ScalarEvolution.cpp revision c6aedf70b3a7d0478b8882bf79b985a48d78d37e
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, uint64_t 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 uint64_t GetConstantFactor(SCEVHandle S) { 1332 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1333 if (uint64_t V = C->getValue()->getZExtValue()) 1334 return V; 1335 else // Zero is a multiple of everything. 1336 return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1); 1337 } 1338 1339 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1340 return GetConstantFactor(T->getOperand()) & 1341 cast<IntegerType>(T->getType())->getBitMask(); 1342 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1343 return GetConstantFactor(E->getOperand()); 1344 1345 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1346 // The result is the min of all operands. 1347 uint64_t Res = GetConstantFactor(A->getOperand(0)); 1348 for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i) 1349 Res = std::min(Res, GetConstantFactor(A->getOperand(i))); 1350 return Res; 1351 } 1352 1353 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1354 // The result is the product of all the operands. 1355 uint64_t Res = GetConstantFactor(M->getOperand(0)); 1356 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) 1357 Res *= GetConstantFactor(M->getOperand(i)); 1358 return Res; 1359 } 1360 1361 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1362 // For now, we just handle linear expressions. 1363 if (A->getNumOperands() == 2) { 1364 // We want the GCD between the start and the stride value. 1365 uint64_t Start = GetConstantFactor(A->getOperand(0)); 1366 if (Start == 1) return 1; 1367 uint64_t Stride = GetConstantFactor(A->getOperand(1)); 1368 return GreatestCommonDivisor64(Start, Stride); 1369 } 1370 } 1371 1372 // SCEVSDivExpr, SCEVUnknown. 1373 return 1; 1374} 1375 1376/// createSCEV - We know that there is no SCEV for the specified value. 1377/// Analyze the expression. 1378/// 1379SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1380 if (Instruction *I = dyn_cast<Instruction>(V)) { 1381 switch (I->getOpcode()) { 1382 case Instruction::Add: 1383 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1384 getSCEV(I->getOperand(1))); 1385 case Instruction::Mul: 1386 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1387 getSCEV(I->getOperand(1))); 1388 case Instruction::SDiv: 1389 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1390 getSCEV(I->getOperand(1))); 1391 break; 1392 1393 case Instruction::Sub: 1394 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1395 getSCEV(I->getOperand(1))); 1396 case Instruction::Or: 1397 // If the RHS of the Or is a constant, we may have something like: 1398 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1399 // optimizations will transparently handle this case. 1400 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1401 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1402 uint64_t CommonFact = GetConstantFactor(LHS); 1403 assert(CommonFact && "Common factor should at least be 1!"); 1404 if (CommonFact > CI->getZExtValue()) { 1405 // If the LHS is a multiple that is larger than the RHS, use +. 1406 return SCEVAddExpr::get(LHS, 1407 getSCEV(I->getOperand(1))); 1408 } 1409 } 1410 break; 1411 1412 case Instruction::Shl: 1413 // Turn shift left of a constant amount into a multiply. 1414 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1415 Constant *X = ConstantInt::get(V->getType(), 1); 1416 X = ConstantExpr::getShl(X, SA); 1417 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1418 } 1419 break; 1420 1421 case Instruction::Trunc: 1422 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1423 1424 case Instruction::ZExt: 1425 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1426 1427 case Instruction::BitCast: 1428 // BitCasts are no-op casts so we just eliminate the cast. 1429 if (I->getType()->isInteger() && 1430 I->getOperand(0)->getType()->isInteger()) 1431 return getSCEV(I->getOperand(0)); 1432 break; 1433 1434 case Instruction::PHI: 1435 return createNodeForPHI(cast<PHINode>(I)); 1436 1437 default: // We cannot analyze this expression. 1438 break; 1439 } 1440 } 1441 1442 return SCEVUnknown::get(V); 1443} 1444 1445 1446 1447//===----------------------------------------------------------------------===// 1448// Iteration Count Computation Code 1449// 1450 1451/// getIterationCount - If the specified loop has a predictable iteration 1452/// count, return it. Note that it is not valid to call this method on a 1453/// loop without a loop-invariant iteration count. 1454SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1455 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1456 if (I == IterationCounts.end()) { 1457 SCEVHandle ItCount = ComputeIterationCount(L); 1458 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1459 if (ItCount != UnknownValue) { 1460 assert(ItCount->isLoopInvariant(L) && 1461 "Computed trip count isn't loop invariant for loop!"); 1462 ++NumTripCountsComputed; 1463 } else if (isa<PHINode>(L->getHeader()->begin())) { 1464 // Only count loops that have phi nodes as not being computable. 1465 ++NumTripCountsNotComputed; 1466 } 1467 } 1468 return I->second; 1469} 1470 1471/// ComputeIterationCount - Compute the number of times the specified loop 1472/// will iterate. 1473SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1474 // If the loop has a non-one exit block count, we can't analyze it. 1475 std::vector<BasicBlock*> ExitBlocks; 1476 L->getExitBlocks(ExitBlocks); 1477 if (ExitBlocks.size() != 1) return UnknownValue; 1478 1479 // Okay, there is one exit block. Try to find the condition that causes the 1480 // loop to be exited. 1481 BasicBlock *ExitBlock = ExitBlocks[0]; 1482 1483 BasicBlock *ExitingBlock = 0; 1484 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1485 PI != E; ++PI) 1486 if (L->contains(*PI)) { 1487 if (ExitingBlock == 0) 1488 ExitingBlock = *PI; 1489 else 1490 return UnknownValue; // More than one block exiting! 