ScalarEvolution.cpp revision 3d739fe3756bf67be23c2ca54ec7b04bef89bfe0
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 << "(trunc " << *Op->getType() << " " << *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 << "(zext " << *Op->getType() << " " << *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 << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 265} 266 267// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 268// particular input. Don't use a SCEVHandle here, or else the object will never 269// be deleted! 270static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >, 271 SCEVCommutativeExpr*> > SCEVCommExprs; 272 273SCEVCommutativeExpr::~SCEVCommutativeExpr() { 274 SCEVCommExprs->erase(std::make_pair(getSCEVType(), 275 std::vector<SCEV*>(Operands.begin(), 276 Operands.end()))); 277} 278 279void SCEVCommutativeExpr::print(raw_ostream &OS) const { 280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 281 const char *OpStr = getOperationStr(); 282 OS << "(" << *Operands[0]; 283 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 284 OS << OpStr << *Operands[i]; 285 OS << ")"; 286} 287 288SCEVHandle SCEVCommutativeExpr:: 289replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 290 const SCEVHandle &Conc, 291 ScalarEvolution &SE) const { 292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 293 SCEVHandle H = 294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 295 if (H != getOperand(i)) { 296 std::vector<SCEVHandle> NewOps; 297 NewOps.reserve(getNumOperands()); 298 for (unsigned j = 0; j != i; ++j) 299 NewOps.push_back(getOperand(j)); 300 NewOps.push_back(H); 301 for (++i; i != e; ++i) 302 NewOps.push_back(getOperand(i)-> 303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 304 305 if (isa<SCEVAddExpr>(this)) 306 return SE.getAddExpr(NewOps); 307 else if (isa<SCEVMulExpr>(this)) 308 return SE.getMulExpr(NewOps); 309 else if (isa<SCEVSMaxExpr>(this)) 310 return SE.getSMaxExpr(NewOps); 311 else if (isa<SCEVUMaxExpr>(this)) 312 return SE.getUMaxExpr(NewOps); 313 else 314 assert(0 && "Unknown commutative expr!"); 315 } 316 } 317 return this; 318} 319 320bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 322 if (!getOperand(i)->dominates(BB, DT)) 323 return false; 324 } 325 return true; 326} 327 328 329// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 330// input. Don't use a SCEVHandle here, or else the object will never be 331// deleted! 332static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>, 333 SCEVUDivExpr*> > SCEVUDivs; 334 335SCEVUDivExpr::~SCEVUDivExpr() { 336 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 337} 338 339bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 341} 342 343void SCEVUDivExpr::print(raw_ostream &OS) const { 344 OS << "(" << *LHS << " /u " << *RHS << ")"; 345} 346 347const Type *SCEVUDivExpr::getType() const { 348 return LHS->getType(); 349} 350 351// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 352// particular input. Don't use a SCEVHandle here, or else the object will never 353// be deleted! 354static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >, 355 SCEVAddRecExpr*> > SCEVAddRecExprs; 356 357SCEVAddRecExpr::~SCEVAddRecExpr() { 358 SCEVAddRecExprs->erase(std::make_pair(L, 359 std::vector<SCEV*>(Operands.begin(), 360 Operands.end()))); 361} 362 363bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 364 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 365 if (!getOperand(i)->dominates(BB, DT)) 366 return false; 367 } 368 return true; 369} 370 371 372SCEVHandle SCEVAddRecExpr:: 373replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 374 const SCEVHandle &Conc, 375 ScalarEvolution &SE) const { 376 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 377 SCEVHandle H = 378 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 379 if (H != getOperand(i)) { 380 std::vector<SCEVHandle> NewOps; 381 NewOps.reserve(getNumOperands()); 382 for (unsigned j = 0; j != i; ++j) 383 NewOps.push_back(getOperand(j)); 384 NewOps.push_back(H); 385 for (++i; i != e; ++i) 386 NewOps.push_back(getOperand(i)-> 387 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 388 389 return SE.getAddRecExpr(NewOps, L); 390 } 391 } 392 return this; 393} 394 395 396bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 397 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 398 // contain L and if the start is invariant. 399 return !QueryLoop->contains(L->getHeader()) && 400 getOperand(0)->isLoopInvariant(QueryLoop); 401} 402 403 404void SCEVAddRecExpr::print(raw_ostream &OS) const { 405 OS << "{" << *Operands[0]; 406 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 407 OS << ",+," << *Operands[i]; 408 OS << "}<" << L->getHeader()->getName() + ">"; 409} 410 411// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 412// value. Don't use a SCEVHandle here, or else the object will never be 413// deleted! 414static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 415 416SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 417 418bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 419 // All non-instruction values are loop invariant. All instructions are loop 420 // invariant if they are not contained in the specified loop. 421 if (Instruction *I = dyn_cast<Instruction>(V)) 422 return !L->contains(I->getParent()); 423 return true; 424} 425 426bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 427 if (Instruction *I = dyn_cast<Instruction>(getValue())) 428 return DT->dominates(I->getParent(), BB); 429 return true; 430} 431 432const Type *SCEVUnknown::getType() const { 433 return V->getType(); 434} 435 436void SCEVUnknown::print(raw_ostream &OS) const { 437 if (isa<PointerType>(V->getType())) 438 OS << "(ptrtoint " << *V->getType() << " "; 439 WriteAsOperand(OS, V, false); 440 if (isa<PointerType>(V->getType())) 441 OS << " to iPTR)"; 442} 443 444//===----------------------------------------------------------------------===// 445// SCEV Utilities 446//===----------------------------------------------------------------------===// 447 448namespace { 449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 450 /// than the complexity of the RHS. This comparator is used to canonicalize 451 /// expressions. 452 struct VISIBILITY_HIDDEN SCEVComplexityCompare { 453 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 454 return LHS->getSCEVType() < RHS->getSCEVType(); 455 } 456 }; 457} 458 459/// GroupByComplexity - Given a list of SCEV objects, order them by their 460/// complexity, and group objects of the same complexity together by value. 461/// When this routine is finished, we know that any duplicates in the vector are 462/// consecutive and that complexity is monotonically increasing. 463/// 464/// Note that we go take special precautions to ensure that we get determinstic 465/// results from this routine. In other words, we don't want the results of 466/// this to depend on where the addresses of various SCEV objects happened to 467/// land in memory. 468/// 469static void GroupByComplexity(std::vector<SCEVHandle> &Ops) { 470 if (Ops.size() < 2) return; // Noop 471 if (Ops.size() == 2) { 472 // This is the common case, which also happens to be trivially simple. 473 // Special case it. 474 if (SCEVComplexityCompare()(Ops[1], Ops[0])) 475 std::swap(Ops[0], Ops[1]); 476 return; 477 } 478 479 // Do the rough sort by complexity. 480 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare()); 481 482 // Now that we are sorted by complexity, group elements of the same 483 // complexity. Note that this is, at worst, N^2, but the vector is likely to 484 // be extremely short in practice. Note that we take this approach because we 485 // do not want to depend on the addresses of the objects we are grouping. 486 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 487 SCEV *S = Ops[i]; 488 unsigned Complexity = S->getSCEVType(); 489 490 // If there are any objects of the same complexity and same value as this 491 // one, group them. 492 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 493 if (Ops[j] == S) { // Found a duplicate. 494 // Move it to immediately after i'th element. 495 std::swap(Ops[i+1], Ops[j]); 496 ++i; // no need to rescan it. 497 if (i == e-2) return; // Done! 498 } 499 } 500 } 501} 502 503 504 505//===----------------------------------------------------------------------===// 506// Simple SCEV method implementations 507//===----------------------------------------------------------------------===// 508 509/// BinomialCoefficient - Compute BC(It, K). The result has width W. 510// Assume, K > 0. 511static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 512 ScalarEvolution &SE, 513 const Type* ResultTy) { 514 // Handle the simplest case efficiently. 515 if (K == 1) 516 return SE.getTruncateOrZeroExtend(It, ResultTy); 517 518 // We are using the following formula for BC(It, K): 519 // 520 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 521 // 522 // Suppose, W is the bitwidth of the return value. We must be prepared for 523 // overflow. Hence, we must assure that the result of our computation is 524 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 525 // safe in modular arithmetic. 526 // 527 // However, this code doesn't use exactly that formula; the formula it uses 528 // is something like the following, where T is the number of factors of 2 in 529 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 530 // exponentiation: 531 // 532 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 533 // 534 // This formula is trivially equivalent to the previous formula. However, 535 // this formula can be implemented much more efficiently. The trick is that 536 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 537 // arithmetic. To do exact division in modular arithmetic, all we have 538 // to do is multiply by the inverse. Therefore, this step can be done at 539 // width W. 540 // 541 // The next issue is how to safely do the division by 2^T. The way this 542 // is done is by doing the multiplication step at a width of at least W + T 543 // bits. This way, the bottom W+T bits of the product are accurate. Then, 544 // when we perform the division by 2^T (which is equivalent to a right shift 545 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 546 // truncated out after the division by 2^T. 547 // 548 // In comparison to just directly using the first formula, this technique 549 // is much more efficient; using the first formula requires W * K bits, 550 // but this formula less than W + K bits. Also, the first formula requires 551 // a division step, whereas this formula only requires multiplies and shifts. 552 // 553 // It doesn't matter whether the subtraction step is done in the calculation 554 // width or the input iteration count's width; if the subtraction overflows, 555 // the result must be zero anyway. We prefer here to do it in the width of 556 // the induction variable because it helps a lot for certain cases; CodeGen 557 // isn't smart enough to ignore the overflow, which leads to much less 558 // efficient code if the width of the subtraction is wider than the native 559 // register width. 560 // 561 // (It's possible to not widen at all by pulling out factors of 2 before 562 // the multiplication; for example, K=2 can be calculated as 563 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 564 // extra arithmetic, so it's not an obvious win, and it gets 565 // much more complicated for K > 3.) 566 567 // Protection from insane SCEVs; this bound is conservative, 568 // but it probably doesn't matter. 569 if (K > 1000) 570 return SE.getCouldNotCompute(); 571 572 unsigned W = SE.getTypeSizeInBits(ResultTy); 573 574 // Calculate K! / 2^T and T; we divide out the factors of two before 575 // multiplying for calculating K! / 2^T to avoid overflow. 576 // Other overflow doesn't matter because we only care about the bottom 577 // W bits of the result. 578 APInt OddFactorial(W, 1); 579 unsigned T = 1; 580 for (unsigned i = 3; i <= K; ++i) { 581 APInt Mult(W, i); 582 unsigned TwoFactors = Mult.countTrailingZeros(); 583 T += TwoFactors; 584 Mult = Mult.lshr(TwoFactors); 585 OddFactorial *= Mult; 586 } 587 588 // We need at least W + T bits for the multiplication step 589 unsigned CalculationBits = W + T; 590 591 // Calcuate 2^T, at width T+W. 592 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 593 594 // Calculate the multiplicative inverse of K! / 2^T; 595 // this multiplication factor will perform the exact division by 596 // K! / 2^T. 597 APInt Mod = APInt::getSignedMinValue(W+1); 598 APInt MultiplyFactor = OddFactorial.zext(W+1); 599 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 600 MultiplyFactor = MultiplyFactor.trunc(W); 601 602 // Calculate the product, at width T+W 603 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 604 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 605 for (unsigned i = 1; i != K; ++i) { 606 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 607 Dividend = SE.getMulExpr(Dividend, 608 SE.getTruncateOrZeroExtend(S, CalculationTy)); 609 } 610 611 // Divide by 2^T 612 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 613 614 // Truncate the result, and divide by K! / 2^T. 615 616 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 617 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 618} 619 620/// evaluateAtIteration - Return the value of this chain of recurrences at 621/// the specified iteration number. We can evaluate this recurrence by 622/// multiplying each element in the chain by the binomial coefficient 623/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 624/// 625/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 626/// 627/// where BC(It, k) stands for binomial coefficient. 628/// 629SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 630 ScalarEvolution &SE) const { 631 SCEVHandle Result = getStart(); 632 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 633 // The computation is correct in the face of overflow provided that the 634 // multiplication is performed _after_ the evaluation of the binomial 635 // coefficient. 636 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType()); 637 if (isa<SCEVCouldNotCompute>(Coeff)) 638 return Coeff; 639 640 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 641 } 642 return Result; 643} 644 645//===----------------------------------------------------------------------===// 646// SCEV Expression folder implementations 647//===----------------------------------------------------------------------===// 648 649SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) { 650 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 651 "This is not a truncating conversion!"); 652 653 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 654 return getUnknown( 655 ConstantExpr::getTrunc(SC->getValue(), Ty)); 656 657 // trunc(trunc(x)) --> trunc(x) 658 if (SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 659 return getTruncateExpr(ST->getOperand(), Ty); 660 661 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 662 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 663 return getTruncateOrSignExtend(SS->getOperand(), Ty); 664 665 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 666 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 667 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 668 669 // If the input value is a chrec scev made out of constants, truncate 670 // all of the constants. 