ScalarEvolution.cpp revision 20900cae35c0d18eed449a985d452a74c98ecdb2
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 // If the input value is a chrec scev made out of constants, truncate 662 // all of the constants. 663 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 664 std::vector<SCEVHandle> Operands; 665 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 666 // FIXME: This should allow truncation of other expression types! 667 if (isa<SCEVConstant>(AddRec->getOperand(i))) 668 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 669 else 670 break; 671 if (Operands.size() == AddRec->getNumOperands()) 672 return getAddRecExpr(Operands, AddRec->getLoop()); 673 } 674 675 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 676 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 677 return Result; 678} 679 680SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 681 const Type *Ty) { 682 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 683 "This is not an extending conversion!"); 684 685 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 686 const Type *IntTy = getEffectiveSCEVType(Ty); 687 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 688 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 689 return getUnknown(C); 690 } 691 692 // zext(zext(x)) --> zext(x) 693 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 694 return getZeroExtendExpr(SZ->getOperand(), Ty); 695 696 // FIXME: If the input value is a chrec scev, and we can prove that the value 697 // did not overflow the old, smaller, value, we can zero extend all of the 698 // operands (often constants). This would allow analysis of something like 699 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 700 701 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 702 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 703 return Result; 704} 705 706SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) { 707 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 708 "This is not an extending conversion!"); 709 710 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 711 const Type *IntTy = getEffectiveSCEVType(Ty); 712 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 713 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 714 return getUnknown(C); 715 } 716 717 // sext(sext(x)) --> sext(x) 718 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 719 return getSignExtendExpr(SS->getOperand(), Ty); 720 721 // FIXME: If the input value is a chrec scev, and we can prove that the value 722 // did not overflow the old, smaller, value, we can sign extend all of the 723 // operands (often constants). This would allow analysis of something like 724 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 725 726 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 727 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 728 return Result; 729} 730 731// get - Get a canonical add expression, or something simpler if possible. 732SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 733 assert(!Ops.empty() && "Cannot get empty add!"); 734 if (Ops.size() == 1) return Ops[0]; 735 736 // Sort by complexity, this groups all similar expression types together. 737 GroupByComplexity(Ops); 738 739 // If there are any constants, fold them together. 740 unsigned Idx = 0; 741 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 742 ++Idx; 743 assert(Idx < Ops.size()); 744 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 745 // We found two constants, fold them together! 746 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 747 RHSC->getValue()->getValue()); 748 Ops[0] = getConstant(Fold); 749 Ops.erase(Ops.begin()+1); // Erase the folded element 750 if (Ops.size() == 1) return Ops[0]; 751 LHSC = cast<SCEVConstant>(Ops[0]); 752 } 753 754 // If we are left with a constant zero being added, strip it off. 755 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 756 Ops.erase(Ops.begin()); 757 --Idx; 758 } 759 } 760 761 if (Ops.size() == 1) return Ops[0]; 762 763 // Okay, check to see if the same value occurs in the operand list twice. If 764 // so, merge them together into an multiply expression. Since we sorted the 765 // list, these values are required to be adjacent. 766 const Type *Ty = Ops[0]->getType(); 767 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 768 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 769 // Found a match, merge the two values into a multiply, and add any 770 // remaining values to the result. 771 SCEVHandle Two = getIntegerSCEV(2, Ty); 772 SCEVHandle Mul = getMulExpr(Ops[i], Two); 773 if (Ops.size() == 2) 774 return Mul; 775 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 776 Ops.push_back(Mul); 777 return getAddExpr(Ops); 778 } 779 780 // Now we know the first non-constant operand. Skip past any cast SCEVs. 781 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 782 ++Idx; 783 784 // If there are add operands they would be next. 785 if (Idx < Ops.size()) { 786 bool DeletedAdd = false; 787 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 788 // If we have an add, expand the add operands onto the end of the operands 789 // list. 790 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 791 Ops.erase(Ops.begin()+Idx); 792 DeletedAdd = true; 793 } 794 795 // If we deleted at least one add, we added operands to the end of the list, 796 // and they are not necessarily sorted. Recurse to resort and resimplify 797 // any operands we just aquired. 798 if (DeletedAdd) 799 return getAddExpr(Ops); 800 } 801 802 // Skip over the add expression until we get to a multiply. 803 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 804 ++Idx; 805 806 // If we are adding something to a multiply expression, make sure the 807 // something is not already an operand of the multiply. If so, merge it into 808 // the multiply. 809 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 810 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 811 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 812 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 813 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 814 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 815 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 816 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 817 if (Mul->getNumOperands() != 2) { 818 // If the multiply has more than two operands, we must get the 819 // Y*Z term. 820 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 821 MulOps.erase(MulOps.begin()+MulOp); 822 InnerMul = getMulExpr(MulOps); 823 } 824 SCEVHandle One = getIntegerSCEV(1, Ty); 825 SCEVHandle AddOne = getAddExpr(InnerMul, One); 826 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 827 if (Ops.size() == 2) return OuterMul; 828 if (AddOp < Idx) { 829 Ops.erase(Ops.begin()+AddOp); 830 Ops.erase(Ops.begin()+Idx-1); 831 } else { 832 Ops.erase(Ops.begin()+Idx); 833 Ops.erase(Ops.begin()+AddOp-1); 834 } 835 Ops.push_back(OuterMul); 836 return getAddExpr(Ops); 837 } 838 839 // Check this multiply against other multiplies being added together. 840 for (unsigned OtherMulIdx = Idx+1; 841 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 842 ++OtherMulIdx) { 843 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 844 // If MulOp occurs in OtherMul, we can fold the two multiplies 845 // together. 846 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 847 OMulOp != e; ++OMulOp) 848 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 849 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 850 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 851 if (Mul->getNumOperands() != 2) { 852 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 853 MulOps.erase(MulOps.begin()+MulOp); 854 InnerMul1 = getMulExpr(MulOps); 855 } 856 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 857 if (OtherMul->getNumOperands() != 2) { 858 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 859 OtherMul->op_end()); 860 MulOps.erase(MulOps.begin()+OMulOp); 861 InnerMul2 = getMulExpr(MulOps); 862 } 863 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 864 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 865 if (Ops.size() == 2) return OuterMul; 866 Ops.erase(Ops.begin()+Idx); 867 Ops.erase(Ops.begin()+OtherMulIdx-1); 868 Ops.push_back(OuterMul); 869 return getAddExpr(Ops); 870 } 871 } 872 } 873 } 874 875 // If there are any add recurrences in the operands list, see if any other 876 // added values are loop invariant. If so, we can fold them into the 877 // recurrence. 878 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 879 ++Idx; 880 881 // Scan over all recurrences, trying to fold loop invariants into them. 882 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 883 // Scan all of the other operands to this add and add them to the vector if 884 // they are loop invariant w.r.t. the recurrence. 885 std::vector<SCEVHandle> LIOps; 886 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 887 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 888 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 889 LIOps.push_back(Ops[i]); 890 Ops.erase(Ops.begin()+i); 891 --i; --e; 892 } 893 894 // If we found some loop invariants, fold them into the recurrence. 895 if (!LIOps.empty()) { 896 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 897 LIOps.push_back(AddRec->getStart()); 898 899 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 900 AddRecOps[0] = getAddExpr(LIOps); 901 902 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 903 // If all of the other operands were loop invariant, we are done. 904 if (Ops.size() == 1) return NewRec; 905 906 // Otherwise, add the folded AddRec by the non-liv parts. 907 for (unsigned i = 0;; ++i) 908 if (Ops[i] == AddRec) { 909 Ops[i] = NewRec; 910 break; 911 } 912 return getAddExpr(Ops); 913 } 914 915 // Okay, if there weren't any loop invariants to be folded, check to see if 916 // there are multiple AddRec's with the same loop induction variable being 917 // added together. If so, we can fold them. 918 for (unsigned OtherIdx = Idx+1; 919 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 920 if (OtherIdx != Idx) { 921 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 922 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 923 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 924 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 925 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 926 if (i >= NewOps.size()) { 927 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 928 OtherAddRec->op_end()); 929 break; 930 } 931 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 932 } 933 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 934 935 if (Ops.size() == 2) return NewAddRec; 936 937 Ops.erase(Ops.begin()+Idx); 938 Ops.erase(Ops.begin()+OtherIdx-1); 939 Ops.push_back(NewAddRec); 940 return getAddExpr(Ops); 941 } 942 } 943 944 // Otherwise couldn't fold anything into this recurrence. Move onto the 945 // next one. 946 } 947 948 // Okay, it looks like we really DO need an add expr. Check to see if we 949 // already have one, otherwise create a new one. 950 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 951 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 952 SCEVOps)]; 953 if (Result == 0) Result = new SCEVAddExpr(Ops); 954 return Result; 955} 956 957 958SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 959 assert(!Ops.empty() && "Cannot get empty mul!"); 960 961 // Sort by complexity, this groups all similar expression types together. 962 GroupByComplexity(Ops); 963 964 // If there are any constants, fold them together. 965 unsigned Idx = 0; 966 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 967 968 // C1*(C2+V) -> C1*C2 + C1*V 969 if (Ops.size() == 2) 970 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 971 if (Add->getNumOperands() == 2 && 972 isa<SCEVConstant>(Add->getOperand(0))) 973 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 974 getMulExpr(LHSC, Add->getOperand(1))); 975 976 977 ++Idx; 978 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 979 // We found two constants, fold them together! 