ScalarEvolution.cpp revision 66a7e857aa5843da3a7d0f52aa09a5935cf565dc
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/Support/CommandLine.h" 74#include "llvm/Support/Compiler.h" 75#include "llvm/Support/ConstantRange.h" 76#include "llvm/Support/GetElementPtrTypeIterator.h" 77#include "llvm/Support/InstIterator.h" 78#include "llvm/Support/ManagedStatic.h" 79#include "llvm/Support/MathExtras.h" 80#include "llvm/Support/raw_ostream.h" 81#include "llvm/ADT/Statistic.h" 82#include "llvm/ADT/STLExtras.h" 83#include <ostream> 84#include <algorithm> 85using namespace llvm; 86 87STATISTIC(NumArrayLenItCounts, 88 "Number of trip counts computed with array length"); 89STATISTIC(NumTripCountsComputed, 90 "Number of loops with predictable loop counts"); 91STATISTIC(NumTripCountsNotComputed, 92 "Number of loops without predictable loop counts"); 93STATISTIC(NumBruteForceTripCountsComputed, 94 "Number of loops with trip counts computed by force"); 95 96static cl::opt<unsigned> 97MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 98 cl::desc("Maximum number of iterations SCEV will " 99 "symbolically execute a constant derived loop"), 100 cl::init(100)); 101 102static RegisterPass<ScalarEvolution> 103R("scalar-evolution", "Scalar Evolution Analysis", false, true); 104char ScalarEvolution::ID = 0; 105 106//===----------------------------------------------------------------------===// 107// SCEV class definitions 108//===----------------------------------------------------------------------===// 109 110//===----------------------------------------------------------------------===// 111// Implementation of the SCEV class. 112// 113SCEV::~SCEV() {} 114void SCEV::dump() const { 115 print(errs()); 116 errs() << '\n'; 117} 118 119void SCEV::print(std::ostream &o) const { 120 raw_os_ostream OS(o); 121 print(OS); 122} 123 124bool SCEV::isZero() const { 125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 126 return SC->getValue()->isZero(); 127 return false; 128} 129 130 131SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {} 132SCEVCouldNotCompute::~SCEVCouldNotCompute() {} 133 134bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 135 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 136 return false; 137} 138 139const Type *SCEVCouldNotCompute::getType() const { 140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 141 return 0; 142} 143 144bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 146 return false; 147} 148 149SCEVHandle SCEVCouldNotCompute:: 150replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 151 const SCEVHandle &Conc, 152 ScalarEvolution &SE) const { 153 return this; 154} 155 156void SCEVCouldNotCompute::print(raw_ostream &OS) const { 157 OS << "***COULDNOTCOMPUTE***"; 158} 159 160bool SCEVCouldNotCompute::classof(const SCEV *S) { 161 return S->getSCEVType() == scCouldNotCompute; 162} 163 164 165// SCEVConstants - Only allow the creation of one SCEVConstant for any 166// particular value. Don't use a SCEVHandle here, or else the object will 167// never be deleted! 168static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants; 169 170 171SCEVConstant::~SCEVConstant() { 172 SCEVConstants->erase(V); 173} 174 175SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) { 176 SCEVConstant *&R = (*SCEVConstants)[V]; 177 if (R == 0) R = new SCEVConstant(V); 178 return R; 179} 180 181SCEVHandle ScalarEvolution::getConstant(const APInt& Val) { 182 return getConstant(ConstantInt::get(Val)); 183} 184 185const Type *SCEVConstant::getType() const { return V->getType(); } 186 187void SCEVConstant::print(raw_ostream &OS) const { 188 WriteAsOperand(OS, V, false); 189} 190 191SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy, 192 const SCEVHandle &op, const Type *ty) 193 : SCEV(SCEVTy), Op(op), Ty(ty) {} 194 195SCEVCastExpr::~SCEVCastExpr() {} 196 197bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 198 return Op->dominates(BB, DT); 199} 200 201// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any 202// particular input. Don't use a SCEVHandle here, or else the object will 203// never be deleted! 204static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 205 SCEVTruncateExpr*> > SCEVTruncates; 206 207SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty) 208 : SCEVCastExpr(scTruncate, op, ty) { 209 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 210 (Ty->isInteger() || isa<PointerType>(Ty)) && 211 "Cannot truncate non-integer value!"); 212} 213 214SCEVTruncateExpr::~SCEVTruncateExpr() { 215 SCEVTruncates->erase(std::make_pair(Op, Ty)); 216} 217 218void SCEVTruncateExpr::print(raw_ostream &OS) const { 219 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 220} 221 222// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any 223// particular input. Don't use a SCEVHandle here, or else the object will never 224// be deleted! 225static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 226 SCEVZeroExtendExpr*> > SCEVZeroExtends; 227 228SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty) 229 : SCEVCastExpr(scZeroExtend, op, ty) { 230 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 231 (Ty->isInteger() || isa<PointerType>(Ty)) && 232 "Cannot zero extend non-integer value!"); 233} 234 235SCEVZeroExtendExpr::~SCEVZeroExtendExpr() { 236 SCEVZeroExtends->erase(std::make_pair(Op, Ty)); 237} 238 239void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 240 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 241} 242 243// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any 244// particular input. Don't use a SCEVHandle here, or else the object will never 245// be deleted! 246static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>, 247 SCEVSignExtendExpr*> > SCEVSignExtends; 248 249SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty) 250 : SCEVCastExpr(scSignExtend, op, ty) { 251 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 252 (Ty->isInteger() || isa<PointerType>(Ty)) && 253 "Cannot sign extend non-integer value!"); 254} 255 256SCEVSignExtendExpr::~SCEVSignExtendExpr() { 257 SCEVSignExtends->erase(std::make_pair(Op, Ty)); 258} 259 260void SCEVSignExtendExpr::print(raw_ostream &OS) const { 261 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 262} 263 264// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any 265// particular input. Don't use a SCEVHandle here, or else the object will never 266// be deleted! 