1491 } 1492 assert(ExitingBlock && "No exits from loop, something is broken!"); 1493 1494 // Okay, we've computed the exiting block. See what condition causes us to 1495 // exit. 1496 // 1497 // FIXME: we should be able to handle switch instructions (with a single exit) 1498 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1499 if (ExitBr == 0) return UnknownValue; 1500 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1501 1502 // At this point, we know we have a conditional branch that determines whether 1503 // the loop is exited. However, we don't know if the branch is executed each 1504 // time through the loop. If not, then the execution count of the branch will 1505 // not be equal to the trip count of the loop. 1506 // 1507 // Currently we check for this by checking to see if the Exit branch goes to 1508 // the loop header. If so, we know it will always execute the same number of 1509 // times as the loop. We also handle the case where the exit block *is* the 1510 // loop header. This is common for un-rotated loops. More extensive analysis 1511 // could be done to handle more cases here. 1512 if (ExitBr->getSuccessor(0) != L->getHeader() && 1513 ExitBr->getSuccessor(1) != L->getHeader() && 1514 ExitBr->getParent() != L->getHeader()) 1515 return UnknownValue; 1516 1517 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1518 1519 // If its not an integer comparison then compute it the hard way. 1520 // Note that ICmpInst deals with pointer comparisons too so we must check 1521 // the type of the operand. 1522 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1523 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1524 ExitBr->getSuccessor(0) == ExitBlock); 1525 1526 // If the condition was exit on true, convert the condition to exit on false 1527 ICmpInst::Predicate Cond; 1528 if (ExitBr->getSuccessor(1) == ExitBlock) 1529 Cond = ExitCond->getPredicate(); 1530 else 1531 Cond = ExitCond->getInversePredicate(); 1532 1533 // Handle common loops like: for (X = "string"; *X; ++X) 1534 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1535 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1536 SCEVHandle ItCnt = 1537 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1538 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1539 } 1540 1541 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1542 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1543 1544 // Try to evaluate any dependencies out of the loop. 1545 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1546 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1547 Tmp = getSCEVAtScope(RHS, L); 1548 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1549 1550 // At this point, we would like to compute how many iterations of the 1551 // loop the predicate will return true for these inputs. 1552 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1553 // If there is a constant, force it into the RHS. 1554 std::swap(LHS, RHS); 1555 Cond = ICmpInst::getSwappedPredicate(Cond); 1556 } 1557 1558 // FIXME: think about handling pointer comparisons! i.e.: 1559 // while (P != P+100) ++P; 1560 1561 // If we have a comparison of a chrec against a constant, try to use value 1562 // ranges to answer this query. 1563 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1564 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1565 if (AddRec->getLoop() == L) { 1566 // Form the comparison range using the constant of the correct type so 1567 // that the ConstantRange class knows to do a signed or unsigned 1568 // comparison. 1569 ConstantInt *CompVal = RHSC->getValue(); 1570 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1571 CompVal = dyn_cast<ConstantInt>( 1572 ConstantExpr::getBitCast(CompVal, RealTy)); 1573 if (CompVal) { 1574 // Form the constant range. 1575 ConstantRange CompRange( 1576 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1577 1578 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, 1579 false /*Always treat as unsigned range*/); 1580 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1581 } 1582 } 1583 1584 switch (Cond) { 1585 case ICmpInst::ICMP_NE: { // while (X != Y) 1586 // Convert to: while (X-Y != 0) 1587 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1588 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1589 break; 1590 } 1591 case ICmpInst::ICMP_EQ: { 1592 // Convert to: while (X-Y == 0) // while (X == Y) 1593 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1594 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1595 break; 1596 } 1597 case ICmpInst::ICMP_SLT: { 1598 SCEVHandle TC = HowManyLessThans(LHS, RHS, L); 1599 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1600 break; 1601 } 1602 case ICmpInst::ICMP_SGT: { 1603 SCEVHandle TC = HowManyLessThans(RHS, LHS, L); 1604 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1605 break; 1606 } 1607 default: 1608#if 0 1609 cerr << "ComputeIterationCount "; 1610 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1611 cerr << "[unsigned] "; 1612 cerr << *LHS << " " 1613 << Instruction::getOpcodeName(Instruction::ICmp) 1614 << " " << *RHS << "\n"; 1615#endif 1616 break; 1617 } 1618 return ComputeIterationCountExhaustively(L, ExitCond, 1619 ExitBr->getSuccessor(0) == ExitBlock); 1620} 1621 1622static ConstantInt * 1623EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1624 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1625 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1626 assert(isa<SCEVConstant>(Val) && 1627 "Evaluation of SCEV at constant didn't fold correctly?"); 1628 return cast<SCEVConstant>(Val)->getValue(); 1629} 1630 1631/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1632/// and a GEP expression (missing the pointer index) indexing into it, return 1633/// the addressed element of the initializer or null if the index expression is 1634/// invalid. 