ScalarEvolution.cpp revision b7211a2ce13a0365e0e1dd2f27adda2ee3d1288b
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} 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117SCEV::~SCEV() {} 118void SCEV::dump() const { 119 print(cerr); 120} 121 122/// getValueRange - Return the tightest constant bounds that this value is 123/// known to have. This method is only valid on integer SCEV objects. 124ConstantRange SCEV::getValueRange() const { 125 const Type *Ty = getType(); 126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 127 // Default to a full range if no better information is available. 128 return ConstantRange(getBitWidth()); 129} 130 131uint32_t SCEV::getBitWidth() const { 132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 133 return ITy->getBitWidth(); 134 return 0; 135} 136 137 138SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 139 140bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return false; 143} 144 145const Type *SCEVCouldNotCompute::getType() const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return 0; 148} 149 150bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 152 return false; 153} 154 155SCEVHandle SCEVCouldNotCompute:: 156replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 157 const SCEVHandle &Conc) const { 158 return this; 159} 160 161void SCEVCouldNotCompute::print(std::ostream &OS) const { 162 OS << "***COULDNOTCOMPUTE***"; 163} 164 165bool SCEVCouldNotCompute::classof(const SCEV *S) { 166 return S->getSCEVType() == scCouldNotCompute; 167} 168 169 170// SCEVConstants - Only allow the creation of one SCEVConstant for any 171// particular value. Don't use a SCEVHandle here, or else the object will 172// never be deleted! 173static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 174 175 176SCEVConstant::~SCEVConstant() { 177 SCEVConstants->erase(V); 178} 179 180SCEVHandle SCEVConstant::get(ConstantInt *V) { 181 SCEVConstant *&R = (*SCEVConstants)[V]; 182 if (R == 0) R = new SCEVConstant(V); 183 return R; 184} 185 186SCEVHandle SCEVConstant::get(const APInt& Val) { 187 return get(ConstantInt::get(Val)); 188} 189 190ConstantRange SCEVConstant::getValueRange() const { 191 return ConstantRange(V->getValue()); 192} 193 194const Type *SCEVConstant::getType() const { return V->getType(); } 195 196void SCEVConstant::print(std::ostream &OS) const { 197 WriteAsOperand(OS, V, false); 198} 199 200// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 201// particular input. Don't use a SCEVHandle here, or else the object will 202// never be deleted! 203static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 204 SCEVTruncateExpr*> > SCEVTruncates; 205 206SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 207 : SCEV(scTruncate), Op(op), Ty(ty) { 208 assert(Op->getType()->isInteger() && Ty->isInteger() && 209 "Cannot truncate non-integer value!"); 210 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 211 && "This is not a truncating conversion!"); 212} 213 214SCEVTruncateExpr::~SCEVTruncateExpr() { 215 SCEVTruncates->erase(std::make_pair(Op, Ty)); 216} 217 218ConstantRange SCEVTruncateExpr::getValueRange() const { 219 return getOperand()->getValueRange().truncate(getBitWidth()); 220} 221 222void SCEVTruncateExpr::print(std::ostream &OS) const { 223 OS << "(truncate " << *Op << " to " << *Ty << ")"; 224} 225 226// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 227// particular input. Don't use a SCEVHandle here, or else the object will never 228// be deleted! 229static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 230 SCEVZeroExtendExpr*> > SCEVZeroExtends; 231 232SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 233 : SCEV(scZeroExtend), Op(op), Ty(ty) { 234 assert(Op->getType()->isInteger() && Ty->isInteger() && 235 "Cannot zero extend non-integer value!"); 236 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 237 && "This is not an extending conversion!"); 238} 239 240SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 241 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 242} 243 244ConstantRange SCEVZeroExtendExpr::getValueRange() const { 245 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 246} 247 248void SCEVZeroExtendExpr::print(std::ostream &OS) const { 249 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 250} 251 252// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 253// particular input. Don't use a SCEVHandle here, or else the object will never 254// be deleted! 255static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 256 SCEVSignExtendExpr*> > SCEVSignExtends; 257 258SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 259 : SCEV(scSignExtend), Op(op), Ty(ty) { 260 assert(Op->getType()->isInteger() && Ty->isInteger() && 261 "Cannot sign extend non-integer value!"); 262 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 263 && "This is not an extending conversion!"); 264} 265 266SCEVSignExtendExpr::~SCEVSignExtendExpr() { 267 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 268} 269 270ConstantRange SCEVSignExtendExpr::getValueRange() const { 271 return getOperand()->getValueRange().signExtend(getBitWidth()); 272} 273 274void SCEVSignExtendExpr::print(std::ostream &OS) const { 275 OS << "(signextend " << *Op << " to " << *Ty << ")"; 276} 277 278// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 279// particular input. Don't use a SCEVHandle here, or else the object will never 280// be deleted! 281static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 282 SCEVCommutativeExpr*> > SCEVCommExprs; 283 284SCEVCommutativeExpr::~SCEVCommutativeExpr() { 285 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 286 std::vector<SCEV*>(Operands.begin(), 287 Operands.end()))); 288} 289 290void SCEVCommutativeExpr::print(std::ostream &OS) const { 291 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 292 const char *OpStr = getOperationStr(); 293 OS << "(" << *Operands[0]; 294 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 295 OS << OpStr << *Operands[i]; 296 OS << ")"; 297} 298 299SCEVHandle SCEVCommutativeExpr:: 300replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 301 const SCEVHandle &Conc) const { 302 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 303 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 304 if (H != getOperand(i)) { 305 std::vector<SCEVHandle> NewOps; 306 NewOps.reserve(getNumOperands()); 307 for (unsigned j = 0; j != i; ++j) 308 NewOps.push_back(getOperand(j)); 309 NewOps.push_back(H); 310 for (++i; i != e; ++i) 311 NewOps.push_back(getOperand(i)-> 312 replaceSymbolicValuesWithConcrete(Sym, Conc)); 313 314 if (isa<SCEVAddExpr>(this)) 315 return SCEVAddExpr::get(NewOps); 316 else if (isa<SCEVMulExpr>(this)) 317 return SCEVMulExpr::get(NewOps); 318 else 319 assert(0 && "Unknown commutative expr!"); 320 } 321 } 322 return this; 323} 324 325 326// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular 327// input. Don't use a SCEVHandle here, or else the object will never be 328// deleted! 329static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 330 SCEVSDivExpr*> > SCEVSDivs; 331 332SCEVSDivExpr::~SCEVSDivExpr() { 333 SCEVSDivs->erase(std::make_pair(LHS, RHS)); 334} 335 336void SCEVSDivExpr::print(std::ostream &OS) const { 337 OS << "(" << *LHS << " /s " << *RHS << ")"; 338} 339 340const Type *SCEVSDivExpr::getType() const { 341 return LHS->getType(); 342} 343 344// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 345// particular input. Don't use a SCEVHandle here, or else the object will never 346// be deleted! 347static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 348 SCEVAddRecExpr*> > SCEVAddRecExprs; 349 350SCEVAddRecExpr::~SCEVAddRecExpr() { 351 SCEVAddRecExprs->erase(std::make_pair(L, 352 std::vector<SCEV*>(Operands.begin(), 353 Operands.end()))); 354} 355 356SCEVHandle SCEVAddRecExpr:: 357replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 358 const SCEVHandle &Conc) const { 359 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 360 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 361 if (H != getOperand(i)) { 362 std::vector<SCEVHandle> NewOps; 363 NewOps.reserve(getNumOperands()); 364 for (unsigned j = 0; j != i; ++j) 365 NewOps.push_back(getOperand(j)); 366 NewOps.push_back(H); 367 for (++i; i != e; ++i) 368 NewOps.push_back(getOperand(i)-> 369 replaceSymbolicValuesWithConcrete(Sym, Conc)); 370 371 return get(NewOps, L); 372 } 373 } 374 return this; 375} 376 377 378bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 379 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 380 // contain L and if the start is invariant. 381 return !QueryLoop->contains(L->getHeader()) && 382 getOperand(0)->isLoopInvariant(QueryLoop); 383} 384 385 386void SCEVAddRecExpr::print(std::ostream &OS) const { 387 OS << "{" << *Operands[0]; 388 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 389 OS << ",+," << *Operands[i]; 390 OS << "}<" << L->getHeader()->getName() + ">"; 391} 392 393// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 394// value. Don't use a SCEVHandle here, or else the object will never be 395// deleted! 396static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 397 398SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 399 400bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 401 // All non-instruction values are loop invariant. All instructions are loop 402 // invariant if they are not contained in the specified loop. 403 if (Instruction *I = dyn_cast<Instruction>(V)) 404 return !L->contains(I->getParent()); 405 return true; 406} 407 408const Type *SCEVUnknown::getType() const { 409 return V->getType(); 410} 411 412void SCEVUnknown::print(std::ostream &OS) const { 413 WriteAsOperand(OS, V, false); 414} 415 416//===----------------------------------------------------------------------===// 417// SCEV Utilities 418//===----------------------------------------------------------------------===// 419 420namespace { 421 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 422 /// than the complexity of the RHS. This comparator is used to canonicalize 423 /// expressions. 424 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 425 bool operator()(SCEV *LHS, SCEV *RHS) { 426 return LHS->getSCEVType() < RHS->getSCEVType(); 427 } 428 }; 429} 430 431/// GroupByComplexity - Given a list of SCEV objects, order them by their 432/// complexity, and group objects of the same complexity together by value. 433/// When this routine is finished, we know that any duplicates in the vector are 434/// consecutive and that complexity is monotonically increasing. 435/// 436/// Note that we go take special precautions to ensure that we get determinstic 437/// results from this routine. In other words, we don't want the results of 438/// this to depend on where the addresses of various SCEV objects happened to 439/// land in memory. 440/// 441static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 442 if (Ops.size() < 2) return; // Noop 443 if (Ops.size() == 2) { 444 // This is the common case, which also happens to be trivially simple. 445 // Special case it. 446 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 447 std::swap(Ops[0], Ops[1]); 448 return; 449 } 450 451 // Do the rough sort by complexity. 452 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 453 454 // Now that we are sorted by complexity, group elements of the same 455 // complexity. Note that this is, at worst, N^2, but the vector is likely to 456 // be extremely short in practice. Note that we take this approach because we 457 // do not want to depend on the addresses of the objects we are grouping. 458 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 459 SCEV *S = Ops[i]; 460 unsigned Complexity = S->getSCEVType(); 461 462 // If there are any objects of the same complexity and same value as this 463 // one, group them. 464 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 465 if (Ops[j] == S) { // Found a duplicate. 466 // Move it to immediately after i'th element. 