267static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >, 268 SCEVCommutativeExpr*> > SCEVCommExprs; 269 270SCEVCommutativeExpr::~SCEVCommutativeExpr() { 271 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 272 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps)); 273} 274 275void SCEVCommutativeExpr::print(raw_ostream &OS) const { 276 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 277 const char *OpStr = getOperationStr(); 278 OS << "(" << *Operands[0]; 279 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 280 OS << OpStr << *Operands[i]; 281 OS << ")"; 282} 283 284SCEVHandle SCEVCommutativeExpr:: 285replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 286 const SCEVHandle &Conc, 287 ScalarEvolution &SE) const { 288 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 289 SCEVHandle H = 290 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 291 if (H != getOperand(i)) { 292 std::vector<SCEVHandle> NewOps; 293 NewOps.reserve(getNumOperands()); 294 for (unsigned j = 0; j != i; ++j) 295 NewOps.push_back(getOperand(j)); 296 NewOps.push_back(H); 297 for (++i; i != e; ++i) 298 NewOps.push_back(getOperand(i)-> 299 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 300 301 if (isa<SCEVAddExpr>(this)) 302 return SE.getAddExpr(NewOps); 303 else if (isa<SCEVMulExpr>(this)) 304 return SE.getMulExpr(NewOps); 305 else if (isa<SCEVSMaxExpr>(this)) 306 return SE.getSMaxExpr(NewOps); 307 else if (isa<SCEVUMaxExpr>(this)) 308 return SE.getUMaxExpr(NewOps); 309 else 310 assert(0 && "Unknown commutative expr!"); 311 } 312 } 313 return this; 314} 315 316bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 317 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 318 if (!getOperand(i)->dominates(BB, DT)) 319 return false; 320 } 321 return true; 322} 323 324 325// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular 326// input. Don't use a SCEVHandle here, or else the object will never be 327// deleted! 328static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>, 329 SCEVUDivExpr*> > SCEVUDivs; 330 331SCEVUDivExpr::~SCEVUDivExpr() { 332 SCEVUDivs->erase(std::make_pair(LHS, RHS)); 333} 334 335bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 336 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 337} 338 339void SCEVUDivExpr::print(raw_ostream &OS) const { 340 OS << "(" << *LHS << " /u " << *RHS << ")"; 341} 342 343const Type *SCEVUDivExpr::getType() const { 344 return LHS->getType(); 345} 346 347// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any 348// particular input. Don't use a SCEVHandle here, or else the object will never 349// be deleted! 350static ManagedStatic<std::map<std::pair<const Loop *, 351 std::vector<const SCEV*> >, 352 SCEVAddRecExpr*> > SCEVAddRecExprs; 353 354SCEVAddRecExpr::~SCEVAddRecExpr() { 355 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 356 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps)); 357} 358 359SCEVHandle SCEVAddRecExpr:: 360replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym, 361 const SCEVHandle &Conc, 362 ScalarEvolution &SE) const { 363 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 364 SCEVHandle H = 365 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 366 if (H != getOperand(i)) { 367 std::vector<SCEVHandle> NewOps; 368 NewOps.reserve(getNumOperands()); 369 for (unsigned j = 0; j != i; ++j) 370 NewOps.push_back(getOperand(j)); 371 NewOps.push_back(H); 372 for (++i; i != e; ++i) 373 NewOps.push_back(getOperand(i)-> 374 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 375 376 return SE.getAddRecExpr(NewOps, L); 377 } 378 } 379 return this; 380} 381 382 383bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 384 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't 385 // contain L and if the start is invariant. 386 return !QueryLoop->contains(L->getHeader()) && 387 getOperand(0)->isLoopInvariant(QueryLoop); 388} 389 390 391void SCEVAddRecExpr::print(raw_ostream &OS) const { 392 OS << "{" << *Operands[0]; 393 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 394 OS << ",+," << *Operands[i]; 395 OS << "}<" << L->getHeader()->getName() + ">"; 396} 397 398// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular 399// value. Don't use a SCEVHandle here, or else the object will never be 400// deleted! 401static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns; 402 403SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); } 404 405bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 406 // All non-instruction values are loop invariant. All instructions are loop 407 // invariant if they are not contained in the specified loop. 408 if (Instruction *I = dyn_cast<Instruction>(V)) 409 return !L->contains(I->getParent()); 410 return true; 411} 412 413bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 414 if (Instruction *I = dyn_cast<Instruction>(getValue())) 415 return DT->dominates(I->getParent(), BB); 416 return true; 417} 418 419const Type *SCEVUnknown::getType() const { 420 return V->getType(); 421} 422 423void SCEVUnknown::print(raw_ostream &OS) const { 424 WriteAsOperand(OS, V, false); 425} 426 427//===----------------------------------------------------------------------===// 428// SCEV Utilities 429//===----------------------------------------------------------------------===// 430 431namespace { 432 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 433 /// than the complexity of the RHS. This comparator is used to canonicalize 434 /// expressions. 435 class VISIBILITY_HIDDEN SCEVComplexityCompare { 436 LoopInfo *LI; 437 public: 438 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 439 440 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 441 // Primarily, sort the SCEVs by their getSCEVType(). 442 if (LHS->getSCEVType() != RHS->getSCEVType()) 443 return LHS->getSCEVType() < RHS->getSCEVType(); 444 445 // Aside from the getSCEVType() ordering, the particular ordering 446 // isn't very important except that it's beneficial to be consistent, 447 // so that (a + b) and (b + a) don't end up as different expressions. 448 449 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 450 // not as complete as it could be. 451 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 452 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 453 454 // Compare getValueID values. 455 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 456 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 457 458 // Sort arguments by their position. 459 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 460 const Argument *RA = cast<Argument>(RU->getValue()); 461 return LA->getArgNo() < RA->getArgNo(); 462 } 463 464 // For instructions, compare their loop depth, and their opcode. 