ScalarEvolution.cpp revision 8ae38e15161696cae57aa1ec725ec4391d1e4c77
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. These classes are reference counted, managed by the SCEVHandle 18// class. We only create one SCEV of a particular shape, so pointer-comparisons 19// for equality are legal. 20// 21// One important aspect of the SCEV objects is that they are never cyclic, even 22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 23// the PHI node is one of the idioms that we can represent (e.g., a polynomial 24// recurrence) then we represent it directly as a recurrence node, otherwise we 25// represent it as a SCEVUnknown node. 26// 27// In addition to being able to represent expressions of various types, we also 28// have folders that are used to build the *canonical* representation for a 29// particular expression. These folders are capable of using a variety of 30// rewrite rules to simplify the expressions. 31// 32// Once the folders are defined, we can implement the more interesting 33// higher-level code, such as the code that recognizes PHI nodes of various 34// types, computes the execution count of a loop, etc. 35// 36// TODO: We should use these routines and value representations to implement 37// dependence analysis! 38// 39//===----------------------------------------------------------------------===// 40// 41// There are several good references for the techniques used in this analysis. 42// 43// Chains of recurrences -- a method to expedite the evaluation 44// of closed-form functions 45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 46// 47// On computational properties of chains of recurrences 48// Eugene V. Zima 49// 50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 51// Robert A. van Engelen 52// 53// Efficient Symbolic Analysis for Optimizing Compilers 54// Robert A. van Engelen 55// 56// Using the chains of recurrences algebra for data dependence testing and 57// induction variable substitution 58// MS Thesis, Johnie Birch 59// 60//===----------------------------------------------------------------------===// 61 62#define DEBUG_TYPE "scalar-evolution" 63#include "llvm/Analysis/ScalarEvolutionExpressions.h" 64#include "llvm/Constants.h" 65#include "llvm/DerivedTypes.h" 66#include "llvm/GlobalVariable.h" 67#include "llvm/Instructions.h" 68#include "llvm/Analysis/ConstantFolding.h" 69#include "llvm/Analysis/LoopInfo.h" 70#include "llvm/Assembly/Writer.h" 71#include "llvm/Transforms/Scalar.h" 72#include "llvm/Support/CFG.h" 73#include "llvm/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/InstIterator.h" 77#include "llvm/Support/ManagedStatic.h" 78#include "llvm/Support/MathExtras.h" 79#include "llvm/Support/Streams.h" 80#include "llvm/ADT/Statistic.h" 81#include <ostream> 82#include <algorithm> 83#include <cmath> 84using namespace llvm; 85 86STATISTIC(NumBruteForceEvaluations, 87 "Number of brute force evaluations needed to " 88 "calculate high-order polynomial exit values"); 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98static cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant derived loop"), 102 cl::init(100)); 103 104static RegisterPass<ScalarEvolution> 105R("scalar-evolution", "Scalar Evolution Analysis", false, true); 106char ScalarEvolution::ID = 0; 107 108//===----------------------------------------------------------------------===// 109// SCEV class definitions 110//===----------------------------------------------------------------------===// 111 112//===----------------------------------------------------------------------===// 113// Implementation of the SCEV class. 114// 115SCEV::~SCEV() {} 116void SCEV::dump() const { 117 print(cerr); 118} 119 120uint32_t SCEV::getBitWidth() const { 121 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 122 return ITy->getBitWidth(); 123 return 0; 124} 125 126bool SCEV::isZero() const { 127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 128 return SC->getValue()->isZero(); 129 return false; 130} 131 132 133SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 134 135bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 136 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 137 return false; 138} 139 140const Type *SCEVCouldNotCompute::getType() const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return 0; 143} 144 145bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return false; 148} 149 150SCEVHandle SCEVCouldNotCompute:: 151replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 152 const SCEVHandle &Conc, 153 ScalarEvolution &SE) const { 154 return this; 155} 156 157void SCEVCouldNotCompute::print(std::ostream &OS) const { 158 OS << "***COULDNOTCOMPUTE***"; 159} 160 161bool SCEVCouldNotCompute::classof(const SCEV *S) { 162 return S->getSCEVType() == scCouldNotCompute; 163} 164 165 166// SCEVConstants - Only allow the creation of one SCEVConstant for any 167// particular value. Don't use a SCEVHandle here, or else the object will 168// never be deleted! 169static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 170 171 172SCEVConstant::~SCEVConstant() { 173 SCEVConstants->erase(V); 174} 175 176SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 177 SCEVConstant *&R = (*SCEVConstants)[V]; 178 if (R == 0) R = new SCEVConstant(V); 179 return R; 180} 181 182SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 183 return getConstant(ConstantInt::get(Val)); 184} 185 186const Type *SCEVConstant::getType() const { return V->getType(); } 187 188void SCEVConstant::print(std::ostream &OS) const { 189 WriteAsOperand(OS, V, false); 190} 191 192// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 193// particular input. Don't use a SCEVHandle here, or else the object will 194// never be deleted! 195static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 196 SCEVTruncateExpr*> > SCEVTruncates; 197 198SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 199 : SCEV(scTruncate), Op(op), Ty(ty) { 200 assert(Op->getType()->isInteger() && Ty->isInteger() && 201 "Cannot truncate non-integer value!"); 202 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 203 && "This is not a truncating conversion!"); 204} 205 206SCEVTruncateExpr::~SCEVTruncateExpr() { 207 SCEVTruncates->erase(std::make_pair(Op, Ty)); 208} 209 210void SCEVTruncateExpr::print(std::ostream &OS) const { 211 OS << "(truncate " << *Op << " to " << *Ty << ")"; 212} 213 214// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 215// particular input. Don't use a SCEVHandle here, or else the object will never 216// be deleted! 217static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 218 SCEVZeroExtendExpr*> > SCEVZeroExtends; 219 220SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 221 : SCEV(scZeroExtend), Op(op), Ty(ty) { 222 assert(Op->getType()->isInteger() && Ty->isInteger() && 223 "Cannot zero extend non-integer value!"); 224 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 225 && "This is not an extending conversion!"); 226} 227 228SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 229 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 230} 231 232void SCEVZeroExtendExpr::print(std::ostream &OS) const { 233 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 234} 235 236// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 237// particular input. Don't use a SCEVHandle here, or else the object will never 238// be deleted! 239static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 240 SCEVSignExtendExpr*> > SCEVSignExtends; 241 242SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 243 : SCEV(scSignExtend), Op(op), Ty(ty) { 244 assert(Op->getType()->isInteger() && Ty->isInteger() && 245 "Cannot sign extend non-integer value!"); 246 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 247 && "This is not an extending conversion!"); 248} 249 250SCEVSignExtendExpr::~SCEVSignExtendExpr() { 251 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 252} 253 254void SCEVSignExtendExpr::print(std::ostream &OS) const { 255 OS << "(signextend " << *Op << " to " << *Ty << ")"; 256} 257 258// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 259// particular input. Don't use a SCEVHandle here, or else the object will never 260// be deleted! 261static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 262 SCEVCommutativeExpr*> > SCEVCommExprs; 263 264SCEVCommutativeExpr::~SCEVCommutativeExpr() { 265 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 266 std::vector<SCEV*>(Operands.begin(), 267 Operands.end()))); 268} 269 270void SCEVCommutativeExpr::print(std::ostream &OS) const { 271 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 272 const char *OpStr = getOperationStr(); 273 OS << "(" << *Operands[0]; 274 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 275 OS << OpStr << *Operands[i]; 276 OS << ")"; 277} 278 279SCEVHandle SCEVCommutativeExpr:: 280replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 281 const SCEVHandle &Conc, 282 ScalarEvolution &SE) const { 283 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 284 SCEVHandle H = 285 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 286 if (H != getOperand(i)) { 287 std::vector<SCEVHandle> NewOps; 288 NewOps.reserve(getNumOperands()); 289 for (unsigned j = 0; j != i; ++j) 290 NewOps.push_back(getOperand(j)); 291 NewOps.push_back(H); 292 for (++i; i != e; ++i) 293 NewOps.push_back(getOperand(i)-> 294 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 295 296 if (isa<SCEVAddExpr>(this)) 297 return SE.getAddExpr(NewOps); 298 else if (isa<SCEVMulExpr>(this)) 299 return SE.getMulExpr(NewOps); 300 else if (isa<SCEVSMaxExpr>(this)) 301 return SE.getSMaxExpr(NewOps); 302 else if (isa<SCEVUMaxExpr>(this)) 303 return SE.getUMaxExpr(NewOps); 304 else 305 assert(0 && "Unknown commutative expr!"); 306 } 307 } 308 return this; 309} 310 311 312// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 313// input. Don't use a SCEVHandle here, or else the object will never be 314// deleted! 315static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 316 SCEVUDivExpr*> > SCEVUDivs; 317 318SCEVUDivExpr::~SCEVUDivExpr() { 319 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 320} 321 322void SCEVUDivExpr::print(std::ostream &OS) const { 323 OS << "(" << *LHS << " /u " << *RHS << ")"; 324} 325 326const Type *SCEVUDivExpr::getType() const { 327 return LHS->getType(); 328} 329 330// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 331// particular input. Don't use a SCEVHandle here, or else the object will never 332// be deleted! 333static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 334 SCEVAddRecExpr*> > SCEVAddRecExprs; 335 336SCEVAddRecExpr::~SCEVAddRecExpr() { 337 SCEVAddRecExprs->erase(std::make_pair(L, 338 std::vector<SCEV*>(Operands.begin(), 339 Operands.end()))); 340} 341 342SCEVHandle SCEVAddRecExpr:: 343replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 344 const SCEVHandle &Conc, 345 ScalarEvolution &SE) const { 346 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 347 SCEVHandle H = 348 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 349 if (H != getOperand(i)) { 350 std::vector<SCEVHandle> NewOps; 351 NewOps.reserve(getNumOperands()); 352 for (unsigned j = 0; j != i; ++j) 353 NewOps.push_back(getOperand(j)); 354 NewOps.push_back(H); 355 for (++i; i != e; ++i) 356 NewOps.push_back(getOperand(i)-> 357 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 358 359 return SE.getAddRecExpr(NewOps, L); 360 } 361 } 362 return this; 363} 364 365 366bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 367 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 368 // contain L and if the start is invariant. 369 return !QueryLoop->contains(L->getHeader()) && 370 getOperand(0)->isLoopInvariant(QueryLoop); 371} 372 373 374void SCEVAddRecExpr::print(std::ostream &OS) const { 375 OS << "{" << *Operands[0]; 376 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 377 OS << ",+," << *Operands[i]; 378 OS << "}<" << L->getHeader()->getName() + ">"; 379} 380 381// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 382// value. Don't use a SCEVHandle here, or else the object will never be 383// deleted! 384static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 385 386SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 387 388bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 389 // All non-instruction values are loop invariant. All instructions are loop 390 // invariant if they are not contained in the specified loop. 391 if (Instruction *I = dyn_cast<Instruction>(V)) 392 return !L->contains(I->getParent()); 393 return true; 394} 395 396const Type *SCEVUnknown::getType() const { 397 return V->getType(); 398} 399 400void SCEVUnknown::print(std::ostream &OS) const { 401 WriteAsOperand(OS, V, false); 402} 403 404//===----------------------------------------------------------------------===// 405// SCEV Utilities 406//===----------------------------------------------------------------------===// 407 408namespace { 409 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 410 /// than the complexity of the RHS. This comparator is used to canonicalize 411 /// expressions. 412 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 413 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 414 return LHS->getSCEVType() < RHS->getSCEVType(); 415 } 416 }; 417} 418 419/// GroupByComplexity - Given a list of SCEV objects, order them by their 420/// complexity, and group objects of the same complexity together by value. 421/// When this routine is finished, we know that any duplicates in the vector are 422/// consecutive and that complexity is monotonically increasing. 423/// 424/// Note that we go take special precautions to ensure that we get determinstic 425/// results from this routine. In other words, we don't want the results of 426/// this to depend on where the addresses of various SCEV objects happened to 427/// land in memory. 