671 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 672 std::vector<SCEVHandle> Operands; 673 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 674 // FIXME: This should allow truncation of other expression types! 675 if (isa<SCEVConstant>(AddRec->getOperand(i))) 676 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 677 else 678 break; 679 if (Operands.size() == AddRec->getNumOperands()) 680 return getAddRecExpr(Operands, AddRec->getLoop()); 681 } 682 683 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 684 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 685 return Result; 686} 687 688SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 689 const Type *Ty) { 690 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 691 "This is not an extending conversion!"); 692 693 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 694 const Type *IntTy = getEffectiveSCEVType(Ty); 695 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 696 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 697 return getUnknown(C); 698 } 699 700 // zext(zext(x)) --> zext(x) 701 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 702 return getZeroExtendExpr(SZ->getOperand(), Ty); 703 704 // If the input value is a chrec scev, and we can prove that the value 705 // did not overflow the old, smaller, value, we can zero extend all of the 706 // operands (often constants). This allows analysis of something like 707 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 708 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 709 if (AR->isAffine()) { 710 // Check whether the backedge-taken count is SCEVCouldNotCompute. 711 // Note that this serves two purposes: It filters out loops that are 712 // simply not analyzable, and it covers the case where this code is 713 // being called from within backedge-taken count analysis, such that 714 // attempting to ask for the backedge-taken count would likely result 715 // in infinite recursion. In the later case, the analysis code will 716 // cope with a conservative value, and it will take care to purge 717 // that value once it has finished. 718 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 719 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 720 // Manually compute the final value for AR, checking for 721 // overflow. 722 SCEVHandle Start = AR->getStart(); 723 SCEVHandle Step = AR->getStepRecurrence(*this); 724 725 // Check whether the backedge-taken count can be losslessly casted to 726 // the addrec's type. The count is always unsigned. 727 SCEVHandle CastedMaxBECount = 728 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 729 if (MaxBECount == 730 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 731 const Type *WideTy = 732 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 733 // Check whether Start+Step*MaxBECount has no unsigned overflow. 734 SCEVHandle ZMul = 735 getMulExpr(CastedMaxBECount, 736 getTruncateOrZeroExtend(Step, Start->getType())); 737 SCEVHandle Add = getAddExpr(Start, ZMul); 738 if (getZeroExtendExpr(Add, WideTy) == 739 getAddExpr(getZeroExtendExpr(Start, WideTy), 740 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 741 getZeroExtendExpr(Step, WideTy)))) 742 // Return the expression with the addrec on the outside. 743 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 744 getZeroExtendExpr(Step, Ty), 745 AR->getLoop()); 746 747 // Similar to above, only this time treat the step value as signed. 748 // This covers loops that count down. 749 SCEVHandle SMul = 750 getMulExpr(CastedMaxBECount, 751 getTruncateOrSignExtend(Step, Start->getType())); 752 Add = getAddExpr(Start, SMul); 753 if (getZeroExtendExpr(Add, WideTy) == 754 getAddExpr(getZeroExtendExpr(Start, WideTy), 755 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 756 getSignExtendExpr(Step, WideTy)))) 757 // Return the expression with the addrec on the outside. 758 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 759 getSignExtendExpr(Step, Ty), 760 AR->getLoop()); 761 } 762 } 763 } 764 765 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 766 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 767 return Result; 768} 769 770SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, 771 const Type *Ty) { 772 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 773 "This is not an extending conversion!"); 774 775 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 776 const Type *IntTy = getEffectiveSCEVType(Ty); 777 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 778 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 779 return getUnknown(C); 780 } 781 782 // sext(sext(x)) --> sext(x) 783 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 784 return getSignExtendExpr(SS->getOperand(), Ty); 785 786 // If the input value is a chrec scev, and we can prove that the value 787 // did not overflow the old, smaller, value, we can sign extend all of the 788 // operands (often constants). This allows analysis of something like 789 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 790 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 791 if (AR->isAffine()) { 792 // Check whether the backedge-taken count is SCEVCouldNotCompute. 793 // Note that this serves two purposes: It filters out loops that are 794 // simply not analyzable, and it covers the case where this code is 795 // being called from within backedge-taken count analysis, such that 796 // attempting to ask for the backedge-taken count would likely result 797 // in infinite recursion. In the later case, the analysis code will 798 // cope with a conservative value, and it will take care to purge 799 // that value once it has finished. 800 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 801 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 802 // Manually compute the final value for AR, checking for 803 // overflow. 804 SCEVHandle Start = AR->getStart(); 805 SCEVHandle Step = AR->getStepRecurrence(*this); 806 807 // Check whether the backedge-taken count can be losslessly casted to 808 // the addrec's type. The count is always unsigned. 809 SCEVHandle CastedMaxBECount = 810 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 811 if (MaxBECount == 812 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 813 const Type *WideTy = 814 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 815 // Check whether Start+Step*MaxBECount has no signed overflow. 816 SCEVHandle SMul = 817 getMulExpr(CastedMaxBECount, 818 getTruncateOrSignExtend(Step, Start->getType())); 819 SCEVHandle Add = getAddExpr(Start, SMul); 820 if (getSignExtendExpr(Add, WideTy) == 821 getAddExpr(getSignExtendExpr(Start, WideTy), 822 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 823 getSignExtendExpr(Step, WideTy)))) 824 // Return the expression with the addrec on the outside. 825 return getAddRecExpr(getSignExtendExpr(Start, Ty), 826 getSignExtendExpr(Step, Ty), 827 AR->getLoop()); 828 } 829 } 830 } 831 832 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 833 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 834 return Result; 835} 836 837// get - Get a canonical add expression, or something simpler if possible. 838SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 839 assert(!Ops.empty() && "Cannot get empty add!"); 840 if (Ops.size() == 1) return Ops[0]; 841 842 // Sort by complexity, this groups all similar expression types together. 843 GroupByComplexity(Ops); 844 845 // If there are any constants, fold them together. 846 unsigned Idx = 0; 847 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 848 ++Idx; 849 assert(Idx < Ops.size()); 850 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 851 // We found two constants, fold them together! 852 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 853 RHSC->getValue()->getValue()); 854 Ops[0] = getConstant(Fold); 855 Ops.erase(Ops.begin()+1); // Erase the folded element 856 if (Ops.size() == 1) return Ops[0]; 857 LHSC = cast<SCEVConstant>(Ops[0]); 858 } 859 860 // If we are left with a constant zero being added, strip it off. 861 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 862 Ops.erase(Ops.begin()); 863 --Idx; 864 } 865 } 866 867 if (Ops.size() == 1) return Ops[0]; 868 869 // Okay, check to see if the same value occurs in the operand list twice. If 870 // so, merge them together into an multiply expression. Since we sorted the 871 // list, these values are required to be adjacent. 872 const Type *Ty = Ops[0]->getType(); 873 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 874 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 875 // Found a match, merge the two values into a multiply, and add any 876 // remaining values to the result. 877 SCEVHandle Two = getIntegerSCEV(2, Ty); 878 SCEVHandle Mul = getMulExpr(Ops[i], Two); 879 if (Ops.size() == 2) 880 return Mul; 881 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 882 Ops.push_back(Mul); 883 return getAddExpr(Ops); 884 } 885 886 // Now we know the first non-constant operand. Skip past any cast SCEVs. 887 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 888 ++Idx; 889 890 // If there are add operands they would be next. 891 if (Idx < Ops.size()) { 892 bool DeletedAdd = false; 893 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 894 // If we have an add, expand the add operands onto the end of the operands 895 // list. 896 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 897 Ops.erase(Ops.begin()+Idx); 898 DeletedAdd = true; 899 } 900 901 // If we deleted at least one add, we added operands to the end of the list, 902 // and they are not necessarily sorted. Recurse to resort and resimplify 903 // any operands we just aquired. 904 if (DeletedAdd) 905 return getAddExpr(Ops); 906 } 907 908 // Skip over the add expression until we get to a multiply. 909 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 910 ++Idx; 911 912 // If we are adding something to a multiply expression, make sure the 913 // something is not already an operand of the multiply. If so, merge it into 914 // the multiply. 915 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 916 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 917 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 918 SCEV *MulOpSCEV = Mul->getOperand(MulOp); 919 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 920 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 921 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 922 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 923 if (Mul->getNumOperands() != 2) { 924 // If the multiply has more than two operands, we must get the 925 // Y*Z term. 926 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 927 MulOps.erase(MulOps.begin()+MulOp); 928 InnerMul = getMulExpr(MulOps); 929 } 930 SCEVHandle One = getIntegerSCEV(1, Ty); 931 SCEVHandle AddOne = getAddExpr(InnerMul, One); 932 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 933 if (Ops.size() == 2) return OuterMul; 934 if (AddOp < Idx) { 935 Ops.erase(Ops.begin()+AddOp); 936 Ops.erase(Ops.begin()+Idx-1); 937 } else { 938 Ops.erase(Ops.begin()+Idx); 939 Ops.erase(Ops.begin()+AddOp-1); 940 } 941 Ops.push_back(OuterMul); 942 return getAddExpr(Ops); 943 } 944 945 // Check this multiply against other multiplies being added together. 946 for (unsigned OtherMulIdx = Idx+1; 947 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 948 ++OtherMulIdx) { 949 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 950 // If MulOp occurs in OtherMul, we can fold the two multiplies 951 // together. 952 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 953 OMulOp != e; ++OMulOp) 954 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 955 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 956 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 957 if (Mul->getNumOperands() != 2) { 958 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 959 MulOps.erase(MulOps.begin()+MulOp); 960 InnerMul1 = getMulExpr(MulOps); 961 } 962 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 963 if (OtherMul->getNumOperands() != 2) { 964 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 965 OtherMul->op_end()); 966 MulOps.erase(MulOps.begin()+OMulOp); 967 InnerMul2 = getMulExpr(MulOps); 968 } 969 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 970 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 971 if (Ops.size() == 2) return OuterMul; 972 Ops.erase(Ops.begin()+Idx); 973 Ops.erase(Ops.begin()+OtherMulIdx-1); 974 Ops.push_back(OuterMul); 975 return getAddExpr(Ops); 976 } 977 } 978 } 979 } 980 981 // If there are any add recurrences in the operands list, see if any other 982 // added values are loop invariant. If so, we can fold them into the 983 // recurrence. 984 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 985 ++Idx; 986 987 // Scan over all recurrences, trying to fold loop invariants into them. 988 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 989 // Scan all of the other operands to this add and add them to the vector if 990 // they are loop invariant w.r.t. the recurrence. 991 std::vector<SCEVHandle> LIOps; 992 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 993 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 994 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 995 LIOps.push_back(Ops[i]); 996 Ops.erase(Ops.begin()+i); 997 --i; --e; 998 } 999 1000 // If we found some loop invariants, fold them into the recurrence. 1001 if (!LIOps.empty()) { 1002 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1003 LIOps.push_back(AddRec->getStart()); 1004 1005 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 1006 AddRecOps[0] = getAddExpr(LIOps); 1007 1008 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1009 // If all of the other operands were loop invariant, we are done. 1010 if (Ops.size() == 1) return NewRec; 1011 1012 // Otherwise, add the folded AddRec by the non-liv parts. 