ScalarEvolution.cpp revision 7ffc07dcf7a0afc5e70e799f26de75750a8008d5
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 LHSC = cast<SCEVConstant>(Ops[0]); 629 } else { 630 // If we couldn't fold the expression, move to the next constant. Note 631 // that this is impossible to happen in practice because we always 632 // constant fold constant ints to constant ints. 633 ++Idx; 634 } 635 } 636 637 // If we are left with a constant zero being added, strip it off. 638 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 639 Ops.erase(Ops.begin()); 640 --Idx; 641 } 642 } 643 644 if (Ops.size() == 1) return Ops[0]; 645 646 // Okay, check to see if the same value occurs in the operand list twice. If 647 // so, merge them together into an multiply expression. Since we sorted the 648 // list, these values are required to be adjacent. 649 const Type *Ty = Ops[0]->getType(); 650 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 651 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 652 // Found a match, merge the two values into a multiply, and add any 653 // remaining values to the result. 654 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty); 655 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two); 656 if (Ops.size() == 2) 657 return Mul; 658 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 659 Ops.push_back(Mul); 660 return SCEVAddExpr::get(Ops); 661 } 662 663 // Okay, now we know the first non-constant operand. If there are add 664 // operands they would be next. 665 if (Idx < Ops.size()) { 666 bool DeletedAdd = false; 667 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 668 // If we have an add, expand the add operands onto the end of the operands 669 // list. 670 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 671 Ops.erase(Ops.begin()+Idx); 672 DeletedAdd = true; 673 } 674 675 // If we deleted at least one add, we added operands to the end of the list, 676 // and they are not necessarily sorted. Recurse to resort and resimplify 677 // any operands we just aquired. 678 if (DeletedAdd) 679 return get(Ops); 680 } 681 682 // Skip over the add expression until we get to a multiply. 683 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 684 ++Idx; 685 686 // If we are adding something to a multiply expression, make sure the 687 // something is not already an operand of the multiply. If so, merge it into 688 // the multiply. 689 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 690 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 691 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 692 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 693 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 694 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 695 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 696 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 697 if (Mul->getNumOperands() != 2) { 698 // If the multiply has more than two operands, we must get the 699 // Y*Z term. 700 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 701 MulOps.erase(MulOps.begin()+MulOp); 702 InnerMul = SCEVMulExpr::get(MulOps); 703 } 704 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty); 705 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One); 706 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]); 707 if (Ops.size() == 2) return OuterMul; 708 if (AddOp < Idx) { 709 Ops.erase(Ops.begin()+AddOp); 710 Ops.erase(Ops.begin()+Idx-1); 711 } else { 712 Ops.erase(Ops.begin()+Idx); 713 Ops.erase(Ops.begin()+AddOp-1); 714 } 715 Ops.push_back(OuterMul); 716 return SCEVAddExpr::get(Ops); 717 } 718 719 // Check this multiply against other multiplies being added together. 720 for (unsigned OtherMulIdx = Idx+1; 721 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 722 ++OtherMulIdx) { 723 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 724 // If MulOp occurs in OtherMul, we can fold the two multiplies 725 // together. 726 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 727 OMulOp != e; ++OMulOp) 728 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 729 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 730 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 731 if (Mul->getNumOperands() != 2) { 732 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 733 MulOps.erase(MulOps.begin()+MulOp); 734 InnerMul1 = SCEVMulExpr::get(MulOps); 735 } 736 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 737 if (OtherMul->getNumOperands() != 2) { 738 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 739 OtherMul->op_end()); 740 MulOps.erase(MulOps.begin()+OMulOp); 741 InnerMul2 = SCEVMulExpr::get(MulOps); 742 } 743 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2); 744 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum); 745 if (Ops.size() == 2) return OuterMul; 746 Ops.erase(Ops.begin()+Idx); 747 Ops.erase(Ops.begin()+OtherMulIdx-1); 748 Ops.push_back(OuterMul); 749 return SCEVAddExpr::get(Ops); 750 } 751 } 752 } 753 } 754 755 // If there are any add recurrences in the operands list, see if any other 756 // added values are loop invariant. If so, we can fold them into the 757 // recurrence. 758 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 759 ++Idx; 760 761 // Scan over all recurrences, trying to fold loop invariants into them. 762 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 763 // Scan all of the other operands to this add and add them to the vector if 764 // they are loop invariant w.r.t. the recurrence. 765 std::vector<SCEVHandle> LIOps; 766 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 767 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 768 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 769 LIOps.push_back(Ops[i]); 770 Ops.erase(Ops.begin()+i); 771 --i; --e; 772 } 773 774 // If we found some loop invariants, fold them into the recurrence. 775 if (!LIOps.empty()) { 776 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 777 LIOps.push_back(AddRec->getStart()); 778 779 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 780 AddRecOps[0] = SCEVAddExpr::get(LIOps); 781 782 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop()); 783 // If all of the other operands were loop invariant, we are done. 784 if (Ops.size() == 1) return NewRec; 785 786 // Otherwise, add the folded AddRec by the non-liv parts. 787 for (unsigned i = 0;; ++i) 788 if (Ops[i] == AddRec) { 789 Ops[i] = NewRec; 790 break; 791 } 792 return SCEVAddExpr::get(Ops); 793 } 794 795 // Okay, if there weren't any loop invariants to be folded, check to see if 796 // there are multiple AddRec's with the same loop induction variable being 797 // added together. If so, we can fold them. 798 for (unsigned OtherIdx = Idx+1; 799 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 800 if (OtherIdx != Idx) { 801 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 802 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 803 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 804 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 805 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 806 if (i >= NewOps.size()) { 807 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 808 OtherAddRec->op_end()); 809 break; 810 } 811 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i)); 812 } 813 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 814 815 if (Ops.size() == 2) return NewAddRec; 816 817 Ops.erase(Ops.begin()+Idx); 818 Ops.erase(Ops.begin()+OtherIdx-1); 819 Ops.push_back(NewAddRec); 820 return SCEVAddExpr::get(Ops); 821 } 822 } 823 824 // Otherwise couldn't fold anything into this recurrence. Move onto the 825 // next one. 826 } 827 828 // Okay, it looks like we really DO need an add expr. Check to see if we 829 // already have one, otherwise create a new one. 830 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 831 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr, 832 SCEVOps)]; 833 if (Result == 0) Result = new SCEVAddExpr(Ops); 834 return Result; 835} 836 837 838SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) { 839 assert(!Ops.empty() && "Cannot get empty mul!"); 840 841 // Sort by complexity, this groups all similar expression types together. 842 GroupByComplexity(Ops); 843 844 // If there are any constants, fold them together. 845 unsigned Idx = 0; 846 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 847 848 // C1*(C2+V) -> C1*C2 + C1*V 849 if (Ops.size() == 2) 850 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 851 if (Add->getNumOperands() == 2 && 852 isa<SCEVConstant>(Add->getOperand(0))) 853 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)), 854 SCEVMulExpr::get(LHSC, Add->getOperand(1))); 855 856 857 ++Idx; 858 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 859 // We found two constants, fold them together! 