ScalarEvolution.cpp revision 4f4c28f75f74fe557efb63feaf5f4f8bf639dcd5
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 98cl::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 104namespace { 105 RegisterPass<ScalarEvolution> 106 R("scalar-evolution", "Scalar Evolution Analysis", false, true); 107} 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117SCEV::~SCEV() {} 118void SCEV::dump() const { 119 print(cerr); 120} 121 122/// getValueRange - Return the tightest constant bounds that this value is 123/// known to have. This method is only valid on integer SCEV objects. 124ConstantRange SCEV::getValueRange() const { 125 const Type *Ty = getType(); 126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!"); 127 // Default to a full range if no better information is available. 128 return ConstantRange(getBitWidth()); 129} 130 131uint32_t SCEV::getBitWidth() const { 132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType())) 133 return ITy->getBitWidth(); 134 return 0; 135} 136 137 138SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 139 140bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 142 return false; 143} 144 145const Type *SCEVCouldNotCompute::getType() const { 146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 147 return 0; 148} 149 150bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 152 return false; 153} 154 155SCEVHandle SCEVCouldNotCompute:: 156replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 157 const SCEVHandle &Conc, 158 ScalarEvolution &SE) const { 159 return this; 160} 161 162void SCEVCouldNotCompute::print(std::ostream &OS) const { 163 OS << "***COULDNOTCOMPUTE***"; 164} 165 166bool SCEVCouldNotCompute::classof(const SCEV *S) { 167 return S->getSCEVType() == scCouldNotCompute; 168} 169 170 171// SCEVConstants - Only allow the creation of one SCEVConstant for any 172// particular value. Don't use a SCEVHandle here, or else the object will 173// never be deleted! 174static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 175 176 177SCEVConstant::~SCEVConstant() { 178 SCEVConstants->erase(V); 179} 180 181SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 182 SCEVConstant *&R = (*SCEVConstants)[V]; 183 if (R == 0) R = new SCEVConstant(V); 184 return R; 185} 186 187SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 188 return getConstant(ConstantInt::get(Val)); 189} 190 191ConstantRange SCEVConstant::getValueRange() const { 192 return ConstantRange(V->getValue()); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(std::ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 202// particular input. Don't use a SCEVHandle here, or else the object will 203// never be deleted! 204static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 205 SCEVTruncateExpr*> > SCEVTruncates; 206 207SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 208 : SCEV(scTruncate), Op(op), Ty(ty) { 209 assert(Op->getType()->isInteger() && Ty->isInteger() && 210 "Cannot truncate non-integer value!"); 211 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits() 212 && "This is not a truncating conversion!"); 213} 214 215SCEVTruncateExpr::~SCEVTruncateExpr() { 216 SCEVTruncates->erase(std::make_pair(Op, Ty)); 217} 218 219ConstantRange SCEVTruncateExpr::getValueRange() const { 220 return getOperand()->getValueRange().truncate(getBitWidth()); 221} 222 223void SCEVTruncateExpr::print(std::ostream &OS) const { 224 OS << "(truncate " << *Op << " to " << *Ty << ")"; 225} 226 227// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 228// particular input. Don't use a SCEVHandle here, or else the object will never 229// be deleted! 230static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 231 SCEVZeroExtendExpr*> > SCEVZeroExtends; 232 233SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 234 : SCEV(scZeroExtend), Op(op), Ty(ty) { 235 assert(Op->getType()->isInteger() && Ty->isInteger() && 236 "Cannot zero extend non-integer value!"); 237 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 238 && "This is not an extending conversion!"); 239} 240 241SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 242 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 243} 244 245ConstantRange SCEVZeroExtendExpr::getValueRange() const { 246 return getOperand()->getValueRange().zeroExtend(getBitWidth()); 247} 248 249void SCEVZeroExtendExpr::print(std::ostream &OS) const { 250 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 251} 252 253// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 254// particular input. Don't use a SCEVHandle here, or else the object will never 255// be deleted! 256static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 257 SCEVSignExtendExpr*> > SCEVSignExtends; 258 259SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 260 : SCEV(scSignExtend), Op(op), Ty(ty) { 261 assert(Op->getType()->isInteger() && Ty->isInteger() && 262 "Cannot sign extend non-integer value!"); 263 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits() 264 && "This is not an extending conversion!"); 265} 266 267SCEVSignExtendExpr::~SCEVSignExtendExpr() { 268 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 269} 270 271ConstantRange SCEVSignExtendExpr::getValueRange() const { 272 return getOperand()->getValueRange().signExtend(getBitWidth()); 273} 274 275void SCEVSignExtendExpr::print(std::ostream &OS) const { 276 OS << "(signextend " << *Op << " to " << *Ty << ")"; 277} 278 279// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 280// particular input. Don't use a SCEVHandle here, or else the object will never 281// be deleted! 282static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 283 SCEVCommutativeExpr*> > SCEVCommExprs; 284 285SCEVCommutativeExpr::~SCEVCommutativeExpr() { 286 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 287 std::vector<SCEV*>(Operands.begin(), 288 Operands.end()))); 289} 290 291void SCEVCommutativeExpr::print(std::ostream &OS) const { 292 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 293 const char *OpStr = getOperationStr(); 294 OS << "(" << *Operands[0]; 295 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 296 OS << OpStr << *Operands[i]; 297 OS << ")"; 298} 299 300SCEVHandle SCEVCommutativeExpr:: 301replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 302 const SCEVHandle &Conc, 303 ScalarEvolution &SE) const { 304 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 305 SCEVHandle H = 306 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 307 if (H != getOperand(i)) { 308 std::vector<SCEVHandle> NewOps; 309 NewOps.reserve(getNumOperands()); 310 for (unsigned j = 0; j != i; ++j) 311 NewOps.push_back(getOperand(j)); 312 NewOps.push_back(H); 313 for (++i; i != e; ++i) 314 NewOps.push_back(getOperand(i)-> 315 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 316 317 if (isa<SCEVAddExpr>(this)) 318 return SE.getAddExpr(NewOps); 319 else if (isa<SCEVMulExpr>(this)) 320 return SE.getMulExpr(NewOps); 321 else if (isa<SCEVSMaxExpr>(this)) 322 return SE.getSMaxExpr(NewOps); 323 else if (isa<SCEVUMaxExpr>(this)) 324 return SE.getUMaxExpr(NewOps); 325 else 326 assert(0 && "Unknown commutative expr!"); 327 } 328 } 329 return this; 330} 331 332 333// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 334// input. Don't use a SCEVHandle here, or else the object will never be 335// deleted! 336static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 337 SCEVUDivExpr*> > SCEVUDivs; 338 339SCEVUDivExpr::~SCEVUDivExpr() { 340 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 341} 342 343void SCEVUDivExpr::print(std::ostream &OS) const { 344 OS << "(" << *LHS << " /u " << *RHS << ")"; 345} 346 347const Type *SCEVUDivExpr::getType() const { 348 return LHS->getType(); 349} 350 351// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 352// particular input. Don't use a SCEVHandle here, or else the object will never 353// be deleted! 354static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 355 SCEVAddRecExpr*> > SCEVAddRecExprs; 356 357SCEVAddRecExpr::~SCEVAddRecExpr() { 358 SCEVAddRecExprs->erase(std::make_pair(L, 359 std::vector<SCEV*>(Operands.begin(), 360 Operands.end()))); 361} 362 363SCEVHandle SCEVAddRecExpr:: 364replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 365 const SCEVHandle &Conc, 366 ScalarEvolution &SE) const { 367 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 368 SCEVHandle H = 369 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 370 if (H != getOperand(i)) { 371 std::vector<SCEVHandle> NewOps; 372 NewOps.reserve(getNumOperands()); 373 for (unsigned j = 0; j != i; ++j) 374 NewOps.push_back(getOperand(j)); 375 NewOps.push_back(H); 376 for (++i; i != e; ++i) 377 NewOps.push_back(getOperand(i)-> 378 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 379 380 return SE.getAddRecExpr(NewOps, L); 381 } 382 } 383 return this; 384} 385 386 387bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 388 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 389 // contain L and if the start is invariant. 390 return !QueryLoop->contains(L->getHeader()) && 391 getOperand(0)->isLoopInvariant(QueryLoop); 392} 393 394 395void SCEVAddRecExpr::print(std::ostream &OS) const { 396 OS << "{" << *Operands[0]; 397 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 398 OS << ",+," << *Operands[i]; 399 OS << "}<" << L->getHeader()->getName() + ">"; 400} 401 402// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 403// value. Don't use a SCEVHandle here, or else the object will never be 404// deleted! 405static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 406 407SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 408 409bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 410 // All non-instruction values are loop invariant. All instructions are loop 411 // invariant if they are not contained in the specified loop. 412 if (Instruction *I = dyn_cast<Instruction>(V)) 413 return !L->contains(I->getParent()); 414 return true; 415} 416 417const Type *SCEVUnknown::getType() const { 418 return V->getType(); 419} 420 421void SCEVUnknown::print(std::ostream &OS) const { 422 WriteAsOperand(OS, V, false); 423} 424 425//===----------------------------------------------------------------------===// 426// SCEV Utilities 427//===----------------------------------------------------------------------===// 428 429namespace { 430 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 431 /// than the complexity of the RHS. This comparator is used to canonicalize 432 /// expressions. 433 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 434 bool operator()(SCEV *LHS, SCEV *RHS) { 435 return LHS->getSCEVType() < RHS->getSCEVType(); 436 } 437 }; 438} 439 440/// GroupByComplexity - Given a list of SCEV objects, order them by their 441/// complexity, and group objects of the same complexity together by value. 442/// When this routine is finished, we know that any duplicates in the vector are 443/// consecutive and that complexity is monotonically increasing. 444/// 445/// Note that we go take special precautions to ensure that we get determinstic 446/// results from this routine. In other words, we don't want the results of 447/// this to depend on where the addresses of various SCEV objects happened to 448/// land in memory. 449/// 450static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 451 if (Ops.size() < 2) return; // Noop 452 if (Ops.size() == 2) { 453 // This is the common case, which also happens to be trivially simple. 454 // Special case it. 455 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 456 std::swap(Ops[0], Ops[1]); 457 return; 458 } 459 460 // Do the rough sort by complexity. 461 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 462 463 // Now that we are sorted by complexity, group elements of the same 464 // complexity. Note that this is, at worst, N^2, but the vector is likely to 465 // be extremely short in practice. Note that we take this approach because we 466 // do not want to depend on the addresses of the objects we are grouping. 467 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 468 SCEV *S = Ops[i]; 469 unsigned Complexity = S->getSCEVType(); 470 471 // If there are any objects of the same complexity and same value as this 472 // one, group them. 473 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 474 if (Ops[j] == S) { // Found a duplicate. 475 // Move it to immediately after i'th element. 476 std::swap(Ops[i+1], Ops[j]); 477 ++i; // no need to rescan it. 478 if (i == e-2) return; // Done! 479 } 480 } 481 } 482} 483 484 485 486//===----------------------------------------------------------------------===// 487// Simple SCEV method implementations 488//===----------------------------------------------------------------------===// 489 490/// getIntegerSCEV - Given an integer or FP type, create a constant for the 491/// specified signed integer value and return a SCEV for the constant. 492SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 493 Constant *C; 494 if (Val == 0) 495 C = Constant::getNullValue(Ty); 496 else if (Ty->isFloatingPoint()) 497 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 498 APFloat::IEEEdouble, Val)); 499 else 500 C = ConstantInt::get(Ty, Val); 501 return getUnknown(C); 502} 503 504/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 505/// input value to the specified type. If the type must be extended, it is zero 506/// extended. 