467 std::swap(Ops[i+1], Ops[j]); 468 ++i; // no need to rescan it. 469 if (i == e-2) return; // Done! 470 } 471 } 472 } 473} 474 475 476 477//===----------------------------------------------------------------------===// 478// Simple SCEV method implementations 479//===----------------------------------------------------------------------===// 480 481/// getIntegerSCEV - Given an integer or FP type, create a constant for the 482/// specified signed integer value and return a SCEV for the constant. 483SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 484 Constant *C; 485 if (Val == 0) 486 C = Constant::getNullValue(Ty); 487 else if (Ty->isFloatingPoint()) 488 C = ConstantFP::get(Ty, Val); 489 else 490 C = ConstantInt::get(Ty, Val); 491 return SCEVUnknown::get(C); 492} 493 494/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 495/// input value to the specified type. If the type must be extended, it is zero 496/// extended. 497static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 498 const Type *SrcTy = V->getType(); 499 assert(SrcTy->isInteger() && Ty->isInteger() && 500 "Cannot truncate or zero extend with non-integer arguments!"); 501 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 502 return V; // No conversion 503 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 504 return SCEVTruncateExpr::get(V, Ty); 505 return SCEVZeroExtendExpr::get(V, Ty); 506} 507 508/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 509/// 510SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) { 511 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 512 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 513 514 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 515} 516 517/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 518/// 519SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 520 // X - Y --> X + -Y 521 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS)); 522} 523 524 525/// PartialFact - Compute V!/(V-NumSteps)! 526static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 527 // Handle this case efficiently, it is common to have constant iteration 528 // counts while computing loop exit values. 529 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 530 const APInt& Val = SC->getValue()->getValue(); 531 APInt Result(Val.getBitWidth(), 1); 532 for (; NumSteps; --NumSteps) 533 Result *= Val-(NumSteps-1); 534 return SCEVConstant::get(Result); 535 } 536 537 const Type *Ty = V->getType(); 538 if (NumSteps == 0) 539 return SCEVUnknown::getIntegerSCEV(1, Ty); 540 541 SCEVHandle Result = V; 542 for (unsigned i = 1; i != NumSteps; ++i) 543 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V, 544 SCEVUnknown::getIntegerSCEV(i, Ty))); 545 return Result; 546} 547 548 549/// evaluateAtIteration - Return the value of this chain of recurrences at 550/// the specified iteration number. We can evaluate this recurrence by 551/// multiplying each element in the chain by the binomial coefficient 552/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 553/// 554/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 555/// 556/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 557/// Is the binomial equation safe using modular arithmetic?? 558/// 559SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 560 SCEVHandle Result = getStart(); 561 int Divisor = 1; 562 const Type *Ty = It->getType(); 563 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 564 SCEVHandle BC = PartialFact(It, i); 565 Divisor *= i; 566 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 567 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 568 Result = SCEVAddExpr::get(Result, Val); 569 } 570 return Result; 571} 572 573 574//===----------------------------------------------------------------------===// 575// SCEV Expression folder implementations 576//===----------------------------------------------------------------------===// 577 578SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 579 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 580 return SCEVUnknown::get( 581 ConstantExpr::getTrunc(SC->getValue(), Ty)); 582 583 // If the input value is a chrec scev made out of constants, truncate 584 // all of the constants. 585 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 586 std::vector<SCEVHandle> Operands; 587 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 588 // FIXME: This should allow truncation of other expression types! 589 if (isa<SCEVConstant>(AddRec->getOperand(i))) 590 Operands.push_back(get(AddRec->getOperand(i), Ty)); 591 else 592 break; 593 if (Operands.size() == AddRec->getNumOperands()) 594 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 595 } 596 597 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 598 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 599 return Result; 600} 601 602SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 603 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 604 return SCEVUnknown::get( 605 ConstantExpr::getZExt(SC->getValue(), Ty)); 606 607 // FIXME: If the input value is a chrec scev, and we can prove that the value 608 // did not overflow the old, smaller, value, we can zero extend all of the 609 // operands (often constants). This would allow analysis of something like 610 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 611 612 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 613 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 614 return Result; 615} 616 617SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 618 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 619 return SCEVUnknown::get( 620 ConstantExpr::getSExt(SC->getValue(), Ty)); 621 622 // FIXME: If the input value is a chrec scev, and we can prove that the value 623 // did not overflow the old, smaller, value, we can sign extend all of the 624 // operands (often constants). This would allow analysis of something like 625 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 626 627 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 628 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 629 return Result; 630} 631 632// get - Get a canonical add expression, or something simpler if possible. 633SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 634 assert(!Ops.empty() && "Cannot get empty add!"); 635 if (Ops.size() == 1) return Ops[0]; 636 637 // Sort by complexity, this groups all similar expression types together. 638 GroupByComplexity(Ops); 639 640 // If there are any constants, fold them together. 641 unsigned Idx = 0; 642 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 643 ++Idx; 644 assert(Idx < Ops.size()); 645 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 646 // We found two constants, fold them together! 647 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 648 RHSC->getValue()->getValue()); 649 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 650 Ops[0] = SCEVConstant::get(CI); 651 Ops.erase(Ops.begin()+1); // Erase the folded element 652 if (Ops.size() == 1) return Ops[0]; 653 LHSC = cast<SCEVConstant>(Ops[0]); 654 } else { 655 // If we couldn't fold the expression, move to the next constant. Note 656 // that this is impossible to happen in practice because we always 657 // constant fold constant ints to constant ints. 658 ++Idx; 659 } 660 } 661 662 // If we are left with a constant zero being added, strip it off. 663 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 664 Ops.erase(Ops.begin()); 665 --Idx; 666 } 667 } 668 669 if (Ops.size() == 1) return Ops[0]; 670 671 // Okay, check to see if the same value occurs in the operand list twice. If 672 // so, merge them together into an multiply expression. Since we sorted the 673 // list, these values are required to be adjacent. 674 const Type *Ty = Ops[0]->getType(); 675 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 676 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 677 // Found a match, merge the two values into a multiply, and add any 678 // remaining values to the result. 679 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 680 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 681 if (Ops.size() == 2) 682 return Mul; 683 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 684 Ops.push_back(Mul); 685 return SCEVAddExpr::get(Ops); 686 } 687 688 // Now we know the first non-constant operand. Skip past any cast SCEVs. 689 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 690 ++Idx; 691 692 // If there are add operands they would be next. 693 if (Idx < Ops.size()) { 694 bool DeletedAdd = false; 695 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 696 // If we have an add, expand the add operands onto the end of the operands 697 // list. 698 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 699 Ops.erase(Ops.begin()+Idx); 700 DeletedAdd = true; 701 } 702 703 // If we deleted at least one add, we added operands to the end of the list, 704 // and they are not necessarily sorted. Recurse to resort and resimplify 705 // any operands we just aquired. 706 if (DeletedAdd) 707 return get(Ops); 708 } 709 710 // Skip over the add expression until we get to a multiply. 711 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 712 ++Idx; 713 714 // If we are adding something to a multiply expression, make sure the 715 // something is not already an operand of the multiply. If so, merge it into 716 // the multiply. 717 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 718 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 719 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 720 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 721 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 722 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 723 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 724 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 725 if (Mul->getNumOperands() != 2) { 726 // If the multiply has more than two operands, we must get the 727 // Y*Z term. 728 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 729 MulOps.erase(MulOps.begin()+MulOp); 730 InnerMul = SCEVMulExpr::get(MulOps); 731 } 732 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 733 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 734 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 735 if (Ops.size() == 2) return OuterMul; 736 if (AddOp < Idx) { 737 Ops.erase(Ops.begin()+AddOp); 738 Ops.erase(Ops.begin()+Idx-1); 739 } else { 740 Ops.erase(Ops.begin()+Idx); 741 Ops.erase(Ops.begin()+AddOp-1); 742 } 743 Ops.push_back(OuterMul); 744 return SCEVAddExpr::get(Ops); 745 } 746 747 // Check this multiply against other multiplies being added together. 748 for (unsigned OtherMulIdx = Idx+1; 749 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 750 ++OtherMulIdx) { 751 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 752 // If MulOp occurs in OtherMul, we can fold the two multiplies 753 // together. 754 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 755 OMulOp != e; ++OMulOp) 756 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 757 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 758 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 759 if (Mul->getNumOperands() != 2) { 760 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 761 MulOps.erase(MulOps.begin()+MulOp); 762 InnerMul1 = SCEVMulExpr::get(MulOps); 763 } 764 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 765 if (OtherMul->getNumOperands() != 2) { 766 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 767 OtherMul->op_end()); 768 MulOps.erase(MulOps.begin()+OMulOp); 769 InnerMul2 = SCEVMulExpr::get(MulOps); 770 } 771 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 772 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 773 if (Ops.size() == 2) return OuterMul; 774 Ops.erase(Ops.begin()+Idx); 775 Ops.erase(Ops.begin()+OtherMulIdx-1); 776 Ops.push_back(OuterMul); 777 return SCEVAddExpr::get(Ops); 778 } 779 } 780 } 781 } 782 783 // If there are any add recurrences in the operands list, see if any other 784 // added values are loop invariant. If so, we can fold them into the 785 // recurrence. 786 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 787 ++Idx; 788 789 // Scan over all recurrences, trying to fold loop invariants into them. 790 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 791 // Scan all of the other operands to this add and add them to the vector if 792 // they are loop invariant w.r.t. the recurrence. 