ScalarEvolution.cpp revision 4dc534c7fe93743f28c093dde9332cdb9d8edfa3
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file was developed by the LLVM research group and is distributed under 6// the University of Illinois Open Source License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/Instructions.h" 67#include "llvm/Analysis/LoopInfo.h" 68#include "llvm/Assembly/Writer.h" 69#include "llvm/Transforms/Scalar.h" 70#include "llvm/Transforms/Utils/Local.h" 71#include "llvm/Support/CFG.h" 72#include "llvm/Support/ConstantRange.h" 73#include "llvm/Support/InstIterator.h" 74#include "llvm/Support/CommandLine.h" 75#include "llvm/ADT/Statistic.h" 76#include <cmath> 77#include <algorithm> 78using namespace llvm; 79 80namespace { 81 RegisterAnalysis<ScalarEvolution> 82 R("scalar-evolution", "Scalar Evolution Analysis"); 83 84 Statistic<> 85 NumBruteForceEvaluations("scalar-evolution", 86 "Number of brute force evaluations needed to " 87 "calculate high-order polynomial exit values"); 88 Statistic<> 89 NumArrayLenItCounts("scalar-evolution", 90 "Number of trip counts computed with array length"); 91 Statistic<> 92 NumTripCountsComputed("scalar-evolution", 93 "Number of loops with predictable loop counts"); 94 Statistic<> 95 NumTripCountsNotComputed("scalar-evolution", 96 "Number of loops without predictable loop counts"); 97 Statistic<> 98 NumBruteForceTripCountsComputed("scalar-evolution", 99 "Number of loops with trip counts computed by force"); 100 101 cl::opt<unsigned> 102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 103 cl::desc("Maximum number of iterations SCEV will symbolically execute a constant derived loop"), 104 cl::init(100)); 105} 106 107//===----------------------------------------------------------------------===// 108// SCEV class definitions 109//===----------------------------------------------------------------------===// 110 111//===----------------------------------------------------------------------===// 112// Implementation of the SCEV class. 113// 114SCEV::~SCEV() {} 115void SCEV::dump() const { 116 print(std::cerr); 117} 118 119/// getValueRange - Return the tightest constant bounds that this value is 120/// known to have. This method is only valid on integer SCEV objects. 121ConstantRange SCEV::getValueRange() const { 122 const Type *Ty = getType(); 123 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 124 Ty = Ty->getUnsignedVersion(); 125 // Default to a full range if no better information is available. 126 return ConstantRange(getType()); 127} 128 129 130SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 131 132bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 133 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 134 return false; 135} 136 137const Type *SCEVCouldNotCompute::getType() const { 138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 139 return 0; 140} 141 142bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 144 return false; 145} 146 147SCEVHandle SCEVCouldNotCompute:: 148replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 149 const SCEVHandle &Conc) const { 150 return this; 151} 152 153void SCEVCouldNotCompute::print(std::ostream &OS) const { 154 OS << "***COULDNOTCOMPUTE***"; 155} 156 157bool SCEVCouldNotCompute::classof(const SCEV *S) { 158 return S->getSCEVType() == scCouldNotCompute; 159} 160 161 162// SCEVConstants - Only allow the creation of one SCEVConstant for any 163// particular value. Don't use a SCEVHandle here, or else the object will 164// never be deleted! 165static std::map<ConstantInt*, SCEVConstant*> SCEVConstants; 166 167 168SCEVConstant::~SCEVConstant() { 169 SCEVConstants.erase(V); 170} 171 172SCEVHandle SCEVConstant::get(ConstantInt *V) { 173 // Make sure that SCEVConstant instances are all unsigned. 174 if (V->getType()->isSigned()) { 175 const Type *NewTy = V->getType()->getUnsignedVersion(); 176 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy)); 177 } 178 179 SCEVConstant *&R = SCEVConstants[V]; 180 if (R == 0) R = new SCEVConstant(V); 181 return R; 182} 183 184ConstantRange SCEVConstant::getValueRange() const { 185 return ConstantRange(V); 186} 187 188const Type *SCEVConstant::getType() const { return V->getType(); } 189 190void SCEVConstant::print(std::ostream &OS) const { 191 WriteAsOperand(OS, V, false); 192} 193 194// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 195// particular input. Don't use a SCEVHandle here, or else the object will 196// never be deleted! 197static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates; 198 199SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 200 : SCEV(scTruncate), Op(op), Ty(ty) { 201 assert(Op->getType()->isInteger() && Ty->isInteger() && 202 Ty->isUnsigned() && 203 "Cannot truncate non-integer value!"); 204 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() && 205 "This is not a truncating conversion!"); 206} 207 208SCEVTruncateExpr::~SCEVTruncateExpr() { 209 SCEVTruncates.erase(std::make_pair(Op, Ty)); 210} 211 212ConstantRange SCEVTruncateExpr::getValueRange() const { 213 return getOperand()->getValueRange().truncate(getType()); 214} 215 216void SCEVTruncateExpr::print(std::ostream &OS) const { 217 OS << "(truncate " << *Op << " to " << *Ty << ")"; 218} 219 220// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 221// particular input. Don't use a SCEVHandle here, or else the object will never 222// be deleted! 223static std::map<std::pair<SCEV*, const Type*>, 224 SCEVZeroExtendExpr*> SCEVZeroExtends; 225 226SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 227 : SCEV(scTruncate), Op(Op), Ty(ty) { 228 assert(Op->getType()->isInteger() && Ty->isInteger() && 229 Ty->isUnsigned() && 230 "Cannot zero extend non-integer value!"); 231 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() && 232 "This is not an extending conversion!"); 233} 234 235SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 236 SCEVZeroExtends.erase(std::make_pair(Op, Ty)); 237} 238 239ConstantRange SCEVZeroExtendExpr::getValueRange() const { 240 return getOperand()->getValueRange().zeroExtend(getType()); 241} 242 243void SCEVZeroExtendExpr::print(std::ostream &OS) const { 244 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 245} 246 247// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 248// particular input. Don't use a SCEVHandle here, or else the object will never 249// be deleted! 250static std::map<std::pair<unsigned, std::vector<SCEV*> >, 251 SCEVCommutativeExpr*> SCEVCommExprs; 252 253SCEVCommutativeExpr::~SCEVCommutativeExpr() { 254 SCEVCommExprs.erase(std::make_pair(getSCEVType(), 255 std::vector<SCEV*>(Operands.begin(), 256 Operands.end()))); 257} 258 259void SCEVCommutativeExpr::print(std::ostream &OS) const { 260 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 261 const char *OpStr = getOperationStr(); 262 OS << "(" << *Operands[0]; 263 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 264 OS << OpStr << *Operands[i]; 265 OS << ")"; 266} 267 268SCEVHandle SCEVCommutativeExpr:: 269replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 270 const SCEVHandle &Conc) const { 271 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 272 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 273 if (H != getOperand(i)) { 274 std::vector<SCEVHandle> NewOps; 275 NewOps.reserve(getNumOperands()); 276 for (unsigned j = 0; j != i; ++j) 277 NewOps.push_back(getOperand(j)); 278 NewOps.push_back(H); 279 for (++i; i != e; ++i) 280 NewOps.push_back(getOperand(i)-> 281 replaceSymbolicValuesWithConcrete(Sym, Conc)); 282 283 if (isa<SCEVAddExpr>(this)) 284 return SCEVAddExpr::get(NewOps); 285 else if (isa<SCEVMulExpr>(this)) 286 return SCEVMulExpr::get(NewOps); 287 else 288 assert(0 && "Unknown commutative expr!"); 289 } 290 } 291 return this; 292} 293 294 295// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 296// input. Don't use a SCEVHandle here, or else the object will never be 297// deleted! 298static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs; 299 300SCEVUDivExpr::~SCEVUDivExpr() { 301 SCEVUDivs.erase(std::make_pair(LHS, RHS)); 302} 303 304void SCEVUDivExpr::print(std::ostream &OS) const { 305 OS << "(" << *LHS << " /u " << *RHS << ")"; 306} 307 308const Type *SCEVUDivExpr::getType() const { 309 const Type *Ty = LHS->getType(); 310 if (Ty->isSigned()) Ty = Ty->getUnsignedVersion(); 311 return Ty; 312} 313 314// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 315// particular input. Don't use a SCEVHandle here, or else the object will never 316// be deleted! 317static std::map<std::pair<const Loop *, std::vector<SCEV*> >, 318 SCEVAddRecExpr*> SCEVAddRecExprs; 319 320SCEVAddRecExpr::~SCEVAddRecExpr() { 321 SCEVAddRecExprs.erase(std::make_pair(L, 322 std::vector<SCEV*>(Operands.begin(), 323 Operands.end()))); 324} 325 326SCEVHandle SCEVAddRecExpr:: 327replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 328 const SCEVHandle &Conc) const { 329 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 330 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc); 331 if (H != getOperand(i)) { 332 std::vector<SCEVHandle> NewOps; 333 NewOps.reserve(getNumOperands()); 334 for (unsigned j = 0; j != i; ++j) 335 NewOps.push_back(getOperand(j)); 336 NewOps.push_back(H); 337 for (++i; i != e; ++i) 338 NewOps.push_back(getOperand(i)-> 339 replaceSymbolicValuesWithConcrete(Sym, Conc)); 340 341 return get(NewOps, L); 342 } 343 } 344 return this; 345} 346 347 348bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 349 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 350 // contain L. 351 return !QueryLoop->contains(L->getHeader()); 352} 353 354 355void SCEVAddRecExpr::print(std::ostream &OS) const { 356 OS << "{" << *Operands[0]; 357 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 358 OS << ",+," << *Operands[i]; 359 OS << "}<" << L->getHeader()->getName() + ">"; 360} 361 362// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 363// value. Don't use a SCEVHandle here, or else the object will never be 364// deleted! 365static std::map<Value*, SCEVUnknown*> SCEVUnknowns; 366 367SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); } 368 369bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 370 // All non-instruction values are loop invariant. All instructions are loop 371 // invariant if they are not contained in the specified loop. 372 if (Instruction *I = dyn_cast<Instruction>(V)) 373 return !L->contains(I->getParent()); 374 return true; 375} 376 377const Type *SCEVUnknown::getType() const { 378 return V->getType(); 379} 380 381void SCEVUnknown::print(std::ostream &OS) const { 382 WriteAsOperand(OS, V, false); 383} 384 385//===----------------------------------------------------------------------===// 386// SCEV Utilities 387//===----------------------------------------------------------------------===// 388 389namespace { 390 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 391 /// than the complexity of the RHS. This comparator is used to canonicalize 392 /// expressions. 393 struct SCEVComplexityCompare { 394 bool operator()(SCEV *LHS, SCEV *RHS) { 395 return LHS->getSCEVType() < RHS->getSCEVType(); 396 } 397 }; 398} 399 400/// GroupByComplexity - Given a list of SCEV objects, order them by their 401/// complexity, and group objects of the same complexity together by value. 