507static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty, 508 ScalarEvolution &SE) { 509 const Type *SrcTy = V->getType(); 510 assert(SrcTy->isInteger() && Ty->isInteger() && 511 "Cannot truncate or zero extend with non-integer arguments!"); 512 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 513 return V; // No conversion 514 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 515 return SE.getTruncateExpr(V, Ty); 516 return SE.getZeroExtendExpr(V, Ty); 517} 518 519/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 520/// 521SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 522 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 523 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 524 525 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType()))); 526} 527 528/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 529SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 530 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 531 return getUnknown(ConstantExpr::getNot(VC->getValue())); 532 533 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType())); 534 return getMinusSCEV(AllOnes, V); 535} 536 537/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 538/// 539SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 540 const SCEVHandle &RHS) { 541 // X - Y --> X + -Y 542 return getAddExpr(LHS, getNegativeSCEV(RHS)); 543} 544 545 546/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as 547/// It. Assume, K > 0. 548static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 549 ScalarEvolution &SE) { 550 // We are using the following formula for BC(It, K): 551 // 552 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 553 // 554 // Suppose, W is the bitwidth of It (and of the return value as well). We 555 // must be prepared for overflow. Hence, we must assure that the result of 556 // our computation is equal to the accurate one modulo 2^W. Unfortunately, 557 // division isn't safe in modular arithmetic. This means we must perform the 558 // whole computation accurately and then truncate the result to W bits. 559 // 560 // The dividend of the formula is a multiplication of K integers of bitwidth 561 // W. K*W bits suffice to compute it accurately. 562 // 563 // FIXME: We assume the divisor can be accurately computed using 16-bit 564 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In 565 // future we may use APInt to use the minimum number of bits necessary to 566 // compute it accurately. 567 // 568 // It is safe to use unsigned division here: the dividend is nonnegative and 569 // the divisor is positive. 570 571 // Handle the simplest case efficiently. 572 if (K == 1) 573 return It; 574 575 assert(K < 9 && "We cannot handle such long AddRecs yet."); 576 577 // FIXME: A temporary hack to remove in future. Arbitrary precision integers 578 // aren't supported by the code generator yet. For the dividend, the bitwidth 579 // we use is the smallest power of 2 greater or equal to K*W and less or equal 580 // to 64. Note that setting the upper bound for bitwidth may still lead to 581 // miscompilation in some cases. 582 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth()); 583 if (DividendBits > 64) 584 DividendBits = 64; 585#if 0 // Waiting for the APInt support in the code generator... 586 unsigned DividendBits = K * It->getBitWidth(); 587#endif 588 589 const IntegerType *DividendTy = IntegerType::get(DividendBits); 590 const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy); 591 592 // The final number of bits we need to perform the division is the maximum of 593 // dividend and divisor bitwidths. 594 const IntegerType *DivisionTy = 595 IntegerType::get(std::max(DividendBits, 16U)); 596 597 // Compute K! We know K >= 2 here. 598 unsigned F = 2; 599 for (unsigned i = 3; i <= K; ++i) 600 F *= i; 601 APInt Divisor(DivisionTy->getBitWidth(), F); 602 603 // Handle this case efficiently, it is common to have constant iteration 604 // counts while computing loop exit values. 605 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) { 606 const APInt& N = SC->getValue()->getValue(); 607 APInt Dividend(N.getBitWidth(), 1); 608 for (; K; --K) 609 Dividend *= N-(K-1); 610 if (DividendTy != DivisionTy) 611 Dividend = Dividend.zext(DivisionTy->getBitWidth()); 612 return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth())); 613 } 614 615 SCEVHandle Dividend = ExIt; 616 for (unsigned i = 1; i != K; ++i) 617 Dividend = 618 SE.getMulExpr(Dividend, 619 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy))); 620 if (DividendTy != DivisionTy) 621 Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy); 622 return 623 SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)), 624 It->getType()); 625} 626 627/// evaluateAtIteration - Return the value of this chain of recurrences at 628/// the specified iteration number. We can evaluate this recurrence by 629/// multiplying each element in the chain by the binomial coefficient 630/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 631/// 632/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 633/// 634/// where BC(It, k) stands for binomial coefficient. 635/// 636SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 637 ScalarEvolution &SE) const { 638 SCEVHandle Result = getStart(); 639 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 640 // The computation is correct in the face of overflow provided that the 641 // multiplication is performed _after_ the evaluation of the binomial 642 // coefficient. 643 SCEVHandle Val = SE.getMulExpr(getOperand(i), 644 BinomialCoefficient(It, i, SE)); 645 Result = SE.getAddExpr(Result, Val); 646 } 647 return Result; 648} 649 650//===----------------------------------------------------------------------===// 651// SCEV Expression folder implementations 652//===----------------------------------------------------------------------===// 653 654SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 655 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 656 return getUnknown( 657 ConstantExpr::getTrunc(SC->getValue(), Ty)); 658 659 // If the input value is a chrec scev made out of constants, truncate 660 // all of the constants. 661 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 662 std::vector<SCEVHandle> Operands; 663 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 664 // FIXME: This should allow truncation of other expression types! 665 if (isa<SCEVConstant>(AddRec->getOperand(i))) 666 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 667 else 668 break; 669 if (Operands.size() == AddRec->getNumOperands()) 670 return getAddRecExpr(Operands, AddRec->getLoop()); 671 } 672 673 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 674 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 675 return Result; 676} 677 678SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 679 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 680 return getUnknown( 681 ConstantExpr::getZExt(SC->getValue(), Ty)); 682 683 // FIXME: If the input value is a chrec scev, and we can prove that the value 684 // did not overflow the old, smaller, value, we can zero extend all of the 685 // operands (often constants). This would allow analysis of something like 686 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 687 688 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 689 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 690 return Result; 691} 692 693SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 694 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 695 return getUnknown( 696 ConstantExpr::getSExt(SC->getValue(), Ty)); 697 698 // FIXME: If the input value is a chrec scev, and we can prove that the value 699 // did not overflow the old, smaller, value, we can sign extend all of the 700 // operands (often constants). This would allow analysis of something like 701 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 702 703 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 704 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 705 return Result; 706} 707 708// get - Get a canonical add expression, or something simpler if possible. 709SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 710 assert(!Ops.empty() && "Cannot get empty add!"); 711 if (Ops.size() == 1) return Ops[0]; 712 713 // Sort by complexity, this groups all similar expression types together. 714 GroupByComplexity(Ops); 715 716 // If there are any constants, fold them together. 717 unsigned Idx = 0; 718 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 719 ++Idx; 720 assert(Idx < Ops.size()); 721 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 722 // We found two constants, fold them together! 723 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 724 RHSC->getValue()->getValue()); 725 Ops[0] = getConstant(Fold); 726 Ops.erase(Ops.begin()+1); // Erase the folded element 727 if (Ops.size() == 1) return Ops[0]; 728 LHSC = cast<SCEVConstant>(Ops[0]); 729 } 730 731 // If we are left with a constant zero being added, strip it off. 732 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 733 Ops.erase(Ops.begin()); 734 --Idx; 735 } 736 } 737 738 if (Ops.size() == 1) return Ops[0]; 739 740 // Okay, check to see if the same value occurs in the operand list twice. If 741 // so, merge them together into an multiply expression. Since we sorted the 742 // list, these values are required to be adjacent. 743 const Type *Ty = Ops[0]->getType(); 744 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 745 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 746 // Found a match, merge the two values into a multiply, and add any 747 // remaining values to the result. 748 SCEVHandle Two = getIntegerSCEV(2, Ty); 749 SCEVHandle Mul = getMulExpr(Ops[i], Two); 750 if (Ops.size() == 2) 751 return Mul; 752 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 753 Ops.push_back(Mul); 754 return getAddExpr(Ops); 755 } 756 757 // Now we know the first non-constant operand. Skip past any cast SCEVs. 758 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 759 ++Idx; 760 761 // If there are add operands they would be next. 762 if (Idx < Ops.size()) { 763 bool DeletedAdd = false; 764 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 765 // If we have an add, expand the add operands onto the end of the operands 766 // list. 767 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 768 Ops.erase(Ops.begin()+Idx); 769 DeletedAdd = true; 770 } 771 772 // If we deleted at least one add, we added operands to the end of the list, 773 // and they are not necessarily sorted. Recurse to resort and resimplify 774 // any operands we just aquired. 775 if (DeletedAdd) 776 return getAddExpr(Ops); 777 } 778 779 // Skip over the add expression until we get to a multiply. 780 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 781 ++Idx; 782 783 // If we are adding something to a multiply expression, make sure the 784 // something is not already an operand of the multiply. If so, merge it into 785 // the multiply. 786 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 787 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 788 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 789 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 790 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 791 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 792 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 793 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 794 if (Mul->getNumOperands() != 2) { 795 // If the multiply has more than two operands, we must get the 796 // Y*Z term. 797 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 798 MulOps.erase(MulOps.begin()+MulOp); 799 InnerMul = getMulExpr(MulOps); 800 } 801 SCEVHandle One = getIntegerSCEV(1, Ty); 802 SCEVHandle AddOne = getAddExpr(InnerMul, One); 803 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 804 if (Ops.size() == 2) return OuterMul; 805 if (AddOp < Idx) { 806 Ops.erase(Ops.begin()+AddOp); 807 Ops.erase(Ops.begin()+Idx-1); 808 } else { 809 Ops.erase(Ops.begin()+Idx); 810 Ops.erase(Ops.begin()+AddOp-1); 811 } 812 Ops.push_back(OuterMul); 813 return getAddExpr(Ops); 814 } 815 816 // Check this multiply against other multiplies being added together. 817 for (unsigned OtherMulIdx = Idx+1; 818 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 819 ++OtherMulIdx) { 820 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 821 // If MulOp occurs in OtherMul, we can fold the two multiplies 822 // together. 