793 std::vector<SCEVHandle> LIOps; 794 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 795 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 796 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 797 LIOps.push_back(Ops[i]); 798 Ops.erase(Ops.begin()+i); 799 --i; --e; 800 } 801 802 // If we found some loop invariants, fold them into the recurrence. 803 if (!LIOps.empty()) { 804 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 805 LIOps.push_back(AddRec->getStart()); 806 807 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 808 AddRecOps[0] = SCEVAddExpr::get(LIOps); 809 810 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 811 // If all of the other operands were loop invariant, we are done. 812 if (Ops.size() == 1) return NewRec; 813 814 // Otherwise, add the folded AddRec by the non-liv parts. 815 for (unsigned i = 0;; ++i) 816 if (Ops[i] == AddRec) { 817 Ops[i] = NewRec; 818 break; 819 } 820 return SCEVAddExpr::get(Ops); 821 } 822 823 // Okay, if there weren't any loop invariants to be folded, check to see if 824 // there are multiple AddRec's with the same loop induction variable being 825 // added together. If so, we can fold them. 826 for (unsigned OtherIdx = Idx+1; 827 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 828 if (OtherIdx != Idx) { 829 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 830 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 831 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 832 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 833 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 834 if (i >= NewOps.size()) { 835 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 836 OtherAddRec->op_end()); 837 break; 838 } 839 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 840 } 841 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 842 843 if (Ops.size() == 2) return NewAddRec; 844 845 Ops.erase(Ops.begin()+Idx); 846 Ops.erase(Ops.begin()+OtherIdx-1); 847 Ops.push_back(NewAddRec); 848 return SCEVAddExpr::get(Ops); 849 } 850 } 851 852 // Otherwise couldn't fold anything into this recurrence. Move onto the 853 // next one. 854 } 855 856 // Okay, it looks like we really DO need an add expr. Check to see if we 857 // already have one, otherwise create a new one. 858 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 859 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 860 SCEVOps)]; 861 if (Result == 0) Result = new SCEVAddExpr(Ops); 862 return Result; 863} 864 865 866SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 867 assert(!Ops.empty() && "Cannot get empty mul!"); 868 869 // Sort by complexity, this groups all similar expression types together. 870 GroupByComplexity(Ops); 871 872 // If there are any constants, fold them together. 873 unsigned Idx = 0; 874 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 875 876 // C1*(C2+V) -> C1*C2 + C1*V 877 if (Ops.size() == 2) 878 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 879 if (Add->getNumOperands() == 2 && 880 isa<SCEVConstant>(Add->getOperand(0))) 881 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 882 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 883 884 885 ++Idx; 886 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 887 // We found two constants, fold them together! 888 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 889 RHSC->getValue()->getValue()); 890 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 891 Ops[0] = SCEVConstant::get(CI); 892 Ops.erase(Ops.begin()+1); // Erase the folded element 893 if (Ops.size() == 1) return Ops[0]; 894 LHSC = cast<SCEVConstant>(Ops[0]); 895 } else { 896 // If we couldn't fold the expression, move to the next constant. Note 897 // that this is impossible to happen in practice because we always 898 // constant fold constant ints to constant ints. 899 ++Idx; 900 } 901 } 902 903 // If we are left with a constant one being multiplied, strip it off. 904 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 905 Ops.erase(Ops.begin()); 906 --Idx; 907 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 908 // If we have a multiply of zero, it will always be zero. 909 return Ops[0]; 910 } 911 } 912 913 // Skip over the add expression until we get to a multiply. 914 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 915 ++Idx; 916 917 if (Ops.size() == 1) 918 return Ops[0]; 919 920 // If there are mul operands inline them all into this expression. 921 if (Idx < Ops.size()) { 922 bool DeletedMul = false; 923 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 924 // If we have an mul, expand the mul operands onto the end of the operands 925 // list. 926 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 927 Ops.erase(Ops.begin()+Idx); 928 DeletedMul = true; 929 } 930 931 // If we deleted at least one mul, we added operands to the end of the list, 932 // and they are not necessarily sorted. Recurse to resort and resimplify 933 // any operands we just aquired. 934 if (DeletedMul) 935 return get(Ops); 936 } 937 938 // If there are any add recurrences in the operands list, see if any other 939 // added values are loop invariant. If so, we can fold them into the 940 // recurrence. 941 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 942 ++Idx; 943 944 // Scan over all recurrences, trying to fold loop invariants into them. 945 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 946 // Scan all of the other operands to this mul and add them to the vector if 947 // they are loop invariant w.r.t. the recurrence. 948 std::vector<SCEVHandle> LIOps; 949 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 950 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 951 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 952 LIOps.push_back(Ops[i]); 953 Ops.erase(Ops.begin()+i); 954 --i; --e; 955 } 956 957 // If we found some loop invariants, fold them into the recurrence. 958 if (!LIOps.empty()) { 959 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 960 std::vector<SCEVHandle> NewOps; 961 NewOps.reserve(AddRec->getNumOperands()); 962 if (LIOps.size() == 1) { 963 SCEV *Scale = LIOps[0]; 964 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 965 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 966 } else { 967 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 968 std::vector<SCEVHandle> MulOps(LIOps); 969 MulOps.push_back(AddRec->getOperand(i)); 970 NewOps.push_back(SCEVMulExpr::get(MulOps)); 971 } 972 } 973 974 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 975 976 // If all of the other operands were loop invariant, we are done. 977 if (Ops.size() == 1) return NewRec; 978 979 // Otherwise, multiply the folded AddRec by the non-liv parts. 980 for (unsigned i = 0;; ++i) 981 if (Ops[i] == AddRec) { 982 Ops[i] = NewRec; 983 break; 984 } 985 return SCEVMulExpr::get(Ops); 986 } 987 988 // Okay, if there weren't any loop invariants to be folded, check to see if 989 // there are multiple AddRec's with the same loop induction variable being 990 // multiplied together. If so, we can fold them. 991 for (unsigned OtherIdx = Idx+1; 992 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 993 if (OtherIdx != Idx) { 994 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 995 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 996 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 997 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 998 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 999 G->getStart()); 1000 SCEVHandle B = F->getStepRecurrence(); 1001 SCEVHandle D = G->getStepRecurrence(); 1002 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 1003 SCEVMulExpr::get(G, B), 1004 SCEVMulExpr::get(B, D)); 1005 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 1006 F->getLoop()); 1007 if (Ops.size() == 2) return NewAddRec; 1008 1009 Ops.erase(Ops.begin()+Idx); 1010 Ops.erase(Ops.begin()+OtherIdx-1); 1011 Ops.push_back(NewAddRec); 1012 return SCEVMulExpr::get(Ops); 1013 } 1014 } 1015 1016 // Otherwise couldn't fold anything into this recurrence. Move onto the 1017 // next one. 1018 } 1019 1020 // Okay, it looks like we really DO need an mul expr. Check to see if we 1021 // already have one, otherwise create a new one. 1022 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1023 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1024 SCEVOps)]; 1025 if (Result == 0) 1026 Result = new SCEVMulExpr(Ops); 1027 return Result; 1028} 1029 1030SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1031 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1032 if (RHSC->getValue()->equalsInt(1)) 1033 return LHS; // X sdiv 1 --> x 1034 if (RHSC->getValue()->isAllOnesValue()) 1035 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x 1036 1037 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1038 Constant *LHSCV = LHSC->getValue(); 1039 Constant *RHSCV = RHSC->getValue(); 1040 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV)); 1041 } 1042 } 1043 1044 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1045 1046 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)]; 1047 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS); 1048 return Result; 1049} 1050 1051 1052/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1053/// specified loop. Simplify the expression as much as possible. 1054SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1055 const SCEVHandle &Step, const Loop *L) { 1056 std::vector<SCEVHandle> Operands; 1057 Operands.push_back(Start); 1058 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1059 if (StepChrec->getLoop() == L) { 1060 Operands.insert(Operands.end(), StepChrec->op_begin(), 1061 StepChrec->op_end()); 1062 return get(Operands, L); 1063 } 1064 1065 Operands.push_back(Step); 1066 return get(Operands, L); 1067} 1068 1069/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1070/// specified loop. Simplify the expression as much as possible. 1071SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1072 const Loop *L) { 1073 if (Operands.size() == 1) return Operands[0]; 1074 1075 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1076 if (StepC->getValue()->isZero()) { 1077 Operands.pop_back(); 1078 return get(Operands, L); // { X,+,0 } --> X 1079 } 1080 1081 SCEVAddRecExpr *&Result = 1082 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1083 Operands.end()))]; 1084 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1085 return Result; 1086} 1087 1088SCEVHandle SCEVUnknown::get(Value *V) { 1089 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1090 return SCEVConstant::get(CI); 1091 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1092 if (Result == 0) Result = new SCEVUnknown(V); 1093 return Result; 1094} 1095 1096 1097//===----------------------------------------------------------------------===// 1098// ScalarEvolutionsImpl Definition and Implementation 1099//===----------------------------------------------------------------------===// 1100// 1101/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1102/// evolution code. 1103/// 1104namespace { 1105 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1106 /// F - The function we are analyzing. 1107 /// 1108 Function &F; 1109 1110 /// LI - The loop information for the function we are currently analyzing. 1111 /// 1112 LoopInfo &LI; 1113 1114 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1115 /// things. 1116 SCEVHandle UnknownValue; 1117 1118 /// Scalars - This is a cache of the scalars we have analyzed so far. 1119 /// 1120 std::map<Value*, SCEVHandle> Scalars; 1121 1122 /// IterationCounts - Cache the iteration count of the loops for this 1123 /// function as they are computed. 1124 std::map<const Loop*, SCEVHandle> IterationCounts; 1125 1126 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1127 /// the PHI instructions that we attempt to compute constant evolutions for. 1128 /// This allows us to avoid potentially expensive recomputation of these 1129 /// properties. An instruction maps to null if we are unable to compute its 1130 /// exit value. 