ScalarEvolution.cpp revision cfeb6a450632f2a6cd05302633c8c2b8c90cfdfd
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} 119 120/// getValueRange - Return the tightest constant bounds that this value is 121/// known to have. This method is only valid on integer SCEV objects. 122ConstantRange SCEV::getValueRange() const { 123 const Type *Ty = getType(); 124 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 125 // Default to a full range if no better information is available. 126 return ConstantRange(getBitWidth()); 127} 128 129uint32_t SCEV::getBitWidth() const { 130 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 131 return ITy->getBitWidth(); 132 return 0; 133} 134 135bool SCEV::isZero() const { 136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 137 return SC->getValue()->isZero(); 138 return false; 139} 140 141 142SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 143 144bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 146 return false; 147} 148 149const Type *SCEVCouldNotCompute::getType() const { 150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 151 return 0; 152} 153 154bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 155 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 156 return false; 157} 158 159SCEVHandle SCEVCouldNotCompute:: 160replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 161 const SCEVHandle &Conc, 162 ScalarEvolution &SE) const { 163 return this; 164} 165 166void SCEVCouldNotCompute::print(std::ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174 175// SCEVConstants - Only allow the creation of one SCEVConstant for any 176// particular value. Don't use a SCEVHandle here, or else the object will 177// never be deleted! 178static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 179 180 181SCEVConstant::~SCEVConstant() { 182 SCEVConstants->erase(V); 183} 184 185SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 186 SCEVConstant *&R = (*SCEVConstants)[V]; 187 if (R == 0) R = new SCEVConstant(V); 188 return R; 189} 190 191SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 192 return getConstant(ConstantInt::get(Val)); 193} 194 195ConstantRange SCEVConstant::getValueRange() const { 196 return ConstantRange(V->getValue()); 197} 198 199const Type *SCEVConstant::getType() const { return V->getType(); } 200 201void SCEVConstant::print(std::ostream &OS) const { 202 WriteAsOperand(OS, V, false); 203} 204 205// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 206// particular input. Don't use a SCEVHandle here, or else the object will 207// never be deleted! 208static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 209 SCEVTruncateExpr*> > SCEVTruncates; 210 211SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 212 : SCEV(scTruncate), Op(op), Ty(ty) { 213 assert(Op->getType()->isInteger() && Ty->isInteger() && 214 "Cannot truncate non-integer value!"); 215 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 216 && "This is not a truncating conversion!"); 217} 218 219SCEVTruncateExpr::~SCEVTruncateExpr() { 220 SCEVTruncates->erase(std::make_pair(Op, Ty)); 221} 222 223ConstantRange SCEVTruncateExpr::getValueRange() const { 224 return getOperand()->getValueRange().truncate(getBitWidth()); 225} 226 227void SCEVTruncateExpr::print(std::ostream &OS) const { 228 OS << "(truncate " << *Op << " to " << *Ty << ")"; 229} 230 231// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 232// particular input. Don't use a SCEVHandle here, or else the object will never 233// be deleted! 234static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 235 SCEVZeroExtendExpr*> > SCEVZeroExtends; 236 237SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 238 : SCEV(scZeroExtend), Op(op), Ty(ty) { 239 assert(Op->getType()->isInteger() && Ty->isInteger() && 240 "Cannot zero extend non-integer value!"); 241 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 242 && "This is not an extending conversion!"); 243} 244 245SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 246 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 247} 248 249ConstantRange SCEVZeroExtendExpr::getValueRange() const { 250 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 251} 252 253void SCEVZeroExtendExpr::print(std::ostream &OS) const { 254 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 255} 256 257// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 258// particular input. Don't use a SCEVHandle here, or else the object will never 259// be deleted! 260static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 261 SCEVSignExtendExpr*> > SCEVSignExtends; 262 263SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 264 : SCEV(scSignExtend), Op(op), Ty(ty) { 265 assert(Op->getType()->isInteger() && Ty->isInteger() && 266 "Cannot sign extend non-integer value!"); 267 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 268 && "This is not an extending conversion!"); 269} 270 271SCEVSignExtendExpr::~SCEVSignExtendExpr() { 272 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 273} 274 275ConstantRange SCEVSignExtendExpr::getValueRange() const { 276 return getOperand()->getValueRange().signExtend(getBitWidth()); 277} 278 279void SCEVSignExtendExpr::print(std::ostream &OS) const { 280 OS << "(signextend " << *Op << " to " << *Ty << ")"; 281} 282 283// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 284// particular input. Don't use a SCEVHandle here, or else the object will never 285// be deleted! 286static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 287 SCEVCommutativeExpr*> > SCEVCommExprs; 288 289SCEVCommutativeExpr::~SCEVCommutativeExpr() { 290 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 291 std::vector<SCEV*>(Operands.begin(), 292 Operands.end()))); 293} 294 295void SCEVCommutativeExpr::print(std::ostream &OS) const { 296 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 297 const char *OpStr = getOperationStr(); 298 OS << "(" << *Operands[0]; 299 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 300 OS << OpStr << *Operands[i]; 301 OS << ")"; 302} 303 304SCEVHandle SCEVCommutativeExpr:: 305replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 306 const SCEVHandle &Conc, 307 ScalarEvolution &SE) const { 308 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 309 SCEVHandle H = 310 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 311 if (H != getOperand(i)) { 312 std::vector<SCEVHandle> NewOps; 313 NewOps.reserve(getNumOperands()); 314 for (unsigned j = 0; j != i; ++j) 315 NewOps.push_back(getOperand(j)); 316 NewOps.push_back(H); 317 for (++i; i != e; ++i) 318 NewOps.push_back(getOperand(i)-> 319 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 320 321 if (isa<SCEVAddExpr>(this)) 322 return SE.getAddExpr(NewOps); 323 else if (isa<SCEVMulExpr>(this)) 324 return SE.getMulExpr(NewOps); 325 else if (isa<SCEVSMaxExpr>(this)) 326 return SE.getSMaxExpr(NewOps); 327 else if (isa<SCEVUMaxExpr>(this)) 328 return SE.getUMaxExpr(NewOps); 329 else 330 assert(0 && "Unknown commutative expr!"); 331 } 332 } 333 return this; 334} 335 336 337// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 338// input. Don't use a SCEVHandle here, or else the object will never be 339// deleted! 340static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 341 SCEVUDivExpr*> > SCEVUDivs; 342 343SCEVUDivExpr::~SCEVUDivExpr() { 344 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 345} 346 347void SCEVUDivExpr::print(std::ostream &OS) const { 348 OS << "(" << *LHS << " /u " << *RHS << ")"; 349} 350 351const Type *SCEVUDivExpr::getType() const { 352 return LHS->getType(); 353} 354 355// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 356// particular input. Don't use a SCEVHandle here, or else the object will never 357// be deleted! 358static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 359 SCEVAddRecExpr*> > SCEVAddRecExprs; 360 361SCEVAddRecExpr::~SCEVAddRecExpr() { 362 SCEVAddRecExprs->erase(std::make_pair(L, 363 std::vector<SCEV*>(Operands.begin(), 364 Operands.end()))); 365} 366 367SCEVHandle SCEVAddRecExpr:: 368replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 369 const SCEVHandle &Conc, 370 ScalarEvolution &SE) const { 371 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 372 SCEVHandle H = 373 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 374 if (H != getOperand(i)) { 375 std::vector<SCEVHandle> NewOps; 376 NewOps.reserve(getNumOperands()); 377 for (unsigned j = 0; j != i; ++j) 378 NewOps.push_back(getOperand(j)); 379 NewOps.push_back(H); 380 for (++i; i != e; ++i) 381 NewOps.push_back(getOperand(i)-> 382 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 383 384 return SE.getAddRecExpr(NewOps, L); 385 } 386 } 387 return this; 388} 389 390 391bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 392 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 393 // contain L and if the start is invariant. 394 return !QueryLoop->contains(L->getHeader()) && 395 getOperand(0)->isLoopInvariant(QueryLoop); 396} 397 398 399void SCEVAddRecExpr::print(std::ostream &OS) const { 400 OS << "{" << *Operands[0]; 401 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 402 OS << ",+," << *Operands[i]; 403 OS << "}<" << L->getHeader()->getName() + ">"; 404} 405 406// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 407// value. Don't use a SCEVHandle here, or else the object will never be 408// deleted! 409static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 410 411SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 412 413bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 414 // All non-instruction values are loop invariant. All instructions are loop 415 // invariant if they are not contained in the specified loop. 416 if (Instruction *I = dyn_cast<Instruction>(V)) 417 return !L->contains(I->getParent()); 418 return true; 419} 420 421const Type *SCEVUnknown::getType() const { 422 return V->getType(); 423} 424 425void SCEVUnknown::print(std::ostream &OS) const { 426 WriteAsOperand(OS, V, false); 427} 428 429//===----------------------------------------------------------------------===// 430// SCEV Utilities 431//===----------------------------------------------------------------------===// 432 433namespace { 434 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 435 /// than the complexity of the RHS. This comparator is used to canonicalize 436 /// expressions. 437 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 438 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 439 return LHS->getSCEVType() < RHS->getSCEVType(); 440 } 441 }; 442} 443 444/// GroupByComplexity - Given a list of SCEV objects, order them by their 445/// complexity, and group objects of the same complexity together by value. 446/// When this routine is finished, we know that any duplicates in the vector are 447/// consecutive and that complexity is monotonically increasing. 448/// 449/// Note that we go take special precautions to ensure that we get determinstic 450/// results from this routine. In other words, we don't want the results of 451/// this to depend on where the addresses of various SCEV objects happened to 452/// land in memory. 453/// 454static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 455 if (Ops.size() < 2) return; // Noop 456 if (Ops.size() == 2) { 457 // This is the common case, which also happens to be trivially simple. 458 // Special case it. 459 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 460 std::swap(Ops[0], Ops[1]); 461 return; 462 } 463 464 // Do the rough sort by complexity. 465 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 466 467 // Now that we are sorted by complexity, group elements of the same 468 // complexity. Note that this is, at worst, N^2, but the vector is likely to 469 // be extremely short in practice. Note that we take this approach because we 470 // do not want to depend on the addresses of the objects we are grouping. 471 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 472 SCEV *S = Ops[i]; 473 unsigned Complexity = S->getSCEVType(); 474 475 // If there are any objects of the same complexity and same value as this 476 // one, group them. 477 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 478 if (Ops[j] == S) { // Found a duplicate. 479 // Move it to immediately after i'th element. 480 std::swap(Ops[i+1], Ops[j]); 481 ++i; // no need to rescan it. 482 if (i == e-2) return; // Done! 483 } 484 } 485 } 486} 487 488 489 490//===----------------------------------------------------------------------===// 491// Simple SCEV method implementations 492//===----------------------------------------------------------------------===// 493 494/// getIntegerSCEV - Given an integer or FP type, create a constant for the 495/// specified signed integer value and return a SCEV for the constant. 496SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 497 Constant *C; 498 if (Val == 0) 499 C = Constant::getNullValue(Ty); 500 else if (Ty->isFloatingPoint()) 501 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 502 APFloat::IEEEdouble, Val)); 503 else 504 C = ConstantInt::get(Ty, Val); 505 return getUnknown(C); 506} 507 508/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 509/// 510SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 511 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 512 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 513 514 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType()))); 515} 516 517/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 518SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 519 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 520 return getUnknown(ConstantExpr::getNot(VC->getValue())); 521 522 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType())); 523 return getMinusSCEV(AllOnes, V); 524} 525 526/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 527/// 528SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 529 const SCEVHandle &RHS) { 530 // X - Y --> X + -Y 531 return getAddExpr(LHS, getNegativeSCEV(RHS)); 532} 533 534 535/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as 536/// It. Assume, K > 0. 537static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 538 ScalarEvolution &SE) { 539 // We are using the following formula for BC(It, K): 540 // 541 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 542 // 543 // Suppose, W is the bitwidth of It (and of the return value as well). We 544 // must be prepared for overflow. Hence, we must assure that the result of 545 // our computation is equal to the accurate one modulo 2^W. Unfortunately, 546 // division isn't safe in modular arithmetic. This means we must perform the 547 // whole computation accurately and then truncate the result to W bits. 548 // 549 // The dividend of the formula is a multiplication of K integers of bitwidth 550 // W. K*W bits suffice to compute it accurately. 551 // 552 // FIXME: We assume the divisor can be accurately computed using 16-bit 553 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In 554 // future we may use APInt to use the minimum number of bits necessary to 555 // compute it accurately. 556 // 557 // It is safe to use unsigned division here: the dividend is nonnegative and 558 // the divisor is positive. 559 560 // Handle the simplest case efficiently. 561 if (K == 1) 562 return It; 563 564 assert(K < 9 && "We cannot handle such long AddRecs yet."); 565 566 // FIXME: A temporary hack to remove in future. Arbitrary precision integers 567 // aren't supported by the code generator yet. For the dividend, the bitwidth 568 // we use is the smallest power of 2 greater or equal to K*W and less or equal 569 // to 64. Note that setting the upper bound for bitwidth may still lead to 570 // miscompilation in some cases. 571 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth()); 572 if (DividendBits > 64) 573 DividendBits = 64; 574#if 0 // Waiting for the APInt support in the code generator... 575 unsigned DividendBits = K * It->getBitWidth(); 576#endif 577 578 const IntegerType *DividendTy = IntegerType::get(DividendBits); 579 const SCEVHandle ExIt = SE.getTruncateOrZeroExtend(It, DividendTy); 580 581 // The final number of bits we need to perform the division is the maximum of 582 // dividend and divisor bitwidths. 583 const IntegerType *DivisionTy = 584 IntegerType::get(std::max(DividendBits, 16U)); 585 586 // Compute K! We know K >= 2 here. 587 unsigned F = 2; 588 for (unsigned i = 3; i <= K; ++i) 589 F *= i; 590 APInt Divisor(DivisionTy->getBitWidth(), F); 591 592 // Handle this case efficiently, it is common to have constant iteration 593 // counts while computing loop exit values. 594 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) { 595 const APInt& N = SC->getValue()->getValue(); 596 APInt Dividend(N.getBitWidth(), 1); 597 for (; K; --K) 598 Dividend *= N-(K-1); 599 if (DividendTy != DivisionTy) 600 Dividend = Dividend.zext(DivisionTy->getBitWidth()); 601 602 APInt Result = Dividend.udiv(Divisor); 603 if (Result.getBitWidth() != It->getBitWidth()) 604 Result = Result.trunc(It->getBitWidth()); 605 606 return SE.getConstant(Result); 607 } 608 609 SCEVHandle Dividend = ExIt; 610 for (unsigned i = 1; i != K; ++i) 611 Dividend = 612 SE.getMulExpr(Dividend, 613 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy))); 614 615 return SE.getTruncateOrZeroExtend( 616 SE.getUDivExpr( 617 SE.getTruncateOrZeroExtend(Dividend, DivisionTy), 618 SE.getConstant(Divisor) 619 ), It->getType()); 620} 621 622/// evaluateAtIteration - Return the value of this chain of recurrences at 623/// the specified iteration number. We can evaluate this recurrence by 624/// multiplying each element in the chain by the binomial coefficient 625/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 626/// 627/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 628/// 629/// where BC(It, k) stands for binomial coefficient. 630/// 631SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 632 ScalarEvolution &SE) const { 633 SCEVHandle Result = getStart(); 634 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 635 // The computation is correct in the face of overflow provided that the 636 // multiplication is performed _after_ the evaluation of the binomial 637 // coefficient. 638 SCEVHandle Val = SE.getMulExpr(getOperand(i), 639 BinomialCoefficient(It, i, SE)); 640 Result = SE.getAddExpr(Result, Val); 641 } 642 return Result; 643} 644 645//===----------------------------------------------------------------------===// 646// SCEV Expression folder implementations 647//===----------------------------------------------------------------------===// 648 649SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 650 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 651 return getUnknown( 652 ConstantExpr::getTrunc(SC->getValue(), Ty)); 653 654 // If the input value is a chrec scev made out of constants, truncate 655 // all of the constants. 656 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 657 std::vector<SCEVHandle> Operands; 658 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 659 // FIXME: This should allow truncation of other expression types! 660 if (isa<SCEVConstant>(AddRec->getOperand(i))) 661 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 662 else 663 break; 664 if (Operands.size() == AddRec->getNumOperands()) 665 return getAddRecExpr(Operands, AddRec->getLoop()); 666 } 667 668 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 669 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 670 return Result; 671} 672 673SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 674 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 675 return getUnknown( 676 ConstantExpr::getZExt(SC->getValue(), Ty)); 677 678 // FIXME: If the input value is a chrec scev, and we can prove that the value 679 // did not overflow the old, smaller, value, we can zero extend all of the 680 // operands (often constants). This would allow analysis of something like 681 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 682 683 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 684 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 685 return Result; 686} 687 688SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 689 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 690 return getUnknown( 691 ConstantExpr::getSExt(SC->getValue(), Ty)); 692 693 // FIXME: If the input value is a chrec scev, and we can prove that the value 694 // did not overflow the old, smaller, value, we can sign extend all of the 695 // operands (often constants). This would allow analysis of something like 696 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 697 698 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 699 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 700 return Result; 701} 702 703/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion 704/// of the input value to the specified type. If the type must be 705/// extended, it is zero extended. 706SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 707 const Type *Ty) { 708 const Type *SrcTy = V->getType(); 709 assert(SrcTy->isInteger() && Ty->isInteger() && 710 "Cannot truncate or zero extend with non-integer arguments!"); 711 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 712 return V; // No conversion 713 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 714 return getTruncateExpr(V, Ty); 715 return getZeroExtendExpr(V, Ty); 716} 717 718// get - Get a canonical add expression, or something simpler if possible. 719SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 720 assert(!Ops.empty() && "Cannot get empty add!"); 721 if (Ops.size() == 1) return Ops[0]; 722 723 // Sort by complexity, this groups all similar expression types together. 724 GroupByComplexity(Ops); 725 726 // If there are any constants, fold them together. 727 unsigned Idx = 0; 728 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 729 ++Idx; 730 assert(Idx < Ops.size()); 731 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 732 // We found two constants, fold them together! 733 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 734 RHSC->getValue()->getValue()); 735 Ops[0] = getConstant(Fold); 736 Ops.erase(Ops.begin()+1); // Erase the folded element 737 if (Ops.size() == 1) return Ops[0]; 738 LHSC = cast<SCEVConstant>(Ops[0]); 739 } 740 741 // If we are left with a constant zero being added, strip it off. 742 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 743 Ops.erase(Ops.begin()); 744 --Idx; 745 } 746 } 747 748 if (Ops.size() == 1) return Ops[0]; 749 750 // Okay, check to see if the same value occurs in the operand list twice. If 751 // so, merge them together into an multiply expression. Since we sorted the 752 // list, these values are required to be adjacent. 753 const Type *Ty = Ops[0]->getType(); 754 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 755 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 756 // Found a match, merge the two values into a multiply, and add any 757 // remaining values to the result. 758 SCEVHandle Two = getIntegerSCEV(2, Ty); 759 SCEVHandle Mul = getMulExpr(Ops[i], Two); 760 if (Ops.size() == 2) 761 return Mul; 762 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 763 Ops.push_back(Mul); 764 return getAddExpr(Ops); 765 } 766 767 // Now we know the first non-constant operand. Skip past any cast SCEVs. 768 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 769 ++Idx; 770 771 // If there are add operands they would be next. 772 if (Idx < Ops.size()) { 773 bool DeletedAdd = false; 774 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 775 // If we have an add, expand the add operands onto the end of the operands 776 // list. 777 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 778 Ops.erase(Ops.begin()+Idx); 779 DeletedAdd = true; 780 } 781 782 // If we deleted at least one add, we added operands to the end of the list, 783 // and they are not necessarily sorted. Recurse to resort and resimplify 784 // any operands we just aquired. 785 if (DeletedAdd) 786 return getAddExpr(Ops); 787 } 788 789 // Skip over the add expression until we get to a multiply. 790 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 791 ++Idx; 792 793 // If we are adding something to a multiply expression, make sure the 794 // something is not already an operand of the multiply. If so, merge it into 795 // the multiply. 796 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 797 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 798 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 799 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 800 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 801 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 802 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 803 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 804 if (Mul->getNumOperands() != 2) { 805 // If the multiply has more than two operands, we must get the 806 // Y*Z term. 807 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 808 MulOps.erase(MulOps.begin()+MulOp); 809 InnerMul = getMulExpr(MulOps); 810 } 811 SCEVHandle One = getIntegerSCEV(1, Ty); 812 SCEVHandle AddOne = getAddExpr(InnerMul, One); 813 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 814 if (Ops.size() == 2) return OuterMul; 815 if (AddOp < Idx) { 816 Ops.erase(Ops.begin()+AddOp); 817 Ops.erase(Ops.begin()+Idx-1); 818 } else { 819 Ops.erase(Ops.begin()+Idx); 820 Ops.erase(Ops.begin()+AddOp-1); 821 } 822 Ops.push_back(OuterMul); 823 return getAddExpr(Ops); 824 } 825 826 // Check this multiply against other multiplies being added together. 827 for (unsigned OtherMulIdx = Idx+1; 828 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 829 ++OtherMulIdx) { 830 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 831 // If MulOp occurs in OtherMul, we can fold the two multiplies 832 // together. 