860 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue()); 861 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 862 Ops[0] = SCEVConstant::get(CI); 863 Ops.erase(Ops.begin()+1); // Erase the folded element 864 if (Ops.size() == 1) return Ops[0]; 865 LHSC = cast<SCEVConstant>(Ops[0]); 866 } else { 867 // If we couldn't fold the expression, move to the next constant. Note 868 // that this is impossible to happen in practice because we always 869 // constant fold constant ints to constant ints. 870 ++Idx; 871 } 872 } 873 874 // If we are left with a constant one being multiplied, strip it off. 875 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 876 Ops.erase(Ops.begin()); 877 --Idx; 878 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) { 879 // If we have a multiply of zero, it will always be zero. 880 return Ops[0]; 881 } 882 } 883 884 // Skip over the add expression until we get to a multiply. 885 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 886 ++Idx; 887 888 if (Ops.size() == 1) 889 return Ops[0]; 890 891 // If there are mul operands inline them all into this expression. 892 if (Idx < Ops.size()) { 893 bool DeletedMul = false; 894 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 895 // If we have an mul, expand the mul operands onto the end of the operands 896 // list. 897 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 898 Ops.erase(Ops.begin()+Idx); 899 DeletedMul = true; 900 } 901 902 // If we deleted at least one mul, we added operands to the end of the list, 903 // and they are not necessarily sorted. Recurse to resort and resimplify 904 // any operands we just aquired. 905 if (DeletedMul) 906 return get(Ops); 907 } 908 909 // If there are any add recurrences in the operands list, see if any other 910 // added values are loop invariant. If so, we can fold them into the 911 // recurrence. 912 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 913 ++Idx; 914 915 // Scan over all recurrences, trying to fold loop invariants into them. 916 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 917 // Scan all of the other operands to this mul and add them to the vector if 918 // they are loop invariant w.r.t. the recurrence. 919 std::vector<SCEVHandle> LIOps; 920 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 921 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 922 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 923 LIOps.push_back(Ops[i]); 924 Ops.erase(Ops.begin()+i); 925 --i; --e; 926 } 927 928 // If we found some loop invariants, fold them into the recurrence. 929 if (!LIOps.empty()) { 930 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 931 std::vector<SCEVHandle> NewOps; 932 NewOps.reserve(AddRec->getNumOperands()); 933 if (LIOps.size() == 1) { 934 SCEV *Scale = LIOps[0]; 935 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 936 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i))); 937 } else { 938 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 939 std::vector<SCEVHandle> MulOps(LIOps); 940 MulOps.push_back(AddRec->getOperand(i)); 941 NewOps.push_back(SCEVMulExpr::get(MulOps)); 942 } 943 } 944 945 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop()); 946 947 // If all of the other operands were loop invariant, we are done. 948 if (Ops.size() == 1) return NewRec; 949 950 // Otherwise, multiply the folded AddRec by the non-liv parts. 951 for (unsigned i = 0;; ++i) 952 if (Ops[i] == AddRec) { 953 Ops[i] = NewRec; 954 break; 955 } 956 return SCEVMulExpr::get(Ops); 957 } 958 959 // Okay, if there weren't any loop invariants to be folded, check to see if 960 // there are multiple AddRec's with the same loop induction variable being 961 // multiplied together. If so, we can fold them. 962 for (unsigned OtherIdx = Idx+1; 963 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 964 if (OtherIdx != Idx) { 965 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 966 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 967 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 968 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 969 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(), 970 G->getStart()); 971 SCEVHandle B = F->getStepRecurrence(); 972 SCEVHandle D = G->getStepRecurrence(); 973 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D), 974 SCEVMulExpr::get(G, B), 975 SCEVMulExpr::get(B, D)); 976 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep, 977 F->getLoop()); 978 if (Ops.size() == 2) return NewAddRec; 979 980 Ops.erase(Ops.begin()+Idx); 981 Ops.erase(Ops.begin()+OtherIdx-1); 982 Ops.push_back(NewAddRec); 983 return SCEVMulExpr::get(Ops); 984 } 985 } 986 987 // Otherwise couldn't fold anything into this recurrence. Move onto the 988 // next one. 989 } 990 991 // Okay, it looks like we really DO need an mul expr. Check to see if we 992 // already have one, otherwise create a new one. 993 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 994 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr, 995 SCEVOps)]; 996 if (Result == 0) 997 Result = new SCEVMulExpr(Ops); 998 return Result; 999} 1000 1001SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1002 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1003 if (RHSC->getValue()->equalsInt(1)) 1004 return LHS; // X /u 1 --> x 1005 if (RHSC->getValue()->isAllOnesValue()) 1006 return getNegativeSCEV(LHS); // X /u -1 --> -x 1007 1008 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1009 Constant *LHSCV = LHSC->getValue(); 1010 Constant *RHSCV = RHSC->getValue(); 1011 if (LHSCV->getType()->isSigned()) 1012 LHSCV = ConstantExpr::getCast(LHSCV, 1013 LHSCV->getType()->getUnsignedVersion()); 1014 if (RHSCV->getType()->isSigned()) 1015 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType()); 1016 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV)); 1017 } 1018 } 1019 1020 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1021 1022 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)]; 1023 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1024 return Result; 1025} 1026 1027 1028/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1029/// specified loop. Simplify the expression as much as possible. 1030SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start, 1031 const SCEVHandle &Step, const Loop *L) { 1032 std::vector<SCEVHandle> Operands; 1033 Operands.push_back(Start); 1034 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1035 if (StepChrec->getLoop() == L) { 1036 Operands.insert(Operands.end(), StepChrec->op_begin(), 1037 StepChrec->op_end()); 1038 return get(Operands, L); 1039 } 1040 1041 Operands.push_back(Step); 1042 return get(Operands, L); 1043} 1044 1045/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1046/// specified loop. Simplify the expression as much as possible. 1047SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands, 1048 const Loop *L) { 1049 if (Operands.size() == 1) return Operands[0]; 1050 1051 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1052 if (StepC->getValue()->isNullValue()) { 1053 Operands.pop_back(); 1054 return get(Operands, L); // { X,+,0 } --> X 1055 } 1056 1057 SCEVAddRecExpr *&Result = 1058 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1059 Operands.end()))]; 1060 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1061 return Result; 1062} 1063 1064SCEVHandle SCEVUnknown::get(Value *V) { 1065 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1066 return SCEVConstant::get(CI); 1067 SCEVUnknown *&Result = SCEVUnknowns[V]; 1068 if (Result == 0) Result = new SCEVUnknown(V); 1069 return Result; 1070} 1071 1072 1073//===----------------------------------------------------------------------===// 1074// ScalarEvolutionsImpl Definition and Implementation 1075//===----------------------------------------------------------------------===// 1076// 1077/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1078/// evolution code. 1079/// 1080namespace { 1081 struct ScalarEvolutionsImpl { 1082 /// F - The function we are analyzing. 1083 /// 1084 Function &F; 1085 1086 /// LI - The loop information for the function we are currently analyzing. 1087 /// 1088 LoopInfo &LI; 1089 1090 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1091 /// things. 1092 SCEVHandle UnknownValue; 1093 1094 /// Scalars - This is a cache of the scalars we have analyzed so far. 1095 /// 1096 std::map<Value*, SCEVHandle> Scalars; 1097 1098 /// IterationCounts - Cache the iteration count of the loops for this 1099 /// function as they are computed. 1100 std::map<const Loop*, SCEVHandle> IterationCounts; 1101 1102 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1103 /// the PHI instructions that we attempt to compute constant evolutions for. 1104 /// This allows us to avoid potentially expensive recomputation of these 1105 /// properties. An instruction maps to null if we are unable to compute its 1106 /// exit value. 