465 // This is pretty loose. 466 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 467 Instruction *RV = cast<Instruction>(RU->getValue()); 468 469 // Compare loop depths. 470 if (LI->getLoopDepth(LV->getParent()) != 471 LI->getLoopDepth(RV->getParent())) 472 return LI->getLoopDepth(LV->getParent()) < 473 LI->getLoopDepth(RV->getParent()); 474 475 // Compare opcodes. 476 if (LV->getOpcode() != RV->getOpcode()) 477 return LV->getOpcode() < RV->getOpcode(); 478 479 // Compare the number of operands. 480 if (LV->getNumOperands() != RV->getNumOperands()) 481 return LV->getNumOperands() < RV->getNumOperands(); 482 } 483 484 return false; 485 } 486 487 // Constant sorting doesn't matter since they'll be folded. 488 if (isa<SCEVConstant>(LHS)) 489 return false; 490 491 // Lexicographically compare n-ary expressions. 492 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 493 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 494 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 495 if (i >= RC->getNumOperands()) 496 return false; 497 if (operator()(LC->getOperand(i), RC->getOperand(i))) 498 return true; 499 if (operator()(RC->getOperand(i), LC->getOperand(i))) 500 return false; 501 } 502 return LC->getNumOperands() < RC->getNumOperands(); 503 } 504 505 // Lexicographically compare udiv expressions. 506 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 507 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 508 if (operator()(LC->getLHS(), RC->getLHS())) 509 return true; 510 if (operator()(RC->getLHS(), LC->getLHS())) 511 return false; 512 if (operator()(LC->getRHS(), RC->getRHS())) 513 return true; 514 if (operator()(RC->getRHS(), LC->getRHS())) 515 return false; 516 return false; 517 } 518 519 // Compare cast expressions by operand. 520 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 521 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 522 return operator()(LC->getOperand(), RC->getOperand()); 523 } 524 525 assert(0 && "Unknown SCEV kind!"); 526 return false; 527 } 528 }; 529} 530 531/// GroupByComplexity - Given a list of SCEV objects, order them by their 532/// complexity, and group objects of the same complexity together by value. 533/// When this routine is finished, we know that any duplicates in the vector are 534/// consecutive and that complexity is monotonically increasing. 535/// 536/// Note that we go take special precautions to ensure that we get determinstic 537/// results from this routine. In other words, we don't want the results of 538/// this to depend on where the addresses of various SCEV objects happened to 539/// land in memory. 540/// 541static void GroupByComplexity(std::vector<SCEVHandle> &Ops, 542 LoopInfo *LI) { 543 if (Ops.size() < 2) return; // Noop 544 if (Ops.size() == 2) { 545 // This is the common case, which also happens to be trivially simple. 546 // Special case it. 547 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 548 std::swap(Ops[0], Ops[1]); 549 return; 550 } 551 552 // Do the rough sort by complexity. 553 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 554 555 // Now that we are sorted by complexity, group elements of the same 556 // complexity. Note that this is, at worst, N^2, but the vector is likely to 557 // be extremely short in practice. Note that we take this approach because we 558 // do not want to depend on the addresses of the objects we are grouping. 559 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 560 const SCEV *S = Ops[i]; 561 unsigned Complexity = S->getSCEVType(); 562 563 // If there are any objects of the same complexity and same value as this 564 // one, group them. 565 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 566 if (Ops[j] == S) { // Found a duplicate. 567 // Move it to immediately after i'th element. 568 std::swap(Ops[i+1], Ops[j]); 569 ++i; // no need to rescan it. 570 if (i == e-2) return; // Done! 571 } 572 } 573 } 574} 575 576 577 578//===----------------------------------------------------------------------===// 579// Simple SCEV method implementations 580//===----------------------------------------------------------------------===// 581 582/// BinomialCoefficient - Compute BC(It, K). The result has width W. 583// Assume, K > 0. 584static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K, 585 ScalarEvolution &SE, 586 const Type* ResultTy) { 587 // Handle the simplest case efficiently. 588 if (K == 1) 589 return SE.getTruncateOrZeroExtend(It, ResultTy); 590 591 // We are using the following formula for BC(It, K): 592 // 593 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 594 // 595 // Suppose, W is the bitwidth of the return value. We must be prepared for 596 // overflow. Hence, we must assure that the result of our computation is 597 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 598 // safe in modular arithmetic. 599 // 600 // However, this code doesn't use exactly that formula; the formula it uses 601 // is something like the following, where T is the number of factors of 2 in 602 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 603 // exponentiation: 604 // 605 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 606 // 607 // This formula is trivially equivalent to the previous formula. However, 608 // this formula can be implemented much more efficiently. The trick is that 609 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 610 // arithmetic. To do exact division in modular arithmetic, all we have 611 // to do is multiply by the inverse. Therefore, this step can be done at 612 // width W. 613 // 614 // The next issue is how to safely do the division by 2^T. The way this 615 // is done is by doing the multiplication step at a width of at least W + T 616 // bits. This way, the bottom W+T bits of the product are accurate. Then, 617 // when we perform the division by 2^T (which is equivalent to a right shift 618 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 619 // truncated out after the division by 2^T. 620 // 621 // In comparison to just directly using the first formula, this technique 622 // is much more efficient; using the first formula requires W * K bits, 623 // but this formula less than W + K bits. Also, the first formula requires 624 // a division step, whereas this formula only requires multiplies and shifts. 