ScalarEvolution.cpp revision a089b104218c46803a1af374f6c441df885e54c2
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"); 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 324 assert(0 && "Unknown commutative expr!"); 325 } 326 } 327 return this; 328} 329 330 331// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 332// input. Don't use a SCEVHandle here, or else the object will never be 333// deleted! 334static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 335 SCEVUDivExpr*> > SCEVUDivs; 336 337SCEVUDivExpr::~SCEVUDivExpr() { 338 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 339} 340 341void SCEVUDivExpr::print(std::ostream &OS) const { 342 OS << "(" << *LHS << " /u " << *RHS << ")"; 343} 344 345const Type *SCEVUDivExpr::getType() const { 346 return LHS->getType(); 347} 348 349// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 350// particular input. Don't use a SCEVHandle here, or else the object will never 351// be deleted! 352static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 353 SCEVAddRecExpr*> > SCEVAddRecExprs; 354 355SCEVAddRecExpr::~SCEVAddRecExpr() { 356 SCEVAddRecExprs->erase(std::make_pair(L, 357 std::vector<SCEV*>(Operands.begin(), 358 Operands.end()))); 359} 360 361SCEVHandle SCEVAddRecExpr:: 362replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 363 const SCEVHandle &Conc, 364 ScalarEvolution &SE) const { 365 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 366 SCEVHandle H = 367 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 368 if (H != getOperand(i)) { 369 std::vector<SCEVHandle> NewOps; 370 NewOps.reserve(getNumOperands()); 371 for (unsigned j = 0; j != i; ++j) 372 NewOps.push_back(getOperand(j)); 373 NewOps.push_back(H); 374 for (++i; i != e; ++i) 375 NewOps.push_back(getOperand(i)-> 376 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 377 378 return SE.getAddRecExpr(NewOps, L); 379 } 380 } 381 return this; 382} 383 384 385bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 386 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 387 // contain L and if the start is invariant. 388 return !QueryLoop->contains(L->getHeader()) && 389 getOperand(0)->isLoopInvariant(QueryLoop); 390} 391 392 393void SCEVAddRecExpr::print(std::ostream &OS) const { 394 OS << "{" << *Operands[0]; 395 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 396 OS << ",+," << *Operands[i]; 397 OS << "}<" << L->getHeader()->getName() + ">"; 398} 399 400// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 401// value. Don't use a SCEVHandle here, or else the object will never be 402// deleted! 403static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 404 405SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 406 407bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 408 // All non-instruction values are loop invariant. All instructions are loop 409 // invariant if they are not contained in the specified loop. 410 if (Instruction *I = dyn_cast<Instruction>(V)) 411 return !L->contains(I->getParent()); 412 return true; 413} 414 415const Type *SCEVUnknown::getType() const { 416 return V->getType(); 417} 418 419void SCEVUnknown::print(std::ostream &OS) const { 420 WriteAsOperand(OS, V, false); 421} 422 423//===----------------------------------------------------------------------===// 424// SCEV Utilities 425//===----------------------------------------------------------------------===// 426 427namespace { 428 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 429 /// than the complexity of the RHS. This comparator is used to canonicalize 430 /// expressions. 431 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 432 bool operator()(SCEV *LHS, SCEV *RHS) { 433 return LHS->getSCEVType() < RHS->getSCEVType(); 434 } 435 }; 436} 437 438/// GroupByComplexity - Given a list of SCEV objects, order them by their 439/// complexity, and group objects of the same complexity together by value. 440/// When this routine is finished, we know that any duplicates in the vector are 441/// consecutive and that complexity is monotonically increasing. 442/// 443/// Note that we go take special precautions to ensure that we get determinstic 444/// results from this routine. In other words, we don't want the results of 445/// this to depend on where the addresses of various SCEV objects happened to 446/// land in memory. 447/// 448static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 449 if (Ops.size() < 2) return; // Noop 450 if (Ops.size() == 2) { 451 // This is the common case, which also happens to be trivially simple. 452 // Special case it. 453 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType()) 454 std::swap(Ops[0], Ops[1]); 455 return; 456 } 457 458 // Do the rough sort by complexity. 459 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 460 461 // Now that we are sorted by complexity, group elements of the same 462 // complexity. Note that this is, at worst, N^2, but the vector is likely to 463 // be extremely short in practice. Note that we take this approach because we 464 // do not want to depend on the addresses of the objects we are grouping. 465 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 466 SCEV *S = Ops[i]; 467 unsigned Complexity = S->getSCEVType(); 468 469 // If there are any objects of the same complexity and same value as this 470 // one, group them. 471 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 472 if (Ops[j] == S) { // Found a duplicate. 473 // Move it to immediately after i'th element. 474 std::swap(Ops[i+1], Ops[j]); 475 ++i; // no need to rescan it. 476 if (i == e-2) return; // Done! 477 } 478 } 479 } 480} 481 482 483 484//===----------------------------------------------------------------------===// 485// Simple SCEV method implementations 486//===----------------------------------------------------------------------===// 487 488/// getIntegerSCEV - Given an integer or FP type, create a constant for the 489/// specified signed integer value and return a SCEV for the constant. 490SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 491 Constant *C; 492 if (Val == 0) 493 C = Constant::getNullValue(Ty); 494 else if (Ty->isFloatingPoint()) 495 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 496 APFloat::IEEEdouble, Val)); 497 else 498 C = ConstantInt::get(Ty, Val); 499 return getUnknown(C); 500} 501 502/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 503/// input value to the specified type. If the type must be extended, it is zero 504/// extended. 505static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty, 506 ScalarEvolution &SE) { 507 const Type *SrcTy = V->getType(); 508 assert(SrcTy->isInteger() && Ty->isInteger() && 509 "Cannot truncate or zero extend with non-integer arguments!"); 510 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits()) 511 return V; // No conversion 512 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()) 513 return SE.getTruncateExpr(V, Ty); 514 return SE.getZeroExtendExpr(V, Ty); 515} 516 517/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 518/// 519SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 520 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 521 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 522 523 return getMulExpr(V, getIntegerSCEV(-1, V->getType())); 524} 525 526/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 527/// 528SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 529 const SCEVHandle &RHS) { 530 // X - Y --> X + -Y 531 return getAddExpr(LHS, getNegativeSCEV(RHS)); 532} 533 534 535/// BinomialCoefficient - Compute BC(It, K). The result is of the same type as 536/// It. Assume, K > 0. 537static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 538 ScalarEvolution &SE) { 539 // We are using the following formula for BC(It, K): 540 // 541 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 542 // 543 // Suppose, W is the bitwidth of It (and of the return value as well). We 544 // must be prepared for overflow. Hence, we must assure that the result of 545 // our computation is equal to the accurate one modulo 2^W. Unfortunately, 546 // division isn't safe in modular arithmetic. This means we must perform the 547 // whole computation accurately and then truncate the result to W bits. 548 // 549 // The dividend of the formula is a multiplication of K integers of bitwidth 550 // W. K*W bits suffice to compute it accurately. 551 // 552 // FIXME: We assume the divisor can be accurately computed using 16-bit 553 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In 554 // future we may use APInt to use the minimum number of bits necessary to 555 // compute it accurately. 556 // 557 // It is safe to use unsigned division here: the dividend is nonnegative and 558 // the divisor is positive. 559 560 // Handle the simplest case efficiently. 561 if (K == 1) 562 return It; 563 564 assert(K < 9 && "We cannot handle such long AddRecs yet."); 565 566 // FIXME: A temporary hack to remove in future. Arbitrary precision integers 567 // aren't supported by the code generator yet. For the dividend, the bitwidth 568 // we use is the smallest power of 2 greater or equal to K*W and less or equal 569 // to 64. Note that setting the upper bound for bitwidth may still lead to 570 // miscompilation in some cases. 571 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth()); 572 if (DividendBits > 64) 573 DividendBits = 64; 574#if 0 // Waiting for the APInt support in the code generator... 575 unsigned DividendBits = K * It->getBitWidth(); 576#endif 577 578 const IntegerType *DividendTy = IntegerType::get(DividendBits); 579 const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy); 580 581 // The final number of bits we need to perform the division is the maximum of 582 // dividend and divisor bitwidths. 583 const IntegerType *DivisionTy = 584 IntegerType::get(std::max(DividendBits, 16U)); 585 586 // Compute K! We know K >= 2 here. 587 unsigned F = 2; 588 for (unsigned i = 3; i <= K; ++i) 589 F *= i; 590 APInt Divisor(DivisionTy->getBitWidth(), F); 591 592 // Handle this case efficiently, it is common to have constant iteration 593 // counts while computing loop exit values. 594 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) { 595 const APInt& N = SC->getValue()->getValue(); 596 APInt Dividend(N.getBitWidth(), 1); 597 for (; K; --K) 598 Dividend *= N-(K-1); 599 if (DividendTy != DivisionTy) 600 Dividend = Dividend.zext(DivisionTy->getBitWidth()); 601 return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth())); 602 } 603 604 SCEVHandle Dividend = ExIt; 605 for (unsigned i = 1; i != K; ++i) 606 Dividend = 607 SE.getMulExpr(Dividend, 608 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy))); 609 if (DividendTy != DivisionTy) 610 Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy); 611 return 612 SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)), 613 It->getType()); 614} 615 616/// evaluateAtIteration - Return the value of this chain of recurrences at 617/// the specified iteration number. We can evaluate this recurrence by 618/// multiplying each element in the chain by the binomial coefficient 619/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 620/// 621/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 622/// 623/// where BC(It, k) stands for binomial coefficient. 624/// 625SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 626 ScalarEvolution &SE) const { 627 SCEVHandle Result = getStart(); 628 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 629 // The computation is correct in the face of overflow provided that the 630 // multiplication is performed _after_ the evaluation of the binomial 631 // coefficient. 