1107 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1108 1109 public: 1110 ScalarEvolutionsImpl(Function &f, LoopInfo &li) 1111 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1112 1113 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1114 /// expression and create a new one. 1115 SCEVHandle getSCEV(Value *V); 1116 1117 /// getSCEVAtScope - Compute the value of the specified expression within 1118 /// the indicated loop (which may be null to indicate in no loop). If the 1119 /// expression cannot be evaluated, return UnknownValue itself. 1120 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1121 1122 1123 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1124 /// an analyzable loop-invariant iteration count. 1125 bool hasLoopInvariantIterationCount(const Loop *L); 1126 1127 /// getIterationCount - If the specified loop has a predictable iteration 1128 /// count, return it. Note that it is not valid to call this method on a 1129 /// loop without a loop-invariant iteration count. 1130 SCEVHandle getIterationCount(const Loop *L); 1131 1132 /// deleteInstructionFromRecords - This method should be called by the 1133 /// client before it removes an instruction from the program, to make sure 1134 /// that no dangling references are left around. 1135 void deleteInstructionFromRecords(Instruction *I); 1136 1137 private: 1138 /// createSCEV - We know that there is no SCEV for the specified value. 1139 /// Analyze the expression. 1140 SCEVHandle createSCEV(Value *V); 1141 SCEVHandle createNodeForCast(CastInst *CI); 1142 1143 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1144 /// SCEVs. 1145 SCEVHandle createNodeForPHI(PHINode *PN); 1146 1147 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1148 /// for the specified instruction and replaces any references to the 1149 /// symbolic value SymName with the specified value. This is used during 1150 /// PHI resolution. 1151 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1152 const SCEVHandle &SymName, 1153 const SCEVHandle &NewVal); 1154 1155 /// ComputeIterationCount - Compute the number of times the specified loop 1156 /// will iterate. 1157 SCEVHandle ComputeIterationCount(const Loop *L); 1158 1159 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1160 /// 'setcc load X, cst', try to se if we can compute the trip count. 1161 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1162 Constant *RHS, 1163 const Loop *L, 1164 unsigned SetCCOpcode); 1165 1166 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1167 /// constant number of times (the condition evolves only from constants), 1168 /// try to evaluate a few iterations of the loop until we get the exit 1169 /// condition gets a value of ExitWhen (true or false). If we cannot 1170 /// evaluate the trip count of the loop, return UnknownValue. 1171 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1172 bool ExitWhen); 1173 1174 /// HowFarToZero - Return the number of times a backedge comparing the 1175 /// specified value to zero will execute. If not computable, return 1176 /// UnknownValue 1177 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1178 1179 /// HowFarToNonZero - Return the number of times a backedge checking the 1180 /// specified value for nonzero will execute. If not computable, return 1181 /// UnknownValue 1182 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1183 1184 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1185 /// in the header of its containing loop, we know the loop executes a 1186 /// constant number of times, and the PHI node is just a recurrence 1187 /// involving constants, fold it. 1188 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, 1189 const Loop *L); 1190 }; 1191} 1192 1193//===----------------------------------------------------------------------===// 1194// Basic SCEV Analysis and PHI Idiom Recognition Code 1195// 1196 1197/// deleteInstructionFromRecords - This method should be called by the 1198/// client before it removes an instruction from the program, to make sure 1199/// that no dangling references are left around. 1200void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) { 1201 Scalars.erase(I); 1202 if (PHINode *PN = dyn_cast<PHINode>(I)) 1203 ConstantEvolutionLoopExitValue.erase(PN); 1204} 1205 1206 1207/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1208/// expression and create a new one. 1209SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1210 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1211 1212 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1213 if (I != Scalars.end()) return I->second; 1214 SCEVHandle S = createSCEV(V); 1215 Scalars.insert(std::make_pair(V, S)); 1216 return S; 1217} 1218 1219/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1220/// the specified instruction and replaces any references to the symbolic value 1221/// SymName with the specified value. This is used during PHI resolution. 1222void ScalarEvolutionsImpl:: 1223ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1224 const SCEVHandle &NewVal) { 1225 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1226 if (SI == Scalars.end()) return; 1227 1228 SCEVHandle NV = 1229 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal); 1230 if (NV == SI->second) return; // No change. 1231 1232 SI->second = NV; // Update the scalars map! 1233 1234 // Any instruction values that use this instruction might also need to be 1235 // updated! 1236 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1237 UI != E; ++UI) 1238 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1239} 1240 1241/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1242/// a loop header, making it a potential recurrence, or it doesn't. 1243/// 1244SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1245 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1246 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1247 if (L->getHeader() == PN->getParent()) { 1248 // If it lives in the loop header, it has two incoming values, one 1249 // from outside the loop, and one from inside. 1250 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1251 unsigned BackEdge = IncomingEdge^1; 1252 1253 // While we are analyzing this PHI node, handle its value symbolically. 1254 SCEVHandle SymbolicName = SCEVUnknown::get(PN); 1255 assert(Scalars.find(PN) == Scalars.end() && 1256 "PHI node already processed?"); 1257 Scalars.insert(std::make_pair(PN, SymbolicName)); 1258 1259 // Using this symbolic name for the PHI, analyze the value coming around 1260 // the back-edge. 1261 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1262 1263 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1264 // has a special value for the first iteration of the loop. 1265 1266 // If the value coming around the backedge is an add with the symbolic 1267 // value we just inserted, then we found a simple induction variable! 1268 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1269 // If there is a single occurrence of the symbolic value, replace it 1270 // with a recurrence. 1271 unsigned FoundIndex = Add->getNumOperands(); 1272 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1273 if (Add->getOperand(i) == SymbolicName) 1274 if (FoundIndex == e) { 1275 FoundIndex = i; 1276 break; 1277 } 1278 1279 if (FoundIndex != Add->getNumOperands()) { 1280 // Create an add with everything but the specified operand. 1281 std::vector<SCEVHandle> Ops; 1282 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1283 if (i != FoundIndex) 1284 Ops.push_back(Add->getOperand(i)); 1285 SCEVHandle Accum = SCEVAddExpr::get(Ops); 1286 1287 // This is not a valid addrec if the step amount is varying each 1288 // loop iteration, but is not itself an addrec in this loop. 1289 if (Accum->isLoopInvariant(L) || 1290 (isa<SCEVAddRecExpr>(Accum) && 1291 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1292 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1293 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L); 1294 1295 // Okay, for the entire analysis of this edge we assumed the PHI 1296 // to be symbolic. We now need to go back and update all of the 1297 // entries for the scalars that use the PHI (except for the PHI 1298 // itself) to use the new analyzed value instead of the "symbolic" 1299 // value. 1300 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1301 return PHISCEV; 1302 } 1303 } 1304 } 1305 1306 return SymbolicName; 1307 } 1308 1309 // If it's not a loop phi, we can't handle it yet. 1310 return SCEVUnknown::get(PN); 1311} 1312 1313/// createNodeForCast - Handle the various forms of casts that we support. 