402/// When this routine is finished, we know that any duplicates in the vector are 403/// consecutive and that complexity is monotonically increasing. 404/// 405/// Note that we go take special precautions to ensure that we get determinstic 406/// results from this routine. In other words, we don't want the results of 407/// this to depend on where the addresses of various SCEV objects happened to 408/// land in memory. 409/// 410static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 411 if (Ops.size() < 2) return; // Noop 412 if (Ops.size() == 2) { 413 // This is the common case, which also happens to be trivially simple. 414 // Special case it. 415 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 416 std::swap(Ops[0], Ops[1]); 417 return; 418 } 419 420 // Do the rough sort by complexity. 421 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 422 423 // Now that we are sorted by complexity, group elements of the same 424 // complexity. Note that this is, at worst, N^2, but the vector is likely to 425 // be extremely short in practice. Note that we take this approach because we 426 // do not want to depend on the addresses of the objects we are grouping. 427 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 428 SCEV *S = Ops[i]; 429 unsigned Complexity = S->getSCEVType(); 430 431 // If there are any objects of the same complexity and same value as this 432 // one, group them. 433 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 434 if (Ops[j] == S) { // Found a duplicate. 435 // Move it to immediately after i'th element. 436 std::swap(Ops[i+1], Ops[j]); 437 ++i; // no need to rescan it. 438 if (i == e-2) return; // Done! 439 } 440 } 441 } 442} 443 444 445 446//===----------------------------------------------------------------------===// 447// Simple SCEV method implementations 448//===----------------------------------------------------------------------===// 449 450/// getIntegerSCEV - Given an integer or FP type, create a constant for the 451/// specified signed integer value and return a SCEV for the constant. 452SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) { 453 Constant *C; 454 if (Val == 0) 455 C = Constant::getNullValue(Ty); 456 else if (Ty->isFloatingPoint()) 457 C = ConstantFP::get(Ty, Val); 458 else if (Ty->isSigned()) 459 C = ConstantSInt::get(Ty, Val); 460 else { 461 C = ConstantSInt::get(Ty->getSignedVersion(), Val); 462 C = ConstantExpr::getCast(C, Ty); 463 } 464 return SCEVUnknown::get(C); 465} 466 467/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 468/// input value to the specified type. If the type must be extended, it is zero 469/// extended. 470static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) { 471 const Type *SrcTy = V->getType(); 472 assert(SrcTy->isInteger() && Ty->isInteger() && 473 "Cannot truncate or zero extend with non-integer arguments!"); 474 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize()) 475 return V; // No conversion 476 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize()) 477 return SCEVTruncateExpr::get(V, Ty); 478 return SCEVZeroExtendExpr::get(V, Ty); 479} 480 481/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 482/// 483static SCEVHandle getNegativeSCEV(const SCEVHandle &V) { 484 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 485 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue())); 486 487 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType())); 488} 489 490/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 491/// 492static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) { 493 // X - Y --> X + -Y 494 return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS)); 495} 496 497 498/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is 499/// often very small, so we try to reduce the number of N! terms we need to 500/// evaluate by evaluating this as (N!/(N-M)!)/M! 501static ConstantInt *Binomial(ConstantInt *N, unsigned M) { 502 uint64_t NVal = N->getRawValue(); 503 uint64_t FirstTerm = 1; 504 for (unsigned i = 0; i != M; ++i) 505 FirstTerm *= NVal-i; 506 507 unsigned MFactorial = 1; 508 for (; M; --M) 509 MFactorial *= M; 510 511 Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial); 512 Result = ConstantExpr::getCast(Result, N->getType()); 513 assert(isa<ConstantInt>(Result) && "Cast of integer not folded??"); 514 return cast<ConstantInt>(Result); 515} 516 517/// PartialFact - Compute V!/(V-NumSteps)! 518static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) { 519 // Handle this case efficiently, it is common to have constant iteration 520 // counts while computing loop exit values. 521 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) { 522 uint64_t Val = SC->getValue()->getRawValue(); 523 uint64_t Result = 1; 524 for (; NumSteps; --NumSteps) 525 Result *= Val-(NumSteps-1); 526 Constant *Res = ConstantUInt::get(Type::ULongTy, Result); 527 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType())); 528 } 529 530 const Type *Ty = V->getType(); 531 if (NumSteps == 0) 532 return SCEVUnknown::getIntegerSCEV(1, Ty); 533 534 SCEVHandle Result = V; 535 for (unsigned i = 1; i != NumSteps; ++i) 536 Result = SCEVMulExpr::get(Result, getMinusSCEV(V, 537 SCEVUnknown::getIntegerSCEV(i, Ty))); 538 return Result; 539} 540 541 542/// evaluateAtIteration - Return the value of this chain of recurrences at 543/// the specified iteration number. We can evaluate this recurrence by 544/// multiplying each element in the chain by the binomial coefficient 545/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 546/// 547/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3) 548/// 549/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow. 550/// Is the binomial equation safe using modular arithmetic?? 551/// 552SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const { 553 SCEVHandle Result = getStart(); 554 int Divisor = 1; 555 const Type *Ty = It->getType(); 556 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 557 SCEVHandle BC = PartialFact(It, i); 558 Divisor *= i; 559 SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)), 560 SCEVUnknown::getIntegerSCEV(Divisor,Ty)); 561 Result = SCEVAddExpr::get(Result, Val); 562 } 563 return Result; 564} 565 566 567//===----------------------------------------------------------------------===// 568// SCEV Expression folder implementations 569//===----------------------------------------------------------------------===// 570 571SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) { 572 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 573 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 574 575 // If the input value is a chrec scev made out of constants, truncate 576 // all of the constants. 577 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 578 std::vector<SCEVHandle> Operands; 579 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 580 // FIXME: This should allow truncation of other expression types! 581 if (isa<SCEVConstant>(AddRec->getOperand(i))) 582 Operands.push_back(get(AddRec->getOperand(i), Ty)); 583 else 584 break; 585 if (Operands.size() == AddRec->getNumOperands()) 586 return SCEVAddRecExpr::get(Operands, AddRec->getLoop()); 587 } 588 589 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)]; 590 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 591 return Result; 592} 593 594SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) { 595 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 596 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty)); 597 598 // FIXME: If the input value is a chrec scev, and we can prove that the value 599 // did not overflow the old, smaller, value, we can zero extend all of the 600 // operands (often constants). This would allow analysis of something like 601 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 602 603 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)]; 604 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 605 return Result; 606} 607 608// get - Get a canonical add expression, or something simpler if possible. 609SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) { 610 assert(!Ops.empty() && "Cannot get empty add!"); 611 if (Ops.size() == 1) return Ops[0]; 612 613 // Sort by complexity, this groups all similar expression types together. 614 GroupByComplexity(Ops); 615 616 // If there are any constants, fold them together. 617 unsigned Idx = 0; 618 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 619 ++Idx; 620 assert(Idx < Ops.size()); 621 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 622 // We found two constants, fold them together! 623 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue()); 624 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 625 Ops[0] = SCEVConstant::get(CI); 626 Ops.erase(Ops.begin()+1); // Erase the folded element 627 if (Ops.size() == 1) return Ops[0]; 628 } else { 629 // If we couldn't fold the expression, move to the next constant. Note 630 // that this is impossible to happen in practice because we always 631 // constant fold constant ints to constant ints. 632 ++Idx; 633 } 634 } 635 636 // If we are left with a constant zero being added, strip it off. 637 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 638 Ops.erase(Ops.begin()); 639 --Idx; 640 } 641 } 642 643 if (Ops.size() == 1) return Ops[0]; 644 645 // Okay, check to see if the same value occurs in the operand list twice. If 646 // so, merge them together into an multiply expression. Since we sorted the 647 // list, these values are required to be adjacent. 648 const Type *Ty = Ops[0]->getType(); 649 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 650 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 651 // Found a match, merge the two values into a multiply, and add any 652 // remaining values to the result. 653 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 654 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 655 if (Ops.size() == 2) 656 return Mul; 657 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 658 Ops.push_back(Mul); 659 return SCEVAddExpr::get(Ops); 660 } 661 662 // Okay, now we know the first non-constant operand. If there are add 663 // operands they would be next. 664 if (Idx < Ops.size()) { 665 bool DeletedAdd = false; 666 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 667 // If we have an add, expand the add operands onto the end of the operands 668 // list. 669 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 670 Ops.erase(Ops.begin()+Idx); 671 DeletedAdd = true; 672 } 673 674 // If we deleted at least one add, we added operands to the end of the list, 675 // and they are not necessarily sorted. Recurse to resort and resimplify 676 // any operands we just aquired. 677 if (DeletedAdd) 678 return get(Ops); 679 } 680 681 // Skip over the add expression until we get to a multiply. 682 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 683 ++Idx; 684 685 // If we are adding something to a multiply expression, make sure the 686 // something is not already an operand of the multiply. If so, merge it into 687 // the multiply. 