823 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 824 OMulOp != e; ++OMulOp) 825 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 826 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 827 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 828 if (Mul->getNumOperands() != 2) { 829 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 830 MulOps.erase(MulOps.begin()+MulOp); 831 InnerMul1 = getMulExpr(MulOps); 832 } 833 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 834 if (OtherMul->getNumOperands() != 2) { 835 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 836 OtherMul->op_end()); 837 MulOps.erase(MulOps.begin()+OMulOp); 838 InnerMul2 = getMulExpr(MulOps); 839 } 840 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 841 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 842 if (Ops.size() == 2) return OuterMul; 843 Ops.erase(Ops.begin()+Idx); 844 Ops.erase(Ops.begin()+OtherMulIdx-1); 845 Ops.push_back(OuterMul); 846 return getAddExpr(Ops); 847 } 848 } 849 } 850 } 851 852 // If there are any add recurrences in the operands list, see if any other 853 // added values are loop invariant. If so, we can fold them into the 854 // recurrence. 855 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 856 ++Idx; 857 858 // Scan over all recurrences, trying to fold loop invariants into them. 859 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 860 // Scan all of the other operands to this add and add them to the vector if 861 // they are loop invariant w.r.t. the recurrence. 862 std::vector<SCEVHandle> LIOps; 863 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 864 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 865 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 866 LIOps.push_back(Ops[i]); 867 Ops.erase(Ops.begin()+i); 868 --i; --e; 869 } 870 871 // If we found some loop invariants, fold them into the recurrence. 872 if (!LIOps.empty()) { 873 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 874 LIOps.push_back(AddRec->getStart()); 875 876 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 877 AddRecOps[0] = getAddExpr(LIOps); 878 879 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 880 // If all of the other operands were loop invariant, we are done. 881 if (Ops.size() == 1) return NewRec; 882 883 // Otherwise, add the folded AddRec by the non-liv parts. 884 for (unsigned i = 0;; ++i) 885 if (Ops[i] == AddRec) { 886 Ops[i] = NewRec; 887 break; 888 } 889 return getAddExpr(Ops); 890 } 891 892 // Okay, if there weren't any loop invariants to be folded, check to see if 893 // there are multiple AddRec's with the same loop induction variable being 894 // added together. If so, we can fold them. 895 for (unsigned OtherIdx = Idx+1; 896 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 897 if (OtherIdx != Idx) { 898 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 899 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 900 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 901 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 902 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 903 if (i >= NewOps.size()) { 904 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 905 OtherAddRec->op_end()); 906 break; 907 } 908 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 909 } 910 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 911 912 if (Ops.size() == 2) return NewAddRec; 913 914 Ops.erase(Ops.begin()+Idx); 915 Ops.erase(Ops.begin()+OtherIdx-1); 916 Ops.push_back(NewAddRec); 917 return getAddExpr(Ops); 918 } 919 } 920 921 // Otherwise couldn't fold anything into this recurrence. Move onto the 922 // next one. 923 } 924 925 // Okay, it looks like we really DO need an add expr. Check to see if we 926 // already have one, otherwise create a new one. 927 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 928 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 929 SCEVOps)]; 930 if (Result == 0) Result = new SCEVAddExpr(Ops); 931 return Result; 932} 933 934 935SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 936 assert(!Ops.empty() && "Cannot get empty mul!"); 937 938 // Sort by complexity, this groups all similar expression types together. 939 GroupByComplexity(Ops); 940 941 // If there are any constants, fold them together. 942 unsigned Idx = 0; 943 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 944 945 // C1*(C2+V) -> C1*C2 + C1*V 946 if (Ops.size() == 2) 947 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 948 if (Add->getNumOperands() == 2 && 949 isa<SCEVConstant>(Add->getOperand(0))) 950 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 951 getMulExpr(LHSC, Add->getOperand(1))); 952 953 954 ++Idx; 955 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 956 // We found two constants, fold them together! 957 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 958 RHSC->getValue()->getValue()); 959 Ops[0] = getConstant(Fold); 960 Ops.erase(Ops.begin()+1); // Erase the folded element 961 if (Ops.size() == 1) return Ops[0]; 962 LHSC = cast<SCEVConstant>(Ops[0]); 963 } 964 965 // If we are left with a constant one being multiplied, strip it off. 966 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 967 Ops.erase(Ops.begin()); 968 --Idx; 969 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 970 // If we have a multiply of zero, it will always be zero. 971 return Ops[0]; 972 } 973 } 974 975 // Skip over the add expression until we get to a multiply. 976 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 977 ++Idx; 978 979 if (Ops.size() == 1) 980 return Ops[0]; 981 982 // If there are mul operands inline them all into this expression. 983 if (Idx < Ops.size()) { 984 bool DeletedMul = false; 985 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 986 // If we have an mul, expand the mul operands onto the end of the operands 987 // list. 988 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 989 Ops.erase(Ops.begin()+Idx); 990 DeletedMul = true; 991 } 992 993 // If we deleted at least one mul, we added operands to the end of the list, 994 // and they are not necessarily sorted. Recurse to resort and resimplify 995 // any operands we just aquired. 996 if (DeletedMul) 997 return getMulExpr(Ops); 998 } 999 1000 // If there are any add recurrences in the operands list, see if any other 1001 // added values are loop invariant. If so, we can fold them into the 1002 // recurrence. 1003 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1004 ++Idx; 1005 1006 // Scan over all recurrences, trying to fold loop invariants into them. 1007 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1008 // Scan all of the other operands to this mul and add them to the vector if 1009 // they are loop invariant w.r.t. the recurrence. 1010 std::vector<SCEVHandle> LIOps; 1011 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1012 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1013 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1014 LIOps.push_back(Ops[i]); 1015 Ops.erase(Ops.begin()+i); 1016 --i; --e; 1017 } 1018 1019 // If we found some loop invariants, fold them into the recurrence. 1020 if (!LIOps.empty()) { 1021 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 1022 std::vector<SCEVHandle> NewOps; 1023 NewOps.reserve(AddRec->getNumOperands()); 1024 if (LIOps.size() == 1) { 1025 SCEV *Scale = LIOps[0]; 1026 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1027 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1028 } else { 1029 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1030 std::vector<SCEVHandle> MulOps(LIOps); 1031 MulOps.push_back(AddRec->getOperand(i)); 1032 NewOps.push_back(getMulExpr(MulOps)); 1033 } 1034 } 1035 1036 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1037 1038 // If all of the other operands were loop invariant, we are done. 1039 if (Ops.size() == 1) return NewRec; 1040 1041 // Otherwise, multiply the folded AddRec by the non-liv parts. 1042 for (unsigned i = 0;; ++i) 1043 if (Ops[i] == AddRec) { 1044 Ops[i] = NewRec; 1045 break; 1046 } 1047 return getMulExpr(Ops); 1048 } 1049 1050 // Okay, if there weren't any loop invariants to be folded, check to see if 1051 // there are multiple AddRec's with the same loop induction variable being 1052 // multiplied together. If so, we can fold them. 1053 for (unsigned OtherIdx = Idx+1; 1054 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1055 if (OtherIdx != Idx) { 1056 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1057 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1058 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1059 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1060 SCEVHandle NewStart = getMulExpr(F->getStart(), 1061 G->getStart()); 1062 SCEVHandle B = F->getStepRecurrence(*this); 1063 SCEVHandle D = G->getStepRecurrence(*this); 1064 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1065 getMulExpr(G, B), 1066 getMulExpr(B, D)); 1067 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1068 F->getLoop()); 1069 if (Ops.size() == 2) return NewAddRec; 1070 1071 Ops.erase(Ops.begin()+Idx); 1072 Ops.erase(Ops.begin()+OtherIdx-1); 1073 Ops.push_back(NewAddRec); 1074 return getMulExpr(Ops); 1075 } 1076 } 1077 1078 // Otherwise couldn't fold anything into this recurrence. Move onto the 1079 // next one. 1080 } 1081 1082 // Okay, it looks like we really DO need an mul expr. Check to see if we 1083 // already have one, otherwise create a new one. 1084 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1085 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1086 SCEVOps)]; 1087 if (Result == 0) 1088 Result = new SCEVMulExpr(Ops); 1089 return Result; 1090} 1091 1092SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1093 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1094 if (RHSC->getValue()->equalsInt(1)) 1095 return LHS; // X udiv 1 --> x 1096 1097 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1098 Constant *LHSCV = LHSC->getValue(); 1099 Constant *RHSCV = RHSC->getValue(); 1100 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1101 } 1102 } 1103 1104 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1105 1106 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1107 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1108 return Result; 1109} 1110 1111 1112/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1113/// specified loop. Simplify the expression as much as possible. 1114SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1115 const SCEVHandle &Step, const Loop *L) { 1116 std::vector<SCEVHandle> Operands; 1117 Operands.push_back(Start); 1118 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1119 if (StepChrec->getLoop() == L) { 1120 Operands.insert(Operands.end(), StepChrec->op_begin(), 1121 StepChrec->op_end()); 1122 return getAddRecExpr(Operands, L); 1123 } 1124 1125 Operands.push_back(Step); 1126 return getAddRecExpr(Operands, L); 1127} 1128 1129/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1130/// specified loop. Simplify the expression as much as possible. 1131SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1132 const Loop *L) { 1133 if (Operands.size() == 1) return Operands[0]; 1134 1135 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1136 if (StepC->getValue()->isZero()) { 1137 Operands.pop_back(); 1138 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1139 } 1140 1141 SCEVAddRecExpr *&Result = 1142 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1143 Operands.end()))]; 1144 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1145 return Result; 1146} 1147 1148SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1149 const SCEVHandle &RHS) { 1150 std::vector<SCEVHandle> Ops; 1151 Ops.push_back(LHS); 1152 Ops.push_back(RHS); 1153 return getSMaxExpr(Ops); 1154} 1155 1156SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1157 assert(!Ops.empty() && "Cannot get empty smax!"); 1158 if (Ops.size() == 1) return Ops[0]; 1159 1160 // Sort by complexity, this groups all similar expression types together. 1161 GroupByComplexity(Ops); 1162 1163 // If there are any constants, fold them together. 1164 unsigned Idx = 0; 1165 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1166 ++Idx; 1167 assert(Idx < Ops.size()); 1168 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1169 // We found two constants, fold them together! 1170 ConstantInt *Fold = ConstantInt::get( 1171 APIntOps::smax(LHSC->getValue()->getValue(), 1172 RHSC->getValue()->getValue())); 1173 Ops[0] = getConstant(Fold); 1174 Ops.erase(Ops.begin()+1); // Erase the folded element 1175 if (Ops.size() == 1) return Ops[0]; 1176 LHSC = cast<SCEVConstant>(Ops[0]); 1177 } 1178 1179 // If we are left with a constant -inf, strip it off. 1180 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1181 Ops.erase(Ops.begin()); 1182 --Idx; 1183 } 1184 } 1185 1186 if (Ops.size() == 1) return Ops[0]; 1187 1188 // Find the first SMax 1189 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1190 ++Idx; 1191 1192 // Check to see if one of the operands is an SMax. If so, expand its operands 1193 // onto our operand list, and recurse to simplify. 1194 if (Idx < Ops.size()) { 1195 bool DeletedSMax = false; 1196 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1197 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1198 Ops.erase(Ops.begin()+Idx); 1199 DeletedSMax = true; 1200 } 1201 1202 if (DeletedSMax) 1203 return getSMaxExpr(Ops); 1204 } 1205 1206 // Okay, check to see if the same value occurs in the operand list twice. If 1207 // so, delete one. Since we sorted the list, these values are required to 1208 // be adjacent. 