1314/// 1315SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) { 1316 const Type *SrcTy = CI->getOperand(0)->getType(); 1317 const Type *DestTy = CI->getType(); 1318 1319 // If this is a noop cast (ie, conversion from int to uint), ignore it. 1320 if (SrcTy->isLosslesslyConvertibleTo(DestTy)) 1321 return getSCEV(CI->getOperand(0)); 1322 1323 if (SrcTy->isInteger() && DestTy->isInteger()) { 1324 // Otherwise, if this is a truncating integer cast, we can represent this 1325 // cast. 1326 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1327 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)), 1328 CI->getType()->getUnsignedVersion()); 1329 if (SrcTy->isUnsigned() && 1330 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize()) 1331 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)), 1332 CI->getType()->getUnsignedVersion()); 1333 } 1334 1335 // If this is an sign or zero extending cast and we can prove that the value 1336 // will never overflow, we could do similar transformations. 1337 1338 // Otherwise, we can't handle this cast! 1339 return SCEVUnknown::get(CI); 1340} 1341 1342 1343/// createSCEV - We know that there is no SCEV for the specified value. 1344/// Analyze the expression. 1345/// 1346SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1347 if (Instruction *I = dyn_cast<Instruction>(V)) { 1348 switch (I->getOpcode()) { 1349 case Instruction::Add: 1350 return SCEVAddExpr::get(getSCEV(I->getOperand(0)), 1351 getSCEV(I->getOperand(1))); 1352 case Instruction::Mul: 1353 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), 1354 getSCEV(I->getOperand(1))); 1355 case Instruction::Div: 1356 if (V->getType()->isInteger() && V->getType()->isUnsigned()) 1357 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), 1358 getSCEV(I->getOperand(1))); 1359 break; 1360 1361 case Instruction::Sub: 1362 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1))); 1363 1364 case Instruction::Shl: 1365 // Turn shift left of a constant amount into a multiply. 1366 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1367 Constant *X = ConstantInt::get(V->getType(), 1); 1368 X = ConstantExpr::getShl(X, SA); 1369 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1370 } 1371 break; 1372 1373 case Instruction::Shr: 1374 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1))) 1375 if (V->getType()->isUnsigned()) { 1376 Constant *X = ConstantInt::get(V->getType(), 1); 1377 X = ConstantExpr::getShl(X, SA); 1378 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X)); 1379 } 1380 break; 1381 1382 case Instruction::Cast: 1383 return createNodeForCast(cast<CastInst>(I)); 1384 1385 case Instruction::PHI: 1386 return createNodeForPHI(cast<PHINode>(I)); 1387 1388 default: // We cannot analyze this expression. 1389 break; 1390 } 1391 } 1392 1393 return SCEVUnknown::get(V); 1394} 1395 1396 1397 1398//===----------------------------------------------------------------------===// 1399// Iteration Count Computation Code 1400// 1401 1402/// getIterationCount - If the specified loop has a predictable iteration 1403/// count, return it. Note that it is not valid to call this method on a 1404/// loop without a loop-invariant iteration count. 1405SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1406 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1407 if (I == IterationCounts.end()) { 1408 SCEVHandle ItCount = ComputeIterationCount(L); 1409 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1410 if (ItCount != UnknownValue) { 1411 assert(ItCount->isLoopInvariant(L) && 1412 "Computed trip count isn't loop invariant for loop!"); 1413 ++NumTripCountsComputed; 1414 } else if (isa<PHINode>(L->getHeader()->begin())) { 1415 // Only count loops that have phi nodes as not being computable. 1416 ++NumTripCountsNotComputed; 1417 } 1418 } 1419 return I->second; 1420} 1421 1422/// ComputeIterationCount - Compute the number of times the specified loop 1423/// will iterate. 1424SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1425 // If the loop has a non-one exit block count, we can't analyze it. 1426 std::vector<BasicBlock*> ExitBlocks; 1427 L->getExitBlocks(ExitBlocks); 1428 if (ExitBlocks.size() != 1) return UnknownValue; 1429 1430 // Okay, there is one exit block. Try to find the condition that causes the 1431 // loop to be exited. 1432 BasicBlock *ExitBlock = ExitBlocks[0]; 1433 1434 BasicBlock *ExitingBlock = 0; 1435 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1436 PI != E; ++PI) 1437 if (L->contains(*PI)) { 1438 if (ExitingBlock == 0) 1439 ExitingBlock = *PI; 1440 else 1441 return UnknownValue; // More than one block exiting! 1442 } 1443 assert(ExitingBlock && "No exits from loop, something is broken!"); 1444 1445 // Okay, we've computed the exiting block. See what condition causes us to 1446 // exit. 1447 // 1448 // FIXME: we should be able to handle switch instructions (with a single exit) 1449 // FIXME: We should handle cast of int to bool as well 1450 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1451 if (ExitBr == 0) return UnknownValue; 1452 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1453 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition()); 1454 if (ExitCond == 0) // Not a setcc 1455 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1456 ExitBr->getSuccessor(0) == ExitBlock); 1457 1458 // If the condition was exit on true, convert the condition to exit on false. 1459 Instruction::BinaryOps Cond; 1460 if (ExitBr->getSuccessor(1) == ExitBlock) 1461 Cond = ExitCond->getOpcode(); 1462 else 1463 Cond = ExitCond->getInverseCondition(); 1464 1465 // Handle common loops like: for (X = "string"; *X; ++X) 1466 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1467 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1468 SCEVHandle ItCnt = 1469 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1470 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1471 } 1472 1473 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1474 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1475 1476 // Try to evaluate any dependencies out of the loop. 1477 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1478 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1479 Tmp = getSCEVAtScope(RHS, L); 1480 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1481 1482 // At this point, we would like to compute how many iterations of the loop the 1483 // predicate will return true for these inputs. 1484 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1485 // If there is a constant, force it into the RHS. 1486 std::swap(LHS, RHS); 1487 Cond = SetCondInst::getSwappedCondition(Cond); 1488 } 1489 1490 // FIXME: think about handling pointer comparisons! i.e.: 1491 // while (P != P+100) ++P; 1492 1493 // If we have a comparison of a chrec against a constant, try to use value 1494 // ranges to answer this query. 1495 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1496 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1497 if (AddRec->getLoop() == L) { 1498 // Form the comparison range using the constant of the correct type so 1499 // that the ConstantRange class knows to do a signed or unsigned 1500 // comparison. 1501 ConstantInt *CompVal = RHSC->getValue(); 1502 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1503 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy)); 1504 if (CompVal) { 1505 // Form the constant range. 1506 ConstantRange CompRange(Cond, CompVal); 1507 1508 // Now that we have it, if it's signed, convert it to an unsigned 1509 // range. 1510 if (CompRange.getLower()->getType()->isSigned()) { 1511 const Type *NewTy = RHSC->getValue()->getType(); 1512 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy); 1513 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy); 1514 CompRange = ConstantRange(NewL, NewU); 1515 } 1516 1517 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange); 1518 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1519 } 1520 } 1521 1522 switch (Cond) { 1523 case Instruction::SetNE: // while (X != Y) 1524 // Convert to: while (X-Y != 0) 1525 if (LHS->getType()->isInteger()) { 1526 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 1527 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1528 } 1529 break; 1530 case Instruction::SetEQ: 1531 // Convert to: while (X-Y == 0) // while (X == Y) 1532 if (LHS->getType()->isInteger()) { 1533 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 1534 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1535 } 1536 break; 1537 default: 1538#if 0 1539 std::cerr << "ComputeIterationCount "; 1540 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1541 std::cerr << "[unsigned] "; 1542 std::cerr << *LHS << " " 1543 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n"; 1544#endif 1545 break; 1546 } 1547 1548 return ComputeIterationCountExhaustively(L, ExitCond, 1549 ExitBr->getSuccessor(0) == ExitBlock); 1550} 1551 1552static ConstantInt * 1553EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) { 1554 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C)); 1555 SCEVHandle Val = AddRec->evaluateAtIteration(InVal); 1556 assert(isa<SCEVConstant>(Val) && 1557 "Evaluation of SCEV at constant didn't fold correctly?"); 1558 return cast<SCEVConstant>(Val)->getValue(); 1559} 1560 1561/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1562/// and a GEP expression (missing the pointer index) indexing into it, return 1563/// the addressed element of the initializer or null if the index expression is 1564/// invalid. 