688 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 689 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 690 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 691 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 692 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 693 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 694 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 695 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 696 if (Mul->getNumOperands() != 2) { 697 // If the multiply has more than two operands, we must get the 698 // Y*Z term. 699 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 700 MulOps.erase(MulOps.begin()+MulOp); 701 InnerMul = SCEVMulExpr::get(MulOps); 702 } 703 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 704 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 705 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 706 if (Ops.size() == 2) return OuterMul; 707 if (AddOp < Idx) { 708 Ops.erase(Ops.begin()+AddOp); 709 Ops.erase(Ops.begin()+Idx-1); 710 } else { 711 Ops.erase(Ops.begin()+Idx); 712 Ops.erase(Ops.begin()+AddOp-1); 713 } 714 Ops.push_back(OuterMul); 715 return SCEVAddExpr::get(Ops); 716 } 717 718 // Check this multiply against other multiplies being added together. 719 for (unsigned OtherMulIdx = Idx+1; 720 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 721 ++OtherMulIdx) { 722 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 723 // If MulOp occurs in OtherMul, we can fold the two multiplies 724 // together. 725 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 726 OMulOp != e; ++OMulOp) 727 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 728 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 729 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 730 if (Mul->getNumOperands() != 2) { 731 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 732 MulOps.erase(MulOps.begin()+MulOp); 733 InnerMul1 = SCEVMulExpr::get(MulOps); 734 } 735 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 736 if (OtherMul->getNumOperands() != 2) { 737 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 738 OtherMul->op_end()); 739 MulOps.erase(MulOps.begin()+OMulOp); 740 InnerMul2 = SCEVMulExpr::get(MulOps); 741 } 742 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 743 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 744 if (Ops.size() == 2) return OuterMul; 745 Ops.erase(Ops.begin()+Idx); 746 Ops.erase(Ops.begin()+OtherMulIdx-1); 747 Ops.push_back(OuterMul); 748 return SCEVAddExpr::get(Ops); 749 } 750 } 751 } 752 } 753 754 // If there are any add recurrences in the operands list, see if any other 755 // added values are loop invariant. If so, we can fold them into the 756 // recurrence. 757 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 758 ++Idx; 759 760 // Scan over all recurrences, trying to fold loop invariants into them. 761 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 762 // Scan all of the other operands to this add and add them to the vector if 763 // they are loop invariant w.r.t. the recurrence. 764 std::vector<SCEVHandle> LIOps; 765 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 766 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 767 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 768 LIOps.push_back(Ops[i]); 769 Ops.erase(Ops.begin()+i); 770 --i; --e; 771 } 772 773 // If we found some loop invariants, fold them into the recurrence. 774 if (!LIOps.empty()) { 775 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 776 LIOps.push_back(AddRec->getStart()); 777 778 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 779 AddRecOps[0] = SCEVAddExpr::get(LIOps); 780 781 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 782 // If all of the other operands were loop invariant, we are done. 783 if (Ops.size() == 1) return NewRec; 784 785 // Otherwise, add the folded AddRec by the non-liv parts. 786 for (unsigned i = 0;; ++i) 787 if (Ops[i] == AddRec) { 788 Ops[i] = NewRec; 789 break; 790 } 791 return SCEVAddExpr::get(Ops); 792 } 793 794 // Okay, if there weren't any loop invariants to be folded, check to see if 795 // there are multiple AddRec's with the same loop induction variable being 796 // added together. If so, we can fold them. 797 for (unsigned OtherIdx = Idx+1; 798 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 799 if (OtherIdx != Idx) { 800 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 801 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 802 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 803 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 804 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 805 if (i >= NewOps.size()) { 806 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 807 OtherAddRec->op_end()); 808 break; 809 } 810 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 811 } 812 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 813 814 if (Ops.size() == 2) return NewAddRec; 815 816 Ops.erase(Ops.begin()+Idx); 817 Ops.erase(Ops.begin()+OtherIdx-1); 818 Ops.push_back(NewAddRec); 819 return SCEVAddExpr::get(Ops); 820 } 821 } 822 823 // Otherwise couldn't fold anything into this recurrence. Move onto the 824 // next one. 825 } 826 827 // Okay, it looks like we really DO need an add expr. Check to see if we 828 // already have one, otherwise create a new one. 829 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 830 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 831 SCEVOps)]; 832 if (Result == 0) Result = new SCEVAddExpr(Ops); 833 return Result; 834} 835 836 837SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 838 assert(!Ops.empty() && "Cannot get empty mul!"); 839 840 // Sort by complexity, this groups all similar expression types together. 841 GroupByComplexity(Ops); 842 843 // If there are any constants, fold them together. 844 unsigned Idx = 0; 845 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 846 847 // C1*(C2+V) -> C1*C2 + C1*V 848 if (Ops.size() == 2) 849 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 850 if (Add->getNumOperands() == 2 && 851 isa<SCEVConstant>(Add->getOperand(0))) 852 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 853 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 854 855 856 ++Idx; 857 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 858 // We found two constants, fold them together! 859 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 860 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 861 Ops[0] = SCEVConstant::get(CI); 862 Ops.erase(Ops.begin()+1); // Erase the folded element 863 if (Ops.size() == 1) return Ops[0]; 864 } else { 865 // If we couldn't fold the expression, move to the next constant. Note 866 // that this is impossible to happen in practice because we always 867 // constant fold constant ints to constant ints. 868 ++Idx; 869 } 870 } 871 872 // If we are left with a constant one being multiplied, strip it off. 873 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 874 Ops.erase(Ops.begin()); 875 --Idx; 876 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 877 // If we have a multiply of zero, it will always be zero. 878 return Ops[0]; 879 } 880 } 881 882 // Skip over the add expression until we get to a multiply. 883 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 884 ++Idx; 885 886 if (Ops.size() == 1) 887 return Ops[0]; 888 889 // If there are mul operands inline them all into this expression. 890 if (Idx < Ops.size()) { 891 bool DeletedMul = false; 892 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 893 // If we have an mul, expand the mul operands onto the end of the operands 894 // list. 895 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 896 Ops.erase(Ops.begin()+Idx); 897 DeletedMul = true; 898 } 899 900 // If we deleted at least one mul, we added operands to the end of the list, 901 // and they are not necessarily sorted. Recurse to resort and resimplify 902 // any operands we just aquired. 903 if (DeletedMul) 904 return get(Ops); 905 } 906 907 // If there are any add recurrences in the operands list, see if any other 908 // added values are loop invariant. If so, we can fold them into the 909 // recurrence. 910 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 911 ++Idx; 912 913 // Scan over all recurrences, trying to fold loop invariants into them. 914 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 915 // Scan all of the other operands to this mul and add them to the vector if 916 // they are loop invariant w.r.t. the recurrence. 917 std::vector<SCEVHandle> LIOps; 918 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 919 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 920 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 921 LIOps.push_back(Ops[i]); 922 Ops.erase(Ops.begin()+i); 923 --i; --e; 924 } 925 926 // If we found some loop invariants, fold them into the recurrence. 927 if (!LIOps.empty()) { 928 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 929 std::vector<SCEVHandle> NewOps; 930 NewOps.reserve(AddRec->getNumOperands()); 931 if (LIOps.size() == 1) { 932 SCEV *Scale = LIOps[0]; 933 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 934 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 935 } else { 936 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 937 std::vector<SCEVHandle> MulOps(LIOps); 938 MulOps.push_back(AddRec->getOperand(i)); 939 NewOps.push_back(SCEVMulExpr::get(MulOps)); 940 } 941 } 942 943 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 944 945 // If all of the other operands were loop invariant, we are done. 946 if (Ops.size() == 1) return NewRec; 947 948 // Otherwise, multiply the folded AddRec by the non-liv parts. 949 for (unsigned i = 0;; ++i) 950 if (Ops[i] == AddRec) { 951 Ops[i] = NewRec; 952 break; 953 } 954 return SCEVMulExpr::get(Ops); 955 } 956 957 // Okay, if there weren't any loop invariants to be folded, check to see if 958 // there are multiple AddRec's with the same loop induction variable being 959 // multiplied together. If so, we can fold them. 960 for (unsigned OtherIdx = Idx+1; 961 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 962 if (OtherIdx != Idx) { 963 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 964 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 965 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 966 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 967 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 968 G->getStart()); 969 SCEVHandle B = F->getStepRecurrence(); 970 SCEVHandle D = G->getStepRecurrence(); 971 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 972 SCEVMulExpr::get(G, B), 973 SCEVMulExpr::get(B, D)); 974 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 975 F->getLoop()); 976 if (Ops.size() == 2) return NewAddRec; 977 978 Ops.erase(Ops.begin()+Idx); 979 Ops.erase(Ops.begin()+OtherIdx-1); 980 Ops.push_back(NewAddRec); 981 return SCEVMulExpr::get(Ops); 982 } 983 } 984 985 // Otherwise couldn't fold anything into this recurrence. Move onto the 986 // next one. 987 } 988 989 // Okay, it looks like we really DO need an mul expr. Check to see if we 990 // already have one, otherwise create a new one. 991 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 992 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 993 SCEVOps)]; 994 if (Result == 0) 995 Result = new SCEVMulExpr(Ops); 996 return Result; 997} 998 999SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1000 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1001 if (RHSC->getValue()->equalsInt(1)) 1002 return LHS; // X /u 1 --> x 1003 if (RHSC->getValue()->isAllOnesValue()) 1004 return getNegativeSCEV(LHS); // X /u -1 --> -x 1005 1006 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1007 Constant *LHSCV = LHSC->getValue(); 1008 Constant *RHSCV = RHSC->getValue(); 1009 if (LHSCV->getType()->isSigned()) 1010 LHSCV = ConstantExpr::getCast(LHSCV, 1011 LHSCV->getType()->getUnsignedVersion()); 1012 if (RHSCV->getType()->isSigned()) 1013 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 1014 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 1015 } 1016 } 1017 1018 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1019 1020 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)]; 1021 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1022 return Result; 1023} 1024 1025 1026/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1027/// specified loop. Simplify the expression as much as possible. 