1131 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1132 1133 public: 1134 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1135 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1136 1137 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1138 /// expression and create a new one. 1139 SCEVHandle getSCEV(Value *V); 1140 1141 /// hasSCEV - Return true if the SCEV for this value has already been 1142 /// computed. 1143 bool hasSCEV(Value *V) const { 1144 return Scalars.count(V); 1145 } 1146 1147 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1148 /// the specified value. 1149 void setSCEV(Value *V, const SCEVHandle &H) { 1150 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1151 assert(isNew && "This entry already existed!"); 1152 } 1153 1154 1155 /// getSCEVAtScope - Compute the value of the specified expression within 1156 /// the indicated loop (which may be null to indicate in no loop). If the 1157 /// expression cannot be evaluated, return UnknownValue itself. 1158 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1159 1160 1161 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1162 /// an analyzable loop-invariant iteration count. 1163 bool hasLoopInvariantIterationCount(const Loop *L); 1164 1165 /// getIterationCount - If the specified loop has a predictable iteration 1166 /// count, return it. Note that it is not valid to call this method on a 1167 /// loop without a loop-invariant iteration count. 1168 SCEVHandle getIterationCount(const Loop *L); 1169 1170 /// deleteValueFromRecords - This method should be called by the 1171 /// client before it removes a value from the program, to make sure 1172 /// that no dangling references are left around. 1173 void deleteValueFromRecords(Value *V); 1174 1175 private: 1176 /// createSCEV - We know that there is no SCEV for the specified value. 1177 /// Analyze the expression. 1178 SCEVHandle createSCEV(Value *V); 1179 1180 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1181 /// SCEVs. 1182 SCEVHandle createNodeForPHI(PHINode *PN); 1183 1184 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1185 /// for the specified instruction and replaces any references to the 1186 /// symbolic value SymName with the specified value. This is used during 1187 /// PHI resolution. 1188 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1189 const SCEVHandle &SymName, 1190 const SCEVHandle &NewVal); 1191 1192 /// ComputeIterationCount - Compute the number of times the specified loop 1193 /// will iterate. 1194 SCEVHandle ComputeIterationCount(const Loop *L); 1195 1196 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1197 /// 'setcc load X, cst', try to see if we can compute the trip count. 1198 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1199 Constant *RHS, 1200 const Loop *L, 1201 ICmpInst::Predicate p); 1202 1203 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1204 /// constant number of times (the condition evolves only from constants), 1205 /// try to evaluate a few iterations of the loop until we get the exit 1206 /// condition gets a value of ExitWhen (true or false). If we cannot 1207 /// evaluate the trip count of the loop, return UnknownValue. 1208 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1209 bool ExitWhen); 1210 1211 /// HowFarToZero - Return the number of times a backedge comparing the 1212 /// specified value to zero will execute. If not computable, return 1213 /// UnknownValue. 1214 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1215 1216 /// HowFarToNonZero - Return the number of times a backedge checking the 1217 /// specified value for nonzero will execute. If not computable, return 1218 /// UnknownValue. 1219 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1220 1221 /// HowManyLessThans - Return the number of times a backedge containing the 1222 /// specified less-than comparison will execute. If not computable, return 1223 /// UnknownValue. isSigned specifies whether the less-than is signed. 1224 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1225 bool isSigned); 1226 1227 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1228 /// in the header of its containing loop, we know the loop executes a 1229 /// constant number of times, and the PHI node is just a recurrence 1230 /// involving constants, fold it. 1231 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1232 const Loop *L); 1233 }; 1234} 1235 1236//===----------------------------------------------------------------------===// 1237// Basic SCEV Analysis and PHI Idiom Recognition Code 1238// 1239 1240/// deleteValueFromRecords - This method should be called by the 1241/// client before it removes an instruction from the program, to make sure 1242/// that no dangling references are left around. 1243void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1244 SmallVector<Value *, 16> Worklist; 1245 1246 if (Scalars.erase(V)) { 1247 if (PHINode *PN = dyn_cast<PHINode>(V)) 1248 ConstantEvolutionLoopExitValue.erase(PN); 1249 Worklist.push_back(V); 1250 } 1251 1252 while (!Worklist.empty()) { 1253 Value *VV = Worklist.back(); 1254 Worklist.pop_back(); 1255 1256 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1257 UI != UE; ++UI) { 1258 Instruction *Inst = cast<Instruction>(*UI); 1259 if (Scalars.erase(Inst)) { 1260 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1261 ConstantEvolutionLoopExitValue.erase(PN); 1262 Worklist.push_back(Inst); 1263 } 1264 } 1265 } 1266} 1267 1268 1269/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1270/// expression and create a new one. 1271SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1272 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1273 1274 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1275 if (I != Scalars.end()) return I->second; 1276 SCEVHandle S = createSCEV(V); 1277 Scalars.insert(std::make_pair(V, S)); 1278 return S; 1279} 1280 1281/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1282/// the specified instruction and replaces any references to the symbolic value 1283/// SymName with the specified value. This is used during PHI resolution. 1284void ScalarEvolutionsImpl:: 1285ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1286 const SCEVHandle &NewVal) { 1287 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1288 if (SI == Scalars.end()) return; 1289 1290 SCEVHandle NV = 1291 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1292 if (NV == SI->second) return; // No change. 1293 1294 SI->second = NV; // Update the scalars map! 1295 1296 // Any instruction values that use this instruction might also need to be 1297 // updated! 1298 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1299 UI != E; ++UI) 1300 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1301} 1302 1303/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1304/// a loop header, making it a potential recurrence, or it doesn't. 1305/// 1306SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1307 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1308 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1309 if (L->getHeader() == PN->getParent()) { 1310 // If it lives in the loop header, it has two incoming values, one 1311 // from outside the loop, and one from inside. 1312 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1313 unsigned BackEdge = IncomingEdge^1; 1314 1315 // While we are analyzing this PHI node, handle its value symbolically. 1316 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1317 assert(Scalars.find(PN) == Scalars.end() && 1318 "PHI node already processed?"); 1319 Scalars.insert(std::make_pair(PN, SymbolicName)); 1320 1321 // Using this symbolic name for the PHI, analyze the value coming around 1322 // the back-edge. 1323 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1324 1325 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1326 // has a special value for the first iteration of the loop. 1327 1328 // If the value coming around the backedge is an add with the symbolic 1329 // value we just inserted, then we found a simple induction variable! 1330 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1331 // If there is a single occurrence of the symbolic value, replace it 1332 // with a recurrence. 1333 unsigned FoundIndex = Add->getNumOperands(); 1334 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1335 if (Add->getOperand(i) == SymbolicName) 1336 if (FoundIndex == e) { 1337 FoundIndex = i; 1338 break; 1339 } 1340 1341 if (FoundIndex != Add->getNumOperands()) { 1342 // Create an add with everything but the specified operand. 1343 std::vector<SCEVHandle> Ops; 1344 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1345 if (i != FoundIndex) 1346 Ops.push_back(Add->getOperand(i)); 1347 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1348 1349 // This is not a valid addrec if the step amount is varying each 1350 // loop iteration, but is not itself an addrec in this loop. 1351 if (Accum->isLoopInvariant(L) || 1352 (isa<SCEVAddRecExpr>(Accum) && 1353 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1354 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1355 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1356 1357 // Okay, for the entire analysis of this edge we assumed the PHI 1358 // to be symbolic. We now need to go back and update all of the 1359 // entries for the scalars that use the PHI (except for the PHI 1360 // itself) to use the new analyzed value instead of the "symbolic" 1361 // value. 1362 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1363 return PHISCEV; 1364 } 1365 } 1366 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1367 // Otherwise, this could be a loop like this: 1368 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1369 // In this case, j = {1,+,1} and BEValue is j. 1370 // Because the other in-value of i (0) fits the evolution of BEValue 1371 // i really is an addrec evolution. 1372 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1373 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1374 1375 // If StartVal = j.start - j.stride, we can use StartVal as the 1376 // initial step of the addrec evolution. 1377 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0), 1378 AddRec->getOperand(1))) { 1379 SCEVHandle PHISCEV = 1380 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L); 1381 1382 // Okay, for the entire analysis of this edge we assumed the PHI 1383 // to be symbolic. We now need to go back and update all of the 1384 // entries for the scalars that use the PHI (except for the PHI 1385 // itself) to use the new analyzed value instead of the "symbolic" 1386 // value. 1387 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1388 return PHISCEV; 1389 } 1390 } 1391 } 1392 1393 return SymbolicName; 1394 } 1395 1396 // If it's not a loop phi, we can't handle it yet. 1397 return SCEVUnknown::get(PN); 1398} 1399 1400/// GetConstantFactor - Determine the largest constant factor that S has. For 1401/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero. 1402static APInt GetConstantFactor(SCEVHandle S) { 1403 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 1404 const APInt& V = C->getValue()->getValue(); 1405 if (!V.isMinValue()) 1406 return V; 1407 else // Zero is a multiple of everything. 1408 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1); 1409 } 1410 1411 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) { 1412 return GetConstantFactor(T->getOperand()).trunc( 1413 cast<IntegerType>(T->getType())->getBitWidth()); 1414 } 1415 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) 1416 return GetConstantFactor(E->getOperand()).zext( 1417 cast<IntegerType>(E->getType())->getBitWidth()); 1418 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) 1419 return GetConstantFactor(E->getOperand()).sext( 1420 cast<IntegerType>(E->getType())->getBitWidth()); 1421 1422 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1423 // The result is the min of all operands. 1424 APInt Res(GetConstantFactor(A->getOperand(0))); 1425 for (unsigned i = 1, e = A->getNumOperands(); 1426 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) { 1427 APInt Tmp(GetConstantFactor(A->getOperand(i))); 1428 Res = APIntOps::umin(Res, Tmp); 1429 } 1430 return Res; 1431 } 1432 1433 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1434 // The result is the product of all the operands. 