632 SCEVHandle Val = SE.getMulExpr(getOperand(i), 633 BinomialCoefficient(It, i, SE)); 634 Result = SE.getAddExpr(Result, Val); 635 } 636 return Result; 637} 638 639//===----------------------------------------------------------------------===// 640// SCEV Expression folder implementations 641//===----------------------------------------------------------------------===// 642 643SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 644 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 645 return getUnknown( 646 ConstantExpr::getTrunc(SC->getValue(), Ty)); 647 648 // If the input value is a chrec scev made out of constants, truncate 649 // all of the constants. 650 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 651 std::vector<SCEVHandle> Operands; 652 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 653 // FIXME: This should allow truncation of other expression types! 654 if (isa<SCEVConstant>(AddRec->getOperand(i))) 655 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 656 else 657 break; 658 if (Operands.size() == AddRec->getNumOperands()) 659 return getAddRecExpr(Operands, AddRec->getLoop()); 660 } 661 662 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 663 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 664 return Result; 665} 666 667SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) { 668 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 669 return getUnknown( 670 ConstantExpr::getZExt(SC->getValue(), Ty)); 671 672 // FIXME: If the input value is a chrec scev, and we can prove that the value 673 // did not overflow the old, smaller, value, we can zero extend all of the 674 // operands (often constants). This would allow analysis of something like 675 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 676 677 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 678 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 679 return Result; 680} 681 682SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 683 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 684 return getUnknown( 685 ConstantExpr::getSExt(SC->getValue(), Ty)); 686 687 // FIXME: If the input value is a chrec scev, and we can prove that the value 688 // did not overflow the old, smaller, value, we can sign extend all of the 689 // operands (often constants). This would allow analysis of something like 690 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 691 692 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 693 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 694 return Result; 695} 696 697// get - Get a canonical add expression, or something simpler if possible. 698SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 699 assert(!Ops.empty() && "Cannot get empty add!"); 700 if (Ops.size() == 1) return Ops[0]; 701 702 // Sort by complexity, this groups all similar expression types together. 703 GroupByComplexity(Ops); 704 705 // If there are any constants, fold them together. 706 unsigned Idx = 0; 707 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 708 ++Idx; 709 assert(Idx < Ops.size()); 710 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 711 // We found two constants, fold them together! 712 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 713 RHSC->getValue()->getValue()); 714 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 715 Ops[0] = getConstant(CI); 716 Ops.erase(Ops.begin()+1); // Erase the folded element 717 if (Ops.size() == 1) return Ops[0]; 718 LHSC = cast<SCEVConstant>(Ops[0]); 719 } else { 720 // If we couldn't fold the expression, move to the next constant. Note 721 // that this is impossible to happen in practice because we always 722 // constant fold constant ints to constant ints. 723 ++Idx; 724 } 725 } 726 727 // If we are left with a constant zero being added, strip it off. 728 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 729 Ops.erase(Ops.begin()); 730 --Idx; 731 } 732 } 733 734 if (Ops.size() == 1) return Ops[0]; 735 736 // Okay, check to see if the same value occurs in the operand list twice. If 737 // so, merge them together into an multiply expression. Since we sorted the 738 // list, these values are required to be adjacent. 739 const Type *Ty = Ops[0]->getType(); 740 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 741 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 742 // Found a match, merge the two values into a multiply, and add any 743 // remaining values to the result. 744 SCEVHandle Two = getIntegerSCEV(2, Ty); 745 SCEVHandle Mul = getMulExpr(Ops[i], Two); 746 if (Ops.size() == 2) 747 return Mul; 748 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 749 Ops.push_back(Mul); 750 return getAddExpr(Ops); 751 } 752 753 // Now we know the first non-constant operand. Skip past any cast SCEVs. 754 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 755 ++Idx; 756 757 // If there are add operands they would be next. 758 if (Idx < Ops.size()) { 759 bool DeletedAdd = false; 760 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 761 // If we have an add, expand the add operands onto the end of the operands 762 // list. 763 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 764 Ops.erase(Ops.begin()+Idx); 765 DeletedAdd = true; 766 } 767 768 // If we deleted at least one add, we added operands to the end of the list, 769 // and they are not necessarily sorted. Recurse to resort and resimplify 770 // any operands we just aquired. 771 if (DeletedAdd) 772 return getAddExpr(Ops); 773 } 774 775 // Skip over the add expression until we get to a multiply. 776 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 777 ++Idx; 778 779 // If we are adding something to a multiply expression, make sure the 780 // something is not already an operand of the multiply. If so, merge it into 781 // the multiply. 782 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 783 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 784 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 785 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 786 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 787 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 788 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 789 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 790 if (Mul->getNumOperands() != 2) { 791 // If the multiply has more than two operands, we must get the 792 // Y*Z term. 793 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 794 MulOps.erase(MulOps.begin()+MulOp); 795 InnerMul = getMulExpr(MulOps); 796 } 797 SCEVHandle One = getIntegerSCEV(1, Ty); 798 SCEVHandle AddOne = getAddExpr(InnerMul, One); 799 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 800 if (Ops.size() == 2) return OuterMul; 801 if (AddOp < Idx) { 802 Ops.erase(Ops.begin()+AddOp); 803 Ops.erase(Ops.begin()+Idx-1); 804 } else { 805 Ops.erase(Ops.begin()+Idx); 806 Ops.erase(Ops.begin()+AddOp-1); 807 } 808 Ops.push_back(OuterMul); 809 return getAddExpr(Ops); 810 } 811 812 // Check this multiply against other multiplies being added together. 813 for (unsigned OtherMulIdx = Idx+1; 814 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 815 ++OtherMulIdx) { 816 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 817 // If MulOp occurs in OtherMul, we can fold the two multiplies 818 // together. 819 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 820 OMulOp != e; ++OMulOp) 821 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 822 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 823 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 824 if (Mul->getNumOperands() != 2) { 825 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 826 MulOps.erase(MulOps.begin()+MulOp); 827 InnerMul1 = getMulExpr(MulOps); 828 } 829 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 830 if (OtherMul->getNumOperands() != 2) { 831 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 832 OtherMul->op_end()); 833 MulOps.erase(MulOps.begin()+OMulOp); 834 InnerMul2 = getMulExpr(MulOps); 835 } 836 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 837 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 838 if (Ops.size() == 2) return OuterMul; 839 Ops.erase(Ops.begin()+Idx); 840 Ops.erase(Ops.begin()+OtherMulIdx-1); 841 Ops.push_back(OuterMul); 842 return getAddExpr(Ops); 843 } 844 } 845 } 846 } 847 848 // If there are any add recurrences in the operands list, see if any other 849 // added values are loop invariant. If so, we can fold them into the 850 // recurrence. 851 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 852 ++Idx; 853 854 // Scan over all recurrences, trying to fold loop invariants into them. 855 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 856 // Scan all of the other operands to this add and add them to the vector if 857 // they are loop invariant w.r.t. the recurrence. 858 std::vector<SCEVHandle> LIOps; 859 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 860 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 861 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 862 LIOps.push_back(Ops[i]); 863 Ops.erase(Ops.begin()+i); 864 --i; --e; 865 } 866 867 // If we found some loop invariants, fold them into the recurrence. 868 if (!LIOps.empty()) { 869 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step } 870 LIOps.push_back(AddRec->getStart()); 871 872 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 873 AddRecOps[0] = getAddExpr(LIOps); 874 875 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 876 // If all of the other operands were loop invariant, we are done. 877 if (Ops.size() == 1) return NewRec; 878 879 // Otherwise, add the folded AddRec by the non-liv parts. 880 for (unsigned i = 0;; ++i) 881 if (Ops[i] == AddRec) { 882 Ops[i] = NewRec; 883 break; 884 } 885 return getAddExpr(Ops); 886 } 887 888 // Okay, if there weren't any loop invariants to be folded, check to see if 889 // there are multiple AddRec's with the same loop induction variable being 890 // added together. If so, we can fold them. 891 for (unsigned OtherIdx = Idx+1; 892 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 893 if (OtherIdx != Idx) { 894 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 895 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 896 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 897 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 898 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 899 if (i >= NewOps.size()) { 900 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 901 OtherAddRec->op_end()); 902 break; 903 } 904 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 905 } 906 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 907 908 if (Ops.size() == 2) return NewAddRec; 909 910 Ops.erase(Ops.begin()+Idx); 911 Ops.erase(Ops.begin()+OtherIdx-1); 912 Ops.push_back(NewAddRec); 913 return getAddExpr(Ops); 914 } 915 } 916 917 // Otherwise couldn't fold anything into this recurrence. Move onto the 918 // next one. 919 } 920 921 // Okay, it looks like we really DO need an add expr. Check to see if we 922 // already have one, otherwise create a new one. 923 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 924 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 925 SCEVOps)]; 926 if (Result == 0) Result = new SCEVAddExpr(Ops); 927 return Result; 928} 929 930 931SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 932 assert(!Ops.empty() && "Cannot get empty mul!"); 933 934 // Sort by complexity, this groups all similar expression types together. 935 GroupByComplexity(Ops); 936 937 // If there are any constants, fold them together. 938 unsigned Idx = 0; 939 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 940 941 // C1*(C2+V) -> C1*C2 + C1*V 942 if (Ops.size() == 2) 943 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 944 if (Add->getNumOperands() == 2 && 945 isa<SCEVConstant>(Add->getOperand(0))) 946 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 947 getMulExpr(LHSC, Add->getOperand(1))); 948 949 950 ++Idx; 951 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 952 // We found two constants, fold them together! 