625 // 626 // It doesn't matter whether the subtraction step is done in the calculation 627 // width or the input iteration count's width; if the subtraction overflows, 628 // the result must be zero anyway. We prefer here to do it in the width of 629 // the induction variable because it helps a lot for certain cases; CodeGen 630 // isn't smart enough to ignore the overflow, which leads to much less 631 // efficient code if the width of the subtraction is wider than the native 632 // register width. 633 // 634 // (It's possible to not widen at all by pulling out factors of 2 before 635 // the multiplication; for example, K=2 can be calculated as 636 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 637 // extra arithmetic, so it's not an obvious win, and it gets 638 // much more complicated for K > 3.) 639 640 // Protection from insane SCEVs; this bound is conservative, 641 // but it probably doesn't matter. 642 if (K > 1000) 643 return SE.getCouldNotCompute(); 644 645 unsigned W = SE.getTypeSizeInBits(ResultTy); 646 647 // Calculate K! / 2^T and T; we divide out the factors of two before 648 // multiplying for calculating K! / 2^T to avoid overflow. 649 // Other overflow doesn't matter because we only care about the bottom 650 // W bits of the result. 651 APInt OddFactorial(W, 1); 652 unsigned T = 1; 653 for (unsigned i = 3; i <= K; ++i) { 654 APInt Mult(W, i); 655 unsigned TwoFactors = Mult.countTrailingZeros(); 656 T += TwoFactors; 657 Mult = Mult.lshr(TwoFactors); 658 OddFactorial *= Mult; 659 } 660 661 // We need at least W + T bits for the multiplication step 662 unsigned CalculationBits = W + T; 663 664 // Calcuate 2^T, at width T+W. 665 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 666 667 // Calculate the multiplicative inverse of K! / 2^T; 668 // this multiplication factor will perform the exact division by 669 // K! / 2^T. 670 APInt Mod = APInt::getSignedMinValue(W+1); 671 APInt MultiplyFactor = OddFactorial.zext(W+1); 672 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 673 MultiplyFactor = MultiplyFactor.trunc(W); 674 675 // Calculate the product, at width T+W 676 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 677 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 678 for (unsigned i = 1; i != K; ++i) { 679 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 680 Dividend = SE.getMulExpr(Dividend, 681 SE.getTruncateOrZeroExtend(S, CalculationTy)); 682 } 683 684 // Divide by 2^T 685 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 686 687 // Truncate the result, and divide by K! / 2^T. 688 689 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 690 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 691} 692 693/// evaluateAtIteration - Return the value of this chain of recurrences at 694/// the specified iteration number. We can evaluate this recurrence by 695/// multiplying each element in the chain by the binomial coefficient 696/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 697/// 698/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 699/// 700/// where BC(It, k) stands for binomial coefficient. 701/// 702SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It, 703 ScalarEvolution &SE) const { 704 SCEVHandle Result = getStart(); 705 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 706 // The computation is correct in the face of overflow provided that the 707 // multiplication is performed _after_ the evaluation of the binomial 708 // coefficient. 709 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType()); 710 if (isa<SCEVCouldNotCompute>(Coeff)) 711 return Coeff; 712 713 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 714 } 715 return Result; 716} 717 718//===----------------------------------------------------------------------===// 719// SCEV Expression folder implementations 720//===----------------------------------------------------------------------===// 721 722SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, 723 const Type *Ty) { 724 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 725 "This is not a truncating conversion!"); 726 assert(isSCEVable(Ty) && 727 "This is not a conversion to a SCEVable type!"); 728 Ty = getEffectiveSCEVType(Ty); 729 730 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 731 return getUnknown( 732 ConstantExpr::getTrunc(SC->getValue(), Ty)); 733 734 // trunc(trunc(x)) --> trunc(x) 735 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 736 return getTruncateExpr(ST->getOperand(), Ty); 737 738 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 739 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 740 return getTruncateOrSignExtend(SS->getOperand(), Ty); 741 742 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 743 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 744 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 745 746 // If the input value is a chrec scev made out of constants, truncate 747 // all of the constants. 748 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 749 std::vector<SCEVHandle> Operands; 750 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 751 // FIXME: This should allow truncation of other expression types! 752 if (isa<SCEVConstant>(AddRec->getOperand(i))) 753 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 754 else 755 break; 756 if (Operands.size() == AddRec->getNumOperands()) 757 return getAddRecExpr(Operands, AddRec->getLoop()); 758 } 759 760 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 761 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 762 return Result; 763} 764 765SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 766 const Type *Ty) { 767 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 768 "This is not an extending conversion!"); 769 assert(isSCEVable(Ty) && 770 "This is not a conversion to a SCEVable type!"); 771 Ty = getEffectiveSCEVType(Ty); 772 773 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 774 const Type *IntTy = getEffectiveSCEVType(Ty); 775 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 776 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 777 return getUnknown(C); 778 } 779 780 // zext(zext(x)) --> zext(x) 781 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 782 return getZeroExtendExpr(SZ->getOperand(), Ty); 783 784 // If the input value is a chrec scev, and we can prove that the value 785 // did not overflow the old, smaller, value, we can zero extend all of the 786 // operands (often constants). This allows analysis of something like 787 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 788 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 789 if (AR->isAffine()) { 790 // Check whether the backedge-taken count is SCEVCouldNotCompute. 