1435 APInt Res(GetConstantFactor(M->getOperand(0))); 1436 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) { 1437 APInt Tmp(GetConstantFactor(M->getOperand(i))); 1438 Res *= Tmp; 1439 } 1440 return Res; 1441 } 1442 1443 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1444 // For now, we just handle linear expressions. 1445 if (A->getNumOperands() == 2) { 1446 // We want the GCD between the start and the stride value. 1447 APInt Start(GetConstantFactor(A->getOperand(0))); 1448 if (Start == 1) 1449 return Start; 1450 APInt Stride(GetConstantFactor(A->getOperand(1))); 1451 return APIntOps::GreatestCommonDivisor(Start, Stride); 1452 } 1453 } 1454 1455 // SCEVSDivExpr, SCEVUnknown. 1456 return APInt(S->getBitWidth(), 1); 1457} 1458 1459/// createSCEV - We know that there is no SCEV for the specified value. 1460/// Analyze the expression. 1461/// 1462SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1463 if (Instruction *I = dyn_cast<Instruction>(V)) { 1464 switch (I->getOpcode()) { 1465 case Instruction::Add: 1466 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1467 getSCEV(I->getOperand(1))); 1468 case Instruction::Mul: 1469 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1470 getSCEV(I->getOperand(1))); 1471 case Instruction::SDiv: 1472 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)), 1473 getSCEV(I->getOperand(1))); 1474 break; 1475 1476 case Instruction::Sub: 1477 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)), 1478 getSCEV(I->getOperand(1))); 1479 case Instruction::Or: 1480 // If the RHS of the Or is a constant, we may have something like: 1481 // X*4+1 which got turned into X*4|1. Handle this as an add so loop 1482 // optimizations will transparently handle this case. 1483 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1484 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1485 APInt CommonFact(GetConstantFactor(LHS)); 1486 assert(!CommonFact.isMinValue() && 1487 "Common factor should at least be 1!"); 1488 if (CommonFact.ugt(CI->getValue())) { 1489 // If the LHS is a multiple that is larger than the RHS, use +. 1490 return SCEVAddExpr::get(LHS, 1491 getSCEV(I->getOperand(1))); 1492 } 1493 } 1494 break; 1495 case Instruction::Xor: 1496 // If the RHS of the xor is a signbit, then this is just an add. 1497 // Instcombine turns add of signbit into xor as a strength reduction step. 1498 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1499 if (CI->getValue().isSignBit()) 1500 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1501 getSCEV(I->getOperand(1))); 1502 } 1503 break; 1504 1505 case Instruction::Shl: 1506 // Turn shift left of a constant amount into a multiply. 1507 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1508 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1509 Constant *X = ConstantInt::get( 1510 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1511 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1512 } 1513 break; 1514 1515 case Instruction::Trunc: 1516 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1517 1518 case Instruction::ZExt: 1519 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1520 1521 case Instruction::SExt: 1522 return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType()); 1523 1524 case Instruction::BitCast: 1525 // BitCasts are no-op casts so we just eliminate the cast. 1526 if (I->getType()->isInteger() && 1527 I->getOperand(0)->getType()->isInteger()) 1528 return getSCEV(I->getOperand(0)); 1529 break; 1530 1531 case Instruction::PHI: 1532 return createNodeForPHI(cast<PHINode>(I)); 1533 1534 default: // We cannot analyze this expression. 1535 break; 1536 } 1537 } 1538 1539 return SCEVUnknown::get(V); 1540} 1541 1542 1543 1544//===----------------------------------------------------------------------===// 1545// Iteration Count Computation Code 1546// 1547 1548/// getIterationCount - If the specified loop has a predictable iteration 1549/// count, return it. Note that it is not valid to call this method on a 1550/// loop without a loop-invariant iteration count. 1551SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1552 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1553 if (I == IterationCounts.end()) { 1554 SCEVHandle ItCount = ComputeIterationCount(L); 1555 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1556 if (ItCount != UnknownValue) { 1557 assert(ItCount->isLoopInvariant(L) && 1558 "Computed trip count isn't loop invariant for loop!"); 1559 ++NumTripCountsComputed; 1560 } else if (isa<PHINode>(L->getHeader()->begin())) { 1561 // Only count loops that have phi nodes as not being computable. 1562 ++NumTripCountsNotComputed; 1563 } 1564 } 1565 return I->second; 1566} 1567 1568/// ComputeIterationCount - Compute the number of times the specified loop 1569/// will iterate. 1570SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1571 // If the loop has a non-one exit block count, we can't analyze it. 1572 SmallVector<BasicBlock*, 8> ExitBlocks; 1573 L->getExitBlocks(ExitBlocks); 1574 if (ExitBlocks.size() != 1) return UnknownValue; 1575 1576 // Okay, there is one exit block. Try to find the condition that causes the 1577 // loop to be exited. 1578 BasicBlock *ExitBlock = ExitBlocks[0]; 1579 1580 BasicBlock *ExitingBlock = 0; 1581 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1582 PI != E; ++PI) 1583 if (L->contains(*PI)) { 1584 if (ExitingBlock == 0) 1585 ExitingBlock = *PI; 1586 else 1587 return UnknownValue; // More than one block exiting! 1588 } 1589 assert(ExitingBlock && "No exits from loop, something is broken!"); 1590 1591 // Okay, we've computed the exiting block. See what condition causes us to 1592 // exit. 1593 // 1594 // FIXME: we should be able to handle switch instructions (with a single exit) 1595 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1596 if (ExitBr == 0) return UnknownValue; 1597 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1598 1599 // At this point, we know we have a conditional branch that determines whether 1600 // the loop is exited. However, we don't know if the branch is executed each 1601 // time through the loop. If not, then the execution count of the branch will 1602 // not be equal to the trip count of the loop. 1603 // 1604 // Currently we check for this by checking to see if the Exit branch goes to 1605 // the loop header. If so, we know it will always execute the same number of 1606 // times as the loop. We also handle the case where the exit block *is* the 1607 // loop header. This is common for un-rotated loops. More extensive analysis 1608 // could be done to handle more cases here. 1609 if (ExitBr->getSuccessor(0) != L->getHeader() && 1610 ExitBr->getSuccessor(1) != L->getHeader() && 1611 ExitBr->getParent() != L->getHeader()) 1612 return UnknownValue; 1613 1614 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1615 1616 // If its not an integer comparison then compute it the hard way. 1617 // Note that ICmpInst deals with pointer comparisons too so we must check 1618 // the type of the operand. 1619 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1620 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1621 ExitBr->getSuccessor(0) == ExitBlock); 1622 1623 // If the condition was exit on true, convert the condition to exit on false 1624 ICmpInst::Predicate Cond; 1625 if (ExitBr->getSuccessor(1) == ExitBlock) 1626 Cond = ExitCond->getPredicate(); 1627 else 1628 Cond = ExitCond->getInversePredicate(); 1629 1630 // Handle common loops like: for (X = "string"; *X; ++X) 1631 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1632 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1633 SCEVHandle ItCnt = 1634 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1635 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1636 } 1637 1638 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1639 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1640 1641 // Try to evaluate any dependencies out of the loop. 1642 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1643 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1644 Tmp = getSCEVAtScope(RHS, L); 1645 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1646 1647 // At this point, we would like to compute how many iterations of the 1648 // loop the predicate will return true for these inputs. 1649 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1650 // If there is a constant, force it into the RHS. 1651 std::swap(LHS, RHS); 1652 Cond = ICmpInst::getSwappedPredicate(Cond); 1653 } 1654 1655 // FIXME: think about handling pointer comparisons! i.e.: 1656 // while (P != P+100) ++P; 1657 1658 // If we have a comparison of a chrec against a constant, try to use value 1659 // ranges to answer this query. 1660 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1661 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1662 if (AddRec->getLoop() == L) { 1663 // Form the comparison range using the constant of the correct type so 1664 // that the ConstantRange class knows to do a signed or unsigned 1665 // comparison. 1666 ConstantInt *CompVal = RHSC->getValue(); 1667 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1668 CompVal = dyn_cast<ConstantInt>( 1669 ConstantExpr::getBitCast(CompVal, RealTy)); 1670 if (CompVal) { 1671 // Form the constant range. 1672 ConstantRange CompRange( 1673 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1674 1675 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1676 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1677 } 1678 } 1679 1680 switch (Cond) { 1681 case ICmpInst::ICMP_NE: { // while (X != Y) 1682 // Convert to: while (X-Y != 0) 1683 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L); 1684 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1685 break; 1686 } 1687 case ICmpInst::ICMP_EQ: { 1688 // Convert to: while (X-Y == 0) // while (X == Y) 1689 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L); 1690 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1691 break; 1692 } 1693 case ICmpInst::ICMP_SLT: { 1694 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1695 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1696 break; 1697 } 1698 case ICmpInst::ICMP_SGT: { 1699 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS), 1700 SCEV::getNegativeSCEV(RHS), L, true); 1701 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1702 break; 1703 } 1704 case ICmpInst::ICMP_ULT: { 1705 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1706 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1707 break; 1708 } 1709 case ICmpInst::ICMP_UGT: { 1710 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS), 1711 SCEV::getNegativeSCEV(RHS), L, false); 1712 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1713 break; 1714 } 1715 default: 1716#if 0 1717 cerr << "ComputeIterationCount "; 1718 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1719 cerr << "[unsigned] "; 1720 cerr << *LHS << " " 1721 << Instruction::getOpcodeName(Instruction::ICmp) 1722 << " " << *RHS << "\n"; 1723#endif 1724 break; 1725 } 1726 return ComputeIterationCountExhaustively(L, ExitCond, 1727 ExitBr->getSuccessor(0) == ExitBlock); 1728} 1729 1730static ConstantInt * 1731EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C) { 1732 SCEVHandle InVal = SCEVConstant::get(C); 1733 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1734 assert(isa<SCEVConstant>(Val) && 1735 "Evaluation of SCEV at constant didn't fold correctly?"); 1736 return cast<SCEVConstant>(Val)->getValue(); 1737} 1738 1739/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1740/// and a GEP expression (missing the pointer index) indexing into it, return 1741/// the addressed element of the initializer or null if the index expression is 1742/// invalid. 