1013 for (unsigned i = 0;; ++i) 1014 if (Ops[i] == AddRec) { 1015 Ops[i] = NewRec; 1016 break; 1017 } 1018 return getAddExpr(Ops); 1019 } 1020 1021 // Okay, if there weren't any loop invariants to be folded, check to see if 1022 // there are multiple AddRec's with the same loop induction variable being 1023 // added together. If so, we can fold them. 1024 for (unsigned OtherIdx = Idx+1; 1025 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1026 if (OtherIdx != Idx) { 1027 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1028 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1029 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1030 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 1031 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1032 if (i >= NewOps.size()) { 1033 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1034 OtherAddRec->op_end()); 1035 break; 1036 } 1037 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1038 } 1039 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1040 1041 if (Ops.size() == 2) return NewAddRec; 1042 1043 Ops.erase(Ops.begin()+Idx); 1044 Ops.erase(Ops.begin()+OtherIdx-1); 1045 Ops.push_back(NewAddRec); 1046 return getAddExpr(Ops); 1047 } 1048 } 1049 1050 // Otherwise couldn't fold anything into this recurrence. Move onto the 1051 // next one. 1052 } 1053 1054 // Okay, it looks like we really DO need an add expr. Check to see if we 1055 // already have one, otherwise create a new one. 1056 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1057 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 1058 SCEVOps)]; 1059 if (Result == 0) Result = new SCEVAddExpr(Ops); 1060 return Result; 1061} 1062 1063 1064SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 1065 assert(!Ops.empty() && "Cannot get empty mul!"); 1066 1067 // Sort by complexity, this groups all similar expression types together. 1068 GroupByComplexity(Ops); 1069 1070 // If there are any constants, fold them together. 1071 unsigned Idx = 0; 1072 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1073 1074 // C1*(C2+V) -> C1*C2 + C1*V 1075 if (Ops.size() == 2) 1076 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1077 if (Add->getNumOperands() == 2 && 1078 isa<SCEVConstant>(Add->getOperand(0))) 1079 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1080 getMulExpr(LHSC, Add->getOperand(1))); 1081 1082 1083 ++Idx; 1084 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1085 // We found two constants, fold them together! 1086 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1087 RHSC->getValue()->getValue()); 1088 Ops[0] = getConstant(Fold); 1089 Ops.erase(Ops.begin()+1); // Erase the folded element 1090 if (Ops.size() == 1) return Ops[0]; 1091 LHSC = cast<SCEVConstant>(Ops[0]); 1092 } 1093 1094 // If we are left with a constant one being multiplied, strip it off. 1095 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1096 Ops.erase(Ops.begin()); 1097 --Idx; 1098 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1099 // If we have a multiply of zero, it will always be zero. 1100 return Ops[0]; 1101 } 1102 } 1103 1104 // Skip over the add expression until we get to a multiply. 1105 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1106 ++Idx; 1107 1108 if (Ops.size() == 1) 1109 return Ops[0]; 1110 1111 // If there are mul operands inline them all into this expression. 1112 if (Idx < Ops.size()) { 1113 bool DeletedMul = false; 1114 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1115 // If we have an mul, expand the mul operands onto the end of the operands 1116 // list. 1117 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1118 Ops.erase(Ops.begin()+Idx); 1119 DeletedMul = true; 1120 } 1121 1122 // If we deleted at least one mul, we added operands to the end of the list, 1123 // and they are not necessarily sorted. Recurse to resort and resimplify 1124 // any operands we just aquired. 1125 if (DeletedMul) 1126 return getMulExpr(Ops); 1127 } 1128 1129 // If there are any add recurrences in the operands list, see if any other 1130 // added values are loop invariant. If so, we can fold them into the 1131 // recurrence. 1132 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1133 ++Idx; 1134 1135 // Scan over all recurrences, trying to fold loop invariants into them. 1136 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1137 // Scan all of the other operands to this mul and add them to the vector if 1138 // they are loop invariant w.r.t. the recurrence. 1139 std::vector<SCEVHandle> LIOps; 1140 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1141 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1142 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1143 LIOps.push_back(Ops[i]); 1144 Ops.erase(Ops.begin()+i); 1145 --i; --e; 1146 } 1147 1148 // If we found some loop invariants, fold them into the recurrence. 1149 if (!LIOps.empty()) { 1150 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1151 std::vector<SCEVHandle> NewOps; 1152 NewOps.reserve(AddRec->getNumOperands()); 1153 if (LIOps.size() == 1) { 1154 SCEV *Scale = LIOps[0]; 1155 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1156 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1157 } else { 1158 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1159 std::vector<SCEVHandle> MulOps(LIOps); 1160 MulOps.push_back(AddRec->getOperand(i)); 1161 NewOps.push_back(getMulExpr(MulOps)); 1162 } 1163 } 1164 1165 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1166 1167 // If all of the other operands were loop invariant, we are done. 1168 if (Ops.size() == 1) return NewRec; 1169 1170 // Otherwise, multiply the folded AddRec by the non-liv parts. 1171 for (unsigned i = 0;; ++i) 1172 if (Ops[i] == AddRec) { 1173 Ops[i] = NewRec; 1174 break; 1175 } 1176 return getMulExpr(Ops); 1177 } 1178 1179 // Okay, if there weren't any loop invariants to be folded, check to see if 1180 // there are multiple AddRec's with the same loop induction variable being 1181 // multiplied together. If so, we can fold them. 1182 for (unsigned OtherIdx = Idx+1; 1183 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1184 if (OtherIdx != Idx) { 1185 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1186 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1187 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1188 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1189 SCEVHandle NewStart = getMulExpr(F->getStart(), 1190 G->getStart()); 1191 SCEVHandle B = F->getStepRecurrence(*this); 1192 SCEVHandle D = G->getStepRecurrence(*this); 1193 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1194 getMulExpr(G, B), 1195 getMulExpr(B, D)); 1196 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1197 F->getLoop()); 1198 if (Ops.size() == 2) return NewAddRec; 1199 1200 Ops.erase(Ops.begin()+Idx); 1201 Ops.erase(Ops.begin()+OtherIdx-1); 1202 Ops.push_back(NewAddRec); 1203 return getMulExpr(Ops); 1204 } 1205 } 1206 1207 // Otherwise couldn't fold anything into this recurrence. Move onto the 1208 // next one. 1209 } 1210 1211 // Okay, it looks like we really DO need an mul expr. Check to see if we 1212 // already have one, otherwise create a new one. 1213 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1214 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1215 SCEVOps)]; 1216 if (Result == 0) 1217 Result = new SCEVMulExpr(Ops); 1218 return Result; 1219} 1220 1221SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) { 1222 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1223 if (RHSC->getValue()->equalsInt(1)) 1224 return LHS; // X udiv 1 --> x 1225 1226 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1227 Constant *LHSCV = LHSC->getValue(); 1228 Constant *RHSCV = RHSC->getValue(); 1229 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1230 } 1231 } 1232 1233 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow. 1234 1235 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1236 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1237 return Result; 1238} 1239 1240 1241/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1242/// specified loop. Simplify the expression as much as possible. 1243SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1244 const SCEVHandle &Step, const Loop *L) { 1245 std::vector<SCEVHandle> Operands; 1246 Operands.push_back(Start); 1247 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1248 if (StepChrec->getLoop() == L) { 1249 Operands.insert(Operands.end(), StepChrec->op_begin(), 1250 StepChrec->op_end()); 1251 return getAddRecExpr(Operands, L); 1252 } 1253 1254 Operands.push_back(Step); 1255 return getAddRecExpr(Operands, L); 1256} 1257 1258/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1259/// specified loop. Simplify the expression as much as possible. 1260SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1261 const Loop *L) { 1262 if (Operands.size() == 1) return Operands[0]; 1263 1264 if (Operands.back()->isZero()) { 1265 Operands.pop_back(); 1266 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1267 } 1268 1269 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1270 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1271 const Loop* NestedLoop = NestedAR->getLoop(); 1272 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1273 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1274 NestedAR->op_end()); 1275 SCEVHandle NestedARHandle(NestedAR); 1276 Operands[0] = NestedAR->getStart(); 1277 NestedOperands[0] = getAddRecExpr(Operands, L); 1278 return getAddRecExpr(NestedOperands, NestedLoop); 1279 } 1280 } 1281 1282 SCEVAddRecExpr *&Result = 1283 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(), 1284 Operands.end()))]; 1285 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1286 return Result; 1287} 1288 1289SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1290 const SCEVHandle &RHS) { 1291 std::vector<SCEVHandle> Ops; 1292 Ops.push_back(LHS); 1293 Ops.push_back(RHS); 1294 return getSMaxExpr(Ops); 1295} 1296 1297SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1298 assert(!Ops.empty() && "Cannot get empty smax!"); 1299 if (Ops.size() == 1) return Ops[0]; 1300 1301 // Sort by complexity, this groups all similar expression types together. 1302 GroupByComplexity(Ops); 1303 1304 // If there are any constants, fold them together. 1305 unsigned Idx = 0; 1306 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1307 ++Idx; 1308 assert(Idx < Ops.size()); 1309 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1310 // We found two constants, fold them together! 1311 ConstantInt *Fold = ConstantInt::get( 1312 APIntOps::smax(LHSC->getValue()->getValue(), 1313 RHSC->getValue()->getValue())); 1314 Ops[0] = getConstant(Fold); 1315 Ops.erase(Ops.begin()+1); // Erase the folded element 1316 if (Ops.size() == 1) return Ops[0]; 1317 LHSC = cast<SCEVConstant>(Ops[0]); 1318 } 1319 1320 // If we are left with a constant -inf, strip it off. 1321 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1322 Ops.erase(Ops.begin()); 1323 --Idx; 1324 } 1325 } 1326 1327 if (Ops.size() == 1) return Ops[0]; 1328 1329 // Find the first SMax 1330 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1331 ++Idx; 1332 1333 // Check to see if one of the operands is an SMax. If so, expand its operands 1334 // onto our operand list, and recurse to simplify. 1335 if (Idx < Ops.size()) { 1336 bool DeletedSMax = false; 1337 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1338 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1339 Ops.erase(Ops.begin()+Idx); 1340 DeletedSMax = true; 1341 } 1342 1343 if (DeletedSMax) 1344 return getSMaxExpr(Ops); 1345 } 1346 1347 // Okay, check to see if the same value occurs in the operand list twice. If 1348 // so, delete one. Since we sorted the list, these values are required to 1349 // be adjacent. 1350 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1351 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1352 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1353 --i; --e; 1354 } 1355 1356 if (Ops.size() == 1) return Ops[0]; 1357 1358 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1359 1360 // Okay, it looks like we really DO need an smax expr. Check to see if we 1361 // already have one, otherwise create a new one. 1362 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1363 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1364 SCEVOps)]; 1365 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1366 return Result; 1367} 1368 1369SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1370 const SCEVHandle &RHS) { 1371 std::vector<SCEVHandle> Ops; 1372 Ops.push_back(LHS); 1373 Ops.push_back(RHS); 1374 return getUMaxExpr(Ops); 1375} 1376 1377SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1378 assert(!Ops.empty() && "Cannot get empty umax!"); 1379 if (Ops.size() == 1) return Ops[0]; 1380 1381 // Sort by complexity, this groups all similar expression types together. 1382 GroupByComplexity(Ops); 1383 1384 // If there are any constants, fold them together. 1385 unsigned Idx = 0; 1386 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1387 ++Idx; 1388 assert(Idx < Ops.size()); 1389 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1390 // We found two constants, fold them together! 1391 ConstantInt *Fold = ConstantInt::get( 1392 APIntOps::umax(LHSC->getValue()->getValue(), 1393 RHSC->getValue()->getValue())); 1394 Ops[0] = getConstant(Fold); 1395 Ops.erase(Ops.begin()+1); // Erase the folded element 1396 if (Ops.size() == 1) return Ops[0]; 1397 LHSC = cast<SCEVConstant>(Ops[0]); 1398 } 1399 1400 // If we are left with a constant zero, strip it off. 1401 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1402 Ops.erase(Ops.begin()); 1403 --Idx; 1404 } 1405 } 1406 1407 if (Ops.size() == 1) return Ops[0]; 1408 1409 // Find the first UMax 1410 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1411 ++Idx; 1412 1413 // Check to see if one of the operands is a UMax. If so, expand its operands 1414 // onto our operand list, and recurse to simplify. 1415 if (Idx < Ops.size()) { 1416 bool DeletedUMax = false; 1417 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1418 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1419 Ops.erase(Ops.begin()+Idx); 1420 DeletedUMax = true; 1421 } 1422 1423 if (DeletedUMax) 1424 return getUMaxExpr(Ops); 1425 } 1426 1427 // Okay, check to see if the same value occurs in the operand list twice. If 1428 // so, delete one. Since we sorted the list, these values are required to 1429 // be adjacent. 1430 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1431 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1432 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1433 --i; --e; 1434 } 1435 1436 if (Ops.size() == 1) return Ops[0]; 1437 1438 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1439 1440 // Okay, it looks like we really DO need a umax expr. Check to see if we 1441 // already have one, otherwise create a new one. 1442 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1443 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1444 SCEVOps)]; 1445 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1446 return Result; 1447} 1448 1449SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1450 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1451 return getConstant(CI); 1452 if (isa<ConstantPointerNull>(V)) 1453 return getIntegerSCEV(0, V->getType()); 1454 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1455 if (Result == 0) Result = new SCEVUnknown(V); 1456 return Result; 1457} 1458 1459//===----------------------------------------------------------------------===// 1460// Basic SCEV Analysis and PHI Idiom Recognition Code 1461// 1462 1463/// deleteValueFromRecords - This method should be called by the 1464/// client before it removes an instruction from the program, to make sure 1465/// that no dangling references are left around. 