ScalarEvolution.cpp revision 5cd28fad15b3bab840dac5ecdc2bdfde4f74816a
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/Dominators.h" 70#include "llvm/Analysis/LoopInfo.h" 71#include "llvm/Assembly/Writer.h" 72#include "llvm/Target/TargetData.h" 73#include "llvm/Transforms/Scalar.h" 74#include "llvm/Support/CFG.h" 75#include "llvm/Support/CommandLine.h" 76#include "llvm/Support/Compiler.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/GetElementPtrTypeIterator.h" 79#include "llvm/Support/InstIterator.h" 80#include "llvm/Support/ManagedStatic.h" 81#include "llvm/Support/MathExtras.h" 82#include "llvm/Support/raw_ostream.h" 83#include "llvm/ADT/Statistic.h" 84#include "llvm/ADT/STLExtras.h" 85#include <ostream> 86#include <algorithm> 87#include <cmath> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant derived loop"), 103 cl::init(100)); 104 105static RegisterPass<ScalarEvolution> 106R("scalar-evolution", "Scalar Evolution Analysis", false, true); 107char ScalarEvolution::ID = 0; 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116SCEV::~SCEV() {} 117void SCEV::dump() const { 118 print(errs()); 119 errs() << '\n'; 120} 121 122void SCEV::print(std::ostream &o) const { 123 raw_os_ostream OS(o); 124 print(OS); 125} 126 127bool SCEV::isZero() const { 128 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 129 return SC->getValue()->isZero(); 130 return false; 131} 132 133 134SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 135SCEVCouldNotCompute::~SCEVCouldNotCompute() {} 136 137bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 139 return false; 140} 141 142const Type *SCEVCouldNotCompute::getType() const { 143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 144 return 0; 145} 146 147bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 149 return false; 150} 151 152SCEVHandle SCEVCouldNotCompute:: 153replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 154 const SCEVHandle &Conc, 155 ScalarEvolution &SE) const { 156 return this; 157} 158 159void SCEVCouldNotCompute::print(raw_ostream &OS) const { 160 OS << "***COULDNOTCOMPUTE***"; 161} 162 163bool SCEVCouldNotCompute::classof(const SCEV *S) { 164 return S->getSCEVType() == scCouldNotCompute; 165} 166 167 168// SCEVConstants - Only allow the creation of one SCEVConstant for any 169// particular value. Don't use a SCEVHandle here, or else the object will 170// never be deleted! 171static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 172 173 174SCEVConstant::~SCEVConstant() { 175 SCEVConstants->erase(V); 176} 177 178SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 179 SCEVConstant *&R = (*SCEVConstants)[V]; 180 if (R == 0) R = new SCEVConstant(V); 181 return R; 182} 183 184SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 185 return getConstant(ConstantInt::get(Val)); 186} 187 188const Type *SCEVConstant::getType() const { return V->getType(); } 189 190void SCEVConstant::print(raw_ostream &OS) const { 191 WriteAsOperand(OS, V, false); 192} 193 194SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy, 195 const SCEVHandle &op, const Type *ty) 196 : SCEV(SCEVTy), Op(op), Ty(ty) {} 197 198SCEVCastExpr::~SCEVCastExpr() {} 199 200bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 201 return Op->dominates(BB, DT); 202} 203 204// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 205// particular input. Don't use a SCEVHandle here, or else the object will 206// never be deleted! 207static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 208 SCEVTruncateExpr*> > SCEVTruncates; 209 210SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 211 : SCEVCastExpr(scTruncate, op, ty) { 212 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 213 (Ty->isInteger() || isa<PointerType>(Ty)) && 214 "Cannot truncate non-integer value!"); 215} 216 217SCEVTruncateExpr::~SCEVTruncateExpr() { 218 SCEVTruncates->erase(std::make_pair(Op, Ty)); 219} 220 221void SCEVTruncateExpr::print(raw_ostream &OS) const { 222 OS << "(truncate " << *Op << " to " << *Ty << ")"; 223} 224 225// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 226// particular input. Don't use a SCEVHandle here, or else the object will never 227// be deleted! 228static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 229 SCEVZeroExtendExpr*> > SCEVZeroExtends; 230 231SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 232 : SCEVCastExpr(scZeroExtend, op, ty) { 233 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 234 (Ty->isInteger() || isa<PointerType>(Ty)) && 235 "Cannot zero extend non-integer value!"); 236} 237 238SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 239 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 240} 241 242void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 243 OS << "(zeroextend " << *Op << " to " << *Ty << ")"; 244} 245 246// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 247// particular input. Don't use a SCEVHandle here, or else the object will never 248// be deleted! 249static ManagedStatic<std::map<std::pair<SCEV*, const Type*>, 250 SCEVSignExtendExpr*> > SCEVSignExtends; 251 252SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 253 : SCEVCastExpr(scSignExtend, op, ty) { 254 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 255 (Ty->isInteger() || isa<PointerType>(Ty)) && 256 "Cannot sign extend non-integer value!"); 257} 258 259SCEVSignExtendExpr::~SCEVSignExtendExpr() { 260 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 261} 262 263void SCEVSignExtendExpr::print(raw_ostream &OS) const { 264 OS << "(signextend " << *Op << " to " << *Ty << ")"; 265} 266 267// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 268// particular input. Don't use a SCEVHandle here, or else the object will never 269// be deleted! 270static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 271 SCEVCommutativeExpr*> > SCEVCommExprs; 272 273SCEVCommutativeExpr::~SCEVCommutativeExpr() { 274 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 275 std::vector<SCEV*>(Operands.begin(), 276 Operands.end()))); 277} 278 279void SCEVCommutativeExpr::print(raw_ostream &OS) const { 280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 281 const char *OpStr = getOperationStr(); 282 OS << "(" << *Operands[0]; 283 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 284 OS << OpStr << *Operands[i]; 285 OS << ")"; 286} 287 288SCEVHandle SCEVCommutativeExpr:: 289replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 290 const SCEVHandle &Conc, 291 ScalarEvolution &SE) const { 292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 293 SCEVHandle H = 294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 295 if (H != getOperand(i)) { 296 std::vector<SCEVHandle> NewOps; 297 NewOps.reserve(getNumOperands()); 298 for (unsigned j = 0; j != i; ++j) 299 NewOps.push_back(getOperand(j)); 300 NewOps.push_back(H); 301 for (++i; i != e; ++i) 302 NewOps.push_back(getOperand(i)-> 303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 304 305 if (isa<SCEVAddExpr>(this)) 306 return SE.getAddExpr(NewOps); 307 else if (isa<SCEVMulExpr>(this)) 308 return SE.getMulExpr(NewOps); 309 else if (isa<SCEVSMaxExpr>(this)) 310 return SE.getSMaxExpr(NewOps); 311 else if (isa<SCEVUMaxExpr>(this)) 312 return SE.getUMaxExpr(NewOps); 313 else 314 assert(0 && "Unknown commutative expr!"); 315 } 316 } 317 return this; 318} 319 320bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 322 if (!getOperand(i)->dominates(BB, DT)) 323 return false; 324 } 325 return true; 326} 327 328 329// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 330// input. Don't use a SCEVHandle here, or else the object will never be 331// deleted! 332static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 333 SCEVUDivExpr*> > SCEVUDivs; 334 335SCEVUDivExpr::~SCEVUDivExpr() { 336 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 337} 338 339bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 341} 342 343void SCEVUDivExpr::print(raw_ostream &OS) const { 344 OS << "(" << *LHS << " /u " << *RHS << ")"; 345} 346 347const Type *SCEVUDivExpr::getType() const { 348 return LHS->getType(); 349} 350 351// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 352// particular input. Don't use a SCEVHandle here, or else the object will never 353// be deleted! 354static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 355 SCEVAddRecExpr*> > SCEVAddRecExprs; 356 357SCEVAddRecExpr::~SCEVAddRecExpr() { 358 SCEVAddRecExprs->erase(std::make_pair(L, 359 std::vector<SCEV*>(Operands.begin(), 360 Operands.end()))); 361} 362 363bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 364 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 365 if (!getOperand(i)->dominates(BB, DT)) 366 return false; 367 } 368 return true; 369} 370 371 372SCEVHandle SCEVAddRecExpr:: 373replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 374 const SCEVHandle &Conc, 375 ScalarEvolution &SE) const { 376 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 377 SCEVHandle H = 378 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 379 if (H != getOperand(i)) { 380 std::vector<SCEVHandle> NewOps; 381 NewOps.reserve(getNumOperands()); 382 for (unsigned j = 0; j != i; ++j) 383 NewOps.push_back(getOperand(j)); 384 NewOps.push_back(H); 385 for (++i; i != e; ++i) 386 NewOps.push_back(getOperand(i)-> 387 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 388 389 return SE.getAddRecExpr(NewOps, L); 390 } 391 } 392 return this; 393} 394 395 396bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 397 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 398 // contain L and if the start is invariant. 399 return !QueryLoop->contains(L->getHeader()) && 400 getOperand(0)->isLoopInvariant(QueryLoop); 401} 402 403 404void SCEVAddRecExpr::print(raw_ostream &OS) const { 405 OS << "{" << *Operands[0]; 406 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 407 OS << ",+," << *Operands[i]; 408 OS << "}<" << L->getHeader()->getName() + ">"; 409} 410 411// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 412// value. Don't use a SCEVHandle here, or else the object will never be 413// deleted! 414static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 415 416SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 417 418bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 419 // All non-instruction values are loop invariant. All instructions are loop 420 // invariant if they are not contained in the specified loop. 421 if (Instruction *I = dyn_cast<Instruction>(V)) 422 return !L->contains(I->getParent()); 423 return true; 424} 425 426bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 427 if (Instruction *I = dyn_cast<Instruction>(getValue())) 428 return DT->dominates(I->getParent(), BB); 429 return true; 430} 431 432const Type *SCEVUnknown::getType() const { 433 return V->getType(); 434} 435 436void SCEVUnknown::print(raw_ostream &OS) const { 437 if (isa<PointerType>(V->getType())) 438 OS << "(ptrtoint " << *V->getType() << " "; 439 WriteAsOperand(OS, V, false); 440 if (isa<PointerType>(V->getType())) 441 OS << " to iPTR)"; 442} 443 444//===----------------------------------------------------------------------===// 445// SCEV Utilities 446//===----------------------------------------------------------------------===// 447 448namespace { 449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 450 /// than the complexity of the RHS. This comparator is used to canonicalize 451 /// expressions. 452 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 453 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 454 return LHS->getSCEVType() < RHS->getSCEVType(); 455 } 456 }; 457} 458 459/// GroupByComplexity - Given a list of SCEV objects, order them by their 460/// complexity, and group objects of the same complexity together by value. 461/// When this routine is finished, we know that any duplicates in the vector are 462/// consecutive and that complexity is monotonically increasing. 463/// 464/// Note that we go take special precautions to ensure that we get determinstic 465/// results from this routine. In other words, we don't want the results of 466/// this to depend on where the addresses of various SCEV objects happened to 467/// land in memory. 468/// 469static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 470 if (Ops.size() < 2) return; // Noop 471 if (Ops.size() == 2) { 472 // This is the common case, which also happens to be trivially simple. 473 // Special case it. 474 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 475 std::swap(Ops[0], Ops[1]); 476 return; 477 } 478 479 // Do the rough sort by complexity. 480 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 481 482 // Now that we are sorted by complexity, group elements of the same 483 // complexity. Note that this is, at worst, N^2, but the vector is likely to 484 // be extremely short in practice. Note that we take this approach because we 485 // do not want to depend on the addresses of the objects we are grouping. 486 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 487 SCEV *S = Ops[i]; 488 unsigned Complexity = S->getSCEVType(); 489 490 // If there are any objects of the same complexity and same value as this 491 // one, group them. 492 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 493 if (Ops[j] == S) { // Found a duplicate. 494 // Move it to immediately after i'th element. 495 std::swap(Ops[i+1], Ops[j]); 496 ++i; // no need to rescan it. 497 if (i == e-2) return; // Done! 498 } 499 } 500 } 501} 502 503 504 505//===----------------------------------------------------------------------===// 506// Simple SCEV method implementations 507//===----------------------------------------------------------------------===// 508 509/// BinomialCoefficient - Compute BC(It, K). The result has width W. 510// Assume, K > 0. 511static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 512 ScalarEvolution &SE, 513 const Type* ResultTy) { 514 // Handle the simplest case efficiently. 515 if (K == 1) 516 return SE.getTruncateOrZeroExtend(It, ResultTy); 517 518 // We are using the following formula for BC(It, K): 519 // 520 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 521 // 522 // Suppose, W is the bitwidth of the return value. We must be prepared for 523 // overflow. Hence, we must assure that the result of our computation is 524 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 525 // safe in modular arithmetic. 