833 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 834 OMulOp != e; ++OMulOp) 835 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 836 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 837 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 838 if (Mul->getNumOperands() != 2) { 839 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 840 MulOps.erase(MulOps.begin()+MulOp); 841 InnerMul1 = getMulExpr(MulOps); 842 } 843 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 844 if (OtherMul->getNumOperands() != 2) { 845 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 846 OtherMul->op_end()); 847 MulOps.erase(MulOps.begin()+OMulOp); 848 InnerMul2 = getMulExpr(MulOps); 849 } 850 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 851 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 852 if (Ops.size() == 2) return OuterMul; 853 Ops.erase(Ops.begin()+Idx); 854 Ops.erase(Ops.begin()+OtherMulIdx-1); 855 Ops.push_back(OuterMul); 856 return getAddExpr(Ops); 857 } 858 } 859 } 860 } 861 862 // If there are any add recurrences in the operands list, see if any other 863 // added values are loop invariant. If so, we can fold them into the 864 // recurrence. 865 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 866 ++Idx; 867 868 // Scan over all recurrences, trying to fold loop invariants into them. 869 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 870 // Scan all of the other operands to this add and add them to the vector if 871 // they are loop invariant w.r.t. the recurrence. 872 std::vector<SCEVHandle> LIOps; 873 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 874 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 875 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 876 LIOps.push_back(Ops[i]); 877 Ops.erase(Ops.begin()+i); 878 --i; --e; 879 } 880 881 // If we found some loop invariants, fold them into the recurrence. 882 if (!LIOps.empty()) { 883 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 884 LIOps.push_back(AddRec->getStart()); 885 886 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 887 AddRecOps[0] = getAddExpr(LIOps); 888 889 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 890 // If all of the other operands were loop invariant, we are done. 891 if (Ops.size() == 1) return NewRec; 892 893 // Otherwise, add the folded AddRec by the non-liv parts. 894 for (unsigned i = 0;; ++i) 895 if (Ops[i] == AddRec) { 896 Ops[i] = NewRec; 897 break; 898 } 899 return getAddExpr(Ops); 900 } 901 902 // Okay, if there weren't any loop invariants to be folded, check to see if 903 // there are multiple AddRec's with the same loop induction variable being 904 // added together. If so, we can fold them. 905 for (unsigned OtherIdx = Idx+1; 906 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 907 if (OtherIdx != Idx) { 908 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 909 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 910 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 911 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 912 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 913 if (i >= NewOps.size()) { 914 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 915 OtherAddRec->op_end()); 916 break; 917 } 918 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 919 } 920 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 921 922 if (Ops.size() == 2) return NewAddRec; 923 924 Ops.erase(Ops.begin()+Idx); 925 Ops.erase(Ops.begin()+OtherIdx-1); 926 Ops.push_back(NewAddRec); 927 return getAddExpr(Ops); 928 } 929 } 930 931 // Otherwise couldn't fold anything into this recurrence. Move onto the 932 // next one. 933 } 934 935 // Okay, it looks like we really DO need an add expr. Check to see if we 936 // already have one, otherwise create a new one. 937 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 938 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 939 SCEVOps)]; 940 if (Result == 0) Result = new SCEVAddExpr(Ops); 941 return Result; 942} 943 944 945SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 946 assert(!Ops.empty() && "Cannot get empty mul!"); 947 948 // Sort by complexity, this groups all similar expression types together. 949 GroupByComplexity(Ops); 950 951 // If there are any constants, fold them together. 952 unsigned Idx = 0; 953 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 954 955 // C1*(C2+V) -> C1*C2 + C1*V 956 if (Ops.size() == 2) 957 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 958 if (Add->getNumOperands() == 2 && 959 isa<SCEVConstant>(Add->getOperand(0))) 960 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 961 getMulExpr(LHSC, Add->getOperand(1))); 962 963 964 ++Idx; 965 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 966 // We found two constants, fold them together! 967 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 968 RHSC->getValue()->getValue()); 969 Ops[0] = getConstant(Fold); 970 Ops.erase(Ops.begin()+1); // Erase the folded element 971 if (Ops.size() == 1) return Ops[0]; 972 LHSC = cast<SCEVConstant>(Ops[0]); 973 } 974 975 // If we are left with a constant one being multiplied, strip it off. 976 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 977 Ops.erase(Ops.begin()); 978 --Idx; 979 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 980 // If we have a multiply of zero, it will always be zero. 981 return Ops[0]; 982 } 983 } 984 985 // Skip over the add expression until we get to a multiply. 986 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 987 ++Idx; 988 989 if (Ops.size() == 1) 990 return Ops[0]; 991 992 // If there are mul operands inline them all into this expression. 993 if (Idx < Ops.size()) { 994 bool DeletedMul = false; 995 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 996 // If we have an mul, expand the mul operands onto the end of the operands 997 // list. 998 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 999 Ops.erase(Ops.begin()+Idx); 1000 DeletedMul = true; 1001 } 1002 1003 // If we deleted at least one mul, we added operands to the end of the list, 1004 // and they are not necessarily sorted. Recurse to resort and resimplify 1005 // any operands we just aquired. 1006 if (DeletedMul) 1007 return getMulExpr(Ops); 1008 } 1009 1010 // If there are any add recurrences in the operands list, see if any other 1011 // added values are loop invariant. If so, we can fold them into the 1012 // recurrence. 1013 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1014 ++Idx; 1015 1016 // Scan over all recurrences, trying to fold loop invariants into them. 1017 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1018 // Scan all of the other operands to this mul and add them to the vector if 1019 // they are loop invariant w.r.t. the recurrence. 1020 std::vector<SCEVHandle> LIOps; 1021 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1022 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1023 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1024 LIOps.push_back(Ops[i]); 1025 Ops.erase(Ops.begin()+i); 1026 --i; --e; 1027 } 1028 1029 // If we found some loop invariants, fold them into the recurrence. 1030 if (!LIOps.empty()) { 1031 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 1032 std::vector<SCEVHandle> NewOps; 1033 NewOps.reserve(AddRec->getNumOperands()); 1034 if (LIOps.size() == 1) { 1035 SCEV *Scale = LIOps[0]; 1036 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1037 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1038 } else { 1039 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1040 std::vector<SCEVHandle> MulOps(LIOps); 1041 MulOps.push_back(AddRec->getOperand(i)); 1042 NewOps.push_back(getMulExpr(MulOps)); 1043 } 1044 } 1045 1046 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1047 1048 // If all of the other operands were loop invariant, we are done. 1049 if (Ops.size() == 1) return NewRec; 1050 1051 // Otherwise, multiply the folded AddRec by the non-liv parts. 1052 for (unsigned i = 0;; ++i) 1053 if (Ops[i] == AddRec) { 1054 Ops[i] = NewRec; 1055 break; 1056 } 1057 return getMulExpr(Ops); 1058 } 1059 1060 // Okay, if there weren't any loop invariants to be folded, check to see if 1061 // there are multiple AddRec's with the same loop induction variable being 1062 // multiplied together. If so, we can fold them. 1063 for (unsigned OtherIdx = Idx+1; 1064 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1065 if (OtherIdx != Idx) { 1066 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1067 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1068 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1069 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1070 SCEVHandle NewStart = getMulExpr(F->getStart(), 1071 G->getStart()); 1072 SCEVHandle B = F->getStepRecurrence(*this); 1073 SCEVHandle D = G->getStepRecurrence(*this); 1074 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1075 getMulExpr(G, B), 1076 getMulExpr(B, D)); 1077 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1078 F->getLoop()); 1079 if (Ops.size() == 2) return NewAddRec; 1080 1081 Ops.erase(Ops.begin()+Idx); 1082 Ops.erase(Ops.begin()+OtherIdx-1); 1083 Ops.push_back(NewAddRec); 1084 return getMulExpr(Ops); 1085 } 1086 } 1087 1088 // Otherwise couldn't fold anything into this recurrence. Move onto the 1089 // next one. 1090 } 1091 1092 // Okay, it looks like we really DO need an mul expr. Check to see if we 1093 // already have one, otherwise create a new one. 1094 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1095 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1096 SCEVOps)]; 1097 if (Result == 0) 1098 Result = new SCEVMulExpr(Ops); 1099 return Result; 1100} 1101 1102SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1103 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1104 if (RHSC->getValue()->equalsInt(1)) 1105 return LHS; // X udiv 1 --> x 1106 1107 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1108 Constant *LHSCV = LHSC->getValue(); 1109 Constant *RHSCV = RHSC->getValue(); 1110 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1111 } 1112 } 1113 1114 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1115 1116 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1117 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1118 return Result; 1119} 1120 1121 1122/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1123/// specified loop. Simplify the expression as much as possible. 1124SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1125 const SCEVHandle &Step, const Loop *L) { 1126 std::vector<SCEVHandle> Operands; 1127 Operands.push_back(Start); 1128 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1129 if (StepChrec->getLoop() == L) { 1130 Operands.insert(Operands.end(), StepChrec->op_begin(), 1131 StepChrec->op_end()); 1132 return getAddRecExpr(Operands, L); 1133 } 1134 1135 Operands.push_back(Step); 1136 return getAddRecExpr(Operands, L); 1137} 1138 1139/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1140/// specified loop. Simplify the expression as much as possible. 1141SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1142 const Loop *L) { 1143 if (Operands.size() == 1) return Operands[0]; 1144 1145 if (Operands.back()->isZero()) { 1146 Operands.pop_back(); 1147 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1148 } 1149 1150 SCEVAddRecExpr *&Result = 1151 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1152 Operands.end()))]; 1153 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1154 return Result; 1155} 1156 1157SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1158 const SCEVHandle &RHS) { 1159 std::vector<SCEVHandle> Ops; 1160 Ops.push_back(LHS); 1161 Ops.push_back(RHS); 1162 return getSMaxExpr(Ops); 1163} 1164 1165SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1166 assert(!Ops.empty() && "Cannot get empty smax!"); 1167 if (Ops.size() == 1) return Ops[0]; 1168 1169 // Sort by complexity, this groups all similar expression types together. 1170 GroupByComplexity(Ops); 1171 1172 // If there are any constants, fold them together. 1173 unsigned Idx = 0; 1174 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1175 ++Idx; 1176 assert(Idx < Ops.size()); 1177 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1178 // We found two constants, fold them together! 1179 ConstantInt *Fold = ConstantInt::get( 1180 APIntOps::smax(LHSC->getValue()->getValue(), 1181 RHSC->getValue()->getValue())); 1182 Ops[0] = getConstant(Fold); 1183 Ops.erase(Ops.begin()+1); // Erase the folded element 1184 if (Ops.size() == 1) return Ops[0]; 1185 LHSC = cast<SCEVConstant>(Ops[0]); 1186 } 1187 1188 // If we are left with a constant -inf, strip it off. 1189 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1190 Ops.erase(Ops.begin()); 1191 --Idx; 1192 } 1193 } 1194 1195 if (Ops.size() == 1) return Ops[0]; 1196 1197 // Find the first SMax 1198 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1199 ++Idx; 1200 1201 // Check to see if one of the operands is an SMax. If so, expand its operands 1202 // onto our operand list, and recurse to simplify. 1203 if (Idx < Ops.size()) { 1204 bool DeletedSMax = false; 1205 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1206 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1207 Ops.erase(Ops.begin()+Idx); 1208 DeletedSMax = true; 1209 } 1210 1211 if (DeletedSMax) 1212 return getSMaxExpr(Ops); 1213 } 1214 1215 // Okay, check to see if the same value occurs in the operand list twice. If 1216 // so, delete one. Since we sorted the list, these values are required to 1217 // be adjacent. 