1466void ScalarEvolution::deleteValueFromRecords(Value *V) { 1467 SmallVector<Value *, 16> Worklist; 1468 1469 if (Scalars.erase(V)) { 1470 if (PHINode *PN = dyn_cast<PHINode>(V)) 1471 ConstantEvolutionLoopExitValue.erase(PN); 1472 Worklist.push_back(V); 1473 } 1474 1475 while (!Worklist.empty()) { 1476 Value *VV = Worklist.back(); 1477 Worklist.pop_back(); 1478 1479 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end(); 1480 UI != UE; ++UI) { 1481 Instruction *Inst = cast<Instruction>(*UI); 1482 if (Scalars.erase(Inst)) { 1483 if (PHINode *PN = dyn_cast<PHINode>(VV)) 1484 ConstantEvolutionLoopExitValue.erase(PN); 1485 Worklist.push_back(Inst); 1486 } 1487 } 1488 } 1489} 1490 1491/// isSCEVable - Test if values of the given type are analyzable within 1492/// the SCEV framework. This primarily includes integer types, and it 1493/// can optionally include pointer types if the ScalarEvolution class 1494/// has access to target-specific information. 1495bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1496 // Integers are always SCEVable. 1497 if (Ty->isInteger()) 1498 return true; 1499 1500 // Pointers are SCEVable if TargetData information is available 1501 // to provide pointer size information. 1502 if (isa<PointerType>(Ty)) 1503 return TD != NULL; 1504 1505 // Otherwise it's not SCEVable. 1506 return false; 1507} 1508 1509/// getTypeSizeInBits - Return the size in bits of the specified type, 1510/// for which isSCEVable must return true. 1511uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1512 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1513 1514 // If we have a TargetData, use it! 1515 if (TD) 1516 return TD->getTypeSizeInBits(Ty); 1517 1518 // Otherwise, we support only integer types. 1519 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1520 return Ty->getPrimitiveSizeInBits(); 1521} 1522 1523/// getEffectiveSCEVType - Return a type with the same bitwidth as 1524/// the given type and which represents how SCEV will treat the given 1525/// type, for which isSCEVable must return true. For pointer types, 1526/// this is the pointer-sized integer type. 1527const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1528 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1529 1530 if (Ty->isInteger()) 1531 return Ty; 1532 1533 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1534 return TD->getIntPtrType(); 1535} 1536 1537SCEVHandle ScalarEvolution::getCouldNotCompute() { 1538 return UnknownValue; 1539} 1540 1541/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1542/// expression and create a new one. 1543SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1544 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1545 1546 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V); 1547 if (I != Scalars.end()) return I->second; 1548 SCEVHandle S = createSCEV(V); 1549 Scalars.insert(std::make_pair(V, S)); 1550 return S; 1551} 1552 1553/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1554/// specified signed integer value and return a SCEV for the constant. 1555SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 1556 Ty = getEffectiveSCEVType(Ty); 1557 Constant *C; 1558 if (Val == 0) 1559 C = Constant::getNullValue(Ty); 1560 else if (Ty->isFloatingPoint()) 1561 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1562 APFloat::IEEEdouble, Val)); 1563 else 1564 C = ConstantInt::get(Ty, Val); 1565 return getUnknown(C); 1566} 1567 1568/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1569/// 1570SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 1571 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1572 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 1573 1574 const Type *Ty = V->getType(); 1575 Ty = getEffectiveSCEVType(Ty); 1576 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 1577} 1578 1579/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1580SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 1581 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1582 return getUnknown(ConstantExpr::getNot(VC->getValue())); 1583 1584 const Type *Ty = V->getType(); 1585 Ty = getEffectiveSCEVType(Ty); 1586 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 1587 return getMinusSCEV(AllOnes, V); 1588} 1589 1590/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1591/// 1592SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 1593 const SCEVHandle &RHS) { 1594 // X - Y --> X + -Y 1595 return getAddExpr(LHS, getNegativeSCEV(RHS)); 1596} 1597 1598/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1599/// input value to the specified type. If the type must be extended, it is zero 1600/// extended. 1601SCEVHandle 1602ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 1603 const Type *Ty) { 1604 const Type *SrcTy = V->getType(); 1605 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1606 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1607 "Cannot truncate or zero extend with non-integer arguments!"); 1608 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1609 return V; // No conversion 1610 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1611 return getTruncateExpr(V, Ty); 1612 return getZeroExtendExpr(V, Ty); 1613} 1614 1615/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1616/// input value to the specified type. If the type must be extended, it is sign 1617/// extended. 1618SCEVHandle 1619ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 1620 const Type *Ty) { 1621 const Type *SrcTy = V->getType(); 1622 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1623 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1624 "Cannot truncate or zero extend with non-integer arguments!"); 1625 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1626 return V; // No conversion 1627 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1628 return getTruncateExpr(V, Ty); 1629 return getSignExtendExpr(V, Ty); 1630} 1631 1632/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1633/// the specified instruction and replaces any references to the symbolic value 1634/// SymName with the specified value. This is used during PHI resolution. 1635void ScalarEvolution:: 1636ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1637 const SCEVHandle &NewVal) { 1638 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I); 1639 if (SI == Scalars.end()) return; 1640 1641 SCEVHandle NV = 1642 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 1643 if (NV == SI->second) return; // No change. 1644 1645 SI->second = NV; // Update the scalars map! 1646 1647 // Any instruction values that use this instruction might also need to be 1648 // updated! 1649 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1650 UI != E; ++UI) 1651 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1652} 1653 1654/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1655/// a loop header, making it a potential recurrence, or it doesn't. 1656/// 1657SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 1658 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1659 if (const Loop *L = LI->getLoopFor(PN->getParent())) 1660 if (L->getHeader() == PN->getParent()) { 1661 // If it lives in the loop header, it has two incoming values, one 1662 // from outside the loop, and one from inside. 1663 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1664 unsigned BackEdge = IncomingEdge^1; 1665 1666 // While we are analyzing this PHI node, handle its value symbolically. 1667 SCEVHandle SymbolicName = getUnknown(PN); 1668 assert(Scalars.find(PN) == Scalars.end() && 1669 "PHI node already processed?"); 1670 Scalars.insert(std::make_pair(PN, SymbolicName)); 1671 1672 // Using this symbolic name for the PHI, analyze the value coming around 1673 // the back-edge. 1674 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1675 1676 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1677 // has a special value for the first iteration of the loop. 1678 1679 // If the value coming around the backedge is an add with the symbolic 1680 // value we just inserted, then we found a simple induction variable! 1681 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1682 // If there is a single occurrence of the symbolic value, replace it 1683 // with a recurrence. 1684 unsigned FoundIndex = Add->getNumOperands(); 1685 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1686 if (Add->getOperand(i) == SymbolicName) 1687 if (FoundIndex == e) { 1688 FoundIndex = i; 1689 break; 1690 } 1691 1692 if (FoundIndex != Add->getNumOperands()) { 1693 // Create an add with everything but the specified operand. 1694 std::vector<SCEVHandle> Ops; 1695 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1696 if (i != FoundIndex) 1697 Ops.push_back(Add->getOperand(i)); 1698 SCEVHandle Accum = getAddExpr(Ops); 1699 1700 // This is not a valid addrec if the step amount is varying each 1701 // loop iteration, but is not itself an addrec in this loop. 1702 if (Accum->isLoopInvariant(L) || 1703 (isa<SCEVAddRecExpr>(Accum) && 1704 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1705 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1706 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 1707 1708 // Okay, for the entire analysis of this edge we assumed the PHI 1709 // to be symbolic. We now need to go back and update all of the 1710 // entries for the scalars that use the PHI (except for the PHI 1711 // itself) to use the new analyzed value instead of the "symbolic" 1712 // value. 1713 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1714 return PHISCEV; 1715 } 1716 } 1717 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) { 1718 // Otherwise, this could be a loop like this: 1719 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1720 // In this case, j = {1,+,1} and BEValue is j. 1721 // Because the other in-value of i (0) fits the evolution of BEValue 1722 // i really is an addrec evolution. 1723 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1724 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1725 1726 // If StartVal = j.start - j.stride, we can use StartVal as the 1727 // initial step of the addrec evolution. 1728 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 1729 AddRec->getOperand(1))) { 1730 SCEVHandle PHISCEV = 1731 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1732 1733 // Okay, for the entire analysis of this edge we assumed the PHI 1734 // to be symbolic. We now need to go back and update all of the 1735 // entries for the scalars that use the PHI (except for the PHI 1736 // itself) to use the new analyzed value instead of the "symbolic" 1737 // value. 1738 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1739 return PHISCEV; 1740 } 1741 } 1742 } 1743 1744 return SymbolicName; 1745 } 1746 1747 // If it's not a loop phi, we can't handle it yet. 1748 return getUnknown(PN); 1749} 1750 1751/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1752/// guaranteed to end in (at every loop iteration). It is, at the same time, 1753/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1754/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1755static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) { 1756 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1757 return C->getValue()->getValue().countTrailingZeros(); 1758 1759 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1760 return std::min(GetMinTrailingZeros(T->getOperand(), SE), 1761 (uint32_t)SE.getTypeSizeInBits(T->getType())); 1762 1763 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1764 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1765 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1766 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1767 } 1768 1769 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1770 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1771 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1772 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1773 } 1774 1775 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1776 // The result is the min of all operands results. 1777 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1778 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1779 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1780 return MinOpRes; 1781 } 1782 1783 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1784 // The result is the sum of all operands results. 1785 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1786 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType()); 1787 for (unsigned i = 1, e = M->getNumOperands(); 1788 SumOpRes != BitWidth && i != e; ++i) 1789 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE), 1790 BitWidth); 1791 return SumOpRes; 1792 } 1793 1794 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1795 // The result is the min of all operands results. 1796 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1797 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1798 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1799 return MinOpRes; 1800 } 1801 1802 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1803 // The result is the min of all operands results. 1804 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1805 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1806 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1807 return MinOpRes; 1808 } 1809 1810 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1811 // The result is the min of all operands results. 1812 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1813 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1814 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1815 return MinOpRes; 1816 } 1817 1818 // SCEVUDivExpr, SCEVUnknown 1819 return 0; 1820} 1821 1822/// createSCEV - We know that there is no SCEV for the specified value. 1823/// Analyze the expression. 1824/// 1825SCEVHandle ScalarEvolution::createSCEV(Value *V) { 1826 if (!isSCEVable(V->getType())) 1827 return getUnknown(V); 1828 1829 unsigned Opcode = Instruction::UserOp1; 1830 if (Instruction *I = dyn_cast<Instruction>(V)) 1831 Opcode = I->getOpcode(); 1832 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1833 Opcode = CE->getOpcode(); 1834 else 1835 return getUnknown(V); 1836 1837 User *U = cast<User>(V); 1838 switch (Opcode) { 1839 case Instruction::Add: 1840 return getAddExpr(getSCEV(U->getOperand(0)), 1841 getSCEV(U->getOperand(1))); 1842 case Instruction::Mul: 1843 return getMulExpr(getSCEV(U->getOperand(0)), 1844 getSCEV(U->getOperand(1))); 1845 case Instruction::UDiv: 1846 return getUDivExpr(getSCEV(U->getOperand(0)), 1847 getSCEV(U->getOperand(1))); 1848 case Instruction::Sub: 1849 return getMinusSCEV(getSCEV(U->getOperand(0)), 1850 getSCEV(U->getOperand(1))); 1851 case Instruction::And: 1852 // For an expression like x&255 that merely masks off the high bits, 1853 // use zext(trunc(x)) as the SCEV expression. 