526 // 527 // However, this code doesn't use exactly that formula; the formula it uses 528 // is something like the following, where T is the number of factors of 2 in 529 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 530 // exponentiation: 531 // 532 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 533 // 534 // This formula is trivially equivalent to the previous formula. However, 535 // this formula can be implemented much more efficiently. The trick is that 536 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 537 // arithmetic. To do exact division in modular arithmetic, all we have 538 // to do is multiply by the inverse. Therefore, this step can be done at 539 // width W. 540 // 541 // The next issue is how to safely do the division by 2^T. The way this 542 // is done is by doing the multiplication step at a width of at least W + T 543 // bits. This way, the bottom W+T bits of the product are accurate. Then, 544 // when we perform the division by 2^T (which is equivalent to a right shift 545 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 546 // truncated out after the division by 2^T. 547 // 548 // In comparison to just directly using the first formula, this technique 549 // is much more efficient; using the first formula requires W * K bits, 550 // but this formula less than W + K bits. Also, the first formula requires 551 // a division step, whereas this formula only requires multiplies and shifts. 552 // 553 // It doesn't matter whether the subtraction step is done in the calculation 554 // width or the input iteration count's width; if the subtraction overflows, 555 // the result must be zero anyway. We prefer here to do it in the width of 556 // the induction variable because it helps a lot for certain cases; CodeGen 557 // isn't smart enough to ignore the overflow, which leads to much less 558 // efficient code if the width of the subtraction is wider than the native 559 // register width. 560 // 561 // (It's possible to not widen at all by pulling out factors of 2 before 562 // the multiplication; for example, K=2 can be calculated as 563 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 564 // extra arithmetic, so it's not an obvious win, and it gets 565 // much more complicated for K > 3.) 566 567 // Protection from insane SCEVs; this bound is conservative, 568 // but it probably doesn't matter. 569 if (K > 1000) 570 return SE.getCouldNotCompute(); 571 572 unsigned W = SE.getTypeSizeInBits(ResultTy); 573 574 // Calculate K! / 2^T and T; we divide out the factors of two before 575 // multiplying for calculating K! / 2^T to avoid overflow. 576 // Other overflow doesn't matter because we only care about the bottom 577 // W bits of the result. 578 APInt OddFactorial(W, 1); 579 unsigned T = 1; 580 for (unsigned i = 3; i <= K; ++i) { 581 APInt Mult(W, i); 582 unsigned TwoFactors = Mult.countTrailingZeros(); 583 T += TwoFactors; 584 Mult = Mult.lshr(TwoFactors); 585 OddFactorial *= Mult; 586 } 587 588 // We need at least W + T bits for the multiplication step 589 unsigned CalculationBits = W + T; 590 591 // Calcuate 2^T, at width T+W. 592 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 593 594 // Calculate the multiplicative inverse of K! / 2^T; 595 // this multiplication factor will perform the exact division by 596 // K! / 2^T. 597 APInt Mod = APInt::getSignedMinValue(W+1); 598 APInt MultiplyFactor = OddFactorial.zext(W+1); 599 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 600 MultiplyFactor = MultiplyFactor.trunc(W); 601 602 // Calculate the product, at width T+W 603 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 604 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 605 for (unsigned i = 1; i != K; ++i) { 606 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 607 Dividend = SE.getMulExpr(Dividend, 608 SE.getTruncateOrZeroExtend(S, CalculationTy)); 609 } 610 611 // Divide by 2^T 612 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 613 614 // Truncate the result, and divide by K! / 2^T. 615 616 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 617 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 618} 619 620/// evaluateAtIteration - Return the value of this chain of recurrences at 621/// the specified iteration number. We can evaluate this recurrence by 622/// multiplying each element in the chain by the binomial coefficient 623/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 624/// 625/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 626/// 627/// where BC(It, k) stands for binomial coefficient. 628/// 629SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 630 ScalarEvolution &SE) const { 631 SCEVHandle Result = getStart(); 632 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 633 // The computation is correct in the face of overflow provided that the 634 // multiplication is performed _after_ the evaluation of the binomial 635 // coefficient. 636 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType()); 637 if (isa<SCEVCouldNotCompute>(Coeff)) 638 return Coeff; 639 640 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 641 } 642 return Result; 643} 644 645//===----------------------------------------------------------------------===// 646// SCEV Expression folder implementations 647//===----------------------------------------------------------------------===// 648 649SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 650 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 651 "This is not a truncating conversion!"); 652 653 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 654 return getUnknown( 655 ConstantExpr::getTrunc(SC->getValue(), Ty)); 656 657 // trunc(trunc(x)) --> trunc(x) 658 if (SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 659 return getTruncateExpr(ST->getOperand(), Ty); 660 661 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 662 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 663 return getTruncateOrSignExtend(SS->getOperand(), Ty); 664 665 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 666 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 667 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 668 669 // If the input value is a chrec scev made out of constants, truncate 670 // all of the constants. 671 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 672 std::vector<SCEVHandle> Operands; 673 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 674 // FIXME: This should allow truncation of other expression types! 675 if (isa<SCEVConstant>(AddRec->getOperand(i))) 676 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 677 else 678 break; 679 if (Operands.size() == AddRec->getNumOperands()) 680 return getAddRecExpr(Operands, AddRec->getLoop()); 681 } 682 683 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 684 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 685 return Result; 686} 687 688SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 689 const Type *Ty) { 690 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 691 "This is not an extending conversion!"); 692 693 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 694 const Type *IntTy = getEffectiveSCEVType(Ty); 695 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 696 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 697 return getUnknown(C); 698 } 699 700 // zext(zext(x)) --> zext(x) 701 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 702 return getZeroExtendExpr(SZ->getOperand(), Ty); 703 704 // FIXME: If the input value is a chrec scev, and we can prove that the value 705 // did not overflow the old, smaller, value, we can zero extend all of the 706 // operands (often constants). This would allow analysis of something like 707 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 708 709 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 710 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 711 return Result; 712} 713 714SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 715 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 716 "This is not an extending conversion!"); 717 718 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 719 const Type *IntTy = getEffectiveSCEVType(Ty); 720 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 721 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 722 return getUnknown(C); 723 } 724 725 // sext(sext(x)) --> sext(x) 726 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 727 return getSignExtendExpr(SS->getOperand(), Ty); 728 729 // FIXME: If the input value is a chrec scev, and we can prove that the value 730 // did not overflow the old, smaller, value, we can sign extend all of the 731 // operands (often constants). This would allow analysis of something like 732 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 733 734 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 735 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 736 return Result; 737} 738 739// get - Get a canonical add expression, or something simpler if possible. 740SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 741 assert(!Ops.empty() && "Cannot get empty add!"); 742 if (Ops.size() == 1) return Ops[0]; 743 744 // Sort by complexity, this groups all similar expression types together. 745 GroupByComplexity(Ops); 746 747 // If there are any constants, fold them together. 748 unsigned Idx = 0; 749 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 750 ++Idx; 751 assert(Idx < Ops.size()); 752 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 753 // We found two constants, fold them together! 754 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 755 RHSC->getValue()->getValue()); 756 Ops[0] = getConstant(Fold); 757 Ops.erase(Ops.begin()+1); // Erase the folded element 758 if (Ops.size() == 1) return Ops[0]; 759 LHSC = cast<SCEVConstant>(Ops[0]); 760 } 761 762 // If we are left with a constant zero being added, strip it off. 763 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 764 Ops.erase(Ops.begin()); 765 --Idx; 766 } 767 } 768 769 if (Ops.size() == 1) return Ops[0]; 770 771 // Okay, check to see if the same value occurs in the operand list twice. If 772 // so, merge them together into an multiply expression. Since we sorted the 773 // list, these values are required to be adjacent. 774 const Type *Ty = Ops[0]->getType(); 775 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 776 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 777 // Found a match, merge the two values into a multiply, and add any 778 // remaining values to the result. 779 SCEVHandle Two = getIntegerSCEV(2, Ty); 780 SCEVHandle Mul = getMulExpr(Ops[i], Two); 781 if (Ops.size() == 2) 782 return Mul; 783 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 784 Ops.push_back(Mul); 785 return getAddExpr(Ops); 786 } 787 788 // Now we know the first non-constant operand. Skip past any cast SCEVs. 789 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 790 ++Idx; 791 792 // If there are add operands they would be next. 793 if (Idx < Ops.size()) { 794 bool DeletedAdd = false; 795 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 796 // If we have an add, expand the add operands onto the end of the operands 797 // list. 798 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 799 Ops.erase(Ops.begin()+Idx); 800 DeletedAdd = true; 801 } 802 803 // If we deleted at least one add, we added operands to the end of the list, 804 // and they are not necessarily sorted. Recurse to resort and resimplify 805 // any operands we just aquired. 806 if (DeletedAdd) 807 return getAddExpr(Ops); 808 } 809 810 // Skip over the add expression until we get to a multiply. 811 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 812 ++Idx; 813 814 // If we are adding something to a multiply expression, make sure the 815 // something is not already an operand of the multiply. If so, merge it into 816 // the multiply. 817 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 818 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 819 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 820 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 821 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 822 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 823 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 824 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 825 if (Mul->getNumOperands() != 2) { 826 // If the multiply has more than two operands, we must get the 827 // Y*Z term. 828 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 829 MulOps.erase(MulOps.begin()+MulOp); 830 InnerMul = getMulExpr(MulOps); 831 } 832 SCEVHandle One = getIntegerSCEV(1, Ty); 833 SCEVHandle AddOne = getAddExpr(InnerMul, One); 834 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 835 if (Ops.size() == 2) return OuterMul; 836 if (AddOp < Idx) { 837 Ops.erase(Ops.begin()+AddOp); 838 Ops.erase(Ops.begin()+Idx-1); 839 } else { 840 Ops.erase(Ops.begin()+Idx); 841 Ops.erase(Ops.begin()+AddOp-1); 842 } 843 Ops.push_back(OuterMul); 844 return getAddExpr(Ops); 845 } 846 847 // Check this multiply against other multiplies being added together. 848 for (unsigned OtherMulIdx = Idx+1; 849 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 850 ++OtherMulIdx) { 851 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 852 // If MulOp occurs in OtherMul, we can fold the two multiplies 853 // together. 854 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 855 OMulOp != e; ++OMulOp) 856 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 857 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 858 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 859 if (Mul->getNumOperands() != 2) { 860 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 861 MulOps.erase(MulOps.begin()+MulOp); 862 InnerMul1 = getMulExpr(MulOps); 863 } 864 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 865 if (OtherMul->getNumOperands() != 2) { 866 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 867 OtherMul->op_end()); 868 MulOps.erase(MulOps.begin()+OMulOp); 869 InnerMul2 = getMulExpr(MulOps); 870 } 871 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 872 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 873 if (Ops.size() == 2) return OuterMul; 874 Ops.erase(Ops.begin()+Idx); 875 Ops.erase(Ops.begin()+OtherMulIdx-1); 876 Ops.push_back(OuterMul); 877 return getAddExpr(Ops); 878 } 879 } 880 } 881 } 882 883 // If there are any add recurrences in the operands list, see if any other 884 // added values are loop invariant. If so, we can fold them into the 885 // recurrence. 886 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 887 ++Idx; 888 889 // Scan over all recurrences, trying to fold loop invariants into them. 890 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 891 // Scan all of the other operands to this add and add them to the vector if 892 // they are loop invariant w.r.t. the recurrence. 