980 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 981 RHSC->getValue()->getValue()); 982 Ops[0] = getConstant(Fold); 983 Ops.erase(Ops.begin()+1); // Erase the folded element 984 if (Ops.size() == 1) return Ops[0]; 985 LHSC = cast<SCEVConstant>(Ops[0]); 986 } 987 988 // If we are left with a constant one being multiplied, strip it off. 989 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 990 Ops.erase(Ops.begin()); 991 --Idx; 992 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 993 // If we have a multiply of zero, it will always be zero. 994 return Ops[0]; 995 } 996 } 997 998 // Skip over the add expression until we get to a multiply. 999 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1000 ++Idx; 1001 1002 if (Ops.size() == 1) 1003 return Ops[0]; 1004 1005 // If there are mul operands inline them all into this expression. 1006 if (Idx < Ops.size()) { 1007 bool DeletedMul = false; 1008 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1009 // If we have an mul, expand the mul operands onto the end of the operands 1010 // list. 1011 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1012 Ops.erase(Ops.begin()+Idx); 1013 DeletedMul = true; 1014 } 1015 1016 // If we deleted at least one mul, we added operands to the end of the list, 1017 // and they are not necessarily sorted. Recurse to resort and resimplify 1018 // any operands we just aquired. 1019 if (DeletedMul) 1020 return getMulExpr(Ops); 1021 } 1022 1023 // If there are any add recurrences in the operands list, see if any other 1024 // added values are loop invariant. If so, we can fold them into the 1025 // recurrence. 1026 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1027 ++Idx; 1028 1029 // Scan over all recurrences, trying to fold loop invariants into them. 1030 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1031 // Scan all of the other operands to this mul and add them to the vector if 1032 // they are loop invariant w.r.t. the recurrence. 1033 std::vector<SCEVHandle> LIOps; 1034 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1035 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1036 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1037 LIOps.push_back(Ops[i]); 1038 Ops.erase(Ops.begin()+i); 1039 --i; --e; 1040 } 1041 1042 // If we found some loop invariants, fold them into the recurrence. 1043 if (!LIOps.empty()) { 1044 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1045 std::vector<SCEVHandle> NewOps; 1046 NewOps.reserve(AddRec->getNumOperands()); 1047 if (LIOps.size() == 1) { 1048 SCEV *Scale = LIOps[0]; 1049 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1050 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1051 } else { 1052 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1053 std::vector<SCEVHandle> MulOps(LIOps); 1054 MulOps.push_back(AddRec->getOperand(i)); 1055 NewOps.push_back(getMulExpr(MulOps)); 1056 } 1057 } 1058 1059 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1060 1061 // If all of the other operands were loop invariant, we are done. 1062 if (Ops.size() == 1) return NewRec; 1063 1064 // Otherwise, multiply the folded AddRec by the non-liv parts. 1065 for (unsigned i = 0;; ++i) 1066 if (Ops[i] == AddRec) { 1067 Ops[i] = NewRec; 1068 break; 1069 } 1070 return getMulExpr(Ops); 1071 } 1072 1073 // Okay, if there weren't any loop invariants to be folded, check to see if 1074 // there are multiple AddRec's with the same loop induction variable being 1075 // multiplied together. If so, we can fold them. 1076 for (unsigned OtherIdx = Idx+1; 1077 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1078 if (OtherIdx != Idx) { 1079 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1080 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1081 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1082 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1083 SCEVHandle NewStart = getMulExpr(F->getStart(), 1084 G->getStart()); 1085 SCEVHandle B = F->getStepRecurrence(*this); 1086 SCEVHandle D = G->getStepRecurrence(*this); 1087 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1088 getMulExpr(G, B), 1089 getMulExpr(B, D)); 1090 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1091 F->getLoop()); 1092 if (Ops.size() == 2) return NewAddRec; 1093 1094 Ops.erase(Ops.begin()+Idx); 1095 Ops.erase(Ops.begin()+OtherIdx-1); 1096 Ops.push_back(NewAddRec); 1097 return getMulExpr(Ops); 1098 } 1099 } 1100 1101 // Otherwise couldn't fold anything into this recurrence. Move onto the 1102 // next one. 1103 } 1104 1105 // Okay, it looks like we really DO need an mul expr. Check to see if we 1106 // already have one, otherwise create a new one. 1107 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1108 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1109 SCEVOps)]; 1110 if (Result == 0) 1111 Result = new SCEVMulExpr(Ops); 1112 return Result; 1113} 1114 1115SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1116 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1117 if (RHSC->getValue()->equalsInt(1)) 1118 return LHS; // X udiv 1 --> x 1119 1120 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1121 Constant *LHSCV = LHSC->getValue(); 1122 Constant *RHSCV = RHSC->getValue(); 1123 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1124 } 1125 } 1126 1127 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1128 1129 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1130 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1131 return Result; 1132} 1133 1134 1135/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1136/// specified loop. Simplify the expression as much as possible. 1137SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1138 const SCEVHandle &Step, const Loop *L) { 1139 std::vector<SCEVHandle> Operands; 1140 Operands.push_back(Start); 1141 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1142 if (StepChrec->getLoop() == L) { 1143 Operands.insert(Operands.end(), StepChrec->op_begin(), 1144 StepChrec->op_end()); 1145 return getAddRecExpr(Operands, L); 1146 } 1147 1148 Operands.push_back(Step); 1149 return getAddRecExpr(Operands, L); 1150} 1151 1152/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1153/// specified loop. Simplify the expression as much as possible. 1154SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1155 const Loop *L) { 1156 if (Operands.size() == 1) return Operands[0]; 1157 1158 if (Operands.back()->isZero()) { 1159 Operands.pop_back(); 1160 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1161 } 1162 1163 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1164 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1165 const Loop* NestedLoop = NestedAR->getLoop(); 1166 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1167 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1168 NestedAR->op_end()); 1169 SCEVHandle NestedARHandle(NestedAR); 1170 Operands[0] = NestedAR->getStart(); 1171 NestedOperands[0] = getAddRecExpr(Operands, L); 1172 return getAddRecExpr(NestedOperands, NestedLoop); 1173 } 1174 } 1175 1176 SCEVAddRecExpr *&Result = 1177 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1178 Operands.end()))]; 1179 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1180 return Result; 1181} 1182 1183SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1184 const SCEVHandle &RHS) { 1185 std::vector<SCEVHandle> Ops; 1186 Ops.push_back(LHS); 1187 Ops.push_back(RHS); 1188 return getSMaxExpr(Ops); 1189} 1190 1191SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1192 assert(!Ops.empty() && "Cannot get empty smax!"); 1193 if (Ops.size() == 1) return Ops[0]; 1194 1195 // Sort by complexity, this groups all similar expression types together. 1196 GroupByComplexity(Ops); 1197 1198 // If there are any constants, fold them together. 1199 unsigned Idx = 0; 1200 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1201 ++Idx; 1202 assert(Idx < Ops.size()); 1203 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1204 // We found two constants, fold them together! 1205 ConstantInt *Fold = ConstantInt::get( 1206 APIntOps::smax(LHSC->getValue()->getValue(), 1207 RHSC->getValue()->getValue())); 1208 Ops[0] = getConstant(Fold); 1209 Ops.erase(Ops.begin()+1); // Erase the folded element 1210 if (Ops.size() == 1) return Ops[0]; 1211 LHSC = cast<SCEVConstant>(Ops[0]); 1212 } 1213 1214 // If we are left with a constant -inf, strip it off. 1215 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1216 Ops.erase(Ops.begin()); 1217 --Idx; 1218 } 1219 } 1220 1221 if (Ops.size() == 1) return Ops[0]; 1222 1223 // Find the first SMax 1224 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1225 ++Idx; 1226 1227 // Check to see if one of the operands is an SMax. If so, expand its operands 1228 // onto our operand list, and recurse to simplify. 1229 if (Idx < Ops.size()) { 1230 bool DeletedSMax = false; 1231 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1232 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1233 Ops.erase(Ops.begin()+Idx); 1234 DeletedSMax = true; 1235 } 1236 1237 if (DeletedSMax) 1238 return getSMaxExpr(Ops); 1239 } 1240 1241 // Okay, check to see if the same value occurs in the operand list twice. If 1242 // so, delete one. Since we sorted the list, these values are required to 1243 // be adjacent. 1244 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1245 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1246 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1247 --i; --e; 1248 } 1249 1250 if (Ops.size() == 1) return Ops[0]; 1251 1252 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1253 1254 // Okay, it looks like we really DO need an smax expr. Check to see if we 1255 // already have one, otherwise create a new one. 1256 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1257 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1258 SCEVOps)]; 1259 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1260 return Result; 1261} 1262 1263SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1264 const SCEVHandle &RHS) { 1265 std::vector<SCEVHandle> Ops; 1266 Ops.push_back(LHS); 1267 Ops.push_back(RHS); 1268 return getUMaxExpr(Ops); 1269} 1270 1271SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1272 assert(!Ops.empty() && "Cannot get empty umax!"); 1273 if (Ops.size() == 1) return Ops[0]; 1274 1275 // Sort by complexity, this groups all similar expression types together. 1276 GroupByComplexity(Ops); 1277 1278 // If there are any constants, fold them together. 1279 unsigned Idx = 0; 1280 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1281 ++Idx; 1282 assert(Idx < Ops.size()); 1283 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1284 // We found two constants, fold them together! 1285 ConstantInt *Fold = ConstantInt::get( 1286 APIntOps::umax(LHSC->getValue()->getValue(), 1287 RHSC->getValue()->getValue())); 1288 Ops[0] = getConstant(Fold); 1289 Ops.erase(Ops.begin()+1); // Erase the folded element 1290 if (Ops.size() == 1) return Ops[0]; 1291 LHSC = cast<SCEVConstant>(Ops[0]); 1292 } 1293 1294 // If we are left with a constant zero, strip it off. 1295 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1296 Ops.erase(Ops.begin()); 1297 --Idx; 1298 } 1299 } 1300 1301 if (Ops.size() == 1) return Ops[0]; 1302 1303 // Find the first UMax 1304 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1305 ++Idx; 1306 1307 // Check to see if one of the operands is a UMax. If so, expand its operands 1308 // onto our operand list, and recurse to simplify. 1309 if (Idx < Ops.size()) { 1310 bool DeletedUMax = false; 1311 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1312 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1313 Ops.erase(Ops.begin()+Idx); 1314 DeletedUMax = true; 1315 } 1316 1317 if (DeletedUMax) 1318 return getUMaxExpr(Ops); 1319 } 1320 1321 // Okay, check to see if the same value occurs in the operand list twice. If 1322 // so, delete one. Since we sorted the list, these values are required to 1323 // be adjacent. 