ScalarEvolution.cpp revision 2c73d5fb9e3d68c96bb2242bbbf2930a8db10343
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 if (CI->isNullValue()) 1758 return getSCEV(U->getOperand(1)); 1759 const APInt &A = CI->getValue(); 1760 unsigned Ones = A.countTrailingOnes(); 1761 if (APIntOps::isMask(Ones, A)) 1762 return 1763 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 1764 IntegerType::get(Ones)), 1765 U->getType()); 1766 } 1767 break; 1768 case Instruction::Or: 1769 // If the RHS of the Or is a constant, we may have something like: 1770 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1771 // optimizations will transparently handle this case. 1772 // 1773 // In order for this transformation to be safe, the LHS must be of the 1774 // form X*(2^n) and the Or constant must be less than 2^n. 1775 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1776 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1777 const APInt &CIVal = CI->getValue(); 1778 if (GetMinTrailingZeros(LHS, *this) >= 1779 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1780 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 1781 } 1782 break; 1783 case Instruction::Xor: 1784 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1785 // If the RHS of the xor is a signbit, then this is just an add. 1786 // Instcombine turns add of signbit into xor as a strength reduction step. 1787 if (CI->getValue().isSignBit()) 1788 return getAddExpr(getSCEV(U->getOperand(0)), 1789 getSCEV(U->getOperand(1))); 1790 1791 // If the RHS of xor is -1, then this is a not operation. 1792 else if (CI->isAllOnesValue()) 1793 return getNotSCEV(getSCEV(U->getOperand(0))); 1794 } 1795 break; 1796 1797 case Instruction::Shl: 1798 // Turn shift left of a constant amount into a multiply. 1799 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1800 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1801 Constant *X = ConstantInt::get( 1802 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1803 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1804 } 1805 break; 1806 1807 case Instruction::LShr: 1808 // Turn logical shift right of a constant into a unsigned divide. 1809 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1810 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1811 Constant *X = ConstantInt::get( 1812 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1813 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1814 } 1815 break; 1816 1817 case Instruction::AShr: 1818 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 1819 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 1820 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 1821 if (L->getOpcode() == Instruction::Shl && 1822 L->getOperand(1) == U->getOperand(1)) { 1823 unsigned BitWidth = getTypeSizeInBits(U->getType()); 1824 uint64_t Amt = BitWidth - CI->getZExtValue(); 1825 if (Amt == BitWidth) 1826 return getSCEV(L->getOperand(0)); // shift by zero --> noop 1827 if (Amt > BitWidth) 1828 return getIntegerSCEV(0, U->getType()); // value is undefined 1829 return 1830 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 1831 IntegerType::get(Amt)), 1832 U->getType()); 1833 } 1834 break; 1835 1836 case Instruction::Trunc: 1837 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1838 1839 case Instruction::ZExt: 1840 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1841 1842 case Instruction::SExt: 1843 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1844 1845 case Instruction::BitCast: 1846 // BitCasts are no-op casts so we just eliminate the cast. 1847 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 1848 return getSCEV(U->getOperand(0)); 1849 break; 1850 1851 case Instruction::IntToPtr: 1852 if (!TD) break; // Without TD we can't analyze pointers. 1853 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1854 TD->getIntPtrType()); 1855 1856 case Instruction::PtrToInt: 1857 if (!TD) break; // Without TD we can't analyze pointers. 1858 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1859 U->getType()); 1860 1861 case Instruction::GetElementPtr: { 1862 if (!TD) break; // Without TD we can't analyze pointers. 1863 const Type *IntPtrTy = TD->getIntPtrType(); 1864 Value *Base = U->getOperand(0); 1865 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1866 gep_type_iterator GTI = gep_type_begin(U); 1867 for (GetElementPtrInst::op_iterator I = next(U->op_begin()), 1868 E = U->op_end(); 1869 I != E; ++I) { 1870 Value *Index = *I; 1871 // Compute the (potentially symbolic) offset in bytes for this index. 1872 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1873 // For a struct, add the member offset. 1874 const StructLayout &SL = *TD->getStructLayout(STy); 1875 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1876 uint64_t Offset = SL.getElementOffset(FieldNo); 1877 TotalOffset = getAddExpr(TotalOffset, 1878 getIntegerSCEV(Offset, IntPtrTy)); 1879 } else { 1880 // For an array, add the element offset, explicitly scaled. 1881 SCEVHandle LocalOffset = getSCEV(Index); 1882 if (!isa<PointerType>(LocalOffset->getType())) 1883 // Getelementptr indicies are signed. 1884 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1885 IntPtrTy); 1886 LocalOffset = 1887 getMulExpr(LocalOffset, 1888 getIntegerSCEV(TD->getTypePaddedSize(*GTI), 1889 IntPtrTy)); 1890 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1891 } 1892 } 1893 return getAddExpr(getSCEV(Base), TotalOffset); 1894 } 1895 1896 case Instruction::PHI: 1897 return createNodeForPHI(cast<PHINode>(U)); 1898 1899 case Instruction::Select: 1900 // This could be a smax or umax that was lowered earlier. 1901 // Try to recover it. 1902 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1903 Value *LHS = ICI->getOperand(0); 1904 Value *RHS = ICI->getOperand(1); 1905 switch (ICI->getPredicate()) { 1906 case ICmpInst::ICMP_SLT: 1907 case ICmpInst::ICMP_SLE: 1908 std::swap(LHS, RHS); 1909 // fall through 1910 case ICmpInst::ICMP_SGT: 1911 case ICmpInst::ICMP_SGE: 1912 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1913 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1914 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1915 // ~smax(~x, ~y) == smin(x, y). 1916 return getNotSCEV(getSMaxExpr( 1917 getNotSCEV(getSCEV(LHS)), 1918 getNotSCEV(getSCEV(RHS)))); 1919 break; 1920 case ICmpInst::ICMP_ULT: 1921 case ICmpInst::ICMP_ULE: 1922 std::swap(LHS, RHS); 1923 // fall through 1924 case ICmpInst::ICMP_UGT: 1925 case ICmpInst::ICMP_UGE: 1926 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1927 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1928 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1929 // ~umax(~x, ~y) == umin(x, y) 1930 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 1931 getNotSCEV(getSCEV(RHS)))); 1932 break; 1933 default: 1934 break; 1935 } 1936 } 1937 1938 default: // We cannot analyze this expression. 