1028SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1029 const SCEVHandle &Step, const Loop *L) { 1030 std::vector<SCEVHandle> Operands; 1031 Operands.push_back(Start); 1032 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1033 if (StepChrec->getLoop() == L) { 1034 Operands.insert(Operands.end(), StepChrec->op_begin(), 1035 StepChrec->op_end()); 1036 return get(Operands, L); 1037 } 1038 1039 Operands.push_back(Step); 1040 return get(Operands, L); 1041} 1042 1043/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1044/// specified loop. Simplify the expression as much as possible. 1045SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1046 const Loop *L) { 1047 if (Operands.size() == 1) return Operands[0]; 1048 1049 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1050 if (StepC->getValue()->isNullValue()) { 1051 Operands.pop_back(); 1052 return get(Operands, L); // { X,+,0 } --> X 1053 } 1054 1055 SCEVAddRecExpr *&Result = 1056 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1057 Operands.end()))]; 1058 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1059 return Result; 1060} 1061 1062SCEVHandle SCEVUnknown::get(Value *V) { 1063 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1064 return SCEVConstant::get(CI); 1065 SCEVUnknown *&Result = SCEVUnknowns[V]; 1066 if (Result == 0) Result = new SCEVUnknown(V); 1067 return Result; 1068} 1069 1070 1071//===----------------------------------------------------------------------===// 1072// ScalarEvolutionsImpl Definition and Implementation 1073//===----------------------------------------------------------------------===// 1074// 1075/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1076/// evolution code. 1077/// 1078namespace { 1079 struct ScalarEvolutionsImpl { 1080 /// F - The function we are analyzing. 1081 /// 1082 Function &F; 1083 1084 /// LI - The loop information for the function we are currently analyzing. 1085 /// 1086 LoopInfo &LI; 1087 1088 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1089 /// things. 1090 SCEVHandle UnknownValue; 1091 1092 /// Scalars - This is a cache of the scalars we have analyzed so far. 1093 /// 1094 std::map<Value*, SCEVHandle> Scalars; 1095 1096 /// IterationCounts - Cache the iteration count of the loops for this 1097 /// function as they are computed. 1098 std::map<const Loop*, SCEVHandle> IterationCounts; 1099 1100 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1101 /// the PHI instructions that we attempt to compute constant evolutions for. 1102 /// This allows us to avoid potentially expensive recomputation of these 1103 /// properties. An instruction maps to null if we are unable to compute its 1104 /// exit value. 1105 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1106 1107 public: 1108 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1109 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1110 1111 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1112 /// expression and create a new one. 1113 SCEVHandle getSCEV(Value *V); 1114 1115 /// getSCEVAtScope - Compute the value of the specified expression within 1116 /// the indicated loop (which may be null to indicate in no loop). If the 1117 /// expression cannot be evaluated, return UnknownValue itself. 1118 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1119 1120 1121 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1122 /// an analyzable loop-invariant iteration count. 1123 bool hasLoopInvariantIterationCount(const Loop *L); 1124 1125 /// getIterationCount - If the specified loop has a predictable iteration 1126 /// count, return it. Note that it is not valid to call this method on a 1127 /// loop without a loop-invariant iteration count. 1128 SCEVHandle getIterationCount(const Loop *L); 1129 1130 /// deleteInstructionFromRecords - This method should be called by the 1131 /// client before it removes an instruction from the program, to make sure 1132 /// that no dangling references are left around. 1133 void deleteInstructionFromRecords(Instruction *I); 1134 1135 private: 1136 /// createSCEV - We know that there is no SCEV for the specified value. 1137 /// Analyze the expression. 1138 SCEVHandle createSCEV(Value *V); 1139 SCEVHandle createNodeForCast(CastInst *CI); 1140 1141 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1142 /// SCEVs. 1143 SCEVHandle createNodeForPHI(PHINode *PN); 1144 1145 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1146 /// for the specified instruction and replaces any references to the 1147 /// symbolic value SymName with the specified value. This is used during 1148 /// PHI resolution. 1149 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1150 const SCEVHandle &SymName, 1151 const SCEVHandle &NewVal); 1152 1153 /// ComputeIterationCount - Compute the number of times the specified loop 1154 /// will iterate. 1155 SCEVHandle ComputeIterationCount(const Loop *L); 1156 1157 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1158 /// 'setcc load X, cst', try to se if we can compute the trip count. 1159 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1160 Constant *RHS, 1161 const Loop *L, 1162 unsigned SetCCOpcode); 1163 1164 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1165 /// constant number of times (the condition evolves only from constants), 1166 /// try to evaluate a few iterations of the loop until we get the exit 1167 /// condition gets a value of ExitWhen (true or false). If we cannot 1168 /// evaluate the trip count of the loop, return UnknownValue. 1169 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1170 bool ExitWhen); 1171 1172 /// HowFarToZero - Return the number of times a backedge comparing the 1173 /// specified value to zero will execute. If not computable, return 1174 /// UnknownValue 1175 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1176 1177 /// HowFarToNonZero - Return the number of times a backedge checking the 1178 /// specified value for nonzero will execute. If not computable, return 1179 /// UnknownValue 1180 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1181 1182 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1183 /// in the header of its containing loop, we know the loop executes a 1184 /// constant number of times, and the PHI node is just a recurrence 1185 /// involving constants, fold it. 1186 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1187 const Loop *L); 1188 }; 1189} 1190 1191//===----------------------------------------------------------------------===// 1192// Basic SCEV Analysis and PHI Idiom Recognition Code 1193// 1194 1195/// deleteInstructionFromRecords - This method should be called by the 1196/// client before it removes an instruction from the program, to make sure 1197/// that no dangling references are left around. 1198void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1199 Scalars.erase(I); 1200 if (PHINode *PN = dyn_cast<PHINode>(I)) 1201 ConstantEvolutionLoopExitValue.erase(PN); 1202} 1203 1204 1205/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1206/// expression and create a new one. 1207SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1208 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1209 1210 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1211 if (I != Scalars.end()) return I->second; 1212 SCEVHandle S = createSCEV(V); 1213 Scalars.insert(std::make_pair(V, S)); 1214 return S; 1215} 1216 1217/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1218/// the specified instruction and replaces any references to the symbolic value 1219/// SymName with the specified value. This is used during PHI resolution. 1220void ScalarEvolutionsImpl:: 1221ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1222 const SCEVHandle &NewVal) { 1223 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1224 if (SI == Scalars.end()) return; 1225 1226 SCEVHandle NV = 1227 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1228 if (NV == SI->second) return; // No change. 1229 1230 SI->second = NV; // Update the scalars map! 1231 1232 // Any instruction values that use this instruction might also need to be 1233 // updated! 1234 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1235 UI != E; ++UI) 1236 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1237} 1238 1239/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1240/// a loop header, making it a potential recurrence, or it doesn't. 1241/// 1242SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1243 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1244 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1245 if (L->getHeader() == PN->getParent()) { 1246 // If it lives in the loop header, it has two incoming values, one 1247 // from outside the loop, and one from inside. 1248 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1249 unsigned BackEdge = IncomingEdge^1; 1250 1251 // While we are analyzing this PHI node, handle its value symbolically. 1252 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1253 assert(Scalars.find(PN) == Scalars.end() && 1254 "PHI node already processed?"); 1255 Scalars.insert(std::make_pair(PN, SymbolicName)); 1256 1257 // Using this symbolic name for the PHI, analyze the value coming around 1258 // the back-edge. 1259 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1260 1261 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1262 // has a special value for the first iteration of the loop. 1263 1264 // If the value coming around the backedge is an add with the symbolic 1265 // value we just inserted, then we found a simple induction variable! 1266 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1267 // If there is a single occurrence of the symbolic value, replace it 1268 // with a recurrence. 1269 unsigned FoundIndex = Add->getNumOperands(); 1270 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1271 if (Add->getOperand(i) == SymbolicName) 1272 if (FoundIndex == e) { 1273 FoundIndex = i; 1274 break; 1275 } 1276 1277 if (FoundIndex != Add->getNumOperands()) { 1278 // Create an add with everything but the specified operand. 