ScalarEvolution.cpp revision 2ceb40f3da2290d37e9a4faa35bd5199e5dc90d5
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 unsigned DividendBits = K * It->getBitWidth(); 542 if (DividendBits > 256) 543 return new SCEVCouldNotCompute(); 544 545 const IntegerType *DividendTy = IntegerType::get(DividendBits); 546 const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy); 547 548 // The final number of bits we need to perform the division is the maximum of 549 // dividend and divisor bitwidths. 550 const IntegerType *DivisionTy = 551 IntegerType::get(std::max(DividendBits, 16U)); 552 553 // Compute K! We know K >= 2 here. 554 unsigned F = 2; 555 for (unsigned i = 3; i <= K; ++i) 556 F *= i; 557 APInt Divisor(DivisionTy->getBitWidth(), F); 558 559 // Handle this case efficiently, it is common to have constant iteration 560 // counts while computing loop exit values. 561 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) { 562 const APInt& N = SC->getValue()->getValue(); 563 APInt Dividend(N.getBitWidth(), 1); 564 for (; K; --K) 565 Dividend *= N-(K-1); 566 if (DividendTy != DivisionTy) 567 Dividend = Dividend.zext(DivisionTy->getBitWidth()); 568 return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth())); 569 } 570 571 SCEVHandle Dividend = ExIt; 572 for (unsigned i = 1; i != K; ++i) 573 Dividend = 574 SE.getMulExpr(Dividend, 575 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy))); 576 577 if (DividendTy != DivisionTy) 578 Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy); 579 return SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)), 580 It->getType()); 581} 582 583/// evaluateAtIteration - Return the value of this chain of recurrences at 584/// the specified iteration number. We can evaluate this recurrence by 585/// multiplying each element in the chain by the binomial coefficient 586/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 587/// 588/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 589/// 590/// where BC(It, k) stands for binomial coefficient. 591/// 592SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 593 ScalarEvolution &SE) const { 594 SCEVHandle Result = getStart(); 595 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 596 // The computation is correct in the face of overflow provided that the 597 // multiplication is performed _after_ the evaluation of the binomial 598 // coefficient. 599 SCEVHandle Val = SE.getMulExpr(getOperand(i), 600 BinomialCoefficient(It, i, SE)); 601 Result = SE.getAddExpr(Result, Val); 602 } 603 return Result; 604} 605 606//===----------------------------------------------------------------------===// 607// SCEV Expression folder implementations 608//===----------------------------------------------------------------------===// 609 610SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 611 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 612 return getUnknown( 613 ConstantExpr::getTrunc(SC->getValue(), Ty)); 614 615 // If the input value is a chrec scev made out of constants, truncate 616 // all of the constants. 617 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 618 std::vector<SCEVHandle> Operands; 619 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 620 // FIXME: This should allow truncation of other expression types! 621 if (isa<SCEVConstant>(AddRec->getOperand(i))) 622 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 623 else 624 break; 625 if (Operands.size() == AddRec->getNumOperands()) 626 return getAddRecExpr(Operands, AddRec->getLoop()); 627 } 628 629 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 630 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 631 return Result; 632} 633 634SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 635 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 636 return getUnknown( 637 ConstantExpr::getZExt(SC->getValue(), Ty)); 638 639 // FIXME: If the input value is a chrec scev, and we can prove that the value 640 // did not overflow the old, smaller, value, we can zero extend all of the 641 // operands (often constants). This would allow analysis of something like 642 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 643 644 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 645 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 646 return Result; 647} 648 649SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 650 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 651 return getUnknown( 652 ConstantExpr::getSExt(SC->getValue(), Ty)); 653 654 // FIXME: If the input value is a chrec scev, and we can prove that the value 655 // did not overflow the old, smaller, value, we can sign extend all of the 656 // operands (often constants). This would allow analysis of something like 657 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 658 659 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 660 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 661 return Result; 662} 663 664/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 665/// of the input value to the specified type. If the type must be 666/// extended, it is zero extended. 667SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 668 const Type *Ty) { 669 const Type *SrcTy = V->getType(); 670 assert(SrcTy->isInteger() && Ty->isInteger() && 671 "Cannot truncate or zero extend with non-integer arguments!"); 672 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 673 return V; // No conversion 674 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 675 return getTruncateExpr(V, Ty); 676 return getZeroExtendExpr(V, Ty); 677} 678 679// get - Get a canonical add expression, or something simpler if possible. 680SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 681 assert(!Ops.empty() && "Cannot get empty add!"); 682 if (Ops.size() == 1) return Ops[0]; 683 684 // Sort by complexity, this groups all similar expression types together. 685 GroupByComplexity(Ops); 686 687 // If there are any constants, fold them together. 688 unsigned Idx = 0; 689 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 690 ++Idx; 691 assert(Idx < Ops.size()); 692 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 693 // We found two constants, fold them together! 694 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 695 RHSC->getValue()->getValue()); 696 Ops[0] = getConstant(Fold); 697 Ops.erase(Ops.begin()+1); // Erase the folded element 698 if (Ops.size() == 1) return Ops[0]; 699 LHSC = cast<SCEVConstant>(Ops[0]); 700 } 701 702 // If we are left with a constant zero being added, strip it off. 703 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 704 Ops.erase(Ops.begin()); 705 --Idx; 706 } 707 } 708 709 if (Ops.size() == 1) return Ops[0]; 710 711 // Okay, check to see if the same value occurs in the operand list twice. If 712 // so, merge them together into an multiply expression. Since we sorted the 713 // list, these values are required to be adjacent. 714 const Type *Ty = Ops[0]->getType(); 715 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 716 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 717 // Found a match, merge the two values into a multiply, and add any 718 // remaining values to the result. 719 SCEVHandle Two = getIntegerSCEV(2, Ty); 720 SCEVHandle Mul = getMulExpr(Ops[i], Two); 721 if (Ops.size() == 2) 722 return Mul; 723 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 724 Ops.push_back(Mul); 725 return getAddExpr(Ops); 726 } 727 728 // Now we know the first non-constant operand. Skip past any cast SCEVs. 729 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 730 ++Idx; 731 732 // If there are add operands they would be next. 733 if (Idx < Ops.size()) { 734 bool DeletedAdd = false; 735 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 736 // If we have an add, expand the add operands onto the end of the operands 737 // list. 738 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 739 Ops.erase(Ops.begin()+Idx); 740 DeletedAdd = true; 741 } 742 743 // If we deleted at least one add, we added operands to the end of the list, 744 // and they are not necessarily sorted. Recurse to resort and resimplify 745 // any operands we just aquired. 746 if (DeletedAdd) 747 return getAddExpr(Ops); 748 } 749 750 // Skip over the add expression until we get to a multiply. 751 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 752 ++Idx; 753 754 // If we are adding something to a multiply expression, make sure the 755 // something is not already an operand of the multiply. If so, merge it into 756 // the multiply. 757 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 758 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 759 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 760 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 761 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 762 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 763 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 764 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 765 if (Mul->getNumOperands() != 2) { 766 // If the multiply has more than two operands, we must get the 767 // Y*Z term. 768 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 769 MulOps.erase(MulOps.begin()+MulOp); 770 InnerMul = getMulExpr(MulOps); 771 } 772 SCEVHandle One = getIntegerSCEV(1, Ty); 773 SCEVHandle AddOne = getAddExpr(InnerMul, One); 774 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 775 if (Ops.size() == 2) return OuterMul; 776 if (AddOp < Idx) { 777 Ops.erase(Ops.begin()+AddOp); 778 Ops.erase(Ops.begin()+Idx-1); 779 } else { 780 Ops.erase(Ops.begin()+Idx); 781 Ops.erase(Ops.begin()+AddOp-1); 782 } 783 Ops.push_back(OuterMul); 784 return getAddExpr(Ops); 785 } 786 787 // Check this multiply against other multiplies being added together. 788 for (unsigned OtherMulIdx = Idx+1; 789 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 790 ++OtherMulIdx) { 791 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 792 // If MulOp occurs in OtherMul, we can fold the two multiplies 793 // together. 794 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 795 OMulOp != e; ++OMulOp) 796 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 797 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 798 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 799 if (Mul->getNumOperands() != 2) { 800 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 801 MulOps.erase(MulOps.begin()+MulOp); 802 InnerMul1 = getMulExpr(MulOps); 803 } 804 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 805 if (OtherMul->getNumOperands() != 2) { 806 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 807 OtherMul->op_end()); 808 MulOps.erase(MulOps.begin()+OMulOp); 809 InnerMul2 = getMulExpr(MulOps); 810 } 811 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 812 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 813 if (Ops.size() == 2) return OuterMul; 814 Ops.erase(Ops.begin()+Idx); 815 Ops.erase(Ops.begin()+OtherMulIdx-1); 816 Ops.push_back(OuterMul); 817 return getAddExpr(Ops); 818 } 819 } 820 } 821 } 822 823 // If there are any add recurrences in the operands list, see if any other 824 // added values are loop invariant. If so, we can fold them into the 825 // recurrence. 826 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 827 ++Idx; 828 829 // Scan over all recurrences, trying to fold loop invariants into them. 830 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 831 // Scan all of the other operands to this add and add them to the vector if 832 // they are loop invariant w.r.t. the recurrence. 833 std::vector<SCEVHandle> LIOps; 834 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 835 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 836 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 837 LIOps.push_back(Ops[i]); 838 Ops.erase(Ops.begin()+i); 839 --i; --e; 840 } 841 842 // If we found some loop invariants, fold them into the recurrence. 