1218 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1219 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1220 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1221 --i; --e; 1222 } 1223 1224 if (Ops.size() == 1) return Ops[0]; 1225 1226 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1227 1228 // Okay, it looks like we really DO need an smax expr. Check to see if we 1229 // already have one, otherwise create a new one. 1230 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1231 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1232 SCEVOps)]; 1233 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1234 return Result; 1235} 1236 1237SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1238 const SCEVHandle &RHS) { 1239 std::vector<SCEVHandle> Ops; 1240 Ops.push_back(LHS); 1241 Ops.push_back(RHS); 1242 return getUMaxExpr(Ops); 1243} 1244 1245SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1246 assert(!Ops.empty() && "Cannot get empty umax!"); 1247 if (Ops.size() == 1) return Ops[0]; 1248 1249 // Sort by complexity, this groups all similar expression types together. 1250 GroupByComplexity(Ops); 1251 1252 // If there are any constants, fold them together. 1253 unsigned Idx = 0; 1254 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1255 ++Idx; 1256 assert(Idx < Ops.size()); 1257 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1258 // We found two constants, fold them together! 1259 ConstantInt *Fold = ConstantInt::get( 1260 APIntOps::umax(LHSC->getValue()->getValue(), 1261 RHSC->getValue()->getValue())); 1262 Ops[0] = getConstant(Fold); 1263 Ops.erase(Ops.begin()+1); // Erase the folded element 1264 if (Ops.size() == 1) return Ops[0]; 1265 LHSC = cast<SCEVConstant>(Ops[0]); 1266 } 1267 1268 // If we are left with a constant zero, strip it off. 1269 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1270 Ops.erase(Ops.begin()); 1271 --Idx; 1272 } 1273 } 1274 1275 if (Ops.size() == 1) return Ops[0]; 1276 1277 // Find the first UMax 1278 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1279 ++Idx; 1280 1281 // Check to see if one of the operands is a UMax. If so, expand its operands 1282 // onto our operand list, and recurse to simplify. 1283 if (Idx < Ops.size()) { 1284 bool DeletedUMax = false; 1285 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1286 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1287 Ops.erase(Ops.begin()+Idx); 1288 DeletedUMax = true; 1289 } 1290 1291 if (DeletedUMax) 1292 return getUMaxExpr(Ops); 1293 } 1294 1295 // Okay, check to see if the same value occurs in the operand list twice. If 1296 // so, delete one. Since we sorted the list, these values are required to 1297 // be adjacent. 1298 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1299 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1300 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1301 --i; --e; 1302 } 1303 1304 if (Ops.size() == 1) return Ops[0]; 1305 1306 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1307 1308 // Okay, it looks like we really DO need a umax expr. Check to see if we 1309 // already have one, otherwise create a new one. 1310 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1311 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1312 SCEVOps)]; 1313 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1314 return Result; 1315} 1316 1317SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1318 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1319 return getConstant(CI); 1320 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1321 if (Result == 0) Result = new SCEVUnknown(V); 1322 return Result; 1323} 1324 1325 1326//===----------------------------------------------------------------------===// 1327// ScalarEvolutionsImpl Definition and Implementation 1328//===----------------------------------------------------------------------===// 1329// 1330/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1331/// evolution code. 1332/// 1333namespace { 1334 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1335 /// SE - A reference to the public ScalarEvolution object. 1336 ScalarEvolution &SE; 1337 1338 /// F - The function we are analyzing. 1339 /// 1340 Function &F; 1341 1342 /// LI - The loop information for the function we are currently analyzing. 1343 /// 1344 LoopInfo &LI; 1345 1346 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1347 /// things. 1348 SCEVHandle UnknownValue; 1349 1350 /// Scalars - This is a cache of the scalars we have analyzed so far. 1351 /// 1352 std::map<Value*, SCEVHandle> Scalars; 1353 1354 /// IterationCounts - Cache the iteration count of the loops for this 1355 /// function as they are computed. 1356 std::map<const Loop*, SCEVHandle> IterationCounts; 1357 1358 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1359 /// the PHI instructions that we attempt to compute constant evolutions for. 1360 /// This allows us to avoid potentially expensive recomputation of these 1361 /// properties. An instruction maps to null if we are unable to compute its 1362 /// exit value. 1363 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1364 1365 public: 1366 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1367 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1368 1369 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1370 /// expression and create a new one. 1371 SCEVHandle getSCEV(Value *V); 1372 1373 /// hasSCEV - Return true if the SCEV for this value has already been 1374 /// computed. 1375 bool hasSCEV(Value *V) const { 1376 return Scalars.count(V); 1377 } 1378 1379 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1380 /// the specified value. 1381 void setSCEV(Value *V, const SCEVHandle &H) { 1382 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1383 assert(isNew && "This entry already existed!"); 1384 } 1385 1386 1387 /// getSCEVAtScope - Compute the value of the specified expression within 1388 /// the indicated loop (which may be null to indicate in no loop). If the 1389 /// expression cannot be evaluated, return UnknownValue itself. 1390 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1391 1392 1393 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1394 /// an analyzable loop-invariant iteration count. 1395 bool hasLoopInvariantIterationCount(const Loop *L); 1396 1397 /// getIterationCount - If the specified loop has a predictable iteration 1398 /// count, return it. Note that it is not valid to call this method on a 1399 /// loop without a loop-invariant iteration count. 1400 SCEVHandle getIterationCount(const Loop *L); 1401 1402 /// deleteValueFromRecords - This method should be called by the 1403 /// client before it removes a value from the program, to make sure 1404 /// that no dangling references are left around. 1405 void deleteValueFromRecords(Value *V); 1406 1407 private: 1408 /// createSCEV - We know that there is no SCEV for the specified value. 1409 /// Analyze the expression. 1410 SCEVHandle createSCEV(Value *V); 1411 1412 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1413 /// SCEVs. 1414 SCEVHandle createNodeForPHI(PHINode *PN); 1415 1416 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1417 /// for the specified instruction and replaces any references to the 1418 /// symbolic value SymName with the specified value. This is used during 1419 /// PHI resolution. 1420 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1421 const SCEVHandle &SymName, 1422 const SCEVHandle &NewVal); 1423 1424 /// ComputeIterationCount - Compute the number of times the specified loop 1425 /// will iterate. 1426 SCEVHandle ComputeIterationCount(const Loop *L); 1427 1428 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1429 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1430 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1431 Constant *RHS, 1432 const Loop *L, 1433 ICmpInst::Predicate p); 1434 1435 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1436 /// constant number of times (the condition evolves only from constants), 1437 /// try to evaluate a few iterations of the loop until we get the exit 1438 /// condition gets a value of ExitWhen (true or false). If we cannot 1439 /// evaluate the trip count of the loop, return UnknownValue. 1440 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1441 bool ExitWhen); 1442 1443 /// HowFarToZero - Return the number of times a backedge comparing the 1444 /// specified value to zero will execute. If not computable, return 1445 /// UnknownValue. 1446 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1447 1448 /// HowFarToNonZero - Return the number of times a backedge checking the 1449 /// specified value for nonzero will execute. If not computable, return 1450 /// UnknownValue. 1451 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1452 1453 /// HowManyLessThans - Return the number of times a backedge containing the 1454 /// specified less-than comparison will execute. If not computable, return 1455 /// UnknownValue. isSigned specifies whether the less-than is signed. 1456 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1457 bool isSigned); 1458 1459 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1460 /// in the header of its containing loop, we know the loop executes a 1461 /// constant number of times, and the PHI node is just a recurrence 1462 /// involving constants, fold it. 1463 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1464 const Loop *L); 1465 }; 1466} 1467 1468//===----------------------------------------------------------------------===// 1469// Basic SCEV Analysis and PHI Idiom Recognition Code 1470// 1471 1472/// deleteValueFromRecords - This method should be called by the 1473/// client before it removes an instruction from the program, to make sure 1474/// that no dangling references are left around. 1475void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1476 SmallVector<Value *, 16> Worklist; 1477 1478 if (Scalars.erase(V)) { 1479 if (PHINode *PN = dyn_cast<PHINode>(V)) 1480 ConstantEvolutionLoopExitValue.erase(PN); 1481 Worklist.push_back(V); 1482 } 1483 1484 while (!Worklist.empty()) { 1485 Value *VV = Worklist.back(); 1486 Worklist.pop_back(); 1487 1488 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1489 UI != UE; ++UI) { 1490 Instruction *Inst = cast<Instruction>(*UI); 1491 if (Scalars.erase(Inst)) { 1492 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1493 ConstantEvolutionLoopExitValue.erase(PN); 1494 Worklist.push_back(Inst); 1495 } 1496 } 1497 } 1498} 1499 1500 1501/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1502/// expression and create a new one. 1503SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1504 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1505 1506 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1507 if (I != Scalars.end()) return I->second; 1508 SCEVHandle S = createSCEV(V); 1509 Scalars.insert(std::make_pair(V, S)); 1510 return S; 1511} 1512 1513/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1514/// the specified instruction and replaces any references to the symbolic value 1515/// SymName with the specified value. This is used during PHI resolution. 1516void ScalarEvolutionsImpl:: 1517ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1518 const SCEVHandle &NewVal) { 1519 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1520 if (SI == Scalars.end()) return; 1521 1522 SCEVHandle NV = 1523 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1524 if (NV == SI->second) return; // No change. 1525 1526 SI->second = NV; // Update the scalars map! 1527 1528 // Any instruction values that use this instruction might also need to be 1529 // updated! 1530 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1531 UI != E; ++UI) 1532 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1533} 1534 1535/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1536/// a loop header, making it a potential recurrence, or it doesn't. 1537/// 1538SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1539 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1540 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1541 if (L->getHeader() == PN->getParent()) { 1542 // If it lives in the loop header, it has two incoming values, one 1543 // from outside the loop, and one from inside. 1544 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1545 unsigned BackEdge = IncomingEdge^1; 1546 1547 // While we are analyzing this PHI node, handle its value symbolically. 1548 SCEVHandle SymbolicName = SE.getUnknown(PN); 1549 assert(Scalars.find(PN) == Scalars.end() && 1550 "PHI node already processed?"); 1551 Scalars.insert(std::make_pair(PN, SymbolicName)); 1552 1553 // Using this symbolic name for the PHI, analyze the value coming around 1554 // the back-edge. 1555 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1556 1557 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1558 // has a special value for the first iteration of the loop. 1559 1560 // If the value coming around the backedge is an add with the symbolic 1561 // value we just inserted, then we found a simple induction variable! 1562 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1563 // If there is a single occurrence of the symbolic value, replace it 1564 // with a recurrence. 