953 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 954 RHSC->getValue()->getValue()); 955 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 956 Ops[0] = getConstant(CI); 957 Ops.erase(Ops.begin()+1); // Erase the folded element 958 if (Ops.size() == 1) return Ops[0]; 959 LHSC = cast<SCEVConstant>(Ops[0]); 960 } else { 961 // If we couldn't fold the expression, move to the next constant. Note 962 // that this is impossible to happen in practice because we always 963 // constant fold constant ints to constant ints. 964 ++Idx; 965 } 966 } 967 968 // If we are left with a constant one being multiplied, strip it off. 969 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 970 Ops.erase(Ops.begin()); 971 --Idx; 972 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 973 // If we have a multiply of zero, it will always be zero. 974 return Ops[0]; 975 } 976 } 977 978 // Skip over the add expression until we get to a multiply. 979 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 980 ++Idx; 981 982 if (Ops.size() == 1) 983 return Ops[0]; 984 985 // If there are mul operands inline them all into this expression. 986 if (Idx < Ops.size()) { 987 bool DeletedMul = false; 988 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 989 // If we have an mul, expand the mul operands onto the end of the operands 990 // list. 991 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 992 Ops.erase(Ops.begin()+Idx); 993 DeletedMul = true; 994 } 995 996 // If we deleted at least one mul, we added operands to the end of the list, 997 // and they are not necessarily sorted. Recurse to resort and resimplify 998 // any operands we just aquired. 999 if (DeletedMul) 1000 return getMulExpr(Ops); 1001 } 1002 1003 // If there are any add recurrences in the operands list, see if any other 1004 // added values are loop invariant. If so, we can fold them into the 1005 // recurrence. 1006 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1007 ++Idx; 1008 1009 // Scan over all recurrences, trying to fold loop invariants into them. 1010 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1011 // Scan all of the other operands to this mul and add them to the vector if 1012 // they are loop invariant w.r.t. the recurrence. 1013 std::vector<SCEVHandle> LIOps; 1014 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1015 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1016 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1017 LIOps.push_back(Ops[i]); 1018 Ops.erase(Ops.begin()+i); 1019 --i; --e; 1020 } 1021 1022 // If we found some loop invariants, fold them into the recurrence. 1023 if (!LIOps.empty()) { 1024 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step } 1025 std::vector<SCEVHandle> NewOps; 1026 NewOps.reserve(AddRec->getNumOperands()); 1027 if (LIOps.size() == 1) { 1028 SCEV *Scale = LIOps[0]; 1029 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1030 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1031 } else { 1032 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1033 std::vector<SCEVHandle> MulOps(LIOps); 1034 MulOps.push_back(AddRec->getOperand(i)); 1035 NewOps.push_back(getMulExpr(MulOps)); 1036 } 1037 } 1038 1039 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1040 1041 // If all of the other operands were loop invariant, we are done. 1042 if (Ops.size() == 1) return NewRec; 1043 1044 // Otherwise, multiply the folded AddRec by the non-liv parts. 1045 for (unsigned i = 0;; ++i) 1046 if (Ops[i] == AddRec) { 1047 Ops[i] = NewRec; 1048 break; 1049 } 1050 return getMulExpr(Ops); 1051 } 1052 1053 // Okay, if there weren't any loop invariants to be folded, check to see if 1054 // there are multiple AddRec's with the same loop induction variable being 1055 // multiplied together. If so, we can fold them. 1056 for (unsigned OtherIdx = Idx+1; 1057 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1058 if (OtherIdx != Idx) { 1059 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1060 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1061 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1062 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1063 SCEVHandle NewStart = getMulExpr(F->getStart(), 1064 G->getStart()); 1065 SCEVHandle B = F->getStepRecurrence(*this); 1066 SCEVHandle D = G->getStepRecurrence(*this); 1067 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1068 getMulExpr(G, B), 1069 getMulExpr(B, D)); 1070 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1071 F->getLoop()); 1072 if (Ops.size() == 2) return NewAddRec; 1073 1074 Ops.erase(Ops.begin()+Idx); 1075 Ops.erase(Ops.begin()+OtherIdx-1); 1076 Ops.push_back(NewAddRec); 1077 return getMulExpr(Ops); 1078 } 1079 } 1080 1081 // Otherwise couldn't fold anything into this recurrence. Move onto the 1082 // next one. 1083 } 1084 1085 // Okay, it looks like we really DO need an mul expr. Check to see if we 1086 // already have one, otherwise create a new one. 1087 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1088 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1089 SCEVOps)]; 1090 if (Result == 0) 1091 Result = new SCEVMulExpr(Ops); 1092 return Result; 1093} 1094 1095SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1096 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1097 if (RHSC->getValue()->equalsInt(1)) 1098 return LHS; // X udiv 1 --> x 1099 1100 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1101 Constant *LHSCV = LHSC->getValue(); 1102 Constant *RHSCV = RHSC->getValue(); 1103 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1104 } 1105 } 1106 1107 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1108 1109 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1110 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1111 return Result; 1112} 1113 1114 1115/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1116/// specified loop. Simplify the expression as much as possible. 1117SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1118 const SCEVHandle &Step, const Loop *L) { 1119 std::vector<SCEVHandle> Operands; 1120 Operands.push_back(Start); 1121 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1122 if (StepChrec->getLoop() == L) { 1123 Operands.insert(Operands.end(), StepChrec->op_begin(), 1124 StepChrec->op_end()); 1125 return getAddRecExpr(Operands, L); 1126 } 1127 1128 Operands.push_back(Step); 1129 return getAddRecExpr(Operands, L); 1130} 1131 1132/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1133/// specified loop. Simplify the expression as much as possible. 1134SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1135 const Loop *L) { 1136 if (Operands.size() == 1) return Operands[0]; 1137 1138 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back())) 1139 if (StepC->getValue()->isZero()) { 1140 Operands.pop_back(); 1141 return getAddRecExpr(Operands, L); // { X,+,0 } --> X 1142 } 1143 1144 SCEVAddRecExpr *&Result = 1145 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1146 Operands.end()))]; 1147 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1148 return Result; 1149} 1150 1151SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1152 const SCEVHandle &RHS) { 1153 std::vector<SCEVHandle> Ops; 1154 Ops.push_back(LHS); 1155 Ops.push_back(RHS); 1156 return getSMaxExpr(Ops); 1157} 1158 1159SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1160 assert(!Ops.empty() && "Cannot get empty smax!"); 1161 if (Ops.size() == 1) return Ops[0]; 1162 1163 // Sort by complexity, this groups all similar expression types together. 1164 GroupByComplexity(Ops); 1165 1166 // If there are any constants, fold them together. 1167 unsigned Idx = 0; 1168 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1169 ++Idx; 1170 assert(Idx < Ops.size()); 1171 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1172 // We found two constants, fold them together! 1173 Constant *Fold = ConstantInt::get( 1174 APIntOps::smax(LHSC->getValue()->getValue(), 1175 RHSC->getValue()->getValue())); 1176 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) { 1177 Ops[0] = getConstant(CI); 1178 Ops.erase(Ops.begin()+1); // Erase the folded element 1179 if (Ops.size() == 1) return Ops[0]; 1180 LHSC = cast<SCEVConstant>(Ops[0]); 1181 } else { 1182 // If we couldn't fold the expression, move to the next constant. Note 1183 // that this is impossible to happen in practice because we always 1184 // constant fold constant ints to constant ints. 1185 ++Idx; 1186 } 1187 } 1188 1189 // If we are left with a constant -inf, strip it off. 1190 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1191 Ops.erase(Ops.begin()); 1192 --Idx; 1193 } 1194 } 1195 1196 if (Ops.size() == 1) return Ops[0]; 1197 1198 // Find the first SMax 1199 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1200 ++Idx; 1201 1202 // Check to see if one of the operands is an SMax. If so, expand its operands 1203 // onto our operand list, and recurse to simplify. 1204 if (Idx < Ops.size()) { 1205 bool DeletedSMax = false; 1206 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1207 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1208 Ops.erase(Ops.begin()+Idx); 1209 DeletedSMax = true; 1210 } 1211 1212 if (DeletedSMax) 1213 return getSMaxExpr(Ops); 1214 } 1215 1216 // Okay, check to see if the same value occurs in the operand list twice. If 1217 // so, delete one. Since we sorted the list, these values are required to 1218 // be adjacent. 1219 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1220 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1221 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1222 --i; --e; 1223 } 1224 1225 if (Ops.size() == 1) return Ops[0]; 1226 1227 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1228 1229 // Okay, it looks like we really DO need an add expr. Check to see if we 1230 // already have one, otherwise create a new one. 1231 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1232 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1233 SCEVOps)]; 1234 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1235 return Result; 1236} 1237 1238SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1239 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1240 return getConstant(CI); 1241 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1242 if (Result == 0) Result = new SCEVUnknown(V); 1243 return Result; 1244} 1245 1246 1247//===----------------------------------------------------------------------===// 1248// ScalarEvolutionsImpl Definition and Implementation 1249//===----------------------------------------------------------------------===// 1250// 1251/// ScalarEvolutionsImpl - This class implements the main driver for the scalar 1252/// evolution code. 1253/// 1254namespace { 1255 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl { 1256 /// SE - A reference to the public ScalarEvolution object. 1257 ScalarEvolution &SE; 1258 1259 /// F - The function we are analyzing. 1260 /// 1261 Function &F; 1262 1263 /// LI - The loop information for the function we are currently analyzing. 1264 /// 1265 LoopInfo &LI; 1266 1267 /// UnknownValue - This SCEV is used to represent unknown trip counts and 1268 /// things. 1269 SCEVHandle UnknownValue; 1270 1271 /// Scalars - This is a cache of the scalars we have analyzed so far. 1272 /// 1273 std::map<Value*, SCEVHandle> Scalars; 1274 1275 /// IterationCounts - Cache the iteration count of the loops for this 1276 /// function as they are computed. 1277 std::map<const Loop*, SCEVHandle> IterationCounts; 1278 1279 /// ConstantEvolutionLoopExitValue - This map contains entries for all of 1280 /// the PHI instructions that we attempt to compute constant evolutions for. 1281 /// This allows us to avoid potentially expensive recomputation of these 1282 /// properties. An instruction maps to null if we are unable to compute its 1283 /// exit value. 1284 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue; 1285 1286 public: 1287 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li) 1288 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {} 1289 1290 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1291 /// expression and create a new one. 1292 SCEVHandle getSCEV(Value *V); 1293 1294 /// hasSCEV - Return true if the SCEV for this value has already been 1295 /// computed. 