1565static Constant * 1566GetAddressedElementFromGlobal(GlobalVariable *GV, 1567 const std::vector<ConstantInt*> &Indices) { 1568 Constant *Init = GV->getInitializer(); 1569 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1570 uint64_t Idx = Indices[i]->getRawValue(); 1571 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1572 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1573 Init = cast<Constant>(CS->getOperand(Idx)); 1574 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1575 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1576 Init = cast<Constant>(CA->getOperand(Idx)); 1577 } else if (isa<ConstantAggregateZero>(Init)) { 1578 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1579 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1580 Init = Constant::getNullValue(STy->getElementType(Idx)); 1581 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1582 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1583 Init = Constant::getNullValue(ATy->getElementType()); 1584 } else { 1585 assert(0 && "Unknown constant aggregate type!"); 1586 } 1587 return 0; 1588 } else { 1589 return 0; // Unknown initializer type 1590 } 1591 } 1592 return Init; 1593} 1594 1595/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1596/// 'setcc load X, cst', try to se if we can compute the trip count. 1597SCEVHandle ScalarEvolutionsImpl:: 1598ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1599 const Loop *L, unsigned SetCCOpcode) { 1600 if (LI->isVolatile()) return UnknownValue; 1601 1602 // Check to see if the loaded pointer is a getelementptr of a global. 1603 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1604 if (!GEP) return UnknownValue; 1605 1606 // Make sure that it is really a constant global we are gepping, with an 1607 // initializer, and make sure the first IDX is really 0. 1608 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1609 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1610 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1611 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1612 return UnknownValue; 1613 1614 // Okay, we allow one non-constant index into the GEP instruction. 1615 Value *VarIdx = 0; 1616 std::vector<ConstantInt*> Indexes; 1617 unsigned VarIdxNum = 0; 1618 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1619 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1620 Indexes.push_back(CI); 1621 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1622 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1623 VarIdx = GEP->getOperand(i); 1624 VarIdxNum = i-2; 1625 Indexes.push_back(0); 1626 } 1627 1628 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1629 // Check to see if X is a loop variant variable value now. 1630 SCEVHandle Idx = getSCEV(VarIdx); 1631 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1632 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1633 1634 // We can only recognize very limited forms of loop index expressions, in 1635 // particular, only affine AddRec's like {C1,+,C2}. 1636 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1637 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1638 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1639 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1640 return UnknownValue; 1641 1642 unsigned MaxSteps = MaxBruteForceIterations; 1643 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1644 ConstantUInt *ItCst = 1645 ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum); 1646 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst); 1647 1648 // Form the GEP offset. 1649 Indexes[VarIdxNum] = Val; 1650 1651 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 1652 if (Result == 0) break; // Cannot compute! 1653 1654 // Evaluate the condition for this iteration. 1655 Result = ConstantExpr::get(SetCCOpcode, Result, RHS); 1656 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure 1657 if (Result == ConstantBool::False) { 1658#if 0 1659 std::cerr << "\n***\n*** Computed loop count " << *ItCst 1660 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 1661 << "***\n"; 1662#endif 1663 ++NumArrayLenItCounts; 1664 return SCEVConstant::get(ItCst); // Found terminating iteration! 1665 } 1666 } 1667 return UnknownValue; 1668} 1669 1670 1671/// CanConstantFold - Return true if we can constant fold an instruction of the 1672/// specified type, assuming that all operands were constants. 1673static bool CanConstantFold(const Instruction *I) { 1674 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || 1675 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 1676 return true; 1677 1678 if (const CallInst *CI = dyn_cast<CallInst>(I)) 1679 if (const Function *F = CI->getCalledFunction()) 1680 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast 1681 return false; 1682} 1683 1684/// ConstantFold - Constant fold an instruction of the specified type with the 1685/// specified constant operands. This function may modify the operands vector. 1686static Constant *ConstantFold(const Instruction *I, 1687 std::vector<Constant*> &Operands) { 1688 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I)) 1689 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]); 1690 1691 switch (I->getOpcode()) { 1692 case Instruction::Cast: 1693 return ConstantExpr::getCast(Operands[0], I->getType()); 1694 case Instruction::Select: 1695 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]); 1696 case Instruction::Call: 1697 if (Function *GV = dyn_cast<Function>(Operands[0])) { 1698 Operands.erase(Operands.begin()); 1699 return ConstantFoldCall(cast<Function>(GV), Operands); 1700 } 1701 1702 return 0; 1703 case Instruction::GetElementPtr: 1704 Constant *Base = Operands[0]; 1705 Operands.erase(Operands.begin()); 1706 return ConstantExpr::getGetElementPtr(Base, Operands); 1707 } 1708 return 0; 1709} 1710 1711 1712/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 1713/// in the loop that V is derived from. We allow arbitrary operations along the 1714/// way, but the operands of an operation must either be constants or a value 1715/// derived from a constant PHI. If this expression does not fit with these 1716/// constraints, return null. 1717static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 1718 // If this is not an instruction, or if this is an instruction outside of the 1719 // loop, it can't be derived from a loop PHI. 1720 Instruction *I = dyn_cast<Instruction>(V); 1721 if (I == 0 || !L->contains(I->getParent())) return 0; 1722 1723 if (PHINode *PN = dyn_cast<PHINode>(I)) 1724 if (L->getHeader() == I->getParent()) 1725 return PN; 1726 else 1727 // We don't currently keep track of the control flow needed to evaluate 1728 // PHIs, so we cannot handle PHIs inside of loops. 1729 return 0; 1730 1731 // If we won't be able to constant fold this expression even if the operands 1732 // are constants, return early. 1733 if (!CanConstantFold(I)) return 0; 1734 1735 // Otherwise, we can evaluate this instruction if all of its operands are 1736 // constant or derived from a PHI node themselves. 1737 PHINode *PHI = 0; 1738 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 1739 if (!(isa<Constant>(I->getOperand(Op)) || 1740 isa<GlobalValue>(I->getOperand(Op)))) { 1741 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 1742 if (P == 0) return 0; // Not evolving from PHI 1743 if (PHI == 0) 1744 PHI = P; 1745 else if (PHI != P) 1746 return 0; // Evolving from multiple different PHIs. 1747 } 1748 1749 // This is a expression evolving from a constant PHI! 1750 return PHI; 1751} 1752 1753/// EvaluateExpression - Given an expression that passes the 1754/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 1755/// in the loop has the value PHIVal. If we can't fold this expression for some 1756/// reason, return null. 1757static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 1758 if (isa<PHINode>(V)) return PHIVal; 1759 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 1760 return GV; 1761 if (Constant *C = dyn_cast<Constant>(V)) return C; 1762 Instruction *I = cast<Instruction>(V); 1763 1764 std::vector<Constant*> Operands; 1765 Operands.resize(I->getNumOperands()); 1766 1767 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1768 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 1769 if (Operands[i] == 0) return 0; 1770 } 1771 1772 return ConstantFold(I, Operands); 1773} 1774 1775/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1776/// in the header of its containing loop, we know the loop executes a 1777/// constant number of times, and the PHI node is just a recurrence 1778/// involving constants, fold it. 1779Constant *ScalarEvolutionsImpl:: 1780getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) { 1781 std::map<PHINode*, Constant*>::iterator I = 1782 ConstantEvolutionLoopExitValue.find(PN); 1783 if (I != ConstantEvolutionLoopExitValue.end()) 1784 return I->second; 1785 1786 if (Its > MaxBruteForceIterations) 1787 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 1788 1789 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 1790 1791 // Since the loop is canonicalized, the PHI node must have two entries. One 1792 // entry must be a constant (coming in from outside of the loop), and the 1793 // second must be derived from the same PHI. 1794 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1795 Constant *StartCST = 1796 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1797 if (StartCST == 0) 1798 return RetVal = 0; // Must be a constant. 