791 // Note that this serves two purposes: It filters out loops that are 792 // simply not analyzable, and it covers the case where this code is 793 // being called from within backedge-taken count analysis, such that 794 // attempting to ask for the backedge-taken count would likely result 795 // in infinite recursion. In the later case, the analysis code will 796 // cope with a conservative value, and it will take care to purge 797 // that value once it has finished. 798 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 799 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 800 // Manually compute the final value for AR, checking for 801 // overflow. 802 SCEVHandle Start = AR->getStart(); 803 SCEVHandle Step = AR->getStepRecurrence(*this); 804 805 // Check whether the backedge-taken count can be losslessly casted to 806 // the addrec's type. The count is always unsigned. 807 SCEVHandle CastedMaxBECount = 808 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 809 if (MaxBECount == 810 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 811 const Type *WideTy = 812 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 813 // Check whether Start+Step*MaxBECount has no unsigned overflow. 814 SCEVHandle ZMul = 815 getMulExpr(CastedMaxBECount, 816 getTruncateOrZeroExtend(Step, Start->getType())); 817 SCEVHandle Add = getAddExpr(Start, ZMul); 818 if (getZeroExtendExpr(Add, WideTy) == 819 getAddExpr(getZeroExtendExpr(Start, WideTy), 820 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 821 getZeroExtendExpr(Step, WideTy)))) 822 // Return the expression with the addrec on the outside. 823 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 824 getZeroExtendExpr(Step, Ty), 825 AR->getLoop()); 826 827 // Similar to above, only this time treat the step value as signed. 828 // This covers loops that count down. 829 SCEVHandle SMul = 830 getMulExpr(CastedMaxBECount, 831 getTruncateOrSignExtend(Step, Start->getType())); 832 Add = getAddExpr(Start, SMul); 833 if (getZeroExtendExpr(Add, WideTy) == 834 getAddExpr(getZeroExtendExpr(Start, WideTy), 835 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 836 getSignExtendExpr(Step, WideTy)))) 837 // Return the expression with the addrec on the outside. 838 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 839 getSignExtendExpr(Step, Ty), 840 AR->getLoop()); 841 } 842 } 843 } 844 845 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 846 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 847 return Result; 848} 849 850SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, 851 const Type *Ty) { 852 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 853 "This is not an extending conversion!"); 854 assert(isSCEVable(Ty) && 855 "This is not a conversion to a SCEVable type!"); 856 Ty = getEffectiveSCEVType(Ty); 857 858 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 859 const Type *IntTy = getEffectiveSCEVType(Ty); 860 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 861 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 862 return getUnknown(C); 863 } 864 865 // sext(sext(x)) --> sext(x) 866 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 867 return getSignExtendExpr(SS->getOperand(), Ty); 868 869 // If the input value is a chrec scev, and we can prove that the value 870 // did not overflow the old, smaller, value, we can sign extend all of the 871 // operands (often constants). This allows analysis of something like 872 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 873 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 874 if (AR->isAffine()) { 875 // Check whether the backedge-taken count is SCEVCouldNotCompute. 876 // Note that this serves two purposes: It filters out loops that are 877 // simply not analyzable, and it covers the case where this code is 878 // being called from within backedge-taken count analysis, such that 879 // attempting to ask for the backedge-taken count would likely result 880 // in infinite recursion. In the later case, the analysis code will 881 // cope with a conservative value, and it will take care to purge 882 // that value once it has finished. 883 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 884 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 885 // Manually compute the final value for AR, checking for 886 // overflow. 887 SCEVHandle Start = AR->getStart(); 888 SCEVHandle Step = AR->getStepRecurrence(*this); 889 890 // Check whether the backedge-taken count can be losslessly casted to 891 // the addrec's type. The count is always unsigned. 892 SCEVHandle CastedMaxBECount = 893 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 894 if (MaxBECount == 895 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 896 const Type *WideTy = 897 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 898 // Check whether Start+Step*MaxBECount has no signed overflow. 899 SCEVHandle SMul = 900 getMulExpr(CastedMaxBECount, 901 getTruncateOrSignExtend(Step, Start->getType())); 902 SCEVHandle Add = getAddExpr(Start, SMul); 903 if (getSignExtendExpr(Add, WideTy) == 904 getAddExpr(getSignExtendExpr(Start, WideTy), 905 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 906 getSignExtendExpr(Step, WideTy)))) 907 // Return the expression with the addrec on the outside. 908 return getAddRecExpr(getSignExtendExpr(Start, Ty), 909 getSignExtendExpr(Step, Ty), 910 AR->getLoop()); 911 } 912 } 913 } 914 915 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 916 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 917 return Result; 918} 919 920// get - Get a canonical add expression, or something simpler if possible. 921SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 922 assert(!Ops.empty() && "Cannot get empty add!"); 923 if (Ops.size() == 1) return Ops[0]; 924 925 // Sort by complexity, this groups all similar expression types together. 926 GroupByComplexity(Ops, LI); 927 928 // If there are any constants, fold them together. 929 unsigned Idx = 0; 930 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 931 ++Idx; 932 assert(Idx < Ops.size()); 933 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 934 // We found two constants, fold them together! 