1296 bool hasSCEV(Value *V) const { 1297 return Scalars.count(V); 1298 } 1299 1300 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for 1301 /// the specified value. 1302 void setSCEV(Value *V, const SCEVHandle &H) { 1303 bool isNew = Scalars.insert(std::make_pair(V, H)).second; 1304 assert(isNew && "This entry already existed!"); 1305 } 1306 1307 1308 /// getSCEVAtScope - Compute the value of the specified expression within 1309 /// the indicated loop (which may be null to indicate in no loop). If the 1310 /// expression cannot be evaluated, return UnknownValue itself. 1311 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L); 1312 1313 1314 /// hasLoopInvariantIterationCount - Return true if the specified loop has 1315 /// an analyzable loop-invariant iteration count. 1316 bool hasLoopInvariantIterationCount(const Loop *L); 1317 1318 /// getIterationCount - If the specified loop has a predictable iteration 1319 /// count, return it. Note that it is not valid to call this method on a 1320 /// loop without a loop-invariant iteration count. 1321 SCEVHandle getIterationCount(const Loop *L); 1322 1323 /// deleteValueFromRecords - This method should be called by the 1324 /// client before it removes a value from the program, to make sure 1325 /// that no dangling references are left around. 1326 void deleteValueFromRecords(Value *V); 1327 1328 private: 1329 /// createSCEV - We know that there is no SCEV for the specified value. 1330 /// Analyze the expression. 1331 SCEVHandle createSCEV(Value *V); 1332 1333 /// createNodeForPHI - Provide the special handling we need to analyze PHI 1334 /// SCEVs. 1335 SCEVHandle createNodeForPHI(PHINode *PN); 1336 1337 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value 1338 /// for the specified instruction and replaces any references to the 1339 /// symbolic value SymName with the specified value. This is used during 1340 /// PHI resolution. 1341 void ReplaceSymbolicValueWithConcrete(Instruction *I, 1342 const SCEVHandle &SymName, 1343 const SCEVHandle &NewVal); 1344 1345 /// ComputeIterationCount - Compute the number of times the specified loop 1346 /// will iterate. 1347 SCEVHandle ComputeIterationCount(const Loop *L); 1348 1349 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1350 /// 'icmp op load X, cst', try to see if we can compute the trip count. 1351 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI, 1352 Constant *RHS, 1353 const Loop *L, 1354 ICmpInst::Predicate p); 1355 1356 /// ComputeIterationCountExhaustively - If the trip is known to execute a 1357 /// constant number of times (the condition evolves only from constants), 1358 /// try to evaluate a few iterations of the loop until we get the exit 1359 /// condition gets a value of ExitWhen (true or false). If we cannot 1360 /// evaluate the trip count of the loop, return UnknownValue. 1361 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond, 1362 bool ExitWhen); 1363 1364 /// HowFarToZero - Return the number of times a backedge comparing the 1365 /// specified value to zero will execute. If not computable, return 1366 /// UnknownValue. 1367 SCEVHandle HowFarToZero(SCEV *V, const Loop *L); 1368 1369 /// HowFarToNonZero - Return the number of times a backedge checking the 1370 /// specified value for nonzero will execute. If not computable, return 1371 /// UnknownValue. 1372 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L); 1373 1374 /// HowManyLessThans - Return the number of times a backedge containing the 1375 /// specified less-than comparison will execute. If not computable, return 1376 /// UnknownValue. isSigned specifies whether the less-than is signed. 1377 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, 1378 bool isSigned); 1379 1380 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 1381 /// in the header of its containing loop, we know the loop executes a 1382 /// constant number of times, and the PHI node is just a recurrence 1383 /// involving constants, fold it. 1384 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, 1385 const Loop *L); 1386 }; 1387} 1388 1389//===----------------------------------------------------------------------===// 1390// Basic SCEV Analysis and PHI Idiom Recognition Code 1391// 1392 1393/// deleteValueFromRecords - This method should be called by the 1394/// client before it removes an instruction from the program, to make sure 1395/// that no dangling references are left around. 1396void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) { 1397 SmallVector<Value *, 16> Worklist; 1398 1399 if (Scalars.erase(V)) { 1400 if (PHINode *PN = dyn_cast<PHINode>(V)) 1401 ConstantEvolutionLoopExitValue.erase(PN); 1402 Worklist.push_back(V); 1403 } 1404 1405 while (!Worklist.empty()) { 1406 Value *VV = Worklist.back(); 1407 Worklist.pop_back(); 1408 1409 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1410 UI != UE; ++UI) { 1411 Instruction *Inst = cast<Instruction>(*UI); 1412 if (Scalars.erase(Inst)) { 1413 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1414 ConstantEvolutionLoopExitValue.erase(PN); 1415 Worklist.push_back(Inst); 1416 } 1417 } 1418 } 1419} 1420 1421 1422/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1423/// expression and create a new one. 1424SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) { 1425 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!"); 1426 1427 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1428 if (I != Scalars.end()) return I->second; 1429 SCEVHandle S = createSCEV(V); 1430 Scalars.insert(std::make_pair(V, S)); 1431 return S; 1432} 1433 1434/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1435/// the specified instruction and replaces any references to the symbolic value 1436/// SymName with the specified value. This is used during PHI resolution. 1437void ScalarEvolutionsImpl:: 1438ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1439 const SCEVHandle &NewVal) { 1440 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1441 if (SI == Scalars.end()) return; 1442 1443 SCEVHandle NV = 1444 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE); 1445 if (NV == SI->second) return; // No change. 1446 1447 SI->second = NV; // Update the scalars map! 1448 1449 // Any instruction values that use this instruction might also need to be 1450 // updated! 1451 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1452 UI != E; ++UI) 1453 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1454} 1455 1456/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1457/// a loop header, making it a potential recurrence, or it doesn't. 1458/// 1459SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) { 1460 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1461 if (const Loop *L = LI.getLoopFor(PN->getParent())) 1462 if (L->getHeader() == PN->getParent()) { 1463 // If it lives in the loop header, it has two incoming values, one 1464 // from outside the loop, and one from inside. 1465 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1466 unsigned BackEdge = IncomingEdge^1; 1467 1468 // While we are analyzing this PHI node, handle its value symbolically. 1469 SCEVHandle SymbolicName = SE.getUnknown(PN); 1470 assert(Scalars.find(PN) == Scalars.end() && 1471 "PHI node already processed?"); 1472 Scalars.insert(std::make_pair(PN, SymbolicName)); 1473 1474 // Using this symbolic name for the PHI, analyze the value coming around 1475 // the back-edge. 1476 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1477 1478 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1479 // has a special value for the first iteration of the loop. 1480 1481 // If the value coming around the backedge is an add with the symbolic 1482 // value we just inserted, then we found a simple induction variable! 1483 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1484 // If there is a single occurrence of the symbolic value, replace it 1485 // with a recurrence. 1486 unsigned FoundIndex = Add->getNumOperands(); 1487 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1488 if (Add->getOperand(i) == SymbolicName) 1489 if (FoundIndex == e) { 1490 FoundIndex = i; 1491 break; 1492 } 1493 1494 if (FoundIndex != Add->getNumOperands()) { 1495 // Create an add with everything but the specified operand. 1496 std::vector<SCEVHandle> Ops; 1497 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1498 if (i != FoundIndex) 1499 Ops.push_back(Add->getOperand(i)); 1500 SCEVHandle Accum = SE.getAddExpr(Ops); 1501 1502 // This is not a valid addrec if the step amount is varying each 1503 // loop iteration, but is not itself an addrec in this loop. 1504 if (Accum->isLoopInvariant(L) || 1505 (isa<SCEVAddRecExpr>(Accum) && 1506 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1507 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1508 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L); 1509 1510 // Okay, for the entire analysis of this edge we assumed the PHI 1511 // to be symbolic. We now need to go back and update all of the 1512 // entries for the scalars that use the PHI (except for the PHI 1513 // itself) to use the new analyzed value instead of the "symbolic" 1514 // value. 1515 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1516 return PHISCEV; 1517 } 1518 } 1519 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1520 // Otherwise, this could be a loop like this: 1521 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1522 // In this case, j = {1,+,1} and BEValue is j. 1523 // Because the other in-value of i (0) fits the evolution of BEValue 1524 // i really is an addrec evolution. 1525 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1526 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1527 1528 // If StartVal = j.start - j.stride, we can use StartVal as the 1529 // initial step of the addrec evolution. 1530 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0), 1531 AddRec->getOperand(1))) { 1532 SCEVHandle PHISCEV = 1533 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1534 1535 // Okay, for the entire analysis of this edge we assumed the PHI 1536 // to be symbolic. We now need to go back and update all of the 1537 // entries for the scalars that use the PHI (except for the PHI 1538 // itself) to use the new analyzed value instead of the "symbolic" 1539 // value. 1540 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1541 return PHISCEV; 1542 } 1543 } 1544 } 1545 1546 return SymbolicName; 1547 } 1548 1549 // If it's not a loop phi, we can't handle it yet. 1550 return SE.getUnknown(PN); 1551} 1552 1553/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1554/// guaranteed to end in (at every loop iteration). It is, at the same time, 1555/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1556/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1557static uint32_t GetMinTrailingZeros(SCEVHandle S) { 1558 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1559 return C->getValue()->getValue().countTrailingZeros(); 1560 1561 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1562 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth()); 1563 1564 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1565 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1566 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1567 } 1568 1569 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1570 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 1571 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes; 1572 } 1573 1574 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1575 // The result is the min of all operands results. 1576 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1577 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1578 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1579 return MinOpRes; 1580 } 1581 1582 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1583 // The result is the sum of all operands results. 