1279 std::vector<SCEVHandle> Ops; 1280 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1281 if (i != FoundIndex) 1282 Ops.push_back(Add->getOperand(i)); 1283 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1284 1285 // This is not a valid addrec if the step amount is varying each 1286 // loop iteration, but is not itself an addrec in this loop. 1287 if (Accum->isLoopInvariant(L) || 1288 (isa<SCEVAddRecExpr>(Accum) && 1289 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1290 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1291 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1292 1293 // Okay, for the entire analysis of this edge we assumed the PHI 1294 // to be symbolic. We now need to go back and update all of the 1295 // entries for the scalars that use the PHI (except for the PHI 1296 // itself) to use the new analyzed value instead of the "symbolic" 1297 // value. 1298 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1299 return PHISCEV; 1300 } 1301 } 1302 } 1303 1304 return SymbolicName; 1305 } 1306 1307 // If it's not a loop phi, we can't handle it yet. 1308 return SCEVUnknown::get(PN); 1309} 1310 1311/// createNodeForCast - Handle the various forms of casts that we support. 1312/// 1313SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 1314 const Type *SrcTy = CI->getOperand(0)->getType(); 1315 const Type *DestTy = CI->getType(); 1316 1317 // If this is a noop cast (ie, conversion from int to uint), ignore it. 1318 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 1319 return getSCEV(CI->getOperand(0)); 1320 1321 if (SrcTy->isInteger() && DestTy->isInteger()) { 1322 // Otherwise, if this is a truncating integer cast, we can represent this 1323 // cast. 1324 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1325 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 1326 CI->getType()->getUnsignedVersion()); 1327 if (SrcTy->isUnsigned() && 1328 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1329 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 1330 CI->getType()->getUnsignedVersion()); 1331 } 1332 1333 // If this is an sign or zero extending cast and we can prove that the value 1334 // will never overflow, we could do similar transformations. 1335 1336 // Otherwise, we can't handle this cast! 1337 return SCEVUnknown::get(CI); 1338} 1339 1340 1341/// createSCEV - We know that there is no SCEV for the specified value. 1342/// Analyze the expression. 1343/// 1344SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1345 if (Instruction *I = dyn_cast<Instruction>(V)) { 1346 switch (I->getOpcode()) { 1347 case Instruction::Add: 1348 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1349 getSCEV(I->getOperand(1))); 1350 case Instruction::Mul: 1351 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1352 getSCEV(I->getOperand(1))); 1353 case Instruction::Div: 1354 if (V->getType()->isInteger() && V->getType()->isUnsigned()) 1355 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), 1356 getSCEV(I->getOperand(1))); 1357 break; 1358 1359 case Instruction::Sub: 1360 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1))); 1361 1362 case Instruction::Shl: 1363 // Turn shift left of a constant amount into a multiply. 1364 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1365 Constant *X = ConstantInt::get(V->getType(), 1); 1366 X = ConstantExpr::getShl(X, SA); 1367 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1368 } 1369 break; 1370 1371 case Instruction::Shr: 1372 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1))) 1373 if (V->getType()->isUnsigned()) { 1374 Constant *X = ConstantInt::get(V->getType(), 1); 1375 X = ConstantExpr::getShl(X, SA); 1376 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1377 } 1378 break; 1379 1380 case Instruction::Cast: 1381 return createNodeForCast(cast<CastInst>(I)); 1382 1383 case Instruction::PHI: 1384 return createNodeForPHI(cast<PHINode>(I)); 1385 1386 default: // We cannot analyze this expression. 1387 break; 1388 } 1389 } 1390 1391 return SCEVUnknown::get(V); 1392} 1393 1394 1395 1396//===----------------------------------------------------------------------===// 1397// Iteration Count Computation Code 1398// 1399 1400/// getIterationCount - If the specified loop has a predictable iteration 1401/// count, return it. Note that it is not valid to call this method on a 1402/// loop without a loop-invariant iteration count. 1403SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1404 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1405 if (I == IterationCounts.end()) { 1406 SCEVHandle ItCount = ComputeIterationCount(L); 1407 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1408 if (ItCount != UnknownValue) { 1409 assert(ItCount->isLoopInvariant(L) && 1410 "Computed trip count isn't loop invariant for loop!"); 1411 ++NumTripCountsComputed; 1412 } else if (isa<PHINode>(L->getHeader()->begin())) { 1413 // Only count loops that have phi nodes as not being computable. 1414 ++NumTripCountsNotComputed; 1415 } 1416 } 1417 return I->second; 1418} 1419 1420/// ComputeIterationCount - Compute the number of times the specified loop 1421/// will iterate. 1422SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1423 // If the loop has a non-one exit block count, we can't analyze it. 1424 std::vector<BasicBlock*> ExitBlocks; 1425 L->getExitBlocks(ExitBlocks); 1426 if (ExitBlocks.size() != 1) return UnknownValue; 1427 1428 // Okay, there is one exit block. Try to find the condition that causes the 1429 // loop to be exited. 1430 BasicBlock *ExitBlock = ExitBlocks[0]; 1431 1432 BasicBlock *ExitingBlock = 0; 1433 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1434 PI != E; ++PI) 1435 if (L->contains(*PI)) { 1436 if (ExitingBlock == 0) 1437 ExitingBlock = *PI; 1438 else 1439 return UnknownValue; // More than one block exiting! 1440 } 1441 assert(ExitingBlock && "No exits from loop, something is broken!"); 1442 1443 // Okay, we've computed the exiting block. See what condition causes us to 1444 // exit. 1445 // 1446 // FIXME: we should be able to handle switch instructions (with a single exit) 1447 // FIXME: We should handle cast of int to bool as well 1448 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1449 if (ExitBr == 0) return UnknownValue; 1450 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1451 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1452 if (ExitCond == 0) // Not a setcc 1453 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1454 ExitBr->getSuccessor(0) == ExitBlock); 1455 1456 // If the condition was exit on true, convert the condition to exit on false. 1457 Instruction::BinaryOps Cond; 1458 if (ExitBr->getSuccessor(1) == ExitBlock) 1459 Cond = ExitCond->getOpcode(); 1460 else 1461 Cond = ExitCond->getInverseCondition(); 1462 1463 // Handle common loops like: for (X = "string"; *X; ++X) 1464 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1465 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1466 SCEVHandle ItCnt = 1467 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1468 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1469 } 1470 1471 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1472 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1473 1474 // Try to evaluate any dependencies out of the loop. 1475 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1476 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1477 Tmp = getSCEVAtScope(RHS, L); 1478 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1479 1480 // At this point, we would like to compute how many iterations of the loop the 1481 // predicate will return true for these inputs. 1482 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1483 // If there is a constant, force it into the RHS. 1484 std::swap(LHS, RHS); 1485 Cond = SetCondInst::getSwappedCondition(Cond); 1486 } 1487 1488 // FIXME: think about handling pointer comparisons! i.e.: 1489 // while (P != P+100) ++P; 1490 1491 // If we have a comparison of a chrec against a constant, try to use value 1492 // ranges to answer this query. 1493 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1494 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1495 if (AddRec->getLoop() == L) { 1496 // Form the comparison range using the constant of the correct type so 1497 // that the ConstantRange class knows to do a signed or unsigned 1498 // comparison. 1499 ConstantInt *CompVal = RHSC->getValue(); 1500 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1501 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 1502 if (CompVal) { 1503 // Form the constant range. 1504 ConstantRange CompRange(Cond, CompVal); 1505 1506 // Now that we have it, if it's signed, convert it to an unsigned 1507 // range. 1508 if (CompRange.getLower()->getType()->isSigned()) { 1509 const Type *NewTy = RHSC->getValue()->getType(); 1510 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 1511 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 1512 CompRange = ConstantRange(NewL, NewU); 1513 } 1514 1515 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1516 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1517 } 1518 } 1519 1520 switch (Cond) { 1521 case Instruction::SetNE: // while (X != Y) 1522 // Convert to: while (X-Y != 0) 1523 if (LHS->getType()->isInteger()) { 1524 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 1525 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1526 } 1527 break; 1528 case Instruction::SetEQ: 1529 // Convert to: while (X-Y == 0) // while (X == Y) 1530 if (LHS->getType()->isInteger()) { 1531 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 1532 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1533 } 1534 break; 1535 default: 1536#if 0 1537 std::cerr << "ComputeIterationCount "; 1538 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1539 std::cerr << "[unsigned] "; 1540 std::cerr << *LHS << " " 1541 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1542#endif 1543 break; 1544 } 1545 1546 return ComputeIterationCountExhaustively(L, ExitCond, 1547 ExitBr->getSuccessor(0) == ExitBlock); 1548} 1549 1550static ConstantInt * 1551EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1552 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1553 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1554 assert(isa<SCEVConstant>(Val) && 1555 "Evaluation of SCEV at constant didn't fold correctly?"); 1556 return cast<SCEVConstant>(Val)->getValue(); 1557} 1558 1559/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1560/// and a GEP expression (missing the pointer index) indexing into it, return 1561/// the addressed element of the initializer or null if the index expression is 1562/// invalid. 1563static Constant * 1564GetAddressedElementFromGlobal(GlobalVariable *GV, 1565 const std::vector<ConstantInt*> &Indices) { 1566 Constant *Init = GV->getInitializer(); 1567 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1568 uint64_t Idx = Indices[i]->getRawValue(); 1569 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1570 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1571 Init = cast<Constant>(CS->getOperand(Idx)); 1572 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1573 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1574 Init = cast<Constant>(CA->getOperand(Idx)); 1575 } else if (isa<ConstantAggregateZero>(Init)) { 1576 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1577 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1578 Init = Constant::getNullValue(STy->getElementType(Idx)); 1579 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1580 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1581 Init = Constant::getNullValue(ATy->getElementType()); 1582 } else { 1583 assert(0 && "Unknown constant aggregate type!"); 1584 } 1585 return 0; 1586 } else { 1587 return 0; // Unknown initializer type 1588 } 1589 } 1590 return Init; 1591} 1592 1593/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1594/// 'setcc load X, cst', try to se if we can compute the trip count. 