1939 break; 1940 } 1941 1942 return getUnknown(V); 1943} 1944 1945 1946 1947//===----------------------------------------------------------------------===// 1948// Iteration Count Computation Code 1949// 1950 1951/// getBackedgeTakenCount - If the specified loop has a predictable 1952/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 1953/// object. The backedge-taken count is the number of times the loop header 1954/// will be branched to from within the loop. This is one less than the 1955/// trip count of the loop, since it doesn't count the first iteration, 1956/// when the header is branched to from outside the loop. 1957/// 1958/// Note that it is not valid to call this method on a loop without a 1959/// loop-invariant backedge-taken count (see 1960/// hasLoopInvariantBackedgeTakenCount). 1961/// 1962SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 1963 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L); 1964 if (I == BackedgeTakenCounts.end()) { 1965 SCEVHandle ItCount = ComputeBackedgeTakenCount(L); 1966 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first; 1967 if (ItCount != UnknownValue) { 1968 assert(ItCount->isLoopInvariant(L) && 1969 "Computed trip count isn't loop invariant for loop!"); 1970 ++NumTripCountsComputed; 1971 } else if (isa<PHINode>(L->getHeader()->begin())) { 1972 // Only count loops that have phi nodes as not being computable. 1973 ++NumTripCountsNotComputed; 1974 } 1975 } 1976 return I->second; 1977} 1978 1979/// forgetLoopBackedgeTakenCount - This method should be called by the 1980/// client when it has changed a loop in a way that may effect 1981/// ScalarEvolution's ability to compute a trip count, or if the loop 1982/// is deleted. 1983void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 1984 BackedgeTakenCounts.erase(L); 1985} 1986 1987/// ComputeBackedgeTakenCount - Compute the number of times the backedge 1988/// of the specified loop will execute. 1989SCEVHandle ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 1990 // If the loop has a non-one exit block count, we can't analyze it. 1991 SmallVector<BasicBlock*, 8> ExitBlocks; 1992 L->getExitBlocks(ExitBlocks); 1993 if (ExitBlocks.size() != 1) return UnknownValue; 1994 1995 // Okay, there is one exit block. Try to find the condition that causes the 1996 // loop to be exited. 1997 BasicBlock *ExitBlock = ExitBlocks[0]; 1998 1999 BasicBlock *ExitingBlock = 0; 2000 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 2001 PI != E; ++PI) 2002 if (L->contains(*PI)) { 2003 if (ExitingBlock == 0) 2004 ExitingBlock = *PI; 2005 else 2006 return UnknownValue; // More than one block exiting! 2007 } 2008 assert(ExitingBlock && "No exits from loop, something is broken!"); 2009 2010 // Okay, we've computed the exiting block. See what condition causes us to 2011 // exit. 2012 // 2013 // FIXME: we should be able to handle switch instructions (with a single exit) 2014 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2015 if (ExitBr == 0) return UnknownValue; 2016 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2017 2018 // At this point, we know we have a conditional branch that determines whether 2019 // the loop is exited. However, we don't know if the branch is executed each 2020 // time through the loop. If not, then the execution count of the branch will 2021 // not be equal to the trip count of the loop. 2022 // 2023 // Currently we check for this by checking to see if the Exit branch goes to 2024 // the loop header. If so, we know it will always execute the same number of 2025 // times as the loop. We also handle the case where the exit block *is* the 2026 // loop header. This is common for un-rotated loops. More extensive analysis 2027 // could be done to handle more cases here. 2028 if (ExitBr->getSuccessor(0) != L->getHeader() && 2029 ExitBr->getSuccessor(1) != L->getHeader() && 2030 ExitBr->getParent() != L->getHeader()) 2031 return UnknownValue; 2032 2033 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2034 2035 // If it's not an integer comparison then compute it the hard way. 2036 // Note that ICmpInst deals with pointer comparisons too so we must check 2037 // the type of the operand. 2038 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2039 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2040 ExitBr->getSuccessor(0) == ExitBlock); 2041 2042 // If the condition was exit on true, convert the condition to exit on false 2043 ICmpInst::Predicate Cond; 2044 if (ExitBr->getSuccessor(1) == ExitBlock) 2045 Cond = ExitCond->getPredicate(); 2046 else 2047 Cond = ExitCond->getInversePredicate(); 2048 2049 // Handle common loops like: for (X = "string"; *X; ++X) 2050 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2051 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2052 SCEVHandle ItCnt = 2053 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2054 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2055 } 2056 2057 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2058 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2059 2060 // Try to evaluate any dependencies out of the loop. 2061 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2062 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2063 Tmp = getSCEVAtScope(RHS, L); 2064 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2065 2066 // At this point, we would like to compute how many iterations of the 2067 // loop the predicate will return true for these inputs. 2068 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2069 // If there is a loop-invariant, force it into the RHS. 2070 std::swap(LHS, RHS); 2071 Cond = ICmpInst::getSwappedPredicate(Cond); 2072 } 2073 2074 // If we have a comparison of a chrec against a constant, try to use value 2075 // ranges to answer this query. 2076 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2077 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2078 if (AddRec->getLoop() == L) { 2079 // Form the comparison range using the constant of the correct type so 2080 // that the ConstantRange class knows to do a signed or unsigned 2081 // comparison. 2082 ConstantInt *CompVal = RHSC->getValue(); 2083 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2084 CompVal = dyn_cast<ConstantInt>( 2085 ConstantExpr::getBitCast(CompVal, RealTy)); 2086 if (CompVal) { 2087 // Form the constant range. 