843 if (!LIOps.empty()) { 844 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 845 LIOps.push_back(AddRec->getStart()); 846 847 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 848 AddRecOps[0] = getAddExpr(LIOps); 849 850 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 851 // If all of the other operands were loop invariant, we are done. 852 if (Ops.size() == 1) return NewRec; 853 854 // Otherwise, add the folded AddRec by the non-liv parts. 855 for (unsigned i = 0;; ++i) 856 if (Ops[i] == AddRec) { 857 Ops[i] = NewRec; 858 break; 859 } 860 return getAddExpr(Ops); 861 } 862 863 // Okay, if there weren't any loop invariants to be folded, check to see if 864 // there are multiple AddRec's with the same loop induction variable being 865 // added together. If so, we can fold them. 866 for (unsigned OtherIdx = Idx+1; 867 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 868 if (OtherIdx != Idx) { 869 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 870 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 871 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 872 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 873 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 874 if (i >= NewOps.size()) { 875 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 876 OtherAddRec->op_end()); 877 break; 878 } 879 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 880 } 881 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 882 883 if (Ops.size() == 2) return NewAddRec; 884 885 Ops.erase(Ops.begin()+Idx); 886 Ops.erase(Ops.begin()+OtherIdx-1); 887 Ops.push_back(NewAddRec); 888 return getAddExpr(Ops); 889 } 890 } 891 892 // Otherwise couldn't fold anything into this recurrence. Move onto the 893 // next one. 894 } 895 896 // Okay, it looks like we really DO need an add expr. Check to see if we 897 // already have one, otherwise create a new one. 898 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 899 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 900 SCEVOps)]; 901 if (Result == 0) Result = new SCEVAddExpr(Ops); 902 return Result; 903} 904 905 906SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 907 assert(!Ops.empty() && "Cannot get empty mul!"); 908 909 // Sort by complexity, this groups all similar expression types together. 910 GroupByComplexity(Ops); 911 912 // If there are any constants, fold them together. 913 unsigned Idx = 0; 914 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 915 916 // C1*(C2+V) -> C1*C2 + C1*V 917 if (Ops.size() == 2) 918 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 919 if (Add->getNumOperands() == 2 && 920 isa<SCEVConstant>(Add->getOperand(0))) 921 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 922 getMulExpr(LHSC, Add->getOperand(1))); 923 924 925 ++Idx; 926 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 927 // We found two constants, fold them together! 928 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 929 RHSC->getValue()->getValue()); 930 Ops[0] = getConstant(Fold); 931 Ops.erase(Ops.begin()+1); // Erase the folded element 932 if (Ops.size() == 1) return Ops[0]; 933 LHSC = cast<SCEVConstant>(Ops[0]); 934 } 935 936 // If we are left with a constant one being multiplied, strip it off. 937 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 938 Ops.erase(Ops.begin()); 939 --Idx; 940 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 941 // If we have a multiply of zero, it will always be zero. 942 return Ops[0]; 943 } 944 } 945 946 // Skip over the add expression until we get to a multiply. 947 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 948 ++Idx; 949 950 if (Ops.size() == 1) 951 return Ops[0]; 952 953 // If there are mul operands inline them all into this expression. 954 if (Idx < Ops.size()) { 955 bool DeletedMul = false; 956 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 957 // If we have an mul, expand the mul operands onto the end of the operands 958 // list. 959 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 960 Ops.erase(Ops.begin()+Idx); 961 DeletedMul = true; 962 } 963 964 // If we deleted at least one mul, we added operands to the end of the list, 965 // and they are not necessarily sorted. Recurse to resort and resimplify 966 // any operands we just aquired. 967 if (DeletedMul) 968 return getMulExpr(Ops); 969 } 970 971 // If there are any add recurrences in the operands list, see if any other 972 // added values are loop invariant. If so, we can fold them into the 973 // recurrence. 974 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 975 ++Idx; 976 977 // Scan over all recurrences, trying to fold loop invariants into them. 978 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 979 // Scan all of the other operands to this mul and add them to the vector if 980 // they are loop invariant w.r.t. the recurrence. 981 std::vector<SCEVHandle> LIOps; 982 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 983 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 984 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 985 LIOps.push_back(Ops[i]); 986 Ops.erase(Ops.begin()+i); 987 --i; --e; 988 } 989 990 // If we found some loop invariants, fold them into the recurrence. 991 if (!LIOps.empty()) { 992 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 993 std::vector<SCEVHandle> NewOps; 994 NewOps.reserve(AddRec->getNumOperands()); 995 if (LIOps.size() == 1) { 996 SCEV *Scale = LIOps[0]; 997 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 998 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 999 } else { 1000 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1001 std::vector<SCEVHandle> MulOps(LIOps); 1002 MulOps.push_back(AddRec->getOperand(i)); 1003 NewOps.push_back(getMulExpr(MulOps)); 1004 } 1005 } 1006 1007 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1008 1009 // If all of the other operands were loop invariant, we are done. 1010 if (Ops.size() == 1) return NewRec; 1011 1012 // Otherwise, multiply the folded AddRec by the non-liv parts. 1013 for (unsigned i = 0;; ++i) 1014 if (Ops[i] == AddRec) { 1015 Ops[i] = NewRec; 1016 break; 1017 } 1018 return getMulExpr(Ops); 1019 } 1020 1021 // Okay, if there weren't any loop invariants to be folded, check to see if 1022 // there are multiple AddRec's with the same loop induction variable being 1023 // multiplied together. If so, we can fold them. 1024 for (unsigned OtherIdx = Idx+1; 1025 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1026 if (OtherIdx != Idx) { 1027 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1028 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1029 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1030 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1031 SCEVHandle NewStart = getMulExpr(F->getStart(), 1032 G->getStart()); 1033 SCEVHandle B = F->getStepRecurrence(*this); 1034 SCEVHandle D = G->getStepRecurrence(*this); 1035 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1036 getMulExpr(G, B), 1037 getMulExpr(B, D)); 1038 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1039 F->getLoop()); 1040 if (Ops.size() == 2) return NewAddRec; 1041 1042 Ops.erase(Ops.begin()+Idx); 1043 Ops.erase(Ops.begin()+OtherIdx-1); 1044 Ops.push_back(NewAddRec); 1045 return getMulExpr(Ops); 1046 } 1047 } 1048 1049 // Otherwise couldn't fold anything into this recurrence. Move onto the 1050 // next one. 1051 } 1052 1053 // Okay, it looks like we really DO need an mul expr. Check to see if we 1054 // already have one, otherwise create a new one. 1055 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1056 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1057 SCEVOps)]; 1058 if (Result == 0) 1059 Result = new SCEVMulExpr(Ops); 1060 return Result; 1061} 1062 1063SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1064 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1065 if (RHSC->getValue()->equalsInt(1)) 1066 return LHS; // X udiv 1 --> x 1067 1068 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1069 Constant *LHSCV = LHSC->getValue(); 1070 Constant *RHSCV = RHSC->getValue(); 1071 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1072 } 1073 } 1074 1075 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1076 1077 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1078 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1079 return Result; 1080} 1081 1082 1083/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1084/// specified loop. Simplify the expression as much as possible. 1085SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1086 const SCEVHandle &Step, const Loop *L) { 1087 std::vector<SCEVHandle> Operands; 1088 Operands.push_back(Start); 1089 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1090 if (StepChrec->getLoop() == L) { 1091 Operands.insert(Operands.end(), StepChrec->op_begin(), 1092 StepChrec->op_end()); 1093 return getAddRecExpr(Operands, L); 1094 } 1095 1096 Operands.push_back(Step); 1097 return getAddRecExpr(Operands, L); 1098} 1099 1100/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1101/// specified loop. Simplify the expression as much as possible. 1102SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1103 const Loop *L) { 1104 if (Operands.size() == 1) return Operands[0]; 1105 1106 if (Operands.back()->isZero()) { 1107 Operands.pop_back(); 1108 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1109 } 1110 1111 SCEVAddRecExpr *&Result = 1112 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1113 Operands.end()))]; 1114 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1115 return Result; 1116} 1117 1118SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1119 const SCEVHandle &RHS) { 1120 std::vector<SCEVHandle> Ops; 1121 Ops.push_back(LHS); 1122 Ops.push_back(RHS); 1123 return getSMaxExpr(Ops); 1124} 1125 1126SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1127 assert(!Ops.empty() && "Cannot get empty smax!"); 1128 if (Ops.size() == 1) return Ops[0]; 1129 1130 // Sort by complexity, this groups all similar expression types together. 1131 GroupByComplexity(Ops); 1132 1133 // If there are any constants, fold them together. 1134 unsigned Idx = 0; 1135 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1136 ++Idx; 1137 assert(Idx < Ops.size()); 1138 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1139 // We found two constants, fold them together! 1140 ConstantInt *Fold = ConstantInt::get( 1141 APIntOps::smax(LHSC->getValue()->getValue(), 1142 RHSC->getValue()->getValue())); 1143 Ops[0] = getConstant(Fold); 1144 Ops.erase(Ops.begin()+1); // Erase the folded element 1145 if (Ops.size() == 1) return Ops[0]; 1146 LHSC = cast<SCEVConstant>(Ops[0]); 1147 } 1148 1149 // If we are left with a constant -inf, strip it off. 1150 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1151 Ops.erase(Ops.begin()); 1152 --Idx; 1153 } 1154 } 1155 1156 if (Ops.size() == 1) return Ops[0]; 1157 1158 // Find the first SMax 1159 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1160 ++Idx; 1161 1162 // Check to see if one of the operands is an SMax. If so, expand its operands 1163 // onto our operand list, and recurse to simplify. 1164 if (Idx < Ops.size()) { 1165 bool DeletedSMax = false; 1166 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1167 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1168 Ops.erase(Ops.begin()+Idx); 1169 DeletedSMax = true; 1170 } 1171 1172 if (DeletedSMax) 1173 return getSMaxExpr(Ops); 1174 } 1175 1176 // Okay, check to see if the same value occurs in the operand list twice. If 1177 // so, delete one. Since we sorted the list, these values are required to 1178 // be adjacent. 