1635static Constant * 1636GetAddressedElementFromGlobal(GlobalVariable *GV, 1637 const std::vector<ConstantInt*> &Indices) { 1638 Constant *Init = GV->getInitializer(); 1639 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1640 uint64_t Idx = Indices[i]->getZExtValue(); 1641 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1642 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1643 Init = cast<Constant>(CS->getOperand(Idx)); 1644 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1645 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1646 Init = cast<Constant>(CA->getOperand(Idx)); 1647 } else if (isa<ConstantAggregateZero>(Init)) { 1648 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1649 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1650 Init = Constant::getNullValue(STy->getElementType(Idx)); 1651 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1652 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1653 Init = Constant::getNullValue(ATy->getElementType()); 1654 } else { 1655 assert(0 && "Unknown constant aggregate type!"); 1656 } 1657 return 0; 1658 } else { 1659 return 0; // Unknown initializer type 1660 } 1661 } 1662 return Init; 1663} 1664 1665/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1666/// 'setcc load X, cst', try to se if we can compute the trip count. 1667SCEVHandle ScalarEvolutionsImpl:: 1668ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1669 const Loop *L, 1670 ICmpInst::Predicate predicate) { 1671 if (LI->isVolatile()) return UnknownValue; 1672 1673 // Check to see if the loaded pointer is a getelementptr of a global. 1674 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1675 if (!GEP) return UnknownValue; 1676 1677 // Make sure that it is really a constant global we are gepping, with an 1678 // initializer, and make sure the first IDX is really 0. 1679 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1680 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1681 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1682 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1683 return UnknownValue; 1684 1685 // Okay, we allow one non-constant index into the GEP instruction. 1686 Value *VarIdx = 0; 1687 std::vector<ConstantInt*> Indexes; 1688 unsigned VarIdxNum = 0; 1689 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1690 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1691 Indexes.push_back(CI); 1692 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1693 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1694 VarIdx = GEP->getOperand(i); 1695 VarIdxNum = i-2; 1696 Indexes.push_back(0); 1697 } 1698 1699 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1700 // Check to see if X is a loop variant variable value now. 1701 SCEVHandle Idx = getSCEV(VarIdx); 1702 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1703 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1704 1705 // We can only recognize very limited forms of loop index expressions, in 1706 // particular, only affine AddRec's like {C1,+,C2}. 1707 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1708 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1709 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1710 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1711 return UnknownValue; 1712 1713 unsigned MaxSteps = MaxBruteForceIterations; 1714 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1715 ConstantInt *ItCst = 1716 ConstantInt::get(IdxExpr->getType(), IterationNum); 1717 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1718 1719 // Form the GEP offset. 1720 Indexes[VarIdxNum] = Val; 1721 1722 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1723 if (Result == 0) break; // Cannot compute! 1724 1725 // Evaluate the condition for this iteration. 1726 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1727 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1728 if (cast<ConstantInt>(Result)->getZExtValue() == false) { 1729#if 0 1730 cerr << "\n***\n*** Computed loop count " << *ItCst 1731 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1732 << "***\n"; 1733#endif 1734 ++NumArrayLenItCounts; 1735 return SCEVConstant::get(ItCst); // Found terminating iteration! 1736 } 1737 } 1738 return UnknownValue; 1739} 1740 1741 1742/// CanConstantFold - Return true if we can constant fold an instruction of the 1743/// specified type, assuming that all operands were constants. 1744static bool CanConstantFold(const Instruction *I) { 1745 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 1746 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1747 return true; 1748 1749 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1750 if (const Function *F = CI->getCalledFunction()) 1751 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1752 return false; 1753} 1754 1755/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1756/// in the loop that V is derived from. We allow arbitrary operations along the 1757/// way, but the operands of an operation must either be constants or a value 1758/// derived from a constant PHI. If this expression does not fit with these 1759/// constraints, return null. 1760static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1761 // If this is not an instruction, or if this is an instruction outside of the 1762 // loop, it can't be derived from a loop PHI. 1763 Instruction *I = dyn_cast<Instruction>(V); 1764 if (I == 0 || !L->contains(I->getParent())) return 0; 1765 1766 if (PHINode *PN = dyn_cast<PHINode>(I)) 1767 if (L->getHeader() == I->getParent()) 1768 return PN; 1769 else 1770 // We don't currently keep track of the control flow needed to evaluate 1771 // PHIs, so we cannot handle PHIs inside of loops. 1772 return 0; 1773 1774 // If we won't be able to constant fold this expression even if the operands 1775 // are constants, return early. 1776 if (!CanConstantFold(I)) return 0; 1777 1778 // Otherwise, we can evaluate this instruction if all of its operands are 1779 // constant or derived from a PHI node themselves. 1780 PHINode *PHI = 0; 1781 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1782 if (!