1324 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1325 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1326 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1327 --i; --e; 1328 } 1329 1330 if (Ops.size() == 1) return Ops[0]; 1331 1332 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1333 1334 // Okay, it looks like we really DO need a umax expr. Check to see if we 1335 // already have one, otherwise create a new one. 1336 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1337 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1338 SCEVOps)]; 1339 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1340 return Result; 1341} 1342 1343SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1344 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1345 return getConstant(CI); 1346 if (isa<ConstantPointerNull>(V)) 1347 return getIntegerSCEV(0, V->getType()); 1348 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1349 if (Result == 0) Result = new SCEVUnknown(V); 1350 return Result; 1351} 1352 1353//===----------------------------------------------------------------------===// 1354// Basic SCEV Analysis and PHI Idiom Recognition Code 1355// 1356 1357/// deleteValueFromRecords - This method should be called by the 1358/// client before it removes an instruction from the program, to make sure 1359/// that no dangling references are left around. 1360void ScalarEvolution::deleteValueFromRecords(Value *V) { 1361 SmallVector<Value *, 16> Worklist; 1362 1363 if (Scalars.erase(V)) { 1364 if (PHINode *PN = dyn_cast<PHINode>(V)) 1365 ConstantEvolutionLoopExitValue.erase(PN); 1366 Worklist.push_back(V); 1367 } 1368 1369 while (!Worklist.empty()) { 1370 Value *VV = Worklist.back(); 1371 Worklist.pop_back(); 1372 1373 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1374 UI != UE; ++UI) { 1375 Instruction *Inst = cast<Instruction>(*UI); 1376 if (Scalars.erase(Inst)) { 1377 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1378 ConstantEvolutionLoopExitValue.erase(PN); 1379 Worklist.push_back(Inst); 1380 } 1381 } 1382 } 1383} 1384 1385/// isSCEVable - Test if values of the given type are analyzable within 1386/// the SCEV framework. This primarily includes integer types, and it 1387/// can optionally include pointer types if the ScalarEvolution class 1388/// has access to target-specific information. 1389bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1390 // Integers are always SCEVable. 1391 if (Ty->isInteger()) 1392 return true; 1393 1394 // Pointers are SCEVable if TargetData information is available 1395 // to provide pointer size information. 1396 if (isa<PointerType>(Ty)) 1397 return TD != NULL; 1398 1399 // Otherwise it's not SCEVable. 1400 return false; 1401} 1402 1403/// getTypeSizeInBits - Return the size in bits of the specified type, 1404/// for which isSCEVable must return true. 1405uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1406 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1407 1408 // If we have a TargetData, use it! 1409 if (TD) 1410 return TD->getTypeSizeInBits(Ty); 1411 1412 // Otherwise, we support only integer types. 1413 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1414 return Ty->getPrimitiveSizeInBits(); 1415} 1416 1417/// getEffectiveSCEVType - Return a type with the same bitwidth as 1418/// the given type and which represents how SCEV will treat the given 1419/// type, for which isSCEVable must return true. For pointer types, 1420/// this is the pointer-sized integer type. 1421const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1422 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1423 1424 if (Ty->isInteger()) 1425 return Ty; 1426 1427 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1428 return TD->getIntPtrType(); 1429} 1430 1431SCEVHandle ScalarEvolution::getCouldNotCompute() { 1432 return UnknownValue; 1433} 1434 1435/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1436/// expression and create a new one. 1437SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1438 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1439 1440 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1441 if (I != Scalars.end()) return I->second; 1442 SCEVHandle S = createSCEV(V); 1443 Scalars.insert(std::make_pair(V, S)); 1444 return S; 1445} 1446 1447/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1448/// specified signed integer value and return a SCEV for the constant. 1449SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 1450 Ty = getEffectiveSCEVType(Ty); 1451 Constant *C; 1452 if (Val == 0) 1453 C = Constant::getNullValue(Ty); 1454 else if (Ty->isFloatingPoint()) 1455 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1456 APFloat::IEEEdouble, Val)); 1457 else 1458 C = ConstantInt::get(Ty, Val); 1459 return getUnknown(C); 1460} 1461 1462/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1463/// 1464SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 1465 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1466 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 1467 1468 const Type *Ty = V->getType(); 1469 Ty = getEffectiveSCEVType(Ty); 1470 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 1471} 1472 1473/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1474SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 1475 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1476 return getUnknown(ConstantExpr::getNot(VC->getValue())); 1477 1478 const Type *Ty = V->getType(); 1479 Ty = getEffectiveSCEVType(Ty); 1480 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 1481 return getMinusSCEV(AllOnes, V); 1482} 1483 1484/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1485/// 1486SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 1487 const SCEVHandle &RHS) { 1488 // X - Y --> X + -Y 1489 return getAddExpr(LHS, getNegativeSCEV(RHS)); 1490} 1491 1492/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1493/// input value to the specified type. If the type must be extended, it is zero 1494/// extended. 1495SCEVHandle 1496ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 1497 const Type *Ty) { 1498 const Type *SrcTy = V->getType(); 1499 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1500 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1501 "Cannot truncate or zero extend with non-integer arguments!"); 1502 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1503 return V; // No conversion 1504 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1505 return getTruncateExpr(V, Ty); 1506 return getZeroExtendExpr(V, Ty); 1507} 1508 1509/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1510/// input value to the specified type. If the type must be extended, it is sign 1511/// extended. 1512SCEVHandle 1513ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 1514 const Type *Ty) { 1515 const Type *SrcTy = V->getType(); 1516 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1517 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1518 "Cannot truncate or zero extend with non-integer arguments!"); 1519 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1520 return V; // No conversion 1521 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1522 return getTruncateExpr(V, Ty); 1523 return getSignExtendExpr(V, Ty); 1524} 1525 1526/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1527/// the specified instruction and replaces any references to the symbolic value 1528/// SymName with the specified value. This is used during PHI resolution. 1529void ScalarEvolution:: 1530ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1531 const SCEVHandle &NewVal) { 1532 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1533 if (SI == Scalars.end()) return; 1534 1535 SCEVHandle NV = 1536 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 1537 if (NV == SI->second) return; // No change. 1538 1539 SI->second = NV; // Update the scalars map! 1540 1541 // Any instruction values that use this instruction might also need to be 1542 // updated! 1543 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1544 UI != E; ++UI) 1545 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1546} 1547 1548/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1549/// a loop header, making it a potential recurrence, or it doesn't. 1550/// 1551SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 1552 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1553 if (const Loop *L = LI->getLoopFor(PN->getParent())) 1554 if (L->getHeader() == PN->getParent()) { 1555 // If it lives in the loop header, it has two incoming values, one 1556 // from outside the loop, and one from inside. 1557 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1558 unsigned BackEdge = IncomingEdge^1; 1559 1560 // While we are analyzing this PHI node, handle its value symbolically. 1561 SCEVHandle SymbolicName = getUnknown(PN); 1562 assert(Scalars.find(PN) == Scalars.end() && 1563 "PHI node already processed?"); 1564 Scalars.insert(std::make_pair(PN, SymbolicName)); 1565 1566 // Using this symbolic name for the PHI, analyze the value coming around 1567 // the back-edge. 1568 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1569 1570 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1571 // has a special value for the first iteration of the loop. 1572 1573 // If the value coming around the backedge is an add with the symbolic 1574 // value we just inserted, then we found a simple induction variable! 1575 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1576 // If there is a single occurrence of the symbolic value, replace it 1577 // with a recurrence. 1578 unsigned FoundIndex = Add->getNumOperands(); 1579 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1580 if (Add->getOperand(i) == SymbolicName) 1581 if (FoundIndex == e) { 1582 FoundIndex = i; 1583 break; 1584 } 1585 1586 if (FoundIndex != Add->getNumOperands()) { 1587 // Create an add with everything but the specified operand. 1588 std::vector<SCEVHandle> Ops; 1589 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1590 if (i != FoundIndex) 1591 Ops.push_back(Add->getOperand(i)); 1592 SCEVHandle Accum = getAddExpr(Ops); 1593 1594 // This is not a valid addrec if the step amount is varying each 1595 // loop iteration, but is not itself an addrec in this loop. 1596 if (Accum->isLoopInvariant(L) || 1597 (isa<SCEVAddRecExpr>(Accum) && 1598 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1599 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1600 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 1601 1602 // Okay, for the entire analysis of this edge we assumed the PHI 1603 // to be symbolic. We now need to go back and update all of the 1604 // entries for the scalars that use the PHI (except for the PHI 1605 // itself) to use the new analyzed value instead of the "symbolic" 1606 // value. 1607 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1608 return PHISCEV; 1609 } 1610 } 1611 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1612 // Otherwise, this could be a loop like this: 1613 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1614 // In this case, j = {1,+,1} and BEValue is j. 1615 // Because the other in-value of i (0) fits the evolution of BEValue 1616 // i really is an addrec evolution. 1617 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1618 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1619 1620 // If StartVal = j.start - j.stride, we can use StartVal as the 1621 // initial step of the addrec evolution. 1622 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 1623 AddRec->getOperand(1))) { 1624 SCEVHandle PHISCEV = 1625 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1626 1627 // Okay, for the entire analysis of this edge we assumed the PHI 1628 // to be symbolic. We now need to go back and update all of the 1629 // entries for the scalars that use the PHI (except for the PHI 1630 // itself) to use the new analyzed value instead of the "symbolic" 1631 // value. 