1179 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1180 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1181 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1182 --i; --e; 1183 } 1184 1185 if (Ops.size() == 1) return Ops[0]; 1186 1187 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1188 1189 // Okay, it looks like we really DO need an smax expr. Check to see if we 1190 // already have one, otherwise create a new one. 1191 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1192 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1193 SCEVOps)]; 1194 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1195 return Result; 1196} 1197 1198SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1199 const SCEVHandle &RHS) { 1200 std::vector<SCEVHandle> Ops; 1201 Ops.push_back(LHS); 1202 Ops.push_back(RHS); 1203 return getUMaxExpr(Ops); 1204} 1205 1206SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1207 assert(!Ops.empty() && "Cannot get empty umax!"); 1208 if (Ops.size() == 1) return Ops[0]; 1209 1210 // Sort by complexity, this groups all similar expression types together. 1211 GroupByComplexity(Ops); 1212 1213 // If there are any constants, fold them together. 1214 unsigned Idx = 0; 1215 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1216 ++Idx; 1217 assert(Idx < Ops.size()); 1218 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1219 // We found two constants, fold them together! 1220 ConstantInt *Fold = ConstantInt::get( 1221 APIntOps::umax(LHSC->getValue()->getValue(), 1222 RHSC->getValue()->getValue())); 1223 Ops[0] = getConstant(Fold); 1224 Ops.erase(Ops.begin()+1); // Erase the folded element 1225 if (Ops.size() == 1) return Ops[0]; 1226 LHSC = cast<SCEVConstant>(Ops[0]); 1227 } 1228 1229 // If we are left with a constant zero, strip it off. 1230 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1231 Ops.erase(Ops.begin()); 1232 --Idx; 1233 } 1234 } 1235 1236 if (Ops.size() == 1) return Ops[0]; 1237 1238 // Find the first UMax 1239 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1240 ++Idx; 1241 1242 // Check to see if one of the operands is a UMax. If so, expand its operands 1243 // onto our operand list, and recurse to simplify. 1244 if (Idx < Ops.size()) { 1245 bool DeletedUMax = false; 1246 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1247 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1248 Ops.erase(Ops.begin()+Idx); 1249 DeletedUMax = true; 1250 } 1251 1252 if (DeletedUMax) 1253 return getUMaxExpr(Ops); 1254 } 1255 1256 // Okay, check to see if the same value occurs in the operand list twice. If 1257 // so, delete one. Since we sorted the list, these values are required to 1258 // be adjacent. 1259 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1260 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1261 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1262 --i; --e; 1263 } 1264 1265 if (Ops.size() == 1) return Ops[0]; 1266 1267 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1268 1269 // Okay, it looks like we really DO need a umax expr. Check to see if we 1270 // already have one, otherwise create a new one. 1271 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1272 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1273 SCEVOps)]; 1274 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1275 return Result; 1276} 1277 1278SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1279 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1280 return getConstant(CI); 1281 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1282 if (Result == 0) Result = new SCEVUnknown(V); 1283 return Result; 1284} 1285 1286 1287//===----------------------------------------------------------------------===// 1288// ScalarEvolutionsImpl Definition and Implementation 1289//===----------------------------------------------------------------------===// 1290// 1291/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1292/// evolution code. 1293/// 1294namespace { 1295 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1296 /// SE - A reference to the public ScalarEvolution object. 1297 ScalarEvolution &SE; 1298 1299 /// F - The function we are analyzing. 1300 /// 1301 Function &F; 1302 1303 /// LI - The loop information for the function we are currently analyzing. 1304 /// 1305 LoopInfo &LI; 1306 1307 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1308 /// things. 1309 SCEVHandle UnknownValue; 1310 1311 /// Scalars - This is a cache of the scalars we have analyzed so far. 1312 /// 1313 std::map<Value*, SCEVHandle> Scalars; 1314 1315 /// IterationCounts - Cache the iteration count of the loops for this 1316 /// function as they are computed. 1317 std::map<const Loop*, SCEVHandle> IterationCounts; 1318 1319 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1320 /// the PHI instructions that we attempt to compute constant evolutions for. 1321 /// This allows us to avoid potentially expensive recomputation of these 1322 /// properties. An instruction maps to null if we are unable to compute its 1323 /// exit value. 1324 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1325 1326 public: 1327 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1328 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1329 1330 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1331 /// expression and create a new one. 1332 SCEVHandle getSCEV(Value *V); 1333 1334 /// hasSCEV - Return true if the SCEV for this value has already been 1335 /// computed. 1336 bool hasSCEV(Value *V) const { 1337 return Scalars.count(V); 1338 } 1339 1340 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1341 /// the specified value. 1342 void setSCEV(Value *V, const SCEVHandle &H) { 1343 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1344 assert(isNew && "This entry already existed!"); 1345 } 1346 1347 1348 /// getSCEVAtScope - Compute the value of the specified expression within 1349 /// the indicated loop (which may be null to indicate in no loop). If the 1350 /// expression cannot be evaluated, return UnknownValue itself. 1351 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1352 1353 1354 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1355 /// an analyzable loop-invariant iteration count. 1356 bool hasLoopInvariantIterationCount(const Loop *L); 1357 1358 /// getIterationCount - If the specified loop has a predictable iteration 1359 /// count, return it. Note that it is not valid to call this method on a 1360 /// loop without a loop-invariant iteration count. 1361 SCEVHandle getIterationCount(const Loop *L); 1362 1363 /// deleteValueFromRecords - This method should be called by the 1364 /// client before it removes a value from the program, to make sure 1365 /// that no dangling references are left around. 1366 void deleteValueFromRecords(Value *V); 1367 1368 private: 1369 /// createSCEV - We know that there is no SCEV for the specified value. 1370 /// Analyze the expression. 1371 SCEVHandle createSCEV(Value *V); 1372 1373 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1374 /// SCEVs. 1375 SCEVHandle createNodeForPHI(PHINode *PN); 1376 1377 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1378 /// for the specified instruction and replaces any references to the 1379 /// symbolic value SymName with the specified value. This is used during 1380 /// PHI resolution. 1381 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1382 const SCEVHandle &SymName, 1383 const SCEVHandle &NewVal); 1384 1385 /// ComputeIterationCount - Compute the number of times the specified loop 1386 /// will iterate. 1387 SCEVHandle ComputeIterationCount(const Loop *L); 1388 1389 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1390 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1391 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1392 Constant *RHS, 1393 const Loop *L, 1394 ICmpInst::Predicate p); 1395 1396 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1397 /// constant number of times (the condition evolves only from constants), 1398 /// try to evaluate a few iterations of the loop until we get the exit 1399 /// condition gets a value of ExitWhen (true or false). If we cannot 1400 /// evaluate the trip count of the loop, return UnknownValue. 1401 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1402 bool ExitWhen); 1403 1404 /// HowFarToZero - Return the number of times a backedge comparing the 1405 /// specified value to zero will execute. If not computable, return 1406 /// UnknownValue. 1407 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1408 1409 /// HowFarToNonZero - Return the number of times a backedge checking the 1410 /// specified value for nonzero will execute. If not computable, return 1411 /// UnknownValue. 1412 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1413 1414 /// HowManyLessThans - Return the number of times a backedge containing the 1415 /// specified less-than comparison will execute. If not computable, return 1416 /// UnknownValue. isSigned specifies whether the less-than is signed. 1417 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1418 bool isSigned); 1419 1420 /// executesAtLeastOnce - Test whether entry to the loop is protected by 1421 /// a conditional between LHS and RHS. 1422 bool executesAtLeastOnce(const Loop *L, bool isSigned, SCEV *LHS, SCEV *RHS); 1423 1424 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1425 /// in the header of its containing loop, we know the loop executes a 1426 /// constant number of times, and the PHI node is just a recurrence 1427 /// involving constants, fold it. 1428 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1429 const Loop *L); 1430 }; 1431} 1432 1433//===----------------------------------------------------------------------===// 1434// Basic SCEV Analysis and PHI Idiom Recognition Code 1435// 1436 1437/// deleteValueFromRecords - This method should be called by the 1438/// client before it removes an instruction from the program, to make sure 1439/// that no dangling references are left around. 1440void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1441 SmallVector<Value *, 16> Worklist; 1442 1443 if (Scalars.erase(V)) { 1444 if (PHINode *PN = dyn_cast<PHINode>(V)) 1445 ConstantEvolutionLoopExitValue.erase(PN); 1446 Worklist.push_back(V); 1447 } 1448 1449 while (!Worklist.empty()) { 1450 Value *VV = Worklist.back(); 1451 Worklist.pop_back(); 1452 1453 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1454 UI != UE; ++UI) { 1455 Instruction *Inst = cast<Instruction>(*UI); 1456 if (Scalars.erase(Inst)) { 1457 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1458 ConstantEvolutionLoopExitValue.erase(PN); 1459 Worklist.push_back(Inst); 1460 } 1461 } 1462 } 1463} 1464 1465 1466/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1467/// expression and create a new one. 1468SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1469 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1470 1471 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1472 if (I != Scalars.end()) return I->second; 1473 SCEVHandle S = createSCEV(V); 1474 Scalars.insert(std::make_pair(V, S)); 1475 return S; 1476} 1477 1478/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1479/// the specified instruction and replaces any references to the symbolic value 1480/// SymName with the specified value. This is used during PHI resolution. 1481void ScalarEvolutionsImpl:: 1482ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1483 const SCEVHandle &NewVal) { 1484 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1485 if (SI == Scalars.end()) return; 1486 1487 SCEVHandle NV = 1488 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1489 if (NV == SI->second) return; // No change. 1490 1491 SI->second = NV; // Update the scalars map! 1492 1493 // Any instruction values that use this instruction might also need to be 1494 // updated! 