1565 unsigned FoundIndex = Add->getNumOperands(); 1566 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1567 if (Add->getOperand(i) == SymbolicName) 1568 if (FoundIndex == e) { 1569 FoundIndex = i; 1570 break; 1571 } 1572 1573 if (FoundIndex != Add->getNumOperands()) { 1574 // Create an add with everything but the specified operand. 1575 std::vector<SCEVHandle> Ops; 1576 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1577 if (i != FoundIndex) 1578 Ops.push_back(Add->getOperand(i)); 1579 SCEVHandle Accum = SE.getAddExpr(Ops); 1580 1581 // This is not a valid addrec if the step amount is varying each 1582 // loop iteration, but is not itself an addrec in this loop. 1583 if (Accum->isLoopInvariant(L) || 1584 (isa<SCEVAddRecExpr>(Accum) && 1585 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1586 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1587 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1588 1589 // Okay, for the entire analysis of this edge we assumed the PHI 1590 // to be symbolic. We now need to go back and update all of the 1591 // entries for the scalars that use the PHI (except for the PHI 1592 // itself) to use the new analyzed value instead of the "symbolic" 1593 // value. 1594 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1595 return PHISCEV; 1596 } 1597 } 1598 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1599 // Otherwise, this could be a loop like this: 1600 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1601 // In this case, j = {1,+,1} and BEValue is j. 1602 // Because the other in-value of i (0) fits the evolution of BEValue 1603 // i really is an addrec evolution. 1604 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1605 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1606 1607 // If StartVal = j.start - j.stride, we can use StartVal as the 1608 // initial step of the addrec evolution. 1609 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1610 AddRec->getOperand(1))) { 1611 SCEVHandle PHISCEV = 1612 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1613 1614 // Okay, for the entire analysis of this edge we assumed the PHI 1615 // to be symbolic. We now need to go back and update all of the 1616 // entries for the scalars that use the PHI (except for the PHI 1617 // itself) to use the new analyzed value instead of the "symbolic" 1618 // value. 1619 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1620 return PHISCEV; 1621 } 1622 } 1623 } 1624 1625 return SymbolicName; 1626 } 1627 1628 // If it's not a loop phi, we can't handle it yet. 1629 return SE.getUnknown(PN); 1630} 1631 1632/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1633/// guaranteed to end in (at every loop iteration). It is, at the same time, 1634/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1635/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1636static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1637 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1638 return C->getValue()->getValue().countTrailingZeros(); 1639 1640 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1641 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1642 1643 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1644 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1645 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1646 } 1647 1648 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1649 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1650 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1651 } 1652 1653 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1654 // The result is the min of all operands results. 1655 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1656 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1658 return MinOpRes; 1659 } 1660 1661 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1662 // The result is the sum of all operands results. 1663 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1664 uint32_t BitWidth = M->getBitWidth(); 1665 for (unsigned i = 1, e = M->getNumOperands(); 1666 SumOpRes != BitWidth && i != e; ++i) 1667 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1668 BitWidth); 1669 return SumOpRes; 1670 } 1671 1672 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1673 // The result is the min of all operands results. 1674 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1675 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1676 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1677 return MinOpRes; 1678 } 1679 1680 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1681 // The result is the min of all operands results. 1682 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1683 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1684 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1685 return MinOpRes; 1686 } 1687 1688 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1689 // The result is the min of all operands results. 1690 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1691 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1692 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1693 return MinOpRes; 1694 } 1695 1696 // SCEVUDivExpr, SCEVUnknown 1697 return 0; 1698} 1699 1700/// createSCEV - We know that there is no SCEV for the specified value. 1701/// Analyze the expression. 1702/// 1703SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1704 if (!isa<IntegerType>(V->getType())) 1705 return SE.getUnknown(V); 1706 1707 if (Instruction *I = dyn_cast<Instruction>(V)) { 1708 switch (I->getOpcode()) { 1709 case Instruction::Add: 1710 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1711 getSCEV(I->getOperand(1))); 1712 case Instruction::Mul: 1713 return SE.getMulExpr(getSCEV(I->getOperand(0)), 1714 getSCEV(I->getOperand(1))); 1715 case Instruction::UDiv: 1716 return SE.getUDivExpr(getSCEV(I->getOperand(0)), 1717 getSCEV(I->getOperand(1))); 1718 case Instruction::Sub: 1719 return SE.getMinusSCEV(getSCEV(I->getOperand(0)), 1720 getSCEV(I->getOperand(1))); 1721 case Instruction::Or: 1722 // If the RHS of the Or is a constant, we may have something like: 1723 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1724 // optimizations will transparently handle this case. 1725 // 1726 // In order for this transformation to be safe, the LHS must be of the 1727 // form X*(2^n) and the Or constant must be less than 2^n. 1728 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1729 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1730 const APInt &CIVal = CI->getValue(); 1731 if (GetMinTrailingZeros(LHS) >= 1732 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1733 return SE.getAddExpr(LHS, getSCEV(I->getOperand(1))); 1734 } 1735 break; 1736 case Instruction::Xor: 1737 // If the RHS of the xor is a signbit, then this is just an add. 1738 // Instcombine turns add of signbit into xor as a strength reduction step. 1739 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1740 if (CI->getValue().isSignBit()) 1741 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1742 getSCEV(I->getOperand(1))); 1743 else if (CI->isAllOnesValue()) 1744 return SE.getNotSCEV(getSCEV(I->getOperand(0))); 1745 } 1746 break; 1747 1748 case Instruction::Shl: 1749 // Turn shift left of a constant amount into a multiply. 1750 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1751 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1752 Constant *X = ConstantInt::get( 1753 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1754 return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X)); 1755 } 1756 break; 1757 1758 case Instruction::Trunc: 1759 return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType()); 1760 1761 case Instruction::ZExt: 1762 return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1763 1764 case Instruction::SExt: 1765 return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1766 1767 case Instruction::BitCast: 1768 // BitCasts are no-op casts so we just eliminate the cast. 1769 if (I->getType()->isInteger() && 1770 I->getOperand(0)->getType()->isInteger()) 1771 return getSCEV(I->getOperand(0)); 1772 break; 1773 1774 case Instruction::PHI: 1775 return createNodeForPHI(cast<PHINode>(I)); 1776 1777 case Instruction::Select: 1778 // This could be a smax or umax that was lowered earlier. 1779 // Try to recover it. 1780 if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) { 1781 Value *LHS = ICI->getOperand(0); 1782 Value *RHS = ICI->getOperand(1); 1783 switch (ICI->getPredicate()) { 1784 case ICmpInst::ICMP_SLT: 1785 case ICmpInst::ICMP_SLE: 1786 std::swap(LHS, RHS); 1787 // fall through 1788 case ICmpInst::ICMP_SGT: 1789 case ICmpInst::ICMP_SGE: 1790 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1791 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1792 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1)) 1793 // -smax(-x, -y) == smin(x, y). 1794 return SE.getNegativeSCEV(SE.getSMaxExpr( 1795 SE.getNegativeSCEV(getSCEV(LHS)), 1796 SE.getNegativeSCEV(getSCEV(RHS)))); 1797 break; 1798 case ICmpInst::ICMP_ULT: 1799 case ICmpInst::ICMP_ULE: 1800 std::swap(LHS, RHS); 1801 // fall through 1802 case ICmpInst::ICMP_UGT: 1803 case ICmpInst::ICMP_UGE: 1804 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1805 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1806 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1)) 1807 // ~umax(~x, ~y) == umin(x, y) 1808 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1809 SE.getNotSCEV(getSCEV(RHS)))); 1810 break; 1811 default: 1812 break; 1813 } 1814 } 1815 1816 default: // We cannot analyze this expression. 1817 break; 1818 } 1819 } 1820 1821 return SE.getUnknown(V); 1822} 1823 1824 1825 1826//===----------------------------------------------------------------------===// 1827// Iteration Count Computation Code 1828// 1829 1830/// getIterationCount - If the specified loop has a predictable iteration 1831/// count, return it. Note that it is not valid to call this method on a 1832/// loop without a loop-invariant iteration count. 1833SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1834 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1835 if (I == IterationCounts.end()) { 1836 SCEVHandle ItCount = ComputeIterationCount(L); 1837 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1838 if (ItCount != UnknownValue) { 1839 assert(ItCount->isLoopInvariant(L) && 1840 "Computed trip count isn't loop invariant for loop!"); 1841 ++NumTripCountsComputed; 1842 } else if (isa<PHINode>(L->getHeader()->begin())) { 1843 // Only count loops that have phi nodes as not being computable. 1844 ++NumTripCountsNotComputed; 1845 } 1846 } 1847 return I->second; 1848} 1849 1850/// ComputeIterationCount - Compute the number of times the specified loop 1851/// will iterate. 1852SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1853 // If the loop has a non-one exit block count, we can't analyze it. 1854 SmallVector<BasicBlock*, 8> ExitBlocks; 1855 L->getExitBlocks(ExitBlocks); 1856 if (ExitBlocks.size() != 1) return UnknownValue; 1857 1858 // Okay, there is one exit block. Try to find the condition that causes the 1859 // loop to be exited. 1860 BasicBlock *ExitBlock = ExitBlocks[0]; 1861 1862 BasicBlock *ExitingBlock = 0; 1863 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1864 PI != E; ++PI) 1865 if (L->contains(*PI)) { 1866 if (ExitingBlock == 0) 1867 ExitingBlock = *PI; 1868 else 1869 return UnknownValue; // More than one block exiting! 1870 } 1871 assert(ExitingBlock && "No exits from loop, something is broken!"); 1872 1873 // Okay, we've computed the exiting block. See what condition causes us to 1874 // exit. 1875 // 1876 // FIXME: we should be able to handle switch instructions (with a single exit) 1877 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1878 if (ExitBr == 0) return UnknownValue; 1879 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1880 1881 // At this point, we know we have a conditional branch that determines whether 1882 // the loop is exited. However, we don't know if the branch is executed each 1883 // time through the loop. If not, then the execution count of the branch will 1884 // not be equal to the trip count of the loop. 1885 // 1886 // Currently we check for this by checking to see if the Exit branch goes to 1887 // the loop header. If so, we know it will always execute the same number of 1888 // times as the loop. We also handle the case where the exit block *is* the 1889 // loop header. This is common for un-rotated loops. More extensive analysis 1890 // could be done to handle more cases here. 1891 if (ExitBr->getSuccessor(0) != L->getHeader() && 1892 ExitBr->getSuccessor(1) != L->getHeader() && 1893 ExitBr->getParent() != L->getHeader()) 1894 return UnknownValue; 1895 1896 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1897 1898 // If it's not an integer comparison then compute it the hard way. 1899 // Note that ICmpInst deals with pointer comparisons too so we must check 1900 // the type of the operand. 