1799 1800 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1801 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1802 if (PN2 != PN) 1803 return RetVal = 0; // Not derived from same PHI. 1804 1805 // Execute the loop symbolically to determine the exit value. 1806 unsigned IterationNum = 0; 1807 unsigned NumIterations = Its; 1808 if (NumIterations != Its) 1809 return RetVal = 0; // More than 2^32 iterations?? 1810 1811 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 1812 if (IterationNum == NumIterations) 1813 return RetVal = PHIVal; // Got exit value! 1814 1815 // Compute the value of the PHI node for the next iteration. 1816 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1817 if (NextPHI == PHIVal) 1818 return RetVal = NextPHI; // Stopped evolving! 1819 if (NextPHI == 0) 1820 return 0; // Couldn't evaluate! 1821 PHIVal = NextPHI; 1822 } 1823} 1824 1825/// ComputeIterationCountExhaustively - If the trip is known to execute a 1826/// constant number of times (the condition evolves only from constants), 1827/// try to evaluate a few iterations of the loop until we get the exit 1828/// condition gets a value of ExitWhen (true or false). If we cannot 1829/// evaluate the trip count of the loop, return UnknownValue. 1830SCEVHandle ScalarEvolutionsImpl:: 1831ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 1832 PHINode *PN = getConstantEvolvingPHI(Cond, L); 1833 if (PN == 0) return UnknownValue; 1834 1835 // Since the loop is canonicalized, the PHI node must have two entries. One 1836 // entry must be a constant (coming in from outside of the loop), and the 1837 // second must be derived from the same PHI. 1838 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 1839 Constant *StartCST = 1840 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 1841 if (StartCST == 0) return UnknownValue; // Must be a constant. 1842 1843 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 1844 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 1845 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 1846 1847 // Okay, we find a PHI node that defines the trip count of this loop. Execute 1848 // the loop symbolically to determine when the condition gets a value of 1849 // "ExitWhen". 1850 unsigned IterationNum = 0; 1851 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 1852 for (Constant *PHIVal = StartCST; 1853 IterationNum != MaxIterations; ++IterationNum) { 1854 ConstantBool *CondVal = 1855 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal)); 1856 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate. 1857 1858 if (CondVal->getValue() == ExitWhen) { 1859 ConstantEvolutionLoopExitValue[PN] = PHIVal; 1860 ++NumBruteForceTripCountsComputed; 1861 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum)); 1862 } 1863 1864 // Compute the value of the PHI node for the next iteration. 1865 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 1866 if (NextPHI == 0 || NextPHI == PHIVal) 1867 return UnknownValue; // Couldn't evaluate or not making progress... 1868 PHIVal = NextPHI; 1869 } 1870 1871 // Too many iterations were needed to evaluate. 1872 return UnknownValue; 1873} 1874 1875/// getSCEVAtScope - Compute the value of the specified expression within the 1876/// indicated loop (which may be null to indicate in no loop). If the 1877/// expression cannot be evaluated, return UnknownValue. 1878SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 1879 // FIXME: this should be turned into a virtual method on SCEV! 1880 1881 if (isa<SCEVConstant>(V)) return V; 1882 1883 // If this instruction is evolves from a constant-evolving PHI, compute the 1884 // exit value from the loop without using SCEVs. 1885 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 1886 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 1887 const Loop *LI = this->LI[I->getParent()]; 1888 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 1889 if (PHINode *PN = dyn_cast<PHINode>(I)) 1890 if (PN->getParent() == LI->getHeader()) { 1891 // Okay, there is no closed form solution for the PHI node. Check 1892 // to see if the loop that contains it has a known iteration count. 1893 // If so, we may be able to force computation of the exit value. 1894 SCEVHandle IterationCount = getIterationCount(LI); 1895 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 1896 // Okay, we know how many times the containing loop executes. If 1897 // this is a constant evolving PHI node, get the final value at 1898 // the specified iteration number. 1899 Constant *RV = getConstantEvolutionLoopExitValue(PN, 1900 ICC->getValue()->getRawValue(), 1901 LI); 1902 if (RV) return SCEVUnknown::get(RV); 1903 } 1904 } 1905 1906 // Okay, this is a some expression that we cannot symbolically evaluate 1907 // into a SCEV. Check to see if it's possible to symbolically evaluate 1908 // the arguments into constants, and if see, try to constant propagate the 1909 // result. This is particularly useful for computing loop exit values. 1910 if (CanConstantFold(I)) { 1911 std::vector<Constant*> Operands; 1912 Operands.reserve(I->getNumOperands()); 1913 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 1914 Value *Op = I->getOperand(i); 1915 if (Constant *C = dyn_cast<Constant>(Op)) { 1916 Operands.push_back(C); 1917 } else { 1918 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 1919 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 1920 Operands.push_back(ConstantExpr::getCast(SC->getValue(), 1921 Op->getType())); 1922 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 1923 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 1924 Operands.push_back(ConstantExpr::getCast(C, Op->getType())); 1925 else 1926 return V; 1927 } else { 1928 return V; 1929 } 1930 } 1931 } 1932 return SCEVUnknown::get(ConstantFold(I, Operands)); 1933 } 1934 } 1935 1936 // This is some other type of SCEVUnknown, just return it. 1937 return V; 1938 } 1939 1940 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 1941 // Avoid performing the look-up in the common case where the specified 1942 // expression has no loop-variant portions. 1943 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 1944 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1945 if (OpAtScope != Comm->getOperand(i)) { 1946 if (OpAtScope == UnknownValue) return UnknownValue; 1947 // Okay, at least one of these operands is loop variant but might be 1948 // foldable. Build a new instance of the folded commutative expression. 1949 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 1950 NewOps.push_back(OpAtScope); 1951 1952 for (++i; i != e; ++i) { 1953 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 1954 if (OpAtScope == UnknownValue) return UnknownValue; 1955 NewOps.push_back(OpAtScope); 1956 } 1957 if (isa<SCEVAddExpr>(Comm)) 1958 return SCEVAddExpr::get(NewOps); 1959 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!"); 1960 return SCEVMulExpr::get(NewOps); 1961 } 1962 } 1963 // If we got here, all operands are loop invariant. 1964 return Comm; 1965 } 1966 1967 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) { 1968 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L); 1969 if (LHS == UnknownValue) return LHS; 1970 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L); 1971 if (RHS == UnknownValue) return RHS; 1972 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS()) 1973 return UDiv; // must be loop invariant 1974 return SCEVUDivExpr::get(LHS, RHS); 1975 } 1976 1977 // If this is a loop recurrence for a loop that does not contain L, then we 1978 // are dealing with the final value computed by the loop. 1979 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 1980 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 1981 // To evaluate this recurrence, we need to know how many times the AddRec 1982 // loop iterates. Compute this now. 1983 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 1984 if (IterationCount == UnknownValue) return UnknownValue; 1985 IterationCount = getTruncateOrZeroExtend(IterationCount, 1986 AddRec->getType()); 1987 1988 // If the value is affine, simplify the expression evaluation to just 1989 // Start + Step*IterationCount. 