428/// 429static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 430 if (Ops.size() < 2) return; // Noop 431 if (Ops.size() == 2) { 432 // This is the common case, which also happens to be trivially simple. 433 // Special case it. 434 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 435 std::swap(Ops[0], Ops[1]); 436 return; 437 } 438 439 // Do the rough sort by complexity. 440 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 441 442 // Now that we are sorted by complexity, group elements of the same 443 // complexity. Note that this is, at worst, N^2, but the vector is likely to 444 // be extremely short in practice. Note that we take this approach because we 445 // do not want to depend on the addresses of the objects we are grouping. 446 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 447 SCEV *S = Ops[i]; 448 unsigned Complexity = S->getSCEVType(); 449 450 // If there are any objects of the same complexity and same value as this 451 // one, group them. 452 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 453 if (Ops[j] == S) { // Found a duplicate. 454 // Move it to immediately after i'th element. 455 std::swap(Ops[i+1], Ops[j]); 456 ++i; // no need to rescan it. 457 if (i == e-2) return; // Done! 458 } 459 } 460 } 461} 462 463 464 465//===----------------------------------------------------------------------===// 466// Simple SCEV method implementations 467//===----------------------------------------------------------------------===// 468 469/// getIntegerSCEV - Given an integer or FP type, create a constant for the 470/// specified signed integer value and return a SCEV for the constant. 471SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 472 Constant *C; 473 if (Val == 0) 474 C = Constant::getNullValue(Ty); 475 else if (Ty->isFloatingPoint()) 476 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 477 APFloat::IEEEdouble, Val)); 478 else 479 C = ConstantInt::get(Ty, Val); 480 return getUnknown(C); 481} 482 483/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 484/// 485SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 486 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 487 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 488 489 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType()))); 490} 491 492/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 493SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 494 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 495 return getUnknown(ConstantExpr::getNot(VC->getValue())); 496 497 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType())); 498 return getMinusSCEV(AllOnes, V); 499} 500 501/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 502/// 503SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 504 const SCEVHandle &RHS) { 505 // X - Y --> X + -Y 506 return getAddExpr(LHS, getNegativeSCEV(RHS)); 507} 508 509 510/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as 511/// It. Assume, K > 0. 512static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 513 ScalarEvolution &SE) { 514 // We are using the following formula for BC(It, K): 515 // 516 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 517 // 518 // Suppose, W is the bitwidth of It (and of the return value as well). We 519 // must be prepared for overflow. Hence, we must assure that the result of 520 // our computation is equal to the accurate one modulo 2^W. Unfortunately, 521 // division isn't safe in modular arithmetic. This means we must perform the 522 // whole computation accurately and then truncate the result to W bits. 523 // 524 // The dividend of the formula is a multiplication of K integers of bitwidth 525 // W. K*W bits suffice to compute it accurately. 526 // 527 // FIXME: We assume the divisor can be accurately computed using 16-bit 528 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In 529 // future we may use APInt to use the minimum number of bits necessary to 530 // compute it accurately. 531 // 532 // It is safe to use unsigned division here: the dividend is nonnegative and 533 // the divisor is positive. 534 535 // Handle the simplest case efficiently. 536 if (K == 1) 537 return It; 538 539 assert(K < 9 && "We cannot handle such long AddRecs yet."); 540 541 // FIXME: A temporary hack to remove in future. Arbitrary precision integers 542 // aren't supported by the code generator yet. For the dividend, the bitwidth 543 // we use is the smallest power of 2 greater or equal to K*W and less or equal 544 // to 64. Note that setting the upper bound for bitwidth may still lead to 545 // miscompilation in some cases. 546 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth()); 547 if (DividendBits > 64) 548 DividendBits = 64; 549#if 0 // Waiting for the APInt support in the code generator... 550 unsigned DividendBits = K * It->getBitWidth(); 551#endif 552 553 const IntegerType *DividendTy = IntegerType::get(DividendBits); 554 const SCEVHandle ExIt = SE.getTruncateOrZeroExtend(It, DividendTy); 555 556 // The final number of bits we need to perform the division is the maximum of 557 // dividend and divisor bitwidths. 558 const IntegerType *DivisionTy = 559 IntegerType::get(std::max(DividendBits, 16U)); 560 561 // Compute K! We know K >= 2 here. 562 unsigned F = 2; 563 for (unsigned i = 3; i <= K; ++i) 564 F *= i; 565 APInt Divisor(DivisionTy->getBitWidth(), F); 566 567 // Handle this case efficiently, it is common to have constant iteration 568 // counts while computing loop exit values. 569 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) { 570 const APInt& N = SC->getValue()->getValue(); 571 APInt Dividend(N.getBitWidth(), 1); 572 for (; K; --K) 573 Dividend *= N-(K-1); 574 if (DividendTy != DivisionTy) 575 Dividend = Dividend.zext(DivisionTy->getBitWidth()); 576 577 APInt Result = Dividend.udiv(Divisor); 578 if (Result.getBitWidth() != It->getBitWidth()) 579 Result = Result.trunc(It->getBitWidth()); 580 581 return SE.getConstant(Result); 582 } 583 584 SCEVHandle Dividend = ExIt; 585 for (unsigned i = 1; i != K; ++i) 586 Dividend = 587 SE.getMulExpr(Dividend, 588 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy))); 589 590 return SE.getTruncateOrZeroExtend( 591 SE.getUDivExpr( 592 SE.getTruncateOrZeroExtend(Dividend, DivisionTy), 593 SE.getConstant(Divisor) 594 ), It->getType()); 595} 596 597/// evaluateAtIteration - Return the value of this chain of recurrences at 598/// the specified iteration number. We can evaluate this recurrence by 599/// multiplying each element in the chain by the binomial coefficient 600/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 601/// 602/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 603/// 604/// where BC(It, k) stands for binomial coefficient. 605/// 606SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 607 ScalarEvolution &SE) const { 608 SCEVHandle Result = getStart(); 609 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 610 // The computation is correct in the face of overflow provided that the 611 // multiplication is performed _after_ the evaluation of the binomial 612 // coefficient. 613 SCEVHandle Val = SE.getMulExpr(getOperand(i), 614 BinomialCoefficient(It, i, SE)); 615 Result = SE.getAddExpr(Result, Val); 616 } 617 return Result; 618} 619 620//===----------------------------------------------------------------------===// 621// SCEV Expression folder implementations 622//===----------------------------------------------------------------------===// 623 624SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 625 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 626 return getUnknown( 627 ConstantExpr::getTrunc(SC->getValue(), Ty)); 628 629 // If the input value is a chrec scev made out of constants, truncate 630 // all of the constants. 631 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 632 std::vector<SCEVHandle> Operands; 633 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 634 // FIXME: This should allow truncation of other expression types! 635 if (isa<SCEVConstant>(AddRec->getOperand(i))) 636 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 637 else 638 break; 639 if (Operands.size() == AddRec->getNumOperands()) 640 return getAddRecExpr(Operands, AddRec->getLoop()); 641 } 642 643 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 644 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 645 return Result; 646} 647 648SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 649 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 650 return getUnknown( 651 ConstantExpr::getZExt(SC->getValue(), Ty)); 652 653 // FIXME: If the input value is a chrec scev, and we can prove that the value 654 // did not overflow the old, smaller, value, we can zero extend all of the 655 // operands (often constants). This would allow analysis of something like 656 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 657 658 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 659 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 660 return Result; 661} 662 663SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 664 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 665 return getUnknown( 666 ConstantExpr::getSExt(SC->getValue(), Ty)); 667 668 // FIXME: If the input value is a chrec scev, and we can prove that the value 669 // did not overflow the old, smaller, value, we can sign extend all of the 670 // operands (often constants). This would allow analysis of something like 671 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 672 673 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 674 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 675 return Result; 676} 677 678/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 679/// of the input value to the specified type. If the type must be 680/// extended, it is zero extended. 681SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 682 const Type *Ty) { 683 const Type *SrcTy = V->getType(); 684 assert(SrcTy->isInteger() && Ty->isInteger() && 685 "Cannot truncate or zero extend with non-integer arguments!"); 686 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 687 return V; // No conversion 688 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 689 return getTruncateExpr(V, Ty); 690 return getZeroExtendExpr(V, Ty); 691} 692 693// get - Get a canonical add expression, or something simpler if possible. 694SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 695 assert(!Ops.empty() && "Cannot get empty add!"); 696 if (Ops.size() == 1) return Ops[0]; 697 698 // Sort by complexity, this groups all similar expression types together. 699 GroupByComplexity(Ops); 700 701 // If there are any constants, fold them together. 702 unsigned Idx = 0; 703 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 704 ++Idx; 705 assert(Idx < Ops.size()); 706 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 707 // We found two constants, fold them together! 708 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 709 RHSC->getValue()->getValue()); 710 Ops[0] = getConstant(Fold); 711 Ops.erase(Ops.begin()+1); // Erase the folded element 712 if (Ops.size() == 1) return Ops[0]; 713 LHSC = cast<SCEVConstant>(Ops[0]); 714 } 715 716 // If we are left with a constant zero being added, strip it off. 717 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 718 Ops.erase(Ops.begin()); 719 --Idx; 720 } 721 } 722 723 if (Ops.size() == 1) return Ops[0]; 724 725 // Okay, check to see if the same value occurs in the operand list twice. If 726 // so, merge them together into an multiply expression. Since we sorted the 727 // list, these values are required to be adjacent. 728 const Type *Ty = Ops[0]->getType(); 729 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 730 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 731 // Found a match, merge the two values into a multiply, and add any 732 // remaining values to the result. 733 SCEVHandle Two = getIntegerSCEV(2, Ty); 734 SCEVHandle Mul = getMulExpr(Ops[i], Two); 735 if (Ops.size() == 2) 736 return Mul; 737 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 738 Ops.push_back(Mul); 739 return getAddExpr(Ops); 740 } 741 742 // Now we know the first non-constant operand. Skip past any cast SCEVs. 743 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 744 ++Idx; 745 746 // If there are add operands they would be next. 747 if (Idx < Ops.size()) { 748 bool DeletedAdd = false; 749 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 750 // If we have an add, expand the add operands onto the end of the operands 751 // list. 752 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 753 Ops.erase(Ops.begin()+Idx); 754 DeletedAdd = true; 755 } 756 757 // If we deleted at least one add, we added operands to the end of the list, 758 // and they are not necessarily sorted. Recurse to resort and resimplify 759 // any operands we just aquired. 760 if (DeletedAdd) 761 return getAddExpr(Ops); 762 } 763 764 // Skip over the add expression until we get to a multiply. 765 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 766 ++Idx; 767 768 // If we are adding something to a multiply expression, make sure the 769 // something is not already an operand of the multiply. If so, merge it into 770 // the multiply. 771 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 772 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 773 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 774 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 775 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 776 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 777 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 778 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 779 if (Mul->getNumOperands() != 2) { 780 // If the multiply has more than two operands, we must get the 781 // Y*Z term. 782 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 783 MulOps.erase(MulOps.begin()+MulOp); 784 InnerMul = getMulExpr(MulOps); 785 } 786 SCEVHandle One = getIntegerSCEV(1, Ty); 787 SCEVHandle AddOne = getAddExpr(InnerMul, One); 788 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 789 if (Ops.size() == 2) return OuterMul; 790 if (AddOp < Idx) { 791 Ops.erase(Ops.begin()+AddOp); 792 Ops.erase(Ops.begin()+Idx-1); 793 } else { 794 Ops.erase(Ops.begin()+Idx); 795 Ops.erase(Ops.begin()+AddOp-1); 796 } 797 Ops.push_back(OuterMul); 798 return getAddExpr(Ops); 799 } 800 801 // Check this multiply against other multiplies being added together. 