1632 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1633 return PHISCEV; 1634 } 1635 } 1636 } 1637 1638 return SymbolicName; 1639 } 1640 1641 // If it's not a loop phi, we can't handle it yet. 1642 return getUnknown(PN); 1643} 1644 1645/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1646/// guaranteed to end in (at every loop iteration). It is, at the same time, 1647/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1648/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1649static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) { 1650 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1651 return C->getValue()->getValue().countTrailingZeros(); 1652 1653 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1654 return std::min(GetMinTrailingZeros(T->getOperand(), SE), 1655 (uint32_t)SE.getTypeSizeInBits(T->getType())); 1656 1657 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1658 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1659 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1660 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1661 } 1662 1663 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1664 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1665 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1666 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1667 } 1668 1669 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1670 // The result is the min of all operands results. 1671 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1672 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1673 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1674 return MinOpRes; 1675 } 1676 1677 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1678 // The result is the sum of all operands results. 1679 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1680 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType()); 1681 for (unsigned i = 1, e = M->getNumOperands(); 1682 SumOpRes != BitWidth && i != e; ++i) 1683 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE), 1684 BitWidth); 1685 return SumOpRes; 1686 } 1687 1688 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1689 // The result is the min of all operands results. 1690 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1691 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1692 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1693 return MinOpRes; 1694 } 1695 1696 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1697 // The result is the min of all operands results. 1698 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1699 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1700 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1701 return MinOpRes; 1702 } 1703 1704 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(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 // SCEVUDivExpr, SCEVUnknown 1713 return 0; 1714} 1715 1716/// createSCEV - We know that there is no SCEV for the specified value. 1717/// Analyze the expression. 1718/// 1719SCEVHandle ScalarEvolution::createSCEV(Value *V) { 1720 if (!isSCEVable(V->getType())) 1721 return getUnknown(V); 1722 1723 unsigned Opcode = Instruction::UserOp1; 1724 if (Instruction *I = dyn_cast<Instruction>(V)) 1725 Opcode = I->getOpcode(); 1726 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1727 Opcode = CE->getOpcode(); 1728 else 1729 return getUnknown(V); 1730 1731 User *U = cast<User>(V); 1732 switch (Opcode) { 1733 case Instruction::Add: 1734 return getAddExpr(getSCEV(U->getOperand(0)), 1735 getSCEV(U->getOperand(1))); 1736 case Instruction::Mul: 1737 return getMulExpr(getSCEV(U->getOperand(0)), 1738 getSCEV(U->getOperand(1))); 1739 case Instruction::UDiv: 1740 return getUDivExpr(getSCEV(U->getOperand(0)), 1741 getSCEV(U->getOperand(1))); 1742 case Instruction::Sub: 1743 return getMinusSCEV(getSCEV(U->getOperand(0)), 1744 getSCEV(U->getOperand(1))); 1745 case Instruction::And: 1746 // For an expression like x&255 that merely masks off the high bits, 1747 // use zext(trunc(x)) as the SCEV expression. 1748 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1749 const APInt &A = CI->getValue(); 1750 unsigned Ones = A.countTrailingOnes(); 1751 if (APIntOps::isMask(Ones, A)) 1752 return 1753 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 1754 IntegerType::get(Ones)), 1755 U->getType()); 1756 } 1757 break; 1758 case Instruction::Or: 1759 // If the RHS of the Or is a constant, we may have something like: 1760 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1761 // optimizations will transparently handle this case. 1762 // 1763 // In order for this transformation to be safe, the LHS must be of the 1764 // form X*(2^n) and the Or constant must be less than 2^n. 1765 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1766 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1767 const APInt &CIVal = CI->getValue(); 1768 if (GetMinTrailingZeros(LHS, *this) >= 1769 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1770 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 1771 } 1772 break; 1773 case Instruction::Xor: 1774 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1775 // If the RHS of the xor is a signbit, then this is just an add. 1776 // Instcombine turns add of signbit into xor as a strength reduction step. 1777 if (CI->getValue().isSignBit()) 1778 return getAddExpr(getSCEV(U->getOperand(0)), 1779 getSCEV(U->getOperand(1))); 1780 1781 // If the RHS of xor is -1, then this is a not operation. 1782 else if (CI->isAllOnesValue()) 1783 return getNotSCEV(getSCEV(U->getOperand(0))); 1784 } 1785 break; 1786 1787 case Instruction::Shl: 1788 // Turn shift left of a constant amount into a multiply. 1789 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1790 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1791 Constant *X = ConstantInt::get( 1792 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1793 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1794 } 1795 break; 1796 1797 case Instruction::LShr: 1798 // Turn logical shift right of a constant into a unsigned divide. 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 getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1804 } 1805 break; 1806 1807 case Instruction::AShr: 1808 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 1809 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 1810 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 1811 if (L->getOpcode() == Instruction::Shl && 1812 L->getOperand(1) == U->getOperand(1)) { 1813 uint64_t Amt = getTypeSizeInBits(U->getType()) - CI->getZExtValue(); 1814 return 1815 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 1816 IntegerType::get(Amt)), 1817 U->getType()); 1818 } 1819 break; 1820 1821 case Instruction::Trunc: 1822 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1823 1824 case Instruction::ZExt: 1825 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1826 1827 case Instruction::SExt: 1828 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1829 1830 case Instruction::BitCast: 1831 // BitCasts are no-op casts so we just eliminate the cast. 1832 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 1833 return getSCEV(U->getOperand(0)); 1834 break; 1835 1836 case Instruction::IntToPtr: 1837 if (!TD) break; // Without TD we can't analyze pointers. 1838 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1839 TD->getIntPtrType()); 1840 1841 case Instruction::PtrToInt: 1842 if (!TD) break; // Without TD we can't analyze pointers. 1843 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1844 U->getType()); 1845 1846 case Instruction::GetElementPtr: { 1847 if (!TD) break; // Without TD we can't analyze pointers. 1848 const Type *IntPtrTy = TD->getIntPtrType(); 1849 Value *Base = U->getOperand(0); 1850 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1851 gep_type_iterator GTI = gep_type_begin(U); 1852 for (GetElementPtrInst::op_iterator I = next(U->op_begin()), 1853 E = U->op_end(); 1854 I != E; ++I) { 1855 Value *Index = *I; 1856 // Compute the (potentially symbolic) offset in bytes for this index. 1857 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1858 // For a struct, add the member offset. 1859 const StructLayout &SL = *TD->getStructLayout(STy); 1860 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1861 uint64_t Offset = SL.getElementOffset(FieldNo); 1862 TotalOffset = getAddExpr(TotalOffset, 1863 getIntegerSCEV(Offset, IntPtrTy)); 1864 } else { 1865 // For an array, add the element offset, explicitly scaled. 1866 SCEVHandle LocalOffset = getSCEV(Index); 1867 if (!isa<PointerType>(LocalOffset->getType())) 1868 // Getelementptr indicies are signed. 1869 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1870 IntPtrTy); 1871 LocalOffset = 1872 getMulExpr(LocalOffset, 1873 getIntegerSCEV(TD->getTypePaddedSize(*GTI), 1874 IntPtrTy)); 1875 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1876 } 1877 } 1878 return getAddExpr(getSCEV(Base), TotalOffset); 1879 } 1880 1881 case Instruction::PHI: 1882 return createNodeForPHI(cast<PHINode>(U)); 1883 1884 case Instruction::Select: 1885 // This could be a smax or umax that was lowered earlier. 1886 // Try to recover it. 1887 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 1888 Value *LHS = ICI->getOperand(0); 1889 Value *RHS = ICI->getOperand(1); 1890 switch (ICI->getPredicate()) { 1891 case ICmpInst::ICMP_SLT: 1892 case ICmpInst::ICMP_SLE: 1893 std::swap(LHS, RHS); 1894 // fall through 1895 case ICmpInst::ICMP_SGT: 1896 case ICmpInst::ICMP_SGE: 1897 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1898 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1899 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1900 // ~smax(~x, ~y) == smin(x, y). 1901 return getNotSCEV(getSMaxExpr( 1902 getNotSCEV(getSCEV(LHS)), 1903 getNotSCEV(getSCEV(RHS)))); 1904 break; 1905 case ICmpInst::ICMP_ULT: 1906 case ICmpInst::ICMP_ULE: 1907 std::swap(LHS, RHS); 1908 // fall through 1909 case ICmpInst::ICMP_UGT: 1910 case ICmpInst::ICMP_UGE: 1911 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 1912 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 1913 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 1914 // ~umax(~x, ~y) == umin(x, y) 1915 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 1916 getNotSCEV(getSCEV(RHS)))); 1917 break; 1918 default: 1919 break; 1920 } 1921 } 1922 1923 default: // We cannot analyze this expression. 1924 break; 1925 } 1926 1927 return getUnknown(V); 1928} 1929 1930 1931 1932//===----------------------------------------------------------------------===// 1933// Iteration Count Computation Code 1934// 1935 1936/// getBackedgeTakenCount - If the specified loop has a predictable 1937/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 1938/// object. The backedge-taken count is the number of times the loop header 1939/// will be branched to from within the loop. This is one less than the 1940/// trip count of the loop, since it doesn't count the first iteration, 1941/// when the header is branched to from outside the loop. 1942/// 1943/// Note that it is not valid to call this method on a loop without a 1944/// loop-invariant backedge-taken count (see 1945/// hasLoopInvariantBackedgeTakenCount). 1946/// 1947SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 1948 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L); 1949 if (I == BackedgeTakenCounts.end()) { 1950 SCEVHandle ItCount = ComputeBackedgeTakenCount(L); 1951 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first; 1952 if (ItCount != UnknownValue) { 1953 assert(ItCount->isLoopInvariant(L) && 1954 "Computed trip count isn't loop invariant for loop!"); 1955 ++NumTripCountsComputed; 1956 } else if (isa<PHINode>(L->getHeader()->begin())) { 1957 // Only count loops that have phi nodes as not being computable. 