2088 ConstantRange CompRange( 2089 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2090 2091 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2092 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2093 } 2094 } 2095 2096 switch (Cond) { 2097 case ICmpInst::ICMP_NE: { // while (X != Y) 2098 // Convert to: while (X-Y != 0) 2099 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2100 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2101 break; 2102 } 2103 case ICmpInst::ICMP_EQ: { 2104 // Convert to: while (X-Y == 0) // while (X == Y) 2105 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2106 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2107 break; 2108 } 2109 case ICmpInst::ICMP_SLT: { 2110 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2111 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2112 break; 2113 } 2114 case ICmpInst::ICMP_SGT: { 2115 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2116 getNotSCEV(RHS), L, true); 2117 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2118 break; 2119 } 2120 case ICmpInst::ICMP_ULT: { 2121 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2122 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2123 break; 2124 } 2125 case ICmpInst::ICMP_UGT: { 2126 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2127 getNotSCEV(RHS), L, false); 2128 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2129 break; 2130 } 2131 default: 2132#if 0 2133 errs() << "ComputeBackedgeTakenCount "; 2134 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2135 errs() << "[unsigned] "; 2136 errs() << *LHS << " " 2137 << Instruction::getOpcodeName(Instruction::ICmp) 2138 << " " << *RHS << "\n"; 2139#endif 2140 break; 2141 } 2142 return 2143 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2144 ExitBr->getSuccessor(0) == ExitBlock); 2145} 2146 2147static ConstantInt * 2148EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2149 ScalarEvolution &SE) { 2150 SCEVHandle InVal = SE.getConstant(C); 2151 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2152 assert(isa<SCEVConstant>(Val) && 2153 "Evaluation of SCEV at constant didn't fold correctly?"); 2154 return cast<SCEVConstant>(Val)->getValue(); 2155} 2156 2157/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2158/// and a GEP expression (missing the pointer index) indexing into it, return 2159/// the addressed element of the initializer or null if the index expression is 2160/// invalid. 2161static Constant * 2162GetAddressedElementFromGlobal(GlobalVariable *GV, 2163 const std::vector<ConstantInt*> &Indices) { 2164 Constant *Init = GV->getInitializer(); 2165 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2166 uint64_t Idx = Indices[i]->getZExtValue(); 2167 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2168 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2169 Init = cast<Constant>(CS->getOperand(Idx)); 2170 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2171 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2172 Init = cast<Constant>(CA->getOperand(Idx)); 2173 } else if (isa<ConstantAggregateZero>(Init)) { 2174 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2175 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2176 Init = Constant::getNullValue(STy->getElementType(Idx)); 2177 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2178 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2179 Init = Constant::getNullValue(ATy->getElementType()); 2180 } else { 2181 assert(0 && "Unknown constant aggregate type!"); 2182 } 2183 return 0; 2184 } else { 2185 return 0; // Unknown initializer type 2186 } 2187 } 2188 return Init; 2189} 2190 2191/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2192/// 'icmp op load X, cst', try to see if we can compute the backedge 2193/// execution count. 2194SCEVHandle ScalarEvolution:: 2195ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2196 const Loop *L, 2197 ICmpInst::Predicate predicate) { 2198 if (LI->isVolatile()) return UnknownValue; 2199 2200 // Check to see if the loaded pointer is a getelementptr of a global. 2201 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2202 if (!GEP) return UnknownValue; 2203 2204 // Make sure that it is really a constant global we are gepping, with an 2205 // initializer, and make sure the first IDX is really 0. 2206 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2207 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2208 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2209 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2210 return UnknownValue; 2211 2212 // Okay, we allow one non-constant index into the GEP instruction. 2213 Value *VarIdx = 0; 2214 std::vector<ConstantInt*> Indexes; 2215 unsigned VarIdxNum = 0; 2216 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2217 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2218 Indexes.push_back(CI); 2219 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2220 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2221 VarIdx = GEP->getOperand(i); 2222 VarIdxNum = i-2; 2223 Indexes.push_back(0); 2224 } 2225 2226 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2227 // Check to see if X is a loop variant variable value now. 2228 SCEVHandle Idx = getSCEV(VarIdx); 2229 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2230 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2231 2232 // We can only recognize very limited forms of loop index expressions, in 2233 // particular, only affine AddRec's like {C1,+,C2}. 2234 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2235 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2236 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2237 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2238 return UnknownValue; 2239 2240 unsigned MaxSteps = MaxBruteForceIterations; 2241 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2242 ConstantInt *ItCst = 2243 ConstantInt::get(IdxExpr->getType(), IterationNum); 2244 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2245 2246 // Form the GEP offset. 2247 Indexes[VarIdxNum] = Val; 2248 2249 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2250 if (Result == 0) break; // Cannot compute! 2251 2252 // Evaluate the condition for this iteration. 2253 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2254 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2255 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2256#if 0 2257 errs() << "\n***\n*** Computed loop count " << *ItCst 2258 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2259 << "***\n"; 2260#endif 2261 ++NumArrayLenItCounts; 2262 return getConstant(ItCst); // Found terminating iteration! 2263 } 2264 } 2265 return UnknownValue; 2266} 2267 2268 2269/// CanConstantFold - Return true if we can constant fold an instruction of the 2270/// specified type, assuming that all operands were constants. 2271static bool CanConstantFold(const Instruction *I) { 2272 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2273 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2274 return true; 2275 2276 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2277 if (const Function *F = CI->getCalledFunction()) 2278 return canConstantFoldCallTo(F); 2279 return false; 2280} 2281 2282/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2283/// in the loop that V is derived from. We allow arbitrary operations along the 2284/// way, but the operands of an operation must either be constants or a value 2285/// derived from a constant PHI. If this expression does not fit with these 2286/// constraints, return null. 2287static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2288 // If this is not an instruction, or if this is an instruction outside of the 2289 // loop, it can't be derived from a loop PHI. 2290 Instruction *I = dyn_cast<Instruction>(V); 2291 if (I == 0 || !L->contains(I->getParent())) return 0; 2292 2293 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2294 if (L->getHeader() == I->getParent()) 2295 return PN; 2296 else 2297 // We don't currently keep track of the control flow needed to evaluate 2298 // PHIs, so we cannot handle PHIs inside of loops. 