802 for (unsigned OtherMulIdx = Idx+1; 803 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 804 ++OtherMulIdx) { 805 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 806 // If MulOp occurs in OtherMul, we can fold the two multiplies 807 // together. 808 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 809 OMulOp != e; ++OMulOp) 810 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 811 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 812 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 813 if (Mul->getNumOperands() != 2) { 814 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 815 MulOps.erase(MulOps.begin()+MulOp); 816 InnerMul1 = getMulExpr(MulOps); 817 } 818 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 819 if (OtherMul->getNumOperands() != 2) { 820 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 821 OtherMul->op_end()); 822 MulOps.erase(MulOps.begin()+OMulOp); 823 InnerMul2 = getMulExpr(MulOps); 824 } 825 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 826 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 827 if (Ops.size() == 2) return OuterMul; 828 Ops.erase(Ops.begin()+Idx); 829 Ops.erase(Ops.begin()+OtherMulIdx-1); 830 Ops.push_back(OuterMul); 831 return getAddExpr(Ops); 832 } 833 } 834 } 835 } 836 837 // If there are any add recurrences in the operands list, see if any other 838 // added values are loop invariant. If so, we can fold them into the 839 // recurrence. 840 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 841 ++Idx; 842 843 // Scan over all recurrences, trying to fold loop invariants into them. 844 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 845 // Scan all of the other operands to this add and add them to the vector if 846 // they are loop invariant w.r.t. the recurrence. 847 std::vector<SCEVHandle> LIOps; 848 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 849 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 850 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 851 LIOps.push_back(Ops[i]); 852 Ops.erase(Ops.begin()+i); 853 --i; --e; 854 } 855 856 // If we found some loop invariants, fold them into the recurrence. 857 if (!LIOps.empty()) { 858 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 859 LIOps.push_back(AddRec->getStart()); 860 861 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 862 AddRecOps[0] = getAddExpr(LIOps); 863 864 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 865 // If all of the other operands were loop invariant, we are done. 866 if (Ops.size() == 1) return NewRec; 867 868 // Otherwise, add the folded AddRec by the non-liv parts. 869 for (unsigned i = 0;; ++i) 870 if (Ops[i] == AddRec) { 871 Ops[i] = NewRec; 872 break; 873 } 874 return getAddExpr(Ops); 875 } 876 877 // Okay, if there weren't any loop invariants to be folded, check to see if 878 // there are multiple AddRec's with the same loop induction variable being 879 // added together. If so, we can fold them. 880 for (unsigned OtherIdx = Idx+1; 881 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 882 if (OtherIdx != Idx) { 883 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 884 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 885 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 886 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 887 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 888 if (i >= NewOps.size()) { 889 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 890 OtherAddRec->op_end()); 891 break; 892 } 893 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 894 } 895 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 896 897 if (Ops.size() == 2) return NewAddRec; 898 899 Ops.erase(Ops.begin()+Idx); 900 Ops.erase(Ops.begin()+OtherIdx-1); 901 Ops.push_back(NewAddRec); 902 return getAddExpr(Ops); 903 } 904 } 905 906 // Otherwise couldn't fold anything into this recurrence. Move onto the 907 // next one. 908 } 909 910 // Okay, it looks like we really DO need an add expr. Check to see if we 911 // already have one, otherwise create a new one. 912 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 913 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 914 SCEVOps)]; 915 if (Result == 0) Result = new SCEVAddExpr(Ops); 916 return Result; 917} 918 919 920SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 921 assert(!Ops.empty() && "Cannot get empty mul!"); 922 923 // Sort by complexity, this groups all similar expression types together. 924 GroupByComplexity(Ops); 925 926 // If there are any constants, fold them together. 927 unsigned Idx = 0; 928 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 929 930 // C1*(C2+V) -> C1*C2 + C1*V 931 if (Ops.size() == 2) 932 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 933 if (Add->getNumOperands() == 2 && 934 isa<SCEVConstant>(Add->getOperand(0))) 935 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 936 getMulExpr(LHSC, Add->getOperand(1))); 937 938 939 ++Idx; 940 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 941 // We found two constants, fold them together! 942 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 943 RHSC->getValue()->getValue()); 944 Ops[0] = getConstant(Fold); 945 Ops.erase(Ops.begin()+1); // Erase the folded element 946 if (Ops.size() == 1) return Ops[0]; 947 LHSC = cast<SCEVConstant>(Ops[0]); 948 } 949 950 // If we are left with a constant one being multiplied, strip it off. 951 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 952 Ops.erase(Ops.begin()); 953 --Idx; 954 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 955 // If we have a multiply of zero, it will always be zero. 956 return Ops[0]; 957 } 958 } 959 960 // Skip over the add expression until we get to a multiply. 961 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 962 ++Idx; 963 964 if (Ops.size() == 1) 965 return Ops[0]; 966 967 // If there are mul operands inline them all into this expression. 968 if (Idx < Ops.size()) { 969 bool DeletedMul = false; 970 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 971 // If we have an mul, expand the mul operands onto the end of the operands 972 // list. 973 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 974 Ops.erase(Ops.begin()+Idx); 975 DeletedMul = true; 976 } 977 978 // If we deleted at least one mul, we added operands to the end of the list, 979 // and they are not necessarily sorted. Recurse to resort and resimplify 980 // any operands we just aquired. 981 if (DeletedMul) 982 return getMulExpr(Ops); 983 } 984 985 // If there are any add recurrences in the operands list, see if any other 986 // added values are loop invariant. If so, we can fold them into the 987 // recurrence. 988 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 989 ++Idx; 990 991 // Scan over all recurrences, trying to fold loop invariants into them. 992 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 993 // Scan all of the other operands to this mul and add them to the vector if 994 // they are loop invariant w.r.t. the recurrence. 995 std::vector<SCEVHandle> LIOps; 996 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 997 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 998 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 999 LIOps.push_back(Ops[i]); 1000 Ops.erase(Ops.begin()+i); 1001 --i; --e; 1002 } 1003 1004 // If we found some loop invariants, fold them into the recurrence. 1005 if (!LIOps.empty()) { 1006 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 1007 std::vector<SCEVHandle> NewOps; 1008 NewOps.reserve(AddRec->getNumOperands()); 1009 if (LIOps.size() == 1) { 1010 SCEV *Scale = LIOps[0]; 1011 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1012 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1013 } else { 1014 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1015 std::vector<SCEVHandle> MulOps(LIOps); 1016 MulOps.push_back(AddRec->getOperand(i)); 1017 NewOps.push_back(getMulExpr(MulOps)); 1018 } 1019 } 1020 1021 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1022 1023 // If all of the other operands were loop invariant, we are done. 1024 if (Ops.size() == 1) return NewRec; 1025 1026 // Otherwise, multiply the folded AddRec by the non-liv parts. 1027 for (unsigned i = 0;; ++i) 1028 if (Ops[i] == AddRec) { 1029 Ops[i] = NewRec; 1030 break; 1031 } 1032 return getMulExpr(Ops); 1033 } 1034 1035 // Okay, if there weren't any loop invariants to be folded, check to see if 1036 // there are multiple AddRec's with the same loop induction variable being 1037 // multiplied together. If so, we can fold them. 1038 for (unsigned OtherIdx = Idx+1; 1039 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1040 if (OtherIdx != Idx) { 1041 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1042 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1043 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1044 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1045 SCEVHandle NewStart = getMulExpr(F->getStart(), 1046 G->getStart()); 1047 SCEVHandle B = F->getStepRecurrence(*this); 1048 SCEVHandle D = G->getStepRecurrence(*this); 1049 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1050 getMulExpr(G, B), 1051 getMulExpr(B, D)); 1052 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1053 F->getLoop()); 1054 if (Ops.size() == 2) return NewAddRec; 1055 1056 Ops.erase(Ops.begin()+Idx); 1057 Ops.erase(Ops.begin()+OtherIdx-1); 1058 Ops.push_back(NewAddRec); 1059 return getMulExpr(Ops); 1060 } 1061 } 1062 1063 // Otherwise couldn't fold anything into this recurrence. Move onto the 1064 // next one. 1065 } 1066 1067 // Okay, it looks like we really DO need an mul expr. Check to see if we 1068 // already have one, otherwise create a new one. 1069 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1070 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1071 SCEVOps)]; 1072 if (Result == 0) 1073 Result = new SCEVMulExpr(Ops); 1074 return Result; 1075} 1076 1077SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1078 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1079 if (RHSC->getValue()->equalsInt(1)) 1080 return LHS; // X udiv 1 --> x 1081 1082 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1083 Constant *LHSCV = LHSC->getValue(); 1084 Constant *RHSCV = RHSC->getValue(); 1085 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1086 } 1087 } 1088 1089 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1090 1091 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1092 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1093 return Result; 1094} 1095 1096 1097/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1098/// specified loop. Simplify the expression as much as possible. 1099SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1100 const SCEVHandle &Step, const Loop *L) { 1101 std::vector<SCEVHandle> Operands; 1102 Operands.push_back(Start); 1103 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1104 if (StepChrec->getLoop() == L) { 1105 Operands.insert(Operands.end(), StepChrec->op_begin(), 1106 StepChrec->op_end()); 1107 return getAddRecExpr(Operands, L); 1108 } 1109 1110 Operands.push_back(Step); 1111 return getAddRecExpr(Operands, L); 1112} 1113 1114/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1115/// specified loop. Simplify the expression as much as possible. 1116SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1117 const Loop *L) { 1118 if (Operands.size() == 1) return Operands[0]; 1119 1120 if (Operands.back()->isZero()) { 1121 Operands.pop_back(); 1122 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1123 } 1124 1125 SCEVAddRecExpr *&Result = 1126 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1127 Operands.end()))]; 1128 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1129 return Result; 1130} 1131 1132SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1133 const SCEVHandle &RHS) { 1134 std::vector<SCEVHandle> Ops; 1135 Ops.push_back(LHS); 1136 Ops.push_back(RHS); 1137 return getSMaxExpr(Ops); 1138} 1139 1140SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1141 assert(!Ops.empty() && "Cannot get empty smax!"); 1142 if (Ops.size() == 1) return Ops[0]; 1143 1144 // Sort by complexity, this groups all similar expression types together. 1145 GroupByComplexity(Ops); 1146 1147 // If there are any constants, fold them together. 1148 unsigned Idx = 0; 1149 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1150 ++Idx; 1151 assert(Idx < Ops.size()); 1152 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1153 // We found two constants, fold them together! 1154 ConstantInt *Fold = ConstantInt::get( 1155 APIntOps::smax(LHSC->getValue()->getValue(), 1156 RHSC->getValue()->getValue())); 1157 Ops[0] = getConstant(Fold); 1158 Ops.erase(Ops.begin()+1); // Erase the folded element 1159 if (Ops.size() == 1) return Ops[0]; 1160 LHSC = cast<SCEVConstant>(Ops[0]); 1161 } 1162 1163 // If we are left with a constant -inf, strip it off. 1164 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1165 Ops.erase(Ops.begin()); 1166 --Idx; 1167 } 1168 } 1169 1170 if (Ops.size() == 1) return Ops[0]; 1171 1172 // Find the first SMax 1173 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1174 ++Idx; 1175 1176 // Check to see if one of the operands is an SMax. If so, expand its operands 1177 // onto our operand list, and recurse to simplify. 