1958 ++NumTripCountsNotComputed; 1959 } 1960 } 1961 return I->second; 1962} 1963 1964/// forgetLoopBackedgeTakenCount - This method should be called by the 1965/// client when it has changed a loop in a way that may effect 1966/// ScalarEvolution's ability to compute a trip count, or if the loop 1967/// is deleted. 1968void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 1969 BackedgeTakenCounts.erase(L); 1970} 1971 1972/// ComputeBackedgeTakenCount - Compute the number of times the backedge 1973/// of the specified loop will execute. 1974SCEVHandle ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 1975 // If the loop has a non-one exit block count, we can't analyze it. 1976 SmallVector<BasicBlock*, 8> ExitBlocks; 1977 L->getExitBlocks(ExitBlocks); 1978 if (ExitBlocks.size() != 1) return UnknownValue; 1979 1980 // Okay, there is one exit block. Try to find the condition that causes the 1981 // loop to be exited. 1982 BasicBlock *ExitBlock = ExitBlocks[0]; 1983 1984 BasicBlock *ExitingBlock = 0; 1985 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 1986 PI != E; ++PI) 1987 if (L->contains(*PI)) { 1988 if (ExitingBlock == 0) 1989 ExitingBlock = *PI; 1990 else 1991 return UnknownValue; // More than one block exiting! 1992 } 1993 assert(ExitingBlock && "No exits from loop, something is broken!"); 1994 1995 // Okay, we've computed the exiting block. See what condition causes us to 1996 // exit. 1997 // 1998 // FIXME: we should be able to handle switch instructions (with a single exit) 1999 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2000 if (ExitBr == 0) return UnknownValue; 2001 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2002 2003 // At this point, we know we have a conditional branch that determines whether 2004 // the loop is exited. However, we don't know if the branch is executed each 2005 // time through the loop. If not, then the execution count of the branch will 2006 // not be equal to the trip count of the loop. 2007 // 2008 // Currently we check for this by checking to see if the Exit branch goes to 2009 // the loop header. If so, we know it will always execute the same number of 2010 // times as the loop. We also handle the case where the exit block *is* the 2011 // loop header. This is common for un-rotated loops. More extensive analysis 2012 // could be done to handle more cases here. 2013 if (ExitBr->getSuccessor(0) != L->getHeader() && 2014 ExitBr->getSuccessor(1) != L->getHeader() && 2015 ExitBr->getParent() != L->getHeader()) 2016 return UnknownValue; 2017 2018 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2019 2020 // If it's not an integer comparison then compute it the hard way. 2021 // Note that ICmpInst deals with pointer comparisons too so we must check 2022 // the type of the operand. 2023 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2024 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2025 ExitBr->getSuccessor(0) == ExitBlock); 2026 2027 // If the condition was exit on true, convert the condition to exit on false 2028 ICmpInst::Predicate Cond; 2029 if (ExitBr->getSuccessor(1) == ExitBlock) 2030 Cond = ExitCond->getPredicate(); 2031 else 2032 Cond = ExitCond->getInversePredicate(); 2033 2034 // Handle common loops like: for (X = "string"; *X; ++X) 2035 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2036 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2037 SCEVHandle ItCnt = 2038 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2039 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2040 } 2041 2042 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2043 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2044 2045 // Try to evaluate any dependencies out of the loop. 2046 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2047 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2048 Tmp = getSCEVAtScope(RHS, L); 2049 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2050 2051 // At this point, we would like to compute how many iterations of the 2052 // loop the predicate will return true for these inputs. 2053 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2054 // If there is a loop-invariant, force it into the RHS. 2055 std::swap(LHS, RHS); 2056 Cond = ICmpInst::getSwappedPredicate(Cond); 2057 } 2058 2059 // If we have a comparison of a chrec against a constant, try to use value 2060 // ranges to answer this query. 2061 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2062 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2063 if (AddRec->getLoop() == L) { 2064 // Form the comparison range using the constant of the correct type so 2065 // that the ConstantRange class knows to do a signed or unsigned 2066 // comparison. 2067 ConstantInt *CompVal = RHSC->getValue(); 2068 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2069 CompVal = dyn_cast<ConstantInt>( 2070 ConstantExpr::getBitCast(CompVal, RealTy)); 2071 if (CompVal) { 2072 // Form the constant range. 2073 ConstantRange CompRange( 2074 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2075 2076 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2077 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2078 } 2079 } 2080 2081 switch (Cond) { 2082 case ICmpInst::ICMP_NE: { // while (X != Y) 2083 // Convert to: while (X-Y != 0) 2084 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2085 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2086 break; 2087 } 2088 case ICmpInst::ICMP_EQ: { 2089 // Convert to: while (X-Y == 0) // while (X == Y) 2090 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2091 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2092 break; 2093 } 2094 case ICmpInst::ICMP_SLT: { 2095 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true); 2096 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2097 break; 2098 } 2099 case ICmpInst::ICMP_SGT: { 2100 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2101 getNotSCEV(RHS), L, true); 2102 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2103 break; 2104 } 2105 case ICmpInst::ICMP_ULT: { 2106 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false); 2107 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2108 break; 2109 } 2110 case ICmpInst::ICMP_UGT: { 2111 SCEVHandle TC = HowManyLessThans(getNotSCEV(LHS), 2112 getNotSCEV(RHS), L, false); 2113 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2114 break; 2115 } 2116 default: 2117#if 0 2118 errs() << "ComputeBackedgeTakenCount "; 2119 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2120 errs() << "[unsigned] "; 2121 errs() << *LHS << " " 2122 << Instruction::getOpcodeName(Instruction::ICmp) 2123 << " " << *RHS << "\n"; 2124#endif 2125 break; 2126 } 2127 return 2128 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2129 ExitBr->getSuccessor(0) == ExitBlock); 2130} 2131 2132static ConstantInt * 2133EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2134 ScalarEvolution &SE) { 2135 SCEVHandle InVal = SE.getConstant(C); 2136 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2137 assert(isa<SCEVConstant>(Val) && 2138 "Evaluation of SCEV at constant didn't fold correctly?"); 2139 return cast<SCEVConstant>(Val)->getValue(); 2140} 2141 2142/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2143/// and a GEP expression (missing the pointer index) indexing into it, return 2144/// the addressed element of the initializer or null if the index expression is 2145/// invalid. 2146static Constant * 2147GetAddressedElementFromGlobal(GlobalVariable *GV, 2148 const std::vector<ConstantInt*> &Indices) { 2149 Constant *Init = GV->getInitializer(); 2150 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2151 uint64_t Idx = Indices[i]->getZExtValue(); 2152 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2153 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2154 Init = cast<Constant>(CS->getOperand(Idx)); 2155 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2156 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2157 Init = cast<Constant>(CA->getOperand(Idx)); 2158 } else if (isa<ConstantAggregateZero>(Init)) { 2159 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2160 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2161 Init = Constant::getNullValue(STy->getElementType(Idx)); 2162 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2163 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2164 Init = Constant::getNullValue(ATy->getElementType()); 2165 } else { 2166 assert(0 && "Unknown constant aggregate type!"); 2167 } 2168 return 0; 2169 } else { 2170 return 0; // Unknown initializer type 2171 } 2172 } 2173 return Init; 2174} 2175 2176/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2177/// 'icmp op load X, cst', try to see if we can compute the backedge 2178/// execution count. 2179SCEVHandle ScalarEvolution:: 2180ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2181 const Loop *L, 2182 ICmpInst::Predicate predicate) { 2183 if (LI->isVolatile()) return UnknownValue; 2184 2185 // Check to see if the loaded pointer is a getelementptr of a global. 2186 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2187 if (!GEP) return UnknownValue; 2188 2189 // Make sure that it is really a constant global we are gepping, with an 2190 // initializer, and make sure the first IDX is really 0. 2191 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2192 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2193 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2194 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2195 return UnknownValue; 2196 2197 // Okay, we allow one non-constant index into the GEP instruction. 2198 Value *VarIdx = 0; 2199 std::vector<ConstantInt*> Indexes; 2200 unsigned VarIdxNum = 0; 2201 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2202 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2203 Indexes.push_back(CI); 2204 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2205 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2206 VarIdx = GEP->getOperand(i); 2207 VarIdxNum = i-2; 2208 Indexes.push_back(0); 2209 } 2210 2211 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2212 // Check to see if X is a loop variant variable value now. 2213 SCEVHandle Idx = getSCEV(VarIdx); 2214 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2215 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2216 2217 // We can only recognize very limited forms of loop index expressions, in 2218 // particular, only affine AddRec's like {C1,+,C2}. 2219 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2220 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2221 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2222 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2223 return UnknownValue; 2224 2225 unsigned MaxSteps = MaxBruteForceIterations; 2226 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2227 ConstantInt *ItCst = 2228 ConstantInt::get(IdxExpr->getType(), IterationNum); 2229 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2230 2231 // Form the GEP offset. 2232 Indexes[VarIdxNum] = Val; 2233 2234 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2235 if (Result == 0) break; // Cannot compute! 2236 2237 // Evaluate the condition for this iteration. 2238 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2239 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2240 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2241#if 0 2242 errs() << "\n***\n*** Computed loop count " << *ItCst 2243 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2244 << "***\n"; 2245#endif 2246 ++NumArrayLenItCounts; 2247 return getConstant(ItCst); // Found terminating iteration! 2248 } 2249 } 2250 return UnknownValue; 2251} 2252 2253 2254/// CanConstantFold - Return true if we can constant fold an instruction of the 2255/// specified type, assuming that all operands were constants. 