893 std::vector<SCEVHandle> LIOps; 894 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 895 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 896 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 897 LIOps.push_back(Ops[i]); 898 Ops.erase(Ops.begin()+i); 899 --i; --e; 900 } 901 902 // If we found some loop invariants, fold them into the recurrence. 903 if (!LIOps.empty()) { 904 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 905 LIOps.push_back(AddRec->getStart()); 906 907 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 908 AddRecOps[0] = getAddExpr(LIOps); 909 910 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 911 // If all of the other operands were loop invariant, we are done. 912 if (Ops.size() == 1) return NewRec; 913 914 // Otherwise, add the folded AddRec by the non-liv parts. 915 for (unsigned i = 0;; ++i) 916 if (Ops[i] == AddRec) { 917 Ops[i] = NewRec; 918 break; 919 } 920 return getAddExpr(Ops); 921 } 922 923 // Okay, if there weren't any loop invariants to be folded, check to see if 924 // there are multiple AddRec's with the same loop induction variable being 925 // added together. If so, we can fold them. 926 for (unsigned OtherIdx = Idx+1; 927 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 928 if (OtherIdx != Idx) { 929 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 930 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 931 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 932 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 933 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 934 if (i >= NewOps.size()) { 935 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 936 OtherAddRec->op_end()); 937 break; 938 } 939 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 940 } 941 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 942 943 if (Ops.size() == 2) return NewAddRec; 944 945 Ops.erase(Ops.begin()+Idx); 946 Ops.erase(Ops.begin()+OtherIdx-1); 947 Ops.push_back(NewAddRec); 948 return getAddExpr(Ops); 949 } 950 } 951 952 // Otherwise couldn't fold anything into this recurrence. Move onto the 953 // next one. 954 } 955 956 // Okay, it looks like we really DO need an add expr. Check to see if we 957 // already have one, otherwise create a new one. 958 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 959 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 960 SCEVOps)]; 961 if (Result == 0) Result = new SCEVAddExpr(Ops); 962 return Result; 963} 964 965 966SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 967 assert(!Ops.empty() && "Cannot get empty mul!"); 968 969 // Sort by complexity, this groups all similar expression types together. 970 GroupByComplexity(Ops); 971 972 // If there are any constants, fold them together. 973 unsigned Idx = 0; 974 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 975 976 // C1*(C2+V) -> C1*C2 + C1*V 977 if (Ops.size() == 2) 978 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 979 if (Add->getNumOperands() == 2 && 980 isa<SCEVConstant>(Add->getOperand(0))) 981 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 982 getMulExpr(LHSC, Add->getOperand(1))); 983 984 985 ++Idx; 986 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 987 // We found two constants, fold them together! 988 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 989 RHSC->getValue()->getValue()); 990 Ops[0] = getConstant(Fold); 991 Ops.erase(Ops.begin()+1); // Erase the folded element 992 if (Ops.size() == 1) return Ops[0]; 993 LHSC = cast<SCEVConstant>(Ops[0]); 994 } 995 996 // If we are left with a constant one being multiplied, strip it off. 997 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 998 Ops.erase(Ops.begin()); 999 --Idx; 1000 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1001 // If we have a multiply of zero, it will always be zero. 1002 return Ops[0]; 1003 } 1004 } 1005 1006 // Skip over the add expression until we get to a multiply. 1007 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1008 ++Idx; 1009 1010 if (Ops.size() == 1) 1011 return Ops[0]; 1012 1013 // If there are mul operands inline them all into this expression. 1014 if (Idx < Ops.size()) { 1015 bool DeletedMul = false; 1016 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1017 // If we have an mul, expand the mul operands onto the end of the operands 1018 // list. 1019 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1020 Ops.erase(Ops.begin()+Idx); 1021 DeletedMul = true; 1022 } 1023 1024 // If we deleted at least one mul, we added operands to the end of the list, 1025 // and they are not necessarily sorted. Recurse to resort and resimplify 1026 // any operands we just aquired. 1027 if (DeletedMul) 1028 return getMulExpr(Ops); 1029 } 1030 1031 // If there are any add recurrences in the operands list, see if any other 1032 // added values are loop invariant. If so, we can fold them into the 1033 // recurrence. 1034 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1035 ++Idx; 1036 1037 // Scan over all recurrences, trying to fold loop invariants into them. 1038 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1039 // Scan all of the other operands to this mul and add them to the vector if 1040 // they are loop invariant w.r.t. the recurrence. 1041 std::vector<SCEVHandle> LIOps; 1042 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1043 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1044 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1045 LIOps.push_back(Ops[i]); 1046 Ops.erase(Ops.begin()+i); 1047 --i; --e; 1048 } 1049 1050 // If we found some loop invariants, fold them into the recurrence. 1051 if (!LIOps.empty()) { 1052 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1053 std::vector<SCEVHandle> NewOps; 1054 NewOps.reserve(AddRec->getNumOperands()); 1055 if (LIOps.size() == 1) { 1056 SCEV *Scale = LIOps[0]; 1057 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1058 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1059 } else { 1060 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1061 std::vector<SCEVHandle> MulOps(LIOps); 1062 MulOps.push_back(AddRec->getOperand(i)); 1063 NewOps.push_back(getMulExpr(MulOps)); 1064 } 1065 } 1066 1067 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1068 1069 // If all of the other operands were loop invariant, we are done. 1070 if (Ops.size() == 1) return NewRec; 1071 1072 // Otherwise, multiply the folded AddRec by the non-liv parts. 1073 for (unsigned i = 0;; ++i) 1074 if (Ops[i] == AddRec) { 1075 Ops[i] = NewRec; 1076 break; 1077 } 1078 return getMulExpr(Ops); 1079 } 1080 1081 // Okay, if there weren't any loop invariants to be folded, check to see if 1082 // there are multiple AddRec's with the same loop induction variable being 1083 // multiplied together. If so, we can fold them. 1084 for (unsigned OtherIdx = Idx+1; 1085 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1086 if (OtherIdx != Idx) { 1087 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1088 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1089 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1090 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1091 SCEVHandle NewStart = getMulExpr(F->getStart(), 1092 G->getStart()); 1093 SCEVHandle B = F->getStepRecurrence(*this); 1094 SCEVHandle D = G->getStepRecurrence(*this); 1095 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1096 getMulExpr(G, B), 1097 getMulExpr(B, D)); 1098 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1099 F->getLoop()); 1100 if (Ops.size() == 2) return NewAddRec; 1101 1102 Ops.erase(Ops.begin()+Idx); 1103 Ops.erase(Ops.begin()+OtherIdx-1); 1104 Ops.push_back(NewAddRec); 1105 return getMulExpr(Ops); 1106 } 1107 } 1108 1109 // Otherwise couldn't fold anything into this recurrence. Move onto the 1110 // next one. 1111 } 1112 1113 // Okay, it looks like we really DO need an mul expr. Check to see if we 1114 // already have one, otherwise create a new one. 1115 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1116 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1117 SCEVOps)]; 1118 if (Result == 0) 1119 Result = new SCEVMulExpr(Ops); 1120 return Result; 1121} 1122 1123SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1124 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1125 if (RHSC->getValue()->equalsInt(1)) 1126 return LHS; // X udiv 1 --> x 1127 1128 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1129 Constant *LHSCV = LHSC->getValue(); 1130 Constant *RHSCV = RHSC->getValue(); 1131 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1132 } 1133 } 1134 1135 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1136 1137 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1138 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1139 return Result; 1140} 1141 1142 1143/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1144/// specified loop. Simplify the expression as much as possible. 1145SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1146 const SCEVHandle &Step, const Loop *L) { 1147 std::vector<SCEVHandle> Operands; 1148 Operands.push_back(Start); 1149 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1150 if (StepChrec->getLoop() == L) { 1151 Operands.insert(Operands.end(), StepChrec->op_begin(), 1152 StepChrec->op_end()); 1153 return getAddRecExpr(Operands, L); 1154 } 1155 1156 Operands.push_back(Step); 1157 return getAddRecExpr(Operands, L); 1158} 1159 1160/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1161/// specified loop. Simplify the expression as much as possible. 1162SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1163 const Loop *L) { 1164 if (Operands.size() == 1) return Operands[0]; 1165 1166 if (Operands.back()->isZero()) { 1167 Operands.pop_back(); 1168 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1169 } 1170 1171 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1172 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1173 const Loop* NestedLoop = NestedAR->getLoop(); 1174 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1175 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1176 NestedAR->op_end()); 1177 SCEVHandle NestedARHandle(NestedAR); 1178 Operands[0] = NestedAR->getStart(); 1179 NestedOperands[0] = getAddRecExpr(Operands, L); 1180 return getAddRecExpr(NestedOperands, NestedLoop); 1181 } 1182 } 1183 1184 SCEVAddRecExpr *&Result = 1185 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1186 Operands.end()))]; 1187 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1188 return Result; 1189} 1190 1191SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1192 const SCEVHandle &RHS) { 1193 std::vector<SCEVHandle> Ops; 1194 Ops.push_back(LHS); 1195 Ops.push_back(RHS); 1196 return getSMaxExpr(Ops); 1197} 1198 1199SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1200 assert(!Ops.empty() && "Cannot get empty smax!"); 1201 if (Ops.size() == 1) return Ops[0]; 1202 1203 // Sort by complexity, this groups all similar expression types together. 1204 GroupByComplexity(Ops); 1205 1206 // If there are any constants, fold them together. 1207 unsigned Idx = 0; 1208 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1209 ++Idx; 1210 assert(Idx < Ops.size()); 1211 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1212 // We found two constants, fold them together! 1213 ConstantInt *Fold = ConstantInt::get( 1214 APIntOps::smax(LHSC->getValue()->getValue(), 1215 RHSC->getValue()->getValue())); 1216 Ops[0] = getConstant(Fold); 1217 Ops.erase(Ops.begin()+1); // Erase the folded element 1218 if (Ops.size() == 1) return Ops[0]; 1219 LHSC = cast<SCEVConstant>(Ops[0]); 1220 } 1221 1222 // If we are left with a constant -inf, strip it off. 1223 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1224 Ops.erase(Ops.begin()); 1225 --Idx; 1226 } 1227 } 1228 1229 if (Ops.size() == 1) return Ops[0]; 1230 1231 // Find the first SMax 1232 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1233 ++Idx; 1234 1235 // Check to see if one of the operands is an SMax. If so, expand its operands 1236 // onto our operand list, and recurse to simplify. 1237 if (Idx < Ops.size()) { 1238 bool DeletedSMax = false; 1239 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1240 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1241 Ops.erase(Ops.begin()+Idx); 1242 DeletedSMax = true; 1243 } 1244 1245 if (DeletedSMax) 1246 return getSMaxExpr(Ops); 1247 } 1248 1249 // Okay, check to see if the same value occurs in the operand list twice. If 1250 // so, delete one. Since we sorted the list, these values are required to 1251 // be adjacent. 1252 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1253 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1254 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1255 --i; --e; 1256 } 1257 1258 if (Ops.size() == 1) return Ops[0]; 1259 1260 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1261 1262 // Okay, it looks like we really DO need an smax expr. Check to see if we 1263 // already have one, otherwise create a new one. 1264 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1265 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1266 SCEVOps)]; 1267 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1268 return Result; 1269} 1270 1271SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1272 const SCEVHandle &RHS) { 1273 std::vector<SCEVHandle> Ops; 1274 Ops.push_back(LHS); 1275 Ops.push_back(RHS); 1276 return getUMaxExpr(Ops); 1277} 1278 1279SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1280 assert(!Ops.empty() && "Cannot get empty umax!"); 1281 if (Ops.size() == 1) return Ops[0]; 1282 1283 // Sort by complexity, this groups all similar expression types together. 1284 GroupByComplexity(Ops); 1285 1286 // If there are any constants, fold them together. 1287 unsigned Idx = 0; 1288 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1289 ++Idx; 1290 assert(Idx < Ops.size()); 1291 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1292 // We found two constants, fold them together! 1293 ConstantInt *Fold = ConstantInt::get( 1294 APIntOps::umax(LHSC->getValue()->getValue(), 1295 RHSC->getValue()->getValue())); 1296 Ops[0] = getConstant(Fold); 1297 Ops.erase(Ops.begin()+1); // Erase the folded element 1298 if (Ops.size() == 1) return Ops[0]; 1299 LHSC = cast<SCEVConstant>(Ops[0]); 1300 } 1301 1302 // If we are left with a constant zero, strip it off. 1303 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1304 Ops.erase(Ops.begin()); 1305 --Idx; 1306 } 1307 } 1308 1309 if (Ops.size() == 1) return Ops[0]; 1310 1311 // Find the first UMax 1312 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1313 ++Idx; 1314 1315 // Check to see if one of the operands is a UMax. If so, expand its operands 1316 // onto our operand list, and recurse to simplify. 