1178 if (Idx < Ops.size()) { 1179 bool DeletedSMax = false; 1180 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1181 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1182 Ops.erase(Ops.begin()+Idx); 1183 DeletedSMax = true; 1184 } 1185 1186 if (DeletedSMax) 1187 return getSMaxExpr(Ops); 1188 } 1189 1190 // Okay, check to see if the same value occurs in the operand list twice. If 1191 // so, delete one. Since we sorted the list, these values are required to 1192 // be adjacent. 1193 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1194 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1195 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1196 --i; --e; 1197 } 1198 1199 if (Ops.size() == 1) return Ops[0]; 1200 1201 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1202 1203 // Okay, it looks like we really DO need an smax expr. Check to see if we 1204 // already have one, otherwise create a new one. 1205 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1206 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1207 SCEVOps)]; 1208 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1209 return Result; 1210} 1211 1212SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1213 const SCEVHandle &RHS) { 1214 std::vector<SCEVHandle> Ops; 1215 Ops.push_back(LHS); 1216 Ops.push_back(RHS); 1217 return getUMaxExpr(Ops); 1218} 1219 1220SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1221 assert(!Ops.empty() && "Cannot get empty umax!"); 1222 if (Ops.size() == 1) return Ops[0]; 1223 1224 // Sort by complexity, this groups all similar expression types together. 1225 GroupByComplexity(Ops); 1226 1227 // If there are any constants, fold them together. 1228 unsigned Idx = 0; 1229 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1230 ++Idx; 1231 assert(Idx < Ops.size()); 1232 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1233 // We found two constants, fold them together! 1234 ConstantInt *Fold = ConstantInt::get( 1235 APIntOps::umax(LHSC->getValue()->getValue(), 1236 RHSC->getValue()->getValue())); 1237 Ops[0] = getConstant(Fold); 1238 Ops.erase(Ops.begin()+1); // Erase the folded element 1239 if (Ops.size() == 1) return Ops[0]; 1240 LHSC = cast<SCEVConstant>(Ops[0]); 1241 } 1242 1243 // If we are left with a constant zero, strip it off. 1244 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1245 Ops.erase(Ops.begin()); 1246 --Idx; 1247 } 1248 } 1249 1250 if (Ops.size() == 1) return Ops[0]; 1251 1252 // Find the first UMax 1253 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1254 ++Idx; 1255 1256 // Check to see if one of the operands is a UMax. If so, expand its operands 1257 // onto our operand list, and recurse to simplify. 1258 if (Idx < Ops.size()) { 1259 bool DeletedUMax = false; 1260 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1261 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1262 Ops.erase(Ops.begin()+Idx); 1263 DeletedUMax = true; 1264 } 1265 1266 if (DeletedUMax) 1267 return getUMaxExpr(Ops); 1268 } 1269 1270 // Okay, check to see if the same value occurs in the operand list twice. If 1271 // so, delete one. Since we sorted the list, these values are required to 1272 // be adjacent. 1273 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1274 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1275 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1276 --i; --e; 1277 } 1278 1279 if (Ops.size() == 1) return Ops[0]; 1280 1281 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1282 1283 // Okay, it looks like we really DO need a umax expr. Check to see if we 1284 // already have one, otherwise create a new one. 1285 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1286 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1287 SCEVOps)]; 1288 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1289 return Result; 1290} 1291 1292SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1293 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1294 return getConstant(CI); 1295 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1296 if (Result == 0) Result = new SCEVUnknown(V); 1297 return Result; 1298} 1299 1300 1301//===----------------------------------------------------------------------===// 1302// ScalarEvolutionsImpl Definition and Implementation 1303//===----------------------------------------------------------------------===// 1304// 1305/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1306/// evolution code. 1307/// 1308namespace { 1309 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1310 /// SE - A reference to the public ScalarEvolution object. 1311 ScalarEvolution &SE; 1312 1313 /// F - The function we are analyzing. 1314 /// 1315 Function &F; 1316 1317 /// LI - The loop information for the function we are currently analyzing. 1318 /// 1319 LoopInfo &LI; 1320 1321 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1322 /// things. 1323 SCEVHandle UnknownValue; 1324 1325 /// Scalars - This is a cache of the scalars we have analyzed so far. 1326 /// 1327 std::map<Value*, SCEVHandle> Scalars; 1328 1329 /// IterationCounts - Cache the iteration count of the loops for this 1330 /// function as they are computed. 1331 std::map<const Loop*, SCEVHandle> IterationCounts; 1332 1333 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1334 /// the PHI instructions that we attempt to compute constant evolutions for. 1335 /// This allows us to avoid potentially expensive recomputation of these 1336 /// properties. An instruction maps to null if we are unable to compute its 1337 /// exit value. 1338 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1339 1340 public: 1341 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1342 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1343 1344 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1345 /// expression and create a new one. 1346 SCEVHandle getSCEV(Value *V); 1347 1348 /// hasSCEV - Return true if the SCEV for this value has already been 1349 /// computed. 1350 bool hasSCEV(Value *V) const { 1351 return Scalars.count(V); 1352 } 1353 1354 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1355 /// the specified value. 1356 void setSCEV(Value *V, const SCEVHandle &H) { 1357 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1358 assert(isNew && "This entry already existed!"); 1359 } 1360 1361 1362 /// getSCEVAtScope - Compute the value of the specified expression within 1363 /// the indicated loop (which may be null to indicate in no loop). If the 1364 /// expression cannot be evaluated, return UnknownValue itself. 1365 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1366 1367 1368 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1369 /// an analyzable loop-invariant iteration count. 1370 bool hasLoopInvariantIterationCount(const Loop *L); 1371 1372 /// getIterationCount - If the specified loop has a predictable iteration 1373 /// count, return it. Note that it is not valid to call this method on a 1374 /// loop without a loop-invariant iteration count. 1375 SCEVHandle getIterationCount(const Loop *L); 1376 1377 /// deleteValueFromRecords - This method should be called by the 1378 /// client before it removes a value from the program, to make sure 1379 /// that no dangling references are left around. 1380 void deleteValueFromRecords(Value *V); 1381 1382 private: 1383 /// createSCEV - We know that there is no SCEV for the specified value. 1384 /// Analyze the expression. 1385 SCEVHandle createSCEV(Value *V); 1386 1387 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1388 /// SCEVs. 1389 SCEVHandle createNodeForPHI(PHINode *PN); 1390 1391 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1392 /// for the specified instruction and replaces any references to the 1393 /// symbolic value SymName with the specified value. This is used during 1394 /// PHI resolution. 1395 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1396 const SCEVHandle &SymName, 1397 const SCEVHandle &NewVal); 1398 1399 /// ComputeIterationCount - Compute the number of times the specified loop 1400 /// will iterate. 1401 SCEVHandle ComputeIterationCount(const Loop *L); 1402 1403 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1404 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1405 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1406 Constant *RHS, 1407 const Loop *L, 1408 ICmpInst::Predicate p); 1409 1410 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1411 /// constant number of times (the condition evolves only from constants), 1412 /// try to evaluate a few iterations of the loop until we get the exit 1413 /// condition gets a value of ExitWhen (true or false). If we cannot 1414 /// evaluate the trip count of the loop, return UnknownValue. 1415 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1416 bool ExitWhen); 1417 1418 /// HowFarToZero - Return the number of times a backedge comparing the 1419 /// specified value to zero will execute. If not computable, return 1420 /// UnknownValue. 1421 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1422 1423 /// HowFarToNonZero - Return the number of times a backedge checking the 1424 /// specified value for nonzero will execute. If not computable, return 1425 /// UnknownValue. 1426 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1427 1428 /// HowManyLessThans - Return the number of times a backedge containing the 1429 /// specified less-than comparison will execute. If not computable, return 1430 /// UnknownValue. isSigned specifies whether the less-than is signed. 1431 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1432 bool isSigned); 1433 1434 /// executesAtLeastOnce - Test whether entry to the loop is protected by 1435 /// a conditional between LHS and RHS. 1436 bool executesAtLeastOnce(const Loop *L, bool isSigned, SCEV *LHS, SCEV *RHS); 1437 1438 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1439 /// in the header of its containing loop, we know the loop executes a 1440 /// constant number of times, and the PHI node is just a recurrence 1441 /// involving constants, fold it. 1442 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1443 const Loop *L); 1444 }; 1445} 1446 1447//===----------------------------------------------------------------------===// 1448// Basic SCEV Analysis and PHI Idiom Recognition Code 1449// 1450 1451/// deleteValueFromRecords - This method should be called by the 1452/// client before it removes an instruction from the program, to make sure 1453/// that no dangling references are left around. 1454void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1455 SmallVector<Value *, 16> Worklist; 1456 1457 if (Scalars.erase(V)) { 1458 if (PHINode *PN = dyn_cast<PHINode>(V)) 1459 ConstantEvolutionLoopExitValue.erase(PN); 1460 Worklist.push_back(V); 1461 } 1462 1463 while (!Worklist.empty()) { 1464 Value *VV = Worklist.back(); 1465 Worklist.pop_back(); 1466 1467 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1468 UI != UE; ++UI) { 1469 Instruction *Inst = cast<Instruction>(*UI); 1470 if (Scalars.erase(Inst)) { 1471 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1472 ConstantEvolutionLoopExitValue.erase(PN); 1473 Worklist.push_back(Inst); 1474 } 1475 } 1476 } 1477} 1478 1479 1480/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1481/// expression and create a new one. 1482SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1483 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1484 1485 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1486 if (I != Scalars.end()) return I->second; 1487 SCEVHandle S = createSCEV(V); 1488 Scalars.insert(std::make_pair(V, S)); 1489 return S; 1490} 1491 1492/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1493/// the specified instruction and replaces any references to the symbolic value 1494/// SymName with the specified value. This is used during PHI resolution. 1495void ScalarEvolutionsImpl:: 1496ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1497 const SCEVHandle &NewVal) { 1498 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1499 if (SI == Scalars.end()) return; 1500 1501 SCEVHandle NV = 1502 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1503 if (NV == SI->second) return; // No change. 1504 1505 SI->second = NV; // Update the scalars map! 1506 1507 // Any instruction values that use this instruction might also need to be 1508 // updated! 1509 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1510 UI != E; ++UI) 1511 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1512} 1513 1514/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1515/// a loop header, making it a potential recurrence, or it doesn't. 1516/// 1517SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1518 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1519 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1520 if (L->getHeader() == PN->getParent()) { 1521 // If it lives in the loop header, it has two incoming values, one 1522 // from outside the loop, and one from inside. 1523 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1524 unsigned BackEdge = IncomingEdge^1; 1525 1526 // While we are analyzing this PHI node, handle its value symbolically. 1527 SCEVHandle SymbolicName = SE.getUnknown(PN); 1528 assert(Scalars.find(PN) == Scalars.end() && 1529 "PHI node already processed?"); 1530 Scalars.insert(std::make_pair(PN, SymbolicName)); 1531 1532 // Using this symbolic name for the PHI, analyze the value coming around 1533 // the back-edge. 1534 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1535 1536 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1537 // has a special value for the first iteration of the loop. 1538 1539 // If the value coming around the backedge is an add with the symbolic 1540 // value we just inserted, then we found a simple induction variable! 1541 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1542 // If there is a single occurrence of the symbolic value, replace it 1543 // with a recurrence. 