(isa<Constant>(I->getOperand(Op)) || 1783 isa<GlobalValue>(I->getOperand(Op)))) { 1784 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1785 if (P == 0) return 0; // Not evolving from PHI 1786 if (PHI == 0) 1787 PHI = P; 1788 else if (PHI != P) 1789 return 0; // Evolving from multiple different PHIs. 1790 } 1791 1792 // This is a expression evolving from a constant PHI! 1793 return PHI; 1794} 1795 1796/// EvaluateExpression - Given an expression that passes the 1797/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1798/// in the loop has the value PHIVal. If we can't fold this expression for some 1799/// reason, return null. 1800static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1801 if (isa<PHINode>(V)) return PHIVal; 1802 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1803 return GV; 1804 if (Constant *C = dyn_cast<Constant>(V)) return C; 1805 Instruction *I = cast<Instruction>(V); 1806 1807 std::vector<Constant*> Operands; 1808 Operands.resize(I->getNumOperands()); 1809 1810 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1811 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1812 if (Operands[i] == 0) return 0; 1813 } 1814 1815 return ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1816} 1817 1818/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1819/// in the header of its containing loop, we know the loop executes a 1820/// constant number of times, and the PHI node is just a recurrence 1821/// involving constants, fold it. 1822Constant *ScalarEvolutionsImpl:: 1823getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1824 std::map<PHINode*, Constant*>::iterator I = 1825 ConstantEvolutionLoopExitValue.find(PN); 1826 if (I != ConstantEvolutionLoopExitValue.end()) 1827 return I->second; 1828 1829 if (Its > MaxBruteForceIterations) 1830 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1831 1832 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1833 1834 // Since the loop is canonicalized, the PHI node must have two entries. One 1835 // entry must be a constant (coming in from outside of the loop), and the 1836 // second must be derived from the same PHI. 1837 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1838 Constant *StartCST = 1839 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1840 if (StartCST == 0) 1841 return RetVal = 0; // Must be a constant. 1842 1843 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1844 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1845 if (PN2 != PN) 1846 return RetVal = 0; // Not derived from same PHI. 1847 1848 // Execute the loop symbolically to determine the exit value. 1849 unsigned IterationNum = 0; 1850 unsigned NumIterations = Its; 1851 if (NumIterations != Its) 1852 return RetVal = 0; // More than 2^32 iterations?? 1853 1854 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1855 if (IterationNum == NumIterations) 1856 return RetVal = PHIVal; // Got exit value! 1857 1858 // Compute the value of the PHI node for the next iteration. 1859 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1860 if (NextPHI == PHIVal) 1861 return RetVal = NextPHI; // Stopped evolving! 1862 if (NextPHI == 0) 1863 return 0; // Couldn't evaluate! 1864 PHIVal = NextPHI; 1865 } 1866} 1867 1868/// ComputeIterationCountExhaustively - If the trip is known to execute a 1869/// constant number of times (the condition evolves only from constants), 1870/// try to evaluate a few iterations of the loop until we get the exit 1871/// condition gets a value of ExitWhen (true or false). If we cannot 1872/// evaluate the trip count of the loop, return UnknownValue. 1873SCEVHandle ScalarEvolutionsImpl:: 1874ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1875 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1876 if (PN == 0) return UnknownValue; 1877 1878 // Since the loop is canonicalized, the PHI node must have two entries. One 1879 // entry must be a constant (coming in from outside of the loop), and the 1880 // second must be derived from the same PHI. 1881 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1882 Constant *StartCST = 1883 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1884 if (StartCST == 0) return UnknownValue; // Must be a constant. 1885 1886 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1887 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1888 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1889 1890 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1891 // the loop symbolically to determine when the condition gets a value of 1892 // "ExitWhen". 1893 unsigned IterationNum = 0; 1894 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1895 for (Constant *PHIVal = StartCST; 1896 IterationNum != MaxIterations; ++IterationNum) { 1897 ConstantInt *CondVal = 1898 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 1899 1900 // Couldn't symbolically evaluate. 1901 if (!CondVal) return UnknownValue; 1902 1903 if (CondVal->getZExtValue() == uint64_t(ExitWhen)) { 1904 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1905 ++NumBruteForceTripCountsComputed; 1906 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum)); 1907 } 1908 1909 // Compute the value of the PHI node for the next iteration. 1910 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1911 if (NextPHI == 0 || NextPHI == PHIVal) 1912 return UnknownValue; // Couldn't evaluate or not making progress... 1913 PHIVal = NextPHI; 1914 } 1915 1916 // Too many iterations were needed to evaluate. 1917 return UnknownValue; 1918} 1919 1920/// getSCEVAtScope - Compute the value of the specified expression within the 1921/// indicated loop (which may be null to indicate in no loop). If the 1922/// expression cannot be evaluated, return UnknownValue. 1923SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1924 // FIXME: this should be turned into a virtual method on SCEV! 1925 1926 if (isa<SCEVConstant>(V)) return V; 1927 1928 // If this instruction is evolves from a constant-evolving PHI, compute the 1929 // exit value from the loop without using SCEVs. 1930 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1931 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1932 const Loop *LI = this->LI[I->getParent()]; 1933 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1934 if (PHINode *PN = dyn_cast<PHINode>(I)) 1935 if (PN->getParent() == LI->getHeader()) { 1936 // Okay, there is no closed form solution for the PHI node. Check 1937 // to see if the loop that contains it has a known iteration count. 1938 // If so, we may be able to force computation of the exit value. 