2299 return 0; 2300 } 2301 2302 // If we won't be able to constant fold this expression even if the operands 2303 // are constants, return early. 2304 if (!CanConstantFold(I)) return 0; 2305 2306 // Otherwise, we can evaluate this instruction if all of its operands are 2307 // constant or derived from a PHI node themselves. 2308 PHINode *PHI = 0; 2309 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2310 if (!(isa<Constant>(I->getOperand(Op)) || 2311 isa<GlobalValue>(I->getOperand(Op)))) { 2312 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2313 if (P == 0) return 0; // Not evolving from PHI 2314 if (PHI == 0) 2315 PHI = P; 2316 else if (PHI != P) 2317 return 0; // Evolving from multiple different PHIs. 2318 } 2319 2320 // This is a expression evolving from a constant PHI! 2321 return PHI; 2322} 2323 2324/// EvaluateExpression - Given an expression that passes the 2325/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2326/// in the loop has the value PHIVal. If we can't fold this expression for some 2327/// reason, return null. 2328static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2329 if (isa<PHINode>(V)) return PHIVal; 2330 if (Constant *C = dyn_cast<Constant>(V)) return C; 2331 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2332 Instruction *I = cast<Instruction>(V); 2333 2334 std::vector<Constant*> Operands; 2335 Operands.resize(I->getNumOperands()); 2336 2337 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2338 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2339 if (Operands[i] == 0) return 0; 2340 } 2341 2342 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2343 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2344 &Operands[0], Operands.size()); 2345 else 2346 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2347 &Operands[0], Operands.size()); 2348} 2349 2350/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2351/// in the header of its containing loop, we know the loop executes a 2352/// constant number of times, and the PHI node is just a recurrence 2353/// involving constants, fold it. 2354Constant *ScalarEvolution:: 2355getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2356 std::map<PHINode*, Constant*>::iterator I = 2357 ConstantEvolutionLoopExitValue.find(PN); 2358 if (I != ConstantEvolutionLoopExitValue.end()) 2359 return I->second; 2360 2361 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2362 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2363 2364 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2365 2366 // Since the loop is canonicalized, the PHI node must have two entries. One 2367 // entry must be a constant (coming in from outside of the loop), and the 2368 // second must be derived from the same PHI. 2369 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2370 Constant *StartCST = 2371 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2372 if (StartCST == 0) 2373 return RetVal = 0; // Must be a constant. 2374 2375 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2376 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2377 if (PN2 != PN) 2378 return RetVal = 0; // Not derived from same PHI. 2379 2380 // Execute the loop symbolically to determine the exit value. 2381 if (BEs.getActiveBits() >= 32) 2382 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2383 2384 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2385 unsigned IterationNum = 0; 2386 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2387 if (IterationNum == NumIterations) 2388 return RetVal = PHIVal; // Got exit value! 2389 2390 // Compute the value of the PHI node for the next iteration. 2391 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2392 if (NextPHI == PHIVal) 2393 return RetVal = NextPHI; // Stopped evolving! 2394 if (NextPHI == 0) 2395 return 0; // Couldn't evaluate! 2396 PHIVal = NextPHI; 2397 } 2398} 2399 2400/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2401/// constant number of times (the condition evolves only from constants), 2402/// try to evaluate a few iterations of the loop until we get the exit 2403/// condition gets a value of ExitWhen (true or false). If we cannot 2404/// evaluate the trip count of the loop, return UnknownValue. 2405SCEVHandle ScalarEvolution:: 2406ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2407 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2408 if (PN == 0) return UnknownValue; 2409 2410 // Since the loop is canonicalized, the PHI node must have two entries. One 2411 // entry must be a constant (coming in from outside of the loop), and the 2412 // second must be derived from the same PHI. 2413 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2414 Constant *StartCST = 2415 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2416 if (StartCST == 0) return UnknownValue; // Must be a constant. 2417 2418 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2419 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2420 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2421 2422 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2423 // the loop symbolically to determine when the condition gets a value of 2424 // "ExitWhen". 2425 unsigned IterationNum = 0; 2426 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2427 for (Constant *PHIVal = StartCST; 2428 IterationNum != MaxIterations; ++IterationNum) { 2429 ConstantInt *CondVal = 2430 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2431 2432 // Couldn't symbolically evaluate. 2433 if (!CondVal) return UnknownValue; 2434 2435 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2436 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2437 ++NumBruteForceTripCountsComputed; 2438 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2439 } 2440 2441 // Compute the value of the PHI node for the next iteration. 2442 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2443 if (NextPHI == 0 || NextPHI == PHIVal) 2444 return UnknownValue; // Couldn't evaluate or not making progress... 2445 PHIVal = NextPHI; 2446 } 2447 2448 // Too many iterations were needed to evaluate. 2449 return UnknownValue; 2450} 2451 2452/// getSCEVAtScope - Compute the value of the specified expression within the 2453/// indicated loop (which may be null to indicate in no loop). If the 2454/// expression cannot be evaluated, return UnknownValue. 2455SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) { 2456 // FIXME: this should be turned into a virtual method on SCEV! 2457 2458 if (isa<SCEVConstant>(V)) return V; 2459 2460 // If this instruction is evolved from a constant-evolving PHI, compute the 2461 // exit value from the loop without using SCEVs. 