2256static bool CanConstantFold(const Instruction *I) { 2257 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2258 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2259 return true; 2260 2261 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2262 if (const Function *F = CI->getCalledFunction()) 2263 return canConstantFoldCallTo(F); 2264 return false; 2265} 2266 2267/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2268/// in the loop that V is derived from. We allow arbitrary operations along the 2269/// way, but the operands of an operation must either be constants or a value 2270/// derived from a constant PHI. If this expression does not fit with these 2271/// constraints, return null. 2272static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2273 // If this is not an instruction, or if this is an instruction outside of the 2274 // loop, it can't be derived from a loop PHI. 2275 Instruction *I = dyn_cast<Instruction>(V); 2276 if (I == 0 || !L->contains(I->getParent())) return 0; 2277 2278 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2279 if (L->getHeader() == I->getParent()) 2280 return PN; 2281 else 2282 // We don't currently keep track of the control flow needed to evaluate 2283 // PHIs, so we cannot handle PHIs inside of loops. 2284 return 0; 2285 } 2286 2287 // If we won't be able to constant fold this expression even if the operands 2288 // are constants, return early. 2289 if (!CanConstantFold(I)) return 0; 2290 2291 // Otherwise, we can evaluate this instruction if all of its operands are 2292 // constant or derived from a PHI node themselves. 2293 PHINode *PHI = 0; 2294 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2295 if (!(isa<Constant>(I->getOperand(Op)) || 2296 isa<GlobalValue>(I->getOperand(Op)))) { 2297 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2298 if (P == 0) return 0; // Not evolving from PHI 2299 if (PHI == 0) 2300 PHI = P; 2301 else if (PHI != P) 2302 return 0; // Evolving from multiple different PHIs. 2303 } 2304 2305 // This is a expression evolving from a constant PHI! 2306 return PHI; 2307} 2308 2309/// EvaluateExpression - Given an expression that passes the 2310/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2311/// in the loop has the value PHIVal. If we can't fold this expression for some 2312/// reason, return null. 2313static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2314 if (isa<PHINode>(V)) return PHIVal; 2315 if (Constant *C = dyn_cast<Constant>(V)) return C; 2316 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2317 Instruction *I = cast<Instruction>(V); 2318 2319 std::vector<Constant*> Operands; 2320 Operands.resize(I->getNumOperands()); 2321 2322 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2323 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2324 if (Operands[i] == 0) return 0; 2325 } 2326 2327 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2328 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2329 &Operands[0], Operands.size()); 2330 else 2331 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2332 &Operands[0], Operands.size()); 2333} 2334 2335/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2336/// in the header of its containing loop, we know the loop executes a 2337/// constant number of times, and the PHI node is just a recurrence 2338/// involving constants, fold it. 2339Constant *ScalarEvolution:: 2340getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2341 std::map<PHINode*, Constant*>::iterator I = 2342 ConstantEvolutionLoopExitValue.find(PN); 2343 if (I != ConstantEvolutionLoopExitValue.end()) 2344 return I->second; 2345 2346 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2347 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2348 2349 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2350 2351 // Since the loop is canonicalized, the PHI node must have two entries. One 2352 // entry must be a constant (coming in from outside of the loop), and the 2353 // second must be derived from the same PHI. 2354 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2355 Constant *StartCST = 2356 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2357 if (StartCST == 0) 2358 return RetVal = 0; // Must be a constant. 2359 2360 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2361 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2362 if (PN2 != PN) 2363 return RetVal = 0; // Not derived from same PHI. 2364 2365 // Execute the loop symbolically to determine the exit value. 2366 if (BEs.getActiveBits() >= 32) 2367 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2368 2369 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2370 unsigned IterationNum = 0; 2371 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2372 if (IterationNum == NumIterations) 2373 return RetVal = PHIVal; // Got exit value! 2374 2375 // Compute the value of the PHI node for the next iteration. 2376 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2377 if (NextPHI == PHIVal) 2378 return RetVal = NextPHI; // Stopped evolving! 2379 if (NextPHI == 0) 2380 return 0; // Couldn't evaluate! 2381 PHIVal = NextPHI; 2382 } 2383} 2384 2385/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2386/// constant number of times (the condition evolves only from constants), 2387/// try to evaluate a few iterations of the loop until we get the exit 2388/// condition gets a value of ExitWhen (true or false). If we cannot 2389/// evaluate the trip count of the loop, return UnknownValue. 2390SCEVHandle ScalarEvolution:: 2391ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2392 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2393 if (PN == 0) return UnknownValue; 2394 2395 // Since the loop is canonicalized, the PHI node must have two entries. One 2396 // entry must be a constant (coming in from outside of the loop), and the 2397 // second must be derived from the same PHI. 2398 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2399 Constant *StartCST = 2400 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2401 if (StartCST == 0) return UnknownValue; // Must be a constant. 2402 2403 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2404 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2405 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2406 2407 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2408 // the loop symbolically to determine when the condition gets a value of 2409 // "ExitWhen". 2410 unsigned IterationNum = 0; 2411 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2412 for (Constant *PHIVal = StartCST; 2413 IterationNum != MaxIterations; ++IterationNum) { 2414 ConstantInt *CondVal = 2415 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2416 2417 // Couldn't symbolically evaluate. 2418 if (!CondVal) return UnknownValue; 2419 2420 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2421 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2422 ++NumBruteForceTripCountsComputed; 2423 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2424 } 2425 2426 // Compute the value of the PHI node for the next iteration. 2427 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2428 if (NextPHI == 0 || NextPHI == PHIVal) 2429 return UnknownValue; // Couldn't evaluate or not making progress... 2430 PHIVal = NextPHI; 2431 } 2432 2433 // Too many iterations were needed to evaluate. 2434 return UnknownValue; 2435} 2436 2437/// getSCEVAtScope - Compute the value of the specified expression within the 2438/// indicated loop (which may be null to indicate in no loop). If the 2439/// expression cannot be evaluated, return UnknownValue. 2440SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) { 2441 // FIXME: this should be turned into a virtual method on SCEV! 2442 2443 if (isa<SCEVConstant>(V)) return V; 2444 2445 // If this instruction is evolved from a constant-evolving PHI, compute the 2446 // exit value from the loop without using SCEVs. 2447 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2448 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2449 const Loop *LI = (*this->LI)[I->getParent()]; 2450 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2451 if (PHINode *PN = dyn_cast<PHINode>(I)) 2452 if (PN->getParent() == LI->getHeader()) { 2453 // Okay, there is no closed form solution for the PHI node. Check 2454 // to see if the loop that contains it has a known backedge-taken 2455 // count. If so, we may be able to force computation of the exit 2456 // value. 2457 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2458 if (SCEVConstant *BTCC = 2459 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2460 // Okay, we know how many times the containing loop executes. If 2461 // this is a constant evolving PHI node, get the final value at 2462 // the specified iteration number. 2463 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2464 BTCC->getValue()->getValue(), 2465 LI); 2466 if (RV) return getUnknown(RV); 2467 } 2468 } 2469 2470 // Okay, this is an expression that we cannot symbolically evaluate 2471 // into a SCEV. Check to see if it's possible to symbolically evaluate 2472 // the arguments into constants, and if so, try to constant propagate the 2473 // result. This is particularly useful for computing loop exit values. 2474 if (CanConstantFold(I)) { 2475 std::vector<Constant*> Operands; 2476 Operands.reserve(I->getNumOperands()); 2477 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2478 Value *Op = I->getOperand(i); 2479 if (Constant *C = dyn_cast<Constant>(Op)) { 2480 Operands.push_back(C); 2481 } else { 2482 // If any of the operands is non-constant and if they are 2483 // non-integer and non-pointer, don't even try to analyze them 2484 // with scev techniques. 2485 if (!isa<IntegerType>(Op->getType()) && 2486 !isa<PointerType>(Op->getType())) 2487 return V; 2488 2489 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2490 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 2491 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(), 2492 Op->getType(), 2493 false)); 2494 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2495 if (Constant *C = dyn_cast<Constant>(SU->getValue())) 2496 Operands.push_back(ConstantExpr::getIntegerCast(C, 2497 Op->getType(), 2498 false)); 2499 else 2500 return V; 2501 } else { 2502 return V; 2503 } 2504 } 2505 } 2506 2507 Constant *C; 2508 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2509 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2510 &Operands[0], Operands.size()); 2511 else 2512 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2513 &Operands[0], Operands.size()); 2514 return getUnknown(C); 2515 } 2516 } 2517 2518 // This is some other type of SCEVUnknown, just return it. 2519 return V; 2520 } 2521 2522 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2523 // Avoid performing the look-up in the common case where the specified 2524 // expression has no loop-variant portions. 2525 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2526 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2527 if (OpAtScope != Comm->getOperand(i)) { 2528 if (OpAtScope == UnknownValue) return UnknownValue; 2529 // Okay, at least one of these operands is loop variant but might be 2530 // foldable. Build a new instance of the folded commutative expression. 2531 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2532 NewOps.push_back(OpAtScope); 2533 2534 for (++i; i != e; ++i) { 2535 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2536 if (OpAtScope == UnknownValue) return UnknownValue; 2537 NewOps.push_back(OpAtScope); 2538 } 2539 if (isa<SCEVAddExpr>(Comm)) 2540 return getAddExpr(NewOps); 2541 if (isa<SCEVMulExpr>(Comm)) 2542 return getMulExpr(NewOps); 2543 if (isa<SCEVSMaxExpr>(Comm)) 2544 return getSMaxExpr(NewOps); 2545 if (isa<SCEVUMaxExpr>(Comm)) 2546 return getUMaxExpr(NewOps); 2547 assert(0 && "Unknown commutative SCEV type!"); 2548 } 2549 } 2550 // If we got here, all operands are loop invariant. 