1495 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1496 UI != E; ++UI) 1497 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1498} 1499 1500/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1501/// a loop header, making it a potential recurrence, or it doesn't. 1502/// 1503SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1504 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1505 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1506 if (L->getHeader() == PN->getParent()) { 1507 // If it lives in the loop header, it has two incoming values, one 1508 // from outside the loop, and one from inside. 1509 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1510 unsigned BackEdge = IncomingEdge^1; 1511 1512 // While we are analyzing this PHI node, handle its value symbolically. 1513 SCEVHandle SymbolicName = SE.getUnknown(PN); 1514 assert(Scalars.find(PN) == Scalars.end() && 1515 "PHI node already processed?"); 1516 Scalars.insert(std::make_pair(PN, SymbolicName)); 1517 1518 // Using this symbolic name for the PHI, analyze the value coming around 1519 // the back-edge. 1520 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1521 1522 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1523 // has a special value for the first iteration of the loop. 1524 1525 // If the value coming around the backedge is an add with the symbolic 1526 // value we just inserted, then we found a simple induction variable! 1527 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1528 // If there is a single occurrence of the symbolic value, replace it 1529 // with a recurrence. 1530 unsigned FoundIndex = Add->getNumOperands(); 1531 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1532 if (Add->getOperand(i) == SymbolicName) 1533 if (FoundIndex == e) { 1534 FoundIndex = i; 1535 break; 1536 } 1537 1538 if (FoundIndex != Add->getNumOperands()) { 1539 // Create an add with everything but the specified operand. 1540 std::vector<SCEVHandle> Ops; 1541 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1542 if (i != FoundIndex) 1543 Ops.push_back(Add->getOperand(i)); 1544 SCEVHandle Accum = SE.getAddExpr(Ops); 1545 1546 // This is not a valid addrec if the step amount is varying each 1547 // loop iteration, but is not itself an addrec in this loop. 1548 if (Accum->isLoopInvariant(L) || 1549 (isa<SCEVAddRecExpr>(Accum) && 1550 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1551 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1552 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1553 1554 // Okay, for the entire analysis of this edge we assumed the PHI 1555 // to be symbolic. We now need to go back and update all of the 1556 // entries for the scalars that use the PHI (except for the PHI 1557 // itself) to use the new analyzed value instead of the "symbolic" 1558 // value. 1559 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1560 return PHISCEV; 1561 } 1562 } 1563 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1564 // Otherwise, this could be a loop like this: 1565 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1566 // In this case, j = {1,+,1} and BEValue is j. 1567 // Because the other in-value of i (0) fits the evolution of BEValue 1568 // i really is an addrec evolution. 1569 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1570 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1571 1572 // If StartVal = j.start - j.stride, we can use StartVal as the 1573 // initial step of the addrec evolution. 1574 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1575 AddRec->getOperand(1))) { 1576 SCEVHandle PHISCEV = 1577 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1578 1579 // Okay, for the entire analysis of this edge we assumed the PHI 1580 // to be symbolic. We now need to go back and update all of the 1581 // entries for the scalars that use the PHI (except for the PHI 1582 // itself) to use the new analyzed value instead of the "symbolic" 1583 // value. 1584 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1585 return PHISCEV; 1586 } 1587 } 1588 } 1589 1590 return SymbolicName; 1591 } 1592 1593 // If it's not a loop phi, we can't handle it yet. 1594 return SE.getUnknown(PN); 1595} 1596 1597/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1598/// guaranteed to end in (at every loop iteration). It is, at the same time, 1599/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1600/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1601static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1602 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1603 return C->getValue()->getValue().countTrailingZeros(); 1604 1605 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1606 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1607 1608 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1609 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1610 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1611 } 1612 1613 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1614 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1615 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1616 } 1617 1618 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1619 // The result is the min of all operands results. 1620 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1621 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1622 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1623 return MinOpRes; 1624 } 1625 1626 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1627 // The result is the sum of all operands results. 1628 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1629 uint32_t BitWidth = M->getBitWidth(); 1630 for (unsigned i = 1, e = M->getNumOperands(); 1631 SumOpRes != BitWidth && i != e; ++i) 1632 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1633 BitWidth); 1634 return SumOpRes; 1635 } 1636 1637 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1638 // The result is the min of all operands results. 1639 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1640 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1641 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1642 return MinOpRes; 1643 } 1644 1645 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1646 // The result is the min of all operands results. 1647 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1648 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1649 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1650 return MinOpRes; 1651 } 1652 1653 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1654 // The result is the min of all operands results. 1655 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1656 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1658 return MinOpRes; 1659 } 1660 1661 // SCEVUDivExpr, SCEVUnknown 1662 return 0; 1663} 1664 1665/// createSCEV - We know that there is no SCEV for the specified value. 1666/// Analyze the expression. 1667/// 1668SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1669 if (!isa<IntegerType>(V->getType())) 1670 return SE.getUnknown(V); 1671 1672 unsigned Opcode = Instruction::UserOp1; 1673 if (Instruction *I = dyn_cast<Instruction>(V)) 1674 Opcode = I->getOpcode(); 1675 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1676 Opcode = CE->getOpcode(); 1677 else 1678 return SE.getUnknown(V); 1679 1680 User *U = cast<User>(V); 1681 switch (Opcode) { 1682 case Instruction::Add: 1683 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1684 getSCEV(U->getOperand(1))); 1685 case Instruction::Mul: 1686 return SE.getMulExpr(getSCEV(U->getOperand(0)), 1687 getSCEV(U->getOperand(1))); 1688 case Instruction::UDiv: 1689 return SE.getUDivExpr(getSCEV(U->getOperand(0)), 1690 getSCEV(U->getOperand(1))); 1691 case Instruction::Sub: 1692 return SE.getMinusSCEV(getSCEV(U->getOperand(0)), 1693 getSCEV(U->getOperand(1))); 1694 case Instruction::Or: 1695 // If the RHS of the Or is a constant, we may have something like: 1696 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1697 // optimizations will transparently handle this case. 1698 // 1699 // In order for this transformation to be safe, the LHS must be of the 1700 // form X*(2^n) and the Or constant must be less than 2^n. 1701 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1702 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1703 const APInt &CIVal = CI->getValue(); 1704 if (GetMinTrailingZeros(LHS) >= 1705 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1706 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1))); 1707 } 1708 break; 1709 case Instruction::Xor: 1710 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1711 // If the RHS of the xor is a signbit, then this is just an add. 1712 // Instcombine turns add of signbit into xor as a strength reduction step. 1713 if (CI->getValue().isSignBit()) 1714 return SE.getAddExpr(getSCEV(U->getOperand(0)), 1715 getSCEV(U->getOperand(1))); 1716 1717 // If the RHS of xor is -1, then this is a not operation. 1718 else if (CI->isAllOnesValue()) 1719 return SE.getNotSCEV(getSCEV(U->getOperand(0))); 1720 } 1721 break; 1722 1723 case Instruction::Shl: 1724 // Turn shift left of a constant amount into a multiply. 1725 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1726 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1727 Constant *X = ConstantInt::get( 1728 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1729 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1730 } 1731 break; 1732 1733 case Instruction::LShr: 1734 // Turn logical shift right of a constant into a unsigned divide. 1735 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1736 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1737 Constant *X = ConstantInt::get( 1738 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1739 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1740 } 1741 break; 1742 1743 case Instruction::Trunc: 1744 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1745 1746 case Instruction::ZExt: 1747 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1748 1749 case Instruction::SExt: 1750 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1751 1752 case Instruction::BitCast: 1753 // BitCasts are no-op casts so we just eliminate the cast. 1754 if (U->getType()->isInteger() && 1755 U->getOperand(0)->getType()->isInteger()) 1756 return getSCEV(U->getOperand(0)); 1757 break; 1758 1759 case Instruction::PHI: 1760 return createNodeForPHI(cast<PHINode>(U)); 1761 1762 case Instruction::Select: 1763 // This could be a smax or umax that was lowered earlier. 1764 // Try to recover it. 1765 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1766 Value *LHS = ICI->getOperand(0); 1767 Value *RHS = ICI->getOperand(1); 1768 switch (ICI->getPredicate()) { 1769 case ICmpInst::ICMP_SLT: 1770 case ICmpInst::ICMP_SLE: 1771 std::swap(LHS, RHS); 1772 // fall through 1773 case ICmpInst::ICMP_SGT: 1774 case ICmpInst::ICMP_SGE: 1775 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1776 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1777 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1778 // -smax(-x, -y) == smin(x, y). 1779 return SE.getNegativeSCEV(SE.getSMaxExpr( 1780 SE.getNegativeSCEV(getSCEV(LHS)), 1781 SE.getNegativeSCEV(getSCEV(RHS)))); 1782 break; 1783 case ICmpInst::ICMP_ULT: 1784 case ICmpInst::ICMP_ULE: 1785 std::swap(LHS, RHS); 1786 // fall through 1787 case ICmpInst::ICMP_UGT: 1788 case ICmpInst::ICMP_UGE: 1789 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1790 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1791 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1792 // ~umax(~x, ~y) == umin(x, y) 1793 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1794 SE.getNotSCEV(getSCEV(RHS)))); 1795 break; 1796 default: 1797 break; 1798 } 1799 } 1800 1801 default: // We cannot analyze this expression. 