1544 unsigned FoundIndex = Add->getNumOperands(); 1545 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1546 if (Add->getOperand(i) == SymbolicName) 1547 if (FoundIndex == e) { 1548 FoundIndex = i; 1549 break; 1550 } 1551 1552 if (FoundIndex != Add->getNumOperands()) { 1553 // Create an add with everything but the specified operand. 1554 std::vector<SCEVHandle> Ops; 1555 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1556 if (i != FoundIndex) 1557 Ops.push_back(Add->getOperand(i)); 1558 SCEVHandle Accum = SE.getAddExpr(Ops); 1559 1560 // This is not a valid addrec if the step amount is varying each 1561 // loop iteration, but is not itself an addrec in this loop. 1562 if (Accum->isLoopInvariant(L) || 1563 (isa<SCEVAddRecExpr>(Accum) && 1564 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1565 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1566 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1567 1568 // Okay, for the entire analysis of this edge we assumed the PHI 1569 // to be symbolic. We now need to go back and update all of the 1570 // entries for the scalars that use the PHI (except for the PHI 1571 // itself) to use the new analyzed value instead of the "symbolic" 1572 // value. 1573 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1574 return PHISCEV; 1575 } 1576 } 1577 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1578 // Otherwise, this could be a loop like this: 1579 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1580 // In this case, j = {1,+,1} and BEValue is j. 1581 // Because the other in-value of i (0) fits the evolution of BEValue 1582 // i really is an addrec evolution. 1583 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1584 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1585 1586 // If StartVal = j.start - j.stride, we can use StartVal as the 1587 // initial step of the addrec evolution. 1588 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1589 AddRec->getOperand(1))) { 1590 SCEVHandle PHISCEV = 1591 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1592 1593 // Okay, for the entire analysis of this edge we assumed the PHI 1594 // to be symbolic. We now need to go back and update all of the 1595 // entries for the scalars that use the PHI (except for the PHI 1596 // itself) to use the new analyzed value instead of the "symbolic" 1597 // value. 1598 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1599 return PHISCEV; 1600 } 1601 } 1602 } 1603 1604 return SymbolicName; 1605 } 1606 1607 // If it's not a loop phi, we can't handle it yet. 1608 return SE.getUnknown(PN); 1609} 1610 1611/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1612/// guaranteed to end in (at every loop iteration). It is, at the same time, 1613/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1614/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1615static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1616 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1617 return C->getValue()->getValue().countTrailingZeros(); 1618 1619 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1620 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1621 1622 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1623 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1624 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1625 } 1626 1627 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1628 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1629 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1630 } 1631 1632 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1633 // The result is the min of all operands results. 1634 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1635 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1636 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1637 return MinOpRes; 1638 } 1639 1640 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1641 // The result is the sum of all operands results. 1642 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1643 uint32_t BitWidth = M->getBitWidth(); 1644 for (unsigned i = 1, e = M->getNumOperands(); 1645 SumOpRes != BitWidth && i != e; ++i) 1646 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1647 BitWidth); 1648 return SumOpRes; 1649 } 1650 1651 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1652 // The result is the min of all operands results. 1653 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1654 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1655 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1656 return MinOpRes; 1657 } 1658 1659 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1660 // The result is the min of all operands results. 1661 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1662 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1663 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1664 return MinOpRes; 1665 } 1666 1667 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1668 // The result is the min of all operands results. 1669 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1670 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1671 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1672 return MinOpRes; 1673 } 1674 1675 // SCEVUDivExpr, SCEVUnknown 1676 return 0; 1677} 1678 1679/// createSCEV - We know that there is no SCEV for the specified value. 1680/// Analyze the expression. 1681/// 1682SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1683 if (!isa<IntegerType>(V->getType())) 1684 return SE.getUnknown(V); 1685 1686 unsigned Opcode = Instruction::UserOp1; 1687 if (Instruction *I = dyn_cast<Instruction>(V)) 1688 Opcode = I->getOpcode(); 1689 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1690 Opcode = CE->getOpcode(); 1691 else 1692 return SE.getUnknown(V); 1693 1694 User *U = cast<User>(V); 1695 switch (Opcode) { 1696 case Instruction::Add: 1697 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1698 getSCEV(U->getOperand(1))); 1699 case Instruction::Mul: 1700 return SE.getMulExpr(getSCEV(U->getOperand(0)), 1701 getSCEV(U->getOperand(1))); 1702 case Instruction::UDiv: 1703 return SE.getUDivExpr(getSCEV(U->getOperand(0)), 1704 getSCEV(U->getOperand(1))); 1705 case Instruction::Sub: 1706 return SE.getMinusSCEV(getSCEV(U->getOperand(0)), 1707 getSCEV(U->getOperand(1))); 1708 case Instruction::Or: 1709 // If the RHS of the Or is a constant, we may have something like: 1710 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1711 // optimizations will transparently handle this case. 1712 // 1713 // In order for this transformation to be safe, the LHS must be of the 1714 // form X*(2^n) and the Or constant must be less than 2^n. 1715 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1716 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1717 const APInt &CIVal = CI->getValue(); 1718 if (GetMinTrailingZeros(LHS) >= 1719 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1720 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1))); 1721 } 1722 break; 1723 case Instruction::Xor: 1724 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1725 // If the RHS of the xor is a signbit, then this is just an add. 1726 // Instcombine turns add of signbit into xor as a strength reduction step. 1727 if (CI->getValue().isSignBit()) 1728 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1729 getSCEV(U->getOperand(1))); 1730 1731 // If the RHS of xor is -1, then this is a not operation. 1732 else if (CI->isAllOnesValue()) 1733 return SE.getNotSCEV(getSCEV(U->getOperand(0))); 1734 } 1735 break; 1736 1737 case Instruction::Shl: 1738 // Turn shift left of a constant amount into a multiply. 1739 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1740 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1741 Constant *X = ConstantInt::get( 1742 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1743 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1744 } 1745 break; 1746 1747 case Instruction::LShr: 1748 // Turn logical shift right of a constant into a unsigned divide. 1749 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1750 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1751 Constant *X = ConstantInt::get( 1752 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1753 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1754 } 1755 break; 1756 1757 case Instruction::Trunc: 1758 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1759 1760 case Instruction::ZExt: 1761 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1762 1763 case Instruction::SExt: 1764 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1765 1766 case Instruction::BitCast: 1767 // BitCasts are no-op casts so we just eliminate the cast. 1768 if (U->getType()->isInteger() && 1769 U->getOperand(0)->getType()->isInteger()) 1770 return getSCEV(U->getOperand(0)); 1771 break; 1772 1773 case Instruction::PHI: 1774 return createNodeForPHI(cast<PHINode>(U)); 1775 1776 case Instruction::Select: 1777 // This could be a smax or umax that was lowered earlier. 1778 // Try to recover it. 1779 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1780 Value *LHS = ICI->getOperand(0); 1781 Value *RHS = ICI->getOperand(1); 1782 switch (ICI->getPredicate()) { 1783 case ICmpInst::ICMP_SLT: 1784 case ICmpInst::ICMP_SLE: 1785 std::swap(LHS, RHS); 1786 // fall through 1787 case ICmpInst::ICMP_SGT: 1788 case ICmpInst::ICMP_SGE: 1789 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1790 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1791 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1792 // -smax(-x, -y) == smin(x, y). 1793 return SE.getNegativeSCEV(SE.getSMaxExpr( 1794 SE.getNegativeSCEV(getSCEV(LHS)), 1795 SE.getNegativeSCEV(getSCEV(RHS)))); 1796 break; 1797 case ICmpInst::ICMP_ULT: 1798 case ICmpInst::ICMP_ULE: 1799 std::swap(LHS, RHS); 1800 // fall through 1801 case ICmpInst::ICMP_UGT: 1802 case ICmpInst::ICMP_UGE: 1803 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1804 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1805 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1806 // ~umax(~x, ~y) == umin(x, y) 1807 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1808 SE.getNotSCEV(getSCEV(RHS)))); 1809 break; 1810 default: 1811 break; 1812 } 1813 } 1814 1815 default: // We cannot analyze this expression. 1816 break; 1817 } 1818 1819 return SE.getUnknown(V); 1820} 1821 1822 1823 1824//===----------------------------------------------------------------------===// 1825// Iteration Count Computation Code 1826// 1827 1828/// getIterationCount - If the specified loop has a predictable iteration 1829/// count, return it. Note that it is not valid to call this method on a 1830/// loop without a loop-invariant iteration count. 1831SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1832 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1833 if (I == IterationCounts.end()) { 1834 SCEVHandle ItCount = ComputeIterationCount(L); 1835 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1836 if (ItCount != UnknownValue) { 1837 assert(ItCount->isLoopInvariant(L) && 1838 "Computed trip count isn't loop invariant for loop!"); 1839 ++NumTripCountsComputed; 1840 } else if (isa<PHINode>(L->getHeader()->begin())) { 1841 // Only count loops that have phi nodes as not being computable. 1842 ++NumTripCountsNotComputed; 1843 } 1844 } 1845 return I->second; 1846} 1847 1848/// ComputeIterationCount - Compute the number of times the specified loop 1849/// will iterate. 1850SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1851 // If the loop has a non-one exit block count, we can't analyze it. 1852 SmallVector<BasicBlock*, 8> ExitBlocks; 1853 L->getExitBlocks(ExitBlocks); 1854 if (ExitBlocks.size() != 1) return UnknownValue; 1855 1856 // Okay, there is one exit block. Try to find the condition that causes the 1857 // loop to be exited. 1858 BasicBlock *ExitBlock = ExitBlocks[0]; 1859 1860 BasicBlock *ExitingBlock = 0; 1861 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1862 PI != E; ++PI) 1863 if (L->contains(*PI)) { 1864 if (ExitingBlock == 0) 1865 ExitingBlock = *PI; 1866 else 1867 return UnknownValue; // More than one block exiting! 1868 } 1869 assert(ExitingBlock && "No exits from loop, something is broken!"); 1870 1871 // Okay, we've computed the exiting block. See what condition causes us to 1872 // exit. 1873 // 1874 // FIXME: we should be able to handle switch instructions (with a single exit) 1875 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1876 if (ExitBr == 0) return UnknownValue; 1877 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1878 1879 // At this point, we know we have a conditional branch that determines whether 1880 // the loop is exited. However, we don't know if the branch is executed each 1881 // time through the loop. If not, then the execution count of the branch will 1882 // not be equal to the trip count of the loop. 1883 // 1884 // Currently we check for this by checking to see if the Exit branch goes to 1885 // the loop header. If so, we know it will always execute the same number of 1886 // times as the loop. We also handle the case where the exit block *is* the 1887 // loop header. This is common for un-rotated loops. More extensive analysis 1888 // could be done to handle more cases here. 1889 if (ExitBr->getSuccessor(0) != L->getHeader() && 1890 ExitBr->getSuccessor(1) != L->getHeader() && 1891 ExitBr->getParent() != L->getHeader()) 1892 return UnknownValue; 1893 1894 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1895 1896 // If it's not an integer comparison then compute it the hard way. 1897 // Note that ICmpInst deals with pointer comparisons too so we must check 1898 // the type of the operand. 