1743static Constant * 1744GetAddressedElementFromGlobal(GlobalVariable *GV, 1745 const std::vector<ConstantInt*> &Indices) { 1746 Constant *Init = GV->getInitializer(); 1747 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1748 uint64_t Idx = Indices[i]->getZExtValue(); 1749 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1750 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1751 Init = cast<Constant>(CS->getOperand(Idx)); 1752 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1753 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1754 Init = cast<Constant>(CA->getOperand(Idx)); 1755 } else if (isa<ConstantAggregateZero>(Init)) { 1756 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1757 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1758 Init = Constant::getNullValue(STy->getElementType(Idx)); 1759 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1760 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1761 Init = Constant::getNullValue(ATy->getElementType()); 1762 } else { 1763 assert(0 && "Unknown constant aggregate type!"); 1764 } 1765 return 0; 1766 } else { 1767 return 0; // Unknown initializer type 1768 } 1769 } 1770 return Init; 1771} 1772 1773/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1774/// 'setcc load X, cst', try to se if we can compute the trip count. 1775SCEVHandle ScalarEvolutionsImpl:: 1776ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1777 const Loop *L, 1778 ICmpInst::Predicate predicate) { 1779 if (LI->isVolatile()) return UnknownValue; 1780 1781 // Check to see if the loaded pointer is a getelementptr of a global. 1782 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1783 if (!GEP) return UnknownValue; 1784 1785 // Make sure that it is really a constant global we are gepping, with an 1786 // initializer, and make sure the first IDX is really 0. 1787 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1788 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1789 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1790 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1791 return UnknownValue; 1792 1793 // Okay, we allow one non-constant index into the GEP instruction. 1794 Value *VarIdx = 0; 1795 std::vector<ConstantInt*> Indexes; 1796 unsigned VarIdxNum = 0; 1797 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1798 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1799 Indexes.push_back(CI); 1800 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1801 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1802 VarIdx = GEP->getOperand(i); 1803 VarIdxNum = i-2; 1804 Indexes.push_back(0); 1805 } 1806 1807 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1808 // Check to see if X is a loop variant variable value now. 1809 SCEVHandle Idx = getSCEV(VarIdx); 1810 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1811 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1812 1813 // We can only recognize very limited forms of loop index expressions, in 1814 // particular, only affine AddRec's like {C1,+,C2}. 1815 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1816 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1817 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1818 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1819 return UnknownValue; 1820 1821 unsigned MaxSteps = MaxBruteForceIterations; 1822 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1823 ConstantInt *ItCst = 1824 ConstantInt::get(IdxExpr->getType(), IterationNum); 1825 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1826 1827 // Form the GEP offset. 1828 Indexes[VarIdxNum] = Val; 1829 1830 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1831 if (Result == 0) break; // Cannot compute! 1832 1833 // Evaluate the condition for this iteration. 1834 Result = ConstantExpr::getICmp(predicate, Result, RHS); 1835 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 1836 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 1837#if 0 1838 cerr << "\n***\n*** Computed loop count " << *ItCst 1839 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1840 << "***\n"; 1841#endif 1842 ++NumArrayLenItCounts; 1843 return SCEVConstant::get(ItCst); // Found terminating iteration! 1844 } 1845 } 1846 return UnknownValue; 1847} 1848 1849 1850/// CanConstantFold - Return true if we can constant fold an instruction of the 1851/// specified type, assuming that all operands were constants. 1852static bool CanConstantFold(const Instruction *I) { 1853 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 1854 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1855 return true; 1856 1857 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1858 if (const Function *F = CI->getCalledFunction()) 1859 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1860 return false; 1861} 1862 1863/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1864/// in the loop that V is derived from. We allow arbitrary operations along the 1865/// way, but the operands of an operation must either be constants or a value 1866/// derived from a constant PHI. If this expression does not fit with these 1867/// constraints, return null. 1868static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1869 // If this is not an instruction, or if this is an instruction outside of the 1870 // loop, it can't be derived from a loop PHI. 1871 Instruction *I = dyn_cast<Instruction>(V); 1872 if (I == 0 || !L->contains(I->getParent())) return 0; 1873 1874 if (PHINode *PN = dyn_cast<PHINode>(I)) 1875 if (L->getHeader() == I->getParent()) 1876 return PN; 1877 else 1878 // We don't currently keep track of the control flow needed to evaluate 1879 // PHIs, so we cannot handle PHIs inside of loops. 1880 return 0; 1881 1882 // If we won't be able to constant fold this expression even if the operands 1883 // are constants, return early. 1884 if (!CanConstantFold(I)) return 0; 1885 1886 // Otherwise, we can evaluate this instruction if all of its operands are 1887 // constant or derived from a PHI node themselves. 1888 PHINode *PHI = 0; 1889 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1890 if (!(isa<Constant>(I->getOperand(Op)) || 1891 isa<GlobalValue>(I->getOperand(Op)))) { 1892 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1893 if (P == 0) return 0; // Not evolving from PHI 1894 if (PHI == 0) 1895 PHI = P; 1896 else if (PHI != P) 1897 return 0; // Evolving from multiple different PHIs. 1898 } 1899 1900 // This is a expression evolving from a constant PHI! 1901 return PHI; 1902} 1903 1904/// EvaluateExpression - Given an expression that passes the 1905/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1906/// in the loop has the value PHIVal. If we can't fold this expression for some 1907/// reason, return null. 1908static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1909 if (isa<PHINode>(V)) return PHIVal; 1910 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1911 return GV; 1912 if (Constant *C = dyn_cast<Constant>(V)) return C; 1913 Instruction *I = cast<Instruction>(V); 1914 1915 std::vector<Constant*> Operands; 1916 Operands.resize(I->getNumOperands()); 1917 1918 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1919 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1920 if (Operands[i] == 0) return 0; 1921 } 1922 1923 return ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 1924} 1925 1926/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1927/// in the header of its containing loop, we know the loop executes a 1928/// constant number of times, and the PHI node is just a recurrence 1929/// involving constants, fold it. 1930Constant *ScalarEvolutionsImpl:: 1931getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 1932 std::map<PHINode*, Constant*>::iterator I = 1933 ConstantEvolutionLoopExitValue.find(PN); 1934 if (I != ConstantEvolutionLoopExitValue.end()) 1935 return I->second; 1936 1937 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 1938 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1939 1940 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1941 1942 // Since the loop is canonicalized, the PHI node must have two entries. One 1943 // entry must be a constant (coming in from outside of the loop), and the 1944 // second must be derived from the same PHI. 1945 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1946 Constant *StartCST = 1947 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1948 if (StartCST == 0) 1949 return RetVal = 0; // Must be a constant. 1950 1951 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1952 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1953 if (PN2 != PN) 1954 return RetVal = 0; // Not derived from same PHI. 1955 1956 // Execute the loop symbolically to determine the exit value. 1957 if (Its.getActiveBits() >= 32) 1958 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 1959 1960 unsigned NumIterations = Its.getZExtValue(); // must be in range 1961 unsigned IterationNum = 0; 1962 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1963 if (IterationNum == NumIterations) 1964 return RetVal = PHIVal; // Got exit value! 1965 1966 // Compute the value of the PHI node for the next iteration. 1967 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1968 if (NextPHI == PHIVal) 1969 return RetVal = NextPHI; // Stopped evolving! 1970 if (NextPHI == 0) 1971 return 0; // Couldn't evaluate! 1972 PHIVal = NextPHI; 1973 } 1974} 1975 1976/// ComputeIterationCountExhaustively - If the trip is known to execute a 1977/// constant number of times (the condition evolves only from constants), 1978/// try to evaluate a few iterations of the loop until we get the exit 1979/// condition gets a value of ExitWhen (true or false). If we cannot 1980/// evaluate the trip count of the loop, return UnknownValue. 1981SCEVHandle ScalarEvolutionsImpl:: 1982ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1983 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1984 if (PN == 0) return UnknownValue; 1985 1986 // Since the loop is canonicalized, the PHI node must have two entries. One 1987 // entry must be a constant (coming in from outside of the loop), and the 1988 // second must be derived from the same PHI. 1989 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1990 Constant *StartCST = 1991 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1992 if (StartCST == 0) return UnknownValue; // Must be a constant. 1993 1994 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1995 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1996 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1997 1998 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1999 // the loop symbolically to determine when the condition gets a value of 2000 // "ExitWhen". 2001 unsigned IterationNum = 0; 2002 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2003 for (Constant *PHIVal = StartCST; 2004 IterationNum != MaxIterations; ++IterationNum) { 2005 ConstantInt *CondVal = 2006 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2007 2008 // Couldn't symbolically evaluate. 2009 if (!CondVal) return UnknownValue; 2010 2011 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2012 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2013 ++NumBruteForceTripCountsComputed; 2014 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum)); 2015 } 2016 2017 // Compute the value of the PHI node for the next iteration. 2018 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2019 if (NextPHI == 0 || NextPHI == PHIVal) 2020 return UnknownValue; // Couldn't evaluate or not making progress... 2021 PHIVal = NextPHI; 2022 } 2023 2024 // Too many iterations were needed to evaluate. 2025 return UnknownValue; 2026} 2027 2028/// getSCEVAtScope - Compute the value of the specified expression within the 2029/// indicated loop (which may be null to indicate in no loop). If the 2030/// expression cannot be evaluated, return UnknownValue. 2031SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2032 // FIXME: this should be turned into a virtual method on SCEV! 2033 2034 if (isa<SCEVConstant>(V)) return V; 2035 2036 // If this instruction is evolves from a constant-evolving PHI, compute the 2037 // exit value from the loop without using SCEVs. 2038 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2039 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2040 const Loop *LI = this->LI[I->getParent()]; 2041 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2042 if (PHINode *PN = dyn_cast<PHINode>(I)) 2043 if (PN->getParent() == LI->getHeader()) { 2044 // Okay, there is no closed form solution for the PHI node. Check 2045 // to see if the loop that contains it has a known iteration count. 