1209 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1210 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1211 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1212 --i; --e; 1213 } 1214 1215 if (Ops.size() == 1) return Ops[0]; 1216 1217 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1218 1219 // Okay, it looks like we really DO need an smax expr. Check to see if we 1220 // already have one, otherwise create a new one. 1221 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1222 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1223 SCEVOps)]; 1224 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1225 return Result; 1226} 1227 1228SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1229 const SCEVHandle &RHS) { 1230 std::vector<SCEVHandle> Ops; 1231 Ops.push_back(LHS); 1232 Ops.push_back(RHS); 1233 return getUMaxExpr(Ops); 1234} 1235 1236SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1237 assert(!Ops.empty() && "Cannot get empty umax!"); 1238 if (Ops.size() == 1) return Ops[0]; 1239 1240 // Sort by complexity, this groups all similar expression types together. 1241 GroupByComplexity(Ops); 1242 1243 // If there are any constants, fold them together. 1244 unsigned Idx = 0; 1245 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1246 ++Idx; 1247 assert(Idx < Ops.size()); 1248 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1249 // We found two constants, fold them together! 1250 ConstantInt *Fold = ConstantInt::get( 1251 APIntOps::umax(LHSC->getValue()->getValue(), 1252 RHSC->getValue()->getValue())); 1253 Ops[0] = getConstant(Fold); 1254 Ops.erase(Ops.begin()+1); // Erase the folded element 1255 if (Ops.size() == 1) return Ops[0]; 1256 LHSC = cast<SCEVConstant>(Ops[0]); 1257 } 1258 1259 // If we are left with a constant zero, strip it off. 1260 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1261 Ops.erase(Ops.begin()); 1262 --Idx; 1263 } 1264 } 1265 1266 if (Ops.size() == 1) return Ops[0]; 1267 1268 // Find the first UMax 1269 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1270 ++Idx; 1271 1272 // Check to see if one of the operands is a UMax. If so, expand its operands 1273 // onto our operand list, and recurse to simplify. 1274 if (Idx < Ops.size()) { 1275 bool DeletedUMax = false; 1276 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1277 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1278 Ops.erase(Ops.begin()+Idx); 1279 DeletedUMax = true; 1280 } 1281 1282 if (DeletedUMax) 1283 return getUMaxExpr(Ops); 1284 } 1285 1286 // Okay, check to see if the same value occurs in the operand list twice. If 1287 // so, delete one. Since we sorted the list, these values are required to 1288 // be adjacent. 1289 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1290 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1291 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1292 --i; --e; 1293 } 1294 1295 if (Ops.size() == 1) return Ops[0]; 1296 1297 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1298 1299 // Okay, it looks like we really DO need a umax expr. Check to see if we 1300 // already have one, otherwise create a new one. 1301 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1302 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1303 SCEVOps)]; 1304 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1305 return Result; 1306} 1307 1308SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1309 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1310 return getConstant(CI); 1311 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1312 if (Result == 0) Result = new SCEVUnknown(V); 1313 return Result; 1314} 1315 1316 1317//===----------------------------------------------------------------------===// 1318// ScalarEvolutionsImpl Definition and Implementation 1319//===----------------------------------------------------------------------===// 1320// 1321/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1322/// evolution code. 1323/// 1324namespace { 1325 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1326 /// SE - A reference to the public ScalarEvolution object. 1327 ScalarEvolution &SE; 1328 1329 /// F - The function we are analyzing. 1330 /// 1331 Function &F; 1332 1333 /// LI - The loop information for the function we are currently analyzing. 1334 /// 1335 LoopInfo &LI; 1336 1337 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1338 /// things. 1339 SCEVHandle UnknownValue; 1340 1341 /// Scalars - This is a cache of the scalars we have analyzed so far. 1342 /// 1343 std::map<Value*, SCEVHandle> Scalars; 1344 1345 /// IterationCounts - Cache the iteration count of the loops for this 1346 /// function as they are computed. 1347 std::map<const Loop*, SCEVHandle> IterationCounts; 1348 1349 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1350 /// the PHI instructions that we attempt to compute constant evolutions for. 1351 /// This allows us to avoid potentially expensive recomputation of these 1352 /// properties. An instruction maps to null if we are unable to compute its 1353 /// exit value. 1354 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1355 1356 public: 1357 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1358 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1359 1360 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1361 /// expression and create a new one. 1362 SCEVHandle getSCEV(Value *V); 1363 1364 /// hasSCEV - Return true if the SCEV for this value has already been 1365 /// computed. 1366 bool hasSCEV(Value *V) const { 1367 return Scalars.count(V); 1368 } 1369 1370 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1371 /// the specified value. 1372 void setSCEV(Value *V, const SCEVHandle &H) { 1373 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1374 assert(isNew && "This entry already existed!"); 1375 } 1376 1377 1378 /// getSCEVAtScope - Compute the value of the specified expression within 1379 /// the indicated loop (which may be null to indicate in no loop). If the 1380 /// expression cannot be evaluated, return UnknownValue itself. 1381 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1382 1383 1384 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1385 /// an analyzable loop-invariant iteration count. 1386 bool hasLoopInvariantIterationCount(const Loop *L); 1387 1388 /// getIterationCount - If the specified loop has a predictable iteration 1389 /// count, return it. Note that it is not valid to call this method on a 1390 /// loop without a loop-invariant iteration count. 1391 SCEVHandle getIterationCount(const Loop *L); 1392 1393 /// deleteValueFromRecords - This method should be called by the 1394 /// client before it removes a value from the program, to make sure 1395 /// that no dangling references are left around. 1396 void deleteValueFromRecords(Value *V); 1397 1398 private: 1399 /// createSCEV - We know that there is no SCEV for the specified value. 1400 /// Analyze the expression. 1401 SCEVHandle createSCEV(Value *V); 1402 1403 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1404 /// SCEVs. 1405 SCEVHandle createNodeForPHI(PHINode *PN); 1406 1407 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1408 /// for the specified instruction and replaces any references to the 1409 /// symbolic value SymName with the specified value. This is used during 1410 /// PHI resolution. 1411 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1412 const SCEVHandle &SymName, 1413 const SCEVHandle &NewVal); 1414 1415 /// ComputeIterationCount - Compute the number of times the specified loop 1416 /// will iterate. 1417 SCEVHandle ComputeIterationCount(const Loop *L); 1418 1419 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1420 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1421 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1422 Constant *RHS, 1423 const Loop *L, 1424 ICmpInst::Predicate p); 1425 1426 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1427 /// constant number of times (the condition evolves only from constants), 1428 /// try to evaluate a few iterations of the loop until we get the exit 1429 /// condition gets a value of ExitWhen (true or false). If we cannot 1430 /// evaluate the trip count of the loop, return UnknownValue. 1431 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1432 bool ExitWhen); 1433 1434 /// HowFarToZero - Return the number of times a backedge comparing the 1435 /// specified value to zero will execute. If not computable, return 1436 /// UnknownValue. 1437 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1438 1439 /// HowFarToNonZero - Return the number of times a backedge checking the 1440 /// specified value for nonzero will execute. If not computable, return 1441 /// UnknownValue. 1442 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1443 1444 /// HowManyLessThans - Return the number of times a backedge containing the 1445 /// specified less-than comparison will execute. If not computable, return 1446 /// UnknownValue. isSigned specifies whether the less-than is signed. 1447 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1448 bool isSigned); 1449 1450 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1451 /// in the header of its containing loop, we know the loop executes a 1452 /// constant number of times, and the PHI node is just a recurrence 1453 /// involving constants, fold it. 1454 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1455 const Loop *L); 1456 }; 1457} 1458 1459//===----------------------------------------------------------------------===// 1460// Basic SCEV Analysis and PHI Idiom Recognition Code 1461// 1462 1463/// deleteValueFromRecords - This method should be called by the 1464/// client before it removes an instruction from the program, to make sure 1465/// that no dangling references are left around. 1466void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1467 SmallVector<Value *, 16> Worklist; 1468 1469 if (Scalars.erase(V)) { 1470 if (PHINode *PN = dyn_cast<PHINode>(V)) 1471 ConstantEvolutionLoopExitValue.erase(PN); 1472 Worklist.push_back(V); 1473 } 1474 1475 while (!Worklist.empty()) { 1476 Value *VV = Worklist.back(); 1477 Worklist.pop_back(); 1478 1479 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1480 UI != UE; ++UI) { 1481 Instruction *Inst = cast<Instruction>(*UI); 1482 if (Scalars.erase(Inst)) { 1483 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1484 ConstantEvolutionLoopExitValue.erase(PN); 1485 Worklist.push_back(Inst); 1486 } 1487 } 1488 } 1489} 1490 1491 1492/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1493/// expression and create a new one. 1494SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1495 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1496 1497 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1498 if (I != Scalars.end()) return I->second; 1499 SCEVHandle S = createSCEV(V); 1500 Scalars.insert(std::make_pair(V, S)); 1501 return S; 1502} 1503 1504/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1505/// the specified instruction and replaces any references to the symbolic value 1506/// SymName with the specified value. This is used during PHI resolution. 1507void ScalarEvolutionsImpl:: 1508ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1509 const SCEVHandle &NewVal) { 1510 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1511 if (SI == Scalars.end()) return; 1512 1513 SCEVHandle NV = 1514 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1515 if (NV == SI->second) return; // No change. 1516 1517 SI->second = NV; // Update the scalars map! 1518 1519 // Any instruction values that use this instruction might also need to be 1520 // updated! 1521 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1522 UI != E; ++UI) 1523 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1524} 1525 1526/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1527/// a loop header, making it a potential recurrence, or it doesn't. 1528/// 1529SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1530 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1531 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1532 if (L->getHeader() == PN->getParent()) { 1533 // If it lives in the loop header, it has two incoming values, one 1534 // from outside the loop, and one from inside. 1535 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1536 unsigned BackEdge = IncomingEdge^1; 1537 1538 // While we are analyzing this PHI node, handle its value symbolically. 1539 SCEVHandle SymbolicName = SE.getUnknown(PN); 1540 assert(Scalars.find(PN) == Scalars.end() && 1541 "PHI node already processed?"); 1542 Scalars.insert(std::make_pair(PN, SymbolicName)); 1543 1544 // Using this symbolic name for the PHI, analyze the value coming around 1545 // the back-edge. 1546 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1547 1548 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1549 // has a special value for the first iteration of the loop. 1550 1551 // If the value coming around the backedge is an add with the symbolic 1552 // value we just inserted, then we found a simple induction variable! 1553 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1554 // If there is a single occurrence of the symbolic value, replace it 1555 // with a recurrence. 