1899 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1900 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1901 ExitBr->getSuccessor(0) == ExitBlock); 1902 1903 // If the condition was exit on true, convert the condition to exit on false 1904 ICmpInst::Predicate Cond; 1905 if (ExitBr->getSuccessor(1) == ExitBlock) 1906 Cond = ExitCond->getPredicate(); 1907 else 1908 Cond = ExitCond->getInversePredicate(); 1909 1910 // Handle common loops like: for (X = "string"; *X; ++X) 1911 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1912 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1913 SCEVHandle ItCnt = 1914 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1915 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1916 } 1917 1918 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1919 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1920 1921 // Try to evaluate any dependencies out of the loop. 1922 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1923 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1924 Tmp = getSCEVAtScope(RHS, L); 1925 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1926 1927 // At this point, we would like to compute how many iterations of the 1928 // loop the predicate will return true for these inputs. 1929 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1930 // If there is a constant, force it into the RHS. 1931 std::swap(LHS, RHS); 1932 Cond = ICmpInst::getSwappedPredicate(Cond); 1933 } 1934 1935 // FIXME: think about handling pointer comparisons! i.e.: 1936 // while (P != P+100) ++P; 1937 1938 // If we have a comparison of a chrec against a constant, try to use value 1939 // ranges to answer this query. 1940 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1941 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1942 if (AddRec->getLoop() == L) { 1943 // Form the comparison range using the constant of the correct type so 1944 // that the ConstantRange class knows to do a signed or unsigned 1945 // comparison. 1946 ConstantInt *CompVal = RHSC->getValue(); 1947 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1948 CompVal = dyn_cast<ConstantInt>( 1949 ConstantExpr::getBitCast(CompVal, RealTy)); 1950 if (CompVal) { 1951 // Form the constant range. 1952 ConstantRange CompRange( 1953 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1954 1955 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1956 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1957 } 1958 } 1959 1960 switch (Cond) { 1961 case ICmpInst::ICMP_NE: { // while (X != Y) 1962 // Convert to: while (X-Y != 0) 1963 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1964 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1965 break; 1966 } 1967 case ICmpInst::ICMP_EQ: { 1968 // Convert to: while (X-Y == 0) // while (X == Y) 1969 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1970 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1971 break; 1972 } 1973 case ICmpInst::ICMP_SLT: { 1974 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1975 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1976 break; 1977 } 1978 case ICmpInst::ICMP_SGT: { 1979 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1980 SE.getNegativeSCEV(RHS), L, true); 1981 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1982 break; 1983 } 1984 case ICmpInst::ICMP_ULT: { 1985 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1986 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1987 break; 1988 } 1989 case ICmpInst::ICMP_UGT: { 1990 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 1991 SE.getNotSCEV(RHS), L, false); 1992 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1993 break; 1994 } 1995 default: 1996#if 0 1997 cerr << "ComputeIterationCount "; 1998 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1999 cerr << "[unsigned] "; 2000 cerr << *LHS << " " 2001 << Instruction::getOpcodeName(Instruction::ICmp) 2002 << " " << *RHS << "\n"; 2003#endif 2004 break; 2005 } 2006 return ComputeIterationCountExhaustively(L, ExitCond, 2007 ExitBr->getSuccessor(0) == ExitBlock); 2008} 2009 2010static ConstantInt * 2011EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2012 ScalarEvolution &SE) { 2013 SCEVHandle InVal = SE.getConstant(C); 2014 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2015 assert(isa<SCEVConstant>(Val) && 2016 "Evaluation of SCEV at constant didn't fold correctly?"); 2017 return cast<SCEVConstant>(Val)->getValue(); 2018} 2019 2020/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2021/// and a GEP expression (missing the pointer index) indexing into it, return 2022/// the addressed element of the initializer or null if the index expression is 2023/// invalid. 2024static Constant * 2025GetAddressedElementFromGlobal(GlobalVariable *GV, 2026 const std::vector<ConstantInt*> &Indices) { 2027 Constant *Init = GV->getInitializer(); 2028 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2029 uint64_t Idx = Indices[i]->getZExtValue(); 2030 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2031 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2032 Init = cast<Constant>(CS->getOperand(Idx)); 2033 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2034 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2035 Init = cast<Constant>(CA->getOperand(Idx)); 2036 } else if (isa<ConstantAggregateZero>(Init)) { 2037 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2038 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2039 Init = Constant::getNullValue(STy->getElementType(Idx)); 2040 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2041 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2042 Init = Constant::getNullValue(ATy->getElementType()); 2043 } else { 2044 assert(0 && "Unknown constant aggregate type!"); 2045 } 2046 return 0; 2047 } else { 2048 return 0; // Unknown initializer type 2049 } 2050 } 2051 return Init; 2052} 2053 2054/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2055/// 'icmp op load X, cst', try to see if we can compute the trip count. 2056SCEVHandle ScalarEvolutionsImpl:: 2057ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2058 const Loop *L, 2059 ICmpInst::Predicate predicate) { 2060 if (LI->isVolatile()) return UnknownValue; 2061 2062 // Check to see if the loaded pointer is a getelementptr of a global. 2063 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2064 if (!GEP) return UnknownValue; 2065 2066 // Make sure that it is really a constant global we are gepping, with an 2067 // initializer, and make sure the first IDX is really 0. 2068 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2069 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2070 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2071 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2072 return UnknownValue; 2073 2074 // Okay, we allow one non-constant index into the GEP instruction. 2075 Value *VarIdx = 0; 2076 std::vector<ConstantInt*> Indexes; 2077 unsigned VarIdxNum = 0; 2078 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2079 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2080 Indexes.push_back(CI); 2081 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2082 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2083 VarIdx = GEP->getOperand(i); 2084 VarIdxNum = i-2; 2085 Indexes.push_back(0); 2086 } 2087 2088 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2089 // Check to see if X is a loop variant variable value now. 2090 SCEVHandle Idx = getSCEV(VarIdx); 2091 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2092 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2093 2094 // We can only recognize very limited forms of loop index expressions, in 2095 // particular, only affine AddRec's like {C1,+,C2}. 2096 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2097 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2098 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2099 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2100 return UnknownValue; 2101 2102 unsigned MaxSteps = MaxBruteForceIterations; 2103 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2104 ConstantInt *ItCst = 2105 ConstantInt::get(IdxExpr->getType(), IterationNum); 2106 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2107 2108 // Form the GEP offset. 2109 Indexes[VarIdxNum] = Val; 2110 2111 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2112 if (Result == 0) break; // Cannot compute! 2113 2114 // Evaluate the condition for this iteration. 2115 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2116 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2117 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2118#if 0 2119 cerr << "\n***\n*** Computed loop count " << *ItCst 2120 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2121 << "***\n"; 2122#endif 2123 ++NumArrayLenItCounts; 2124 return SE.getConstant(ItCst); // Found terminating iteration! 2125 } 2126 } 2127 return UnknownValue; 2128} 2129 2130 2131/// CanConstantFold - Return true if we can constant fold an instruction of the 2132/// specified type, assuming that all operands were constants. 2133static bool CanConstantFold(const Instruction *I) { 2134 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2135 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2136 return true; 2137 2138 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2139 if (const Function *F = CI->getCalledFunction()) 2140 return canConstantFoldCallTo(F); 2141 return false; 2142} 2143 2144/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2145/// in the loop that V is derived from. We allow arbitrary operations along the 2146/// way, but the operands of an operation must either be constants or a value 2147/// derived from a constant PHI. If this expression does not fit with these 2148/// constraints, return null. 2149static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2150 // If this is not an instruction, or if this is an instruction outside of the 2151 // loop, it can't be derived from a loop PHI. 2152 Instruction *I = dyn_cast<Instruction>(V); 2153 if (I == 0 || !L->contains(I->getParent())) return 0; 2154 2155 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2156 if (L->getHeader() == I->getParent()) 2157 return PN; 2158 else 2159 // We don't currently keep track of the control flow needed to evaluate 2160 // PHIs, so we cannot handle PHIs inside of loops. 2161 return 0; 2162 } 2163 2164 // If we won't be able to constant fold this expression even if the operands 2165 // are constants, return early. 2166 if (!CanConstantFold(I)) return 0; 2167 2168 // Otherwise, we can evaluate this instruction if all of its operands are 2169 // constant or derived from a PHI node themselves. 2170 PHINode *PHI = 0; 2171 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2172 if (!(isa<Constant>(I->getOperand(Op)) || 2173 isa<GlobalValue>(I->getOperand(Op)))) { 2174 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2175 if (P == 0) return 0; // Not evolving from PHI 2176 if (PHI == 0) 2177 PHI = P; 2178 else if (PHI != P) 2179 return 0; // Evolving from multiple different PHIs. 2180 } 2181 2182 // This is a expression evolving from a constant PHI! 2183 return PHI; 2184} 2185 2186/// EvaluateExpression - Given an expression that passes the 2187/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2188/// in the loop has the value PHIVal. If we can't fold this expression for some 2189/// reason, return null. 2190static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2191 if (isa<PHINode>(V)) return PHIVal; 2192 if (Constant *C = dyn_cast<Constant>(V)) return C; 2193 Instruction *I = cast<Instruction>(V); 2194 2195 std::vector<Constant*> Operands; 2196 Operands.resize(I->getNumOperands()); 2197 2198 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2199 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2200 if (Operands[i] == 0) return 0; 2201 } 2202 2203 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2204 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2205 &Operands[0], Operands.size()); 2206 else 2207 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2208 &Operands[0], Operands.size()); 2209} 2210 2211/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2212/// in the header of its containing loop, we know the loop executes a 2213/// constant number of times, and the PHI node is just a recurrence 2214/// involving constants, fold it. 2215Constant *ScalarEvolutionsImpl:: 2216getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2217 std::map<PHINode*, Constant*>::iterator I = 2218 ConstantEvolutionLoopExitValue.find(PN); 2219 if (I != ConstantEvolutionLoopExitValue.end()) 2220 return I->second; 2221 2222 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2223 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2224 2225 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2226 2227 // Since the loop is canonicalized, the PHI node must have two entries. One 2228 // entry must be a constant (coming in from outside of the loop), and the 2229 // second must be derived from the same PHI. 2230 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2231 Constant *StartCST = 2232 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2233 if (StartCST == 0) 2234 return RetVal = 0; // Must be a constant. 2235 2236 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2237 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2238 if (PN2 != PN) 2239 return RetVal = 0; // Not derived from same PHI. 2240 2241 // Execute the loop symbolically to determine the exit value. 2242 if (Its.getActiveBits() >= 32) 2243 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2244 2245 unsigned NumIterations = Its.getZExtValue(); // must be in range 2246 unsigned IterationNum = 0; 2247 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2248 if (IterationNum == NumIterations) 2249 return RetVal = PHIVal; // Got exit value! 2250 2251 // Compute the value of the PHI node for the next iteration. 2252 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2253 if (NextPHI == PHIVal) 2254 return RetVal = NextPHI; // Stopped evolving! 2255 if (NextPHI == 0) 2256 return 0; // Couldn't evaluate! 