1584 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 1585 uint32_t BitWidth = M->getBitWidth(); 1586 for (unsigned i = 1, e = M->getNumOperands(); 1587 SumOpRes != BitWidth && i != e; ++i) 1588 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 1589 BitWidth); 1590 return SumOpRes; 1591 } 1592 1593 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1594 // The result is the min of all operands results. 1595 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 1596 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1597 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 1598 return MinOpRes; 1599 } 1600 1601 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1602 // The result is the min of all operands results. 1603 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 1604 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1605 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 1606 return MinOpRes; 1607 } 1608 1609 // SCEVUDivExpr, SCEVUnknown 1610 return 0; 1611} 1612 1613/// createSCEV - We know that there is no SCEV for the specified value. 1614/// Analyze the expression. 1615/// 1616SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) { 1617 if (!isa<IntegerType>(V->getType())) 1618 return SE.getUnknown(V); 1619 1620 if (Instruction *I = dyn_cast<Instruction>(V)) { 1621 switch (I->getOpcode()) { 1622 case Instruction::Add: 1623 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1624 getSCEV(I->getOperand(1))); 1625 case Instruction::Mul: 1626 return SE.getMulExpr(getSCEV(I->getOperand(0)), 1627 getSCEV(I->getOperand(1))); 1628 case Instruction::UDiv: 1629 return SE.getUDivExpr(getSCEV(I->getOperand(0)), 1630 getSCEV(I->getOperand(1))); 1631 case Instruction::Sub: 1632 return SE.getMinusSCEV(getSCEV(I->getOperand(0)), 1633 getSCEV(I->getOperand(1))); 1634 case Instruction::Or: 1635 // If the RHS of the Or is a constant, we may have something like: 1636 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1637 // optimizations will transparently handle this case. 1638 // 1639 // In order for this transformation to be safe, the LHS must be of the 1640 // form X*(2^n) and the Or constant must be less than 2^n. 1641 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1642 SCEVHandle LHS = getSCEV(I->getOperand(0)); 1643 const APInt &CIVal = CI->getValue(); 1644 if (GetMinTrailingZeros(LHS) >= 1645 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1646 return SE.getAddExpr(LHS, getSCEV(I->getOperand(1))); 1647 } 1648 break; 1649 case Instruction::Xor: 1650 // If the RHS of the xor is a signbit, then this is just an add. 1651 // Instcombine turns add of signbit into xor as a strength reduction step. 1652 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) { 1653 if (CI->getValue().isSignBit()) 1654 return SE.getAddExpr(getSCEV(I->getOperand(0)), 1655 getSCEV(I->getOperand(1))); 1656 } 1657 break; 1658 1659 case Instruction::Shl: 1660 // Turn shift left of a constant amount into a multiply. 1661 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) { 1662 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1663 Constant *X = ConstantInt::get( 1664 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1665 return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X)); 1666 } 1667 break; 1668 1669 case Instruction::Trunc: 1670 return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType()); 1671 1672 case Instruction::ZExt: 1673 return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1674 1675 case Instruction::SExt: 1676 return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType()); 1677 1678 case Instruction::BitCast: 1679 // BitCasts are no-op casts so we just eliminate the cast. 1680 if (I->getType()->isInteger() && 1681 I->getOperand(0)->getType()->isInteger()) 1682 return getSCEV(I->getOperand(0)); 1683 break; 1684 1685 case Instruction::PHI: 1686 return createNodeForPHI(cast<PHINode>(I)); 1687 1688 case Instruction::Select: 1689 // This could be an SCEVSMax that was lowered earlier. Try to recover it. 1690 if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) { 1691 Value *LHS = ICI->getOperand(0); 1692 Value *RHS = ICI->getOperand(1); 1693 switch (ICI->getPredicate()) { 1694 case ICmpInst::ICMP_SLT: 1695 case ICmpInst::ICMP_SLE: 1696 std::swap(LHS, RHS); 1697 // fall through 1698 case ICmpInst::ICMP_SGT: 1699 case ICmpInst::ICMP_SGE: 1700 if (LHS == I->getOperand(1) && RHS == I->getOperand(2)) 1701 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1702 default: 1703 break; 1704 } 1705 } 1706 1707 default: // We cannot analyze this expression. 1708 break; 1709 } 1710 } 1711 1712 return SE.getUnknown(V); 1713} 1714 1715 1716 1717//===----------------------------------------------------------------------===// 1718// Iteration Count Computation Code 1719// 1720 1721/// getIterationCount - If the specified loop has a predictable iteration 1722/// count, return it. Note that it is not valid to call this method on a 1723/// loop without a loop-invariant iteration count. 1724SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) { 1725 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L); 1726 if (I == IterationCounts.end()) { 1727 SCEVHandle ItCount = ComputeIterationCount(L); 1728 I = IterationCounts.insert(std::make_pair(L, ItCount)).first; 1729 if (ItCount != UnknownValue) { 1730 assert(ItCount->isLoopInvariant(L) && 1731 "Computed trip count isn't loop invariant for loop!"); 1732 ++NumTripCountsComputed; 1733 } else if (isa<PHINode>(L->getHeader()->begin())) { 1734 // Only count loops that have phi nodes as not being computable. 1735 ++NumTripCountsNotComputed; 1736 } 1737 } 1738 return I->second; 1739} 1740 1741/// ComputeIterationCount - Compute the number of times the specified loop 1742/// will iterate. 1743SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) { 1744 // If the loop has a non-one exit block count, we can't analyze it. 1745 SmallVector<BasicBlock*, 8> ExitBlocks; 1746 L->getExitBlocks(ExitBlocks); 1747 if (ExitBlocks.size() != 1) return UnknownValue; 1748 1749 // Okay, there is one exit block. Try to find the condition that causes the 1750 // loop to be exited. 1751 BasicBlock *ExitBlock = ExitBlocks[0]; 1752 1753 BasicBlock *ExitingBlock = 0; 1754 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1755 PI != E; ++PI) 1756 if (L->contains(*PI)) { 1757 if (ExitingBlock == 0) 1758 ExitingBlock = *PI; 1759 else 1760 return UnknownValue; // More than one block exiting! 1761 } 1762 assert(ExitingBlock && "No exits from loop, something is broken!"); 1763 1764 // Okay, we've computed the exiting block. See what condition causes us to 1765 // exit. 1766 // 1767 // FIXME: we should be able to handle switch instructions (with a single exit) 1768 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 1769 if (ExitBr == 0) return UnknownValue; 1770 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 1771 1772 // At this point, we know we have a conditional branch that determines whether 1773 // the loop is exited. However, we don't know if the branch is executed each 1774 // time through the loop. If not, then the execution count of the branch will 1775 // not be equal to the trip count of the loop. 1776 // 1777 // Currently we check for this by checking to see if the Exit branch goes to 1778 // the loop header. If so, we know it will always execute the same number of 1779 // times as the loop. We also handle the case where the exit block *is* the 1780 // loop header. This is common for un-rotated loops. More extensive analysis 1781 // could be done to handle more cases here. 1782 if (ExitBr->getSuccessor(0) != L->getHeader() && 1783 ExitBr->getSuccessor(1) != L->getHeader() && 1784 ExitBr->getParent() != L->getHeader()) 1785 return UnknownValue; 1786 1787 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 1788 1789 // If its not an integer comparison then compute it the hard way. 1790 // Note that ICmpInst deals with pointer comparisons too so we must check 1791 // the type of the operand. 1792 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 1793 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(), 1794 ExitBr->getSuccessor(0) == ExitBlock); 1795 1796 // If the condition was exit on true, convert the condition to exit on false 1797 ICmpInst::Predicate Cond; 1798 if (ExitBr->getSuccessor(1) == ExitBlock) 1799 Cond = ExitCond->getPredicate(); 1800 else 1801 Cond = ExitCond->getInversePredicate(); 1802 1803 // Handle common loops like: for (X = "string"; *X; ++X) 1804 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 1805 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 1806 SCEVHandle ItCnt = 1807 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond); 1808 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 1809 } 1810 1811 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 1812 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 1813 1814 // Try to evaluate any dependencies out of the loop. 1815 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 1816 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 1817 Tmp = getSCEVAtScope(RHS, L); 1818 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 1819 1820 // At this point, we would like to compute how many iterations of the 1821 // loop the predicate will return true for these inputs. 1822 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 1823 // If there is a loop-invariant, force it into the RHS. 1824 std::swap(LHS, RHS); 1825 Cond = ICmpInst::getSwappedPredicate(Cond); 1826 } 1827 1828 // FIXME: think about handling pointer comparisons! i.e.: 1829 // while (P != P+100) ++P; 1830 1831 // If we have a comparison of a chrec against a constant, try to use value 1832 // ranges to answer this query. 1833 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 1834 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 1835 if (AddRec->getLoop() == L) { 1836 // Form the comparison range using the constant of the correct type so 1837 // that the ConstantRange class knows to do a signed or unsigned 1838 // comparison. 1839 ConstantInt *CompVal = RHSC->getValue(); 1840 const Type *RealTy = ExitCond->getOperand(0)->getType(); 1841 CompVal = dyn_cast<ConstantInt>( 1842 ConstantExpr::getBitCast(CompVal, RealTy)); 1843 if (CompVal) { 1844 // Form the constant range. 1845 ConstantRange CompRange( 1846 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 1847 1848 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE); 1849 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 1850 } 1851 } 1852 1853 switch (Cond) { 1854 case ICmpInst::ICMP_NE: { // while (X != Y) 1855 // Convert to: while (X-Y != 0) 1856 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L); 1857 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1858 break; 1859 } 1860 case ICmpInst::ICMP_EQ: { 1861 // Convert to: while (X-Y == 0) // while (X == Y) 1862 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L); 1863 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1864 break; 1865 } 1866 case ICmpInst::ICMP_SLT: { 1867 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 1868 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1869 break; 1870 } 1871 case ICmpInst::ICMP_SGT: { 1872 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1873 SE.getNegativeSCEV(RHS), L, true); 1874 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1875 break; 1876 } 1877 case ICmpInst::ICMP_ULT: { 1878 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 1879 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1880 break; 1881 } 1882 case ICmpInst::ICMP_UGT: { 1883 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS), 1884 SE.getNegativeSCEV(RHS), L, false); 1885 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 1886 break; 1887 } 1888 default: 1889#if 0 1890 cerr << "ComputeIterationCount "; 1891 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 1892 cerr << "[unsigned] "; 1893 cerr << *LHS << " " 1894 << Instruction::getOpcodeName(Instruction::ICmp) 1895 << " " << *RHS << "\n"; 1896#endif 1897 break; 1898 } 1899 return ComputeIterationCountExhaustively(L, ExitCond, 1900 ExitBr->getSuccessor(0) == ExitBlock); 1901} 1902 1903static ConstantInt * 1904EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 1905 ScalarEvolution &SE) { 1906 SCEVHandle InVal = SE.getConstant(C); 1907 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 1908 assert(isa<SCEVConstant>(Val) && 1909 "Evaluation of SCEV at constant didn't fold correctly?"); 1910 return cast<SCEVConstant>(Val)->getValue(); 1911} 1912 1913/// GetAddressedElementFromGlobal - Given a global variable with an initializer 1914/// and a GEP expression (missing the pointer index) indexing into it, return 1915/// the addressed element of the initializer or null if the index expression is 1916/// invalid. 