1317 if (Idx < Ops.size()) { 1318 bool DeletedUMax = false; 1319 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1320 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1321 Ops.erase(Ops.begin()+Idx); 1322 DeletedUMax = true; 1323 } 1324 1325 if (DeletedUMax) 1326 return getUMaxExpr(Ops); 1327 } 1328 1329 // Okay, check to see if the same value occurs in the operand list twice. If 1330 // so, delete one. Since we sorted the list, these values are required to 1331 // be adjacent. 1332 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1333 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1334 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1335 --i; --e; 1336 } 1337 1338 if (Ops.size() == 1) return Ops[0]; 1339 1340 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1341 1342 // Okay, it looks like we really DO need a umax expr. Check to see if we 1343 // already have one, otherwise create a new one. 1344 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1345 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1346 SCEVOps)]; 1347 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1348 return Result; 1349} 1350 1351SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1352 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1353 return getConstant(CI); 1354 if (isa<ConstantPointerNull>(V)) 1355 return getIntegerSCEV(0, V->getType()); 1356 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1357 if (Result == 0) Result = new SCEVUnknown(V); 1358 return Result; 1359} 1360 1361//===----------------------------------------------------------------------===// 1362// Basic SCEV Analysis and PHI Idiom Recognition Code 1363// 1364 1365/// deleteValueFromRecords - This method should be called by the 1366/// client before it removes an instruction from the program, to make sure 1367/// that no dangling references are left around. 1368void ScalarEvolution::deleteValueFromRecords(Value *V) { 1369 SmallVector<Value *, 16> Worklist; 1370 1371 if (Scalars.erase(V)) { 1372 if (PHINode *PN = dyn_cast<PHINode>(V)) 1373 ConstantEvolutionLoopExitValue.erase(PN); 1374 Worklist.push_back(V); 1375 } 1376 1377 while (!Worklist.empty()) { 1378 Value *VV = Worklist.back(); 1379 Worklist.pop_back(); 1380 1381 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1382 UI != UE; ++UI) { 1383 Instruction *Inst = cast<Instruction>(*UI); 1384 if (Scalars.erase(Inst)) { 1385 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1386 ConstantEvolutionLoopExitValue.erase(PN); 1387 Worklist.push_back(Inst); 1388 } 1389 } 1390 } 1391} 1392 1393/// isSCEVable - Test if values of the given type are analyzable within 1394/// the SCEV framework. This primarily includes integer types, and it 1395/// can optionally include pointer types if the ScalarEvolution class 1396/// has access to target-specific information. 1397bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1398 // Integers are always SCEVable. 1399 if (Ty->isInteger()) 1400 return true; 1401 1402 // Pointers are SCEVable if TargetData information is available 1403 // to provide pointer size information. 1404 if (isa<PointerType>(Ty)) 1405 return TD != NULL; 1406 1407 // Otherwise it's not SCEVable. 1408 return false; 1409} 1410 1411/// getTypeSizeInBits - Return the size in bits of the specified type, 1412/// for which isSCEVable must return true. 1413uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1414 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1415 1416 // If we have a TargetData, use it! 1417 if (TD) 1418 return TD->getTypeSizeInBits(Ty); 1419 1420 // Otherwise, we support only integer types. 1421 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1422 return Ty->getPrimitiveSizeInBits(); 1423} 1424 1425/// getEffectiveSCEVType - Return a type with the same bitwidth as 1426/// the given type and which represents how SCEV will treat the given 1427/// type, for which isSCEVable must return true. For pointer types, 1428/// this is the pointer-sized integer type. 1429const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1430 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1431 1432 if (Ty->isInteger()) 1433 return Ty; 1434 1435 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1436 return TD->getIntPtrType(); 1437} 1438 1439SCEVHandle ScalarEvolution::getCouldNotCompute() { 1440 return UnknownValue; 1441} 1442 1443/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1444/// expression and create a new one. 1445SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1446 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1447 1448 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1449 if (I != Scalars.end()) return I->second; 1450 SCEVHandle S = createSCEV(V); 1451 Scalars.insert(std::make_pair(V, S)); 1452 return S; 1453} 1454 1455/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1456/// specified signed integer value and return a SCEV for the constant. 1457SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 1458 Ty = getEffectiveSCEVType(Ty); 1459 Constant *C; 1460 if (Val == 0) 1461 C = Constant::getNullValue(Ty); 1462 else if (Ty->isFloatingPoint()) 1463 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1464 APFloat::IEEEdouble, Val)); 1465 else 1466 C = ConstantInt::get(Ty, Val); 1467 return getUnknown(C); 1468} 1469 1470/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1471/// 1472SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 1473 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1474 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 1475 1476 const Type *Ty = V->getType(); 1477 Ty = getEffectiveSCEVType(Ty); 1478 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 1479} 1480 1481/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1482SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 1483 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1484 return getUnknown(ConstantExpr::getNot(VC->getValue())); 1485 1486 const Type *Ty = V->getType(); 1487 Ty = getEffectiveSCEVType(Ty); 1488 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 1489 return getMinusSCEV(AllOnes, V); 1490} 1491 1492/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1493/// 1494SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 1495 const SCEVHandle &RHS) { 1496 // X - Y --> X + -Y 1497 return getAddExpr(LHS, getNegativeSCEV(RHS)); 1498} 1499 1500/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1501/// input value to the specified type. If the type must be extended, it is zero 1502/// extended. 1503SCEVHandle 1504ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 1505 const Type *Ty) { 1506 const Type *SrcTy = V->getType(); 1507 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1508 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1509 "Cannot truncate or zero extend with non-integer arguments!"); 1510 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1511 return V; // No conversion 1512 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1513 return getTruncateExpr(V, Ty); 1514 return getZeroExtendExpr(V, Ty); 1515} 1516 1517/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1518/// input value to the specified type. If the type must be extended, it is sign 1519/// extended. 1520SCEVHandle 1521ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 1522 const Type *Ty) { 1523 const Type *SrcTy = V->getType(); 1524 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1525 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1526 "Cannot truncate or zero extend with non-integer arguments!"); 1527 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1528 return V; // No conversion 1529 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1530 return getTruncateExpr(V, Ty); 1531 return getSignExtendExpr(V, Ty); 1532} 1533 1534/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1535/// the specified instruction and replaces any references to the symbolic value 1536/// SymName with the specified value. This is used during PHI resolution. 1537void ScalarEvolution:: 1538ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1539 const SCEVHandle &NewVal) { 1540 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1541 if (SI == Scalars.end()) return; 1542 1543 SCEVHandle NV = 1544 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 1545 if (NV == SI->second) return; // No change. 1546 1547 SI->second = NV; // Update the scalars map! 1548 1549 // Any instruction values that use this instruction might also need to be 1550 // updated! 1551 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1552 UI != E; ++UI) 1553 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1554} 1555 1556/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1557/// a loop header, making it a potential recurrence, or it doesn't. 1558/// 1559SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 1560 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1561 if (const Loop *L = LI->getLoopFor(PN->getParent())) 1562 if (L->getHeader() == PN->getParent()) { 1563 // If it lives in the loop header, it has two incoming values, one 1564 // from outside the loop, and one from inside. 1565 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1566 unsigned BackEdge = IncomingEdge^1; 1567 1568 // While we are analyzing this PHI node, handle its value symbolically. 1569 SCEVHandle SymbolicName = getUnknown(PN); 1570 assert(Scalars.find(PN) == Scalars.end() && 1571 "PHI node already processed?"); 1572 Scalars.insert(std::make_pair(PN, SymbolicName)); 1573 1574 // Using this symbolic name for the PHI, analyze the value coming around 1575 // the back-edge. 1576 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1577 1578 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1579 // has a special value for the first iteration of the loop. 1580 1581 // If the value coming around the backedge is an add with the symbolic 1582 // value we just inserted, then we found a simple induction variable! 1583 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1584 // If there is a single occurrence of the symbolic value, replace it 1585 // with a recurrence. 1586 unsigned FoundIndex = Add->getNumOperands(); 1587 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1588 if (Add->getOperand(i) == SymbolicName) 1589 if (FoundIndex == e) { 1590 FoundIndex = i; 1591 break; 1592 } 1593 1594 if (FoundIndex != Add->getNumOperands()) { 1595 // Create an add with everything but the specified operand. 1596 std::vector<SCEVHandle> Ops; 1597 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1598 if (i != FoundIndex) 1599 Ops.push_back(Add->getOperand(i)); 1600 SCEVHandle Accum = getAddExpr(Ops); 1601 1602 // This is not a valid addrec if the step amount is varying each 1603 // loop iteration, but is not itself an addrec in this loop. 1604 if (Accum->isLoopInvariant(L) || 1605 (isa<SCEVAddRecExpr>(Accum) && 1606 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1607 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1608 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 1609 1610 // Okay, for the entire analysis of this edge we assumed the PHI 1611 // to be symbolic. We now need to go back and update all of the 1612 // entries for the scalars that use the PHI (except for the PHI 1613 // itself) to use the new analyzed value instead of the "symbolic" 1614 // value. 1615 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1616 return PHISCEV; 1617 } 1618 } 1619 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1620 // Otherwise, this could be a loop like this: 1621 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1622 // In this case, j = {1,+,1} and BEValue is j. 1623 // Because the other in-value of i (0) fits the evolution of BEValue 1624 // i really is an addrec evolution. 1625 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1626 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1627 1628 // If StartVal = j.start - j.stride, we can use StartVal as the 1629 // initial step of the addrec evolution. 1630 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 1631 AddRec->getOperand(1))) { 1632 SCEVHandle PHISCEV = 1633 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1634 1635 // Okay, for the entire analysis of this edge we assumed the PHI 1636 // to be symbolic. We now need to go back and update all of the 1637 // entries for the scalars that use the PHI (except for the PHI 1638 // itself) to use the new analyzed value instead of the "symbolic" 1639 // value. 1640 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1641 return PHISCEV; 1642 } 1643 } 1644 } 1645 1646 return SymbolicName; 1647 } 1648 1649 // If it's not a loop phi, we can't handle it yet. 1650 return getUnknown(PN); 1651} 1652 1653/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1654/// guaranteed to end in (at every loop iteration). It is, at the same time, 1655/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1656/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1657static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) { 1658 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1659 return C->getValue()->getValue().countTrailingZeros(); 1660 1661 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1662 return std::min(GetMinTrailingZeros(T->getOperand(), SE), 1663 (uint32_t)SE.getTypeSizeInBits(T->getType())); 1664 1665 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1666 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1667 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1668 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1669 } 1670 1671 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1672 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1673 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1674 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1675 } 1676 1677 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1678 // The result is the min of all operands results. 1679 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1680 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1681 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1682 return MinOpRes; 1683 } 1684 1685 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1686 // The result is the sum of all operands results. 