2462 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2463 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2464 const Loop *LI = (*this->LI)[I->getParent()]; 2465 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2466 if (PHINode *PN = dyn_cast<PHINode>(I)) 2467 if (PN->getParent() == LI->getHeader()) { 2468 // Okay, there is no closed form solution for the PHI node. Check 2469 // to see if the loop that contains it has a known backedge-taken 2470 // count. If so, we may be able to force computation of the exit 2471 // value. 2472 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2473 if (SCEVConstant *BTCC = 2474 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2475 // Okay, we know how many times the containing loop executes. If 2476 // this is a constant evolving PHI node, get the final value at 2477 // the specified iteration number. 2478 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2479 BTCC->getValue()->getValue(), 2480 LI); 2481 if (RV) return getUnknown(RV); 2482 } 2483 } 2484 2485 // Okay, this is an expression that we cannot symbolically evaluate 2486 // into a SCEV. Check to see if it's possible to symbolically evaluate 2487 // the arguments into constants, and if so, try to constant propagate the 2488 // result. This is particularly useful for computing loop exit values. 2489 if (CanConstantFold(I)) { 2490 std::vector<Constant*> Operands; 2491 Operands.reserve(I->getNumOperands()); 2492 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2493 Value *Op = I->getOperand(i); 2494 if (Constant *C = dyn_cast<Constant>(Op)) { 2495 Operands.push_back(C); 2496 } else { 2497 // If any of the operands is non-constant and if they are 2498 // non-integer and non-pointer, don't even try to analyze them 2499 // with scev techniques. 2500 if (!isa<IntegerType>(Op->getType()) && 2501 !isa<PointerType>(Op->getType())) 2502 return V; 2503 2504 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2505 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2506 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2507 Op->getType(), 2508 false)); 2509 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2510 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2511 Operands.push_back(ConstantExpr::getIntegerCast(C, 2512 Op->getType(), 2513 false)); 2514 else 2515 return V; 2516 } else { 2517 return V; 2518 } 2519 } 2520 } 2521 2522 Constant *C; 2523 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2524 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2525 &Operands[0], Operands.size()); 2526 else 2527 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2528 &Operands[0], Operands.size()); 2529 return getUnknown(C); 2530 } 2531 } 2532 2533 // This is some other type of SCEVUnknown, just return it. 2534 return V; 2535 } 2536 2537 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2538 // Avoid performing the look-up in the common case where the specified 2539 // expression has no loop-variant portions. 2540 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2541 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2542 if (OpAtScope != Comm->getOperand(i)) { 2543 if (OpAtScope == UnknownValue) return UnknownValue; 2544 // Okay, at least one of these operands is loop variant but might be 2545 // foldable. Build a new instance of the folded commutative expression. 2546 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2547 NewOps.push_back(OpAtScope); 2548 2549 for (++i; i != e; ++i) { 2550 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2551 if (OpAtScope == UnknownValue) return UnknownValue; 2552 NewOps.push_back(OpAtScope); 2553 } 2554 if (isa<SCEVAddExpr>(Comm)) 2555 return getAddExpr(NewOps); 2556 if (isa<SCEVMulExpr>(Comm)) 2557 return getMulExpr(NewOps); 2558 if (isa<SCEVSMaxExpr>(Comm)) 2559 return getSMaxExpr(NewOps); 2560 if (isa<SCEVUMaxExpr>(Comm)) 2561 return getUMaxExpr(NewOps); 2562 assert(0 && "Unknown commutative SCEV type!"); 2563 } 2564 } 2565 // If we got here, all operands are loop invariant. 2566 return Comm; 2567 } 2568 2569 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2570 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2571 if (LHS == UnknownValue) return LHS; 2572 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2573 if (RHS == UnknownValue) return RHS; 2574 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2575 return Div; // must be loop invariant 2576 return getUDivExpr(LHS, RHS); 2577 } 2578 2579 // If this is a loop recurrence for a loop that does not contain L, then we 2580 // are dealing with the final value computed by the loop. 2581 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2582 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2583 // To evaluate this recurrence, we need to know how many times the AddRec 2584 // loop iterates. Compute this now. 2585 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2586 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2587 2588 // Then, evaluate the AddRec. 2589 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2590 } 2591 return UnknownValue; 2592 } 2593 2594 //assert(0 && "Unknown SCEV type!"); 2595 return UnknownValue; 2596} 2597 2598/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2599/// at the specified scope in the program. The L value specifies a loop 2600/// nest to evaluate the expression at, where null is the top-level or a 2601/// specified loop is immediately inside of the loop. 2602/// 2603/// This method can be used to compute the exit value for a variable defined 2604/// in a loop by querying what the value will hold in the parent loop. 2605/// 2606/// If this value is not computable at this scope, a SCEVCouldNotCompute 2607/// object is returned. 2608SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2609 return getSCEVAtScope(getSCEV(V), L); 2610} 2611 2612/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2613/// following equation: 2614/// 2615/// A * X = B (mod N) 2616/// 2617/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2618/// A and B isn't important. 2619/// 2620/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2621static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2622 ScalarEvolution &SE) { 2623 uint32_t BW = A.getBitWidth(); 2624 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2625 assert(A != 0 && "A must be non-zero."); 2626 2627 // 1. D = gcd(A, N) 2628 // 2629 // The gcd of A and N may have only one prime factor: 2. The number of 2630 // trailing zeros in A is its multiplicity 2631 uint32_t Mult2 = A.countTrailingZeros(); 2632 // D = 2^Mult2 2633 2634 // 2. Check if B is divisible by D. 2635 // 2636 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2637 // is not less than multiplicity of this prime factor for D. 2638 if (B.countTrailingZeros() < Mult2) 2639 return SE.getCouldNotCompute(); 2640 2641 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2642 // modulo (N / D). 2643 // 2644 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2645 // bit width during computations. 