1595SCEVHandle ScalarEvolutionsImpl:: 1596ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1597 const Loop *L, unsigned SetCCOpcode) { 1598 if (LI->isVolatile()) return UnknownValue; 1599 1600 // Check to see if the loaded pointer is a getelementptr of a global. 1601 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1602 if (!GEP) return UnknownValue; 1603 1604 // Make sure that it is really a constant global we are gepping, with an 1605 // initializer, and make sure the first IDX is really 0. 1606 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1607 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1608 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1609 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1610 return UnknownValue; 1611 1612 // Okay, we allow one non-constant index into the GEP instruction. 1613 Value *VarIdx = 0; 1614 std::vector<ConstantInt*> Indexes; 1615 unsigned VarIdxNum = 0; 1616 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1617 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1618 Indexes.push_back(CI); 1619 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1620 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1621 VarIdx = GEP->getOperand(i); 1622 VarIdxNum = i-2; 1623 Indexes.push_back(0); 1624 } 1625 1626 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1627 // Check to see if X is a loop variant variable value now. 1628 SCEVHandle Idx = getSCEV(VarIdx); 1629 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1630 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1631 1632 // We can only recognize very limited forms of loop index expressions, in 1633 // particular, only affine AddRec's like {C1,+,C2}. 1634 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1635 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1636 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1637 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1638 return UnknownValue; 1639 1640 unsigned MaxSteps = MaxBruteForceIterations; 1641 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1642 ConstantUInt *ItCst = 1643 ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 1644 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1645 1646 // Form the GEP offset. 1647 Indexes[VarIdxNum] = Val; 1648 1649 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1650 if (Result == 0) break; // Cannot compute! 1651 1652 // Evaluate the condition for this iteration. 1653 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 1654 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 1655 if (Result == ConstantBool::False) { 1656#if 0 1657 std::cerr << "\n***\n*** Computed loop count " << *ItCst 1658 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1659 << "***\n"; 1660#endif 1661 ++NumArrayLenItCounts; 1662 return SCEVConstant::get(ItCst); // Found terminating iteration! 1663 } 1664 } 1665 return UnknownValue; 1666} 1667 1668 1669/// CanConstantFold - Return true if we can constant fold an instruction of the 1670/// specified type, assuming that all operands were constants. 1671static bool CanConstantFold(const Instruction *I) { 1672 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1673 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1674 return true; 1675 1676 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1677 if (const Function *F = CI->getCalledFunction()) 1678 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1679 return false; 1680} 1681 1682/// ConstantFold - Constant fold an instruction of the specified type with the 1683/// specified constant operands. This function may modify the operands vector. 1684static Constant *ConstantFold(const Instruction *I, 1685 std::vector<Constant*> &Operands) { 1686 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1687 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1688 1689 switch (I->getOpcode()) { 1690 case Instruction::Cast: 1691 return ConstantExpr::getCast(Operands[0], I->getType()); 1692 case Instruction::Select: 1693 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1694 case Instruction::Call: 1695 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1696 Operands.erase(Operands.begin()); 1697 return ConstantFoldCall(cast<Function>(GV), Operands); 1698 } 1699 1700 return 0; 1701 case Instruction::GetElementPtr: 1702 Constant *Base = Operands[0]; 1703 Operands.erase(Operands.begin()); 1704 return ConstantExpr::getGetElementPtr(Base, Operands); 1705 } 1706 return 0; 1707} 1708 1709 1710/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1711/// in the loop that V is derived from. We allow arbitrary operations along the 1712/// way, but the operands of an operation must either be constants or a value 1713/// derived from a constant PHI. If this expression does not fit with these 1714/// constraints, return null. 1715static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1716 // If this is not an instruction, or if this is an instruction outside of the 1717 // loop, it can't be derived from a loop PHI. 1718 Instruction *I = dyn_cast<Instruction>(V); 1719 if (I == 0 || !L->contains(I->getParent())) return 0; 1720 1721 if (PHINode *PN = dyn_cast<PHINode>(I)) 1722 if (L->getHeader() == I->getParent()) 1723 return PN; 1724 else 1725 // We don't currently keep track of the control flow needed to evaluate 1726 // PHIs, so we cannot handle PHIs inside of loops. 1727 return 0; 1728 1729 // If we won't be able to constant fold this expression even if the operands 1730 // are constants, return early. 1731 if (!CanConstantFold(I)) return 0; 1732 1733 // Otherwise, we can evaluate this instruction if all of its operands are 1734 // constant or derived from a PHI node themselves. 1735 PHINode *PHI = 0; 1736 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1737 if (!(isa<Constant>(I->getOperand(Op)) || 1738 isa<GlobalValue>(I->getOperand(Op)))) { 1739 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1740 if (P == 0) return 0; // Not evolving from PHI 1741 if (PHI == 0) 1742 PHI = P; 1743 else if (PHI != P) 1744 return 0; // Evolving from multiple different PHIs. 1745 } 1746 1747 // This is a expression evolving from a constant PHI! 1748 return PHI; 1749} 1750 1751/// EvaluateExpression - Given an expression that passes the 1752/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1753/// in the loop has the value PHIVal. If we can't fold this expression for some 1754/// reason, return null. 1755static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1756 if (isa<PHINode>(V)) return PHIVal; 1757 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1758 return GV; 1759 if (Constant *C = dyn_cast<Constant>(V)) return C; 1760 Instruction *I = cast<Instruction>(V); 1761 1762 std::vector<Constant*> Operands; 1763 Operands.resize(I->getNumOperands()); 1764 1765 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1766 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1767 if (Operands[i] == 0) return 0; 1768 } 1769 1770 return ConstantFold(I, Operands); 1771} 1772 1773/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1774/// in the header of its containing loop, we know the loop executes a 1775/// constant number of times, and the PHI node is just a recurrence 1776/// involving constants, fold it. 1777Constant *ScalarEvolutionsImpl:: 1778getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1779 std::map<PHINode*, Constant*>::iterator I = 1780 ConstantEvolutionLoopExitValue.find(PN); 1781 if (I != ConstantEvolutionLoopExitValue.end()) 1782 return I->second; 1783 1784 if (Its > MaxBruteForceIterations) 1785 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1786 1787 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1788 1789 // Since the loop is canonicalized, the PHI node must have two entries. One 1790 // entry must be a constant (coming in from outside of the loop), and the 1791 // second must be derived from the same PHI. 1792 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1793 Constant *StartCST = 1794 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1795 if (StartCST == 0) 1796 return RetVal = 0; // Must be a constant. 1797 1798 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1799 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1800 if (PN2 != PN) 1801 return RetVal = 0; // Not derived from same PHI. 1802 1803 // Execute the loop symbolically to determine the exit value. 1804 unsigned IterationNum = 0; 1805 unsigned NumIterations = Its; 1806 if (NumIterations != Its) 1807 return RetVal = 0; // More than 2^32 iterations?? 1808 1809 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1810 if (IterationNum == NumIterations) 1811 return RetVal = PHIVal; // Got exit value! 1812 1813 // Compute the value of the PHI node for the next iteration. 1814 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1815 if (NextPHI == PHIVal) 1816 return RetVal = NextPHI; // Stopped evolving! 1817 if (NextPHI == 0) 1818 return 0; // Couldn't evaluate! 1819 PHIVal = NextPHI; 1820 } 1821} 1822 1823/// ComputeIterationCountExhaustively - If the trip is known to execute a 1824/// constant number of times (the condition evolves only from constants), 1825/// try to evaluate a few iterations of the loop until we get the exit 1826/// condition gets a value of ExitWhen (true or false). If we cannot 1827/// evaluate the trip count of the loop, return UnknownValue. 1828SCEVHandle ScalarEvolutionsImpl:: 1829ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1830 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1831 if (PN == 0) return UnknownValue; 1832 1833 // Since the loop is canonicalized, the PHI node must have two entries. One 1834 // entry must be a constant (coming in from outside of the loop), and the 1835 // second must be derived from the same PHI. 1836 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1837 Constant *StartCST = 1838 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1839 if (StartCST == 0) return UnknownValue; // Must be a constant. 1840 1841 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1842 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1843 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1844 1845 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1846 // the loop symbolically to determine when the condition gets a value of 1847 // "ExitWhen". 1848 unsigned IterationNum = 0; 1849 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1850 for (Constant *PHIVal = StartCST; 1851 IterationNum != MaxIterations; ++IterationNum) { 1852 ConstantBool *CondVal = 1853 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1854 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1855 1856 if (CondVal->getValue() == ExitWhen) { 1857 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1858 ++NumBruteForceTripCountsComputed; 1859 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 1860 } 1861 1862 // Compute the value of the PHI node for the next iteration. 