1556 unsigned FoundIndex = Add->getNumOperands(); 1557 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1558 if (Add->getOperand(i) == SymbolicName) 1559 if (FoundIndex == e) { 1560 FoundIndex = i; 1561 break; 1562 } 1563 1564 if (FoundIndex != Add->getNumOperands()) { 1565 // Create an add with everything but the specified operand. 1566 std::vector<SCEVHandle> Ops; 1567 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1568 if (i != FoundIndex) 1569 Ops.push_back(Add->getOperand(i)); 1570 SCEVHandle Accum = SE.getAddExpr(Ops); 1571 1572 // This is not a valid addrec if the step amount is varying each 1573 // loop iteration, but is not itself an addrec in this loop. 1574 if (Accum->isLoopInvariant(L) || 1575 (isa<SCEVAddRecExpr>(Accum) && 1576 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1577 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1578 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1579 1580 // Okay, for the entire analysis of this edge we assumed the PHI 1581 // to be symbolic. We now need to go back and update all of the 1582 // entries for the scalars that use the PHI (except for the PHI 1583 // itself) to use the new analyzed value instead of the "symbolic" 1584 // value. 1585 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1586 return PHISCEV; 1587 } 1588 } 1589 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1590 // Otherwise, this could be a loop like this: 1591 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1592 // In this case, j = {1,+,1} and BEValue is j. 1593 // Because the other in-value of i (0) fits the evolution of BEValue 1594 // i really is an addrec evolution. 1595 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1596 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1597 1598 // If StartVal = j.start - j.stride, we can use StartVal as the 1599 // initial step of the addrec evolution. 1600 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1601 AddRec->getOperand(1))) { 1602 SCEVHandle PHISCEV = 1603 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1604 1605 // Okay, for the entire analysis of this edge we assumed the PHI 1606 // to be symbolic. We now need to go back and update all of the 1607 // entries for the scalars that use the PHI (except for the PHI 1608 // itself) to use the new analyzed value instead of the "symbolic" 1609 // value. 1610 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1611 return PHISCEV; 1612 } 1613 } 1614 } 1615 1616 return SymbolicName; 1617 } 1618 1619 // If it's not a loop phi, we can't handle it yet. 1620 return SE.getUnknown(PN); 1621} 1622 1623/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1624/// guaranteed to end in (at every loop iteration). It is, at the same time, 1625/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1626/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1627static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1628 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1629 return C->getValue()->getValue().countTrailingZeros(); 1630 1631 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1632 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1633 1634 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1635 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1636 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1637 } 1638 1639 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1640 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1641 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1642 } 1643 1644 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1645 // The result is the min of all operands results. 1646 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1647 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1648 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1649 return MinOpRes; 1650 } 1651 1652 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1653 // The result is the sum of all operands results. 1654 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1655 uint32_t BitWidth = M->getBitWidth(); 1656 for (unsigned i = 1, e = M->getNumOperands(); 1657 SumOpRes != BitWidth && i != e; ++i) 1658 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1659 BitWidth); 1660 return SumOpRes; 1661 } 1662 1663 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1664 // The result is the min of all operands results. 1665 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1666 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1667 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1668 return MinOpRes; 1669 } 1670 1671 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1672 // The result is the min of all operands results. 1673 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1674 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1675 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1676 return MinOpRes; 1677 } 1678 1679 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1680 // The result is the min of all operands results. 1681 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1682 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1683 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1684 return MinOpRes; 1685 } 1686 1687 // SCEVUDivExpr, SCEVUnknown 1688 return 0; 1689} 1690 1691/// createSCEV - We know that there is no SCEV for the specified value. 1692/// Analyze the expression. 1693/// 1694SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1695 if (!isa<IntegerType>(V->getType())) 1696 return SE.getUnknown(V); 1697 1698 if (Instruction *I = dyn_cast<Instruction>(V)) { 1699 switch (I->getOpcode()) { 1700 case Instruction::Add: 1701 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1702 getSCEV(I->getOperand(1))); 1703 case Instruction::Mul: 1704 return SE.getMulExpr(getSCEV(I->getOperand(0)), 1705 getSCEV(I->getOperand(1))); 1706 case Instruction::UDiv: 1707 return SE.getUDivExpr(getSCEV(I->getOperand(0)), 1708 getSCEV(I->getOperand(1))); 1709 case Instruction::Sub: 1710 return SE.getMinusSCEV(getSCEV(I->getOperand(0)), 1711 getSCEV(I->getOperand(1))); 1712 case Instruction::Or: 1713 // If the RHS of the Or is a constant, we may have something like: 1714 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1715 // optimizations will transparently handle this case. 1716 // 1717 // In order for this transformation to be safe, the LHS must be of the 1718 // form X*(2^n) and the Or constant must be less than 2^n. 1719 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1720 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1721 const APInt &CIVal = CI->getValue(); 1722 if (GetMinTrailingZeros(LHS) >= 1723 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1724 return SE.getAddExpr(LHS, getSCEV(I->getOperand(1))); 1725 } 1726 break; 1727 case Instruction::Xor: 1728 // If the RHS of the xor is a signbit, then this is just an add. 1729 // Instcombine turns add of signbit into xor as a strength reduction step. 1730 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1731 if (CI->getValue().isSignBit()) 1732 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1733 getSCEV(I->getOperand(1))); 1734 else if (CI->isAllOnesValue()) 1735 return SE.getNotSCEV(getSCEV(I->getOperand(0))); 1736 } 1737 break; 1738 1739 case Instruction::Shl: 1740 // Turn shift left of a constant amount into a multiply. 1741 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1742 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1743 Constant *X = ConstantInt::get( 1744 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1745 return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X)); 1746 } 1747 break; 1748 1749 case Instruction::Trunc: 1750 return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType()); 1751 1752 case Instruction::ZExt: 1753 return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1754 1755 case Instruction::SExt: 1756 return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1757 1758 case Instruction::BitCast: 1759 // BitCasts are no-op casts so we just eliminate the cast. 1760 if (I->getType()->isInteger() && 1761 I->getOperand(0)->getType()->isInteger()) 1762 return getSCEV(I->getOperand(0)); 1763 break; 1764 1765 case Instruction::PHI: 1766 return createNodeForPHI(cast<PHINode>(I)); 1767 1768 case Instruction::Select: 1769 // This could be a smax or umax that was lowered earlier. 1770 // Try to recover it. 1771 if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) { 1772 Value *LHS = ICI->getOperand(0); 1773 Value *RHS = ICI->getOperand(1); 1774 switch (ICI->getPredicate()) { 1775 case ICmpInst::ICMP_SLT: 1776 case ICmpInst::ICMP_SLE: 1777 std::swap(LHS, RHS); 1778 // fall through 1779 case ICmpInst::ICMP_SGT: 1780 case ICmpInst::ICMP_SGE: 1781 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1782 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1783 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1)) 1784 // -smax(-x, -y) == smin(x, y). 1785 return SE.getNegativeSCEV(SE.getSMaxExpr( 1786 SE.getNegativeSCEV(getSCEV(LHS)), 1787 SE.getNegativeSCEV(getSCEV(RHS)))); 1788 break; 1789 case ICmpInst::ICMP_ULT: 1790 case ICmpInst::ICMP_ULE: 1791 std::swap(LHS, RHS); 1792 // fall through 1793 case ICmpInst::ICMP_UGT: 1794 case ICmpInst::ICMP_UGE: 1795 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1796 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1797 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1)) 1798 // ~umax(~x, ~y) == umin(x, y) 1799 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)), 1800 SE.getNotSCEV(getSCEV(RHS)))); 1801 break; 1802 default: 1803 break; 1804 } 1805 } 1806 1807 default: // We cannot analyze this expression. 1808 break; 1809 } 1810 } 1811 1812 return SE.getUnknown(V); 1813} 1814 1815 1816 1817//===----------------------------------------------------------------------===// 1818// Iteration Count Computation Code 1819// 1820 1821/// getIterationCount - If the specified loop has a predictable iteration 1822/// count, return it. Note that it is not valid to call this method on a 1823/// loop without a loop-invariant iteration count. 1824SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1825 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1826 if (I == IterationCounts.end()) { 1827 SCEVHandle ItCount = ComputeIterationCount(L); 1828 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1829 if (ItCount != UnknownValue) { 1830 assert(ItCount->isLoopInvariant(L) && 1831 "Computed trip count isn't loop invariant for loop!"); 1832 ++NumTripCountsComputed; 1833 } else if (isa<PHINode>(L->getHeader()->begin())) { 1834 // Only count loops that have phi nodes as not being computable. 1835 ++NumTripCountsNotComputed; 1836 } 1837 } 1838 return I->second; 1839} 1840 1841/// ComputeIterationCount - Compute the number of times the specified loop 1842/// will iterate. 1843SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1844 // If the loop has a non-one exit block count, we can't analyze it. 1845 SmallVector<BasicBlock*, 8> ExitBlocks; 1846 L->getExitBlocks(ExitBlocks); 1847 if (ExitBlocks.size() != 1) return UnknownValue; 1848 1849 // Okay, there is one exit block. Try to find the condition that causes the 1850 // loop to be exited. 1851 BasicBlock *ExitBlock = ExitBlocks[0]; 1852 1853 BasicBlock *ExitingBlock = 0; 1854 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1855 PI != E; ++PI) 1856 if (L->contains(*PI)) { 1857 if (ExitingBlock == 0) 1858 ExitingBlock = *PI; 1859 else 1860 return UnknownValue; // More than one block exiting! 1861 } 1862 assert(ExitingBlock && "No exits from loop, something is broken!"); 1863 1864 // Okay, we've computed the exiting block. See what condition causes us to 1865 // exit. 1866 // 1867 // FIXME: we should be able to handle switch instructions (with a single exit) 1868 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1869 if (ExitBr == 0) return UnknownValue; 1870 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1871 1872 // At this point, we know we have a conditional branch that determines whether 1873 // the loop is exited. However, we don't know if the branch is executed each 1874 // time through the loop. If not, then the execution count of the branch will 1875 // not be equal to the trip count of the loop. 1876 // 1877 // Currently we check for this by checking to see if the Exit branch goes to 1878 // the loop header. If so, we know it will always execute the same number of 1879 // times as the loop. We also handle the case where the exit block *is* the 1880 // loop header. This is common for un-rotated loops. More extensive analysis 1881 // could be done to handle more cases here. 1882 if (ExitBr->getSuccessor(0) != L->getHeader() && 1883 ExitBr->getSuccessor(1) != L->getHeader() && 1884 ExitBr->getParent() != L->getHeader()) 1885 return UnknownValue; 1886 1887 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1888 1889 // If it's not an integer comparison then compute it the hard way. 1890 // Note that ICmpInst deals with pointer comparisons too so we must check 1891 // the type of the operand. 