1854 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1855 if (CI->isNullValue()) 1856 return getSCEV(U->getOperand(1)); 1857 if (CI->isAllOnesValue()) 1858 return getSCEV(U->getOperand(0)); 1859 const APInt &A = CI->getValue(); 1860 unsigned Ones = A.countTrailingOnes(); 1861 if (APIntOps::isMask(Ones, A)) 1862 return 1863 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 1864 IntegerType::get(Ones)), 1865 U->getType()); 1866 } 1867 break; 1868 case Instruction::Or: 1869 // If the RHS of the Or is a constant, we may have something like: 1870 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 1871 // optimizations will transparently handle this case. 1872 // 1873 // In order for this transformation to be safe, the LHS must be of the 1874 // form X*(2^n) and the Or constant must be less than 2^n. 1875 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1876 SCEVHandle LHS = getSCEV(U->getOperand(0)); 1877 const APInt &CIVal = CI->getValue(); 1878 if (GetMinTrailingZeros(LHS, *this) >= 1879 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 1880 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 1881 } 1882 break; 1883 case Instruction::Xor: 1884 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 1885 // If the RHS of the xor is a signbit, then this is just an add. 1886 // Instcombine turns add of signbit into xor as a strength reduction step. 1887 if (CI->getValue().isSignBit()) 1888 return getAddExpr(getSCEV(U->getOperand(0)), 1889 getSCEV(U->getOperand(1))); 1890 1891 // If the RHS of xor is -1, then this is a not operation. 1892 else if (CI->isAllOnesValue()) 1893 return getNotSCEV(getSCEV(U->getOperand(0))); 1894 } 1895 break; 1896 1897 case Instruction::Shl: 1898 // Turn shift left of a constant amount into a multiply. 1899 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1900 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1901 Constant *X = ConstantInt::get( 1902 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1903 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1904 } 1905 break; 1906 1907 case Instruction::LShr: 1908 // Turn logical shift right of a constant into a unsigned divide. 1909 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 1910 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 1911 Constant *X = ConstantInt::get( 1912 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 1913 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 1914 } 1915 break; 1916 1917 case Instruction::AShr: 1918 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 1919 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 1920 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 1921 if (L->getOpcode() == Instruction::Shl && 1922 L->getOperand(1) == U->getOperand(1)) { 1923 unsigned BitWidth = getTypeSizeInBits(U->getType()); 1924 uint64_t Amt = BitWidth - CI->getZExtValue(); 1925 if (Amt == BitWidth) 1926 return getSCEV(L->getOperand(0)); // shift by zero --> noop 1927 if (Amt > BitWidth) 1928 return getIntegerSCEV(0, U->getType()); // value is undefined 1929 return 1930 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 1931 IntegerType::get(Amt)), 1932 U->getType()); 1933 } 1934 break; 1935 1936 case Instruction::Trunc: 1937 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 1938 1939 case Instruction::ZExt: 1940 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1941 1942 case Instruction::SExt: 1943 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 1944 1945 case Instruction::BitCast: 1946 // BitCasts are no-op casts so we just eliminate the cast. 1947 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 1948 return getSCEV(U->getOperand(0)); 1949 break; 1950 1951 case Instruction::IntToPtr: 1952 if (!TD) break; // Without TD we can't analyze pointers. 1953 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1954 TD->getIntPtrType()); 1955 1956 case Instruction::PtrToInt: 1957 if (!TD) break; // Without TD we can't analyze pointers. 1958 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 1959 U->getType()); 1960 1961 case Instruction::GetElementPtr: { 1962 if (!TD) break; // Without TD we can't analyze pointers. 1963 const Type *IntPtrTy = TD->getIntPtrType(); 1964 Value *Base = U->getOperand(0); 1965 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1966 gep_type_iterator GTI = gep_type_begin(U); 1967 for (GetElementPtrInst::op_iterator I = next(U->op_begin()), 1968 E = U->op_end(); 1969 I != E; ++I) { 1970 Value *Index = *I; 1971 // Compute the (potentially symbolic) offset in bytes for this index. 1972 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1973 // For a struct, add the member offset. 1974 const StructLayout &SL = *TD->getStructLayout(STy); 1975 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1976 uint64_t Offset = SL.getElementOffset(FieldNo); 1977 TotalOffset = getAddExpr(TotalOffset, 1978 getIntegerSCEV(Offset, IntPtrTy)); 1979 } else { 1980 // For an array, add the element offset, explicitly scaled. 1981 SCEVHandle LocalOffset = getSCEV(Index); 1982 if (!isa<PointerType>(LocalOffset->getType())) 1983 // Getelementptr indicies are signed. 1984 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1985 IntPtrTy); 1986 LocalOffset = 1987 getMulExpr(LocalOffset, 1988 getIntegerSCEV(TD->getTypePaddedSize(*GTI), 1989 IntPtrTy)); 1990 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1991 } 1992 } 1993 return getAddExpr(getSCEV(Base), TotalOffset); 1994 } 1995 1996 case Instruction::PHI: 1997 return createNodeForPHI(cast<PHINode>(U)); 1998 1999 case Instruction::Select: 2000 // This could be a smax or umax that was lowered earlier. 2001 // Try to recover it. 2002 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2003 Value *LHS = ICI->getOperand(0); 2004 Value *RHS = ICI->getOperand(1); 2005 switch (ICI->getPredicate()) { 2006 case ICmpInst::ICMP_SLT: 2007 case ICmpInst::ICMP_SLE: 2008 std::swap(LHS, RHS); 2009 // fall through 2010 case ICmpInst::ICMP_SGT: 2011 case ICmpInst::ICMP_SGE: 2012 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2013 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2014 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2015 // ~smax(~x, ~y) == smin(x, y). 2016 return getNotSCEV(getSMaxExpr( 2017 getNotSCEV(getSCEV(LHS)), 2018 getNotSCEV(getSCEV(RHS)))); 2019 break; 2020 case ICmpInst::ICMP_ULT: 2021 case ICmpInst::ICMP_ULE: 2022 std::swap(LHS, RHS); 2023 // fall through 2024 case ICmpInst::ICMP_UGT: 2025 case ICmpInst::ICMP_UGE: 2026 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2027 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2028 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2029 // ~umax(~x, ~y) == umin(x, y) 2030 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 2031 getNotSCEV(getSCEV(RHS)))); 2032 break; 2033 default: 2034 break; 2035 } 2036 } 2037 2038 default: // We cannot analyze this expression. 2039 break; 2040 } 2041 2042 return getUnknown(V); 2043} 2044 2045 2046 2047//===----------------------------------------------------------------------===// 2048// Iteration Count Computation Code 2049// 2050 2051/// getBackedgeTakenCount - If the specified loop has a predictable 2052/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2053/// object. The backedge-taken count is the number of times the loop header 2054/// will be branched to from within the loop. This is one less than the 2055/// trip count of the loop, since it doesn't count the first iteration, 2056/// when the header is branched to from outside the loop. 2057/// 2058/// Note that it is not valid to call this method on a loop without a 2059/// loop-invariant backedge-taken count (see 2060/// hasLoopInvariantBackedgeTakenCount). 2061/// 2062SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2063 return getBackedgeTakenInfo(L).Exact; 2064} 2065 2066/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2067/// return the least SCEV value that is known never to be less than the 2068/// actual backedge taken count. 2069SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2070 return getBackedgeTakenInfo(L).Max; 2071} 2072 2073const ScalarEvolution::BackedgeTakenInfo & 2074ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2075 // Initially insert a CouldNotCompute for this loop. If the insertion 2076 // succeeds, procede to actually compute a backedge-taken count and 2077 // update the value. The temporary CouldNotCompute value tells SCEV 2078 // code elsewhere that it shouldn't attempt to request a new 2079 // backedge-taken count, which could result in infinite recursion. 2080 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2081 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2082 if (Pair.second) { 2083 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2084 if (ItCount.Exact != UnknownValue) { 2085 assert(ItCount.Exact->isLoopInvariant(L) && 2086 ItCount.Max->isLoopInvariant(L) && 2087 "Computed trip count isn't loop invariant for loop!"); 2088 ++NumTripCountsComputed; 2089 2090 // Update the value in the map. 2091 Pair.first->second = ItCount; 2092 } else if (isa<PHINode>(L->getHeader()->begin())) { 2093 // Only count loops that have phi nodes as not being computable. 2094 ++NumTripCountsNotComputed; 2095 } 2096 2097 // Now that we know more about the trip count for this loop, forget any 2098 // existing SCEV values for PHI nodes in this loop since they are only 2099 // conservative estimates made without the benefit 2100 // of trip count information. 2101 if (ItCount.hasAnyInfo()) 2102 for (BasicBlock::iterator I = L->getHeader()->begin(); 2103 PHINode *PN = dyn_cast<PHINode>(I); ++I) 2104 deleteValueFromRecords(PN); 2105 } 2106 return Pair.first->second; 2107} 2108 2109/// forgetLoopBackedgeTakenCount - This method should be called by the 2110/// client when it has changed a loop in a way that may effect 2111/// ScalarEvolution's ability to compute a trip count, or if the loop 2112/// is deleted. 2113void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2114 BackedgeTakenCounts.erase(L); 2115} 2116 2117/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2118/// of the specified loop will execute. 2119ScalarEvolution::BackedgeTakenInfo 2120ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2121 // If the loop has a non-one exit block count, we can't analyze it. 2122 SmallVector<BasicBlock*, 8> ExitBlocks; 2123 L->getExitBlocks(ExitBlocks); 2124 if (ExitBlocks.size() != 1) return UnknownValue; 2125 2126 // Okay, there is one exit block. Try to find the condition that causes the 2127 // loop to be exited. 2128 BasicBlock *ExitBlock = ExitBlocks[0]; 2129 2130 BasicBlock *ExitingBlock = 0; 2131 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 2132 PI != E; ++PI) 2133 if (L->contains(*PI)) { 2134 if (ExitingBlock == 0) 2135 ExitingBlock = *PI; 2136 else 2137 return UnknownValue; // More than one block exiting! 2138 } 2139 assert(ExitingBlock && "No exits from loop, something is broken!"); 2140 2141 // Okay, we've computed the exiting block. See what condition causes us to 2142 // exit. 2143 // 2144 // FIXME: we should be able to handle switch instructions (with a single exit) 2145 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2146 if (ExitBr == 0) return UnknownValue; 2147 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2148 2149 // At this point, we know we have a conditional branch that determines whether 2150 // the loop is exited. However, we don't know if the branch is executed each 2151 // time through the loop. If not, then the execution count of the branch will 2152 // not be equal to the trip count of the loop. 2153 // 2154 // Currently we check for this by checking to see if the Exit branch goes to 2155 // the loop header. If so, we know it will always execute the same number of 2156 // times as the loop. We also handle the case where the exit block *is* the 2157 // loop header. This is common for un-rotated loops. More extensive analysis 2158 // could be done to handle more cases here. 2159 if (ExitBr->getSuccessor(0) != L->getHeader() && 2160 ExitBr->getSuccessor(1) != L->getHeader() && 2161 ExitBr->getParent() != L->getHeader()) 2162 return UnknownValue; 2163 2164 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2165 2166 // If it's not an integer comparison then compute it the hard way. 2167 // Note that ICmpInst deals with pointer comparisons too so we must check 2168 // the type of the operand. 2169 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2170 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2171 ExitBr->getSuccessor(0) == ExitBlock); 2172 2173 // If the condition was exit on true, convert the condition to exit on false 2174 ICmpInst::Predicate Cond; 2175 if (ExitBr->getSuccessor(1) == ExitBlock) 2176 Cond = ExitCond->getPredicate(); 2177 else 2178 Cond = ExitCond->getInversePredicate(); 2179 2180 // Handle common loops like: for (X = "string"; *X; ++X) 2181 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2182 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2183 SCEVHandle ItCnt = 2184 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2185 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2186 } 2187 2188 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2189 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2190 2191 // Try to evaluate any dependencies out of the loop. 2192 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2193 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2194 Tmp = getSCEVAtScope(RHS, L); 2195 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2196 2197 // At this point, we would like to compute how many iterations of the 2198 // loop the predicate will return true for these inputs. 2199 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2200 // If there is a loop-invariant, force it into the RHS. 2201 std::swap(LHS, RHS); 2202 Cond = ICmpInst::getSwappedPredicate(Cond); 2203 } 2204 2205 // If we have a comparison of a chrec against a constant, try to use value 2206 // ranges to answer this query. 2207 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2208 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2209 if (AddRec->getLoop() == L) { 2210 // Form the comparison range using the constant of the correct type so 2211 // that the ConstantRange class knows to do a signed or unsigned 2212 // comparison. 2213 ConstantInt *CompVal = RHSC->getValue(); 2214 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2215 CompVal = dyn_cast<ConstantInt>( 2216 ConstantExpr::getBitCast(CompVal, RealTy)); 2217 if (CompVal) { 2218 // Form the constant range. 