1917static Constant * 1918GetAddressedElementFromGlobal(GlobalVariable *GV, 1919 const std::vector<ConstantInt*> &Indices) { 1920 Constant *Init = GV->getInitializer(); 1921 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 1922 uint64_t Idx = Indices[i]->getZExtValue(); 1923 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 1924 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 1925 Init = cast<Constant>(CS->getOperand(Idx)); 1926 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 1927 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 1928 Init = cast<Constant>(CA->getOperand(Idx)); 1929 } else if (isa<ConstantAggregateZero>(Init)) { 1930 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 1931 assert(Idx < STy->getNumElements() && "Bad struct index!"); 1932 Init = Constant::getNullValue(STy->getElementType(Idx)); 1933 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 1934 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 1935 Init = Constant::getNullValue(ATy->getElementType()); 1936 } else { 1937 assert(0 && "Unknown constant aggregate type!"); 1938 } 1939 return 0; 1940 } else { 1941 return 0; // Unknown initializer type 1942 } 1943 } 1944 return Init; 1945} 1946 1947/// ComputeLoadConstantCompareIterationCount - Given an exit condition of 1948/// 'icmp op load X, cst', try to se if we can compute the trip count. 1949SCEVHandle ScalarEvolutionsImpl:: 1950ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS, 1951 const Loop *L, 1952 ICmpInst::Predicate predicate) { 1953 if (LI->isVolatile()) return UnknownValue; 1954 1955 // Check to see if the loaded pointer is a getelementptr of a global. 1956 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 1957 if (!GEP) return UnknownValue; 1958 1959 // Make sure that it is really a constant global we are gepping, with an 1960 // initializer, and make sure the first IDX is really 0. 1961 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 1962 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 1963 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 1964 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 1965 return UnknownValue; 1966 1967 // Okay, we allow one non-constant index into the GEP instruction. 1968 Value *VarIdx = 0; 1969 std::vector<ConstantInt*> Indexes; 1970 unsigned VarIdxNum = 0; 1971 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 1972 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 1973 Indexes.push_back(CI); 1974 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 1975 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 1976 VarIdx = GEP->getOperand(i); 1977 VarIdxNum = i-2; 1978 Indexes.push_back(0); 1979 } 1980 1981 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 1982 // Check to see if X is a loop variant variable value now. 1983 SCEVHandle Idx = getSCEV(VarIdx); 1984 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 1985 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 1986 1987 // We can only recognize very limited forms of loop index expressions, in 1988 // particular, only affine AddRec's like {C1,+,C2}. 1989 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 1990 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 1991 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 1992 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 1993 return UnknownValue; 1994 1995 unsigned MaxSteps = MaxBruteForceIterations; 1996 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 1997 ConstantInt *ItCst = 1998 ConstantInt::get(IdxExpr->getType(), IterationNum); 1999 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE); 2000 2001 // Form the GEP offset. 2002 Indexes[VarIdxNum] = Val; 2003 2004 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2005 if (Result == 0) break; // Cannot compute! 2006 2007 // Evaluate the condition for this iteration. 2008 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2009 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2010 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2011#if 0 2012 cerr << "\n***\n*** Computed loop count " << *ItCst 2013 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2014 << "***\n"; 2015#endif 2016 ++NumArrayLenItCounts; 2017 return SE.getConstant(ItCst); // Found terminating iteration! 2018 } 2019 } 2020 return UnknownValue; 2021} 2022 2023 2024/// CanConstantFold - Return true if we can constant fold an instruction of the 2025/// specified type, assuming that all operands were constants. 2026static bool CanConstantFold(const Instruction *I) { 2027 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2028 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2029 return true; 2030 2031 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2032 if (const Function *F = CI->getCalledFunction()) 2033 return canConstantFoldCallTo(F); 2034 return false; 2035} 2036 2037/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2038/// in the loop that V is derived from. We allow arbitrary operations along the 2039/// way, but the operands of an operation must either be constants or a value 2040/// derived from a constant PHI. If this expression does not fit with these 2041/// constraints, return null. 2042static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2043 // If this is not an instruction, or if this is an instruction outside of the 2044 // loop, it can't be derived from a loop PHI. 2045 Instruction *I = dyn_cast<Instruction>(V); 2046 if (I == 0 || !L->contains(I->getParent())) return 0; 2047 2048 if (PHINode *PN = dyn_cast<PHINode>(I)) 2049 if (L->getHeader() == I->getParent()) 2050 return PN; 2051 else 2052 // We don't currently keep track of the control flow needed to evaluate 2053 // PHIs, so we cannot handle PHIs inside of loops. 2054 return 0; 2055 2056 // If we won't be able to constant fold this expression even if the operands 2057 // are constants, return early. 2058 if (!CanConstantFold(I)) return 0; 2059 2060 // Otherwise, we can evaluate this instruction if all of its operands are 2061 // constant or derived from a PHI node themselves. 2062 PHINode *PHI = 0; 2063 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2064 if (!(isa<Constant>(I->getOperand(Op)) || 2065 isa<GlobalValue>(I->getOperand(Op)))) { 2066 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2067 if (P == 0) return 0; // Not evolving from PHI 2068 if (PHI == 0) 2069 PHI = P; 2070 else if (PHI != P) 2071 return 0; // Evolving from multiple different PHIs. 2072 } 2073 2074 // This is a expression evolving from a constant PHI! 2075 return PHI; 2076} 2077 2078/// EvaluateExpression - Given an expression that passes the 2079/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2080/// in the loop has the value PHIVal. If we can't fold this expression for some 2081/// reason, return null. 2082static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2083 if (isa<PHINode>(V)) return PHIVal; 2084 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) 2085 return GV; 2086 if (Constant *C = dyn_cast<Constant>(V)) return C; 2087 Instruction *I = cast<Instruction>(V); 2088 2089 std::vector<Constant*> Operands; 2090 Operands.resize(I->getNumOperands()); 2091 2092 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2093 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2094 if (Operands[i] == 0) return 0; 2095 } 2096 2097 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2098 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2099 &Operands[0], Operands.size()); 2100 else 2101 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2102 &Operands[0], Operands.size()); 2103} 2104 2105/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2106/// in the header of its containing loop, we know the loop executes a 2107/// constant number of times, and the PHI node is just a recurrence 2108/// involving constants, fold it. 2109Constant *ScalarEvolutionsImpl:: 2110getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){ 2111 std::map<PHINode*, Constant*>::iterator I = 2112 ConstantEvolutionLoopExitValue.find(PN); 2113 if (I != ConstantEvolutionLoopExitValue.end()) 2114 return I->second; 2115 2116 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations))) 2117 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2118 2119 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2120 2121 // Since the loop is canonicalized, the PHI node must have two entries. One 2122 // entry must be a constant (coming in from outside of the loop), and the 2123 // second must be derived from the same PHI. 2124 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2125 Constant *StartCST = 2126 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2127 if (StartCST == 0) 2128 return RetVal = 0; // Must be a constant. 2129 2130 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2131 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2132 if (PN2 != PN) 2133 return RetVal = 0; // Not derived from same PHI. 2134 2135 // Execute the loop symbolically to determine the exit value. 2136 if (Its.getActiveBits() >= 32) 2137 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2138 2139 unsigned NumIterations = Its.getZExtValue(); // must be in range 2140 unsigned IterationNum = 0; 2141 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2142 if (IterationNum == NumIterations) 2143 return RetVal = PHIVal; // Got exit value! 2144 2145 // Compute the value of the PHI node for the next iteration. 2146 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2147 if (NextPHI == PHIVal) 2148 return RetVal = NextPHI; // Stopped evolving! 2149 if (NextPHI == 0) 2150 return 0; // Couldn't evaluate! 2151 PHIVal = NextPHI; 2152 } 2153} 2154 2155/// ComputeIterationCountExhaustively - If the trip is known to execute a 2156/// constant number of times (the condition evolves only from constants), 2157/// try to evaluate a few iterations of the loop until we get the exit 2158/// condition gets a value of ExitWhen (true or false). If we cannot 2159/// evaluate the trip count of the loop, return UnknownValue. 2160SCEVHandle ScalarEvolutionsImpl:: 2161ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2162 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2163 if (PN == 0) return UnknownValue; 2164 2165 // Since the loop is canonicalized, the PHI node must have two entries. One 2166 // entry must be a constant (coming in from outside of the loop), and the 2167 // second must be derived from the same PHI. 2168 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2169 Constant *StartCST = 2170 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2171 if (StartCST == 0) return UnknownValue; // Must be a constant. 2172 2173 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2174 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2175 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2176 2177 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2178 // the loop symbolically to determine when the condition gets a value of 2179 // "ExitWhen". 2180 unsigned IterationNum = 0; 2181 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2182 for (Constant *PHIVal = StartCST; 2183 IterationNum != MaxIterations; ++IterationNum) { 2184 ConstantInt *CondVal = 2185 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2186 2187 // Couldn't symbolically evaluate. 