1687 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1688 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType()); 1689 for (unsigned i = 1, e = M->getNumOperands(); 1690 SumOpRes != BitWidth && i != e; ++i) 1691 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE), 1692 BitWidth); 1693 return SumOpRes; 1694 } 1695 1696 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1697 // The result is the min of all operands results. 1698 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1699 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1700 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1701 return MinOpRes; 1702 } 1703 1704 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1705 // The result is the min of all operands results. 1706 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1707 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1708 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1709 return MinOpRes; 1710 } 1711 1712 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1713 // The result is the min of all operands results. 1714 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1715 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1716 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1717 return MinOpRes; 1718 } 1719 1720 // SCEVUDivExpr, SCEVUnknown 1721 return 0; 1722} 1723 1724/// createSCEV - We know that there is no SCEV for the specified value. 1725/// Analyze the expression. 1726/// 1727SCEVHandle ScalarEvolution::createSCEV(Value *V) { 1728 if (!isSCEVable(V->getType())) 1729 return getUnknown(V); 1730 1731 unsigned Opcode = Instruction::UserOp1; 1732 if (Instruction *I = dyn_cast<Instruction>(V)) 1733 Opcode = I->getOpcode(); 1734 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1735 Opcode = CE->getOpcode(); 1736 else 1737 return getUnknown(V); 1738 1739 User *U = cast<User>(V); 1740 switch (Opcode) { 1741 case Instruction::Add: 1742 return getAddExpr(getSCEV(U->getOperand(0)), 1743 getSCEV(U->getOperand(1))); 1744 case Instruction::Mul: 1745 return getMulExpr(getSCEV(U->getOperand(0)), 1746 getSCEV(U->getOperand(1))); 1747 case Instruction::UDiv: 1748 return getUDivExpr(getSCEV(U->getOperand(0)), 1749 getSCEV(U->getOperand(1))); 1750 case Instruction::Sub: 1751 return getMinusSCEV(getSCEV(U->getOperand(0)), 1752 getSCEV(U->getOperand(1))); 1753 case Instruction::And: 1754 // For an expression like x&255 that merely masks off the high bits, 1755 // use zext(trunc(x)) as the SCEV expression. 1756 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1757 const APInt &A = CI->getValue(); 1758 unsigned Ones = A.countTrailingOnes(); 1759 if (APIntOps::isMask(Ones, A)) 1760 return 1761 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 1762 IntegerType::get(Ones)), 1763 U->getType()); 1764 } 1765 break; 1766 case Instruction::Or: 1767 // If the RHS of the Or is a constant, we may have something like: 1768 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1769 // optimizations will transparently handle this case. 1770 // 1771 // In order for this transformation to be safe, the LHS must be of the 1772 // form X*(2^n) and the Or constant must be less than 2^n. 1773 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1774 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1775 const APInt &CIVal = CI->getValue(); 1776 if (GetMinTrailingZeros(LHS, *this) >= 1777 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1778 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 1779 } 1780 break; 1781 case Instruction::Xor: 1782 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1783 // If the RHS of the xor is a signbit, then this is just an add. 1784 // Instcombine turns add of signbit into xor as a strength reduction step. 1785 if (CI->getValue().isSignBit()) 1786 return getAddExpr(getSCEV(U->getOperand(0)), 1787 getSCEV(U->getOperand(1))); 1788 1789 // If the RHS of xor is -1, then this is a not operation. 1790 else if (CI->isAllOnesValue()) 1791 return getNotSCEV(getSCEV(U->getOperand(0))); 1792 } 1793 break; 1794 1795 case Instruction::Shl: 1796 // Turn shift left of a constant amount into a multiply. 1797 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1798 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1799 Constant *X = ConstantInt::get( 1800 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1801 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1802 } 1803 break; 1804 1805 case Instruction::LShr: 1806 // Turn logical shift right of a constant into a unsigned divide. 1807 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1808 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1809 Constant *X = ConstantInt::get( 1810 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1811 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1812 } 1813 break; 1814 1815 case Instruction::AShr: 1816 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 1817 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 1818 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 1819 if (L->getOpcode() == Instruction::Shl && 1820 L->getOperand(1) == U->getOperand(1)) { 1821 uint64_t Amt = getTypeSizeInBits(U->getType()) - CI->getZExtValue(); 1822 return 1823 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 1824 IntegerType::get(Amt)), 1825 U->getType()); 1826 } 1827 break; 1828 1829 case Instruction::Trunc: 1830 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1831 1832 case Instruction::ZExt: 1833 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1834 1835 case Instruction::SExt: 1836 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1837 1838 case Instruction::BitCast: 1839 // BitCasts are no-op casts so we just eliminate the cast. 1840 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 1841 return getSCEV(U->getOperand(0)); 1842 break; 1843 1844 case Instruction::IntToPtr: 1845 if (!TD) break; // Without TD we can't analyze pointers. 1846 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1847 TD->getIntPtrType()); 1848 1849 case Instruction::PtrToInt: 1850 if (!TD) break; // Without TD we can't analyze pointers. 1851 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1852 U->getType()); 1853 1854 case Instruction::GetElementPtr: { 1855 if (!TD) break; // Without TD we can't analyze pointers. 1856 const Type *IntPtrTy = TD->getIntPtrType(); 1857 Value *Base = U->getOperand(0); 1858 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1859 gep_type_iterator GTI = gep_type_begin(U); 1860 for (GetElementPtrInst::op_iterator I = next(U->op_begin()), 1861 E = U->op_end(); 1862 I != E; ++I) { 1863 Value *Index = *I; 1864 // Compute the (potentially symbolic) offset in bytes for this index. 1865 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1866 // For a struct, add the member offset. 1867 const StructLayout &SL = *TD->getStructLayout(STy); 1868 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1869 uint64_t Offset = SL.getElementOffset(FieldNo); 1870 TotalOffset = getAddExpr(TotalOffset, 1871 getIntegerSCEV(Offset, IntPtrTy)); 1872 } else { 1873 // For an array, add the element offset, explicitly scaled. 1874 SCEVHandle LocalOffset = getSCEV(Index); 1875 if (!isa<PointerType>(LocalOffset->getType())) 1876 // Getelementptr indicies are signed. 1877 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1878 IntPtrTy); 1879 LocalOffset = 1880 getMulExpr(LocalOffset, 1881 getIntegerSCEV(TD->getTypePaddedSize(*GTI), 1882 IntPtrTy)); 1883 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1884 } 1885 } 1886 return getAddExpr(getSCEV(Base), TotalOffset); 1887 } 1888 1889 case Instruction::PHI: 1890 return createNodeForPHI(cast<PHINode>(U)); 1891 1892 case Instruction::Select: 1893 // This could be a smax or umax that was lowered earlier. 1894 // Try to recover it. 1895 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1896 Value *LHS = ICI->getOperand(0); 1897 Value *RHS = ICI->getOperand(1); 1898 switch (ICI->getPredicate()) { 1899 case ICmpInst::ICMP_SLT: 1900 case ICmpInst::ICMP_SLE: 1901 std::swap(LHS, RHS); 1902 // fall through 1903 case ICmpInst::ICMP_SGT: 1904 case ICmpInst::ICMP_SGE: 1905 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1906 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1907 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1908 // ~smax(~x, ~y) == smin(x, y). 1909 return getNotSCEV(getSMaxExpr( 1910 getNotSCEV(getSCEV(LHS)), 1911 getNotSCEV(getSCEV(RHS)))); 1912 break; 1913 case ICmpInst::ICMP_ULT: 1914 case ICmpInst::ICMP_ULE: 1915 std::swap(LHS, RHS); 1916 // fall through 1917 case ICmpInst::ICMP_UGT: 1918 case ICmpInst::ICMP_UGE: 1919 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1920 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1921 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1922 // ~umax(~x, ~y) == umin(x, y) 1923 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 1924 getNotSCEV(getSCEV(RHS)))); 1925 break; 1926 default: 1927 break; 1928 } 1929 } 1930 1931 default: // We cannot analyze this expression. 1932 break; 1933 } 1934 1935 return getUnknown(V); 1936} 1937 1938 1939 1940//===----------------------------------------------------------------------===// 1941// Iteration Count Computation Code 1942// 1943 1944/// getBackedgeTakenCount - If the specified loop has a predictable 1945/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 1946/// object. The backedge-taken count is the number of times the loop header 1947/// will be branched to from within the loop. This is one less than the 1948/// trip count of the loop, since it doesn't count the first iteration, 1949/// when the header is branched to from outside the loop. 1950/// 1951/// Note that it is not valid to call this method on a loop without a 1952/// loop-invariant backedge-taken count (see 1953/// hasLoopInvariantBackedgeTakenCount). 1954/// 1955SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 1956 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L); 1957 if (I == BackedgeTakenCounts.end()) { 1958 SCEVHandle ItCount = ComputeBackedgeTakenCount(L); 1959 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first; 1960 if (ItCount != UnknownValue) { 1961 assert(ItCount->isLoopInvariant(L) && 1962 "Computed trip count isn't loop invariant for loop!"); 1963 ++NumTripCountsComputed; 1964 } else if (isa<PHINode>(L->getHeader()->begin())) { 1965 // Only count loops that have phi nodes as not being computable. 1966 ++NumTripCountsNotComputed; 1967 } 1968 } 1969 return I->second; 1970} 1971 1972/// forgetLoopBackedgeTakenCount - This method should be called by the 1973/// client when it has changed a loop in a way that may effect 1974/// ScalarEvolution's ability to compute a trip count, or if the loop 1975/// is deleted. 1976void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 1977 BackedgeTakenCounts.erase(L); 1978} 1979 1980/// ComputeBackedgeTakenCount - Compute the number of times the backedge 1981/// of the specified loop will execute. 1982SCEVHandle ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 1983 // If the loop has a non-one exit block count, we can't analyze it. 1984 SmallVector<BasicBlock*, 8> ExitBlocks; 1985 L->getExitBlocks(ExitBlocks); 1986 if (ExitBlocks.size() != 1) return UnknownValue; 1987 1988 // Okay, there is one exit block. Try to find the condition that causes the 1989 // loop to be exited. 1990 BasicBlock *ExitBlock = ExitBlocks[0]; 1991 1992 BasicBlock *ExitingBlock = 0; 1993 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1994 PI != E; ++PI) 1995 if (L->contains(*PI)) { 1996 if (ExitingBlock == 0) 1997 ExitingBlock = *PI; 1998 else 1999 return UnknownValue; // More than one block exiting! 2000 } 2001 assert(ExitingBlock && "No exits from loop, something is broken!"); 2002 2003 // Okay, we've computed the exiting block. See what condition causes us to 2004 // exit. 2005 // 2006 // FIXME: we should be able to handle switch instructions (with a single exit) 2007 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2008 if (ExitBr == 0) return UnknownValue; 2009 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2010 2011 // At this point, we know we have a conditional branch that determines whether 2012 // the loop is exited. However, we don't know if the branch is executed each 2013 // time through the loop. If not, then the execution count of the branch will 2014 // not be equal to the trip count of the loop. 2015 // 2016 // Currently we check for this by checking to see if the Exit branch goes to 2017 // the loop header. If so, we know it will always execute the same number of 2018 // times as the loop. We also handle the case where the exit block *is* the 2019 // loop header. This is common for un-rotated loops. More extensive analysis 2020 // could be done to handle more cases here. 2021 if (ExitBr->getSuccessor(0) != L->getHeader() && 2022 ExitBr->getSuccessor(1) != L->getHeader() && 2023 ExitBr->getParent() != L->getHeader()) 2024 return UnknownValue; 2025 2026 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2027 2028 // If it's not an integer comparison then compute it the hard way. 2029 // Note that ICmpInst deals with pointer comparisons too so we must check 2030 // the type of the operand. 2031 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2032 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2033 ExitBr->getSuccessor(0) == ExitBlock); 2034 2035 // If the condition was exit on true, convert the condition to exit on false 2036 ICmpInst::Predicate Cond; 2037 if (ExitBr->getSuccessor(1) == ExitBlock) 2038 Cond = ExitCond->getPredicate(); 2039 else 2040 Cond = ExitCond->getInversePredicate(); 2041 2042 // Handle common loops like: for (X = "string"; *X; ++X) 2043 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2044 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2045 SCEVHandle ItCnt = 2046 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2047 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2048 } 2049 2050 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2051 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2052 2053 // Try to evaluate any dependencies out of the loop. 2054 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2055 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2056 Tmp = getSCEVAtScope(RHS, L); 2057 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2058 2059 // At this point, we would like to compute how many iterations of the 2060 // loop the predicate will return true for these inputs. 