2257 PHIVal = NextPHI; 2258 } 2259} 2260 2261/// ComputeIterationCountExhaustively - If the trip is known to execute a 2262/// constant number of times (the condition evolves only from constants), 2263/// try to evaluate a few iterations of the loop until we get the exit 2264/// condition gets a value of ExitWhen (true or false). If we cannot 2265/// evaluate the trip count of the loop, return UnknownValue. 2266SCEVHandle ScalarEvolutionsImpl:: 2267ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2268 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2269 if (PN == 0) return UnknownValue; 2270 2271 // Since the loop is canonicalized, the PHI node must have two entries. One 2272 // entry must be a constant (coming in from outside of the loop), and the 2273 // second must be derived from the same PHI. 2274 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2275 Constant *StartCST = 2276 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2277 if (StartCST == 0) return UnknownValue; // Must be a constant. 2278 2279 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2280 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2281 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2282 2283 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2284 // the loop symbolically to determine when the condition gets a value of 2285 // "ExitWhen". 2286 unsigned IterationNum = 0; 2287 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2288 for (Constant *PHIVal = StartCST; 2289 IterationNum != MaxIterations; ++IterationNum) { 2290 ConstantInt *CondVal = 2291 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2292 2293 // Couldn't symbolically evaluate. 2294 if (!CondVal) return UnknownValue; 2295 2296 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2297 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2298 ++NumBruteForceTripCountsComputed; 2299 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2300 } 2301 2302 // Compute the value of the PHI node for the next iteration. 2303 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2304 if (NextPHI == 0 || NextPHI == PHIVal) 2305 return UnknownValue; // Couldn't evaluate or not making progress... 2306 PHIVal = NextPHI; 2307 } 2308 2309 // Too many iterations were needed to evaluate. 2310 return UnknownValue; 2311} 2312 2313/// getSCEVAtScope - Compute the value of the specified expression within the 2314/// indicated loop (which may be null to indicate in no loop). If the 2315/// expression cannot be evaluated, return UnknownValue. 2316SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2317 // FIXME: this should be turned into a virtual method on SCEV! 2318 2319 if (isa<SCEVConstant>(V)) return V; 2320 2321 // If this instruction is evolved from a constant-evolving PHI, compute the 2322 // exit value from the loop without using SCEVs. 2323 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2324 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2325 const Loop *LI = this->LI[I->getParent()]; 2326 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2327 if (PHINode *PN = dyn_cast<PHINode>(I)) 2328 if (PN->getParent() == LI->getHeader()) { 2329 // Okay, there is no closed form solution for the PHI node. Check 2330 // to see if the loop that contains it has a known iteration count. 2331 // If so, we may be able to force computation of the exit value. 2332 SCEVHandle IterationCount = getIterationCount(LI); 2333 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2334 // Okay, we know how many times the containing loop executes. If 2335 // this is a constant evolving PHI node, get the final value at 2336 // the specified iteration number. 2337 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2338 ICC->getValue()->getValue(), 2339 LI); 2340 if (RV) return SE.getUnknown(RV); 2341 } 2342 } 2343 2344 // Okay, this is an expression that we cannot symbolically evaluate 2345 // into a SCEV. Check to see if it's possible to symbolically evaluate 2346 // the arguments into constants, and if so, try to constant propagate the 2347 // result. This is particularly useful for computing loop exit values. 2348 if (CanConstantFold(I)) { 2349 std::vector<Constant*> Operands; 2350 Operands.reserve(I->getNumOperands()); 2351 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2352 Value *Op = I->getOperand(i); 2353 if (Constant *C = dyn_cast<Constant>(Op)) { 2354 Operands.push_back(C); 2355 } else { 2356 // If any of the operands is non-constant and if they are 2357 // non-integer, don't even try to analyze them with scev techniques. 2358 if (!isa<IntegerType>(Op->getType())) 2359 return V; 2360 2361 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2362 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2363 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2364 Op->getType(), 2365 false)); 2366 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2367 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2368 Operands.push_back(ConstantExpr::getIntegerCast(C, 2369 Op->getType(), 2370 false)); 2371 else 2372 return V; 2373 } else { 2374 return V; 2375 } 2376 } 2377 } 2378 2379 Constant *C; 2380 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2381 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2382 &Operands[0], Operands.size()); 2383 else 2384 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2385 &Operands[0], Operands.size()); 2386 return SE.getUnknown(C); 2387 } 2388 } 2389 2390 // This is some other type of SCEVUnknown, just return it. 2391 return V; 2392 } 2393 2394 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2395 // Avoid performing the look-up in the common case where the specified 2396 // expression has no loop-variant portions. 2397 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2398 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2399 if (OpAtScope != Comm->getOperand(i)) { 2400 if (OpAtScope == UnknownValue) return UnknownValue; 2401 // Okay, at least one of these operands is loop variant but might be 2402 // foldable. Build a new instance of the folded commutative expression. 2403 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2404 NewOps.push_back(OpAtScope); 2405 2406 for (++i; i != e; ++i) { 2407 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2408 if (OpAtScope == UnknownValue) return UnknownValue; 2409 NewOps.push_back(OpAtScope); 2410 } 2411 if (isa<SCEVAddExpr>(Comm)) 2412 return SE.getAddExpr(NewOps); 2413 if (isa<SCEVMulExpr>(Comm)) 2414 return SE.getMulExpr(NewOps); 2415 if (isa<SCEVSMaxExpr>(Comm)) 2416 return SE.getSMaxExpr(NewOps); 2417 if (isa<SCEVUMaxExpr>(Comm)) 2418 return SE.getUMaxExpr(NewOps); 2419 assert(0 && "Unknown commutative SCEV type!"); 2420 } 2421 } 2422 // If we got here, all operands are loop invariant. 2423 return Comm; 2424 } 2425 2426 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2427 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2428 if (LHS == UnknownValue) return LHS; 2429 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2430 if (RHS == UnknownValue) return RHS; 2431 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2432 return Div; // must be loop invariant 2433 return SE.getUDivExpr(LHS, RHS); 2434 } 2435 2436 // If this is a loop recurrence for a loop that does not contain L, then we 2437 // are dealing with the final value computed by the loop. 2438 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2439 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2440 // To evaluate this recurrence, we need to know how many times the AddRec 2441 // loop iterates. Compute this now. 2442 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2443 if (IterationCount == UnknownValue) return UnknownValue; 2444 IterationCount = SE.getTruncateOrZeroExtend(IterationCount, 2445 AddRec->getType()); 2446 2447 // If the value is affine, simplify the expression evaluation to just 2448 // Start + Step*IterationCount. 2449 if (AddRec->isAffine()) 2450 return SE.getAddExpr(AddRec->getStart(), 2451 SE.getMulExpr(IterationCount, 2452 AddRec->getOperand(1))); 2453 2454 // Otherwise, evaluate it the hard way. 2455 return AddRec->evaluateAtIteration(IterationCount, SE); 2456 } 2457 return UnknownValue; 2458 } 2459 2460 //assert(0 && "Unknown SCEV type!"); 2461 return UnknownValue; 2462} 2463 2464 2465/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2466/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2467/// might be the same) or two SCEVCouldNotCompute objects. 2468/// 2469static std::pair<SCEVHandle,SCEVHandle> 2470SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2471 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2472 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2473 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2474 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2475 2476 // We currently can only solve this if the coefficients are constants. 2477 if (!LC || !MC || !NC) { 2478 SCEV *CNC = new SCEVCouldNotCompute(); 2479 return std::make_pair(CNC, CNC); 2480 } 2481 2482 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2483 const APInt &L = LC->getValue()->getValue(); 2484 const APInt &M = MC->getValue()->getValue(); 2485 const APInt &N = NC->getValue()->getValue(); 2486 APInt Two(BitWidth, 2); 2487 APInt Four(BitWidth, 4); 2488 2489 { 2490 using namespace APIntOps; 2491 const APInt& C = L; 2492 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2493 // The B coefficient is M-N/2 2494 APInt B(M); 2495 B -= sdiv(N,Two); 2496 2497 // The A coefficient is N/2 2498 APInt A(N.sdiv(Two)); 2499 2500 // Compute the B^2-4ac term. 2501 APInt SqrtTerm(B); 2502 SqrtTerm *= B; 2503 SqrtTerm -= Four * (A * C); 2504 2505 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2506 // integer value or else APInt::sqrt() will assert. 2507 APInt SqrtVal(SqrtTerm.sqrt()); 2508 2509 // Compute the two solutions for the quadratic formula. 2510 // The divisions must be performed as signed divisions. 2511 APInt NegB(-B); 2512 APInt TwoA( A << 1 ); 2513 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2514 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2515 2516 return std::make_pair(SE.getConstant(Solution1), 2517 SE.getConstant(Solution2)); 2518 } // end APIntOps namespace 2519} 2520 2521/// HowFarToZero - Return the number of times a backedge comparing the specified 2522/// value to zero will execute. If not computable, return UnknownValue 2523SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2524 // If the value is a constant 2525 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2526 // If the value is already zero, the branch will execute zero times. 2527 if (C->getValue()->isZero()) return C; 2528 return UnknownValue; // Otherwise it will loop infinitely. 2529 } 2530 2531 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2532 if (!AddRec || AddRec->getLoop() != L) 2533 return UnknownValue; 2534 2535 if (AddRec->isAffine()) { 2536 // If this is an affine expression the execution count of this branch is 2537 // equal to: 2538 // 2539 // (0 - Start/Step) iff Start % Step == 0 2540 // 2541 // Get the initial value for the loop. 2542 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2543 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2544 SCEVHandle Step = AddRec->getOperand(1); 2545 2546 Step = getSCEVAtScope(Step, L->getParentLoop()); 2547 2548 // Figure out if Start % Step == 0. 2549 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2550 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2551 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2552 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start 2553 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2554 return Start; // 0 - Start/-1 == Start 2555 2556 // Check to see if Start is divisible by SC with no remainder. 2557 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2558 ConstantInt *StartCC = StartC->getValue(); 2559 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2560 Constant *Rem = ConstantExpr::getURem(StartNegC, StepC->getValue()); 2561 if (Rem->isNullValue()) { 2562 Constant *Result = ConstantExpr::getUDiv(StartNegC,StepC->getValue()); 2563 return SE.getUnknown(Result); 2564 } 2565 } 2566 } 2567 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2568 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2569 // the quadratic equation to solve it. 2570 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2571 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2572 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2573 if (R1) { 2574#if 0 2575 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2576 << " sol#2: " << *R2 << "\n"; 2577#endif 2578 // Pick the smallest positive root value. 2579 if (ConstantInt *CB = 2580 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2581 R1->getValue(), R2->getValue()))) { 2582 if (CB->getZExtValue() == false) 2583 std::swap(R1, R2); // R1 is the minimum root now. 2584 2585 // We can only use this value if the chrec ends up with an exact zero 2586 // value at this index. When solving for "X*X != 5", for example, we 2587 // should not accept a root of 2. 2588 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2589 if (Val->isZero()) 2590 return R1; // We found a quadratic root! 2591 } 2592 } 2593 } 2594 2595 return UnknownValue; 2596} 2597 2598/// HowFarToNonZero - Return the number of times a backedge checking the 2599/// specified value for nonzero will execute. If not computable, return 2600/// UnknownValue 2601SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2602 // Loops that look like: while (X == 0) are very strange indeed. We don't 2603 // handle them yet except for the trivial case. This could be expanded in the 2604 // future as needed. 2605 2606 // If the value is a constant, check to see if it is known to be non-zero 2607 // already. If so, the backedge will execute zero times. 2608 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2609 if (!C->getValue()->isNullValue()) 2610 return SE.getIntegerSCEV(0, C->getType()); 2611 return UnknownValue; // Otherwise it will loop infinitely. 