2188 if (!CondVal) return UnknownValue; 2189 2190 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2191 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2192 ++NumBruteForceTripCountsComputed; 2193 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2194 } 2195 2196 // Compute the value of the PHI node for the next iteration. 2197 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2198 if (NextPHI == 0 || NextPHI == PHIVal) 2199 return UnknownValue; // Couldn't evaluate or not making progress... 2200 PHIVal = NextPHI; 2201 } 2202 2203 // Too many iterations were needed to evaluate. 2204 return UnknownValue; 2205} 2206 2207/// getSCEVAtScope - Compute the value of the specified expression within the 2208/// indicated loop (which may be null to indicate in no loop). If the 2209/// expression cannot be evaluated, return UnknownValue. 2210SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) { 2211 // FIXME: this should be turned into a virtual method on SCEV! 2212 2213 if (isa<SCEVConstant>(V)) return V; 2214 2215 // If this instruction is evolves from a constant-evolving PHI, compute the 2216 // exit value from the loop without using SCEVs. 2217 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2218 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2219 const Loop *LI = this->LI[I->getParent()]; 2220 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2221 if (PHINode *PN = dyn_cast<PHINode>(I)) 2222 if (PN->getParent() == LI->getHeader()) { 2223 // Okay, there is no closed form solution for the PHI node. Check 2224 // to see if the loop that contains it has a known iteration count. 2225 // If so, we may be able to force computation of the exit value. 2226 SCEVHandle IterationCount = getIterationCount(LI); 2227 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) { 2228 // Okay, we know how many times the containing loop executes. If 2229 // this is a constant evolving PHI node, get the final value at 2230 // the specified iteration number. 2231 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2232 ICC->getValue()->getValue(), 2233 LI); 2234 if (RV) return SE.getUnknown(RV); 2235 } 2236 } 2237 2238 // Okay, this is an expression that we cannot symbolically evaluate 2239 // into a SCEV. Check to see if it's possible to symbolically evaluate 2240 // the arguments into constants, and if so, try to constant propagate the 2241 // result. This is particularly useful for computing loop exit values. 2242 if (CanConstantFold(I)) { 2243 std::vector<Constant*> Operands; 2244 Operands.reserve(I->getNumOperands()); 2245 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2246 Value *Op = I->getOperand(i); 2247 if (Constant *C = dyn_cast<Constant>(Op)) { 2248 Operands.push_back(C); 2249 } else { 2250 // If any of the operands is non-constant and if they are 2251 // non-integer, don't even try to analyze them with scev techniques. 2252 if (!isa<IntegerType>(Op->getType())) 2253 return V; 2254 2255 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2256 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2257 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2258 Op->getType(), 2259 false)); 2260 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2261 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2262 Operands.push_back(ConstantExpr::getIntegerCast(C, 2263 Op->getType(), 2264 false)); 2265 else 2266 return V; 2267 } else { 2268 return V; 2269 } 2270 } 2271 } 2272 2273 Constant *C; 2274 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2275 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2276 &Operands[0], Operands.size()); 2277 else 2278 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2279 &Operands[0], Operands.size()); 2280 return SE.getUnknown(C); 2281 } 2282 } 2283 2284 // This is some other type of SCEVUnknown, just return it. 2285 return V; 2286 } 2287 2288 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2289 // Avoid performing the look-up in the common case where the specified 2290 // expression has no loop-variant portions. 2291 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2292 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2293 if (OpAtScope != Comm->getOperand(i)) { 2294 if (OpAtScope == UnknownValue) return UnknownValue; 2295 // Okay, at least one of these operands is loop variant but might be 2296 // foldable. Build a new instance of the folded commutative expression. 2297 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2298 NewOps.push_back(OpAtScope); 2299 2300 for (++i; i != e; ++i) { 2301 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2302 if (OpAtScope == UnknownValue) return UnknownValue; 2303 NewOps.push_back(OpAtScope); 2304 } 2305 if (isa<SCEVAddExpr>(Comm)) 2306 return SE.getAddExpr(NewOps); 2307 if (isa<SCEVMulExpr>(Comm)) 2308 return SE.getMulExpr(NewOps); 2309 if (isa<SCEVSMaxExpr>(Comm)) 2310 return SE.getSMaxExpr(NewOps); 2311 assert(0 && "Unknown commutative SCEV type!"); 2312 } 2313 } 2314 // If we got here, all operands are loop invariant. 2315 return Comm; 2316 } 2317 2318 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2319 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2320 if (LHS == UnknownValue) return LHS; 2321 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2322 if (RHS == UnknownValue) return RHS; 2323 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2324 return Div; // must be loop invariant 2325 return SE.getUDivExpr(LHS, RHS); 2326 } 2327 2328 // If this is a loop recurrence for a loop that does not contain L, then we 2329 // are dealing with the final value computed by the loop. 2330 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2331 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2332 // To evaluate this recurrence, we need to know how many times the AddRec 2333 // loop iterates. Compute this now. 2334 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop()); 2335 if (IterationCount == UnknownValue) return UnknownValue; 2336 IterationCount = getTruncateOrZeroExtend(IterationCount, 2337 AddRec->getType(), SE); 2338 2339 // If the value is affine, simplify the expression evaluation to just 2340 // Start + Step*IterationCount. 2341 if (AddRec->isAffine()) 2342 return SE.getAddExpr(AddRec->getStart(), 2343 SE.getMulExpr(IterationCount, 2344 AddRec->getOperand(1))); 2345 2346 // Otherwise, evaluate it the hard way. 2347 return AddRec->evaluateAtIteration(IterationCount, SE); 2348 } 2349 return UnknownValue; 2350 } 2351 2352 //assert(0 && "Unknown SCEV type!"); 2353 return UnknownValue; 2354} 2355 2356 2357/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2358/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2359/// might be the same) or two SCEVCouldNotCompute objects. 2360/// 2361static std::pair<SCEVHandle,SCEVHandle> 2362SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2363 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2364 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2365 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2366 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2367 2368 // We currently can only solve this if the coefficients are constants. 2369 if (!LC || !MC || !NC) { 2370 SCEV *CNC = new SCEVCouldNotCompute(); 2371 return std::make_pair(CNC, CNC); 2372 } 2373 2374 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2375 const APInt &L = LC->getValue()->getValue(); 2376 const APInt &M = MC->getValue()->getValue(); 2377 const APInt &N = NC->getValue()->getValue(); 2378 APInt Two(BitWidth, 2); 2379 APInt Four(BitWidth, 4); 2380 2381 { 2382 using namespace APIntOps; 2383 const APInt& C = L; 2384 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2385 // The B coefficient is M-N/2 2386 APInt B(M); 2387 B -= sdiv(N,Two); 2388 2389 // The A coefficient is N/2 2390 APInt A(N.sdiv(Two)); 2391 2392 // Compute the B^2-4ac term. 2393 APInt SqrtTerm(B); 2394 SqrtTerm *= B; 2395 SqrtTerm -= Four * (A * C); 2396 2397 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2398 // integer value or else APInt::sqrt() will assert. 2399 APInt SqrtVal(SqrtTerm.sqrt()); 2400 2401 // Compute the two solutions for the quadratic formula. 2402 // The divisions must be performed as signed divisions. 2403 APInt NegB(-B); 2404 APInt TwoA( A << 1 ); 2405 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2406 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2407 2408 return std::make_pair(SE.getConstant(Solution1), 2409 SE.getConstant(Solution2)); 2410 } // end APIntOps namespace 2411} 2412 2413/// HowFarToZero - Return the number of times a backedge comparing the specified 2414/// value to zero will execute. If not computable, return UnknownValue 2415SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) { 2416 // If the value is a constant 2417 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2418 // If the value is already zero, the branch will execute zero times. 2419 if (C->getValue()->isZero()) return C; 2420 return UnknownValue; // Otherwise it will loop infinitely. 2421 } 2422 2423 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2424 if (!AddRec || AddRec->getLoop() != L) 2425 return UnknownValue; 2426 2427 if (AddRec->isAffine()) { 2428 // If this is an affine expression the execution count of this branch is 2429 // equal to: 2430 // 2431 // (0 - Start/Step) iff Start % Step == 0 2432 // 2433 // Get the initial value for the loop. 2434 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2435 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2436 SCEVHandle Step = AddRec->getOperand(1); 2437 2438 Step = getSCEVAtScope(Step, L->getParentLoop()); 2439 2440 // Figure out if Start % Step == 0. 2441 // FIXME: We should add DivExpr and RemExpr operations to our AST. 2442 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2443 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0 2444 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start 2445 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0 2446 return Start; // 0 - Start/-1 == Start 2447 2448 // Check to see if Start is divisible by SC with no remainder. 2449 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) { 2450 ConstantInt *StartCC = StartC->getValue(); 2451 Constant *StartNegC = ConstantExpr::getNeg(StartCC); 2452 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue()); 2453 if (Rem->isNullValue()) { 2454 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue()); 2455 return SE.getUnknown(Result); 2456 } 2457 } 2458 } 2459 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2460 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2461 // the quadratic equation to solve it. 2462 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE); 2463 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2464 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2465 if (R1) { 2466#if 0 2467 cerr << "HFTZ: " << *V << " - sol#1: " << *R1 2468 << " sol#2: " << *R2 << "\n"; 2469#endif 2470 // Pick the smallest positive root value. 2471 if (ConstantInt *CB = 2472 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2473 R1->getValue(), R2->getValue()))) { 2474 if (CB->getZExtValue() == false) 2475 std::swap(R1, R2); // R1 is the minimum root now. 2476 2477 // We can only use this value if the chrec ends up with an exact zero 2478 // value at this index. When solving for "X*X != 5", for example, we 2479 // should not accept a root of 2. 2480 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE); 2481 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val)) 2482 if (EvalVal->getValue()->isZero()) 2483 return R1; // We found a quadratic root! 2484 } 2485 } 2486 } 2487 2488 return UnknownValue; 2489} 2490 2491/// HowFarToNonZero - Return the number of times a backedge checking the 2492/// specified value for nonzero will execute. If not computable, return 2493/// UnknownValue 2494SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) { 2495 // Loops that look like: while (X == 0) are very strange indeed. We don't 2496 // handle them yet except for the trivial case. This could be expanded in the 2497 // future as needed. 