2646 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2647 APInt Mod(BW + 1, 0); 2648 Mod.set(BW - Mult2); // Mod = N / D 2649 APInt I = AD.multiplicativeInverse(Mod); 2650 2651 // 4. Compute the minimum unsigned root of the equation: 2652 // I * (B / D) mod (N / D) 2653 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2654 2655 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2656 // bits. 2657 return SE.getConstant(Result.trunc(BW)); 2658} 2659 2660/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2661/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2662/// might be the same) or two SCEVCouldNotCompute objects. 2663/// 2664static std::pair<SCEVHandle,SCEVHandle> 2665SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2666 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2667 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2668 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2669 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2670 2671 // We currently can only solve this if the coefficients are constants. 2672 if (!LC || !MC || !NC) { 2673 SCEV *CNC = SE.getCouldNotCompute(); 2674 return std::make_pair(CNC, CNC); 2675 } 2676 2677 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2678 const APInt &L = LC->getValue()->getValue(); 2679 const APInt &M = MC->getValue()->getValue(); 2680 const APInt &N = NC->getValue()->getValue(); 2681 APInt Two(BitWidth, 2); 2682 APInt Four(BitWidth, 4); 2683 2684 { 2685 using namespace APIntOps; 2686 const APInt& C = L; 2687 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2688 // The B coefficient is M-N/2 2689 APInt B(M); 2690 B -= sdiv(N,Two); 2691 2692 // The A coefficient is N/2 2693 APInt A(N.sdiv(Two)); 2694 2695 // Compute the B^2-4ac term. 2696 APInt SqrtTerm(B); 2697 SqrtTerm *= B; 2698 SqrtTerm -= Four * (A * C); 2699 2700 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2701 // integer value or else APInt::sqrt() will assert. 2702 APInt SqrtVal(SqrtTerm.sqrt()); 2703 2704 // Compute the two solutions for the quadratic formula. 2705 // The divisions must be performed as signed divisions. 2706 APInt NegB(-B); 2707 APInt TwoA( A << 1 ); 2708 if (TwoA.isMinValue()) { 2709 SCEV *CNC = SE.getCouldNotCompute(); 2710 return std::make_pair(CNC, CNC); 2711 } 2712 2713 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2714 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2715 2716 return std::make_pair(SE.getConstant(Solution1), 2717 SE.getConstant(Solution2)); 2718 } // end APIntOps namespace 2719} 2720 2721/// HowFarToZero - Return the number of times a backedge comparing the specified 2722/// value to zero will execute. If not computable, return UnknownValue 2723SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) { 2724 // If the value is a constant 2725 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2726 // If the value is already zero, the branch will execute zero times. 2727 if (C->getValue()->isZero()) return C; 2728 return UnknownValue; // Otherwise it will loop infinitely. 2729 } 2730 2731 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2732 if (!AddRec || AddRec->getLoop() != L) 2733 return UnknownValue; 2734 2735 if (AddRec->isAffine()) { 2736 // If this is an affine expression, the execution count of this branch is 2737 // the minimum unsigned root of the following equation: 2738 // 2739 // Start + Step*N = 0 (mod 2^BW) 2740 // 2741 // equivalent to: 2742 // 2743 // Step*N = -Start (mod 2^BW) 2744 // 2745 // where BW is the common bit width of Start and Step. 2746 2747 // Get the initial value for the loop. 2748 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2749 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2750 2751 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2752 2753 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2754 // For now we handle only constant steps. 2755 2756 // First, handle unitary steps. 2757 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2758 return getNegativeSCEV(Start); // N = -Start (as unsigned) 2759 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2760 return Start; // N = Start (as unsigned) 2761 2762 // Then, try to solve the above equation provided that Start is constant. 2763 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2764 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2765 -StartC->getValue()->getValue(), 2766 *this); 2767 } 2768 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2769 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2770 // the quadratic equation to solve it. 2771 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 2772 *this); 2773 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2774 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2775 if (R1) { 2776#if 0 2777 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 2778 << " sol#2: " << *R2 << "\n"; 2779#endif 2780 // Pick the smallest positive root value. 2781 if (ConstantInt *CB = 2782 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2783 R1->getValue(), R2->getValue()))) { 2784 if (CB->getZExtValue() == false) 2785 std::swap(R1, R2); // R1 is the minimum root now. 2786 2787 // We can only use this value if the chrec ends up with an exact zero 2788 // value at this index. When solving for "X*X != 5", for example, we 2789 // should not accept a root of 2. 2790 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 2791 if (Val->isZero()) 2792 return R1; // We found a quadratic root! 2793 } 2794 } 2795 } 2796 2797 return UnknownValue; 2798} 2799 2800/// HowFarToNonZero - Return the number of times a backedge checking the 2801/// specified value for nonzero will execute. If not computable, return 2802/// UnknownValue 2803SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) { 2804 // Loops that look like: while (X == 0) are very strange indeed. We don't 2805 // handle them yet except for the trivial case. This could be expanded in the 2806 // future as needed. 2807 2808 // If the value is a constant, check to see if it is known to be non-zero 2809 // already. If so, the backedge will execute zero times. 2810 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2811 if (!C->getValue()->isNullValue()) 2812 return getIntegerSCEV(0, C->getType()); 2813 return UnknownValue; // Otherwise it will loop infinitely. 2814 } 2815 2816 // We could implement others, but I really doubt anyone writes loops like 2817 // this, and if they did, they would already be constant folded. 2818 return UnknownValue; 2819} 2820 2821/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2822/// (which may not be an immediate predecessor) which has exactly one 2823/// successor from which BB is reachable, or null if no such block is 2824/// found. 2825/// 2826BasicBlock * 2827ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2828 // If the block has a unique predecessor, the predecessor must have 2829 // no other successors from which BB is reachable. 