2219 ConstantRange CompRange( 2220 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2221 2222 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2223 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2224 } 2225 } 2226 2227 switch (Cond) { 2228 case ICmpInst::ICMP_NE: { // while (X != Y) 2229 // Convert to: while (X-Y != 0) 2230 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2231 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2232 break; 2233 } 2234 case ICmpInst::ICMP_EQ: { 2235 // Convert to: while (X-Y == 0) // while (X == Y) 2236 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2237 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2238 break; 2239 } 2240 case ICmpInst::ICMP_SLT: { 2241 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 2242 if (BTI.hasAnyInfo()) return BTI; 2243 break; 2244 } 2245 case ICmpInst::ICMP_SGT: { 2246 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2247 getNotSCEV(RHS), L, true); 2248 if (BTI.hasAnyInfo()) return BTI; 2249 break; 2250 } 2251 case ICmpInst::ICMP_ULT: { 2252 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 2253 if (BTI.hasAnyInfo()) return BTI; 2254 break; 2255 } 2256 case ICmpInst::ICMP_UGT: { 2257 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2258 getNotSCEV(RHS), L, false); 2259 if (BTI.hasAnyInfo()) return BTI; 2260 break; 2261 } 2262 default: 2263#if 0 2264 errs() << "ComputeBackedgeTakenCount "; 2265 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2266 errs() << "[unsigned] "; 2267 errs() << *LHS << " " 2268 << Instruction::getOpcodeName(Instruction::ICmp) 2269 << " " << *RHS << "\n"; 2270#endif 2271 break; 2272 } 2273 return 2274 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2275 ExitBr->getSuccessor(0) == ExitBlock); 2276} 2277 2278static ConstantInt * 2279EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2280 ScalarEvolution &SE) { 2281 SCEVHandle InVal = SE.getConstant(C); 2282 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2283 assert(isa<SCEVConstant>(Val) && 2284 "Evaluation of SCEV at constant didn't fold correctly?"); 2285 return cast<SCEVConstant>(Val)->getValue(); 2286} 2287 2288/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2289/// and a GEP expression (missing the pointer index) indexing into it, return 2290/// the addressed element of the initializer or null if the index expression is 2291/// invalid. 2292static Constant * 2293GetAddressedElementFromGlobal(GlobalVariable *GV, 2294 const std::vector<ConstantInt*> &Indices) { 2295 Constant *Init = GV->getInitializer(); 2296 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2297 uint64_t Idx = Indices[i]->getZExtValue(); 2298 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2299 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2300 Init = cast<Constant>(CS->getOperand(Idx)); 2301 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2302 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2303 Init = cast<Constant>(CA->getOperand(Idx)); 2304 } else if (isa<ConstantAggregateZero>(Init)) { 2305 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2306 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2307 Init = Constant::getNullValue(STy->getElementType(Idx)); 2308 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2309 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2310 Init = Constant::getNullValue(ATy->getElementType()); 2311 } else { 2312 assert(0 && "Unknown constant aggregate type!"); 2313 } 2314 return 0; 2315 } else { 2316 return 0; // Unknown initializer type 2317 } 2318 } 2319 return Init; 2320} 2321 2322/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2323/// 'icmp op load X, cst', try to see if we can compute the backedge 2324/// execution count. 2325SCEVHandle ScalarEvolution:: 2326ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2327 const Loop *L, 2328 ICmpInst::Predicate predicate) { 2329 if (LI->isVolatile()) return UnknownValue; 2330 2331 // Check to see if the loaded pointer is a getelementptr of a global. 2332 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2333 if (!GEP) return UnknownValue; 2334 2335 // Make sure that it is really a constant global we are gepping, with an 2336 // initializer, and make sure the first IDX is really 0. 2337 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2338 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2339 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2340 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2341 return UnknownValue; 2342 2343 // Okay, we allow one non-constant index into the GEP instruction. 2344 Value *VarIdx = 0; 2345 std::vector<ConstantInt*> Indexes; 2346 unsigned VarIdxNum = 0; 2347 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2348 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2349 Indexes.push_back(CI); 2350 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2351 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2352 VarIdx = GEP->getOperand(i); 2353 VarIdxNum = i-2; 2354 Indexes.push_back(0); 2355 } 2356 2357 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2358 // Check to see if X is a loop variant variable value now. 2359 SCEVHandle Idx = getSCEV(VarIdx); 2360 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2361 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2362 2363 // We can only recognize very limited forms of loop index expressions, in 2364 // particular, only affine AddRec's like {C1,+,C2}. 2365 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2366 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2367 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2368 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2369 return UnknownValue; 2370 2371 unsigned MaxSteps = MaxBruteForceIterations; 2372 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2373 ConstantInt *ItCst = 2374 ConstantInt::get(IdxExpr->getType(), IterationNum); 2375 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2376 2377 // Form the GEP offset. 2378 Indexes[VarIdxNum] = Val; 2379 2380 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2381 if (Result == 0) break; // Cannot compute! 2382 2383 // Evaluate the condition for this iteration. 2384 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2385 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2386 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2387#if 0 2388 errs() << "\n***\n*** Computed loop count " << *ItCst 2389 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2390 << "***\n"; 2391#endif 2392 ++NumArrayLenItCounts; 2393 return getConstant(ItCst); // Found terminating iteration! 2394 } 2395 } 2396 return UnknownValue; 2397} 2398 2399 2400/// CanConstantFold - Return true if we can constant fold an instruction of the 2401/// specified type, assuming that all operands were constants. 2402static bool CanConstantFold(const Instruction *I) { 2403 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2404 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2405 return true; 2406 2407 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2408 if (const Function *F = CI->getCalledFunction()) 2409 return canConstantFoldCallTo(F); 2410 return false; 2411} 2412 2413/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2414/// in the loop that V is derived from. We allow arbitrary operations along the 2415/// way, but the operands of an operation must either be constants or a value 2416/// derived from a constant PHI. If this expression does not fit with these 2417/// constraints, return null. 2418static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2419 // If this is not an instruction, or if this is an instruction outside of the 2420 // loop, it can't be derived from a loop PHI. 2421 Instruction *I = dyn_cast<Instruction>(V); 2422 if (I == 0 || !L->contains(I->getParent())) return 0; 2423 2424 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2425 if (L->getHeader() == I->getParent()) 2426 return PN; 2427 else 2428 // We don't currently keep track of the control flow needed to evaluate 2429 // PHIs, so we cannot handle PHIs inside of loops. 2430 return 0; 2431 } 2432 2433 // If we won't be able to constant fold this expression even if the operands 2434 // are constants, return early. 2435 if (!CanConstantFold(I)) return 0; 2436 2437 // Otherwise, we can evaluate this instruction if all of its operands are 2438 // constant or derived from a PHI node themselves. 2439 PHINode *PHI = 0; 2440 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2441 if (!(isa<Constant>(I->getOperand(Op)) || 2442 isa<GlobalValue>(I->getOperand(Op)))) { 2443 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2444 if (P == 0) return 0; // Not evolving from PHI 2445 if (PHI == 0) 2446 PHI = P; 2447 else if (PHI != P) 2448 return 0; // Evolving from multiple different PHIs. 2449 } 2450 2451 // This is a expression evolving from a constant PHI! 2452 return PHI; 2453} 2454 2455/// EvaluateExpression - Given an expression that passes the 2456/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2457/// in the loop has the value PHIVal. If we can't fold this expression for some 2458/// reason, return null. 2459static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2460 if (isa<PHINode>(V)) return PHIVal; 2461 if (Constant *C = dyn_cast<Constant>(V)) return C; 2462 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2463 Instruction *I = cast<Instruction>(V); 2464 2465 std::vector<Constant*> Operands; 2466 Operands.resize(I->getNumOperands()); 2467 2468 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2469 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2470 if (Operands[i] == 0) return 0; 2471 } 2472 2473 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2474 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2475 &Operands[0], Operands.size()); 2476 else 2477 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2478 &Operands[0], Operands.size()); 2479} 2480 2481/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2482/// in the header of its containing loop, we know the loop executes a 2483/// constant number of times, and the PHI node is just a recurrence 2484/// involving constants, fold it. 2485Constant *ScalarEvolution:: 2486getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2487 std::map<PHINode*, Constant*>::iterator I = 2488 ConstantEvolutionLoopExitValue.find(PN); 2489 if (I != ConstantEvolutionLoopExitValue.end()) 2490 return I->second; 2491 2492 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2493 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2494 2495 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2496 2497 // Since the loop is canonicalized, the PHI node must have two entries. One 2498 // entry must be a constant (coming in from outside of the loop), and the 2499 // second must be derived from the same PHI. 2500 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2501 Constant *StartCST = 2502 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2503 if (StartCST == 0) 2504 return RetVal = 0; // Must be a constant. 2505 2506 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2507 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2508 if (PN2 != PN) 2509 return RetVal = 0; // Not derived from same PHI. 2510 2511 // Execute the loop symbolically to determine the exit value. 2512 if (BEs.getActiveBits() >= 32) 2513 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2514 2515 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2516 unsigned IterationNum = 0; 2517 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2518 if (IterationNum == NumIterations) 2519 return RetVal = PHIVal; // Got exit value! 2520 2521 // Compute the value of the PHI node for the next iteration. 2522 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2523 if (NextPHI == PHIVal) 2524 return RetVal = NextPHI; // Stopped evolving! 2525 if (NextPHI == 0) 2526 return 0; // Couldn't evaluate! 2527 PHIVal = NextPHI; 2528 } 2529} 2530 2531/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2532/// constant number of times (the condition evolves only from constants), 2533/// try to evaluate a few iterations of the loop until we get the exit 2534/// condition gets a value of ExitWhen (true or false). If we cannot 2535/// evaluate the trip count of the loop, return UnknownValue. 2536SCEVHandle ScalarEvolution:: 2537ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2538 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2539 if (PN == 0) return UnknownValue; 2540 2541 // Since the loop is canonicalized, the PHI node must have two entries. One 2542 // entry must be a constant (coming in from outside of the loop), and the 2543 // second must be derived from the same PHI. 2544 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2545 Constant *StartCST = 2546 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2547 if (StartCST == 0) return UnknownValue; // Must be a constant. 2548 2549 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2550 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2551 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2552 2553 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2554 // the loop symbolically to determine when the condition gets a value of 2555 // "ExitWhen". 2556 unsigned IterationNum = 0; 2557 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2558 for (Constant *PHIVal = StartCST; 2559 IterationNum != MaxIterations; ++IterationNum) { 2560 ConstantInt *CondVal = 2561 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2562 2563 // Couldn't symbolically evaluate. 2564 if (!CondVal) return UnknownValue; 2565 2566 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2567 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2568 ++NumBruteForceTripCountsComputed; 2569 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2570 } 2571 2572 // Compute the value of the PHI node for the next iteration. 2573 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2574 if (NextPHI == 0 || NextPHI == PHIVal) 2575 return UnknownValue; // Couldn't evaluate or not making progress... 2576 PHIVal = NextPHI; 2577 } 2578 2579 // Too many iterations were needed to evaluate. 2580 return UnknownValue; 2581} 2582 2583/// getSCEVAtScope - Compute the value of the specified expression within the 2584/// indicated loop (which may be null to indicate in no loop). If the 2585/// expression cannot be evaluated, return UnknownValue. 2586SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) { 2587 // FIXME: this should be turned into a virtual method on SCEV! 2588 2589 if (isa<SCEVConstant>(V)) return V; 2590 2591 // If this instruction is evolved from a constant-evolving PHI, compute the 2592 // exit value from the loop without using SCEVs. 2593 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2594 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2595 const Loop *LI = (*this->LI)[I->getParent()]; 2596 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2597 if (PHINode *PN = dyn_cast<PHINode>(I)) 2598 if (PN->getParent() == LI->getHeader()) { 2599 // Okay, there is no closed form solution for the PHI node. Check 2600 // to see if the loop that contains it has a known backedge-taken 2601 // count. If so, we may be able to force computation of the exit 2602 // value. 2603 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2604 if (SCEVConstant *BTCC = 2605 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2606 // Okay, we know how many times the containing loop executes. If 2607 // this is a constant evolving PHI node, get the final value at 2608 // the specified iteration number. 2609 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2610 BTCC->getValue()->getValue(), 2611 LI); 2612 if (RV) return getUnknown(RV); 2613 } 2614 } 2615 2616 // Okay, this is an expression that we cannot symbolically evaluate 2617 // into a SCEV. Check to see if it's possible to symbolically evaluate 2618 // the arguments into constants, and if so, try to constant propagate the 2619 // result. This is particularly useful for computing loop exit values. 