantChrecAtConstant(this, 2378 ConstantInt::get(getType(), ExitVal - One))->getValue(), isSigned) && 2379 "Linear scev computation is off in a bad way!"); 2380 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2381 } else if (isQuadratic()) { 2382 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2383 // quadratic equation to solve it. To do this, we must frame our problem in 2384 // terms of figuring out when zero is crossed, instead of when 2385 // Range.getUpper() is crossed. 2386 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2387 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get( 2388 ConstantInt::get(getType(), Range.getUpper()))); 2389 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2390 2391 // Next, solve the constructed addrec 2392 std::pair<SCEVHandle,SCEVHandle> Roots = 2393 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2394 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2395 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2396 if (R1) { 2397 // Pick the smallest positive root value. 2398 if (ConstantInt *CB = 2399 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2400 R1->getValue(), R2->getValue()))) { 2401 if (CB->getZExtValue() == false) 2402 std::swap(R1, R2); // R1 is the minimum root now. 2403 2404 // Make sure the root is not off by one. The returned iteration should 2405 // not be in the range, but the previous one should be. When solving 2406 // for "X*X < 5", for example, we should not return a root of 2. 2407 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2408 R1->getValue()); 2409 if (Range.contains(R1Val->getValue(), isSigned)) { 2410 // The next iteration must be out of the range... 2411 Constant *NextVal = 2412 ConstantExpr::getAdd(R1->getValue(), 2413 ConstantInt::get(R1->getType(), 1)); 2414 2415 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2416 if (!Range.contains(R1Val->getValue(), isSigned)) 2417 return SCEVUnknown::get(NextVal); 2418 return new SCEVCouldNotCompute(); // Something strange happened 2419 } 2420 2421 // If R1 was not in the range, then it is a good return value. Make 2422 // sure that R1-1 WAS in the range though, just in case. 2423 Constant *NextVal = 2424 ConstantExpr::getSub(R1->getValue(), 2425 ConstantInt::get(R1->getType(), 1)); 2426 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2427 if (Range.contains(R1Val->getValue(), isSigned)) 2428 return R1; 2429 return new SCEVCouldNotCompute(); // Something strange happened 2430 } 2431 } 2432 } 2433 2434 // Fallback, if this is a general polynomial, figure out the progression 2435 // through brute force: evaluate until we find an iteration that fails the 2436 // test. This is likely to be slow, but getting an accurate trip count is 2437 // incredibly important, we will be able to simplify the exit test a lot, and 2438 // we are almost guaranteed to get a trip count in this case. 2439 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2440 ConstantInt *One = ConstantInt::get(getType(), 1); 2441 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2442 do { 2443 ++NumBruteForceEvaluations; 2444 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2445 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2446 return new SCEVCouldNotCompute(); 2447 2448 // Check to see if we found the value! 2449 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue(), 2450 isSigned)) 2451 return SCEVConstant::get(TestVal); 2452 2453 // Increment to test the next index. 2454 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2455 } while (TestVal != EndVal); 2456 2457 return new SCEVCouldNotCompute(); 2458} 2459 2460 2461 2462//===----------------------------------------------------------------------===// 2463// ScalarEvolution Class Implementation 2464//===----------------------------------------------------------------------===// 2465 2466bool ScalarEvolution::runOnFunction(Function &F) { 2467 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2468 return false; 2469} 2470 2471void ScalarEvolution::releaseMemory() { 2472 delete (ScalarEvolutionsImpl*)Impl; 2473 Impl = 0; 2474} 2475 2476void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2477 AU.setPreservesAll(); 2478 AU.addRequiredTransitive<LoopInfo>(); 2479} 2480 2481SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2482 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2483} 2484 2485/// hasSCEV - Return true if the SCEV for this value has already been 2486/// computed. 2487bool ScalarEvolution::hasSCEV(Value *V) const { 2488 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2489} 2490 2491 2492/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2493/// the specified value. 2494void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2495 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2496} 2497 2498 2499SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2500 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2501} 2502 2503bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2504 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2505} 2506 2507SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2508 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2509} 2510 2511void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2512 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2513} 2514 2515static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2516 const Loop *L) { 2517 // Print all inner loops first 2518 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2519 PrintLoopInfo(OS, SE, *I); 2520 2521 cerr << "Loop " << L->getHeader()->getName() << ": "; 2522 2523 std::vector<BasicBlock*> ExitBlocks; 2524 L->getExitBlocks(ExitBlocks); 2525 if (ExitBlocks.size() != 1) 2526 cerr << "<multiple exits> "; 2527 2528 if (SE->hasLoopInvariantIterationCount(L)) { 2529 cerr << *SE->getIterationCount(L) << " iterations! "; 2530 } else { 2531 cerr << "Unpredictable iteration count. "; 2532 } 2533 2534 cerr << "\n"; 2535} 2536 2537void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2538 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2539 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2540 2541 OS << "Classifying expressions for: " << F.getName() << "\n"; 2542 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2543 if (I->getType()->isInteger()) { 2544 OS << *I; 2545 OS << " --> "; 2546 SCEVHandle SV = getSCEV(&*I); 2547 SV->print(OS); 2548 OS << "\t\t"; 2549 2550 if ((*I).getType()->isInteger()) { 2551 ConstantRange Bounds = SV->getValueRange(); 2552 if (!Bounds.isFullSet()) 2553 OS << "Bounds: " << Bounds << " "; 2554 } 2555 2556 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2557 OS << "Exits: "; 2558 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2559 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2560 OS << "<<Unknown>>"; 2561 } else { 2562 OS << *ExitValue; 2563 } 2564 } 2565 2566 2567 OS << "\n"; 2568 } 2569 2570 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2571 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2572 PrintLoopInfo(OS, this, *I); 2573} 2574 2575