2061 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2062 // If there is a loop-invariant, force it into the RHS. 2063 std::swap(LHS, RHS); 2064 Cond = ICmpInst::getSwappedPredicate(Cond); 2065 } 2066 2067 // If we have a comparison of a chrec against a constant, try to use value 2068 // ranges to answer this query. 2069 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2070 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2071 if (AddRec->getLoop() == L) { 2072 // Form the comparison range using the constant of the correct type so 2073 // that the ConstantRange class knows to do a signed or unsigned 2074 // comparison. 2075 ConstantInt *CompVal = RHSC->getValue(); 2076 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2077 CompVal = dyn_cast<ConstantInt>( 2078 ConstantExpr::getBitCast(CompVal, RealTy)); 2079 if (CompVal) { 2080 // Form the constant range. 2081 ConstantRange CompRange( 2082 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2083 2084 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2085 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2086 } 2087 } 2088 2089 switch (Cond) { 2090 case ICmpInst::ICMP_NE: { // while (X != Y) 2091 // Convert to: while (X-Y != 0) 2092 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2093 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2094 break; 2095 } 2096 case ICmpInst::ICMP_EQ: { 2097 // Convert to: while (X-Y == 0) // while (X == Y) 2098 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2099 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2100 break; 2101 } 2102 case ICmpInst::ICMP_SLT: { 2103 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2104 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2105 break; 2106 } 2107 case ICmpInst::ICMP_SGT: { 2108 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2109 getNotSCEV(RHS), L, true); 2110 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2111 break; 2112 } 2113 case ICmpInst::ICMP_ULT: { 2114 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2115 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2116 break; 2117 } 2118 case ICmpInst::ICMP_UGT: { 2119 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2120 getNotSCEV(RHS), L, false); 2121 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2122 break; 2123 } 2124 default: 2125#if 0 2126 errs() << "ComputeBackedgeTakenCount "; 2127 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2128 errs() << "[unsigned] "; 2129 errs() << *LHS << " " 2130 << Instruction::getOpcodeName(Instruction::ICmp) 2131 << " " << *RHS << "\n"; 2132#endif 2133 break; 2134 } 2135 return 2136 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2137 ExitBr->getSuccessor(0) == ExitBlock); 2138} 2139 2140static ConstantInt * 2141EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2142 ScalarEvolution &SE) { 2143 SCEVHandle InVal = SE.getConstant(C); 2144 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2145 assert(isa<SCEVConstant>(Val) && 2146 "Evaluation of SCEV at constant didn't fold correctly?"); 2147 return cast<SCEVConstant>(Val)->getValue(); 2148} 2149 2150/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2151/// and a GEP expression (missing the pointer index) indexing into it, return 2152/// the addressed element of the initializer or null if the index expression is 2153/// invalid. 2154static Constant * 2155GetAddressedElementFromGlobal(GlobalVariable *GV, 2156 const std::vector<ConstantInt*> &Indices) { 2157 Constant *Init = GV->getInitializer(); 2158 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2159 uint64_t Idx = Indices[i]->getZExtValue(); 2160 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2161 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2162 Init = cast<Constant>(CS->getOperand(Idx)); 2163 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2164 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2165 Init = cast<Constant>(CA->getOperand(Idx)); 2166 } else if (isa<ConstantAggregateZero>(Init)) { 2167 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2168 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2169 Init = Constant::getNullValue(STy->getElementType(Idx)); 2170 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2171 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2172 Init = Constant::getNullValue(ATy->getElementType()); 2173 } else { 2174 assert(0 && "Unknown constant aggregate type!"); 2175 } 2176 return 0; 2177 } else { 2178 return 0; // Unknown initializer type 2179 } 2180 } 2181 return Init; 2182} 2183 2184/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2185/// 'icmp op load X, cst', try to see if we can compute the backedge 2186/// execution count. 2187SCEVHandle ScalarEvolution:: 2188ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2189 const Loop *L, 2190 ICmpInst::Predicate predicate) { 2191 if (LI->isVolatile()) return UnknownValue; 2192 2193 // Check to see if the loaded pointer is a getelementptr of a global. 2194 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2195 if (!GEP) return UnknownValue; 2196 2197 // Make sure that it is really a constant global we are gepping, with an 2198 // initializer, and make sure the first IDX is really 0. 2199 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2200 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2201 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2202 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2203 return UnknownValue; 2204 2205 // Okay, we allow one non-constant index into the GEP instruction. 2206 Value *VarIdx = 0; 2207 std::vector<ConstantInt*> Indexes; 2208 unsigned VarIdxNum = 0; 2209 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2210 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2211 Indexes.push_back(CI); 2212 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2213 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2214 VarIdx = GEP->getOperand(i); 2215 VarIdxNum = i-2; 2216 Indexes.push_back(0); 2217 } 2218 2219 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2220 // Check to see if X is a loop variant variable value now. 2221 SCEVHandle Idx = getSCEV(VarIdx); 2222 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2223 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2224 2225 // We can only recognize very limited forms of loop index expressions, in 2226 // particular, only affine AddRec's like {C1,+,C2}. 2227 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2228 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2229 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2230 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2231 return UnknownValue; 2232 2233 unsigned MaxSteps = MaxBruteForceIterations; 2234 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2235 ConstantInt *ItCst = 2236 ConstantInt::get(IdxExpr->getType(), IterationNum); 2237 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2238 2239 // Form the GEP offset. 2240 Indexes[VarIdxNum] = Val; 2241 2242 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2243 if (Result == 0) break; // Cannot compute! 2244 2245 // Evaluate the condition for this iteration. 2246 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2247 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2248 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2249#if 0 2250 errs() << "\n***\n*** Computed loop count " << *ItCst 2251 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2252 << "***\n"; 2253#endif 2254 ++NumArrayLenItCounts; 2255 return getConstant(ItCst); // Found terminating iteration! 2256 } 2257 } 2258 return UnknownValue; 2259} 2260 2261 2262/// CanConstantFold - Return true if we can constant fold an instruction of the 2263/// specified type, assuming that all operands were constants. 2264static bool CanConstantFold(const Instruction *I) { 2265 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2266 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2267 return true; 2268 2269 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2270 if (const Function *F = CI->getCalledFunction()) 2271 return canConstantFoldCallTo(F); 2272 return false; 2273} 2274 2275/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2276/// in the loop that V is derived from. We allow arbitrary operations along the 2277/// way, but the operands of an operation must either be constants or a value 2278/// derived from a constant PHI. If this expression does not fit with these 2279/// constraints, return null. 2280static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2281 // If this is not an instruction, or if this is an instruction outside of the 2282 // loop, it can't be derived from a loop PHI. 2283 Instruction *I = dyn_cast<Instruction>(V); 2284 if (I == 0 || !L->contains(I->getParent())) return 0; 2285 2286 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2287 if (L->getHeader() == I->getParent()) 2288 return PN; 2289 else 2290 // We don't currently keep track of the control flow needed to evaluate 2291 // PHIs, so we cannot handle PHIs inside of loops. 2292 return 0; 2293 } 2294 2295 // If we won't be able to constant fold this expression even if the operands 2296 // are constants, return early. 2297 if (!CanConstantFold(I)) return 0; 2298 2299 // Otherwise, we can evaluate this instruction if all of its operands are 2300 // constant or derived from a PHI node themselves. 2301 PHINode *PHI = 0; 2302 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2303 if (!(isa<Constant>(I->getOperand(Op)) || 2304 isa<GlobalValue>(I->getOperand(Op)))) { 2305 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2306 if (P == 0) return 0; // Not evolving from PHI 2307 if (PHI == 0) 2308 PHI = P; 2309 else if (PHI != P) 2310 return 0; // Evolving from multiple different PHIs. 2311 } 2312 2313 // This is a expression evolving from a constant PHI! 2314 return PHI; 2315} 2316 2317/// EvaluateExpression - Given an expression that passes the 2318/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2319/// in the loop has the value PHIVal. If we can't fold this expression for some 2320/// reason, return null. 2321static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2322 if (isa<PHINode>(V)) return PHIVal; 2323 if (Constant *C = dyn_cast<Constant>(V)) return C; 2324 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2325 Instruction *I = cast<Instruction>(V); 2326 2327 std::vector<Constant*> Operands; 2328 Operands.resize(I->getNumOperands()); 2329 2330 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2331 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2332 if (Operands[i] == 0) return 0; 2333 } 2334 2335 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2336 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2337 &Operands[0], Operands.size()); 2338 else 2339 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2340 &Operands[0], Operands.size()); 2341} 2342 2343/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2344/// in the header of its containing loop, we know the loop executes a 2345/// constant number of times, and the PHI node is just a recurrence 2346/// involving constants, fold it. 2347Constant *ScalarEvolution:: 2348getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2349 std::map<PHINode*, Constant*>::iterator I = 2350 ConstantEvolutionLoopExitValue.find(PN); 2351 if (I != ConstantEvolutionLoopExitValue.end()) 2352 return I->second; 2353 2354 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2355 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2356 2357 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2358 2359 // Since the loop is canonicalized, the PHI node must have two entries. One 2360 // entry must be a constant (coming in from outside of the loop), and the 2361 // second must be derived from the same PHI. 2362 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2363 Constant *StartCST = 2364 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2365 if (StartCST == 0) 2366 return RetVal = 0; // Must be a constant. 2367 2368 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2369 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2370 if (PN2 != PN) 2371 return RetVal = 0; // Not derived from same PHI. 2372 2373 // Execute the loop symbolically to determine the exit value. 2374 if (BEs.getActiveBits() >= 32) 2375 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2376 2377 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2378 unsigned IterationNum = 0; 2379 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2380 if (IterationNum == NumIterations) 2381 return RetVal = PHIVal; // Got exit value! 2382 2383 // Compute the value of the PHI node for the next iteration. 2384 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2385 if (NextPHI == PHIVal) 2386 return RetVal = NextPHI; // Stopped evolving! 2387 if (NextPHI == 0) 2388 return 0; // Couldn't evaluate! 2389 PHIVal = NextPHI; 2390 } 2391} 2392 2393/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2394/// constant number of times (the condition evolves only from constants), 2395/// try to evaluate a few iterations of the loop until we get the exit 2396/// condition gets a value of ExitWhen (true or false). If we cannot 2397/// evaluate the trip count of the loop, return UnknownValue. 2398SCEVHandle ScalarEvolution:: 2399ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2400 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2401 if (PN == 0) return UnknownValue; 2402 2403 // Since the loop is canonicalized, the PHI node must have two entries. One 2404 // entry must be a constant (coming in from outside of the loop), and the 2405 // second must be derived from the same PHI. 2406 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2407 Constant *StartCST = 2408 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2409 if (StartCST == 0) return UnknownValue; // Must be a constant. 2410 2411 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2412 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2413 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2414 2415 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2416 // the loop symbolically to determine when the condition gets a value of 2417 // "ExitWhen". 2418 unsigned IterationNum = 0; 2419 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2420 for (Constant *PHIVal = StartCST; 2421 IterationNum != MaxIterations; ++IterationNum) { 2422 ConstantInt *CondVal = 2423 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2424 2425 // Couldn't symbolically evaluate. 