2046 // If so, we may be able to force computation of the exit value. 2047 SCEVHandle IterationCount = getIterationCount(LI); 2048 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2049 // Okay, we know how many times the containing loop executes. If 2050 // this is a constant evolving PHI node, get the final value at 2051 // the specified iteration number. 2052 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2053 ICC->getValue()->getValue(), 2054 LI); 2055 if (RV) return SCEVUnknown::get(RV); 2056 } 2057 } 2058 2059 // Okay, this is an expression that we cannot symbolically evaluate 2060 // into a SCEV. Check to see if it's possible to symbolically evaluate 2061 // the arguments into constants, and if so, try to constant propagate the 2062 // result. This is particularly useful for computing loop exit values. 2063 if (CanConstantFold(I)) { 2064 std::vector<Constant*> Operands; 2065 Operands.reserve(I->getNumOperands()); 2066 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2067 Value *Op = I->getOperand(i); 2068 if (Constant *C = dyn_cast<Constant>(Op)) { 2069 Operands.push_back(C); 2070 } else { 2071 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2072 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2073 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2074 Op->getType(), 2075 false)); 2076 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2077 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2078 Operands.push_back(ConstantExpr::getIntegerCast(C, 2079 Op->getType(), 2080 false)); 2081 else 2082 return V; 2083 } else { 2084 return V; 2085 } 2086 } 2087 } 2088 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size()); 2089 return SCEVUnknown::get(C); 2090 } 2091 } 2092 2093 // This is some other type of SCEVUnknown, just return it. 2094 return V; 2095 } 2096 2097 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2098 // Avoid performing the look-up in the common case where the specified 2099 // expression has no loop-variant portions. 2100 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2101 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2102 if (OpAtScope != Comm->getOperand(i)) { 2103 if (OpAtScope == UnknownValue) return UnknownValue; 2104 // Okay, at least one of these operands is loop variant but might be 2105 // foldable. Build a new instance of the folded commutative expression. 2106 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2107 NewOps.push_back(OpAtScope); 2108 2109 for (++i; i != e; ++i) { 2110 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2111 if (OpAtScope == UnknownValue) return UnknownValue; 2112 NewOps.push_back(OpAtScope); 2113 } 2114 if (isa<SCEVAddExpr>(Comm)) 2115 return SCEVAddExpr::get(NewOps); 2116 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 2117 return SCEVMulExpr::get(NewOps); 2118 } 2119 } 2120 // If we got here, all operands are loop invariant. 2121 return Comm; 2122 } 2123 2124 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) { 2125 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2126 if (LHS == UnknownValue) return LHS; 2127 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2128 if (RHS == UnknownValue) return RHS; 2129 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2130 return Div; // must be loop invariant 2131 return SCEVSDivExpr::get(LHS, RHS); 2132 } 2133 2134 // If this is a loop recurrence for a loop that does not contain L, then we 2135 // are dealing with the final value computed by the loop. 2136 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2137 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2138 // To evaluate this recurrence, we need to know how many times the AddRec 2139 // loop iterates. Compute this now. 2140 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2141 if (IterationCount == UnknownValue) return UnknownValue; 2142 IterationCount = getTruncateOrZeroExtend(IterationCount, 2143 AddRec->getType()); 2144 2145 // If the value is affine, simplify the expression evaluation to just 2146 // Start + Step*IterationCount. 2147 if (AddRec->isAffine()) 2148 return SCEVAddExpr::get(AddRec->getStart(), 2149 SCEVMulExpr::get(IterationCount, 2150 AddRec->getOperand(1))); 2151 2152 // Otherwise, evaluate it the hard way. 2153 return AddRec->evaluateAtIteration(IterationCount); 2154 } 2155 return UnknownValue; 2156 } 2157 2158 //assert(0 && "Unknown SCEV type!"); 2159 return UnknownValue; 2160} 2161 2162 2163/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2164/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2165/// might be the same) or two SCEVCouldNotCompute objects. 2166/// 2167static std::pair<SCEVHandle,SCEVHandle> 2168SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2169 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2170 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2171 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2172 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2173 2174 // We currently can only solve this if the coefficients are constants. 2175 if (!LC || !MC || !NC) { 2176 SCEV *CNC = new SCEVCouldNotCompute(); 2177 return std::make_pair(CNC, CNC); 2178 } 2179 2180 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2181 const APInt &L = LC->getValue()->getValue(); 2182 const APInt &M = MC->getValue()->getValue(); 2183 const APInt &N = NC->getValue()->getValue(); 2184 APInt Two(BitWidth, 2); 2185 APInt Four(BitWidth, 4); 2186 2187 { 2188 using namespace APIntOps; 2189 const APInt& C = L; 2190 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2191 // The B coefficient is M-N/2 2192 APInt B(M); 2193 B -= sdiv(N,Two); 2194 2195 // The A coefficient is N/2 2196 APInt A(N.sdiv(Two)); 2197 2198 // Compute the B^2-4ac term. 2199 APInt SqrtTerm(B); 2200 SqrtTerm *= B; 2201 SqrtTerm -= Four * (A * C); 2202 2203 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2204 // integer value or else APInt::sqrt() will assert. 2205 APInt SqrtVal(SqrtTerm.sqrt()); 2206 2207 // Compute the two solutions for the quadratic formula. 2208 // The divisions must be performed as signed divisions. 2209 APInt NegB(-B); 2210 APInt TwoA( A << 1 ); 2211 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2212 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2213 2214 return std::make_pair(SCEVConstant::get(Solution1), 2215 SCEVConstant::get(Solution2)); 2216 } // end APIntOps namespace 2217} 2218 2219/// HowFarToZero - Return the number of times a backedge comparing the specified 2220/// value to zero will execute. If not computable, return UnknownValue 2221SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2222 // If the value is a constant 2223 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2224 // If the value is already zero, the branch will execute zero times. 2225 if (C->getValue()->isZero()) return C; 2226 return UnknownValue; // Otherwise it will loop infinitely. 2227 } 2228 2229 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2230 if (!AddRec || AddRec->getLoop() != L) 2231 return UnknownValue; 2232 2233 if (AddRec->isAffine()) { 2234 // If this is an affine expression the execution count of this branch is 2235 // equal to: 2236 // 2237 // (0 - Start/Step) iff Start % Step == 0 2238 // 2239 // Get the initial value for the loop. 2240 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2241 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2242 SCEVHandle Step = AddRec->getOperand(1); 2243 2244 Step = getSCEVAtScope(Step, L->getParentLoop()); 2245 2246 // Figure out if Start % Step == 0. 2247 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2248 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2249 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2250 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start 2251 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2252 return Start; // 0 - Start/-1 == Start 2253 2254 // Check to see if Start is divisible by SC with no remainder. 2255 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2256 ConstantInt *StartCC = StartC->getValue(); 2257 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2258 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2259 if (Rem->isNullValue()) { 2260 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2261 return SCEVUnknown::get(Result); 2262 } 2263 } 2264 } 2265 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2266 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2267 // the quadratic equation to solve it. 2268 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2269 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2270 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2271 if (R1) { 2272#if 0 2273 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2274 << " sol#2: " << *R2 << "\n"; 2275#endif 2276 // Pick the smallest positive root value. 2277 if (ConstantInt *CB = 2278 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2279 R1->getValue(), R2->getValue()))) { 2280 if (CB->getZExtValue() == false) 2281 std::swap(R1, R2); // R1 is the minimum root now. 2282 2283 // We can only use this value if the chrec ends up with an exact zero 2284 // value at this index. When solving for "X*X != 5", for example, we 2285 // should not accept a root of 2. 2286 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2287 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2288 if (EvalVal->getValue()->isZero()) 2289 return R1; // We found a quadratic root! 2290 } 2291 } 2292 } 2293 2294 return UnknownValue; 2295} 2296 2297/// HowFarToNonZero - Return the number of times a backedge checking the 2298/// specified value for nonzero will execute. If not computable, return 2299/// UnknownValue 2300SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2301 // Loops that look like: while (X == 0) are very strange indeed. We don't 2302 // handle them yet except for the trivial case. This could be expanded in the 2303 // future as needed. 2304 2305 // If the value is a constant, check to see if it is known to be non-zero 2306 // already. If so, the backedge will execute zero times. 2307 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2308 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2309 Constant *NonZero = 2310 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2311 if (NonZero == ConstantInt::getTrue()) 2312 return getSCEV(Zero); 2313 return UnknownValue; // Otherwise it will loop infinitely. 2314 } 2315 2316 // We could implement others, but I really doubt anyone writes loops like 2317 // this, and if they did, they would already be constant folded. 2318 return UnknownValue; 2319} 2320 2321/// HowManyLessThans - Return the number of times a backedge containing the 2322/// specified less-than comparison will execute. If not computable, return 2323/// UnknownValue. 2324SCEVHandle ScalarEvolutionsImpl:: 2325HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2326 // Only handle: "ADDREC < LoopInvariant". 2327 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2328 2329 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2330 if (!AddRec || AddRec->getLoop() != L) 2331 return UnknownValue; 2332 2333 if (AddRec->isAffine()) { 2334 // FORNOW: We only support unit strides. 2335 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType()); 2336 if (AddRec->getOperand(1) != One) 2337 return UnknownValue; 2338 2339 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't 2340 // know that m is >= n on input to the loop. If it is, the condition return 2341 // true zero times. What we really should return, for full generality, is 2342 // SMAX(0, m-n). Since we cannot check this, we will instead check for a 2343 // canonical loop form: most do-loops will have a check that dominates the 2344 // loop, that only enters the loop if [n-1]<m. If we can find this check, 2345 // we know that the SMAX will evaluate to m-n, because we know that m >= n. 2346 2347 // Search for the check. 