1939 SCEVHandle IterationCount = getIterationCount(LI); 1940 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1941 // Okay, we know how many times the containing loop executes. If 1942 // this is a constant evolving PHI node, get the final value at 1943 // the specified iteration number. 1944 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1945 ICC->getValue()->getZExtValue(), 1946 LI); 1947 if (RV) return SCEVUnknown::get(RV); 1948 } 1949 } 1950 1951 // Okay, this is an expression that we cannot symbolically evaluate 1952 // into a SCEV. Check to see if it's possible to symbolically evaluate 1953 // the arguments into constants, and if so, try to constant propagate the 1954 // result. This is particularly useful for computing loop exit values. 1955 if (CanConstantFold(I)) { 1956 std::vector<Constant*> Operands; 1957 Operands.reserve(I->getNumOperands()); 1958 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1959 Value *Op = I->getOperand(i); 1960 if (Constant *C = dyn_cast<Constant>(Op)) { 1961 Operands.push_back(C); 1962 } else { 1963 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1964 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1965 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 1966 Op->getType(), 1967 false)); 1968 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1969 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1970 Operands.push_back(ConstantExpr::getIntegerCast(C, 1971 Op->getType(), 1972 false)); 1973 else 1974 return V; 1975 } else { 1976 return V; 1977 } 1978 } 1979 } 1980 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1981 return SCEVUnknown::get(C); 1982 } 1983 } 1984 1985 // This is some other type of SCEVUnknown, just return it. 1986 return V; 1987 } 1988 1989 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1990 // Avoid performing the look-up in the common case where the specified 1991 // expression has no loop-variant portions. 1992 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1993 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1994 if (OpAtScope != Comm->getOperand(i)) { 1995 if (OpAtScope == UnknownValue) return UnknownValue; 1996 // Okay, at least one of these operands is loop variant but might be 1997 // foldable. Build a new instance of the folded commutative expression. 1998 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1999 NewOps.push_back(OpAtScope); 2000 2001 for (++i; i != e; ++i) { 2002 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2003 if (OpAtScope == UnknownValue) return UnknownValue; 2004 NewOps.push_back(OpAtScope); 2005 } 2006 if (isa<SCEVAddExpr>(Comm)) 2007 return SCEVAddExpr::get(NewOps); 2008 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2009 return SCEVMulExpr::get(NewOps); 2010 } 2011 } 2012 // If we got here, all operands are loop invariant. 2013 return Comm; 2014 } 2015 2016 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2017 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2018 if (LHS == UnknownValue) return LHS; 2019 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2020 if (RHS == UnknownValue) return RHS; 2021 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2022 return Div; // must be loop invariant 2023 return SCEVSDivExpr::get(LHS, RHS); 2024 } 2025 2026 // If this is a loop recurrence for a loop that does not contain L, then we 2027 // are dealing with the final value computed by the loop. 2028 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2029 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2030 // To evaluate this recurrence, we need to know how many times the AddRec 2031 // loop iterates. Compute this now. 2032 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2033 if (IterationCount == UnknownValue) return UnknownValue; 2034 IterationCount = getTruncateOrZeroExtend(IterationCount, 2035 AddRec->getType()); 2036 2037 // If the value is affine, simplify the expression evaluation to just 2038 // Start + Step*IterationCount. 2039 if (AddRec->isAffine()) 2040 return SCEVAddExpr::get(AddRec->getStart(), 2041 SCEVMulExpr::get(IterationCount, 2042 AddRec->getOperand(1))); 2043 2044 // Otherwise, evaluate it the hard way. 2045 return AddRec->evaluateAtIteration(IterationCount); 2046 } 2047 return UnknownValue; 2048 } 2049 2050 //assert(0 && "Unknown SCEV type!"); 2051 return UnknownValue; 2052} 2053 2054 2055/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2056/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2057/// might be the same) or two SCEVCouldNotCompute objects. 2058/// 2059static std::pair<SCEVHandle,SCEVHandle> 2060SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2061 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2062 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2063 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2064 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2065 2066 // We currently can only solve this if the coefficients are constants. 2067 if (!L || !M || !N) { 2068 SCEV *CNC = new SCEVCouldNotCompute(); 2069 return std::make_pair(CNC, CNC); 2070 } 2071 2072 Constant *C = L->getValue(); 2073 Constant *Two = ConstantInt::get(C->getType(), 2); 2074 2075 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2076 // The B coefficient is M-N/2 2077 Constant *B = ConstantExpr::getSub(M->getValue(), 2078 ConstantExpr::getSDiv(N->getValue(), 2079 Two)); 2080 // The A coefficient is N/2 2081 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two); 2082 2083 // Compute the B^2-4ac term. 2084 Constant *SqrtTerm = 2085 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2086 ConstantExpr::getMul(A, C)); 2087 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2088 2089 // Compute floor(sqrt(B^2-4ac)) 2090 uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue(); 2091 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2092 // The square root might not be precise for arbitrary 64-bit integer 2093 // values. Do some sanity checks to ensure it's correct. 