2612 } 2613 2614 // We could implement others, but I really doubt anyone writes loops like 2615 // this, and if they did, they would already be constant folded. 2616 return UnknownValue; 2617} 2618 2619/// executesAtLeastOnce - Test whether entry to the loop is protected by 2620/// a conditional between LHS and RHS. 2621bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned, 2622 SCEV *LHS, SCEV *RHS) { 2623 BasicBlock *Preheader = L->getLoopPreheader(); 2624 BasicBlock *PreheaderDest = L->getHeader(); 2625 if (Preheader == 0) return false; 2626 2627 BranchInst *LoopEntryPredicate = 2628 dyn_cast<BranchInst>(Preheader->getTerminator()); 2629 if (!LoopEntryPredicate) return false; 2630 2631 // This might be a critical edge broken out. If the loop preheader ends in 2632 // an unconditional branch to the loop, check to see if the preheader has a 2633 // single predecessor, and if so, look for its terminator. 2634 while (LoopEntryPredicate->isUnconditional()) { 2635 PreheaderDest = Preheader; 2636 Preheader = Preheader->getSinglePredecessor(); 2637 if (!Preheader) return false; // Multiple preds. 2638 2639 LoopEntryPredicate = 2640 dyn_cast<BranchInst>(Preheader->getTerminator()); 2641 if (!LoopEntryPredicate) return false; 2642 } 2643 2644 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2645 if (!ICI) return false; 2646 2647 // Now that we found a conditional branch that dominates the loop, check to 2648 // see if it is the comparison we are looking for. 2649 Value *PreCondLHS = ICI->getOperand(0); 2650 Value *PreCondRHS = ICI->getOperand(1); 2651 ICmpInst::Predicate Cond; 2652 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2653 Cond = ICI->getPredicate(); 2654 else 2655 Cond = ICI->getInversePredicate(); 2656 2657 switch (Cond) { 2658 case ICmpInst::ICMP_UGT: 2659 if (isSigned) return false; 2660 std::swap(PreCondLHS, PreCondRHS); 2661 Cond = ICmpInst::ICMP_ULT; 2662 break; 2663 case ICmpInst::ICMP_SGT: 2664 if (!isSigned) return false; 2665 std::swap(PreCondLHS, PreCondRHS); 2666 Cond = ICmpInst::ICMP_SLT; 2667 break; 2668 case ICmpInst::ICMP_ULT: 2669 if (isSigned) return false; 2670 break; 2671 case ICmpInst::ICMP_SLT: 2672 if (!isSigned) return false; 2673 break; 2674 default: 2675 return false; 2676 } 2677 2678 if (!PreCondLHS->getType()->isInteger()) return false; 2679 2680 return LHS == getSCEV(PreCondLHS) && RHS == getSCEV(PreCondRHS); 2681} 2682 2683/// HowManyLessThans - Return the number of times a backedge containing the 2684/// specified less-than comparison will execute. If not computable, return 2685/// UnknownValue. 2686SCEVHandle ScalarEvolutionsImpl:: 2687HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2688 // Only handle: "ADDREC < LoopInvariant". 2689 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2690 2691 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2692 if (!AddRec || AddRec->getLoop() != L) 2693 return UnknownValue; 2694 2695 if (AddRec->isAffine()) { 2696 // FORNOW: We only support unit strides. 2697 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2698 if (AddRec->getOperand(1) != One) 2699 return UnknownValue; 2700 2701 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2702 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2703 // Note that we cannot simply return max(m-n,0) because it's not safe to 2704 // treat m-n as signed nor unsigned due to overflow possibility. 2705 2706 // First, we get the value of the LHS in the first iteration: n 2707 SCEVHandle Start = AddRec->getOperand(0); 2708 2709 if (executesAtLeastOnce(L, isSigned, 2710 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2711 // Since we know that the condition is true in order to enter the loop, 2712 // we know that it will run exactly m-n times. 2713 return SE.getMinusSCEV(RHS, Start); 2714 } else { 2715 // Then, we get the value of the LHS in the first iteration in which the 2716 // above condition doesn't hold. This equals to max(m,n). 2717 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2718 : SE.getUMaxExpr(RHS, Start); 2719 2720 // Finally, we subtract these two values to get the number of times the 2721 // backedge is executed: max(m,n)-n. 2722 return SE.getMinusSCEV(End, Start); 2723 } 2724 } 2725 2726 return UnknownValue; 2727} 2728 2729/// getNumIterationsInRange - Return the number of iterations of this loop that 2730/// produce values in the specified constant range. Another way of looking at 2731/// this is that it returns the first iteration number where the value is not in 2732/// the condition, thus computing the exit count. If the iteration count can't 2733/// be computed, an instance of SCEVCouldNotCompute is returned. 2734SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2735 ScalarEvolution &SE) const { 2736 if (Range.isFullSet()) // Infinite loop. 2737 return new SCEVCouldNotCompute(); 2738 2739 // If the start is a non-zero constant, shift the range to simplify things. 2740 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2741 if (!SC->getValue()->isZero()) { 2742 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2743 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2744 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2745 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2746 return ShiftedAddRec->getNumIterationsInRange( 2747 Range.subtract(SC->getValue()->getValue()), SE); 2748 // This is strange and shouldn't happen. 2749 return new SCEVCouldNotCompute(); 2750 } 2751 2752 // The only time we can solve this is when we have all constant indices. 2753 // Otherwise, we cannot determine the overflow conditions. 2754 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2755 if (!isa<SCEVConstant>(getOperand(i))) 2756 return new SCEVCouldNotCompute(); 2757 2758 2759 // Okay at this point we know that all elements of the chrec are constants and 2760 // that the start element is zero. 2761 2762 // First check to see if the range contains zero. If not, the first 2763 // iteration exits. 2764 if (!Range.contains(APInt(getBitWidth(),0))) 2765 return SE.getConstant(ConstantInt::get(getType(),0)); 2766 2767 if (isAffine()) { 2768 // If this is an affine expression then we have this situation: 2769 // Solve {0,+,A} in Range === Ax in Range 2770 2771 // We know that zero is in the range. If A is positive then we know that 2772 // the upper value of the range must be the first possible exit value. 2773 // If A is negative then the lower of the range is the last possible loop 2774 // value. Also note that we already checked for a full range. 2775 APInt One(getBitWidth(),1); 2776 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2777 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2778 2779 // The exit value should be (End+A)/A. 2780 APInt ExitVal = (End + A).udiv(A); 2781 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2782 2783 // Evaluate at the exit value. If we really did fall out of the valid 2784 // range, then we computed our trip count, otherwise wrap around or other 2785 // things must have happened. 2786 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2787 if (Range.contains(Val->getValue())) 2788 return new SCEVCouldNotCompute(); // Something strange happened 2789 2790 // Ensure that the previous value is in the range. This is a sanity check. 2791 assert(Range.contains( 2792 EvaluateConstantChrecAtConstant(this, 2793 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2794 "Linear scev computation is off in a bad way!"); 2795 return SE.getConstant(ExitValue); 2796 } else if (isQuadratic()) { 2797 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2798 // quadratic equation to solve it. To do this, we must frame our problem in 2799 // terms of figuring out when zero is crossed, instead of when 2800 // Range.getUpper() is crossed. 2801 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2802 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2803 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2804 2805 // Next, solve the constructed addrec 2806 std::pair<SCEVHandle,SCEVHandle> Roots = 2807 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2808 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2809 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2810 if (R1) { 2811 // Pick the smallest positive root value. 2812 if (ConstantInt *CB = 2813 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2814 R1->getValue(), R2->getValue()))) { 2815 if (CB->getZExtValue() == false) 2816 std::swap(R1, R2); // R1 is the minimum root now. 2817 2818 // Make sure the root is not off by one. The returned iteration should 2819 // not be in the range, but the previous one should be. When solving 2820 // for "X*X < 5", for example, we should not return a root of 2. 2821 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2822 R1->getValue(), 2823 SE); 2824 if (Range.contains(R1Val->getValue())) { 2825 // The next iteration must be out of the range... 2826 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2827 2828 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2829 if (!Range.contains(R1Val->getValue())) 2830 return SE.getConstant(NextVal); 2831 return new SCEVCouldNotCompute(); // Something strange happened 2832 } 2833 2834 // If R1 was not in the range, then it is a good return value. Make 2835 // sure that R1-1 WAS in the range though, just in case. 2836 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2837 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2838 if (Range.contains(R1Val->getValue())) 2839 return R1; 2840 return new SCEVCouldNotCompute(); // Something strange happened 2841 } 2842 } 2843 } 2844 2845 // Fallback, if this is a general polynomial, figure out the progression 2846 // through brute force: evaluate until we find an iteration that fails the 2847 // test. This is likely to be slow, but getting an accurate trip count is 2848 // incredibly important, we will be able to simplify the exit test a lot, and 2849 // we are almost guaranteed to get a trip count in this case. 2850 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2851 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2852 do { 2853 ++NumBruteForceEvaluations; 2854 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2855 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2856 return new SCEVCouldNotCompute(); 2857 2858 // Check to see if we found the value! 2859 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2860 return SE.getConstant(TestVal); 2861 2862 // Increment to test the next index. 2863 TestVal = ConstantInt::get(TestVal->getValue()+1); 2864 } while (TestVal != EndVal); 2865 2866 return new SCEVCouldNotCompute(); 2867} 2868 2869 2870 2871//===----------------------------------------------------------------------===// 2872// ScalarEvolution Class Implementation 2873//===----------------------------------------------------------------------===// 2874 2875bool ScalarEvolution::runOnFunction(Function &F) { 2876 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2877 return false; 2878} 2879 2880void ScalarEvolution::releaseMemory() { 2881 delete (ScalarEvolutionsImpl*)Impl; 2882 Impl = 0; 2883} 2884 2885void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2886 AU.setPreservesAll(); 2887 AU.addRequiredTransitive<LoopInfo>(); 2888} 2889 2890SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2891 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2892} 2893 2894/// hasSCEV - Return true if the SCEV for this value has already been 2895/// computed. 2896bool ScalarEvolution::hasSCEV(Value *V) const { 2897 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2898} 2899 2900 2901/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2902/// the specified value. 2903void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2904 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2905} 2906 2907 2908SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2909 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2910} 2911 2912bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2913 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2914} 2915 2916SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2917 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2918} 2919 2920void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2921 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2922} 2923 2924static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2925 const Loop *L) { 2926 // Print all inner loops first 2927 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2928 PrintLoopInfo(OS, SE, *I); 2929 2930 OS << "Loop " << L->getHeader()->getName() << ": "; 2931 2932 SmallVector<BasicBlock*, 8> ExitBlocks; 2933 L->getExitBlocks(ExitBlocks); 2934 if (ExitBlocks.size() != 1) 2935 OS << "<multiple exits> "; 2936 2937 if (SE->hasLoopInvariantIterationCount(L)) { 2938 OS << *SE->getIterationCount(L) << " iterations! "; 2939 } else { 2940 OS << "Unpredictable iteration count. "; 2941 } 2942 2943 OS << "\n"; 2944} 2945 2946void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2947 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2948 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2949 2950 OS << "Classifying expressions for: " << F.getName() << "\n"; 2951 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2952 if (I->getType()->isInteger()) { 2953 OS << *I; 2954 OS << " --> "; 2955 SCEVHandle SV = getSCEV(&*I); 2956 SV->print(OS); 2957 OS << "\t\t"; 2958 2959 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2960 OS << "Exits: "; 2961 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2962 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2963 OS << "<<Unknown>>"; 2964 } else { 2965 OS << *ExitValue; 2966 } 2967 } 2968 2969 2970 OS << "\n"; 2971 } 2972 2973 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2974 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2975 PrintLoopInfo(OS, this, *I); 2976} 2977