1802 break; 1803 } 1804 1805 return SE.getUnknown(V); 1806} 1807 1808 1809 1810//===----------------------------------------------------------------------===// 1811// Iteration Count Computation Code 1812// 1813 1814/// getIterationCount - If the specified loop has a predictable iteration 1815/// count, return it. Note that it is not valid to call this method on a 1816/// loop without a loop-invariant iteration count. 1817SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1818 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1819 if (I == IterationCounts.end()) { 1820 SCEVHandle ItCount = ComputeIterationCount(L); 1821 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1822 if (ItCount != UnknownValue) { 1823 assert(ItCount->isLoopInvariant(L) && 1824 "Computed trip count isn't loop invariant for loop!"); 1825 ++NumTripCountsComputed; 1826 } else if (isa<PHINode>(L->getHeader()->begin())) { 1827 // Only count loops that have phi nodes as not being computable. 1828 ++NumTripCountsNotComputed; 1829 } 1830 } 1831 return I->second; 1832} 1833 1834/// ComputeIterationCount - Compute the number of times the specified loop 1835/// will iterate. 1836SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1837 // If the loop has a non-one exit block count, we can't analyze it. 1838 SmallVector<BasicBlock*, 8> ExitBlocks; 1839 L->getExitBlocks(ExitBlocks); 1840 if (ExitBlocks.size() != 1) return UnknownValue; 1841 1842 // Okay, there is one exit block. Try to find the condition that causes the 1843 // loop to be exited. 1844 BasicBlock *ExitBlock = ExitBlocks[0]; 1845 1846 BasicBlock *ExitingBlock = 0; 1847 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1848 PI != E; ++PI) 1849 if (L->contains(*PI)) { 1850 if (ExitingBlock == 0) 1851 ExitingBlock = *PI; 1852 else 1853 return UnknownValue; // More than one block exiting! 1854 } 1855 assert(ExitingBlock && "No exits from loop, something is broken!"); 1856 1857 // Okay, we've computed the exiting block. See what condition causes us to 1858 // exit. 1859 // 1860 // FIXME: we should be able to handle switch instructions (with a single exit) 1861 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1862 if (ExitBr == 0) return UnknownValue; 1863 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1864 1865 // At this point, we know we have a conditional branch that determines whether 1866 // the loop is exited. However, we don't know if the branch is executed each 1867 // time through the loop. If not, then the execution count of the branch will 1868 // not be equal to the trip count of the loop. 1869 // 1870 // Currently we check for this by checking to see if the Exit branch goes to 1871 // the loop header. If so, we know it will always execute the same number of 1872 // times as the loop. We also handle the case where the exit block *is* the 1873 // loop header. This is common for un-rotated loops. More extensive analysis 1874 // could be done to handle more cases here. 1875 if (ExitBr->getSuccessor(0) != L->getHeader() && 1876 ExitBr->getSuccessor(1) != L->getHeader() && 1877 ExitBr->getParent() != L->getHeader()) 1878 return UnknownValue; 1879 1880 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1881 1882 // If it's not an integer comparison then compute it the hard way. 1883 // Note that ICmpInst deals with pointer comparisons too so we must check 1884 // the type of the operand. 1885 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1886 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1887 ExitBr->getSuccessor(0) == ExitBlock); 1888 1889 // If the condition was exit on true, convert the condition to exit on false 1890 ICmpInst::Predicate Cond; 1891 if (ExitBr->getSuccessor(1) == ExitBlock) 1892 Cond = ExitCond->getPredicate(); 1893 else 1894 Cond = ExitCond->getInversePredicate(); 1895 1896 // Handle common loops like: for (X = "string"; *X; ++X) 1897 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1898 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1899 SCEVHandle ItCnt = 1900 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1901 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1902 } 1903 1904 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1905 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1906 1907 // Try to evaluate any dependencies out of the loop. 1908 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1909 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1910 Tmp = getSCEVAtScope(RHS, L); 1911 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1912 1913 // At this point, we would like to compute how many iterations of the 1914 // loop the predicate will return true for these inputs. 1915 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1916 // If there is a constant, force it into the RHS. 1917 std::swap(LHS, RHS); 1918 Cond = ICmpInst::getSwappedPredicate(Cond); 1919 } 1920 1921 // FIXME: think about handling pointer comparisons! i.e.: 1922 // while (P != P+100) ++P; 1923 1924 // If we have a comparison of a chrec against a constant, try to use value 1925 // ranges to answer this query. 1926 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1927 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1928 if (AddRec->getLoop() == L) { 1929 // Form the comparison range using the constant of the correct type so 1930 // that the ConstantRange class knows to do a signed or unsigned 1931 // comparison. 1932 ConstantInt *CompVal = RHSC->getValue(); 1933 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1934 CompVal = dyn_cast<ConstantInt>( 1935 ConstantExpr::getBitCast(CompVal, RealTy)); 1936 if (CompVal) { 1937 // Form the constant range. 1938 ConstantRange CompRange( 1939 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1940 1941 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1942 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1943 } 1944 } 1945 1946 switch (Cond) { 1947 case ICmpInst::ICMP_NE: { // while (X != Y) 1948 // Convert to: while (X-Y != 0) 1949 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1950 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1951 break; 1952 } 1953 case ICmpInst::ICMP_EQ: { 1954 // Convert to: while (X-Y == 0) // while (X == Y) 1955 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1956 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1957 break; 1958 } 1959 case ICmpInst::ICMP_SLT: { 1960 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1961 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1962 break; 1963 } 1964 case ICmpInst::ICMP_SGT: { 1965 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1966 SE.getNegativeSCEV(RHS), L, true); 1967 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1968 break; 1969 } 1970 case ICmpInst::ICMP_ULT: { 1971 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1972 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1973 break; 1974 } 1975 case ICmpInst::ICMP_UGT: { 1976 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 1977 SE.getNotSCEV(RHS), L, false); 1978 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1979 break; 1980 } 1981 default: 1982#if 0 1983 cerr << "ComputeIterationCount "; 1984 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1985 cerr << "[unsigned] "; 1986 cerr << *LHS << " " 1987 << Instruction::getOpcodeName(Instruction::ICmp) 1988 << " " << *RHS << "\n"; 1989#endif 1990 break; 1991 } 1992 return ComputeIterationCountExhaustively(L, ExitCond, 1993 ExitBr->getSuccessor(0) == ExitBlock); 1994} 1995 1996static ConstantInt * 1997EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 1998 ScalarEvolution &SE) { 1999 SCEVHandle InVal = SE.getConstant(C); 2000 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2001 assert(isa<SCEVConstant>(Val) && 2002 "Evaluation of SCEV at constant didn't fold correctly?"); 2003 return cast<SCEVConstant>(Val)->getValue(); 2004} 2005 2006/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2007/// and a GEP expression (missing the pointer index) indexing into it, return 2008/// the addressed element of the initializer or null if the index expression is 2009/// invalid. 2010static Constant * 2011GetAddressedElementFromGlobal(GlobalVariable *GV, 2012 const std::vector<ConstantInt*> &Indices) { 2013 Constant *Init = GV->getInitializer(); 2014 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2015 uint64_t Idx = Indices[i]->getZExtValue(); 2016 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2017 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2018 Init = cast<Constant>(CS->getOperand(Idx)); 2019 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2020 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2021 Init = cast<Constant>(CA->getOperand(Idx)); 2022 } else if (isa<ConstantAggregateZero>(Init)) { 2023 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2024 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2025 Init = Constant::getNullValue(STy->getElementType(Idx)); 2026 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2027 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2028 Init = Constant::getNullValue(ATy->getElementType()); 2029 } else { 2030 assert(0 && "Unknown constant aggregate type!"); 2031 } 2032 return 0; 2033 } else { 2034 return 0; // Unknown initializer type 2035 } 2036 } 2037 return Init; 2038} 2039 2040/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2041/// 'icmp op load X, cst', try to see if we can compute the trip count. 2042SCEVHandle ScalarEvolutionsImpl:: 2043ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2044 const Loop *L, 2045 ICmpInst::Predicate predicate) { 2046 if (LI->isVolatile()) return UnknownValue; 2047 2048 // Check to see if the loaded pointer is a getelementptr of a global. 2049 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2050 if (!GEP) return UnknownValue; 2051 2052 // Make sure that it is really a constant global we are gepping, with an 2053 // initializer, and make sure the first IDX is really 0. 2054 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2055 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2056 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2057 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2058 return UnknownValue; 2059 2060 // Okay, we allow one non-constant index into the GEP instruction. 2061 Value *VarIdx = 0; 2062 std::vector<ConstantInt*> Indexes; 2063 unsigned VarIdxNum = 0; 2064 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2065 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2066 Indexes.push_back(CI); 2067 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2068 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2069 VarIdx = GEP->getOperand(i); 2070 VarIdxNum = i-2; 2071 Indexes.push_back(0); 2072 } 2073 2074 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2075 // Check to see if X is a loop variant variable value now. 2076 SCEVHandle Idx = getSCEV(VarIdx); 2077 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2078 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2079 2080 // We can only recognize very limited forms of loop index expressions, in 2081 // particular, only affine AddRec's like {C1,+,C2}. 2082 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2083 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2084 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2085 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2086 return UnknownValue; 2087 2088 unsigned MaxSteps = MaxBruteForceIterations; 2089 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2090 ConstantInt *ItCst = 2091 ConstantInt::get(IdxExpr->getType(), IterationNum); 2092 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2093 2094 // Form the GEP offset. 