2094 if (SqrtValV2*SqrtValV2 > SqrtValV || 2095 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2096 SCEV *CNC = new SCEVCouldNotCompute(); 2097 return std::make_pair(CNC, CNC); 2098 } 2099 2100 ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2); 2101 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType()); 2102 2103 Constant *NegB = ConstantExpr::getNeg(B); 2104 Constant *TwoA = ConstantExpr::getMul(A, Two); 2105 2106 // The divisions must be performed as signed divisions. 2107 Constant *Solution1 = 2108 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2109 Constant *Solution2 = 2110 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2111 return std::make_pair(SCEVUnknown::get(Solution1), 2112 SCEVUnknown::get(Solution2)); 2113} 2114 2115/// HowFarToZero - Return the number of times a backedge comparing the specified 2116/// value to zero will execute. If not computable, return UnknownValue 2117SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2118 // If the value is a constant 2119 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2120 // If the value is already zero, the branch will execute zero times. 2121 if (C->getValue()->isNullValue()) return C; 2122 return UnknownValue; // Otherwise it will loop infinitely. 2123 } 2124 2125 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2126 if (!AddRec || AddRec->getLoop() != L) 2127 return UnknownValue; 2128 2129 if (AddRec->isAffine()) { 2130 // If this is an affine expression the execution count of this branch is 2131 // equal to: 2132 // 2133 // (0 - Start/Step) iff Start % Step == 0 2134 // 2135 // Get the initial value for the loop. 2136 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2137 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2138 SCEVHandle Step = AddRec->getOperand(1); 2139 2140 Step = getSCEVAtScope(Step, L->getParentLoop()); 2141 2142 // Figure out if Start % Step == 0. 2143 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2144 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2145 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2146 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2147 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2148 return Start; // 0 - Start/-1 == Start 2149 2150 // Check to see if Start is divisible by SC with no remainder. 2151 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2152 ConstantInt *StartCC = StartC->getValue(); 2153 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2154 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2155 if (Rem->isNullValue()) { 2156 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2157 return SCEVUnknown::get(Result); 2158 } 2159 } 2160 } 2161 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2162 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2163 // the quadratic equation to solve it. 2164 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2165 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2166 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2167 if (R1) { 2168#if 0 2169 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2170 << " sol#2: " << *R2 << "\n"; 2171#endif 2172 // Pick the smallest positive root value. 2173 if (ConstantInt *CB = 2174 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2175 R1->getValue(), R2->getValue()))) { 2176 if (CB->getZExtValue() == false) 2177 std::swap(R1, R2); // R1 is the minimum root now. 2178 2179 // We can only use this value if the chrec ends up with an exact zero 2180 // value at this index. When solving for "X*X != 5", for example, we 2181 // should not accept a root of 2. 2182 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2183 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2184 if (EvalVal->getValue()->isNullValue()) 2185 return R1; // We found a quadratic root! 2186 } 2187 } 2188 } 2189 2190 return UnknownValue; 2191} 2192 2193/// HowFarToNonZero - Return the number of times a backedge checking the 2194/// specified value for nonzero will execute. If not computable, return 2195/// UnknownValue 2196SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2197 // Loops that look like: while (X == 0) are very strange indeed. We don't 2198 // handle them yet except for the trivial case. This could be expanded in the 2199 // future as needed. 2200 2201 // If the value is a constant, check to see if it is known to be non-zero 2202 // already. If so, the backedge will execute zero times. 2203 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2204 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2205 Constant *NonZero = 2206 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2207 if (NonZero == ConstantInt::getTrue()) 2208 return getSCEV(Zero); 2209 return UnknownValue; // Otherwise it will loop infinitely. 2210 } 2211 2212 // We could implement others, but I really doubt anyone writes loops like 2213 // this, and if they did, they would already be constant folded. 2214 return UnknownValue; 2215} 2216 2217/// HowManyLessThans - Return the number of times a backedge containing the 2218/// specified less-than comparison will execute. If not computable, return 2219/// UnknownValue. 2220SCEVHandle ScalarEvolutionsImpl:: 2221HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) { 2222 // Only handle: "ADDREC < LoopInvariant". 2223 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2224 2225 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2226 if (!AddRec || AddRec->getLoop() != L) 2227 return UnknownValue; 2228 2229 if (AddRec->isAffine()) { 2230 // FORNOW: We only support unit strides. 2231 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2232 if (AddRec->getOperand(1) != One) 2233 return UnknownValue; 2234 2235 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2236 // know that m is >= n on input to the loop. If it is, the condition return 2237 // true zero times. What we really should return, for full generality, is 2238 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2239 // canonical loop form: most do-loops will have a check that dominates the 2240 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2241 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2242 2243 // Search for the check. 