2830 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2831 return Pred; 2832 2833 // A loop's header is defined to be a block that dominates the loop. 2834 // If the loop has a preheader, it must be a block that has exactly 2835 // one successor that can reach BB. This is slightly more strict 2836 // than necessary, but works if critical edges are split. 2837 if (Loop *L = LI->getLoopFor(BB)) 2838 return L->getLoopPreheader(); 2839 2840 return 0; 2841} 2842 2843/// isLoopGuardedByCond - Test whether entry to the loop is protected by 2844/// a conditional between LHS and RHS. 2845bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 2846 ICmpInst::Predicate Pred, 2847 SCEV *LHS, SCEV *RHS) { 2848 BasicBlock *Preheader = L->getLoopPreheader(); 2849 BasicBlock *PreheaderDest = L->getHeader(); 2850 2851 // Starting at the preheader, climb up the predecessor chain, as long as 2852 // there are predecessors that can be found that have unique successors 2853 // leading to the original header. 2854 for (; Preheader; 2855 PreheaderDest = Preheader, 2856 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 2857 2858 BranchInst *LoopEntryPredicate = 2859 dyn_cast<BranchInst>(Preheader->getTerminator()); 2860 if (!LoopEntryPredicate || 2861 LoopEntryPredicate->isUnconditional()) 2862 continue; 2863 2864 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2865 if (!ICI) continue; 2866 2867 // Now that we found a conditional branch that dominates the loop, check to 2868 // see if it is the comparison we are looking for. 2869 Value *PreCondLHS = ICI->getOperand(0); 2870 Value *PreCondRHS = ICI->getOperand(1); 2871 ICmpInst::Predicate Cond; 2872 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2873 Cond = ICI->getPredicate(); 2874 else 2875 Cond = ICI->getInversePredicate(); 2876 2877 if (Cond == Pred) 2878 ; // An exact match. 2879 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 2880 ; // The actual condition is beyond sufficient. 2881 else 2882 // Check a few special cases. 2883 switch (Cond) { 2884 case ICmpInst::ICMP_UGT: 2885 if (Pred == ICmpInst::ICMP_ULT) { 2886 std::swap(PreCondLHS, PreCondRHS); 2887 Cond = ICmpInst::ICMP_ULT; 2888 break; 2889 } 2890 continue; 2891 case ICmpInst::ICMP_SGT: 2892 if (Pred == ICmpInst::ICMP_SLT) { 2893 std::swap(PreCondLHS, PreCondRHS); 2894 Cond = ICmpInst::ICMP_SLT; 2895 break; 2896 } 2897 continue; 2898 case ICmpInst::ICMP_NE: 2899 // Expressions like (x >u 0) are often canonicalized to (x != 0), 2900 // so check for this case by checking if the NE is comparing against 2901 // a minimum or maximum constant. 2902 if (!ICmpInst::isTrueWhenEqual(Pred)) 2903 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 2904 const APInt &A = CI->getValue(); 2905 switch (Pred) { 2906 case ICmpInst::ICMP_SLT: 2907 if (A.isMaxSignedValue()) break; 2908 continue; 2909 case ICmpInst::ICMP_SGT: 2910 if (A.isMinSignedValue()) break; 2911 continue; 2912 case ICmpInst::ICMP_ULT: 2913 if (A.isMaxValue()) break; 2914 continue; 2915 case ICmpInst::ICMP_UGT: 2916 if (A.isMinValue()) break; 2917 continue; 2918 default: 2919 continue; 2920 } 2921 Cond = ICmpInst::ICMP_NE; 2922 // NE is symmetric but the original comparison may not be. Swap 2923 // the operands if necessary so that they match below. 2924 if (isa<SCEVConstant>(LHS)) 2925 std::swap(PreCondLHS, PreCondRHS); 2926 break; 2927 } 2928 continue; 2929 default: 2930 // We weren't able to reconcile the condition. 2931 continue; 2932 } 2933 2934 if (!PreCondLHS->getType()->isInteger()) continue; 2935 2936 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 2937 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 2938 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 2939 (LHS == getNotSCEV(PreCondRHSSCEV) && 2940 RHS == getNotSCEV(PreCondLHSSCEV))) 2941 return true; 2942 } 2943 2944 return false; 2945} 2946 2947/// HowManyLessThans - Return the number of times a backedge containing the 2948/// specified less-than comparison will execute. If not computable, return 2949/// UnknownValue. 2950SCEVHandle ScalarEvolution:: 2951HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2952 // Only handle: "ADDREC < LoopInvariant". 2953 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2954 2955 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2956 if (!AddRec || AddRec->getLoop() != L) 2957 return UnknownValue; 2958 2959 if (AddRec->isAffine()) { 2960 // FORNOW: We only support unit strides. 2961 SCEVHandle One = getIntegerSCEV(1, RHS->getType()); 2962 if (AddRec->getOperand(1) != One) 2963 return UnknownValue; 2964 2965 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2966 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2967 // Note that we cannot simply return max(m-n,0) because it's not safe to 2968 // treat m-n as signed nor unsigned due to overflow possibility. 2969 2970 // First, we get the value of the LHS in the first iteration: n 2971 SCEVHandle Start = AddRec->getOperand(0); 2972 2973 if (isLoopGuardedByCond(L, 2974 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 2975 getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2976 // Since we know that the condition is true in order to enter the loop, 2977 // we know that it will run exactly m-n times. 2978 return getMinusSCEV(RHS, Start); 2979 } else { 2980 // Then, we get the value of the LHS in the first iteration in which the 2981 // above condition doesn't hold. This equals to max(m,n). 2982 SCEVHandle End = isSigned ? getSMaxExpr(RHS, Start) 2983 : getUMaxExpr(RHS, Start); 2984 2985 // Finally, we subtract these two values to get the number of times the 2986 // backedge is executed: max(m,n)-n. 2987 return getMinusSCEV(End, Start); 2988 } 2989 } 2990 2991 return UnknownValue; 2992} 2993 2994/// getNumIterationsInRange - Return the number of iterations of this loop that 2995/// produce values in the specified constant range. Another way of looking at 2996/// this is that it returns the first iteration number where the value is not in 2997/// the condition, thus computing the exit count. If the iteration count can't 2998/// be computed, an instance of SCEVCouldNotCompute is returned. 2999SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 3000 ScalarEvolution &SE) const { 3001 if (Range.isFullSet()) // Infinite loop. 3002 return SE.getCouldNotCompute(); 3003 3004 // If the start is a non-zero constant, shift the range to simplify things. 3005 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 3006 if (!SC->getValue()->isZero()) { 3007 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3008 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3009 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3010 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 3011 return ShiftedAddRec->getNumIterationsInRange( 3012 Range.subtract(SC->getValue()->getValue()), SE); 3013 // This is strange and shouldn't happen. 3014 return SE.getCouldNotCompute(); 3015 } 3016 3017 // The only time we can solve this is when we have all constant indices. 3018 // Otherwise, we cannot determine the overflow conditions. 