1990 if (AddRec->isAffine()) 1991 return SCEVAddExpr::get(AddRec->getStart(), 1992 SCEVMulExpr::get(IterationCount, 1993 AddRec->getOperand(1))); 1994 1995 // Otherwise, evaluate it the hard way. 1996 return AddRec->evaluateAtIteration(IterationCount); 1997 } 1998 return UnknownValue; 1999 } 2000 2001 //assert(0 && "Unknown SCEV type!"); 2002 return UnknownValue; 2003} 2004 2005 2006/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2007/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2008/// might be the same) or two SCEVCouldNotCompute objects. 2009/// 2010static std::pair<SCEVHandle,SCEVHandle> 2011SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) { 2012 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2013 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2014 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2015 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2016 2017 // We currently can only solve this if the coefficients are constants. 2018 if (!L || !M || !N) { 2019 SCEV *CNC = new SCEVCouldNotCompute(); 2020 return std::make_pair(CNC, CNC); 2021 } 2022 2023 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2); 2024 2025 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2026 Constant *C = L->getValue(); 2027 // The B coefficient is M-N/2 2028 Constant *B = ConstantExpr::getSub(M->getValue(), 2029 ConstantExpr::getDiv(N->getValue(), 2030 Two)); 2031 // The A coefficient is N/2 2032 Constant *A = ConstantExpr::getDiv(N->getValue(), Two); 2033 2034 // Compute the B^2-4ac term. 2035 Constant *SqrtTerm = 2036 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4), 2037 ConstantExpr::getMul(A, C)); 2038 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm); 2039 2040 // Compute floor(sqrt(B^2-4ac)) 2041 ConstantUInt *SqrtVal = 2042 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm, 2043 SqrtTerm->getType()->getUnsignedVersion())); 2044 uint64_t SqrtValV = SqrtVal->getValue(); 2045 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV); 2046 // The square root might not be precise for arbitrary 64-bit integer 2047 // values. Do some sanity checks to ensure it's correct. 2048 if (SqrtValV2*SqrtValV2 > SqrtValV || 2049 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) { 2050 SCEV *CNC = new SCEVCouldNotCompute(); 2051 return std::make_pair(CNC, CNC); 2052 } 2053 2054 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2); 2055 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType()); 2056 2057 Constant *NegB = ConstantExpr::getNeg(B); 2058 Constant *TwoA = ConstantExpr::getMul(A, Two); 2059 2060 // The divisions must be performed as signed divisions. 2061 const Type *SignedTy = NegB->getType()->getSignedVersion(); 2062 NegB = ConstantExpr::getCast(NegB, SignedTy); 2063 TwoA = ConstantExpr::getCast(TwoA, SignedTy); 2064 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy); 2065 2066 Constant *Solution1 = 2067 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA); 2068 Constant *Solution2 = 2069 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA); 2070 return std::make_pair(SCEVUnknown::get(Solution1), 2071 SCEVUnknown::get(Solution2)); 2072} 2073 2074/// HowFarToZero - Return the number of times a backedge comparing the specified 2075/// value to zero will execute. If not computable, return UnknownValue 2076SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2077 // If the value is a constant 2078 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2079 // If the value is already zero, the branch will execute zero times. 2080 if (C->getValue()->isNullValue()) return C; 2081 return UnknownValue; // Otherwise it will loop infinitely. 2082 } 2083 2084 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2085 if (!AddRec || AddRec->getLoop() != L) 2086 return UnknownValue; 2087 2088 if (AddRec->isAffine()) { 2089 // If this is an affine expression the execution count of this branch is 2090 // equal to: 2091 // 2092 // (0 - Start/Step) iff Start % Step == 0 2093 // 2094 // Get the initial value for the loop. 2095 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2096 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2097 SCEVHandle Step = AddRec->getOperand(1); 2098 2099 Step = getSCEVAtScope(Step, L->getParentLoop()); 2100 2101 // Figure out if Start % Step == 0. 2102 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2103 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2104 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2105 return getNegativeSCEV(Start); // 0 - Start/1 == -Start 2106 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2107 return Start; // 0 - Start/-1 == Start 2108 2109 // Check to see if Start is divisible by SC with no remainder. 2110 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2111 ConstantInt *StartCC = StartC->getValue(); 2112 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2113 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue()); 2114 if (Rem->isNullValue()) { 2115 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue()); 2116 return SCEVUnknown::get(Result); 2117 } 2118 } 2119 } 2120 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2121 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2122 // the quadratic equation to solve it. 2123 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec); 2124 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2125 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2126 if (R1) { 2127#if 0 2128 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2129 << " sol#2: " << *R2 << "\n"; 2130#endif 2131 // Pick the smallest positive root value. 2132 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?"); 2133 if (ConstantBool *CB = 2134 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2135 R2->getValue()))) { 2136 if (CB != ConstantBool::True) 2137 std::swap(R1, R2); // R1 is the minimum root now. 2138 2139 // We can only use this value if the chrec ends up with an exact zero 2140 // value at this index. When solving for "X*X != 5", for example, we 2141 // should not accept a root of 2. 2142 SCEVHandle Val = AddRec->evaluateAtIteration(R1); 2143 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2144 if (EvalVal->getValue()->isNullValue()) 2145 return R1; // We found a quadratic root! 2146 } 2147 } 2148 } 2149 2150 return UnknownValue; 2151} 2152 2153/// HowFarToNonZero - Return the number of times a backedge checking the 2154/// specified value for nonzero will execute. If not computable, return 2155/// UnknownValue 2156SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2157 // Loops that look like: while (X == 0) are very strange indeed. We don't 2158 // handle them yet except for the trivial case. This could be expanded in the 2159 // future as needed. 2160 2161 // If the value is a constant, check to see if it is known to be non-zero 2162 // already. If so, the backedge will execute zero times. 2163 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2164 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2165 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero); 2166 if (NonZero == ConstantBool::True) 2167 return getSCEV(Zero); 2168 return UnknownValue; // Otherwise it will loop infinitely. 2169 } 2170 2171 // We could implement others, but I really doubt anyone writes loops like 2172 // this, and if they did, they would already be constant folded. 2173 return UnknownValue; 2174} 2175 2176/// getNumIterationsInRange - Return the number of iterations of this loop that 2177/// produce values in the specified constant range. Another way of looking at 2178/// this is that it returns the first iteration number where the value is not in 2179/// the condition, thus computing the exit count. If the iteration count can't 2180/// be computed, an instance of SCEVCouldNotCompute is returned. 2181SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const { 2182 if (Range.isFullSet()) // Infinite loop. 2183 return new SCEVCouldNotCompute(); 2184 2185 // If the start is a non-zero constant, shift the range to simplify things. 2186 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2187 if (!SC->getValue()->isNullValue()) { 2188 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2189 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType()); 2190 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop()); 2191 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2192 return ShiftedAddRec->getNumIterationsInRange( 2193 Range.subtract(SC->getValue())); 2194 // This is strange and shouldn't happen. 