1863 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1864 if (NextPHI == 0 || NextPHI == PHIVal) 1865 return UnknownValue; // Couldn't evaluate or not making progress... 1866 PHIVal = NextPHI; 1867 } 1868 1869 // Too many iterations were needed to evaluate. 1870 return UnknownValue; 1871} 1872 1873/// getSCEVAtScope - Compute the value of the specified expression within the 1874/// indicated loop (which may be null to indicate in no loop). If the 1875/// expression cannot be evaluated, return UnknownValue. 1876SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1877 // FIXME: this should be turned into a virtual method on SCEV! 1878 1879 if (isa<SCEVConstant>(V)) return V; 1880 1881 // If this instruction is evolves from a constant-evolving PHI, compute the 1882 // exit value from the loop without using SCEVs. 1883 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1884 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1885 const Loop *LI = this->LI[I->getParent()]; 1886 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1887 if (PHINode *PN = dyn_cast<PHINode>(I)) 1888 if (PN->getParent() == LI->getHeader()) { 1889 // Okay, there is no closed form solution for the PHI node. Check 1890 // to see if the loop that contains it has a known iteration count. 1891 // If so, we may be able to force computation of the exit value. 1892 SCEVHandle IterationCount = getIterationCount(LI); 1893 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1894 // Okay, we know how many times the containing loop executes. If 1895 // this is a constant evolving PHI node, get the final value at 1896 // the specified iteration number. 1897 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1898 ICC->getValue()->getRawValue(), 1899 LI); 1900 if (RV) return SCEVUnknown::get(RV); 1901 } 1902 } 1903 1904 // Okay, this is a some expression that we cannot symbolically evaluate 1905 // into a SCEV. Check to see if it's possible to symbolically evaluate 1906 // the arguments into constants, and if see, try to constant propagate the 1907 // result. This is particularly useful for computing loop exit values. 1908 if (CanConstantFold(I)) { 1909 std::vector<Constant*> Operands; 1910 Operands.reserve(I->getNumOperands()); 1911 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1912 Value *Op = I->getOperand(i); 1913 if (Constant *C = dyn_cast<Constant>(Op)) { 1914 Operands.push_back(C); 1915 } else { 1916 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1917 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1918 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 1919 Op->getType())); 1920 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1921 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1922 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 1923 else 1924 return V; 1925 } else { 1926 return V; 1927 } 1928 } 1929 } 1930 return SCEVUnknown::get(ConstantFold(I, Operands)); 1931 } 1932 } 1933 1934 // This is some other type of SCEVUnknown, just return it. 1935 return V; 1936 } 1937 1938 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1939 // Avoid performing the look-up in the common case where the specified 1940 // expression has no loop-variant portions. 1941 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1942 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1943 if (OpAtScope != Comm->getOperand(i)) { 1944 if (OpAtScope == UnknownValue) return UnknownValue; 1945 // Okay, at least one of these operands is loop variant but might be 1946 // foldable. Build a new instance of the folded commutative expression. 1947 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1948 NewOps.push_back(OpAtScope); 1949 1950 for (++i; i != e; ++i) { 1951 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1952 if (OpAtScope == UnknownValue) return UnknownValue; 1953 NewOps.push_back(OpAtScope); 1954 } 1955 if (isa<SCEVAddExpr>(Comm)) 1956 return SCEVAddExpr::get(NewOps); 1957 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 1958 return SCEVMulExpr::get(NewOps); 1959 } 1960 } 1961 // If we got here, all operands are loop invariant. 1962 return Comm; 1963 } 1964 1965 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) { 1966 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L); 1967 if (LHS == UnknownValue) return LHS; 1968 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L); 1969 if (RHS == UnknownValue) return RHS; 1970 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS()) 1971 return UDiv; // must be loop invariant 1972 return SCEVUDivExpr::get(LHS, RHS); 1973 } 1974 1975 // If this is a loop recurrence for a loop that does not contain L, then we 1976 // are dealing with the final value computed by the loop. 1977 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 1978 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 1979 // To evaluate this recurrence, we need to know how many times the AddRec 1980 // loop iterates. Compute this now. 1981 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 1982 if (IterationCount == UnknownValue) return UnknownValue; 1983 IterationCount = getTruncateOrZeroExtend(IterationCount, 1984 AddRec->getType()); 1985 1986 // If the value is affine, simplify the expression evaluation to just 1987 // Start + Step*IterationCount. 1988 if (AddRec->isAffine()) 1989 return SCEVAddExpr::get(AddRec->getStart(), 1990 SCEVMulExpr::get(IterationCount, 1991 AddRec->getOperand(1))); 1992 1993 // Otherwise, evaluate it the hard way. 1994 return AddRec->evaluateAtIteration(IterationCount); 1995 } 1996 return UnknownValue; 1997 } 1998 1999 //assert(0 && "Unknown SCEV type!"); 2000 return UnknownValue; 2001} 2002 2003 2004/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2005/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2006/// might be the same) or two SCEVCouldNotCompute objects. 2007/// 2008static std::pair<SCEVHandle,SCEVHandle> 2009SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2010 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2011 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2012 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2013 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2014 2015 // We currently can only solve this if the coefficients are constants. 2016 if (!L || !M || !N) { 2017 SCEV *CNC = new SCEVCouldNotCompute(); 2018 return std::make_pair(CNC, CNC); 2019 } 2020 2021 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 2022 2023 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2024 Constant *C = L->getValue(); 2025 // The B coefficient is M-N/2 2026 Constant *B = ConstantExpr::getSub(M->getValue(), 2027 ConstantExpr::getDiv(N->getValue(), 2028 Two)); 2029 // The A coefficient is N/2 2030 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 2031 2032 // Compute the B^2-4ac term. 2033 Constant *SqrtTerm = 2034 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2035 ConstantExpr::getMul(A, C)); 2036 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2037 2038 // Compute floor(sqrt(B^2-4ac)) 2039 ConstantUInt *SqrtVal = 2040 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 2041 SqrtTerm->getType()->getUnsignedVersion())); 2042 uint64_t SqrtValV = SqrtVal->getValue(); 2043 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2044 // The square root might not be precise for arbitrary 64-bit integer 2045 // values. Do some sanity checks to ensure it's correct. 2046 if (SqrtValV2*SqrtValV2 > SqrtValV || 2047 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2048 SCEV *CNC = new SCEVCouldNotCompute(); 2049 return std::make_pair(CNC, CNC); 2050 } 2051 2052 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 2053 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 2054 2055 Constant *NegB = ConstantExpr::getNeg(B); 2056 Constant *TwoA = ConstantExpr::getMul(A, Two); 2057 2058 // The divisions must be performed as signed divisions. 2059 const Type *SignedTy = NegB->getType()->getSignedVersion(); 2060 NegB = ConstantExpr::getCast(NegB, SignedTy); 2061 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 2062 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 2063 2064 Constant *Solution1 = 2065 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2066 Constant *Solution2 = 2067 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2068 return std::make_pair(SCEVUnknown::get(Solution1), 2069 SCEVUnknown::get(Solution2)); 2070} 2071 2072/// HowFarToZero - Return the number of times a backedge comparing the specified 2073/// value to zero will execute. If not computable, return UnknownValue 2074SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2075 // If the value is a constant 2076 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2077 // If the value is already zero, the branch will execute zero times. 2078 if (C->getValue()->isNullValue()) return C; 2079 return UnknownValue; // Otherwise it will loop infinitely. 2080 } 2081 2082 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2083 if (!AddRec || AddRec->getLoop() != L) 2084 return UnknownValue; 2085 2086 if (AddRec->isAffine()) { 2087 // If this is an affine expression the execution count of this branch is 2088 // equal to: 2089 // 2090 // (0 - Start/Step) iff Start % Step == 0 2091 // 2092 // Get the initial value for the loop. 2093 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2094 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2095 SCEVHandle Step = AddRec->getOperand(1); 2096 2097 Step = getSCEVAtScope(Step, L->getParentLoop()); 2098 2099 // Figure out if Start % Step == 0. 2100 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2101 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2102 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2103 return getNegativeSCEV(Start); // 0 - Start/1 == -Start 2104 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2105 return Start; // 0 - Start/-1 == Start 2106 2107 // Check to see if Start is divisible by SC with no remainder. 2108 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2109 ConstantInt *StartCC = StartC->getValue(); 2110 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2111 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 2112 if (Rem->isNullValue()) { 2113 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 2114 return SCEVUnknown::get(Result); 2115 } 2116 } 2117 } 2118 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2119 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2120 // the quadratic equation to solve it. 2121 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2122 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2123 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2124 if (R1) { 2125#if 0 2126 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2127 << " sol#2: " << *R2 << "\n"; 2128#endif 2129 // Pick the smallest positive root value. 