2426 if (!CondVal) return UnknownValue; 2427 2428 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2429 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2430 ++NumBruteForceTripCountsComputed; 2431 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2432 } 2433 2434 // Compute the value of the PHI node for the next iteration. 2435 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2436 if (NextPHI == 0 || NextPHI == PHIVal) 2437 return UnknownValue; // Couldn't evaluate or not making progress... 2438 PHIVal = NextPHI; 2439 } 2440 2441 // Too many iterations were needed to evaluate. 2442 return UnknownValue; 2443} 2444 2445/// getSCEVAtScope - Compute the value of the specified expression within the 2446/// indicated loop (which may be null to indicate in no loop). If the 2447/// expression cannot be evaluated, return UnknownValue. 2448SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) { 2449 // FIXME: this should be turned into a virtual method on SCEV! 2450 2451 if (isa<SCEVConstant>(V)) return V; 2452 2453 // If this instruction is evolved from a constant-evolving PHI, compute the 2454 // exit value from the loop without using SCEVs. 2455 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2456 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2457 const Loop *LI = (*this->LI)[I->getParent()]; 2458 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2459 if (PHINode *PN = dyn_cast<PHINode>(I)) 2460 if (PN->getParent() == LI->getHeader()) { 2461 // Okay, there is no closed form solution for the PHI node. Check 2462 // to see if the loop that contains it has a known backedge-taken 2463 // count. If so, we may be able to force computation of the exit 2464 // value. 2465 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2466 if (SCEVConstant *BTCC = 2467 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2468 // Okay, we know how many times the containing loop executes. If 2469 // this is a constant evolving PHI node, get the final value at 2470 // the specified iteration number. 2471 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2472 BTCC->getValue()->getValue(), 2473 LI); 2474 if (RV) return getUnknown(RV); 2475 } 2476 } 2477 2478 // Okay, this is an expression that we cannot symbolically evaluate 2479 // into a SCEV. Check to see if it's possible to symbolically evaluate 2480 // the arguments into constants, and if so, try to constant propagate the 2481 // result. This is particularly useful for computing loop exit values. 2482 if (CanConstantFold(I)) { 2483 std::vector<Constant*> Operands; 2484 Operands.reserve(I->getNumOperands()); 2485 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2486 Value *Op = I->getOperand(i); 2487 if (Constant *C = dyn_cast<Constant>(Op)) { 2488 Operands.push_back(C); 2489 } else { 2490 // If any of the operands is non-constant and if they are 2491 // non-integer and non-pointer, don't even try to analyze them 2492 // with scev techniques. 2493 if (!isa<IntegerType>(Op->getType()) && 2494 !isa<PointerType>(Op->getType())) 2495 return V; 2496 2497 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2498 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2499 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2500 Op->getType(), 2501 false)); 2502 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2503 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2504 Operands.push_back(ConstantExpr::getIntegerCast(C, 2505 Op->getType(), 2506 false)); 2507 else 2508 return V; 2509 } else { 2510 return V; 2511 } 2512 } 2513 } 2514 2515 Constant *C; 2516 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2517 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2518 &Operands[0], Operands.size()); 2519 else 2520 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2521 &Operands[0], Operands.size()); 2522 return getUnknown(C); 2523 } 2524 } 2525 2526 // This is some other type of SCEVUnknown, just return it. 2527 return V; 2528 } 2529 2530 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2531 // Avoid performing the look-up in the common case where the specified 2532 // expression has no loop-variant portions. 2533 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2534 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2535 if (OpAtScope != Comm->getOperand(i)) { 2536 if (OpAtScope == UnknownValue) return UnknownValue; 2537 // Okay, at least one of these operands is loop variant but might be 2538 // foldable. Build a new instance of the folded commutative expression. 2539 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2540 NewOps.push_back(OpAtScope); 2541 2542 for (++i; i != e; ++i) { 2543 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2544 if (OpAtScope == UnknownValue) return UnknownValue; 2545 NewOps.push_back(OpAtScope); 2546 } 2547 if (isa<SCEVAddExpr>(Comm)) 2548 return getAddExpr(NewOps); 2549 if (isa<SCEVMulExpr>(Comm)) 2550 return getMulExpr(NewOps); 2551 if (isa<SCEVSMaxExpr>(Comm)) 2552 return getSMaxExpr(NewOps); 2553 if (isa<SCEVUMaxExpr>(Comm)) 2554 return getUMaxExpr(NewOps); 2555 assert(0 && "Unknown commutative SCEV type!"); 2556 } 2557 } 2558 // If we got here, all operands are loop invariant. 2559 return Comm; 2560 } 2561 2562 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2563 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2564 if (LHS == UnknownValue) return LHS; 2565 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2566 if (RHS == UnknownValue) return RHS; 2567 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2568 return Div; // must be loop invariant 2569 return getUDivExpr(LHS, RHS); 2570 } 2571 2572 // If this is a loop recurrence for a loop that does not contain L, then we 2573 // are dealing with the final value computed by the loop. 2574 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2575 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2576 // To evaluate this recurrence, we need to know how many times the AddRec 2577 // loop iterates. Compute this now. 2578 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2579 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2580 2581 // Then, evaluate the AddRec. 2582 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2583 } 2584 return UnknownValue; 2585 } 2586 2587 //assert(0 && "Unknown SCEV type!"); 2588 return UnknownValue; 2589} 2590 2591/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2592/// at the specified scope in the program. The L value specifies a loop 2593/// nest to evaluate the expression at, where null is the top-level or a 2594/// specified loop is immediately inside of the loop. 2595/// 2596/// This method can be used to compute the exit value for a variable defined 2597/// in a loop by querying what the value will hold in the parent loop. 2598/// 2599/// If this value is not computable at this scope, a SCEVCouldNotCompute 2600/// object is returned. 2601SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2602 return getSCEVAtScope(getSCEV(V), L); 2603} 2604 2605/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2606/// following equation: 2607/// 2608/// A * X = B (mod N) 2609/// 2610/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2611/// A and B isn't important. 2612/// 2613/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2614static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2615 ScalarEvolution &SE) { 2616 uint32_t BW = A.getBitWidth(); 2617 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2618 assert(A != 0 && "A must be non-zero."); 2619 2620 // 1. D = gcd(A, N) 2621 // 2622 // The gcd of A and N may have only one prime factor: 2. The number of 2623 // trailing zeros in A is its multiplicity 2624 uint32_t Mult2 = A.countTrailingZeros(); 2625 // D = 2^Mult2 2626 2627 // 2. Check if B is divisible by D. 2628 // 2629 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2630 // is not less than multiplicity of this prime factor for D. 2631 if (B.countTrailingZeros() < Mult2) 2632 return SE.getCouldNotCompute(); 2633 2634 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2635 // modulo (N / D). 2636 // 2637 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2638 // bit width during computations. 2639 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2640 APInt Mod(BW + 1, 0); 2641 Mod.set(BW - Mult2); // Mod = N / D 2642 APInt I = AD.multiplicativeInverse(Mod); 2643 2644 // 4. Compute the minimum unsigned root of the equation: 2645 // I * (B / D) mod (N / D) 2646 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2647 2648 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2649 // bits. 2650 return SE.getConstant(Result.trunc(BW)); 2651} 2652 2653/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2654/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2655/// might be the same) or two SCEVCouldNotCompute objects. 2656/// 2657static std::pair<SCEVHandle,SCEVHandle> 2658SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2659 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2660 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2661 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2662 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2663 2664 // We currently can only solve this if the coefficients are constants. 2665 if (!LC || !MC || !NC) { 2666 SCEV *CNC = SE.getCouldNotCompute(); 2667 return std::make_pair(CNC, CNC); 2668 } 2669 2670 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2671 const APInt &L = LC->getValue()->getValue(); 2672 const APInt &M = MC->getValue()->getValue(); 2673 const APInt &N = NC->getValue()->getValue(); 2674 APInt Two(BitWidth, 2); 2675 APInt Four(BitWidth, 4); 2676 2677 { 2678 using namespace APIntOps; 2679 const APInt& C = L; 2680 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2681 // The B coefficient is M-N/2 2682 APInt B(M); 2683 B -= sdiv(N,Two); 2684 2685 // The A coefficient is N/2 2686 APInt A(N.sdiv(Two)); 2687 2688 // Compute the B^2-4ac term. 2689 APInt SqrtTerm(B); 2690 SqrtTerm *= B; 2691 SqrtTerm -= Four * (A * C); 2692 2693 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2694 // integer value or else APInt::sqrt() will assert. 2695 APInt SqrtVal(SqrtTerm.sqrt()); 2696 2697 // Compute the two solutions for the quadratic formula. 2698 // The divisions must be performed as signed divisions. 2699 APInt NegB(-B); 2700 APInt TwoA( A << 1 ); 2701 if (TwoA.isMinValue()) { 2702 SCEV *CNC = SE.getCouldNotCompute(); 2703 return std::make_pair(CNC, CNC); 2704 } 2705 2706 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2707 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2708 2709 return std::make_pair(SE.getConstant(Solution1), 2710 SE.getConstant(Solution2)); 2711 } // end APIntOps namespace 2712} 2713 2714/// HowFarToZero - Return the number of times a backedge comparing the specified 2715/// value to zero will execute. If not computable, return UnknownValue 2716SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) { 2717 // If the value is a constant 2718 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2719 // If the value is already zero, the branch will execute zero times. 2720 if (C->getValue()->isZero()) return C; 2721 return UnknownValue; // Otherwise it will loop infinitely. 2722 } 2723 2724 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2725 if (!AddRec || AddRec->getLoop() != L) 2726 return UnknownValue; 2727 2728 if (AddRec->isAffine()) { 2729 // If this is an affine expression, the execution count of this branch is 2730 // the minimum unsigned root of the following equation: 2731 // 2732 // Start + Step*N = 0 (mod 2^BW) 2733 // 2734 // equivalent to: 2735 // 2736 // Step*N = -Start (mod 2^BW) 2737 // 2738 // where BW is the common bit width of Start and Step. 2739 2740 // Get the initial value for the loop. 2741 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2742 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2743 2744 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2745 2746 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2747 // For now we handle only constant steps. 2748 2749 // First, handle unitary steps. 2750 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2751 return getNegativeSCEV(Start); // N = -Start (as unsigned) 2752 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2753 return Start; // N = Start (as unsigned) 2754 2755 // Then, try to solve the above equation provided that Start is constant. 2756 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2757 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2758 -StartC->getValue()->getValue(), 2759 *this); 2760 } 2761 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2762 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2763 // the quadratic equation to solve it. 2764 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 2765 *this); 2766 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2767 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2768 if (R1) { 2769#if 0 2770 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 2771 << " sol#2: " << *R2 << "\n"; 2772#endif 2773 // Pick the smallest positive root value. 2774 if (ConstantInt *CB = 2775 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2776 R1->getValue(), R2->getValue()))) { 2777 if (CB->getZExtValue() == false) 2778 std::swap(R1, R2); // R1 is the minimum root now. 2779 2780 // We can only use this value if the chrec ends up with an exact zero 2781 // value at this index. When solving for "X*X != 5", for example, we 2782 // should not accept a root of 2. 2783 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 2784 if (Val->isZero()) 2785 return R1; // We found a quadratic root! 2786 } 2787 } 2788 } 2789 2790 return UnknownValue; 2791} 2792 2793/// HowFarToNonZero - Return the number of times a backedge checking the 2794/// specified value for nonzero will execute. If not computable, return 2795/// UnknownValue 2796SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) { 2797 // Loops that look like: while (X == 0) are very strange indeed. We don't 2798 // handle them yet except for the trivial case. This could be expanded in the 2799 // future as needed. 2800 2801 // If the value is a constant, check to see if it is known to be non-zero 2802 // already. If so, the backedge will execute zero times. 2803 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2804 if (!C->getValue()->isNullValue()) 2805 return getIntegerSCEV(0, C->getType()); 2806 return UnknownValue; // Otherwise it will loop infinitely. 2807 } 2808 2809 // We could implement others, but I really doubt anyone writes loops like 2810 // this, and if they did, they would already be constant folded. 