935 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 936 RHSC->getValue()->getValue()); 937 Ops[0] = getConstant(Fold); 938 Ops.erase(Ops.begin()+1); // Erase the folded element 939 if (Ops.size() == 1) return Ops[0]; 940 LHSC = cast<SCEVConstant>(Ops[0]); 941 } 942 943 // If we are left with a constant zero being added, strip it off. 944 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 945 Ops.erase(Ops.begin()); 946 --Idx; 947 } 948 } 949 950 if (Ops.size() == 1) return Ops[0]; 951 952 // Okay, check to see if the same value occurs in the operand list twice. If 953 // so, merge them together into an multiply expression. Since we sorted the 954 // list, these values are required to be adjacent. 955 const Type *Ty = Ops[0]->getType(); 956 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 957 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 958 // Found a match, merge the two values into a multiply, and add any 959 // remaining values to the result. 960 SCEVHandle Two = getIntegerSCEV(2, Ty); 961 SCEVHandle Mul = getMulExpr(Ops[i], Two); 962 if (Ops.size() == 2) 963 return Mul; 964 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 965 Ops.push_back(Mul); 966 return getAddExpr(Ops); 967 } 968 969 // Now we know the first non-constant operand. Skip past any cast SCEVs. 970 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 971 ++Idx; 972 973 // If there are add operands they would be next. 974 if (Idx < Ops.size()) { 975 bool DeletedAdd = false; 976 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 977 // If we have an add, expand the add operands onto the end of the operands 978 // list. 979 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 980 Ops.erase(Ops.begin()+Idx); 981 DeletedAdd = true; 982 } 983 984 // If we deleted at least one add, we added operands to the end of the list, 985 // and they are not necessarily sorted. Recurse to resort and resimplify 986 // any operands we just aquired. 987 if (DeletedAdd) 988 return getAddExpr(Ops); 989 } 990 991 // Skip over the add expression until we get to a multiply. 992 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 993 ++Idx; 994 995 // If we are adding something to a multiply expression, make sure the 996 // something is not already an operand of the multiply. If so, merge it into 997 // the multiply. 998 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 999 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1000 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1001 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1002 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1003 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 1004 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1005 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 1006 if (Mul->getNumOperands() != 2) { 1007 // If the multiply has more than two operands, we must get the 1008 // Y*Z term. 1009 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 1010 MulOps.erase(MulOps.begin()+MulOp); 1011 InnerMul = getMulExpr(MulOps); 1012 } 1013 SCEVHandle One = getIntegerSCEV(1, Ty); 1014 SCEVHandle AddOne = getAddExpr(InnerMul, One); 1015 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1016 if (Ops.size() == 2) return OuterMul; 1017 if (AddOp < Idx) { 1018 Ops.erase(Ops.begin()+AddOp); 1019 Ops.erase(Ops.begin()+Idx-1); 1020 } else { 1021 Ops.erase(Ops.begin()+Idx); 1022 Ops.erase(Ops.begin()+AddOp-1); 1023 } 1024 Ops.push_back(OuterMul); 1025 return getAddExpr(Ops); 1026 } 1027 1028 // Check this multiply against other multiplies being added together. 1029 for (unsigned OtherMulIdx = Idx+1; 1030 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1031 ++OtherMulIdx) { 1032 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1033 // If MulOp occurs in OtherMul, we can fold the two multiplies 1034 // together. 1035 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1036 OMulOp != e; ++OMulOp) 1037 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1038 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1039 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 1040 if (Mul->getNumOperands() != 2) { 1041 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 1042 MulOps.erase(MulOps.begin()+MulOp); 1043 InnerMul1 = getMulExpr(MulOps); 1044 } 1045 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1046 if (OtherMul->getNumOperands() != 2) { 1047 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 1048 OtherMul->op_end()); 1049 MulOps.erase(MulOps.begin()+OMulOp); 1050 InnerMul2 = getMulExpr(MulOps); 1051 } 1052 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1053 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1054 if (Ops.size() == 2) return OuterMul; 1055 Ops.erase(Ops.begin()+Idx); 1056 Ops.erase(Ops.begin()+OtherMulIdx-1); 1057 Ops.push_back(OuterMul); 1058 return getAddExpr(Ops); 1059 } 1060 } 1061 } 1062 } 1063 1064 // If there are any add recurrences in the operands list, see if any other 1065 // added values are loop invariant. If so, we can fold them into the 1066 // recurrence. 1067 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1068 ++Idx; 1069 1070 // Scan over all recurrences, trying to fold loop invariants into them. 1071 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1072 // Scan all of the other operands to this add and add them to the vector if 1073 // they are loop invariant w.r.t. the recurrence. 1074 std::vector<SCEVHandle> LIOps; 1075 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1076 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1077 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1078 LIOps.push_back(Ops[i]); 1079 Ops.erase(Ops.begin()+i); 1080 --i; --e; 1081 } 1082 1083 // If we found some loop invariants, fold them into the recurrence. 1084 if (!LIOps.empty()) { 1085 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1086 LIOps.push_back(AddRec->getStart()); 1087 1088 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 1089 AddRecOps[0] = getAddExpr(LIOps); 1090 1091 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1092 // If all of the other operands were loop invariant, we are done. 1093 if (Ops.size() == 1) return NewRec; 1094 1095 // Otherwise, add the folded AddRec by the non-liv parts. 