1892 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1893 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1894 ExitBr->getSuccessor(0) == ExitBlock); 1895 1896 // If the condition was exit on true, convert the condition to exit on false 1897 ICmpInst::Predicate Cond; 1898 if (ExitBr->getSuccessor(1) == ExitBlock) 1899 Cond = ExitCond->getPredicate(); 1900 else 1901 Cond = ExitCond->getInversePredicate(); 1902 1903 // Handle common loops like: for (X = "string"; *X; ++X) 1904 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1905 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1906 SCEVHandle ItCnt = 1907 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1908 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1909 } 1910 1911 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1912 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1913 1914 // Try to evaluate any dependencies out of the loop. 1915 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1916 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1917 Tmp = getSCEVAtScope(RHS, L); 1918 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1919 1920 // At this point, we would like to compute how many iterations of the 1921 // loop the predicate will return true for these inputs. 1922 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) { 1923 // If there is a constant, force it into the RHS. 1924 std::swap(LHS, RHS); 1925 Cond = ICmpInst::getSwappedPredicate(Cond); 1926 } 1927 1928 // FIXME: think about handling pointer comparisons! i.e.: 1929 // while (P != P+100) ++P; 1930 1931 // If we have a comparison of a chrec against a constant, try to use value 1932 // ranges to answer this query. 1933 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1934 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1935 if (AddRec->getLoop() == L) { 1936 // Form the comparison range using the constant of the correct type so 1937 // that the ConstantRange class knows to do a signed or unsigned 1938 // comparison. 1939 ConstantInt *CompVal = RHSC->getValue(); 1940 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1941 CompVal = dyn_cast<ConstantInt>( 1942 ConstantExpr::getBitCast(CompVal, RealTy)); 1943 if (CompVal) { 1944 // Form the constant range. 1945 ConstantRange CompRange( 1946 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1947 1948 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1949 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1950 } 1951 } 1952 1953 switch (Cond) { 1954 case ICmpInst::ICMP_NE: { // while (X != Y) 1955 // Convert to: while (X-Y != 0) 1956 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1957 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1958 break; 1959 } 1960 case ICmpInst::ICMP_EQ: { 1961 // Convert to: while (X-Y == 0) // while (X == Y) 1962 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1963 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1964 break; 1965 } 1966 case ICmpInst::ICMP_SLT: { 1967 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1968 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1969 break; 1970 } 1971 case ICmpInst::ICMP_SGT: { 1972 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1973 SE.getNegativeSCEV(RHS), L, true); 1974 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1975 break; 1976 } 1977 case ICmpInst::ICMP_ULT: { 1978 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1979 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1980 break; 1981 } 1982 case ICmpInst::ICMP_UGT: { 1983 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1984 SE.getNegativeSCEV(RHS), L, false); 1985 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1986 break; 1987 } 1988 default: 1989#if 0 1990 cerr << "ComputeIterationCount "; 1991 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1992 cerr << "[unsigned] "; 1993 cerr << *LHS << " " 1994 << Instruction::getOpcodeName(Instruction::ICmp) 1995 << " " << *RHS << "\n"; 1996#endif 1997 break; 1998 } 1999 return ComputeIterationCountExhaustively(L, ExitCond, 2000 ExitBr->getSuccessor(0) == ExitBlock); 2001} 2002 2003static ConstantInt * 2004EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2005 ScalarEvolution &SE) { 2006 SCEVHandle InVal = SE.getConstant(C); 2007 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2008 assert(isa<SCEVConstant>(Val) && 2009 "Evaluation of SCEV at constant didn't fold correctly?"); 2010 return cast<SCEVConstant>(Val)->getValue(); 2011} 2012 2013/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2014/// and a GEP expression (missing the pointer index) indexing into it, return 2015/// the addressed element of the initializer or null if the index expression is 2016/// invalid. 2017static Constant * 2018GetAddressedElementFromGlobal(GlobalVariable *GV, 2019 const std::vector<ConstantInt*> &Indices) { 2020 Constant *Init = GV->getInitializer(); 2021 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2022 uint64_t Idx = Indices[i]->getZExtValue(); 2023 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2024 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2025 Init = cast<Constant>(CS->getOperand(Idx)); 2026 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2027 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2028 Init = cast<Constant>(CA->getOperand(Idx)); 2029 } else if (isa<ConstantAggregateZero>(Init)) { 2030 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2031 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2032 Init = Constant::getNullValue(STy->getElementType(Idx)); 2033 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2034 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2035 Init = Constant::getNullValue(ATy->getElementType()); 2036 } else { 2037 assert(0 && "Unknown constant aggregate type!"); 2038 } 2039 return 0; 2040 } else { 2041 return 0; // Unknown initializer type 2042 } 2043 } 2044 return Init; 2045} 2046 2047/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 2048/// 'icmp op load X, cst', try to se if we can compute the trip count. 2049SCEVHandle ScalarEvolutionsImpl:: 2050ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 2051 const Loop *L, 2052 ICmpInst::Predicate predicate) { 2053 if (LI->isVolatile()) return UnknownValue; 2054 2055 // Check to see if the loaded pointer is a getelementptr of a global. 2056 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2057 if (!GEP) return UnknownValue; 2058 2059 // Make sure that it is really a constant global we are gepping, with an 2060 // initializer, and make sure the first IDX is really 0. 2061 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2062 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2063 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2064 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2065 return UnknownValue; 2066 2067 // Okay, we allow one non-constant index into the GEP instruction. 2068 Value *VarIdx = 0; 2069 std::vector<ConstantInt*> Indexes; 2070 unsigned VarIdxNum = 0; 2071 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2072 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2073 Indexes.push_back(CI); 2074 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2075 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2076 VarIdx = GEP->getOperand(i); 2077 VarIdxNum = i-2; 2078 Indexes.push_back(0); 2079 } 2080 2081 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2082 // Check to see if X is a loop variant variable value now. 2083 SCEVHandle Idx = getSCEV(VarIdx); 2084 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2085 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2086 2087 // We can only recognize very limited forms of loop index expressions, in 2088 // particular, only affine AddRec's like {C1,+,C2}. 2089 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2090 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2091 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2092 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2093 return UnknownValue; 2094 2095 unsigned MaxSteps = MaxBruteForceIterations; 2096 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2097 ConstantInt *ItCst = 2098 ConstantInt::get(IdxExpr->getType(), IterationNum); 2099 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2100 2101 // Form the GEP offset. 2102 Indexes[VarIdxNum] = Val; 2103 2104 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2105 if (Result == 0) break; // Cannot compute! 2106 2107 // Evaluate the condition for this iteration. 2108 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2109 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2110 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2111#if 0 2112 cerr << "\n***\n*** Computed loop count " << *ItCst 2113 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2114 << "***\n"; 2115#endif 2116 ++NumArrayLenItCounts; 2117 return SE.getConstant(ItCst); // Found terminating iteration! 2118 } 2119 } 2120 return UnknownValue; 2121} 2122 2123 2124/// CanConstantFold - Return true if we can constant fold an instruction of the 2125/// specified type, assuming that all operands were constants. 2126static bool CanConstantFold(const Instruction *I) { 2127 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2128 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2129 return true; 2130 2131 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2132 if (const Function *F = CI->getCalledFunction()) 2133 return canConstantFoldCallTo(F); 2134 return false; 2135} 2136 2137/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2138/// in the loop that V is derived from. We allow arbitrary operations along the 2139/// way, but the operands of an operation must either be constants or a value 2140/// derived from a constant PHI. If this expression does not fit with these 2141/// constraints, return null. 2142static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2143 // If this is not an instruction, or if this is an instruction outside of the 2144 // loop, it can't be derived from a loop PHI. 2145 Instruction *I = dyn_cast<Instruction>(V); 2146 if (I == 0 || !L->contains(I->getParent())) return 0; 2147 2148 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2149 if (L->getHeader() == I->getParent()) 2150 return PN; 2151 else 2152 // We don't currently keep track of the control flow needed to evaluate 2153 // PHIs, so we cannot handle PHIs inside of loops. 2154 return 0; 2155 } 2156 2157 // If we won't be able to constant fold this expression even if the operands 2158 // are constants, return early. 2159 if (!CanConstantFold(I)) return 0; 2160 2161 // Otherwise, we can evaluate this instruction if all of its operands are 2162 // constant or derived from a PHI node themselves. 2163 PHINode *PHI = 0; 2164 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2165 if (!(isa<Constant>(I->getOperand(Op)) || 2166 isa<GlobalValue>(I->getOperand(Op)))) { 2167 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2168 if (P == 0) return 0; // Not evolving from PHI 2169 if (PHI == 0) 2170 PHI = P; 2171 else if (PHI != P) 2172 return 0; // Evolving from multiple different PHIs. 2173 } 2174 2175 // This is a expression evolving from a constant PHI! 2176 return PHI; 2177} 2178 2179/// EvaluateExpression - Given an expression that passes the 2180/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2181/// in the loop has the value PHIVal. If we can't fold this expression for some 2182/// reason, return null. 2183static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2184 if (isa<PHINode>(V)) return PHIVal; 2185 if (Constant *C = dyn_cast<Constant>(V)) return C; 2186 Instruction *I = cast<Instruction>(V); 2187 2188 std::vector<Constant*> Operands; 2189 Operands.resize(I->getNumOperands()); 2190 2191 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2192 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2193 if (Operands[i] == 0) return 0; 2194 } 2195 2196 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2197 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2198 &Operands[0], Operands.size()); 2199 else 2200 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2201 &Operands[0], Operands.size()); 2202} 2203 2204/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2205/// in the header of its containing loop, we know the loop executes a 2206/// constant number of times, and the PHI node is just a recurrence 2207/// involving constants, fold it. 2208Constant *ScalarEvolutionsImpl:: 2209getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2210 std::map<PHINode*, Constant*>::iterator I = 2211 ConstantEvolutionLoopExitValue.find(PN); 2212 if (I != ConstantEvolutionLoopExitValue.end()) 2213 return I->second; 2214 2215 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2216 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2217 2218 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2219 2220 // Since the loop is canonicalized, the PHI node must have two entries. One 2221 // entry must be a constant (coming in from outside of the loop), and the 2222 // second must be derived from the same PHI. 2223 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2224 Constant *StartCST = 2225 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2226 if (StartCST == 0) 2227 return RetVal = 0; // Must be a constant. 