2244 BasicBlock *Preheader = L->getLoopPreheader(); 2245 BasicBlock *PreheaderDest = L->getHeader(); 2246 if (Preheader == 0) return UnknownValue; 2247 2248 BranchInst *LoopEntryPredicate = 2249 dyn_cast<BranchInst>(Preheader->getTerminator()); 2250 if (!LoopEntryPredicate) return UnknownValue; 2251 2252 // This might be a critical edge broken out. If the loop preheader ends in 2253 // an unconditional branch to the loop, check to see if the preheader has a 2254 // single predecessor, and if so, look for its terminator. 2255 while (LoopEntryPredicate->isUnconditional()) { 2256 PreheaderDest = Preheader; 2257 Preheader = Preheader->getSinglePredecessor(); 2258 if (!Preheader) return UnknownValue; // Multiple preds. 2259 2260 LoopEntryPredicate = 2261 dyn_cast<BranchInst>(Preheader->getTerminator()); 2262 if (!LoopEntryPredicate) return UnknownValue; 2263 } 2264 2265 // Now that we found a conditional branch that dominates the loop, check to 2266 // see if it is the comparison we are looking for. 2267 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){ 2268 Value *PreCondLHS = ICI->getOperand(0); 2269 Value *PreCondRHS = ICI->getOperand(1); 2270 ICmpInst::Predicate Cond; 2271 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2272 Cond = ICI->getPredicate(); 2273 else 2274 Cond = ICI->getInversePredicate(); 2275 2276 switch (Cond) { 2277 case ICmpInst::ICMP_UGT: 2278 std::swap(PreCondLHS, PreCondRHS); 2279 Cond = ICmpInst::ICMP_ULT; 2280 break; 2281 case ICmpInst::ICMP_SGT: 2282 std::swap(PreCondLHS, PreCondRHS); 2283 Cond = ICmpInst::ICMP_SLT; 2284 break; 2285 default: break; 2286 } 2287 2288 if (Cond == ICmpInst::ICMP_SLT) { 2289 if (PreCondLHS->getType()->isInteger()) { 2290 if (RHS != getSCEV(PreCondRHS)) 2291 return UnknownValue; // Not a comparison against 'm'. 2292 2293 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2294 != getSCEV(PreCondLHS)) 2295 return UnknownValue; // Not a comparison against 'n-1'. 2296 } 2297 else return UnknownValue; 2298 } else if (Cond == ICmpInst::ICMP_ULT) 2299 return UnknownValue; 2300 2301 // cerr << "Computed Loop Trip Count as: " 2302 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2303 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2304 } 2305 else 2306 return UnknownValue; 2307 } 2308 2309 return UnknownValue; 2310} 2311 2312/// getNumIterationsInRange - Return the number of iterations of this loop that 2313/// produce values in the specified constant range. Another way of looking at 2314/// this is that it returns the first iteration number where the value is not in 2315/// the condition, thus computing the exit count. If the iteration count can't 2316/// be computed, an instance of SCEVCouldNotCompute is returned. 2317SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2318 bool isSigned) const { 2319 if (Range.isFullSet()) // Infinite loop. 2320 return new SCEVCouldNotCompute(); 2321 2322 // If the start is a non-zero constant, shift the range to simplify things. 2323 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2324 if (!SC->getValue()->isNullValue()) { 2325 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2326 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2327 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2328 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2329 return ShiftedAddRec->getNumIterationsInRange( 2330 Range.subtract(SC->getValue()->getValue()),isSigned); 2331 // This is strange and shouldn't happen. 2332 return new SCEVCouldNotCompute(); 2333 } 2334 2335 // The only time we can solve this is when we have all constant indices. 2336 // Otherwise, we cannot determine the overflow conditions. 2337 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2338 if (!isa<SCEVConstant>(getOperand(i))) 2339 return new SCEVCouldNotCompute(); 2340 2341 2342 // Okay at this point we know that all elements of the chrec are constants and 2343 // that the start element is zero. 2344 2345 // First check to see if the range contains zero. If not, the first 2346 // iteration exits. 2347 if (!Range.contains(APInt(getBitWidth(),0), isSigned)) 2348 return SCEVConstant::get(ConstantInt::get(getType(),0)); 2349 2350 if (isAffine()) { 2351 // If this is an affine expression then we have this situation: 2352 // Solve {0,+,A} in Range === Ax in Range 2353 2354 // Since we know that zero is in the range, we know that the upper value of 2355 // the range must be the first possible exit value. Also note that we 2356 // already checked for a full range. 2357 const APInt &Upper = Range.getUpper(); 2358 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2359 APInt One(getBitWidth(),1); 2360 2361 // The exit value should be (Upper+A-1)/A. 2362 APInt ExitVal(Upper); 2363 if (A != One) 2364 ExitVal = (Upper + A - One).sdiv(A); 2365 ConstantInt *ExitValue = ConstantInt::get(getType(), ExitVal); 2366 2367 // Evaluate at the exit value. If we really did fall out of the valid 2368 // range, then we computed our trip count, otherwise wrap around or other 2369 // things must have happened. 2370 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2371 if (Range.contains(Val->getValue(), isSigned)) 2372 return new SCEVCouldNotCompute(); // Something strange happened 2373 2374 // Ensure that the previous value is in the range. This is a sanity check. 2375 assert(Range.contains( 2376 EvaluateConstantChrecAtConstant(this, 2377 ConstantInt::get(getType(), ExitVal - One))->getValue(), isSigned) && 2378 "Linear scev computation is off in a bad way!"); 2379 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2380 } else if (isQuadratic()) { 2381 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2382 // quadratic equation to solve it. To do this, we must frame our problem in 2383 // terms of figuring out when zero is crossed, instead of when 2384 // Range.getUpper() is crossed. 2385 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2386 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get( 2387 ConstantInt::get(getType(), Range.getUpper()))); 2388 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2389 2390 // Next, solve the constructed addrec 2391 std::pair<SCEVHandle,SCEVHandle> Roots = 2392 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2393 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2394 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2395 if (R1) { 2396 // Pick the smallest positive root value. 