2551 return Comm; 2552 } 2553 2554 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2555 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2556 if (LHS == UnknownValue) return LHS; 2557 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2558 if (RHS == UnknownValue) return RHS; 2559 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2560 return Div; // must be loop invariant 2561 return getUDivExpr(LHS, RHS); 2562 } 2563 2564 // If this is a loop recurrence for a loop that does not contain L, then we 2565 // are dealing with the final value computed by the loop. 2566 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2567 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2568 // To evaluate this recurrence, we need to know how many times the AddRec 2569 // loop iterates. Compute this now. 2570 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2571 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2572 2573 // Then, evaluate the AddRec. 2574 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2575 } 2576 return UnknownValue; 2577 } 2578 2579 //assert(0 && "Unknown SCEV type!"); 2580 return UnknownValue; 2581} 2582 2583/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2584/// at the specified scope in the program. The L value specifies a loop 2585/// nest to evaluate the expression at, where null is the top-level or a 2586/// specified loop is immediately inside of the loop. 2587/// 2588/// This method can be used to compute the exit value for a variable defined 2589/// in a loop by querying what the value will hold in the parent loop. 2590/// 2591/// If this value is not computable at this scope, a SCEVCouldNotCompute 2592/// object is returned. 2593SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2594 return getSCEVAtScope(getSCEV(V), L); 2595} 2596 2597/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2598/// following equation: 2599/// 2600/// A * X = B (mod N) 2601/// 2602/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2603/// A and B isn't important. 2604/// 2605/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2606static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2607 ScalarEvolution &SE) { 2608 uint32_t BW = A.getBitWidth(); 2609 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2610 assert(A != 0 && "A must be non-zero."); 2611 2612 // 1. D = gcd(A, N) 2613 // 2614 // The gcd of A and N may have only one prime factor: 2. The number of 2615 // trailing zeros in A is its multiplicity 2616 uint32_t Mult2 = A.countTrailingZeros(); 2617 // D = 2^Mult2 2618 2619 // 2. Check if B is divisible by D. 2620 // 2621 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2622 // is not less than multiplicity of this prime factor for D. 2623 if (B.countTrailingZeros() < Mult2) 2624 return SE.getCouldNotCompute(); 2625 2626 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2627 // modulo (N / D). 2628 // 2629 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2630 // bit width during computations. 2631 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2632 APInt Mod(BW + 1, 0); 2633 Mod.set(BW - Mult2); // Mod = N / D 2634 APInt I = AD.multiplicativeInverse(Mod); 2635 2636 // 4. Compute the minimum unsigned root of the equation: 2637 // I * (B / D) mod (N / D) 2638 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2639 2640 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2641 // bits. 2642 return SE.getConstant(Result.trunc(BW)); 2643} 2644 2645/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2646/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2647/// might be the same) or two SCEVCouldNotCompute objects. 2648/// 2649static std::pair<SCEVHandle,SCEVHandle> 2650SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2651 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2652 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2653 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2654 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2655 2656 // We currently can only solve this if the coefficients are constants. 2657 if (!LC || !MC || !NC) { 2658 SCEV *CNC = SE.getCouldNotCompute(); 2659 return std::make_pair(CNC, CNC); 2660 } 2661 2662 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2663 const APInt &L = LC->getValue()->getValue(); 2664 const APInt &M = MC->getValue()->getValue(); 2665 const APInt &N = NC->getValue()->getValue(); 2666 APInt Two(BitWidth, 2); 2667 APInt Four(BitWidth, 4); 2668 2669 { 2670 using namespace APIntOps; 2671 const APInt& C = L; 2672 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2673 // The B coefficient is M-N/2 2674 APInt B(M); 2675 B -= sdiv(N,Two); 2676 2677 // The A coefficient is N/2 2678 APInt A(N.sdiv(Two)); 2679 2680 // Compute the B^2-4ac term. 2681 APInt SqrtTerm(B); 2682 SqrtTerm *= B; 2683 SqrtTerm -= Four * (A * C); 2684 2685 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2686 // integer value or else APInt::sqrt() will assert. 2687 APInt SqrtVal(SqrtTerm.sqrt()); 2688 2689 // Compute the two solutions for the quadratic formula. 2690 // The divisions must be performed as signed divisions. 2691 APInt NegB(-B); 2692 APInt TwoA( A << 1 ); 2693 if (TwoA.isMinValue()) { 2694 SCEV *CNC = SE.getCouldNotCompute(); 2695 return std::make_pair(CNC, CNC); 2696 } 2697 2698 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2699 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2700 2701 return std::make_pair(SE.getConstant(Solution1), 2702 SE.getConstant(Solution2)); 2703 } // end APIntOps namespace 2704} 2705 2706/// HowFarToZero - Return the number of times a backedge comparing the specified 2707/// value to zero will execute. If not computable, return UnknownValue 2708SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) { 2709 // If the value is a constant 2710 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2711 // If the value is already zero, the branch will execute zero times. 2712 if (C->getValue()->isZero()) return C; 2713 return UnknownValue; // Otherwise it will loop infinitely. 2714 } 2715 2716 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2717 if (!AddRec || AddRec->getLoop() != L) 2718 return UnknownValue; 2719 2720 if (AddRec->isAffine()) { 2721 // If this is an affine expression, the execution count of this branch is 2722 // the minimum unsigned root of the following equation: 2723 // 2724 // Start + Step*N = 0 (mod 2^BW) 2725 // 2726 // equivalent to: 2727 // 2728 // Step*N = -Start (mod 2^BW) 2729 // 2730 // where BW is the common bit width of Start and Step. 2731 2732 // Get the initial value for the loop. 2733 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2734 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2735 2736 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2737 2738 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2739 // For now we handle only constant steps. 2740 2741 // First, handle unitary steps. 2742 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2743 return getNegativeSCEV(Start); // N = -Start (as unsigned) 2744 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2745 return Start; // N = Start (as unsigned) 2746 2747 // Then, try to solve the above equation provided that Start is constant. 2748 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2749 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2750 -StartC->getValue()->getValue(), 2751 *this); 2752 } 2753 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2754 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2755 // the quadratic equation to solve it. 2756 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 2757 *this); 2758 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2759 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2760 if (R1) { 2761#if 0 2762 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 2763 << " sol#2: " << *R2 << "\n"; 2764#endif 2765 // Pick the smallest positive root value. 2766 if (ConstantInt *CB = 2767 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2768 R1->getValue(), R2->getValue()))) { 2769 if (CB->getZExtValue() == false) 2770 std::swap(R1, R2); // R1 is the minimum root now. 2771 2772 // We can only use this value if the chrec ends up with an exact zero 2773 // value at this index. When solving for "X*X != 5", for example, we 2774 // should not accept a root of 2. 2775 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 2776 if (Val->isZero()) 2777 return R1; // We found a quadratic root! 2778 } 2779 } 2780 } 2781 2782 return UnknownValue; 2783} 2784 2785/// HowFarToNonZero - Return the number of times a backedge checking the 2786/// specified value for nonzero will execute. If not computable, return 2787/// UnknownValue 2788SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) { 2789 // Loops that look like: while (X == 0) are very strange indeed. We don't 2790 // handle them yet except for the trivial case. This could be expanded in the 2791 // future as needed. 2792 2793 // If the value is a constant, check to see if it is known to be non-zero 2794 // already. If so, the backedge will execute zero times. 2795 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2796 if (!C->getValue()->isNullValue()) 2797 return getIntegerSCEV(0, C->getType()); 2798 return UnknownValue; // Otherwise it will loop infinitely. 2799 } 2800 2801 // We could implement others, but I really doubt anyone writes loops like 2802 // this, and if they did, they would already be constant folded. 2803 return UnknownValue; 2804} 2805 2806/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2807/// (which may not be an immediate predecessor) which has exactly one 2808/// successor from which BB is reachable, or null if no such block is 2809/// found. 2810/// 2811BasicBlock * 2812ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2813 // If the block has a unique predecessor, the predecessor must have 2814 // no other successors from which BB is reachable. 2815 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2816 return Pred; 2817 2818 // A loop's header is defined to be a block that dominates the loop. 2819 // If the loop has a preheader, it must be a block that has exactly 2820 // one successor that can reach BB. This is slightly more strict 2821 // than necessary, but works if critical edges are split. 2822 if (Loop *L = LI->getLoopFor(BB)) 2823 return L->getLoopPreheader(); 2824 2825 return 0; 2826} 2827 2828/// isLoopGuardedByCond - Test whether entry to the loop is protected by 2829/// a conditional between LHS and RHS. 2830bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 2831 ICmpInst::Predicate Pred, 2832 SCEV *LHS, SCEV *RHS) { 2833 BasicBlock *Preheader = L->getLoopPreheader(); 2834 BasicBlock *PreheaderDest = L->getHeader(); 2835 2836 // Starting at the preheader, climb up the predecessor chain, as long as 2837 // there are predecessors that can be found that have unique successors 2838 // leading to the original header. 2839 for (; Preheader; 2840 PreheaderDest = Preheader, 2841 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 2842 2843 BranchInst *LoopEntryPredicate = 2844 dyn_cast<BranchInst>(Preheader->getTerminator()); 2845 if (!LoopEntryPredicate || 2846 LoopEntryPredicate->isUnconditional()) 2847 continue; 2848 2849 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 2850 if (!ICI) continue; 2851 2852 // Now that we found a conditional branch that dominates the loop, check to 2853 // see if it is the comparison we are looking for. 2854 Value *PreCondLHS = ICI->getOperand(0); 2855 Value *PreCondRHS = ICI->getOperand(1); 2856 ICmpInst::Predicate Cond; 2857 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 2858 Cond = ICI->getPredicate(); 2859 else 2860 Cond = ICI->getInversePredicate(); 2861 2862 if (Cond == Pred) 2863 ; // An exact match. 2864 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 2865 ; // The actual condition is beyond sufficient. 2866 else 2867 // Check a few special cases. 