2095 Indexes[VarIdxNum] = Val; 2096 2097 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2098 if (Result == 0) break; // Cannot compute! 2099 2100 // Evaluate the condition for this iteration. 2101 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2102 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2103 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2104#if 0 2105 cerr << "\n***\n*** Computed loop count " << *ItCst 2106 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2107 << "***\n"; 2108#endif 2109 ++NumArrayLenItCounts; 2110 return SE.getConstant(ItCst); // Found terminating iteration! 2111 } 2112 } 2113 return UnknownValue; 2114} 2115 2116 2117/// CanConstantFold - Return true if we can constant fold an instruction of the 2118/// specified type, assuming that all operands were constants. 2119static bool CanConstantFold(const Instruction *I) { 2120 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2121 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2122 return true; 2123 2124 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2125 if (const Function *F = CI->getCalledFunction()) 2126 return canConstantFoldCallTo(F); 2127 return false; 2128} 2129 2130/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2131/// in the loop that V is derived from. We allow arbitrary operations along the 2132/// way, but the operands of an operation must either be constants or a value 2133/// derived from a constant PHI. If this expression does not fit with these 2134/// constraints, return null. 2135static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2136 // If this is not an instruction, or if this is an instruction outside of the 2137 // loop, it can't be derived from a loop PHI. 2138 Instruction *I = dyn_cast<Instruction>(V); 2139 if (I == 0 || !L->contains(I->getParent())) return 0; 2140 2141 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2142 if (L->getHeader() == I->getParent()) 2143 return PN; 2144 else 2145 // We don't currently keep track of the control flow needed to evaluate 2146 // PHIs, so we cannot handle PHIs inside of loops. 2147 return 0; 2148 } 2149 2150 // If we won't be able to constant fold this expression even if the operands 2151 // are constants, return early. 2152 if (!CanConstantFold(I)) return 0; 2153 2154 // Otherwise, we can evaluate this instruction if all of its operands are 2155 // constant or derived from a PHI node themselves. 2156 PHINode *PHI = 0; 2157 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2158 if (!(isa<Constant>(I->getOperand(Op)) || 2159 isa<GlobalValue>(I->getOperand(Op)))) { 2160 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2161 if (P == 0) return 0; // Not evolving from PHI 2162 if (PHI == 0) 2163 PHI = P; 2164 else if (PHI != P) 2165 return 0; // Evolving from multiple different PHIs. 2166 } 2167 2168 // This is a expression evolving from a constant PHI! 2169 return PHI; 2170} 2171 2172/// EvaluateExpression - Given an expression that passes the 2173/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2174/// in the loop has the value PHIVal. If we can't fold this expression for some 2175/// reason, return null. 2176static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2177 if (isa<PHINode>(V)) return PHIVal; 2178 if (Constant *C = dyn_cast<Constant>(V)) return C; 2179 Instruction *I = cast<Instruction>(V); 2180 2181 std::vector<Constant*> Operands; 2182 Operands.resize(I->getNumOperands()); 2183 2184 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2185 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2186 if (Operands[i] == 0) return 0; 2187 } 2188 2189 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2190 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2191 &Operands[0], Operands.size()); 2192 else 2193 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2194 &Operands[0], Operands.size()); 2195} 2196 2197/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2198/// in the header of its containing loop, we know the loop executes a 2199/// constant number of times, and the PHI node is just a recurrence 2200/// involving constants, fold it. 2201Constant *ScalarEvolutionsImpl:: 2202getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2203 std::map<PHINode*, Constant*>::iterator I = 2204 ConstantEvolutionLoopExitValue.find(PN); 2205 if (I != ConstantEvolutionLoopExitValue.end()) 2206 return I->second; 2207 2208 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2209 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2210 2211 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2212 2213 // Since the loop is canonicalized, the PHI node must have two entries. One 2214 // entry must be a constant (coming in from outside of the loop), and the 2215 // second must be derived from the same PHI. 2216 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2217 Constant *StartCST = 2218 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2219 if (StartCST == 0) 2220 return RetVal = 0; // Must be a constant. 2221 2222 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2223 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2224 if (PN2 != PN) 2225 return RetVal = 0; // Not derived from same PHI. 2226 2227 // Execute the loop symbolically to determine the exit value. 2228 if (Its.getActiveBits() >= 32) 2229 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2230 2231 unsigned NumIterations = Its.getZExtValue(); // must be in range 2232 unsigned IterationNum = 0; 2233 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2234 if (IterationNum == NumIterations) 2235 return RetVal = PHIVal; // Got exit value! 2236 2237 // Compute the value of the PHI node for the next iteration. 2238 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2239 if (NextPHI == PHIVal) 2240 return RetVal = NextPHI; // Stopped evolving! 2241 if (NextPHI == 0) 2242 return 0; // Couldn't evaluate! 2243 PHIVal = NextPHI; 2244 } 2245} 2246 2247/// ComputeIterationCountExhaustively - If the trip is known to execute a 2248/// constant number of times (the condition evolves only from constants), 2249/// try to evaluate a few iterations of the loop until we get the exit 2250/// condition gets a value of ExitWhen (true or false). If we cannot 2251/// evaluate the trip count of the loop, return UnknownValue. 2252SCEVHandle ScalarEvolutionsImpl:: 2253ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2254 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2255 if (PN == 0) return UnknownValue; 2256 2257 // Since the loop is canonicalized, the PHI node must have two entries. One 2258 // entry must be a constant (coming in from outside of the loop), and the 2259 // second must be derived from the same PHI. 2260 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2261 Constant *StartCST = 2262 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2263 if (StartCST == 0) return UnknownValue; // Must be a constant. 2264 2265 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2266 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2267 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2268 2269 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2270 // the loop symbolically to determine when the condition gets a value of 2271 // "ExitWhen". 2272 unsigned IterationNum = 0; 2273 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2274 for (Constant *PHIVal = StartCST; 2275 IterationNum != MaxIterations; ++IterationNum) { 2276 ConstantInt *CondVal = 2277 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2278 2279 // Couldn't symbolically evaluate. 2280 if (!CondVal) return UnknownValue; 2281 2282 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2283 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2284 ++NumBruteForceTripCountsComputed; 2285 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2286 } 2287 2288 // Compute the value of the PHI node for the next iteration. 2289 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2290 if (NextPHI == 0 || NextPHI == PHIVal) 2291 return UnknownValue; // Couldn't evaluate or not making progress... 2292 PHIVal = NextPHI; 2293 } 2294 2295 // Too many iterations were needed to evaluate. 2296 return UnknownValue; 2297} 2298 2299/// getSCEVAtScope - Compute the value of the specified expression within the 2300/// indicated loop (which may be null to indicate in no loop). If the 2301/// expression cannot be evaluated, return UnknownValue. 2302SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2303 // FIXME: this should be turned into a virtual method on SCEV! 2304 2305 if (isa<SCEVConstant>(V)) return V; 2306 2307 // If this instruction is evolved from a constant-evolving PHI, compute the 2308 // exit value from the loop without using SCEVs. 2309 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2310 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2311 const Loop *LI = this->LI[I->getParent()]; 2312 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2313 if (PHINode *PN = dyn_cast<PHINode>(I)) 2314 if (PN->getParent() == LI->getHeader()) { 2315 // Okay, there is no closed form solution for the PHI node. Check 2316 // to see if the loop that contains it has a known iteration count. 2317 // If so, we may be able to force computation of the exit value. 2318 SCEVHandle IterationCount = getIterationCount(LI); 2319 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2320 // Okay, we know how many times the containing loop executes. If 2321 // this is a constant evolving PHI node, get the final value at 2322 // the specified iteration number. 2323 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2324 ICC->getValue()->getValue(), 2325 LI); 2326 if (RV) return SE.getUnknown(RV); 2327 } 2328 } 2329 2330 // Okay, this is an expression that we cannot symbolically evaluate 2331 // into a SCEV. Check to see if it's possible to symbolically evaluate 2332 // the arguments into constants, and if so, try to constant propagate the 2333 // result. This is particularly useful for computing loop exit values. 2334 if (CanConstantFold(I)) { 2335 std::vector<Constant*> Operands; 2336 Operands.reserve(I->getNumOperands()); 2337 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2338 Value *Op = I->getOperand(i); 2339 if (Constant *C = dyn_cast<Constant>(Op)) { 2340 Operands.push_back(C); 2341 } else { 2342 // If any of the operands is non-constant and if they are 2343 // non-integer, don't even try to analyze them with scev techniques. 2344 if (!isa<IntegerType>(Op->getType())) 2345 return V; 2346 2347 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2348 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2349 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2350 Op->getType(), 2351 false)); 2352 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2353 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2354 Operands.push_back(ConstantExpr::getIntegerCast(C, 2355 Op->getType(), 2356 false)); 2357 else 2358 return V; 2359 } else { 2360 return V; 2361 } 2362 } 2363 } 2364 2365 Constant *C; 2366 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2367 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2368 &Operands[0], Operands.size()); 2369 else 2370 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2371 &Operands[0], Operands.size()); 2372 return SE.getUnknown(C); 2373 } 2374 } 2375 2376 // This is some other type of SCEVUnknown, just return it. 2377 return V; 2378 } 2379 2380 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2381 // Avoid performing the look-up in the common case where the specified 2382 // expression has no loop-variant portions. 2383 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2384 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2385 if (OpAtScope != Comm->getOperand(i)) { 2386 if (OpAtScope == UnknownValue) return UnknownValue; 2387 // Okay, at least one of these operands is loop variant but might be 2388 // foldable. Build a new instance of the folded commutative expression. 