3019 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3020 if (!isa<SCEVConstant>(getOperand(i))) 3021 return SE.getCouldNotCompute(); 3022 3023 3024 // Okay at this point we know that all elements of the chrec are constants and 3025 // that the start element is zero. 3026 3027 // First check to see if the range contains zero. If not, the first 3028 // iteration exits. 3029 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3030 if (!Range.contains(APInt(BitWidth, 0))) 3031 return SE.getConstant(ConstantInt::get(getType(),0)); 3032 3033 if (isAffine()) { 3034 // If this is an affine expression then we have this situation: 3035 // Solve {0,+,A} in Range === Ax in Range 3036 3037 // We know that zero is in the range. If A is positive then we know that 3038 // the upper value of the range must be the first possible exit value. 3039 // If A is negative then the lower of the range is the last possible loop 3040 // value. Also note that we already checked for a full range. 3041 APInt One(BitWidth,1); 3042 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3043 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3044 3045 // The exit value should be (End+A)/A. 3046 APInt ExitVal = (End + A).udiv(A); 3047 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3048 3049 // Evaluate at the exit value. If we really did fall out of the valid 3050 // range, then we computed our trip count, otherwise wrap around or other 3051 // things must have happened. 3052 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3053 if (Range.contains(Val->getValue())) 3054 return SE.getCouldNotCompute(); // Something strange happened 3055 3056 // Ensure that the previous value is in the range. This is a sanity check. 3057 assert(Range.contains( 3058 EvaluateConstantChrecAtConstant(this, 3059 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3060 "Linear scev computation is off in a bad way!"); 3061 return SE.getConstant(ExitValue); 3062 } else if (isQuadratic()) { 3063 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3064 // quadratic equation to solve it. To do this, we must frame our problem in 3065 // terms of figuring out when zero is crossed, instead of when 3066 // Range.getUpper() is crossed. 3067 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3068 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3069 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3070 3071 // Next, solve the constructed addrec 3072 std::pair<SCEVHandle,SCEVHandle> Roots = 3073 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3074 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3075 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3076 if (R1) { 3077 // Pick the smallest positive root value. 3078 if (ConstantInt *CB = 3079 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3080 R1->getValue(), R2->getValue()))) { 3081 if (CB->getZExtValue() == false) 3082 std::swap(R1, R2); // R1 is the minimum root now. 3083 3084 // Make sure the root is not off by one. The returned iteration should 3085 // not be in the range, but the previous one should be. When solving 3086 // for "X*X < 5", for example, we should not return a root of 2. 3087 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3088 R1->getValue(), 3089 SE); 3090 if (Range.contains(R1Val->getValue())) { 3091 // The next iteration must be out of the range... 3092 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3093 3094 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3095 if (!Range.contains(R1Val->getValue())) 3096 return SE.getConstant(NextVal); 3097 return SE.getCouldNotCompute(); // Something strange happened 3098 } 3099 3100 // If R1 was not in the range, then it is a good return value. Make 3101 // sure that R1-1 WAS in the range though, just in case. 3102 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3103 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3104 if (Range.contains(R1Val->getValue())) 3105 return R1; 3106 return SE.getCouldNotCompute(); // Something strange happened 3107 } 3108 } 3109 } 3110 3111 return SE.getCouldNotCompute(); 3112} 3113 3114 3115 3116//===----------------------------------------------------------------------===// 3117// ScalarEvolution Class Implementation 3118//===----------------------------------------------------------------------===// 3119 3120ScalarEvolution::ScalarEvolution() 3121 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3122} 3123 3124bool ScalarEvolution::runOnFunction(Function &F) { 3125 this->F = &F; 3126 LI = &getAnalysis<LoopInfo>(); 3127 TD = getAnalysisIfAvailable<TargetData>(); 3128 return false; 3129} 3130 3131void ScalarEvolution::releaseMemory() { 3132 Scalars.clear(); 3133 BackedgeTakenCounts.clear(); 3134 ConstantEvolutionLoopExitValue.clear(); 3135} 3136 3137void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3138 AU.setPreservesAll(); 3139 AU.addRequiredTransitive<LoopInfo>(); 3140} 3141 3142bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3143 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3144} 3145 3146static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3147 const Loop *L) { 3148 // Print all inner loops first 3149 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3150 PrintLoopInfo(OS, SE, *I); 3151 3152 OS << "Loop " << L->getHeader()->getName() << ": "; 3153 3154 SmallVector<BasicBlock*, 8> ExitBlocks; 3155 L->getExitBlocks(ExitBlocks); 3156 if (ExitBlocks.size() != 1) 3157 OS << "<multiple exits> "; 3158 3159 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3160 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3161 } else { 3162 OS << "Unpredictable backedge-taken count. "; 3163 } 3164 3165 OS << "\n"; 3166} 3167 3168void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3169 // ScalarEvolution's implementaiton of the print method is to print 3170 // out SCEV values of all instructions that are interesting. Doing 3171 // this potentially causes it to create new SCEV objects though, 3172 // which technically conflicts with the const qualifier. This isn't 3173 // observable from outside the class though (the hasSCEV function 3174 // notwithstanding), so casting away the const isn't dangerous. 3175 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3176 3177 OS << "Classifying expressions for: " << F->getName() << "\n"; 3178 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3179 if (I->getType()->isInteger()) { 3180 OS << *I; 3181 OS << " --> "; 3182 SCEVHandle SV = SE.getSCEV(&*I); 3183 SV->print(OS); 3184 OS << "\t\t"; 3185 3186 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3187 OS << "Exits: "; 3188 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3189 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3190 OS << "<<Unknown>>"; 3191 } else { 3192 OS << *ExitValue; 3193 } 3194 } 3195 3196 3197 OS << "\n"; 3198 } 3199 3200 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3201 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3202 PrintLoopInfo(OS, &SE, *I); 3203} 3204 3205void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3206 raw_os_ostream OS(o); 3207 print(OS, M); 3208} 3209