2195 return new SCEVCouldNotCompute(); 2196 } 2197 2198 // The only time we can solve this is when we have all constant indices. 2199 // Otherwise, we cannot determine the overflow conditions. 2200 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2201 if (!isa<SCEVConstant>(getOperand(i))) 2202 return new SCEVCouldNotCompute(); 2203 2204 2205 // Okay at this point we know that all elements of the chrec are constants and 2206 // that the start element is zero. 2207 2208 // First check to see if the range contains zero. If not, the first 2209 // iteration exits. 2210 ConstantInt *Zero = ConstantInt::get(getType(), 0); 2211 if (!Range.contains(Zero)) return SCEVConstant::get(Zero); 2212 2213 if (isAffine()) { 2214 // If this is an affine expression then we have this situation: 2215 // Solve {0,+,A} in Range === Ax in Range 2216 2217 // Since we know that zero is in the range, we know that the upper value of 2218 // the range must be the first possible exit value. Also note that we 2219 // already checked for a full range. 2220 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper()); 2221 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue(); 2222 ConstantInt *One = ConstantInt::get(getType(), 1); 2223 2224 // The exit value should be (Upper+A-1)/A. 2225 Constant *ExitValue = Upper; 2226 if (A != One) { 2227 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One); 2228 ExitValue = ConstantExpr::getDiv(ExitValue, A); 2229 } 2230 assert(isa<ConstantInt>(ExitValue) && 2231 "Constant folding of integers not implemented?"); 2232 2233 // Evaluate at the exit value. If we really did fall out of the valid 2234 // range, then we computed our trip count, otherwise wrap around or other 2235 // things must have happened. 2236 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue); 2237 if (Range.contains(Val)) 2238 return new SCEVCouldNotCompute(); // Something strange happened 2239 2240 // Ensure that the previous value is in the range. This is a sanity check. 2241 assert(Range.contains(EvaluateConstantChrecAtConstant(this, 2242 ConstantExpr::getSub(ExitValue, One))) && 2243 "Linear scev computation is off in a bad way!"); 2244 return SCEVConstant::get(cast<ConstantInt>(ExitValue)); 2245 } else if (isQuadratic()) { 2246 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2247 // quadratic equation to solve it. To do this, we must frame our problem in 2248 // terms of figuring out when zero is crossed, instead of when 2249 // Range.getUpper() is crossed. 2250 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2251 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper())); 2252 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop()); 2253 2254 // Next, solve the constructed addrec 2255 std::pair<SCEVHandle,SCEVHandle> Roots = 2256 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec)); 2257 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2258 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2259 if (R1) { 2260 // Pick the smallest positive root value. 2261 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?"); 2262 if (ConstantBool *CB = 2263 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(), 2264 R2->getValue()))) { 2265 if (CB != ConstantBool::True) 2266 std::swap(R1, R2); // R1 is the minimum root now. 2267 2268 // Make sure the root is not off by one. The returned iteration should 2269 // not be in the range, but the previous one should be. When solving 2270 // for "X*X < 5", for example, we should not return a root of 2. 2271 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2272 R1->getValue()); 2273 if (Range.contains(R1Val)) { 2274 // The next iteration must be out of the range... 2275 Constant *NextVal = 2276 ConstantExpr::getAdd(R1->getValue(), 2277 ConstantInt::get(R1->getType(), 1)); 2278 2279 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2280 if (!Range.contains(R1Val)) 2281 return SCEVUnknown::get(NextVal); 2282 return new SCEVCouldNotCompute(); // Something strange happened 2283 } 2284 2285 // If R1 was not in the range, then it is a good return value. Make 2286 // sure that R1-1 WAS in the range though, just in case. 2287 Constant *NextVal = 2288 ConstantExpr::getSub(R1->getValue(), 2289 ConstantInt::get(R1->getType(), 1)); 2290 R1Val = EvaluateConstantChrecAtConstant(this, NextVal); 2291 if (Range.contains(R1Val)) 2292 return R1; 2293 return new SCEVCouldNotCompute(); // Something strange happened 2294 } 2295 } 2296 } 2297 2298 // Fallback, if this is a general polynomial, figure out the progression 2299 // through brute force: evaluate until we find an iteration that fails the 2300 // test. This is likely to be slow, but getting an accurate trip count is 2301 // incredibly important, we will be able to simplify the exit test a lot, and 2302 // we are almost guaranteed to get a trip count in this case. 2303 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2304 ConstantInt *One = ConstantInt::get(getType(), 1); 2305 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2306 do { 2307 ++NumBruteForceEvaluations; 2308 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal)); 2309 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2310 return new SCEVCouldNotCompute(); 2311 2312 // Check to see if we found the value! 2313 if (!Range.contains(cast<SCEVConstant>(Val)->getValue())) 2314 return SCEVConstant::get(TestVal); 2315 2316 // Increment to test the next index. 2317 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One)); 2318 } while (TestVal != EndVal); 2319 2320 return new SCEVCouldNotCompute(); 2321} 2322 2323 2324 2325//===----------------------------------------------------------------------===// 2326// ScalarEvolution Class Implementation 2327//===----------------------------------------------------------------------===// 2328 2329bool ScalarEvolution::runOnFunction(Function &F) { 2330 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>()); 2331 return false; 2332} 2333 2334void ScalarEvolution::releaseMemory() { 2335 delete (ScalarEvolutionsImpl*)Impl; 2336 Impl = 0; 2337} 2338 2339void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2340 AU.setPreservesAll(); 2341 AU.addRequiredID(LoopSimplifyID); 2342 AU.addRequiredTransitive<LoopInfo>(); 2343} 2344 2345SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2346 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2347} 2348 2349SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2350 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2351} 2352 2353bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2354 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2355} 2356 2357SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2358 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2359} 2360 2361void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const { 2362 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I); 2363} 2364 2365static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2366 const Loop *L) { 2367 // Print all inner loops first 2368 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2369 PrintLoopInfo(OS, SE, *I); 2370 2371 std::cerr << "Loop " << L->getHeader()->getName() << ": "; 2372 2373 std::vector<BasicBlock*> ExitBlocks; 2374 L->getExitBlocks(ExitBlocks); 2375 if (ExitBlocks.size() != 1) 2376 std::cerr << "<multiple exits> "; 2377 2378 if (SE->hasLoopInvariantIterationCount(L)) { 2379 std::cerr << *SE->getIterationCount(L) << " iterations! "; 2380 } else { 2381 std::cerr << "Unpredictable iteration count. "; 2382 } 2383 2384 std::cerr << "\n"; 2385} 2386 2387void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2388 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2389 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2390 2391 OS << "Classifying expressions for: " << F.getName() << "\n"; 2392 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2393 if (I->getType()->isInteger()) { 2394 OS << *I; 2395 OS << " --> "; 2396 SCEVHandle SV = getSCEV(&*I); 2397 SV->print(OS); 2398 OS << "\t\t"; 2399 2400 if ((*I).getType()->isIntegral()) { 2401 ConstantRange Bounds = SV->getValueRange(); 2402 if (!Bounds.isFullSet()) 2403 OS << "Bounds: " << Bounds << " "; 2404 } 2405 2406 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2407 OS << "Exits: "; 2408 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2409 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2410 OS << "<<Unknown>>"; 2411 } else { 2412 OS << *ExitValue; 2413 } 2414 } 2415 2416 2417 OS << "\n"; 2418 } 2419 2420 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2421 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2422 PrintLoopInfo(OS, this, *I); 2423} 2424 2425