1901 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1902 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1903 ExitBr->getSuccessor(0) == ExitBlock); 1904 1905 // If the condition was exit on true, convert the condition to exit on false 1906 ICmpInst::Predicate Cond; 1907 if (ExitBr->getSuccessor(1) == ExitBlock) 1908 Cond = ExitCond->getPredicate(); 1909 else 1910 Cond = ExitCond->getInversePredicate(); 1911 1912 // Handle common loops like: for (X = "string"; *X; ++X) 1913 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1914 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1915 SCEVHandle ItCnt = 1916 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1917 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1918 } 1919 1920 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1921 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1922 1923 // Try to evaluate any dependencies out of the loop. 1924 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1925 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1926 Tmp = getSCEVAtScope(RHS, L); 1927 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1928 1929 // At this point, we would like to compute how many iterations of the 1930 // loop the predicate will return true for these inputs. 1931 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1932 // If there is a constant, force it into the RHS. 1933 std::swap(LHS, RHS); 1934 Cond = ICmpInst::getSwappedPredicate(Cond); 1935 } 1936 1937 // FIXME: think about handling pointer comparisons! i.e.: 1938 // while (P != P+100) ++P; 1939 1940 // If we have a comparison of a chrec against a constant, try to use value 1941 // ranges to answer this query. 1942 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1943 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1944 if (AddRec->getLoop() == L) { 1945 // Form the comparison range using the constant of the correct type so 1946 // that the ConstantRange class knows to do a signed or unsigned 1947 // comparison. 1948 ConstantInt *CompVal = RHSC->getValue(); 1949 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1950 CompVal = dyn_cast<ConstantInt>( 1951 ConstantExpr::getBitCast(CompVal, RealTy)); 1952 if (CompVal) { 1953 // Form the constant range. 1954 ConstantRange CompRange( 1955 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1956 1957 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1958 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1959 } 1960 } 1961 1962 switch (Cond) { 1963 case ICmpInst::ICMP_NE: { // while (X != Y) 1964 // Convert to: while (X-Y != 0) 1965 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1966 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1967 break; 1968 } 1969 case ICmpInst::ICMP_EQ: { 1970 // Convert to: while (X-Y == 0) // while (X == Y) 1971 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1972 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1973 break; 1974 } 1975 case ICmpInst::ICMP_SLT: { 1976 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1977 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1978 break; 1979 } 1980 case ICmpInst::ICMP_SGT: { 1981 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1982 SE.getNegativeSCEV(RHS), L, true); 1983 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1984 break; 1985 } 1986 case ICmpInst::ICMP_ULT: { 1987 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1988 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1989 break; 1990 } 1991 case ICmpInst::ICMP_UGT: { 1992 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS), 1993 SE.getNotSCEV(RHS), L, false); 1994 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1995 break; 1996 } 1997 default: 1998#if 0 1999 cerr << "ComputeIterationCount "; 2000 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2001 cerr << "[unsigned] "; 2002 cerr << *LHS << " " 2003 << Instruction::getOpcodeName(Instruction::ICmp) 2004 << " " << *RHS << "\n"; 2005#endif 2006 break; 2007 } 2008 return ComputeIterationCountExhaustively(L, ExitCond, 2009 ExitBr->getSuccessor(0) == ExitBlock); 2010} 2011 2012static ConstantInt * 2013EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2014 ScalarEvolution &SE) { 2015 SCEVHandle InVal = SE.getConstant(C); 2016 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2017 assert(isa<SCEVConstant>(Val) && 2018 "Evaluation of SCEV at constant didn't fold correctly?"); 2019 return cast<SCEVConstant>(Val)->getValue(); 2020} 2021 2022/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2023/// and a GEP expression (missing the pointer index) indexing into it, return 2024/// the addressed element of the initializer or null if the index expression is 2025/// invalid. 2026static Constant * 2027GetAddressedElementFromGlobal(GlobalVariable *GV, 2028 const std::vector<ConstantInt*> &Indices) { 2029 Constant *Init = GV->getInitializer(); 2030 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2031 uint64_t Idx = Indices[i]->getZExtValue(); 2032 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2033 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2034 Init = cast<Constant>(CS->getOperand(Idx)); 2035 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2036 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2037 Init = cast<Constant>(CA->getOperand(Idx)); 2038 } else if (isa<ConstantAggregateZero>(Init)) { 2039 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2040 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2041 Init = Constant::getNullValue(STy->getElementType(Idx)); 2042 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2043 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2044 Init = Constant::getNullValue(ATy->getElementType()); 2045 } else { 2046 assert(0 && "Unknown constant aggregate type!"); 2047 } 2048 return 0; 2049 } else { 2050 return 0; // Unknown initializer type 2051 } 2052 } 2053 return Init; 2054} 2055 2056/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2057/// 'icmp op load X, cst', try to see if we can compute the trip count. 2058SCEVHandle ScalarEvolutionsImpl:: 2059ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2060 const Loop *L, 2061 ICmpInst::Predicate predicate) { 2062 if (LI->isVolatile()) return UnknownValue; 2063 2064 // Check to see if the loaded pointer is a getelementptr of a global. 2065 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2066 if (!GEP) return UnknownValue; 2067 2068 // Make sure that it is really a constant global we are gepping, with an 2069 // initializer, and make sure the first IDX is really 0. 2070 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2071 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2072 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2073 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2074 return UnknownValue; 2075 2076 // Okay, we allow one non-constant index into the GEP instruction. 2077 Value *VarIdx = 0; 2078 std::vector<ConstantInt*> Indexes; 2079 unsigned VarIdxNum = 0; 2080 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2081 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2082 Indexes.push_back(CI); 2083 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2084 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2085 VarIdx = GEP->getOperand(i); 2086 VarIdxNum = i-2; 2087 Indexes.push_back(0); 2088 } 2089 2090 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2091 // Check to see if X is a loop variant variable value now. 2092 SCEVHandle Idx = getSCEV(VarIdx); 2093 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2094 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2095 2096 // We can only recognize very limited forms of loop index expressions, in 2097 // particular, only affine AddRec's like {C1,+,C2}. 2098 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2099 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2100 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2101 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2102 return UnknownValue; 2103 2104 unsigned MaxSteps = MaxBruteForceIterations; 2105 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2106 ConstantInt *ItCst = 2107 ConstantInt::get(IdxExpr->getType(), IterationNum); 2108 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2109 2110 // Form the GEP offset. 2111 Indexes[VarIdxNum] = Val; 2112 2113 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2114 if (Result == 0) break; // Cannot compute! 2115 2116 // Evaluate the condition for this iteration. 2117 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2118 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2119 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2120#if 0 2121 cerr << "\n***\n*** Computed loop count " << *ItCst 2122 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2123 << "***\n"; 2124#endif 2125 ++NumArrayLenItCounts; 2126 return SE.getConstant(ItCst); // Found terminating iteration! 2127 } 2128 } 2129 return UnknownValue; 2130} 2131 2132 2133/// CanConstantFold - Return true if we can constant fold an instruction of the 2134/// specified type, assuming that all operands were constants. 2135static bool CanConstantFold(const Instruction *I) { 2136 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2137 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2138 return true; 2139 2140 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2141 if (const Function *F = CI->getCalledFunction()) 2142 return canConstantFoldCallTo(F); 2143 return false; 2144} 2145 2146/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2147/// in the loop that V is derived from. We allow arbitrary operations along the 2148/// way, but the operands of an operation must either be constants or a value 2149/// derived from a constant PHI. If this expression does not fit with these 2150/// constraints, return null. 2151static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2152 // If this is not an instruction, or if this is an instruction outside of the 2153 // loop, it can't be derived from a loop PHI. 2154 Instruction *I = dyn_cast<Instruction>(V); 2155 if (I == 0 || !L->contains(I->getParent())) return 0; 2156 2157 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2158 if (L->getHeader() == I->getParent()) 2159 return PN; 2160 else 2161 // We don't currently keep track of the control flow needed to evaluate 2162 // PHIs, so we cannot handle PHIs inside of loops. 2163 return 0; 2164 } 2165 2166 // If we won't be able to constant fold this expression even if the operands 2167 // are constants, return early. 2168 if (!CanConstantFold(I)) return 0; 2169 2170 // Otherwise, we can evaluate this instruction if all of its operands are 2171 // constant or derived from a PHI node themselves. 2172 PHINode *PHI = 0; 2173 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2174 if (!(isa<Constant>(I->getOperand(Op)) || 2175 isa<GlobalValue>(I->getOperand(Op)))) { 2176 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2177 if (P == 0) return 0; // Not evolving from PHI 2178 if (PHI == 0) 2179 PHI = P; 2180 else if (PHI != P) 2181 return 0; // Evolving from multiple different PHIs. 2182 } 2183 2184 // This is a expression evolving from a constant PHI! 2185 return PHI; 2186} 2187 2188/// EvaluateExpression - Given an expression that passes the 2189/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2190/// in the loop has the value PHIVal. If we can't fold this expression for some 2191/// reason, return null. 2192static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2193 if (isa<PHINode>(V)) return PHIVal; 2194 if (Constant *C = dyn_cast<Constant>(V)) return C; 2195 Instruction *I = cast<Instruction>(V); 2196 2197 std::vector<Constant*> Operands; 2198 Operands.resize(I->getNumOperands()); 2199 2200 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2201 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2202 if (Operands[i] == 0) return 0; 2203 } 2204 2205 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2206 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2207 &Operands[0], Operands.size()); 2208 else 2209 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2210 &Operands[0], Operands.size()); 2211} 2212 2213/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2214/// in the header of its containing loop, we know the loop executes a 2215/// constant number of times, and the PHI node is just a recurrence 2216/// involving constants, fold it. 2217Constant *ScalarEvolutionsImpl:: 2218getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2219 std::map<PHINode*, Constant*>::iterator I = 2220 ConstantEvolutionLoopExitValue.find(PN); 2221 if (I != ConstantEvolutionLoopExitValue.end()) 2222 return I->second; 2223 2224 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2225 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2226 2227 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2228 2229 // Since the loop is canonicalized, the PHI node must have two entries. One 2230 // entry must be a constant (coming in from outside of the loop), and the 2231 // second must be derived from the same PHI. 2232 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2233 Constant *StartCST = 2234 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2235 if (StartCST == 0) 2236 return RetVal = 0; // Must be a constant. 