2389 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2390 NewOps.push_back(OpAtScope); 2391 2392 for (++i; i != e; ++i) { 2393 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2394 if (OpAtScope == UnknownValue) return UnknownValue; 2395 NewOps.push_back(OpAtScope); 2396 } 2397 if (isa<SCEVAddExpr>(Comm)) 2398 return SE.getAddExpr(NewOps); 2399 if (isa<SCEVMulExpr>(Comm)) 2400 return SE.getMulExpr(NewOps); 2401 if (isa<SCEVSMaxExpr>(Comm)) 2402 return SE.getSMaxExpr(NewOps); 2403 if (isa<SCEVUMaxExpr>(Comm)) 2404 return SE.getUMaxExpr(NewOps); 2405 assert(0 && "Unknown commutative SCEV type!"); 2406 } 2407 } 2408 // If we got here, all operands are loop invariant. 2409 return Comm; 2410 } 2411 2412 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2413 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2414 if (LHS == UnknownValue) return LHS; 2415 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2416 if (RHS == UnknownValue) return RHS; 2417 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2418 return Div; // must be loop invariant 2419 return SE.getUDivExpr(LHS, RHS); 2420 } 2421 2422 // If this is a loop recurrence for a loop that does not contain L, then we 2423 // are dealing with the final value computed by the loop. 2424 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2425 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2426 // To evaluate this recurrence, we need to know how many times the AddRec 2427 // loop iterates. Compute this now. 2428 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2429 if (IterationCount == UnknownValue) return UnknownValue; 2430 IterationCount = SE.getTruncateOrZeroExtend(IterationCount, 2431 AddRec->getType()); 2432 2433 // If the value is affine, simplify the expression evaluation to just 2434 // Start + Step*IterationCount. 2435 if (AddRec->isAffine()) 2436 return SE.getAddExpr(AddRec->getStart(), 2437 SE.getMulExpr(IterationCount, 2438 AddRec->getOperand(1))); 2439 2440 // Otherwise, evaluate it the hard way. 2441 return AddRec->evaluateAtIteration(IterationCount, SE); 2442 } 2443 return UnknownValue; 2444 } 2445 2446 //assert(0 && "Unknown SCEV type!"); 2447 return UnknownValue; 2448} 2449 2450/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2451/// following equation: 2452/// 2453/// A * X = B (mod N) 2454/// 2455/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2456/// A and B isn't important. 2457/// 2458/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2459static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2460 ScalarEvolution &SE) { 2461 uint32_t BW = A.getBitWidth(); 2462 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2463 assert(A != 0 && "A must be non-zero."); 2464 2465 // 1. D = gcd(A, N) 2466 // 2467 // The gcd of A and N may have only one prime factor: 2. The number of 2468 // trailing zeros in A is its multiplicity 2469 uint32_t Mult2 = A.countTrailingZeros(); 2470 // D = 2^Mult2 2471 2472 // 2. Check if B is divisible by D. 2473 // 2474 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2475 // is not less than multiplicity of this prime factor for D. 2476 if (B.countTrailingZeros() < Mult2) 2477 return new SCEVCouldNotCompute(); 2478 2479 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2480 // modulo (N / D). 2481 // 2482 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2483 // bit width during computations. 2484 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2485 APInt Mod(BW + 1, 0); 2486 Mod.set(BW - Mult2); // Mod = N / D 2487 APInt I = AD.multiplicativeInverse(Mod); 2488 2489 // 4. Compute the minimum unsigned root of the equation: 2490 // I * (B / D) mod (N / D) 2491 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2492 2493 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2494 // bits. 2495 return SE.getConstant(Result.trunc(BW)); 2496} 2497 2498/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2499/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2500/// might be the same) or two SCEVCouldNotCompute objects. 2501/// 2502static std::pair<SCEVHandle,SCEVHandle> 2503SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2504 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2505 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2506 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2507 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2508 2509 // We currently can only solve this if the coefficients are constants. 2510 if (!LC || !MC || !NC) { 2511 SCEV *CNC = new SCEVCouldNotCompute(); 2512 return std::make_pair(CNC, CNC); 2513 } 2514 2515 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2516 const APInt &L = LC->getValue()->getValue(); 2517 const APInt &M = MC->getValue()->getValue(); 2518 const APInt &N = NC->getValue()->getValue(); 2519 APInt Two(BitWidth, 2); 2520 APInt Four(BitWidth, 4); 2521 2522 { 2523 using namespace APIntOps; 2524 const APInt& C = L; 2525 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2526 // The B coefficient is M-N/2 2527 APInt B(M); 2528 B -= sdiv(N,Two); 2529 2530 // The A coefficient is N/2 2531 APInt A(N.sdiv(Two)); 2532 2533 // Compute the B^2-4ac term. 2534 APInt SqrtTerm(B); 2535 SqrtTerm *= B; 2536 SqrtTerm -= Four * (A * C); 2537 2538 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2539 // integer value or else APInt::sqrt() will assert. 2540 APInt SqrtVal(SqrtTerm.sqrt()); 2541 2542 // Compute the two solutions for the quadratic formula. 2543 // The divisions must be performed as signed divisions. 2544 APInt NegB(-B); 2545 APInt TwoA( A << 1 ); 2546 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2547 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2548 2549 return std::make_pair(SE.getConstant(Solution1), 2550 SE.getConstant(Solution2)); 2551 } // end APIntOps namespace 2552} 2553 2554/// HowFarToZero - Return the number of times a backedge comparing the specified 2555/// value to zero will execute. If not computable, return UnknownValue 2556SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2557 // If the value is a constant 2558 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2559 // If the value is already zero, the branch will execute zero times. 2560 if (C->getValue()->isZero()) return C; 2561 return UnknownValue; // Otherwise it will loop infinitely. 2562 } 2563 2564 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2565 if (!AddRec || AddRec->getLoop() != L) 2566 return UnknownValue; 2567 2568 if (AddRec->isAffine()) { 2569 // If this is an affine expression, the execution count of this branch is 2570 // the minimum unsigned root of the following equation: 2571 // 2572 // Start + Step*N = 0 (mod 2^BW) 2573 // 2574 // equivalent to: 2575 // 2576 // Step*N = -Start (mod 2^BW) 2577 // 2578 // where BW is the common bit width of Start and Step. 2579 2580 // Get the initial value for the loop. 2581 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2582 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2583 2584 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2585 2586 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2587 // For now we handle only constant steps. 2588 2589 // First, handle unitary steps. 2590 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2591 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned) 2592 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2593 return Start; // N = Start (as unsigned) 2594 2595 // Then, try to solve the above equation provided that Start is constant. 2596 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2597 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2598 -StartC->getValue()->getValue(),SE); 2599 } 2600 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2601 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2602 // the quadratic equation to solve it. 2603 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2604 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2605 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2606 if (R1) { 2607#if 0 2608 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2609 << " sol#2: " << *R2 << "\n"; 2610#endif 2611 // Pick the smallest positive root value. 2612 if (ConstantInt *CB = 2613 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2614 R1->getValue(), R2->getValue()))) { 2615 if (CB->getZExtValue() == false) 2616 std::swap(R1, R2); // R1 is the minimum root now. 2617 2618 // We can only use this value if the chrec ends up with an exact zero 2619 // value at this index. When solving for "X*X != 5", for example, we 2620 // should not accept a root of 2. 2621 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2622 if (Val->isZero()) 2623 return R1; // We found a quadratic root! 2624 } 2625 } 2626 } 2627 2628 return UnknownValue; 2629} 2630 2631/// HowFarToNonZero - Return the number of times a backedge checking the 2632/// specified value for nonzero will execute. If not computable, return 2633/// UnknownValue 2634SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2635 // Loops that look like: while (X == 0) are very strange indeed. We don't 2636 // handle them yet except for the trivial case. This could be expanded in the 2637 // future as needed. 2638 2639 // If the value is a constant, check to see if it is known to be non-zero 2640 // already. If so, the backedge will execute zero times. 2641 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2642 if (!C->getValue()->isNullValue()) 2643 return SE.getIntegerSCEV(0, C->getType()); 2644 return UnknownValue; // Otherwise it will loop infinitely. 2645 } 2646 2647 // We could implement others, but I really doubt anyone writes loops like 2648 // this, and if they did, they would already be constant folded. 2649 return UnknownValue; 2650} 2651 2652/// executesAtLeastOnce - Test whether entry to the loop is protected by 2653/// a conditional between LHS and RHS. 2654bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned, 2655 SCEV *LHS, SCEV *RHS) { 2656 BasicBlock *Preheader = L->getLoopPreheader(); 2657 BasicBlock *PreheaderDest = L->getHeader(); 2658 if (Preheader == 0) return false; 2659 2660 BranchInst *LoopEntryPredicate = 2661 dyn_cast<BranchInst>(Preheader->getTerminator()); 2662 if (!LoopEntryPredicate) return false; 2663 2664 // This might be a critical edge broken out. If the loop preheader ends in 2665 // an unconditional branch to the loop, check to see if the preheader has a 2666 // single predecessor, and if so, look for its terminator. 2667 while (LoopEntryPredicate->isUnconditional()) { 2668 PreheaderDest = Preheader; 2669 Preheader = Preheader->getSinglePredecessor(); 2670 if (!Preheader) return false; // Multiple preds. 2671 2672 LoopEntryPredicate = 2673 dyn_cast<BranchInst>(Preheader->getTerminator()); 2674 if (!LoopEntryPredicate) return false; 2675 } 2676 2677 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2678 if (!ICI) return false; 2679 2680 // Now that we found a conditional branch that dominates the loop, check to 2681 // see if it is the comparison we are looking for. 2682 Value *PreCondLHS = ICI->getOperand(0); 2683 Value *PreCondRHS = ICI->getOperand(1); 2684 ICmpInst::Predicate Cond; 2685 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2686 Cond = ICI->getPredicate(); 2687 else 2688 Cond = ICI->getInversePredicate(); 2689 2690 switch (Cond) { 2691 case ICmpInst::ICMP_UGT: 2692 if (isSigned) return false; 2693 std::swap(PreCondLHS, PreCondRHS); 2694 Cond = ICmpInst::ICMP_ULT; 2695 break; 2696 case ICmpInst::ICMP_SGT: 2697 if (!isSigned) return false; 2698 std::swap(PreCondLHS, PreCondRHS); 2699 Cond = ICmpInst::ICMP_SLT; 2700 break; 2701 case ICmpInst::ICMP_ULT: 2702 if (isSigned) return false; 2703 break; 2704 case ICmpInst::ICMP_SLT: 2705 if (!isSigned) return false; 2706 break; 2707 default: 2708 return false; 2709 } 2710 2711 if (!PreCondLHS->getType()->isInteger()) return false; 2712 2713 return LHS == getSCEV(PreCondLHS) && RHS == getSCEV(PreCondRHS); 2714} 2715 2716/// HowManyLessThans - Return the number of times a backedge containing the 2717/// specified less-than comparison will execute. If not computable, return 2718/// UnknownValue. 