2868 switch (Cond) { 2869 case ICmpInst::ICMP_UGT: 2870 if (Pred == ICmpInst::ICMP_ULT) { 2871 std::swap(PreCondLHS, PreCondRHS); 2872 Cond = ICmpInst::ICMP_ULT; 2873 break; 2874 } 2875 continue; 2876 case ICmpInst::ICMP_SGT: 2877 if (Pred == ICmpInst::ICMP_SLT) { 2878 std::swap(PreCondLHS, PreCondRHS); 2879 Cond = ICmpInst::ICMP_SLT; 2880 break; 2881 } 2882 continue; 2883 case ICmpInst::ICMP_NE: 2884 // Expressions like (x >u 0) are often canonicalized to (x != 0), 2885 // so check for this case by checking if the NE is comparing against 2886 // a minimum or maximum constant. 2887 if (!ICmpInst::isTrueWhenEqual(Pred)) 2888 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 2889 const APInt &A = CI->getValue(); 2890 switch (Pred) { 2891 case ICmpInst::ICMP_SLT: 2892 if (A.isMaxSignedValue()) break; 2893 continue; 2894 case ICmpInst::ICMP_SGT: 2895 if (A.isMinSignedValue()) break; 2896 continue; 2897 case ICmpInst::ICMP_ULT: 2898 if (A.isMaxValue()) break; 2899 continue; 2900 case ICmpInst::ICMP_UGT: 2901 if (A.isMinValue()) break; 2902 continue; 2903 default: 2904 continue; 2905 } 2906 Cond = ICmpInst::ICMP_NE; 2907 // NE is symmetric but the original comparison may not be. Swap 2908 // the operands if necessary so that they match below. 2909 if (isa<SCEVConstant>(LHS)) 2910 std::swap(PreCondLHS, PreCondRHS); 2911 break; 2912 } 2913 continue; 2914 default: 2915 // We weren't able to reconcile the condition. 2916 continue; 2917 } 2918 2919 if (!PreCondLHS->getType()->isInteger()) continue; 2920 2921 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 2922 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 2923 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 2924 (LHS == getNotSCEV(PreCondRHSSCEV) && 2925 RHS == getNotSCEV(PreCondLHSSCEV))) 2926 return true; 2927 } 2928 2929 return false; 2930} 2931 2932/// HowManyLessThans - Return the number of times a backedge containing the 2933/// specified less-than comparison will execute. If not computable, return 2934/// UnknownValue. 2935SCEVHandle ScalarEvolution:: 2936HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 2937 // Only handle: "ADDREC < LoopInvariant". 2938 if (!RHS->isLoopInvariant(L)) return UnknownValue; 2939 2940 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 2941 if (!AddRec || AddRec->getLoop() != L) 2942 return UnknownValue; 2943 2944 if (AddRec->isAffine()) { 2945 // FORNOW: We only support unit strides. 2946 SCEVHandle One = getIntegerSCEV(1, RHS->getType()); 2947 if (AddRec->getOperand(1) != One) 2948 return UnknownValue; 2949 2950 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant 2951 // m. So, we count the number of iterations in which {n,+,1} < m is true. 2952 // Note that we cannot simply return max(m-n,0) because it's not safe to 2953 // treat m-n as signed nor unsigned due to overflow possibility. 2954 2955 // First, we get the value of the LHS in the first iteration: n 2956 SCEVHandle Start = AddRec->getOperand(0); 2957 2958 if (isLoopGuardedByCond(L, 2959 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 2960 getMinusSCEV(AddRec->getOperand(0), One), RHS)) { 2961 // Since we know that the condition is true in order to enter the loop, 2962 // we know that it will run exactly m-n times. 2963 return getMinusSCEV(RHS, Start); 2964 } else { 2965 // Then, we get the value of the LHS in the first iteration in which the 2966 // above condition doesn't hold. This equals to max(m,n). 2967 SCEVHandle End = isSigned ? getSMaxExpr(RHS, Start) 2968 : getUMaxExpr(RHS, Start); 2969 2970 // Finally, we subtract these two values to get the number of times the 2971 // backedge is executed: max(m,n)-n. 2972 return getMinusSCEV(End, Start); 2973 } 2974 } 2975 2976 return UnknownValue; 2977} 2978 2979/// getNumIterationsInRange - Return the number of iterations of this loop that 2980/// produce values in the specified constant range. Another way of looking at 2981/// this is that it returns the first iteration number where the value is not in 2982/// the condition, thus computing the exit count. If the iteration count can't 2983/// be computed, an instance of SCEVCouldNotCompute is returned. 2984SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 2985 ScalarEvolution &SE) const { 2986 if (Range.isFullSet()) // Infinite loop. 2987 return SE.getCouldNotCompute(); 2988 2989 // If the start is a non-zero constant, shift the range to simplify things. 2990 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 2991 if (!SC->getValue()->isZero()) { 2992 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 2993 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 2994 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 2995 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 2996 return ShiftedAddRec->getNumIterationsInRange( 2997 Range.subtract(SC->getValue()->getValue()), SE); 2998 // This is strange and shouldn't happen. 2999 return SE.getCouldNotCompute(); 3000 } 3001 3002 // The only time we can solve this is when we have all constant indices. 3003 // Otherwise, we cannot determine the overflow conditions. 3004 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3005 if (!isa<SCEVConstant>(getOperand(i))) 3006 return SE.getCouldNotCompute(); 3007 3008 3009 // Okay at this point we know that all elements of the chrec are constants and 3010 // that the start element is zero. 3011 3012 // First check to see if the range contains zero. If not, the first 3013 // iteration exits. 3014 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3015 if (!Range.contains(APInt(BitWidth, 0))) 3016 return SE.getConstant(ConstantInt::get(getType(),0)); 3017 3018 if (isAffine()) { 3019 // If this is an affine expression then we have this situation: 3020 // Solve {0,+,A} in Range === Ax in Range 3021 3022 // We know that zero is in the range. If A is positive then we know that 3023 // the upper value of the range must be the first possible exit value. 3024 // If A is negative then the lower of the range is the last possible loop 3025 // value. Also note that we already checked for a full range. 3026 APInt One(BitWidth,1); 3027 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3028 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3029 3030 // The exit value should be (End+A)/A. 3031 APInt ExitVal = (End + A).udiv(A); 3032 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3033 3034 // Evaluate at the exit value. If we really did fall out of the valid 3035 // range, then we computed our trip count, otherwise wrap around or other 3036 // things must have happened. 3037 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3038 if (Range.contains(Val->getValue())) 3039 return SE.getCouldNotCompute(); // Something strange happened 3040 3041 // Ensure that the previous value is in the range. This is a sanity check. 3042 assert(Range.contains( 3043 EvaluateConstantChrecAtConstant(this, 3044 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3045 "Linear scev computation is off in a bad way!"); 3046 return SE.getConstant(ExitValue); 3047 } else if (isQuadratic()) { 3048 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3049 // quadratic equation to solve it. To do this, we must frame our problem in 3050 // terms of figuring out when zero is crossed, instead of when 3051 // Range.getUpper() is crossed. 3052 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3053 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3054 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3055 3056 // Next, solve the constructed addrec 3057 std::pair<SCEVHandle,SCEVHandle> Roots = 3058 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3059 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3060 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3061 if (R1) { 3062 // Pick the smallest positive root value. 3063 if (ConstantInt *CB = 3064 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3065 R1->getValue(), R2->getValue()))) { 3066 if (CB->getZExtValue() == false) 3067 std::swap(R1, R2); // R1 is the minimum root now. 3068 3069 // Make sure the root is not off by one. The returned iteration should 3070 // not be in the range, but the previous one should be. When solving 3071 // for "X*X < 5", for example, we should not return a root of 2. 3072 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3073 R1->getValue(), 3074 SE); 3075 if (Range.contains(R1Val->getValue())) { 3076 // The next iteration must be out of the range... 3077 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3078 3079 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3080 if (!Range.contains(R1Val->getValue())) 3081 return SE.getConstant(NextVal); 3082 return SE.getCouldNotCompute(); // Something strange happened 3083 } 3084 3085 // If R1 was not in the range, then it is a good return value. Make 3086 // sure that R1-1 WAS in the range though, just in case. 3087 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3088 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3089 if (Range.contains(R1Val->getValue())) 3090 return R1; 3091 return SE.getCouldNotCompute(); // Something strange happened 3092 } 3093 } 3094 } 3095 3096 return SE.getCouldNotCompute(); 3097} 3098 3099 3100 3101//===----------------------------------------------------------------------===// 3102// ScalarEvolution Class Implementation 3103//===----------------------------------------------------------------------===// 3104 3105ScalarEvolution::ScalarEvolution() 3106 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3107} 3108 3109bool ScalarEvolution::runOnFunction(Function &F) { 3110 this->F = &F; 3111 LI = &getAnalysis<LoopInfo>(); 3112 TD = getAnalysisIfAvailable<TargetData>(); 3113 return false; 3114} 3115 3116void ScalarEvolution::releaseMemory() { 3117 Scalars.clear(); 3118 BackedgeTakenCounts.clear(); 3119 ConstantEvolutionLoopExitValue.clear(); 3120} 3121 3122void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3123 AU.setPreservesAll(); 3124 AU.addRequiredTransitive<LoopInfo>(); 3125} 3126 3127bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3128 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3129} 3130 3131static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3132 const Loop *L) { 3133 // Print all inner loops first 3134 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3135 PrintLoopInfo(OS, SE, *I); 3136 3137 OS << "Loop " << L->getHeader()->getName() << ": "; 3138 3139 SmallVector<BasicBlock*, 8> ExitBlocks; 3140 L->getExitBlocks(ExitBlocks); 3141 if (ExitBlocks.size() != 1) 3142 OS << "<multiple exits> "; 3143 3144 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3145 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3146 } else { 3147 OS << "Unpredictable backedge-taken count. "; 3148 } 3149 3150 OS << "\n"; 3151} 3152 3153void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3154 // ScalarEvolution's implementaiton of the print method is to print 3155 // out SCEV values of all instructions that are interesting. Doing 3156 // this potentially causes it to create new SCEV objects though, 3157 // which technically conflicts with the const qualifier. This isn't 3158 // observable from outside the class though (the hasSCEV function 3159 // notwithstanding), so casting away the const isn't dangerous. 3160 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3161 3162 OS << "Classifying expressions for: " << F->getName() << "\n"; 3163 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3164 if (I->getType()->isInteger()) { 3165 OS << *I; 3166 OS << " --> "; 3167 SCEVHandle SV = SE.getSCEV(&*I); 3168 SV->print(OS); 3169 OS << "\t\t"; 3170 3171 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3172 OS << "Exits: "; 3173 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3174 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3175 OS << "<<Unknown>>"; 3176 } else { 3177 OS << *ExitValue; 3178 } 3179 } 3180 3181 3182 OS << "\n"; 3183 } 3184 3185 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3186 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3187 PrintLoopInfo(OS, &SE, *I); 3188} 3189 3190void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3191 raw_os_ostream OS(o); 3192 print(OS, M); 3193} 3194