2130 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 2131 if (ConstantBool *CB = 2132 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2133 R2->getValue()))) { 2134 if (CB != ConstantBool::True) 2135 std::swap(R1, R2); // R1 is the minimum root now. 2136 2137 // We can only use this value if the chrec ends up with an exact zero 2138 // value at this index. When solving for "X*X != 5", for example, we 2139 // should not accept a root of 2. 2140 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2141 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2142 if (EvalVal->getValue()->isNullValue()) 2143 return R1; // We found a quadratic root! 2144 } 2145 } 2146 } 2147 2148 return UnknownValue; 2149} 2150 2151/// HowFarToNonZero - Return the number of times a backedge checking the 2152/// specified value for nonzero will execute. If not computable, return 2153/// UnknownValue 2154SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2155 // Loops that look like: while (X == 0) are very strange indeed. We don't 2156 // handle them yet except for the trivial case. This could be expanded in the 2157 // future as needed. 2158 2159 // If the value is a constant, check to see if it is known to be non-zero 2160 // already. If so, the backedge will execute zero times. 2161 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2162 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2163 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 2164 if (NonZero == ConstantBool::True) 2165 return getSCEV(Zero); 2166 return UnknownValue; // Otherwise it will loop infinitely. 2167 } 2168 2169 // We could implement others, but I really doubt anyone writes loops like 2170 // this, and if they did, they would already be constant folded. 2171 return UnknownValue; 2172} 2173 2174/// getNumIterationsInRange - Return the number of iterations of this loop that 2175/// produce values in the specified constant range. Another way of looking at 2176/// this is that it returns the first iteration number where the value is not in 2177/// the condition, thus computing the exit count. If the iteration count can't 2178/// be computed, an instance of SCEVCouldNotCompute is returned. 2179SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2180 if (Range.isFullSet()) // Infinite loop. 2181 return new SCEVCouldNotCompute(); 2182 2183 // If the start is a non-zero constant, shift the range to simplify things. 2184 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2185 if (!SC->getValue()->isNullValue()) { 2186 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2187 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2188 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2189 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2190 return ShiftedAddRec->getNumIterationsInRange( 2191 Range.subtract(SC->getValue())); 2192 // This is strange and shouldn't happen. 2193 return new SCEVCouldNotCompute(); 2194 } 2195 2196 // The only time we can solve this is when we have all constant indices. 2197 // Otherwise, we cannot determine the overflow conditions. 2198 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2199 if (!isa<SCEVConstant>(getOperand(i))) 2200 return new SCEVCouldNotCompute(); 2201 2202 2203 // Okay at this point we know that all elements of the chrec are constants and 2204 // that the start element is zero. 2205 2206 // First check to see if the range contains zero. If not, the first 2207 // iteration exits. 2208 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2209 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2210 2211 if (isAffine()) { 2212 // If this is an affine expression then we have this situation: 2213 // Solve {0,+,A} in Range === Ax in Range 2214 2215 // Since we know that zero is in the range, we know that the upper value of 2216 // the range must be the first possible exit value. Also note that we 2217 // already checked for a full range. 2218 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2219 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2220 ConstantInt *One = ConstantInt::get(getType(), 1); 2221 2222 // The exit value should be (Upper+A-1)/A. 2223 Constant *ExitValue = Upper; 2224 if (A != One) { 2225 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2226 ExitValue = ConstantExpr::getDiv(ExitValue, A); 2227 } 2228 assert(isa<ConstantInt>(ExitValue) && 2229 "Constant folding of integers not implemented?"); 2230 2231 // Evaluate at the exit value. If we really did fall out of the valid 2232 // range, then we computed our trip count, otherwise wrap around or other 2233 // things must have happened. 2234 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2235 if (Range.contains(Val)) 2236 return new SCEVCouldNotCompute(); // Something strange happened 2237 2238 // Ensure that the previous value is in the range. This is a sanity check. 2239 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2240 ConstantExpr::getSub(ExitValue, One))) && 2241 "Linear scev computation is off in a bad way!"); 2242 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2243 } else if (isQuadratic()) { 2244 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2245 // quadratic equation to solve it. To do this, we must frame our problem in 2246 // terms of figuring out when zero is crossed, instead of when 2247 // Range.getUpper() is crossed. 2248 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2249 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2250 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2251 2252 // Next, solve the constructed addrec 2253 std::pair<SCEVHandle,SCEVHandle> Roots = 2254 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2255 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2256 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2257 if (R1) { 2258 // Pick the smallest positive root value. 2259 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2260 if (ConstantBool *CB = 2261 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2262 R2->getValue()))) { 2263 if (CB != ConstantBool::True) 2264 std::swap(R1, R2); // R1 is the minimum root now. 2265 2266 // Make sure the root is not off by one. The returned iteration should 2267 // not be in the range, but the previous one should be. When solving 2268 // for "X*X < 5", for example, we should not return a root of 2. 2269 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2270 R1->getValue()); 2271 if (Range.contains(R1Val)) { 2272 // The next iteration must be out of the range... 2273 Constant *NextVal = 2274 ConstantExpr::getAdd(R1->getValue(), 2275 ConstantInt::get(R1->getType(), 1)); 2276 2277 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2278 if (!Range.contains(R1Val)) 2279 return SCEVUnknown::get(NextVal); 2280 return new SCEVCouldNotCompute(); // Something strange happened 2281 } 2282 2283 // If R1 was not in the range, then it is a good return value. Make 2284 // sure that R1-1 WAS in the range though, just in case. 2285 Constant *NextVal = 2286 ConstantExpr::getSub(R1->getValue(), 2287 ConstantInt::get(R1->getType(), 1)); 2288 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2289 if (Range.contains(R1Val)) 2290 return R1; 2291 return new SCEVCouldNotCompute(); // Something strange happened 2292 } 2293 } 2294 } 2295 2296 // Fallback, if this is a general polynomial, figure out the progression 2297 // through brute force: evaluate until we find an iteration that fails the 2298 // test. This is likely to be slow, but getting an accurate trip count is 2299 // incredibly important, we will be able to simplify the exit test a lot, and 2300 // we are almost guaranteed to get a trip count in this case. 2301 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2302 ConstantInt *One = ConstantInt::get(getType(), 1); 2303 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2304 do { 2305 ++NumBruteForceEvaluations; 2306 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2307 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2308 return new SCEVCouldNotCompute(); 2309 2310 // Check to see if we found the value! 2311 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2312 return SCEVConstant::get(TestVal); 2313 2314 // Increment to test the next index. 2315 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2316 } while (TestVal != EndVal); 2317 2318 return new SCEVCouldNotCompute(); 2319} 2320 2321 2322 2323//===----------------------------------------------------------------------===// 2324// ScalarEvolution Class Implementation 2325//===----------------------------------------------------------------------===// 2326 2327bool ScalarEvolution::runOnFunction(Function &F) { 2328 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2329 return false; 2330} 2331 2332void ScalarEvolution::releaseMemory() { 2333 delete (ScalarEvolutionsImpl*)Impl; 2334 Impl = 0; 2335} 2336 2337void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2338 AU.setPreservesAll(); 2339 AU.addRequiredID(LoopSimplifyID); 2340 AU.addRequiredTransitive<LoopInfo>(); 2341} 2342 2343SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2344 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2345} 2346 2347SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2348 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2349} 2350 2351bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2352 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2353} 2354 2355SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2356 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2357} 2358 2359void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2360 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2361} 2362 2363static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2364 const Loop *L) { 2365 // Print all inner loops first 2366 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2367 PrintLoopInfo(OS, SE, *I); 2368 2369 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 2370 2371 std::vector<BasicBlock*> ExitBlocks; 2372 L->getExitBlocks(ExitBlocks); 2373 if (ExitBlocks.size() != 1) 2374 std::cerr << "<multiple exits> "; 2375 2376 if (SE->hasLoopInvariantIterationCount(L)) { 2377 std::cerr << *SE->getIterationCount(L) << " iterations! "; 2378 } else { 2379 std::cerr << "Unpredictable iteration count. "; 2380 } 2381 2382 std::cerr << "\n"; 2383} 2384 2385void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2386 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2387 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2388 2389 OS << "Classifying expressions for: " << F.getName() << "\n"; 2390 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2391 if (I->getType()->isInteger()) { 2392 OS << *I; 2393 OS << " --> "; 2394 SCEVHandle SV = getSCEV(&*I); 2395 SV->print(OS); 2396 OS << "\t\t"; 2397 2398 if ((*I).getType()->isIntegral()) { 2399 ConstantRange Bounds = SV->getValueRange(); 2400 if (!Bounds.isFullSet()) 2401 OS << "Bounds: " << Bounds << " "; 2402 } 2403 2404 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2405 OS << "Exits: "; 2406 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2407 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2408 OS << "<<Unknown>>"; 2409 } else { 2410 OS << *ExitValue; 2411 } 2412 } 2413 2414 2415 OS << "\n"; 2416 } 2417 2418 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2419 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2420 PrintLoopInfo(OS, this, *I); 2421} 2422 2423