2719SCEVHandle ScalarEvolutionsImpl:: 2720HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2721 // Only handle: "ADDREC < LoopInvariant". 2722 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2723 2724 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2725 if (!AddRec || AddRec->getLoop() != L) 2726 return UnknownValue; 2727 2728 if (AddRec->isAffine()) { 2729 // FORNOW: We only support unit strides. 2730 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2731 if (AddRec->getOperand(1) != One) 2732 return UnknownValue; 2733 2734 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2735 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2736 // Note that we cannot simply return max(m-n,0) because it's not safe to 2737 // treat m-n as signed nor unsigned due to overflow possibility. 2738 2739 // First, we get the value of the LHS in the first iteration: n 2740 SCEVHandle Start = AddRec->getOperand(0); 2741 2742 if (executesAtLeastOnce(L, isSigned, 2743 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2744 // Since we know that the condition is true in order to enter the loop, 2745 // we know that it will run exactly m-n times. 2746 return SE.getMinusSCEV(RHS, Start); 2747 } else { 2748 // Then, we get the value of the LHS in the first iteration in which the 2749 // above condition doesn't hold. This equals to max(m,n). 2750 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2751 : SE.getUMaxExpr(RHS, Start); 2752 2753 // Finally, we subtract these two values to get the number of times the 2754 // backedge is executed: max(m,n)-n. 2755 return SE.getMinusSCEV(End, Start); 2756 } 2757 } 2758 2759 return UnknownValue; 2760} 2761 2762/// getNumIterationsInRange - Return the number of iterations of this loop that 2763/// produce values in the specified constant range. Another way of looking at 2764/// this is that it returns the first iteration number where the value is not in 2765/// the condition, thus computing the exit count. If the iteration count can't 2766/// be computed, an instance of SCEVCouldNotCompute is returned. 2767SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2768 ScalarEvolution &SE) const { 2769 if (Range.isFullSet()) // Infinite loop. 2770 return new SCEVCouldNotCompute(); 2771 2772 // If the start is a non-zero constant, shift the range to simplify things. 2773 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2774 if (!SC->getValue()->isZero()) { 2775 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2776 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2777 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2778 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2779 return ShiftedAddRec->getNumIterationsInRange( 2780 Range.subtract(SC->getValue()->getValue()), SE); 2781 // This is strange and shouldn't happen. 2782 return new SCEVCouldNotCompute(); 2783 } 2784 2785 // The only time we can solve this is when we have all constant indices. 2786 // Otherwise, we cannot determine the overflow conditions. 2787 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2788 if (!isa<SCEVConstant>(getOperand(i))) 2789 return new SCEVCouldNotCompute(); 2790 2791 2792 // Okay at this point we know that all elements of the chrec are constants and 2793 // that the start element is zero. 2794 2795 // First check to see if the range contains zero. If not, the first 2796 // iteration exits. 2797 if (!Range.contains(APInt(getBitWidth(),0))) 2798 return SE.getConstant(ConstantInt::get(getType(),0)); 2799 2800 if (isAffine()) { 2801 // If this is an affine expression then we have this situation: 2802 // Solve {0,+,A} in Range === Ax in Range 2803 2804 // We know that zero is in the range. If A is positive then we know that 2805 // the upper value of the range must be the first possible exit value. 2806 // If A is negative then the lower of the range is the last possible loop 2807 // value. Also note that we already checked for a full range. 2808 APInt One(getBitWidth(),1); 2809 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2810 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2811 2812 // The exit value should be (End+A)/A. 2813 APInt ExitVal = (End + A).udiv(A); 2814 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2815 2816 // Evaluate at the exit value. If we really did fall out of the valid 2817 // range, then we computed our trip count, otherwise wrap around or other 2818 // things must have happened. 2819 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2820 if (Range.contains(Val->getValue())) 2821 return new SCEVCouldNotCompute(); // Something strange happened 2822 2823 // Ensure that the previous value is in the range. This is a sanity check. 2824 assert(Range.contains( 2825 EvaluateConstantChrecAtConstant(this, 2826 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2827 "Linear scev computation is off in a bad way!"); 2828 return SE.getConstant(ExitValue); 2829 } else if (isQuadratic()) { 2830 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2831 // quadratic equation to solve it. To do this, we must frame our problem in 2832 // terms of figuring out when zero is crossed, instead of when 2833 // Range.getUpper() is crossed. 2834 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2835 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2836 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2837 2838 // Next, solve the constructed addrec 2839 std::pair<SCEVHandle,SCEVHandle> Roots = 2840 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2841 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2842 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2843 if (R1) { 2844 // Pick the smallest positive root value. 2845 if (ConstantInt *CB = 2846 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2847 R1->getValue(), R2->getValue()))) { 2848 if (CB->getZExtValue() == false) 2849 std::swap(R1, R2); // R1 is the minimum root now. 2850 2851 // Make sure the root is not off by one. The returned iteration should 2852 // not be in the range, but the previous one should be. When solving 2853 // for "X*X < 5", for example, we should not return a root of 2. 2854 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2855 R1->getValue(), 2856 SE); 2857 if (Range.contains(R1Val->getValue())) { 2858 // The next iteration must be out of the range... 2859 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2860 2861 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2862 if (!Range.contains(R1Val->getValue())) 2863 return SE.getConstant(NextVal); 2864 return new SCEVCouldNotCompute(); // Something strange happened 2865 } 2866 2867 // If R1 was not in the range, then it is a good return value. Make 2868 // sure that R1-1 WAS in the range though, just in case. 2869 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2870 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2871 if (Range.contains(R1Val->getValue())) 2872 return R1; 2873 return new SCEVCouldNotCompute(); // Something strange happened 2874 } 2875 } 2876 } 2877 2878 // Fallback, if this is a general polynomial, figure out the progression 2879 // through brute force: evaluate until we find an iteration that fails the 2880 // test. This is likely to be slow, but getting an accurate trip count is 2881 // incredibly important, we will be able to simplify the exit test a lot, and 2882 // we are almost guaranteed to get a trip count in this case. 2883 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2884 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2885 do { 2886 ++NumBruteForceEvaluations; 2887 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2888 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2889 return new SCEVCouldNotCompute(); 2890 2891 // Check to see if we found the value! 2892 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2893 return SE.getConstant(TestVal); 2894 2895 // Increment to test the next index. 2896 TestVal = ConstantInt::get(TestVal->getValue()+1); 2897 } while (TestVal != EndVal); 2898 2899 return new SCEVCouldNotCompute(); 2900} 2901 2902 2903 2904//===----------------------------------------------------------------------===// 2905// ScalarEvolution Class Implementation 2906//===----------------------------------------------------------------------===// 2907 2908bool ScalarEvolution::runOnFunction(Function &F) { 2909 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2910 return false; 2911} 2912 2913void ScalarEvolution::releaseMemory() { 2914 delete (ScalarEvolutionsImpl*)Impl; 2915 Impl = 0; 2916} 2917 2918void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2919 AU.setPreservesAll(); 2920 AU.addRequiredTransitive<LoopInfo>(); 2921} 2922 2923SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2924 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2925} 2926 2927/// hasSCEV - Return true if the SCEV for this value has already been 2928/// computed. 2929bool ScalarEvolution::hasSCEV(Value *V) const { 2930 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2931} 2932 2933 2934/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2935/// the specified value. 2936void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2937 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2938} 2939 2940 2941SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2942 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2943} 2944 2945bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2946 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2947} 2948 2949SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2950 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2951} 2952 2953void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2954 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2955} 2956 2957static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2958 const Loop *L) { 2959 // Print all inner loops first 2960 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2961 PrintLoopInfo(OS, SE, *I); 2962 2963 OS << "Loop " << L->getHeader()->getName() << ": "; 2964 2965 SmallVector<BasicBlock*, 8> ExitBlocks; 2966 L->getExitBlocks(ExitBlocks); 2967 if (ExitBlocks.size() != 1) 2968 OS << "<multiple exits> "; 2969 2970 if (SE->hasLoopInvariantIterationCount(L)) { 2971 OS << *SE->getIterationCount(L) << " iterations! "; 2972 } else { 2973 OS << "Unpredictable iteration count. "; 2974 } 2975 2976 OS << "\n"; 2977} 2978 2979void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2980 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2981 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2982 2983 OS << "Classifying expressions for: " << F.getName() << "\n"; 2984 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2985 if (I->getType()->isInteger()) { 2986 OS << *I; 2987 OS << " --> "; 2988 SCEVHandle SV = getSCEV(&*I); 2989 SV->print(OS); 2990 OS << "\t\t"; 2991 2992 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2993 OS << "Exits: "; 2994 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2995 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2996 OS << "<<Unknown>>"; 2997 } else { 2998 OS << *ExitValue; 2999 } 3000 } 3001 3002 3003 OS << "\n"; 3004 } 3005 3006 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 3007 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 3008 PrintLoopInfo(OS, this, *I); 3009} 3010