2620 if (CanConstantFold(I)) { 2621 std::vector<Constant*> Operands; 2622 Operands.reserve(I->getNumOperands()); 2623 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2624 Value *Op = I->getOperand(i); 2625 if (Constant *C = dyn_cast<Constant>(Op)) { 2626 Operands.push_back(C); 2627 } else { 2628 // If any of the operands is non-constant and if they are 2629 // non-integer and non-pointer, don't even try to analyze them 2630 // with scev techniques. 2631 if (!isSCEVable(Op->getType())) 2632 return V; 2633 2634 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2635 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 2636 Constant *C = SC->getValue(); 2637 if (C->getType() != Op->getType()) 2638 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2639 Op->getType(), 2640 false), 2641 C, Op->getType()); 2642 Operands.push_back(C); 2643 } else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2644 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 2645 if (C->getType() != Op->getType()) 2646 C = 2647 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2648 Op->getType(), 2649 false), 2650 C, Op->getType()); 2651 Operands.push_back(C); 2652 } else 2653 return V; 2654 } else { 2655 return V; 2656 } 2657 } 2658 } 2659 2660 Constant *C; 2661 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2662 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2663 &Operands[0], Operands.size()); 2664 else 2665 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2666 &Operands[0], Operands.size()); 2667 return getUnknown(C); 2668 } 2669 } 2670 2671 // This is some other type of SCEVUnknown, just return it. 2672 return V; 2673 } 2674 2675 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2676 // Avoid performing the look-up in the common case where the specified 2677 // expression has no loop-variant portions. 2678 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2679 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2680 if (OpAtScope != Comm->getOperand(i)) { 2681 if (OpAtScope == UnknownValue) return UnknownValue; 2682 // Okay, at least one of these operands is loop variant but might be 2683 // foldable. Build a new instance of the folded commutative expression. 2684 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2685 NewOps.push_back(OpAtScope); 2686 2687 for (++i; i != e; ++i) { 2688 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2689 if (OpAtScope == UnknownValue) return UnknownValue; 2690 NewOps.push_back(OpAtScope); 2691 } 2692 if (isa<SCEVAddExpr>(Comm)) 2693 return getAddExpr(NewOps); 2694 if (isa<SCEVMulExpr>(Comm)) 2695 return getMulExpr(NewOps); 2696 if (isa<SCEVSMaxExpr>(Comm)) 2697 return getSMaxExpr(NewOps); 2698 if (isa<SCEVUMaxExpr>(Comm)) 2699 return getUMaxExpr(NewOps); 2700 assert(0 && "Unknown commutative SCEV type!"); 2701 } 2702 } 2703 // If we got here, all operands are loop invariant. 2704 return Comm; 2705 } 2706 2707 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2708 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2709 if (LHS == UnknownValue) return LHS; 2710 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2711 if (RHS == UnknownValue) return RHS; 2712 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2713 return Div; // must be loop invariant 2714 return getUDivExpr(LHS, RHS); 2715 } 2716 2717 // If this is a loop recurrence for a loop that does not contain L, then we 2718 // are dealing with the final value computed by the loop. 2719 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2720 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2721 // To evaluate this recurrence, we need to know how many times the AddRec 2722 // loop iterates. Compute this now. 2723 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2724 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2725 2726 // Then, evaluate the AddRec. 2727 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2728 } 2729 return UnknownValue; 2730 } 2731 2732 if (SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 2733 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2734 if (Op == UnknownValue) return Op; 2735 if (Op == Cast->getOperand()) 2736 return Cast; // must be loop invariant 2737 return getZeroExtendExpr(Op, Cast->getType()); 2738 } 2739 2740 if (SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 2741 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2742 if (Op == UnknownValue) return Op; 2743 if (Op == Cast->getOperand()) 2744 return Cast; // must be loop invariant 2745 return getSignExtendExpr(Op, Cast->getType()); 2746 } 2747 2748 if (SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 2749 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2750 if (Op == UnknownValue) return Op; 2751 if (Op == Cast->getOperand()) 2752 return Cast; // must be loop invariant 2753 return getTruncateExpr(Op, Cast->getType()); 2754 } 2755 2756 assert(0 && "Unknown SCEV type!"); 2757} 2758 2759/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2760/// at the specified scope in the program. The L value specifies a loop 2761/// nest to evaluate the expression at, where null is the top-level or a 2762/// specified loop is immediately inside of the loop. 2763/// 2764/// This method can be used to compute the exit value for a variable defined 2765/// in a loop by querying what the value will hold in the parent loop. 2766/// 2767/// If this value is not computable at this scope, a SCEVCouldNotCompute 2768/// object is returned. 2769SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2770 return getSCEVAtScope(getSCEV(V), L); 2771} 2772 2773/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2774/// following equation: 2775/// 2776/// A * X = B (mod N) 2777/// 2778/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2779/// A and B isn't important. 2780/// 2781/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2782static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2783 ScalarEvolution &SE) { 2784 uint32_t BW = A.getBitWidth(); 2785 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2786 assert(A != 0 && "A must be non-zero."); 2787 2788 // 1. D = gcd(A, N) 2789 // 2790 // The gcd of A and N may have only one prime factor: 2. The number of 2791 // trailing zeros in A is its multiplicity 2792 uint32_t Mult2 = A.countTrailingZeros(); 2793 // D = 2^Mult2 2794 2795 // 2. Check if B is divisible by D. 2796 // 2797 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2798 // is not less than multiplicity of this prime factor for D. 2799 if (B.countTrailingZeros() < Mult2) 2800 return SE.getCouldNotCompute(); 2801 2802 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2803 // modulo (N / D). 2804 // 2805 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2806 // bit width during computations. 2807 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2808 APInt Mod(BW + 1, 0); 2809 Mod.set(BW - Mult2); // Mod = N / D 2810 APInt I = AD.multiplicativeInverse(Mod); 2811 2812 // 4. Compute the minimum unsigned root of the equation: 2813 // I * (B / D) mod (N / D) 2814 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2815 2816 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2817 // bits. 2818 return SE.getConstant(Result.trunc(BW)); 2819} 2820 2821/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2822/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2823/// might be the same) or two SCEVCouldNotCompute objects. 2824/// 2825static std::pair<SCEVHandle,SCEVHandle> 2826SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2827 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2828 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2829 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2830 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2831 2832 // We currently can only solve this if the coefficients are constants. 2833 if (!LC || !MC || !NC) { 2834 SCEV *CNC = SE.getCouldNotCompute(); 2835 return std::make_pair(CNC, CNC); 2836 } 2837 2838 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2839 const APInt &L = LC->getValue()->getValue(); 2840 const APInt &M = MC->getValue()->getValue(); 2841 const APInt &N = NC->getValue()->getValue(); 2842 APInt Two(BitWidth, 2); 2843 APInt Four(BitWidth, 4); 2844 2845 { 2846 using namespace APIntOps; 2847 const APInt& C = L; 2848 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2849 // The B coefficient is M-N/2 2850 APInt B(M); 2851 B -= sdiv(N,Two); 2852 2853 // The A coefficient is N/2 2854 APInt A(N.sdiv(Two)); 2855 2856 // Compute the B^2-4ac term. 2857 APInt SqrtTerm(B); 2858 SqrtTerm *= B; 2859 SqrtTerm -= Four * (A * C); 2860 2861 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 2862 // integer value or else APInt::sqrt() will assert. 2863 APInt SqrtVal(SqrtTerm.sqrt()); 2864 2865 // Compute the two solutions for the quadratic formula. 2866 // The divisions must be performed as signed divisions. 2867 APInt NegB(-B); 2868 APInt TwoA( A << 1 ); 2869 if (TwoA.isMinValue()) { 2870 SCEV *CNC = SE.getCouldNotCompute(); 2871 return std::make_pair(CNC, CNC); 2872 } 2873 2874 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 2875 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 2876 2877 return std::make_pair(SE.getConstant(Solution1), 2878 SE.getConstant(Solution2)); 2879 } // end APIntOps namespace 2880} 2881 2882/// HowFarToZero - Return the number of times a backedge comparing the specified 2883/// value to zero will execute. If not computable, return UnknownValue 2884SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) { 2885 // If the value is a constant 2886 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2887 // If the value is already zero, the branch will execute zero times. 2888 if (C->getValue()->isZero()) return C; 2889 return UnknownValue; // Otherwise it will loop infinitely. 2890 } 2891 2892 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 2893 if (!AddRec || AddRec->getLoop() != L) 2894 return UnknownValue; 2895 2896 if (AddRec->isAffine()) { 2897 // If this is an affine expression, the execution count of this branch is 2898 // the minimum unsigned root of the following equation: 2899 // 2900 // Start + Step*N = 0 (mod 2^BW) 2901 // 2902 // equivalent to: 2903 // 2904 // Step*N = -Start (mod 2^BW) 2905 // 2906 // where BW is the common bit width of Start and Step. 2907 2908 // Get the initial value for the loop. 2909 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 2910 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 2911 2912 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 2913 2914 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 2915 // For now we handle only constant steps. 2916 2917 // First, handle unitary steps. 2918 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 2919 return getNegativeSCEV(Start); // N = -Start (as unsigned) 2920 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 2921 return Start; // N = Start (as unsigned) 2922 2923 // Then, try to solve the above equation provided that Start is constant. 2924 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 2925 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 2926 -StartC->getValue()->getValue(), 2927 *this); 2928 } 2929 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 2930 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 2931 // the quadratic equation to solve it. 2932 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 2933 *this); 2934 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 2935 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 2936 if (R1) { 2937#if 0 2938 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 2939 << " sol#2: " << *R2 << "\n"; 2940#endif 2941 // Pick the smallest positive root value. 2942 if (ConstantInt *CB = 2943 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 2944 R1->getValue(), R2->getValue()))) { 2945 if (CB->getZExtValue() == false) 2946 std::swap(R1, R2); // R1 is the minimum root now. 2947 2948 // We can only use this value if the chrec ends up with an exact zero 2949 // value at this index. When solving for "X*X != 5", for example, we 2950 // should not accept a root of 2. 2951 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 2952 if (Val->isZero()) 2953 return R1; // We found a quadratic root! 2954 } 2955 } 2956 } 2957 2958 return UnknownValue; 2959} 2960 2961/// HowFarToNonZero - Return the number of times a backedge checking the 2962/// specified value for nonzero will execute. If not computable, return 2963/// UnknownValue 2964SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) { 2965 // Loops that look like: while (X == 0) are very strange indeed. We don't 2966 // handle them yet except for the trivial case. This could be expanded in the 2967 // future as needed. 2968 2969 // If the value is a constant, check to see if it is known to be non-zero 2970 // already. If so, the backedge will execute zero times. 2971 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 2972 if (!C->getValue()->isNullValue()) 2973 return getIntegerSCEV(0, C->getType()); 2974 return UnknownValue; // Otherwise it will loop infinitely. 2975 } 2976 2977 // We could implement others, but I really doubt anyone writes loops like 2978 // this, and if they did, they would already be constant folded. 2979 return UnknownValue; 2980} 2981 2982/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 2983/// (which may not be an immediate predecessor) which has exactly one 2984/// successor from which BB is reachable, or null if no such block is 2985/// found. 2986/// 2987BasicBlock * 2988ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 2989 // If the block has a unique predecessor, then there is no path from the 2990 // predecessor to the block that does not go through the direct edge 2991 // from the predecessor to the block. 2992 if (BasicBlock *Pred = BB->getSinglePredecessor()) 2993 return Pred; 2994 2995 // A loop's header is defined to be a block that dominates the loop. 2996 // If the loop has a preheader, it must be a block that has exactly 2997 // one successor that can reach BB. This is slightly more strict 2998 // than necessary, but works if critical edges are split. 2999 if (Loop *L = LI->getLoopFor(BB)) 3000 return L->getLoopPreheader(); 3001 3002 return 0; 3003} 3004 3005/// isLoopGuardedByCond - Test whether entry to the loop is protected by 3006/// a conditional between LHS and RHS. This is used to help avoid max 3007/// expressions in loop trip counts. 3008bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 3009 ICmpInst::Predicate Pred, 3010 SCEV *LHS, SCEV *RHS) { 3011 BasicBlock *Preheader = L->getLoopPreheader(); 3012 BasicBlock *PreheaderDest = L->getHeader(); 3013 3014 // Starting at the preheader, climb up the predecessor chain, as long as 3015 // there are predecessors that can be found that have unique successors 3016 // leading to the original header. 