1096 for (unsigned i = 0;; ++i) 1097 if (Ops[i] == AddRec) { 1098 Ops[i] = NewRec; 1099 break; 1100 } 1101 return getAddExpr(Ops); 1102 } 1103 1104 // Okay, if there weren't any loop invariants to be folded, check to see if 1105 // there are multiple AddRec's with the same loop induction variable being 1106 // added together. If so, we can fold them. 1107 for (unsigned OtherIdx = Idx+1; 1108 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1109 if (OtherIdx != Idx) { 1110 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1111 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1112 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1113 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 1114 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1115 if (i >= NewOps.size()) { 1116 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1117 OtherAddRec->op_end()); 1118 break; 1119 } 1120 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1121 } 1122 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1123 1124 if (Ops.size() == 2) return NewAddRec; 1125 1126 Ops.erase(Ops.begin()+Idx); 1127 Ops.erase(Ops.begin()+OtherIdx-1); 1128 Ops.push_back(NewAddRec); 1129 return getAddExpr(Ops); 1130 } 1131 } 1132 1133 // Otherwise couldn't fold anything into this recurrence. Move onto the 1134 // next one. 1135 } 1136 1137 // Okay, it looks like we really DO need an add expr. Check to see if we 1138 // already have one, otherwise create a new one. 1139 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1140 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 1141 SCEVOps)]; 1142 if (Result == 0) Result = new SCEVAddExpr(Ops); 1143 return Result; 1144} 1145 1146 1147SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 1148 assert(!Ops.empty() && "Cannot get empty mul!"); 1149 1150 // Sort by complexity, this groups all similar expression types together. 1151 GroupByComplexity(Ops, LI); 1152 1153 // If there are any constants, fold them together. 1154 unsigned Idx = 0; 1155 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1156 1157 // C1*(C2+V) -> C1*C2 + C1*V 1158 if (Ops.size() == 2) 1159 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1160 if (Add->getNumOperands() == 2 && 1161 isa<SCEVConstant>(Add->getOperand(0))) 1162 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1163 getMulExpr(LHSC, Add->getOperand(1))); 1164 1165 1166 ++Idx; 1167 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1168 // We found two constants, fold them together! 1169 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1170 RHSC->getValue()->getValue()); 1171 Ops[0] = getConstant(Fold); 1172 Ops.erase(Ops.begin()+1); // Erase the folded element 1173 if (Ops.size() == 1) return Ops[0]; 1174 LHSC = cast<SCEVConstant>(Ops[0]); 1175 } 1176 1177 // If we are left with a constant one being multiplied, strip it off. 1178 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1179 Ops.erase(Ops.begin()); 1180 --Idx; 1181 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1182 // If we have a multiply of zero, it will always be zero. 1183 return Ops[0]; 1184 } 1185 } 1186 1187 // Skip over the add expression until we get to a multiply. 1188 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1189 ++Idx; 1190 1191 if (Ops.size() == 1) 1192 return Ops[0]; 1193 1194 // If there are mul operands inline them all into this expression. 1195 if (Idx < Ops.size()) { 1196 bool DeletedMul = false; 1197 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1198 // If we have an mul, expand the mul operands onto the end of the operands 1199 // list. 1200 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1201 Ops.erase(Ops.begin()+Idx); 1202 DeletedMul = true; 1203 } 1204 1205 // If we deleted at least one mul, we added operands to the end of the list, 1206 // and they are not necessarily sorted. Recurse to resort and resimplify 1207 // any operands we just aquired. 1208 if (DeletedMul) 1209 return getMulExpr(Ops); 1210 } 1211 1212 // If there are any add recurrences in the operands list, see if any other 1213 // added values are loop invariant. If so, we can fold them into the 1214 // recurrence. 1215 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1216 ++Idx; 1217 1218 // Scan over all recurrences, trying to fold loop invariants into them. 1219 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1220 // Scan all of the other operands to this mul and add them to the vector if 1221 // they are loop invariant w.r.t. the recurrence. 1222 std::vector<SCEVHandle> LIOps; 1223 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1224 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1225 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1226 LIOps.push_back(Ops[i]); 1227 Ops.erase(Ops.begin()+i); 1228 --i; --e; 1229 } 1230 1231 // If we found some loop invariants, fold them into the recurrence. 1232 if (!LIOps.empty()) { 1233 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1234 std::vector<SCEVHandle> NewOps; 1235 NewOps.reserve(AddRec->getNumOperands()); 1236 if (LIOps.size() == 1) { 1237 const SCEV *Scale = LIOps[0]; 1238 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1239 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1240 } else { 1241 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1242 std::vector<SCEVHandle> MulOps(LIOps); 1243 MulOps.push_back(AddRec->getOperand(i)); 1244 NewOps.push_back(getMulExpr(MulOps)); 1245 } 1246 } 1247 1248 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1249 1250 // If all of the other operands were loop invariant, we are done. 1251 if (Ops.size() == 1) return NewRec; 1252 1253 // Otherwise, multiply the folded AddRec by the non-liv parts. 1254 for (unsigned i = 0;; ++i) 1255 if (Ops[i] == AddRec) { 1256 Ops[i] = NewRec; 1257 break; 1258 } 1259 return getMulExpr(Ops); 1260 } 1261 1262 // Okay, if there weren't any loop invariants to be folded, check to see if 1263 // there are multiple AddRec's with the same loop induction variable being 1264 // multiplied together. If so, we can fold them. 1265 for (unsigned OtherIdx = Idx+1; 1266 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1267 if (OtherIdx != Idx) { 1268 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1269 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1270 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1271 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1272 SCEVHandle NewStart = getMulExpr(F->getStart(), 1273 G->getStart()); 1274 SCEVHandle B = F->getStepRecurrence(*this); 1275 SCEVHandle D = G->getStepRecurrence(*this); 1276 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1277 getMulExpr(G, B), 1278 getMulExpr(B, D)); 1279 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1280 F->getLoop()); 1281 if (Ops.size() == 2) return NewAddRec; 1282 1283 Ops.erase(Ops.begin()+Idx); 1284 Ops.erase(Ops.begin()+OtherIdx-1); 1285 Ops.push_back(NewAddRec); 1286 return getMulExpr(Ops); 1287 } 1288 } 1289 1290 // Otherwise couldn't fold anything into this recurrence. Move onto the 1291 // next one. 1292 } 1293 1294 // Okay, it looks like we really DO need an mul expr. Check to see if we 1295 // already have one, otherwise create a new one. 1296 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1297 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1298 SCEVOps)]; 1299 if (Result == 0) 1300 Result = new SCEVMulExpr(Ops); 1301 return Result; 1302} 1303 1304SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, 1305 const SCEVHandle &RHS) { 1306 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1307 if (RHSC->getValue()->equalsInt(1)) 1308 return LHS; // X udiv 1 --> x 1309 if (RHSC->isZero()) 1310 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1311 1312 // Determine if the division can be folded into the operands of 1313 // its operands. 