2348 BasicBlock *Preheader = L->getLoopPreheader(); 2349 BasicBlock *PreheaderDest = L->getHeader(); 2350 if (Preheader == 0) return UnknownValue; 2351 2352 BranchInst *LoopEntryPredicate = 2353 dyn_cast<BranchInst>(Preheader->getTerminator()); 2354 if (!LoopEntryPredicate) return UnknownValue; 2355 2356 // This might be a critical edge broken out. If the loop preheader ends in 2357 // an unconditional branch to the loop, check to see if the preheader has a 2358 // single predecessor, and if so, look for its terminator. 2359 while (LoopEntryPredicate->isUnconditional()) { 2360 PreheaderDest = Preheader; 2361 Preheader = Preheader->getSinglePredecessor(); 2362 if (!Preheader) return UnknownValue; // Multiple preds. 2363 2364 LoopEntryPredicate = 2365 dyn_cast<BranchInst>(Preheader->getTerminator()); 2366 if (!LoopEntryPredicate) return UnknownValue; 2367 } 2368 2369 // Now that we found a conditional branch that dominates the loop, check to 2370 // see if it is the comparison we are looking for. 2371 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){ 2372 Value *PreCondLHS = ICI->getOperand(0); 2373 Value *PreCondRHS = ICI->getOperand(1); 2374 ICmpInst::Predicate Cond; 2375 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2376 Cond = ICI->getPredicate(); 2377 else 2378 Cond = ICI->getInversePredicate(); 2379 2380 switch (Cond) { 2381 case ICmpInst::ICMP_UGT: 2382 if (isSigned) return UnknownValue; 2383 std::swap(PreCondLHS, PreCondRHS); 2384 Cond = ICmpInst::ICMP_ULT; 2385 break; 2386 case ICmpInst::ICMP_SGT: 2387 if (!isSigned) return UnknownValue; 2388 std::swap(PreCondLHS, PreCondRHS); 2389 Cond = ICmpInst::ICMP_SLT; 2390 break; 2391 case ICmpInst::ICMP_ULT: 2392 if (isSigned) return UnknownValue; 2393 break; 2394 case ICmpInst::ICMP_SLT: 2395 if (!isSigned) return UnknownValue; 2396 break; 2397 default: 2398 return UnknownValue; 2399 } 2400 2401 if (PreCondLHS->getType()->isInteger()) { 2402 if (RHS != getSCEV(PreCondRHS)) 2403 return UnknownValue; // Not a comparison against 'm'. 2404 2405 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One) 2406 != getSCEV(PreCondLHS)) 2407 return UnknownValue; // Not a comparison against 'n-1'. 2408 } 2409 else return UnknownValue; 2410 2411 // cerr << "Computed Loop Trip Count as: " 2412 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n"; 2413 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)); 2414 } 2415 else 2416 return UnknownValue; 2417 } 2418 2419 return UnknownValue; 2420} 2421 2422/// getNumIterationsInRange - Return the number of iterations of this loop that 2423/// produce values in the specified constant range. Another way of looking at 2424/// this is that it returns the first iteration number where the value is not in 2425/// the condition, thus computing the exit count. If the iteration count can't 2426/// be computed, an instance of SCEVCouldNotCompute is returned. 2427SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2428 if (Range.isFullSet()) // Infinite loop. 2429 return new SCEVCouldNotCompute(); 2430 2431 // If the start is a non-zero constant, shift the range to simplify things. 2432 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2433 if (!SC->getValue()->isZero()) { 2434 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2435 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2436 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2437 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2438 return ShiftedAddRec->getNumIterationsInRange( 2439 Range.subtract(SC->getValue()->getValue())); 2440 // This is strange and shouldn't happen. 2441 return new SCEVCouldNotCompute(); 2442 } 2443 2444 // The only time we can solve this is when we have all constant indices. 2445 // Otherwise, we cannot determine the overflow conditions. 2446 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2447 if (!isa<SCEVConstant>(getOperand(i))) 2448 return new SCEVCouldNotCompute(); 2449 2450 2451 // Okay at this point we know that all elements of the chrec are constants and 2452 // that the start element is zero. 2453 2454 // First check to see if the range contains zero. If not, the first 2455 // iteration exits. 2456 if (!Range.contains(APInt(getBitWidth(),0))) 2457 return SCEVConstant::get(ConstantInt::get(getType(),0)); 2458 2459 if (isAffine()) { 2460 // If this is an affine expression then we have this situation: 2461 // Solve {0,+,A} in Range === Ax in Range 2462 2463 // We know that zero is in the range. If A is positive then we know that 2464 // the upper value of the range must be the first possible exit value. 2465 // If A is negative then the lower of the range is the last possible loop 2466 // value. Also note that we already checked for a full range. 2467 APInt One(getBitWidth(),1); 2468 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2469 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2470 2471 // The exit value should be (End+A)/A. 2472 APInt ExitVal = (End + A).sdiv(A); 2473 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2474 2475 // Evaluate at the exit value. If we really did fall out of the valid 2476 // range, then we computed our trip count, otherwise wrap around or other 2477 // things must have happened. 2478 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2479 if (Range.contains(Val->getValue())) 2480 return new SCEVCouldNotCompute(); // Something strange happened 2481 2482 // Ensure that the previous value is in the range. This is a sanity check. 2483 assert(Range.contains( 2484 EvaluateConstantChrecAtConstant(this, 2485 ConstantInt::get(ExitVal - One))->getValue()) && 2486 "Linear scev computation is off in a bad way!"); 2487 return SCEVConstant::get(ExitValue); 2488 } else if (isQuadratic()) { 2489 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2490 // quadratic equation to solve it. To do this, we must frame our problem in 2491 // terms of figuring out when zero is crossed, instead of when 2492 // Range.getUpper() is crossed. 2493 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2494 NewOps[0] = SCEV::getNegativeSCEV(SCEVConstant::get(Range.getUpper())); 2495 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2496 2497 // Next, solve the constructed addrec 2498 std::pair<SCEVHandle,SCEVHandle> Roots = 2499 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2500 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2501 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2502 if (R1) { 2503 // Pick the smallest positive root value. 2504 if (ConstantInt *CB = 2505 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2506 R1->getValue(), R2->getValue()))) { 2507 if (CB->getZExtValue() == false) 2508 std::swap(R1, R2); // R1 is the minimum root now. 2509 2510 // Make sure the root is not off by one. The returned iteration should 2511 // not be in the range, but the previous one should be. When solving 2512 // for "X*X < 5", for example, we should not return a root of 2. 2513 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2514 R1->getValue()); 2515 if (Range.contains(R1Val->getValue())) { 2516 // The next iteration must be out of the range... 2517 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2518 2519 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2520 if (!Range.contains(R1Val->getValue())) 2521 return SCEVConstant::get(NextVal); 2522 return new SCEVCouldNotCompute(); // Something strange happened 2523 } 2524 2525 // If R1 was not in the range, then it is a good return value. Make 2526 // sure that R1-1 WAS in the range though, just in case. 2527 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2528 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2529 if (Range.contains(R1Val->getValue())) 2530 return R1; 2531 return new SCEVCouldNotCompute(); // Something strange happened 2532 } 2533 } 2534 } 2535 2536 // Fallback, if this is a general polynomial, figure out the progression 2537 // through brute force: evaluate until we find an iteration that fails the 2538 // test. This is likely to be slow, but getting an accurate trip count is 2539 // incredibly important, we will be able to simplify the exit test a lot, and 2540 // we are almost guaranteed to get a trip count in this case. 2541 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2542 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2543 do { 2544 ++NumBruteForceEvaluations; 2545 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2546 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2547 return new SCEVCouldNotCompute(); 2548 2549 // Check to see if we found the value! 2550 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2551 return SCEVConstant::get(TestVal); 2552 2553 // Increment to test the next index. 2554 TestVal = ConstantInt::get(TestVal->getValue()+1); 2555 } while (TestVal != EndVal); 2556 2557 return new SCEVCouldNotCompute(); 2558} 2559 2560 2561 2562//===----------------------------------------------------------------------===// 2563// ScalarEvolution Class Implementation 2564//===----------------------------------------------------------------------===// 2565 2566bool ScalarEvolution::runOnFunction(Function &F) { 2567 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2568 return false; 2569} 2570 2571void ScalarEvolution::releaseMemory() { 2572 delete (ScalarEvolutionsImpl*)Impl; 2573 Impl = 0; 2574} 2575 2576void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2577 AU.setPreservesAll(); 2578 AU.addRequiredTransitive<LoopInfo>(); 2579} 2580 2581SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2582 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2583} 2584 2585/// hasSCEV - Return true if the SCEV for this value has already been 2586/// computed. 2587bool ScalarEvolution::hasSCEV(Value *V) const { 2588 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2589} 2590 2591 2592/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2593/// the specified value. 2594void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2595 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2596} 2597 2598 2599SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2600 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2601} 2602 2603bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2604 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2605} 2606 2607SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2608 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2609} 2610 2611void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2612 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2613} 2614 2615static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2616 const Loop *L) { 2617 // Print all inner loops first 2618 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2619 PrintLoopInfo(OS, SE, *I); 2620 2621 cerr << "Loop " << L->getHeader()->getName() << ": "; 2622 2623 SmallVector<BasicBlock*, 8> ExitBlocks; 2624 L->getExitBlocks(ExitBlocks); 2625 if (ExitBlocks.size() != 1) 2626 cerr << "<multiple exits> "; 2627 2628 if (SE->hasLoopInvariantIterationCount(L)) { 2629 cerr << *SE->getIterationCount(L) << " iterations! "; 2630 } else { 2631 cerr << "Unpredictable iteration count. "; 2632 } 2633 2634 cerr << "\n"; 2635} 2636 2637void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2638 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2639 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2640 2641 OS << "Classifying expressions for: " << F.getName() << "\n"; 2642 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2643 if (I->getType()->isInteger()) { 2644 OS << *I; 2645 OS << " --> "; 2646 SCEVHandle SV = getSCEV(&*I); 2647 SV->print(OS); 2648 OS << "\t\t"; 2649 2650 if ((*I).getType()->isInteger()) { 2651 ConstantRange Bounds = SV->getValueRange(); 2652 if (!Bounds.isFullSet()) 2653 OS << "Bounds: " << Bounds << " "; 2654 } 2655 2656 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2657 OS << "Exits: "; 2658 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2659 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2660 OS << "<<Unknown>>"; 2661 } else { 2662 OS << *ExitValue; 2663 } 2664 } 2665 2666 2667 OS << "\n"; 2668 } 2669 2670 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2671 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2672 PrintLoopInfo(OS, this, *I); 2673} 2674 2675