2237 2238 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2239 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2240 if (PN2 != PN) 2241 return RetVal = 0; // Not derived from same PHI. 2242 2243 // Execute the loop symbolically to determine the exit value. 2244 if (Its.getActiveBits() >= 32) 2245 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2246 2247 unsigned NumIterations = Its.getZExtValue(); // must be in range 2248 unsigned IterationNum = 0; 2249 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2250 if (IterationNum == NumIterations) 2251 return RetVal = PHIVal; // Got exit value! 2252 2253 // Compute the value of the PHI node for the next iteration. 2254 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2255 if (NextPHI == PHIVal) 2256 return RetVal = NextPHI; // Stopped evolving! 2257 if (NextPHI == 0) 2258 return 0; // Couldn't evaluate! 2259 PHIVal = NextPHI; 2260 } 2261} 2262 2263/// ComputeIterationCountExhaustively - If the trip is known to execute a 2264/// constant number of times (the condition evolves only from constants), 2265/// try to evaluate a few iterations of the loop until we get the exit 2266/// condition gets a value of ExitWhen (true or false). If we cannot 2267/// evaluate the trip count of the loop, return UnknownValue. 2268SCEVHandle ScalarEvolutionsImpl:: 2269ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2270 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2271 if (PN == 0) return UnknownValue; 2272 2273 // Since the loop is canonicalized, the PHI node must have two entries. One 2274 // entry must be a constant (coming in from outside of the loop), and the 2275 // second must be derived from the same PHI. 2276 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2277 Constant *StartCST = 2278 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2279 if (StartCST == 0) return UnknownValue; // Must be a constant. 2280 2281 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2282 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2283 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2284 2285 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2286 // the loop symbolically to determine when the condition gets a value of 2287 // "ExitWhen". 2288 unsigned IterationNum = 0; 2289 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2290 for (Constant *PHIVal = StartCST; 2291 IterationNum != MaxIterations; ++IterationNum) { 2292 ConstantInt *CondVal = 2293 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2294 2295 // Couldn't symbolically evaluate. 2296 if (!CondVal) return UnknownValue; 2297 2298 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2299 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2300 ++NumBruteForceTripCountsComputed; 2301 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2302 } 2303 2304 // Compute the value of the PHI node for the next iteration. 2305 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2306 if (NextPHI == 0 || NextPHI == PHIVal) 2307 return UnknownValue; // Couldn't evaluate or not making progress... 2308 PHIVal = NextPHI; 2309 } 2310 2311 // Too many iterations were needed to evaluate. 2312 return UnknownValue; 2313} 2314 2315/// getSCEVAtScope - Compute the value of the specified expression within the 2316/// indicated loop (which may be null to indicate in no loop). If the 2317/// expression cannot be evaluated, return UnknownValue. 2318SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2319 // FIXME: this should be turned into a virtual method on SCEV! 2320 2321 if (isa<SCEVConstant>(V)) return V; 2322 2323 // If this instruction is evolved from a constant-evolving PHI, compute the 2324 // exit value from the loop without using SCEVs. 2325 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2326 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2327 const Loop *LI = this->LI[I->getParent()]; 2328 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2329 if (PHINode *PN = dyn_cast<PHINode>(I)) 2330 if (PN->getParent() == LI->getHeader()) { 2331 // Okay, there is no closed form solution for the PHI node. Check 2332 // to see if the loop that contains it has a known iteration count. 2333 // If so, we may be able to force computation of the exit value. 2334 SCEVHandle IterationCount = getIterationCount(LI); 2335 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2336 // Okay, we know how many times the containing loop executes. If 2337 // this is a constant evolving PHI node, get the final value at 2338 // the specified iteration number. 2339 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2340 ICC->getValue()->getValue(), 2341 LI); 2342 if (RV) return SE.getUnknown(RV); 2343 } 2344 } 2345 2346 // Okay, this is an expression that we cannot symbolically evaluate 2347 // into a SCEV. Check to see if it's possible to symbolically evaluate 2348 // the arguments into constants, and if so, try to constant propagate the 2349 // result. This is particularly useful for computing loop exit values. 2350 if (CanConstantFold(I)) { 2351 std::vector<Constant*> Operands; 2352 Operands.reserve(I->getNumOperands()); 2353 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2354 Value *Op = I->getOperand(i); 2355 if (Constant *C = dyn_cast<Constant>(Op)) { 2356 Operands.push_back(C); 2357 } else { 2358 // If any of the operands is non-constant and if they are 2359 // non-integer, don't even try to analyze them with scev techniques. 2360 if (!isa<IntegerType>(Op->getType())) 2361 return V; 2362 2363 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2364 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2365 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2366 Op->getType(), 2367 false)); 2368 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2369 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2370 Operands.push_back(ConstantExpr::getIntegerCast(C, 2371 Op->getType(), 2372 false)); 2373 else 2374 return V; 2375 } else { 2376 return V; 2377 } 2378 } 2379 } 2380 2381 Constant *C; 2382 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2383 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2384 &Operands[0], Operands.size()); 2385 else 2386 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2387 &Operands[0], Operands.size()); 2388 return SE.getUnknown(C); 2389 } 2390 } 2391 2392 // This is some other type of SCEVUnknown, just return it. 2393 return V; 2394 } 2395 2396 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2397 // Avoid performing the look-up in the common case where the specified 2398 // expression has no loop-variant portions. 2399 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2400 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2401 if (OpAtScope != Comm->getOperand(i)) { 2402 if (OpAtScope == UnknownValue) return UnknownValue; 2403 // Okay, at least one of these operands is loop variant but might be 2404 // foldable. Build a new instance of the folded commutative expression. 2405 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2406 NewOps.push_back(OpAtScope); 2407 2408 for (++i; i != e; ++i) { 2409 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2410 if (OpAtScope == UnknownValue) return UnknownValue; 2411 NewOps.push_back(OpAtScope); 2412 } 2413 if (isa<SCEVAddExpr>(Comm)) 2414 return SE.getAddExpr(NewOps); 2415 if (isa<SCEVMulExpr>(Comm)) 2416 return SE.getMulExpr(NewOps); 2417 if (isa<SCEVSMaxExpr>(Comm)) 2418 return SE.getSMaxExpr(NewOps); 2419 if (isa<SCEVUMaxExpr>(Comm)) 2420 return SE.getUMaxExpr(NewOps); 2421 assert(0 && "Unknown commutative SCEV type!"); 2422 } 2423 } 2424 // If we got here, all operands are loop invariant. 2425 return Comm; 2426 } 2427 2428 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2429 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2430 if (LHS == UnknownValue) return LHS; 2431 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2432 if (RHS == UnknownValue) return RHS; 2433 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2434 return Div; // must be loop invariant 2435 return SE.getUDivExpr(LHS, RHS); 2436 } 2437 2438 // If this is a loop recurrence for a loop that does not contain L, then we 2439 // are dealing with the final value computed by the loop. 2440 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2441 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2442 // To evaluate this recurrence, we need to know how many times the AddRec 2443 // loop iterates. Compute this now. 2444 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2445 if (IterationCount == UnknownValue) return UnknownValue; 2446 IterationCount = SE.getTruncateOrZeroExtend(IterationCount, 2447 AddRec->getType()); 2448 2449 // If the value is affine, simplify the expression evaluation to just 2450 // Start + Step*IterationCount. 2451 if (AddRec->isAffine()) 2452 return SE.getAddExpr(AddRec->getStart(), 2453 SE.getMulExpr(IterationCount, 2454 AddRec->getOperand(1))); 2455 2456 // Otherwise, evaluate it the hard way. 2457 return AddRec->evaluateAtIteration(IterationCount, SE); 2458 } 2459 return UnknownValue; 2460 } 2461 2462 //assert(0 && "Unknown SCEV type!"); 2463 return UnknownValue; 2464} 2465 2466 2467/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2468/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2469/// might be the same) or two SCEVCouldNotCompute objects. 2470/// 2471static std::pair<SCEVHandle,SCEVHandle> 2472SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2473 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2474 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2475 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2476 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2477 2478 // We currently can only solve this if the coefficients are constants. 2479 if (!LC || !MC || !NC) { 2480 SCEV *CNC = new SCEVCouldNotCompute(); 2481 return std::make_pair(CNC, CNC); 2482 } 2483 2484 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2485 const APInt &L = LC->getValue()->getValue(); 2486 const APInt &M = MC->getValue()->getValue(); 2487 const APInt &N = NC->getValue()->getValue(); 2488 APInt Two(BitWidth, 2); 2489 APInt Four(BitWidth, 4); 2490 2491 { 2492 using namespace APIntOps; 2493 const APInt& C = L; 2494 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2495 // The B coefficient is M-N/2 2496 APInt B(M); 2497 B -= sdiv(N,Two); 2498 2499 // The A coefficient is N/2 2500 APInt A(N.sdiv(Two)); 2501 2502 // Compute the B^2-4ac term. 2503 APInt SqrtTerm(B); 2504 SqrtTerm *= B; 2505 SqrtTerm -= Four * (A * C); 2506 2507 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2508 // integer value or else APInt::sqrt() will assert. 2509 APInt SqrtVal(SqrtTerm.sqrt()); 2510 2511 // Compute the two solutions for the quadratic formula. 2512 // The divisions must be performed as signed divisions. 2513 APInt NegB(-B); 2514 APInt TwoA( A << 1 ); 2515 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2516 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2517 2518 return std::make_pair(SE.getConstant(Solution1), 2519 SE.getConstant(Solution2)); 2520 } // end APIntOps namespace 2521} 2522 2523/// HowFarToZero - Return the number of times a backedge comparing the specified 2524/// value to zero will execute. If not computable, return UnknownValue 2525SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2526 // If the value is a constant 2527 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2528 // If the value is already zero, the branch will execute zero times. 2529 if (C->getValue()->isZero()) return C; 2530 return UnknownValue; // Otherwise it will loop infinitely. 2531 } 2532 2533 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2534 if (!AddRec || AddRec->getLoop() != L) 2535 return UnknownValue; 2536 2537 if (AddRec->isAffine()) { 2538 // If this is an affine expression the execution count of this branch is 2539 // equal to: 2540 // 2541 // (0 - Start/Step) iff Start % Step == 0 2542 // 2543 // Get the initial value for the loop. 2544 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2545 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2546 SCEVHandle Step = AddRec->getOperand(1); 2547 2548 Step = getSCEVAtScope(Step, L->getParentLoop()); 2549 2550 // Figure out if Start % Step == 0. 2551 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2552 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2553 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2554 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start 2555 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2556 return Start; // 0 - Start/-1 == Start 2557 2558 // Check to see if Start is divisible by SC with no remainder. 2559 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2560 ConstantInt *StartCC = StartC->getValue(); 2561 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2562 Constant *Rem = ConstantExpr::getURem(StartNegC, StepC->getValue()); 2563 if (Rem->isNullValue()) { 2564 Constant *Result = ConstantExpr::getUDiv(StartNegC,StepC->getValue()); 2565 return SE.getUnknown(Result); 2566 } 2567 } 2568 } 2569 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2570 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2571 // the quadratic equation to solve it. 2572 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2573 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2574 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2575 if (R1) { 2576#if 0 2577 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2578 << " sol#2: " << *R2 << "\n"; 2579#endif 2580 // Pick the smallest positive root value. 