2228 2229 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2230 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2231 if (PN2 != PN) 2232 return RetVal = 0; // Not derived from same PHI. 2233 2234 // Execute the loop symbolically to determine the exit value. 2235 if (Its.getActiveBits() >= 32) 2236 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2237 2238 unsigned NumIterations = Its.getZExtValue(); // must be in range 2239 unsigned IterationNum = 0; 2240 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2241 if (IterationNum == NumIterations) 2242 return RetVal = PHIVal; // Got exit value! 2243 2244 // Compute the value of the PHI node for the next iteration. 2245 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2246 if (NextPHI == PHIVal) 2247 return RetVal = NextPHI; // Stopped evolving! 2248 if (NextPHI == 0) 2249 return 0; // Couldn't evaluate! 2250 PHIVal = NextPHI; 2251 } 2252} 2253 2254/// ComputeIterationCountExhaustively - If the trip is known to execute a 2255/// constant number of times (the condition evolves only from constants), 2256/// try to evaluate a few iterations of the loop until we get the exit 2257/// condition gets a value of ExitWhen (true or false). If we cannot 2258/// evaluate the trip count of the loop, return UnknownValue. 2259SCEVHandle ScalarEvolutionsImpl:: 2260ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2261 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2262 if (PN == 0) return UnknownValue; 2263 2264 // Since the loop is canonicalized, the PHI node must have two entries. One 2265 // entry must be a constant (coming in from outside of the loop), and the 2266 // second must be derived from the same PHI. 2267 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2268 Constant *StartCST = 2269 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2270 if (StartCST == 0) return UnknownValue; // Must be a constant. 2271 2272 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2273 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2274 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2275 2276 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2277 // the loop symbolically to determine when the condition gets a value of 2278 // "ExitWhen". 2279 unsigned IterationNum = 0; 2280 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2281 for (Constant *PHIVal = StartCST; 2282 IterationNum != MaxIterations; ++IterationNum) { 2283 ConstantInt *CondVal = 2284 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2285 2286 // Couldn't symbolically evaluate. 2287 if (!CondVal) return UnknownValue; 2288 2289 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2290 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2291 ++NumBruteForceTripCountsComputed; 2292 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2293 } 2294 2295 // Compute the value of the PHI node for the next iteration. 2296 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2297 if (NextPHI == 0 || NextPHI == PHIVal) 2298 return UnknownValue; // Couldn't evaluate or not making progress... 2299 PHIVal = NextPHI; 2300 } 2301 2302 // Too many iterations were needed to evaluate. 2303 return UnknownValue; 2304} 2305 2306/// getSCEVAtScope - Compute the value of the specified expression within the 2307/// indicated loop (which may be null to indicate in no loop). If the 2308/// expression cannot be evaluated, return UnknownValue. 2309SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2310 // FIXME: this should be turned into a virtual method on SCEV! 2311 2312 if (isa<SCEVConstant>(V)) return V; 2313 2314 // If this instruction is evolved from a constant-evolving PHI, compute the 2315 // exit value from the loop without using SCEVs. 2316 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2317 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2318 const Loop *LI = this->LI[I->getParent()]; 2319 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2320 if (PHINode *PN = dyn_cast<PHINode>(I)) 2321 if (PN->getParent() == LI->getHeader()) { 2322 // Okay, there is no closed form solution for the PHI node. Check 2323 // to see if the loop that contains it has a known iteration count. 2324 // If so, we may be able to force computation of the exit value. 2325 SCEVHandle IterationCount = getIterationCount(LI); 2326 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2327 // Okay, we know how many times the containing loop executes. If 2328 // this is a constant evolving PHI node, get the final value at 2329 // the specified iteration number. 2330 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2331 ICC->getValue()->getValue(), 2332 LI); 2333 if (RV) return SE.getUnknown(RV); 2334 } 2335 } 2336 2337 // Okay, this is an expression that we cannot symbolically evaluate 2338 // into a SCEV. Check to see if it's possible to symbolically evaluate 2339 // the arguments into constants, and if so, try to constant propagate the 2340 // result. This is particularly useful for computing loop exit values. 2341 if (CanConstantFold(I)) { 2342 std::vector<Constant*> Operands; 2343 Operands.reserve(I->getNumOperands()); 2344 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2345 Value *Op = I->getOperand(i); 2346 if (Constant *C = dyn_cast<Constant>(Op)) { 2347 Operands.push_back(C); 2348 } else { 2349 // If any of the operands is non-constant and if they are 2350 // non-integer, don't even try to analyze them with scev techniques. 2351 if (!isa<IntegerType>(Op->getType())) 2352 return V; 2353 2354 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2355 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2356 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2357 Op->getType(), 2358 false)); 2359 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2360 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2361 Operands.push_back(ConstantExpr::getIntegerCast(C, 2362 Op->getType(), 2363 false)); 2364 else 2365 return V; 2366 } else { 2367 return V; 2368 } 2369 } 2370 } 2371 2372 Constant *C; 2373 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2374 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2375 &Operands[0], Operands.size()); 2376 else 2377 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2378 &Operands[0], Operands.size()); 2379 return SE.getUnknown(C); 2380 } 2381 } 2382 2383 // This is some other type of SCEVUnknown, just return it. 2384 return V; 2385 } 2386 2387 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2388 // Avoid performing the look-up in the common case where the specified 2389 // expression has no loop-variant portions. 2390 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2391 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2392 if (OpAtScope != Comm->getOperand(i)) { 2393 if (OpAtScope == UnknownValue) return UnknownValue; 2394 // Okay, at least one of these operands is loop variant but might be 2395 // foldable. Build a new instance of the folded commutative expression. 2396 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2397 NewOps.push_back(OpAtScope); 2398 2399 for (++i; i != e; ++i) { 2400 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2401 if (OpAtScope == UnknownValue) return UnknownValue; 2402 NewOps.push_back(OpAtScope); 2403 } 2404 if (isa<SCEVAddExpr>(Comm)) 2405 return SE.getAddExpr(NewOps); 2406 if (isa<SCEVMulExpr>(Comm)) 2407 return SE.getMulExpr(NewOps); 2408 if (isa<SCEVSMaxExpr>(Comm)) 2409 return SE.getSMaxExpr(NewOps); 2410 if (isa<SCEVUMaxExpr>(Comm)) 2411 return SE.getUMaxExpr(NewOps); 2412 assert(0 && "Unknown commutative SCEV type!"); 2413 } 2414 } 2415 // If we got here, all operands are loop invariant. 2416 return Comm; 2417 } 2418 2419 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2420 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2421 if (LHS == UnknownValue) return LHS; 2422 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2423 if (RHS == UnknownValue) return RHS; 2424 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2425 return Div; // must be loop invariant 2426 return SE.getUDivExpr(LHS, RHS); 2427 } 2428 2429 // If this is a loop recurrence for a loop that does not contain L, then we 2430 // are dealing with the final value computed by the loop. 2431 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2432 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2433 // To evaluate this recurrence, we need to know how many times the AddRec 2434 // loop iterates. Compute this now. 2435 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2436 if (IterationCount == UnknownValue) return UnknownValue; 2437 IterationCount = getTruncateOrZeroExtend(IterationCount, 2438 AddRec->getType(), SE); 2439 2440 // If the value is affine, simplify the expression evaluation to just 2441 // Start + Step*IterationCount. 2442 if (AddRec->isAffine()) 2443 return SE.getAddExpr(AddRec->getStart(), 2444 SE.getMulExpr(IterationCount, 2445 AddRec->getOperand(1))); 2446 2447 // Otherwise, evaluate it the hard way. 2448 return AddRec->evaluateAtIteration(IterationCount, SE); 2449 } 2450 return UnknownValue; 2451 } 2452 2453 //assert(0 && "Unknown SCEV type!"); 2454 return UnknownValue; 2455} 2456 2457 2458/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2459/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2460/// might be the same) or two SCEVCouldNotCompute objects. 2461/// 2462static std::pair<SCEVHandle,SCEVHandle> 2463SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2464 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2465 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2466 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2467 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2468 2469 // We currently can only solve this if the coefficients are constants. 2470 if (!LC || !MC || !NC) { 2471 SCEV *CNC = new SCEVCouldNotCompute(); 2472 return std::make_pair(CNC, CNC); 2473 } 2474 2475 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2476 const APInt &L = LC->getValue()->getValue(); 2477 const APInt &M = MC->getValue()->getValue(); 2478 const APInt &N = NC->getValue()->getValue(); 2479 APInt Two(BitWidth, 2); 2480 APInt Four(BitWidth, 4); 2481 2482 { 2483 using namespace APIntOps; 2484 const APInt& C = L; 2485 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2486 // The B coefficient is M-N/2 2487 APInt B(M); 2488 B -= sdiv(N,Two); 2489 2490 // The A coefficient is N/2 2491 APInt A(N.sdiv(Two)); 2492 2493 // Compute the B^2-4ac term. 2494 APInt SqrtTerm(B); 2495 SqrtTerm *= B; 2496 SqrtTerm -= Four * (A * C); 2497 2498 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2499 // integer value or else APInt::sqrt() will assert. 2500 APInt SqrtVal(SqrtTerm.sqrt()); 2501 2502 // Compute the two solutions for the quadratic formula. 2503 // The divisions must be performed as signed divisions. 2504 APInt NegB(-B); 2505 APInt TwoA( A << 1 ); 2506 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2507 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2508 2509 return std::make_pair(SE.getConstant(Solution1), 2510 SE.getConstant(Solution2)); 2511 } // end APIntOps namespace 2512} 2513 2514/// HowFarToZero - Return the number of times a backedge comparing the specified 2515/// value to zero will execute. If not computable, return UnknownValue 2516SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2517 // If the value is a constant 2518 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2519 // If the value is already zero, the branch will execute zero times. 2520 if (C->getValue()->isZero()) return C; 2521 return UnknownValue; // Otherwise it will loop infinitely. 2522 } 2523 2524 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2525 if (!AddRec || AddRec->getLoop() != L) 2526 return UnknownValue; 2527 2528 if (AddRec->isAffine()) { 2529 // If this is an affine expression the execution count of this branch is 2530 // equal to: 2531 // 2532 // (0 - Start/Step) iff Start % Step == 0 2533 // 2534 // Get the initial value for the loop. 2535 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2536 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2537 SCEVHandle Step = AddRec->getOperand(1); 2538 2539 Step = getSCEVAtScope(Step, L->getParentLoop()); 2540 2541 // Figure out if Start % Step == 0. 2542 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2543 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2544 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2545 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start 2546 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2547 return Start; // 0 - Start/-1 == Start 2548 2549 // Check to see if Start is divisible by SC with no remainder. 2550 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2551 ConstantInt *StartCC = StartC->getValue(); 2552 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2553 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2554 if (Rem->isNullValue()) { 2555 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2556 return SE.getUnknown(Result); 2557 } 2558 } 2559 } 2560 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2561 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2562 // the quadratic equation to solve it. 2563 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2564 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2565 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2566 if (R1) { 2567#if 0 2568 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2569 << " sol#2: " << *R2 << "\n"; 2570#endif 2571 // Pick the smallest positive root value. 