3017 for (; Preheader; 3018 PreheaderDest = Preheader, 3019 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 3020 3021 BranchInst *LoopEntryPredicate = 3022 dyn_cast<BranchInst>(Preheader->getTerminator()); 3023 if (!LoopEntryPredicate || 3024 LoopEntryPredicate->isUnconditional()) 3025 continue; 3026 3027 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 3028 if (!ICI) continue; 3029 3030 // Now that we found a conditional branch that dominates the loop, check to 3031 // see if it is the comparison we are looking for. 3032 Value *PreCondLHS = ICI->getOperand(0); 3033 Value *PreCondRHS = ICI->getOperand(1); 3034 ICmpInst::Predicate Cond; 3035 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 3036 Cond = ICI->getPredicate(); 3037 else 3038 Cond = ICI->getInversePredicate(); 3039 3040 if (Cond == Pred) 3041 ; // An exact match. 3042 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 3043 ; // The actual condition is beyond sufficient. 3044 else 3045 // Check a few special cases. 3046 switch (Cond) { 3047 case ICmpInst::ICMP_UGT: 3048 if (Pred == ICmpInst::ICMP_ULT) { 3049 std::swap(PreCondLHS, PreCondRHS); 3050 Cond = ICmpInst::ICMP_ULT; 3051 break; 3052 } 3053 continue; 3054 case ICmpInst::ICMP_SGT: 3055 if (Pred == ICmpInst::ICMP_SLT) { 3056 std::swap(PreCondLHS, PreCondRHS); 3057 Cond = ICmpInst::ICMP_SLT; 3058 break; 3059 } 3060 continue; 3061 case ICmpInst::ICMP_NE: 3062 // Expressions like (x >u 0) are often canonicalized to (x != 0), 3063 // so check for this case by checking if the NE is comparing against 3064 // a minimum or maximum constant. 3065 if (!ICmpInst::isTrueWhenEqual(Pred)) 3066 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 3067 const APInt &A = CI->getValue(); 3068 switch (Pred) { 3069 case ICmpInst::ICMP_SLT: 3070 if (A.isMaxSignedValue()) break; 3071 continue; 3072 case ICmpInst::ICMP_SGT: 3073 if (A.isMinSignedValue()) break; 3074 continue; 3075 case ICmpInst::ICMP_ULT: 3076 if (A.isMaxValue()) break; 3077 continue; 3078 case ICmpInst::ICMP_UGT: 3079 if (A.isMinValue()) break; 3080 continue; 3081 default: 3082 continue; 3083 } 3084 Cond = ICmpInst::ICMP_NE; 3085 // NE is symmetric but the original comparison may not be. Swap 3086 // the operands if necessary so that they match below. 3087 if (isa<SCEVConstant>(LHS)) 3088 std::swap(PreCondLHS, PreCondRHS); 3089 break; 3090 } 3091 continue; 3092 default: 3093 // We weren't able to reconcile the condition. 3094 continue; 3095 } 3096 3097 if (!PreCondLHS->getType()->isInteger()) continue; 3098 3099 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 3100 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 3101 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 3102 (LHS == getNotSCEV(PreCondRHSSCEV) && 3103 RHS == getNotSCEV(PreCondLHSSCEV))) 3104 return true; 3105 } 3106 3107 return false; 3108} 3109 3110/// HowManyLessThans - Return the number of times a backedge containing the 3111/// specified less-than comparison will execute. If not computable, return 3112/// UnknownValue. 3113ScalarEvolution::BackedgeTakenInfo ScalarEvolution:: 3114HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) { 3115 // Only handle: "ADDREC < LoopInvariant". 3116 if (!RHS->isLoopInvariant(L)) return UnknownValue; 3117 3118 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 3119 if (!AddRec || AddRec->getLoop() != L) 3120 return UnknownValue; 3121 3122 if (AddRec->isAffine()) { 3123 // FORNOW: We only support unit strides. 3124 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 3125 SCEVHandle Step = AddRec->getStepRecurrence(*this); 3126 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType()); 3127 3128 // TODO: handle non-constant strides. 3129 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 3130 if (!CStep || CStep->isZero()) 3131 return UnknownValue; 3132 if (CStep->getValue()->getValue() == 1) { 3133 // With unit stride, the iteration never steps past the limit value. 3134 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 3135 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 3136 // Test whether a positive iteration iteration can step past the limit 3137 // value and past the maximum value for its type in a single step. 3138 if (isSigned) { 3139 APInt Max = APInt::getSignedMaxValue(BitWidth); 3140 if ((Max - CStep->getValue()->getValue()) 3141 .slt(CLimit->getValue()->getValue())) 3142 return UnknownValue; 3143 } else { 3144 APInt Max = APInt::getMaxValue(BitWidth); 3145 if ((Max - CStep->getValue()->getValue()) 3146 .ult(CLimit->getValue()->getValue())) 3147 return UnknownValue; 3148 } 3149 } else 3150 // TODO: handle non-constant limit values below. 3151 return UnknownValue; 3152 } else 3153 // TODO: handle negative strides below. 3154 return UnknownValue; 3155 3156 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 3157 // m. So, we count the number of iterations in which {n,+,s} < m is true. 3158 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 3159 // treat m-n as signed nor unsigned due to overflow possibility. 3160 3161 // First, we get the value of the LHS in the first iteration: n 3162 SCEVHandle Start = AddRec->getOperand(0); 3163 3164 // Determine the minimum constant start value. 3165 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start : 3166 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 3167 APInt::getMinValue(BitWidth)); 3168 3169 // If we know that the condition is true in order to enter the loop, 3170 // then we know that it will run exactly (m-n)/s times. Otherwise, we 3171 // only know if will execute (max(m,n)-n)/s times. In both cases, the 3172 // division must round up. 3173 SCEVHandle End = RHS; 3174 if (!isLoopGuardedByCond(L, 3175 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 3176 getMinusSCEV(Start, Step), RHS)) 3177 End = isSigned ? getSMaxExpr(RHS, Start) 3178 : getUMaxExpr(RHS, Start); 3179 3180 // Determine the maximum constant end value. 3181 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End : 3182 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) : 3183 APInt::getMaxValue(BitWidth)); 3184 3185 // Finally, we subtract these two values and divide, rounding up, to get 3186 // the number of times the backedge is executed. 3187 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start), 3188 getAddExpr(Step, NegOne)), 3189 Step); 3190 3191 // The maximum backedge count is similar, except using the minimum start 3192 // value and the maximum end value. 3193 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd, 3194 MinStart), 3195 getAddExpr(Step, NegOne)), 3196 Step); 3197 3198 return BackedgeTakenInfo(BECount, MaxBECount); 3199 } 3200 3201 return UnknownValue; 3202} 3203 3204/// getNumIterationsInRange - Return the number of iterations of this loop that 3205/// produce values in the specified constant range. Another way of looking at 3206/// this is that it returns the first iteration number where the value is not in 3207/// the condition, thus computing the exit count. If the iteration count can't 3208/// be computed, an instance of SCEVCouldNotCompute is returned. 3209SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 3210 ScalarEvolution &SE) const { 3211 if (Range.isFullSet()) // Infinite loop. 3212 return SE.getCouldNotCompute(); 3213 3214 // If the start is a non-zero constant, shift the range to simplify things. 3215 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 3216 if (!SC->getValue()->isZero()) { 3217 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3218 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3219 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3220 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted)) 3221 return ShiftedAddRec->getNumIterationsInRange( 3222 Range.subtract(SC->getValue()->getValue()), SE); 3223 // This is strange and shouldn't happen. 3224 return SE.getCouldNotCompute(); 3225 } 3226 3227 // The only time we can solve this is when we have all constant indices. 3228 // Otherwise, we cannot determine the overflow conditions. 3229 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3230 if (!isa<SCEVConstant>(getOperand(i))) 3231 return SE.getCouldNotCompute(); 3232 3233 3234 // Okay at this point we know that all elements of the chrec are constants and 3235 // that the start element is zero. 3236 3237 // First check to see if the range contains zero. If not, the first 3238 // iteration exits. 3239 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3240 if (!Range.contains(APInt(BitWidth, 0))) 3241 return SE.getConstant(ConstantInt::get(getType(),0)); 3242 3243 if (isAffine()) { 3244 // If this is an affine expression then we have this situation: 3245 // Solve {0,+,A} in Range === Ax in Range 3246 3247 // We know that zero is in the range. If A is positive then we know that 3248 // the upper value of the range must be the first possible exit value. 3249 // If A is negative then the lower of the range is the last possible loop 3250 // value. Also note that we already checked for a full range. 3251 APInt One(BitWidth,1); 3252 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3253 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3254 3255 // The exit value should be (End+A)/A. 3256 APInt ExitVal = (End + A).udiv(A); 3257 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3258 3259 // Evaluate at the exit value. If we really did fall out of the valid 3260 // range, then we computed our trip count, otherwise wrap around or other 3261 // things must have happened. 3262 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3263 if (Range.contains(Val->getValue())) 3264 return SE.getCouldNotCompute(); // Something strange happened 3265 3266 // Ensure that the previous value is in the range. This is a sanity check. 3267 assert(Range.contains( 3268 EvaluateConstantChrecAtConstant(this, 3269 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3270 "Linear scev computation is off in a bad way!"); 3271 return SE.getConstant(ExitValue); 3272 } else if (isQuadratic()) { 3273 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3274 // quadratic equation to solve it. To do this, we must frame our problem in 3275 // terms of figuring out when zero is crossed, instead of when 3276 // Range.getUpper() is crossed. 3277 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3278 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3279 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3280 3281 // Next, solve the constructed addrec 3282 std::pair<SCEVHandle,SCEVHandle> Roots = 3283 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3284 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3285 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3286 if (R1) { 3287 // Pick the smallest positive root value. 3288 if (ConstantInt *CB = 3289 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3290 R1->getValue(), R2->getValue()))) { 3291 if (CB->getZExtValue() == false) 3292 std::swap(R1, R2); // R1 is the minimum root now. 3293 3294 // Make sure the root is not off by one. The returned iteration should 3295 // not be in the range, but the previous one should be. When solving 3296 // for "X*X < 5", for example, we should not return a root of 2. 3297 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3298 R1->getValue(), 3299 SE); 3300 if (Range.contains(R1Val->getValue())) { 3301 // The next iteration must be out of the range... 3302 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3303 3304 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3305 if (!Range.contains(R1Val->getValue())) 3306 return SE.getConstant(NextVal); 3307 return SE.getCouldNotCompute(); // Something strange happened 3308 } 3309 3310 // If R1 was not in the range, then it is a good return value. Make 3311 // sure that R1-1 WAS in the range though, just in case. 3312 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3313 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3314 if (Range.contains(R1Val->getValue())) 3315 return R1; 3316 return SE.getCouldNotCompute(); // Something strange happened 3317 } 3318 } 3319 } 3320 3321 return SE.getCouldNotCompute(); 3322} 3323 3324 3325 3326//===----------------------------------------------------------------------===// 3327// ScalarEvolution Class Implementation 3328//===----------------------------------------------------------------------===// 3329 3330ScalarEvolution::ScalarEvolution() 3331 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3332} 3333 3334bool ScalarEvolution::runOnFunction(Function &F) { 3335 this->F = &F; 3336 LI = &getAnalysis<LoopInfo>(); 3337 TD = getAnalysisIfAvailable<TargetData>(); 3338 return false; 3339} 3340 3341void ScalarEvolution::releaseMemory() { 3342 Scalars.clear(); 3343 BackedgeTakenCounts.clear(); 3344 ConstantEvolutionLoopExitValue.clear(); 3345} 3346 3347void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3348 AU.setPreservesAll(); 3349 AU.addRequiredTransitive<LoopInfo>(); 3350} 3351 3352bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3353 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3354} 3355 3356static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3357 const Loop *L) { 3358 // Print all inner loops first 3359 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3360 PrintLoopInfo(OS, SE, *I); 3361 3362 OS << "Loop " << L->getHeader()->getName() << ": "; 3363 3364 SmallVector<BasicBlock*, 8> ExitBlocks; 3365 L->getExitBlocks(ExitBlocks); 3366 if (ExitBlocks.size() != 1) 3367 OS << "<multiple exits> "; 3368 3369 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3370 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3371 } else { 3372 OS << "Unpredictable backedge-taken count. "; 3373 } 3374 3375 OS << "\n"; 3376} 3377 3378void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3379 // ScalarEvolution's implementaiton of the print method is to print 3380 // out SCEV values of all instructions that are interesting. Doing 3381 // this potentially causes it to create new SCEV objects though, 3382 // which technically conflicts with the const qualifier. This isn't 3383 // observable from outside the class though (the hasSCEV function 3384 // notwithstanding), so casting away the const isn't dangerous. 3385 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3386 3387 OS << "Classifying expressions for: " << F->getName() << "\n"; 3388 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3389 if (isSCEVable(I->getType())) { 3390 OS << *I; 3391 OS << " --> "; 3392 SCEVHandle SV = SE.getSCEV(&*I); 3393 SV->print(OS); 3394 OS << "\t\t"; 3395 3396 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3397 OS << "Exits: "; 3398 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3399 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3400 OS << "<<Unknown>>"; 3401 } else { 3402 OS << *ExitValue; 3403 } 3404 } 3405 3406 3407 OS << "\n"; 3408 } 3409 3410 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3411 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3412 PrintLoopInfo(OS, &SE, *I); 3413} 3414 3415void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3416 raw_os_ostream OS(o); 3417 print(OS, M); 3418} 3419