2581 if (ConstantInt *CB = 2582 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2583 R1->getValue(), R2->getValue()))) { 2584 if (CB->getZExtValue() == false) 2585 std::swap(R1, R2); // R1 is the minimum root now. 2586 2587 // We can only use this value if the chrec ends up with an exact zero 2588 // value at this index. When solving for "X*X != 5", for example, we 2589 // should not accept a root of 2. 2590 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2591 if (Val->isZero()) 2592 return R1; // We found a quadratic root! 2593 } 2594 } 2595 } 2596 2597 return UnknownValue; 2598} 2599 2600/// HowFarToNonZero - Return the number of times a backedge checking the 2601/// specified value for nonzero will execute. If not computable, return 2602/// UnknownValue 2603SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2604 // Loops that look like: while (X == 0) are very strange indeed. We don't 2605 // handle them yet except for the trivial case. This could be expanded in the 2606 // future as needed. 2607 2608 // If the value is a constant, check to see if it is known to be non-zero 2609 // already. If so, the backedge will execute zero times. 2610 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2611 if (!C->getValue()->isNullValue()) 2612 return SE.getIntegerSCEV(0, C->getType()); 2613 return UnknownValue; // Otherwise it will loop infinitely. 2614 } 2615 2616 // We could implement others, but I really doubt anyone writes loops like 2617 // this, and if they did, they would already be constant folded. 2618 return UnknownValue; 2619} 2620 2621/// HowManyLessThans - Return the number of times a backedge containing the 2622/// specified less-than comparison will execute. If not computable, return 2623/// UnknownValue. 2624SCEVHandle ScalarEvolutionsImpl:: 2625HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2626 // Only handle: "ADDREC < LoopInvariant". 2627 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2628 2629 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2630 if (!AddRec || AddRec->getLoop() != L) 2631 return UnknownValue; 2632 2633 if (AddRec->isAffine()) { 2634 // FORNOW: We only support unit strides. 2635 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2636 if (AddRec->getOperand(1) != One) 2637 return UnknownValue; 2638 2639 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2640 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2641 // Note that we cannot simply return max(m-n,0) because it's not safe to 2642 // treat m-n as signed nor unsigned due to overflow possibility. 2643 2644 // First, we get the value of the LHS in the first iteration: n 2645 SCEVHandle Start = AddRec->getOperand(0); 2646 2647 // Then, we get the value of the LHS in the first iteration in which the 2648 // above condition doesn't hold. This equals to max(m,n). 2649 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2650 : SE.getUMaxExpr(RHS, Start); 2651 2652 // Finally, we subtract these two values to get the number of times the 2653 // backedge is executed: max(m,n)-n. 2654 return SE.getMinusSCEV(End, Start); 2655 } 2656 2657 return UnknownValue; 2658} 2659 2660/// getNumIterationsInRange - Return the number of iterations of this loop that 2661/// produce values in the specified constant range. Another way of looking at 2662/// this is that it returns the first iteration number where the value is not in 2663/// the condition, thus computing the exit count. If the iteration count can't 2664/// be computed, an instance of SCEVCouldNotCompute is returned. 2665SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2666 ScalarEvolution &SE) const { 2667 if (Range.isFullSet()) // Infinite loop. 2668 return new SCEVCouldNotCompute(); 2669 2670 // If the start is a non-zero constant, shift the range to simplify things. 2671 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2672 if (!SC->getValue()->isZero()) { 2673 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2674 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2675 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2676 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2677 return ShiftedAddRec->getNumIterationsInRange( 2678 Range.subtract(SC->getValue()->getValue()), SE); 2679 // This is strange and shouldn't happen. 2680 return new SCEVCouldNotCompute(); 2681 } 2682 2683 // The only time we can solve this is when we have all constant indices. 2684 // Otherwise, we cannot determine the overflow conditions. 2685 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2686 if (!isa<SCEVConstant>(getOperand(i))) 2687 return new SCEVCouldNotCompute(); 2688 2689 2690 // Okay at this point we know that all elements of the chrec are constants and 2691 // that the start element is zero. 2692 2693 // First check to see if the range contains zero. If not, the first 2694 // iteration exits. 2695 if (!Range.contains(APInt(getBitWidth(),0))) 2696 return SE.getConstant(ConstantInt::get(getType(),0)); 2697 2698 if (isAffine()) { 2699 // If this is an affine expression then we have this situation: 2700 // Solve {0,+,A} in Range === Ax in Range 2701 2702 // We know that zero is in the range. If A is positive then we know that 2703 // the upper value of the range must be the first possible exit value. 2704 // If A is negative then the lower of the range is the last possible loop 2705 // value. Also note that we already checked for a full range. 2706 APInt One(getBitWidth(),1); 2707 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2708 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2709 2710 // The exit value should be (End+A)/A. 2711 APInt ExitVal = (End + A).udiv(A); 2712 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2713 2714 // Evaluate at the exit value. If we really did fall out of the valid 2715 // range, then we computed our trip count, otherwise wrap around or other 2716 // things must have happened. 2717 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2718 if (Range.contains(Val->getValue())) 2719 return new SCEVCouldNotCompute(); // Something strange happened 2720 2721 // Ensure that the previous value is in the range. This is a sanity check. 2722 assert(Range.contains( 2723 EvaluateConstantChrecAtConstant(this, 2724 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2725 "Linear scev computation is off in a bad way!"); 2726 return SE.getConstant(ExitValue); 2727 } else if (isQuadratic()) { 2728 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2729 // quadratic equation to solve it. To do this, we must frame our problem in 2730 // terms of figuring out when zero is crossed, instead of when 2731 // Range.getUpper() is crossed. 2732 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2733 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2734 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2735 2736 // Next, solve the constructed addrec 2737 std::pair<SCEVHandle,SCEVHandle> Roots = 2738 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2739 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2740 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2741 if (R1) { 2742 // Pick the smallest positive root value. 2743 if (ConstantInt *CB = 2744 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2745 R1->getValue(), R2->getValue()))) { 2746 if (CB->getZExtValue() == false) 2747 std::swap(R1, R2); // R1 is the minimum root now. 2748 2749 // Make sure the root is not off by one. The returned iteration should 2750 // not be in the range, but the previous one should be. When solving 2751 // for "X*X < 5", for example, we should not return a root of 2. 2752 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2753 R1->getValue(), 2754 SE); 2755 if (Range.contains(R1Val->getValue())) { 2756 // The next iteration must be out of the range... 2757 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2758 2759 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2760 if (!Range.contains(R1Val->getValue())) 2761 return SE.getConstant(NextVal); 2762 return new SCEVCouldNotCompute(); // Something strange happened 2763 } 2764 2765 // If R1 was not in the range, then it is a good return value. Make 2766 // sure that R1-1 WAS in the range though, just in case. 2767 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2768 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2769 if (Range.contains(R1Val->getValue())) 2770 return R1; 2771 return new SCEVCouldNotCompute(); // Something strange happened 2772 } 2773 } 2774 } 2775 2776 // Fallback, if this is a general polynomial, figure out the progression 2777 // through brute force: evaluate until we find an iteration that fails the 2778 // test. This is likely to be slow, but getting an accurate trip count is 2779 // incredibly important, we will be able to simplify the exit test a lot, and 2780 // we are almost guaranteed to get a trip count in this case. 2781 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2782 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2783 do { 2784 ++NumBruteForceEvaluations; 2785 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2786 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2787 return new SCEVCouldNotCompute(); 2788 2789 // Check to see if we found the value! 2790 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2791 return SE.getConstant(TestVal); 2792 2793 // Increment to test the next index. 2794 TestVal = ConstantInt::get(TestVal->getValue()+1); 2795 } while (TestVal != EndVal); 2796 2797 return new SCEVCouldNotCompute(); 2798} 2799 2800 2801 2802//===----------------------------------------------------------------------===// 2803// ScalarEvolution Class Implementation 2804//===----------------------------------------------------------------------===// 2805 2806bool ScalarEvolution::runOnFunction(Function &F) { 2807 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2808 return false; 2809} 2810 2811void ScalarEvolution::releaseMemory() { 2812 delete (ScalarEvolutionsImpl*)Impl; 2813 Impl = 0; 2814} 2815 2816void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2817 AU.setPreservesAll(); 2818 AU.addRequiredTransitive<LoopInfo>(); 2819} 2820 2821SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2822 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2823} 2824 2825/// hasSCEV - Return true if the SCEV for this value has already been 2826/// computed. 2827bool ScalarEvolution::hasSCEV(Value *V) const { 2828 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2829} 2830 2831 2832/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2833/// the specified value. 2834void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2835 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2836} 2837 2838 2839SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2840 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2841} 2842 2843bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2844 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2845} 2846 2847SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2848 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2849} 2850 2851void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2852 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2853} 2854 2855static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2856 const Loop *L) { 2857 // Print all inner loops first 2858 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2859 PrintLoopInfo(OS, SE, *I); 2860 2861 OS << "Loop " << L->getHeader()->getName() << ": "; 2862 2863 SmallVector<BasicBlock*, 8> ExitBlocks; 2864 L->getExitBlocks(ExitBlocks); 2865 if (ExitBlocks.size() != 1) 2866 OS << "<multiple exits> "; 2867 2868 if (SE->hasLoopInvariantIterationCount(L)) { 2869 OS << *SE->getIterationCount(L) << " iterations! "; 2870 } else { 2871 OS << "Unpredictable iteration count. "; 2872 } 2873 2874 OS << "\n"; 2875} 2876 2877void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2878 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2879 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2880 2881 OS << "Classifying expressions for: " << F.getName() << "\n"; 2882 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2883 if (I->getType()->isInteger()) { 2884 OS << *I; 2885 OS << " --> "; 2886 SCEVHandle SV = getSCEV(&*I); 2887 SV->print(OS); 2888 OS << "\t\t"; 2889 2890 if ((*I).getType()->isInteger()) { 2891 ConstantRange Bounds = SV->getValueRange(); 2892 if (!Bounds.isFullSet()) 2893 OS << "Bounds: " << Bounds << " "; 2894 } 2895 2896 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2897 OS << "Exits: "; 2898 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2899 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2900 OS << "<<Unknown>>"; 2901 } else { 2902 OS << *ExitValue; 2903 } 2904 } 2905 2906 2907 OS << "\n"; 2908 } 2909 2910 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2911 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2912 PrintLoopInfo(OS, this, *I); 2913} 2914