2811 return UnknownValue; 2812} 2813 2814/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2815/// (which may not be an immediate predecessor) which has exactly one 2816/// successor from which BB is reachable, or null if no such block is 2817/// found. 2818/// 2819BasicBlock * 2820ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2821 // If the block has a unique predecessor, the predecessor must have 2822 // no other successors from which BB is reachable. 2823 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2824 return Pred; 2825 2826 // A loop's header is defined to be a block that dominates the loop. 2827 // If the loop has a preheader, it must be a block that has exactly 2828 // one successor that can reach BB. This is slightly more strict 2829 // than necessary, but works if critical edges are split. 2830 if (Loop *L = LI->getLoopFor(BB)) 2831 return L->getLoopPreheader(); 2832 2833 return 0; 2834} 2835 2836/// isLoopGuardedByCond - Test whether entry to the loop is protected by 2837/// a conditional between LHS and RHS. 2838bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 2839 ICmpInst::Predicate Pred, 2840 SCEV *LHS, SCEV *RHS) { 2841 BasicBlock *Preheader = L->getLoopPreheader(); 2842 BasicBlock *PreheaderDest = L->getHeader(); 2843 2844 // Starting at the preheader, climb up the predecessor chain, as long as 2845 // there are predecessors that can be found that have unique successors 2846 // leading to the original header. 2847 for (; Preheader; 2848 PreheaderDest = Preheader, 2849 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 2850 2851 BranchInst *LoopEntryPredicate = 2852 dyn_cast<BranchInst>(Preheader->getTerminator()); 2853 if (!LoopEntryPredicate || 2854 LoopEntryPredicate->isUnconditional()) 2855 continue; 2856 2857 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2858 if (!ICI) continue; 2859 2860 // Now that we found a conditional branch that dominates the loop, check to 2861 // see if it is the comparison we are looking for. 2862 Value *PreCondLHS = ICI->getOperand(0); 2863 Value *PreCondRHS = ICI->getOperand(1); 2864 ICmpInst::Predicate Cond; 2865 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2866 Cond = ICI->getPredicate(); 2867 else 2868 Cond = ICI->getInversePredicate(); 2869 2870 if (Cond == Pred) 2871 ; // An exact match. 2872 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 2873 ; // The actual condition is beyond sufficient. 2874 else 2875 // Check a few special cases. 2876 switch (Cond) { 2877 case ICmpInst::ICMP_UGT: 2878 if (Pred == ICmpInst::ICMP_ULT) { 2879 std::swap(PreCondLHS, PreCondRHS); 2880 Cond = ICmpInst::ICMP_ULT; 2881 break; 2882 } 2883 continue; 2884 case ICmpInst::ICMP_SGT: 2885 if (Pred == ICmpInst::ICMP_SLT) { 2886 std::swap(PreCondLHS, PreCondRHS); 2887 Cond = ICmpInst::ICMP_SLT; 2888 break; 2889 } 2890 continue; 2891 case ICmpInst::ICMP_NE: 2892 // Expressions like (x >u 0) are often canonicalized to (x != 0), 2893 // so check for this case by checking if the NE is comparing against 2894 // a minimum or maximum constant. 2895 if (!ICmpInst::isTrueWhenEqual(Pred)) 2896 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 2897 const APInt &A = CI->getValue(); 2898 switch (Pred) { 2899 case ICmpInst::ICMP_SLT: 2900 if (A.isMaxSignedValue()) break; 2901 continue; 2902 case ICmpInst::ICMP_SGT: 2903 if (A.isMinSignedValue()) break; 2904 continue; 2905 case ICmpInst::ICMP_ULT: 2906 if (A.isMaxValue()) break; 2907 continue; 2908 case ICmpInst::ICMP_UGT: 2909 if (A.isMinValue()) break; 2910 continue; 2911 default: 2912 continue; 2913 } 2914 Cond = ICmpInst::ICMP_NE; 2915 // NE is symmetric but the original comparison may not be. Swap 2916 // the operands if necessary so that they match below. 2917 if (isa<SCEVConstant>(LHS)) 2918 std::swap(PreCondLHS, PreCondRHS); 2919 break; 2920 } 2921 continue; 2922 default: 2923 // We weren't able to reconcile the condition. 2924 continue; 2925 } 2926 2927 if (!PreCondLHS->getType()->isInteger()) continue; 2928 2929 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 2930 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 2931 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 2932 (LHS == getNotSCEV(PreCondRHSSCEV) && 2933 RHS == getNotSCEV(PreCondLHSSCEV))) 2934 return true; 2935 } 2936 2937 return false; 2938} 2939 2940/// HowManyLessThans - Return the number of times a backedge containing the 2941/// specified less-than comparison will execute. If not computable, return 2942/// UnknownValue. 2943SCEVHandle ScalarEvolution:: 2944HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2945 // Only handle: "ADDREC < LoopInvariant". 2946 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2947 2948 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2949 if (!AddRec || AddRec->getLoop() != L) 2950 return UnknownValue; 2951 2952 if (AddRec->isAffine()) { 2953 // FORNOW: We only support unit strides. 2954 SCEVHandle One = getIntegerSCEV(1, RHS->getType()); 2955 if (AddRec->getOperand(1) != One) 2956 return UnknownValue; 2957 2958 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2959 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2960 // Note that we cannot simply return max(m-n,0) because it's not safe to 2961 // treat m-n as signed nor unsigned due to overflow possibility. 2962 2963 // First, we get the value of the LHS in the first iteration: n 2964 SCEVHandle Start = AddRec->getOperand(0); 2965 2966 if (isLoopGuardedByCond(L, 2967 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 2968 getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2969 // Since we know that the condition is true in order to enter the loop, 2970 // we know that it will run exactly m-n times. 2971 return getMinusSCEV(RHS, Start); 2972 } else { 2973 // Then, we get the value of the LHS in the first iteration in which the 2974 // above condition doesn't hold. This equals to max(m,n). 2975 SCEVHandle End = isSigned ? getSMaxExpr(RHS, Start) 2976 : getUMaxExpr(RHS, Start); 2977 2978 // Finally, we subtract these two values to get the number of times the 2979 // backedge is executed: max(m,n)-n. 2980 return getMinusSCEV(End, Start); 2981 } 2982 } 2983 2984 return UnknownValue; 2985} 2986 2987/// getNumIterationsInRange - Return the number of iterations of this loop that 2988/// produce values in the specified constant range. Another way of looking at 2989/// this is that it returns the first iteration number where the value is not in 2990/// the condition, thus computing the exit count. If the iteration count can't 2991/// be computed, an instance of SCEVCouldNotCompute is returned. 2992SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2993 ScalarEvolution &SE) const { 2994 if (Range.isFullSet()) // Infinite loop. 2995 return SE.getCouldNotCompute(); 2996 2997 // If the start is a non-zero constant, shift the range to simplify things. 2998 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2999 if (!SC->getValue()->isZero()) { 3000 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3001 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3002 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3003 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 3004 return ShiftedAddRec->getNumIterationsInRange( 3005 Range.subtract(SC->getValue()->getValue()), SE); 3006 // This is strange and shouldn't happen. 3007 return SE.getCouldNotCompute(); 3008 } 3009 3010 // The only time we can solve this is when we have all constant indices. 3011 // Otherwise, we cannot determine the overflow conditions. 3012 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3013 if (!isa<SCEVConstant>(getOperand(i))) 3014 return SE.getCouldNotCompute(); 3015 3016 3017 // Okay at this point we know that all elements of the chrec are constants and 3018 // that the start element is zero. 3019 3020 // First check to see if the range contains zero. If not, the first 3021 // iteration exits. 3022 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3023 if (!Range.contains(APInt(BitWidth, 0))) 3024 return SE.getConstant(ConstantInt::get(getType(),0)); 3025 3026 if (isAffine()) { 3027 // If this is an affine expression then we have this situation: 3028 // Solve {0,+,A} in Range === Ax in Range 3029 3030 // We know that zero is in the range. If A is positive then we know that 3031 // the upper value of the range must be the first possible exit value. 3032 // If A is negative then the lower of the range is the last possible loop 3033 // value. Also note that we already checked for a full range. 3034 APInt One(BitWidth,1); 3035 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3036 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3037 3038 // The exit value should be (End+A)/A. 3039 APInt ExitVal = (End + A).udiv(A); 3040 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3041 3042 // Evaluate at the exit value. If we really did fall out of the valid 3043 // range, then we computed our trip count, otherwise wrap around or other 3044 // things must have happened. 3045 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3046 if (Range.contains(Val->getValue())) 3047 return SE.getCouldNotCompute(); // Something strange happened 3048 3049 // Ensure that the previous value is in the range. This is a sanity check. 3050 assert(Range.contains( 3051 EvaluateConstantChrecAtConstant(this, 3052 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3053 "Linear scev computation is off in a bad way!"); 3054 return SE.getConstant(ExitValue); 3055 } else if (isQuadratic()) { 3056 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3057 // quadratic equation to solve it. To do this, we must frame our problem in 3058 // terms of figuring out when zero is crossed, instead of when 3059 // Range.getUpper() is crossed. 3060 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3061 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3062 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3063 3064 // Next, solve the constructed addrec 3065 std::pair<SCEVHandle,SCEVHandle> Roots = 3066 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3067 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3068 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3069 if (R1) { 3070 // Pick the smallest positive root value. 3071 if (ConstantInt *CB = 3072 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3073 R1->getValue(), R2->getValue()))) { 3074 if (CB->getZExtValue() == false) 3075 std::swap(R1, R2); // R1 is the minimum root now. 3076 3077 // Make sure the root is not off by one. The returned iteration should 3078 // not be in the range, but the previous one should be. When solving 3079 // for "X*X < 5", for example, we should not return a root of 2. 3080 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3081 R1->getValue(), 3082 SE); 3083 if (Range.contains(R1Val->getValue())) { 3084 // The next iteration must be out of the range... 3085 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3086 3087 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3088 if (!Range.contains(R1Val->getValue())) 3089 return SE.getConstant(NextVal); 3090 return SE.getCouldNotCompute(); // Something strange happened 3091 } 3092 3093 // If R1 was not in the range, then it is a good return value. Make 3094 // sure that R1-1 WAS in the range though, just in case. 3095 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3096 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3097 if (Range.contains(R1Val->getValue())) 3098 return R1; 3099 return SE.getCouldNotCompute(); // Something strange happened 3100 } 3101 } 3102 } 3103 3104 return SE.getCouldNotCompute(); 3105} 3106 3107 3108 3109//===----------------------------------------------------------------------===// 3110// ScalarEvolution Class Implementation 3111//===----------------------------------------------------------------------===// 3112 3113ScalarEvolution::ScalarEvolution() 3114 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3115} 3116 3117bool ScalarEvolution::runOnFunction(Function &F) { 3118 this->F = &F; 3119 LI = &getAnalysis<LoopInfo>(); 3120 TD = getAnalysisIfAvailable<TargetData>(); 3121 return false; 3122} 3123 3124void ScalarEvolution::releaseMemory() { 3125 Scalars.clear(); 3126 BackedgeTakenCounts.clear(); 3127 ConstantEvolutionLoopExitValue.clear(); 3128} 3129 3130void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3131 AU.setPreservesAll(); 3132 AU.addRequiredTransitive<LoopInfo>(); 3133} 3134 3135bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3136 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3137} 3138 3139static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3140 const Loop *L) { 3141 // Print all inner loops first 3142 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3143 PrintLoopInfo(OS, SE, *I); 3144 3145 OS << "Loop " << L->getHeader()->getName() << ": "; 3146 3147 SmallVector<BasicBlock*, 8> ExitBlocks; 3148 L->getExitBlocks(ExitBlocks); 3149 if (ExitBlocks.size() != 1) 3150 OS << "<multiple exits> "; 3151 3152 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3153 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3154 } else { 3155 OS << "Unpredictable backedge-taken count. "; 3156 } 3157 3158 OS << "\n"; 3159} 3160 3161void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3162 // ScalarEvolution's implementaiton of the print method is to print 3163 // out SCEV values of all instructions that are interesting. Doing 3164 // this potentially causes it to create new SCEV objects though, 3165 // which technically conflicts with the const qualifier. This isn't 3166 // observable from outside the class though (the hasSCEV function 3167 // notwithstanding), so casting away the const isn't dangerous. 3168 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3169 3170 OS << "Classifying expressions for: " << F->getName() << "\n"; 3171 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3172 if (I->getType()->isInteger()) { 3173 OS << *I; 3174 OS << " --> "; 3175 SCEVHandle SV = SE.getSCEV(&*I); 3176 SV->print(OS); 3177 OS << "\t\t"; 3178 3179 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3180 OS << "Exits: "; 3181 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3182 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3183 OS << "<<Unknown>>"; 3184 } else { 3185 OS << *ExitValue; 3186 } 3187 } 3188 3189 3190 OS << "\n"; 3191 } 3192 3193 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3194 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3195 PrintLoopInfo(OS, &SE, *I); 3196} 3197 3198void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3199 raw_os_ostream OS(o); 3200 print(OS, M); 3201} 3202