2572 if (ConstantInt *CB = 2573 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2574 R1->getValue(), R2->getValue()))) { 2575 if (CB->getZExtValue() == false) 2576 std::swap(R1, R2); // R1 is the minimum root now. 2577 2578 // We can only use this value if the chrec ends up with an exact zero 2579 // value at this index. When solving for "X*X != 5", for example, we 2580 // should not accept a root of 2. 2581 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2582 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2583 if (EvalVal->getValue()->isZero()) 2584 return R1; // We found a quadratic root! 2585 } 2586 } 2587 } 2588 2589 return UnknownValue; 2590} 2591 2592/// HowFarToNonZero - Return the number of times a backedge checking the 2593/// specified value for nonzero will execute. If not computable, return 2594/// UnknownValue 2595SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2596 // Loops that look like: while (X == 0) are very strange indeed. We don't 2597 // handle them yet except for the trivial case. This could be expanded in the 2598 // future as needed. 2599 2600 // If the value is a constant, check to see if it is known to be non-zero 2601 // already. If so, the backedge will execute zero times. 2602 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2603 if (!C->getValue()->isNullValue()) 2604 return SE.getIntegerSCEV(0, C->getType()); 2605 return UnknownValue; // Otherwise it will loop infinitely. 2606 } 2607 2608 // We could implement others, but I really doubt anyone writes loops like 2609 // this, and if they did, they would already be constant folded. 2610 return UnknownValue; 2611} 2612 2613/// HowManyLessThans - Return the number of times a backedge containing the 2614/// specified less-than comparison will execute. If not computable, return 2615/// UnknownValue. 2616SCEVHandle ScalarEvolutionsImpl:: 2617HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2618 // Only handle: "ADDREC < LoopInvariant". 2619 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2620 2621 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2622 if (!AddRec || AddRec->getLoop() != L) 2623 return UnknownValue; 2624 2625 if (AddRec->isAffine()) { 2626 // FORNOW: We only support unit strides. 2627 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2628 if (AddRec->getOperand(1) != One) 2629 return UnknownValue; 2630 2631 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2632 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2633 // Note that we cannot simply return max(m-n,0) because it's not safe to 2634 // treat m-n as signed nor unsigned due to overflow possibility. 2635 2636 // First, we get the value of the LHS in the first iteration: n 2637 SCEVHandle Start = AddRec->getOperand(0); 2638 2639 // Then, we get the value of the LHS in the first iteration in which the 2640 // above condition doesn't hold. This equals to max(m,n). 2641 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start) 2642 : SE.getUMaxExpr(RHS, Start); 2643 2644 // Finally, we subtract these two values to get the number of times the 2645 // backedge is executed: max(m,n)-n. 2646 return SE.getMinusSCEV(End, Start); 2647 } 2648 2649 return UnknownValue; 2650} 2651 2652/// getNumIterationsInRange - Return the number of iterations of this loop that 2653/// produce values in the specified constant range. Another way of looking at 2654/// this is that it returns the first iteration number where the value is not in 2655/// the condition, thus computing the exit count. If the iteration count can't 2656/// be computed, an instance of SCEVCouldNotCompute is returned. 2657SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2658 ScalarEvolution &SE) const { 2659 if (Range.isFullSet()) // Infinite loop. 2660 return new SCEVCouldNotCompute(); 2661 2662 // If the start is a non-zero constant, shift the range to simplify things. 2663 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2664 if (!SC->getValue()->isZero()) { 2665 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2666 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2667 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2668 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2669 return ShiftedAddRec->getNumIterationsInRange( 2670 Range.subtract(SC->getValue()->getValue()), SE); 2671 // This is strange and shouldn't happen. 2672 return new SCEVCouldNotCompute(); 2673 } 2674 2675 // The only time we can solve this is when we have all constant indices. 2676 // Otherwise, we cannot determine the overflow conditions. 2677 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2678 if (!isa<SCEVConstant>(getOperand(i))) 2679 return new SCEVCouldNotCompute(); 2680 2681 2682 // Okay at this point we know that all elements of the chrec are constants and 2683 // that the start element is zero. 2684 2685 // First check to see if the range contains zero. If not, the first 2686 // iteration exits. 2687 if (!Range.contains(APInt(getBitWidth(),0))) 2688 return SE.getConstant(ConstantInt::get(getType(),0)); 2689 2690 if (isAffine()) { 2691 // If this is an affine expression then we have this situation: 2692 // Solve {0,+,A} in Range === Ax in Range 2693 2694 // We know that zero is in the range. If A is positive then we know that 2695 // the upper value of the range must be the first possible exit value. 2696 // If A is negative then the lower of the range is the last possible loop 2697 // value. Also note that we already checked for a full range. 2698 APInt One(getBitWidth(),1); 2699 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2700 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2701 2702 // The exit value should be (End+A)/A. 2703 APInt ExitVal = (End + A).udiv(A); 2704 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2705 2706 // Evaluate at the exit value. If we really did fall out of the valid 2707 // range, then we computed our trip count, otherwise wrap around or other 2708 // things must have happened. 2709 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2710 if (Range.contains(Val->getValue())) 2711 return new SCEVCouldNotCompute(); // Something strange happened 2712 2713 // Ensure that the previous value is in the range. This is a sanity check. 2714 assert(Range.contains( 2715 EvaluateConstantChrecAtConstant(this, 2716 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2717 "Linear scev computation is off in a bad way!"); 2718 return SE.getConstant(ExitValue); 2719 } else if (isQuadratic()) { 2720 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2721 // quadratic equation to solve it. To do this, we must frame our problem in 2722 // terms of figuring out when zero is crossed, instead of when 2723 // Range.getUpper() is crossed. 2724 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2725 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2726 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2727 2728 // Next, solve the constructed addrec 2729 std::pair<SCEVHandle,SCEVHandle> Roots = 2730 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2731 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2732 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2733 if (R1) { 2734 // Pick the smallest positive root value. 2735 if (ConstantInt *CB = 2736 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2737 R1->getValue(), R2->getValue()))) { 2738 if (CB->getZExtValue() == false) 2739 std::swap(R1, R2); // R1 is the minimum root now. 2740 2741 // Make sure the root is not off by one. The returned iteration should 2742 // not be in the range, but the previous one should be. When solving 2743 // for "X*X < 5", for example, we should not return a root of 2. 2744 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2745 R1->getValue(), 2746 SE); 2747 if (Range.contains(R1Val->getValue())) { 2748 // The next iteration must be out of the range... 2749 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2750 2751 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2752 if (!Range.contains(R1Val->getValue())) 2753 return SE.getConstant(NextVal); 2754 return new SCEVCouldNotCompute(); // Something strange happened 2755 } 2756 2757 // If R1 was not in the range, then it is a good return value. Make 2758 // sure that R1-1 WAS in the range though, just in case. 2759 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2760 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2761 if (Range.contains(R1Val->getValue())) 2762 return R1; 2763 return new SCEVCouldNotCompute(); // Something strange happened 2764 } 2765 } 2766 } 2767 2768 // Fallback, if this is a general polynomial, figure out the progression 2769 // through brute force: evaluate until we find an iteration that fails the 2770 // test. This is likely to be slow, but getting an accurate trip count is 2771 // incredibly important, we will be able to simplify the exit test a lot, and 2772 // we are almost guaranteed to get a trip count in this case. 2773 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2774 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2775 do { 2776 ++NumBruteForceEvaluations; 2777 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2778 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2779 return new SCEVCouldNotCompute(); 2780 2781 // Check to see if we found the value! 2782 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2783 return SE.getConstant(TestVal); 2784 2785 // Increment to test the next index. 2786 TestVal = ConstantInt::get(TestVal->getValue()+1); 2787 } while (TestVal != EndVal); 2788 2789 return new SCEVCouldNotCompute(); 2790} 2791 2792 2793 2794//===----------------------------------------------------------------------===// 2795// ScalarEvolution Class Implementation 2796//===----------------------------------------------------------------------===// 2797 2798bool ScalarEvolution::runOnFunction(Function &F) { 2799 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2800 return false; 2801} 2802 2803void ScalarEvolution::releaseMemory() { 2804 delete (ScalarEvolutionsImpl*)Impl; 2805 Impl = 0; 2806} 2807 2808void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2809 AU.setPreservesAll(); 2810 AU.addRequiredTransitive<LoopInfo>(); 2811} 2812 2813SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2814 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2815} 2816 2817/// hasSCEV - Return true if the SCEV for this value has already been 2818/// computed. 2819bool ScalarEvolution::hasSCEV(Value *V) const { 2820 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2821} 2822 2823 2824/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2825/// the specified value. 2826void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2827 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2828} 2829 2830 2831SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2832 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2833} 2834 2835bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2836 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2837} 2838 2839SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2840 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2841} 2842 2843void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2844 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2845} 2846 2847static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2848 const Loop *L) { 2849 // Print all inner loops first 2850 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2851 PrintLoopInfo(OS, SE, *I); 2852 2853 OS << "Loop " << L->getHeader()->getName() << ": "; 2854 2855 SmallVector<BasicBlock*, 8> ExitBlocks; 2856 L->getExitBlocks(ExitBlocks); 2857 if (ExitBlocks.size() != 1) 2858 OS << "<multiple exits> "; 2859 2860 if (SE->hasLoopInvariantIterationCount(L)) { 2861 OS << *SE->getIterationCount(L) << " iterations! "; 2862 } else { 2863 OS << "Unpredictable iteration count. "; 2864 } 2865 2866 OS << "\n"; 2867} 2868 2869void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2870 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2871 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2872 2873 OS << "Classifying expressions for: " << F.getName() << "\n"; 2874 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2875 if (I->getType()->isInteger()) { 2876 OS << *I; 2877 OS << " --> "; 2878 SCEVHandle SV = getSCEV(&*I); 2879 SV->print(OS); 2880 OS << "\t\t"; 2881 2882 if ((*I).getType()->isInteger()) { 2883 ConstantRange Bounds = SV->getValueRange(); 2884 if (!Bounds.isFullSet()) 2885 OS << "Bounds: " << Bounds << " "; 2886 } 2887 2888 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2889 OS << "Exits: "; 2890 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2891 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2892 OS << "<<Unknown>>"; 2893 } else { 2894 OS << *ExitValue; 2895 } 2896 } 2897 2898 2899 OS << "\n"; 2900 } 2901 2902 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2903 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2904 PrintLoopInfo(OS, this, *I); 2905} 2906