2397 if (ConstantInt *CB = 2398 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2399 R1->getValue(), R2->getValue()))) { 2400 if (CB->getZExtValue() == false) 2401 std::swap(R1, R2); // R1 is the minimum root now. 2402 2403 // Make sure the root is not off by one. The returned iteration should 2404 // not be in the range, but the previous one should be. When solving 2405 // for "X*X < 5", for example, we should not return a root of 2. 2406 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2407 R1->getValue()); 2408 if (Range.contains(R1Val->getValue(), isSigned)) { 2409 // The next iteration must be out of the range... 2410 Constant *NextVal = 2411 ConstantExpr::getAdd(R1->getValue(), 2412 ConstantInt::get(R1->getType(), 1)); 2413 2414 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2415 if (!Range.contains(R1Val->getValue(), isSigned)) 2416 return SCEVUnknown::get(NextVal); 2417 return new SCEVCouldNotCompute(); // Something strange happened 2418 } 2419 2420 // If R1 was not in the range, then it is a good return value. Make 2421 // sure that R1-1 WAS in the range though, just in case. 2422 Constant *NextVal = 2423 ConstantExpr::getSub(R1->getValue(), 2424 ConstantInt::get(R1->getType(), 1)); 2425 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2426 if (Range.contains(R1Val->getValue(), isSigned)) 2427 return R1; 2428 return new SCEVCouldNotCompute(); // Something strange happened 2429 } 2430 } 2431 } 2432 2433 // Fallback, if this is a general polynomial, figure out the progression 2434 // through brute force: evaluate until we find an iteration that fails the 2435 // test. This is likely to be slow, but getting an accurate trip count is 2436 // incredibly important, we will be able to simplify the exit test a lot, and 2437 // we are almost guaranteed to get a trip count in this case. 2438 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2439 ConstantInt *One = ConstantInt::get(getType(), 1); 2440 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2441 do { 2442 ++NumBruteForceEvaluations; 2443 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2444 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2445 return new SCEVCouldNotCompute(); 2446 2447 // Check to see if we found the value! 2448 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue(), 2449 isSigned)) 2450 return SCEVConstant::get(TestVal); 2451 2452 // Increment to test the next index. 2453 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2454 } while (TestVal != EndVal); 2455 2456 return new SCEVCouldNotCompute(); 2457} 2458 2459 2460 2461//===----------------------------------------------------------------------===// 2462// ScalarEvolution Class Implementation 2463//===----------------------------------------------------------------------===// 2464 2465bool ScalarEvolution::runOnFunction(Function &F) { 2466 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2467 return false; 2468} 2469 2470void ScalarEvolution::releaseMemory() { 2471 delete (ScalarEvolutionsImpl*)Impl; 2472 Impl = 0; 2473} 2474 2475void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2476 AU.setPreservesAll(); 2477 AU.addRequiredTransitive<LoopInfo>(); 2478} 2479 2480SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2481 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2482} 2483 2484/// hasSCEV - Return true if the SCEV for this value has already been 2485/// computed. 2486bool ScalarEvolution::hasSCEV(Value *V) const { 2487 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2488} 2489 2490 2491/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2492/// the specified value. 2493void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2494 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2495} 2496 2497 2498SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2499 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2500} 2501 2502bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2503 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2504} 2505 2506SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2507 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2508} 2509 2510void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2511 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2512} 2513 2514static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2515 const Loop *L) { 2516 // Print all inner loops first 2517 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2518 PrintLoopInfo(OS, SE, *I); 2519 2520 cerr << "Loop " << L->getHeader()->getName() << ": "; 2521 2522 std::vector<BasicBlock*> ExitBlocks; 2523 L->getExitBlocks(ExitBlocks); 2524 if (ExitBlocks.size() != 1) 2525 cerr << "<multiple exits> "; 2526 2527 if (SE->hasLoopInvariantIterationCount(L)) { 2528 cerr << *SE->getIterationCount(L) << " iterations! "; 2529 } else { 2530 cerr << "Unpredictable iteration count. "; 2531 } 2532 2533 cerr << "\n"; 2534} 2535 2536void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2537 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2538 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2539 2540 OS << "Classifying expressions for: " << F.getName() << "\n"; 2541 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2542 if (I->getType()->isInteger()) { 2543 OS << *I; 2544 OS << " --> "; 2545 SCEVHandle SV = getSCEV(&*I); 2546 SV->print(OS); 2547 OS << "\t\t"; 2548 2549 if ((*I).getType()->isInteger()) { 2550 ConstantRange Bounds = SV->getValueRange(); 2551 if (!Bounds.isFullSet()) 2552 OS << "Bounds: " << Bounds << " "; 2553 } 2554 2555 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2556 OS << "Exits: "; 2557 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2558 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2559 OS << "<<Unknown>>"; 2560 } else { 2561 OS << *ExitValue; 2562 } 2563 } 2564 2565 2566 OS << "\n"; 2567 } 2568 2569 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2570 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2571 PrintLoopInfo(OS, this, *I); 2572} 2573 2574