2498 2499 // If the value is a constant, check to see if it is known to be non-zero 2500 // already. If so, the backedge will execute zero times. 2501 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2502 Constant *Zero = Constant::getNullValue(C->getValue()->getType()); 2503 Constant *NonZero = 2504 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero); 2505 if (NonZero == ConstantInt::getTrue()) 2506 return getSCEV(Zero); 2507 return UnknownValue; // Otherwise it will loop infinitely. 2508 } 2509 2510 // We could implement others, but I really doubt anyone writes loops like 2511 // this, and if they did, they would already be constant folded. 2512 return UnknownValue; 2513} 2514 2515/// HowManyLessThans - Return the number of times a backedge containing the 2516/// specified less-than comparison will execute. If not computable, return 2517/// UnknownValue. 2518SCEVHandle ScalarEvolutionsImpl:: 2519HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2520 // Only handle: "ADDREC < LoopInvariant". 2521 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2522 2523 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2524 if (!AddRec || AddRec->getLoop() != L) 2525 return UnknownValue; 2526 2527 if (AddRec->isAffine()) { 2528 // The number of iterations for "{n,+,1} < m", is m-n. However, we don't 2529 // know that m is >= n on input to the loop. If it is, the condition 2530 // returns true zero times. To handle both cases, we return SMAX(0, m-n). 2531 2532 // FORNOW: We only support unit strides. 2533 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType()); 2534 if (AddRec->getOperand(1) != One) 2535 return UnknownValue; 2536 2537 SCEVHandle Iters = SE.getMinusSCEV(RHS, AddRec->getOperand(0)); 2538 2539 if (isSigned) 2540 return SE.getSMaxExpr(SE.getIntegerSCEV(0, RHS->getType()), Iters); 2541 else 2542 return Iters; 2543 } 2544 2545 return UnknownValue; 2546} 2547 2548/// getNumIterationsInRange - Return the number of iterations of this loop that 2549/// produce values in the specified constant range. Another way of looking at 2550/// this is that it returns the first iteration number where the value is not in 2551/// the condition, thus computing the exit count. If the iteration count can't 2552/// be computed, an instance of SCEVCouldNotCompute is returned. 2553SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2554 ScalarEvolution &SE) const { 2555 if (Range.isFullSet()) // Infinite loop. 2556 return new SCEVCouldNotCompute(); 2557 2558 // If the start is a non-zero constant, shift the range to simplify things. 2559 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2560 if (!SC->getValue()->isZero()) { 2561 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2562 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2563 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2564 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2565 return ShiftedAddRec->getNumIterationsInRange( 2566 Range.subtract(SC->getValue()->getValue()), SE); 2567 // This is strange and shouldn't happen. 2568 return new SCEVCouldNotCompute(); 2569 } 2570 2571 // The only time we can solve this is when we have all constant indices. 2572 // Otherwise, we cannot determine the overflow conditions. 2573 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 2574 if (!isa<SCEVConstant>(getOperand(i))) 2575 return new SCEVCouldNotCompute(); 2576 2577 2578 // Okay at this point we know that all elements of the chrec are constants and 2579 // that the start element is zero. 2580 2581 // First check to see if the range contains zero. If not, the first 2582 // iteration exits. 2583 if (!Range.contains(APInt(getBitWidth(),0))) 2584 return SE.getConstant(ConstantInt::get(getType(),0)); 2585 2586 if (isAffine()) { 2587 // If this is an affine expression then we have this situation: 2588 // Solve {0,+,A} in Range === Ax in Range 2589 2590 // We know that zero is in the range. If A is positive then we know that 2591 // the upper value of the range must be the first possible exit value. 2592 // If A is negative then the lower of the range is the last possible loop 2593 // value. Also note that we already checked for a full range. 2594 APInt One(getBitWidth(),1); 2595 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 2596 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 2597 2598 // The exit value should be (End+A)/A. 2599 APInt ExitVal = (End + A).udiv(A); 2600 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 2601 2602 // Evaluate at the exit value. If we really did fall out of the valid 2603 // range, then we computed our trip count, otherwise wrap around or other 2604 // things must have happened. 2605 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 2606 if (Range.contains(Val->getValue())) 2607 return new SCEVCouldNotCompute(); // Something strange happened 2608 2609 // Ensure that the previous value is in the range. This is a sanity check. 2610 assert(Range.contains( 2611 EvaluateConstantChrecAtConstant(this, 2612 ConstantInt::get(ExitVal - One), SE)->getValue()) && 2613 "Linear scev computation is off in a bad way!"); 2614 return SE.getConstant(ExitValue); 2615 } else if (isQuadratic()) { 2616 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 2617 // quadratic equation to solve it. To do this, we must frame our problem in 2618 // terms of figuring out when zero is crossed, instead of when 2619 // Range.getUpper() is crossed. 2620 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 2621 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 2622 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 2623 2624 // Next, solve the constructed addrec 2625 std::pair<SCEVHandle,SCEVHandle> Roots = 2626 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 2627 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2628 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2629 if (R1) { 2630 // Pick the smallest positive root value. 2631 if (ConstantInt *CB = 2632 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2633 R1->getValue(), R2->getValue()))) { 2634 if (CB->getZExtValue() == false) 2635 std::swap(R1, R2); // R1 is the minimum root now. 2636 2637 // Make sure the root is not off by one. The returned iteration should 2638 // not be in the range, but the previous one should be. When solving 2639 // for "X*X < 5", for example, we should not return a root of 2. 2640 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 2641 R1->getValue(), 2642 SE); 2643 if (Range.contains(R1Val->getValue())) { 2644 // The next iteration must be out of the range... 2645 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 2646 2647 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2648 if (!Range.contains(R1Val->getValue())) 2649 return SE.getConstant(NextVal); 2650 return new SCEVCouldNotCompute(); // Something strange happened 2651 } 2652 2653 // If R1 was not in the range, then it is a good return value. Make 2654 // sure that R1-1 WAS in the range though, just in case. 2655 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 2656 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 2657 if (Range.contains(R1Val->getValue())) 2658 return R1; 2659 return new SCEVCouldNotCompute(); // Something strange happened 2660 } 2661 } 2662 } 2663 2664 // Fallback, if this is a general polynomial, figure out the progression 2665 // through brute force: evaluate until we find an iteration that fails the 2666 // test. This is likely to be slow, but getting an accurate trip count is 2667 // incredibly important, we will be able to simplify the exit test a lot, and 2668 // we are almost guaranteed to get a trip count in this case. 2669 ConstantInt *TestVal = ConstantInt::get(getType(), 0); 2670 ConstantInt *EndVal = TestVal; // Stop when we wrap around. 2671 do { 2672 ++NumBruteForceEvaluations; 2673 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE); 2674 if (!isa<SCEVConstant>(Val)) // This shouldn't happen. 2675 return new SCEVCouldNotCompute(); 2676 2677 // Check to see if we found the value! 2678 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue())) 2679 return SE.getConstant(TestVal); 2680 2681 // Increment to test the next index. 2682 TestVal = ConstantInt::get(TestVal->getValue()+1); 2683 } while (TestVal != EndVal); 2684 2685 return new SCEVCouldNotCompute(); 2686} 2687 2688 2689 2690//===----------------------------------------------------------------------===// 2691// ScalarEvolution Class Implementation 2692//===----------------------------------------------------------------------===// 2693 2694bool ScalarEvolution::runOnFunction(Function &F) { 2695 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>()); 2696 return false; 2697} 2698 2699void ScalarEvolution::releaseMemory() { 2700 delete (ScalarEvolutionsImpl*)Impl; 2701 Impl = 0; 2702} 2703 2704void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 2705 AU.setPreservesAll(); 2706 AU.addRequiredTransitive<LoopInfo>(); 2707} 2708 2709SCEVHandle ScalarEvolution::getSCEV(Value *V) const { 2710 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V); 2711} 2712 2713/// hasSCEV - Return true if the SCEV for this value has already been 2714/// computed. 2715bool ScalarEvolution::hasSCEV(Value *V) const { 2716 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V); 2717} 2718 2719 2720/// setSCEV - Insert the specified SCEV into the map of current SCEVs for 2721/// the specified value. 2722void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) { 2723 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H); 2724} 2725 2726 2727SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const { 2728 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L); 2729} 2730 2731bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const { 2732 return !isa<SCEVCouldNotCompute>(getIterationCount(L)); 2733} 2734 2735SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const { 2736 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L); 2737} 2738 2739void ScalarEvolution::deleteValueFromRecords(Value *V) const { 2740 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V); 2741} 2742 2743static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE, 2744 const Loop *L) { 2745 // Print all inner loops first 2746 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 2747 PrintLoopInfo(OS, SE, *I); 2748 2749 OS << "Loop " << L->getHeader()->getName() << ": "; 2750 2751 SmallVector<BasicBlock*, 8> ExitBlocks; 2752 L->getExitBlocks(ExitBlocks); 2753 if (ExitBlocks.size() != 1) 2754 OS << "<multiple exits> "; 2755 2756 if (SE->hasLoopInvariantIterationCount(L)) { 2757 OS << *SE->getIterationCount(L) << " iterations! "; 2758 } else { 2759 OS << "Unpredictable iteration count. "; 2760 } 2761 2762 OS << "\n"; 2763} 2764 2765void ScalarEvolution::print(std::ostream &OS, const Module* ) const { 2766 Function &F = ((ScalarEvolutionsImpl*)Impl)->F; 2767 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI; 2768 2769 OS << "Classifying expressions for: " << F.getName() << "\n"; 2770 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 2771 if (I->getType()->isInteger()) { 2772 OS << *I; 2773 OS << " --> "; 2774 SCEVHandle SV = getSCEV(&*I); 2775 SV->print(OS); 2776 OS << "\t\t"; 2777 2778 if ((*I).getType()->isInteger()) { 2779 ConstantRange Bounds = SV->getValueRange(); 2780 if (!Bounds.isFullSet()) 2781 OS << "Bounds: " << Bounds << " "; 2782 } 2783 2784 if (const Loop *L = LI.getLoopFor((*I).getParent())) { 2785 OS << "Exits: "; 2786 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop()); 2787 if (isa<SCEVCouldNotCompute>(ExitValue)) { 2788 OS << "<<Unknown>>"; 2789 } else { 2790 OS << *ExitValue; 2791 } 2792 } 2793 2794 2795 OS << "\n"; 2796 } 2797 2798 OS << "Determining loop execution counts for: " << F.getName() << "\n"; 2799 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I) 2800 PrintLoopInfo(OS, this, *I); 2801} 2802