1314 // TODO: Generalize this to non-constants by using known-bits information. 1315 const Type *Ty = LHS->getType(); 1316 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1317 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1318 // For non-power-of-two values, effectively round the value up to the 1319 // nearest power of two. 1320 if (!RHSC->getValue()->getValue().isPowerOf2()) 1321 ++MaxShiftAmt; 1322 const IntegerType *ExtTy = 1323 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1324 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1325 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1326 if (const SCEVConstant *Step = 1327 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1328 if (!Step->getValue()->getValue() 1329 .urem(RHSC->getValue()->getValue()) && 1330 getTruncateExpr(getZeroExtendExpr(AR, ExtTy), Ty) == AR) { 1331 std::vector<SCEVHandle> Operands; 1332 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1333 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1334 return getAddRecExpr(Operands, AR->getLoop()); 1335 } 1336 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1337 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) 1338 if (getTruncateExpr(getZeroExtendExpr(M, ExtTy), Ty) == M) 1339 // Find an operand that's safely divisible. 1340 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1341 SCEVHandle Op = M->getOperand(i); 1342 SCEVHandle Div = getUDivExpr(Op, RHSC); 1343 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1344 std::vector<SCEVHandle> Operands = M->getOperands(); 1345 Operands[i] = Div; 1346 return getMulExpr(Operands); 1347 } 1348 } 1349 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1350 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) 1351 if (getTruncateExpr(getZeroExtendExpr(A, ExtTy), Ty) == A) { 1352 std::vector<SCEVHandle> Operands; 1353 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1354 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS); 1355 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1356 break; 1357 Operands.push_back(Op); 1358 } 1359 if (Operands.size() == A->getNumOperands()) 1360 return getAddExpr(Operands); 1361 } 1362 1363 // Fold if both operands are constant. 1364 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1365 Constant *LHSCV = LHSC->getValue(); 1366 Constant *RHSCV = RHSC->getValue(); 1367 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1368 } 1369 } 1370 1371 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1372 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1373 return Result; 1374} 1375 1376 1377/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1378/// specified loop. Simplify the expression as much as possible. 1379SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1380 const SCEVHandle &Step, const Loop *L) { 1381 std::vector<SCEVHandle> Operands; 1382 Operands.push_back(Start); 1383 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1384 if (StepChrec->getLoop() == L) { 1385 Operands.insert(Operands.end(), StepChrec->op_begin(), 1386 StepChrec->op_end()); 1387 return getAddRecExpr(Operands, L); 1388 } 1389 1390 Operands.push_back(Step); 1391 return getAddRecExpr(Operands, L); 1392} 1393 1394/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1395/// specified loop. Simplify the expression as much as possible. 1396SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1397 const Loop *L) { 1398 if (Operands.size() == 1) return Operands[0]; 1399 1400 if (Operands.back()->isZero()) { 1401 Operands.pop_back(); 1402 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1403 } 1404 1405 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1406 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1407 const Loop* NestedLoop = NestedAR->getLoop(); 1408 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1409 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1410 NestedAR->op_end()); 1411 SCEVHandle NestedARHandle(NestedAR); 1412 Operands[0] = NestedAR->getStart(); 1413 NestedOperands[0] = getAddRecExpr(Operands, L); 1414 return getAddRecExpr(NestedOperands, NestedLoop); 1415 } 1416 } 1417 1418 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 1419 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)]; 1420 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1421 return Result; 1422} 1423 1424SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1425 const SCEVHandle &RHS) { 1426 std::vector<SCEVHandle> Ops; 1427 Ops.push_back(LHS); 1428 Ops.push_back(RHS); 1429 return getSMaxExpr(Ops); 1430} 1431 1432SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1433 assert(!Ops.empty() && "Cannot get empty smax!"); 1434 if (Ops.size() == 1) return Ops[0]; 1435 1436 // Sort by complexity, this groups all similar expression types together. 1437 GroupByComplexity(Ops, LI); 1438 1439 // If there are any constants, fold them together. 1440 unsigned Idx = 0; 1441 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1442 ++Idx; 1443 assert(Idx < Ops.size()); 1444 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1445 // We found two constants, fold them together! 1446 ConstantInt *Fold = ConstantInt::get( 1447 APIntOps::smax(LHSC->getValue()->getValue(), 1448 RHSC->getValue()->getValue())); 1449 Ops[0] = getConstant(Fold); 1450 Ops.erase(Ops.begin()+1); // Erase the folded element 1451 if (Ops.size() == 1) return Ops[0]; 1452 LHSC = cast<SCEVConstant>(Ops[0]); 1453 } 1454 1455 // If we are left with a constant -inf, strip it off. 1456 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1457 Ops.erase(Ops.begin()); 1458 --Idx; 1459 } 1460 } 1461 1462 if (Ops.size() == 1) return Ops[0]; 1463 1464 // Find the first SMax 1465 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1466 ++Idx; 1467 1468 // Check to see if one of the operands is an SMax. If so, expand its operands 1469 // onto our operand list, and recurse to simplify. 1470 if (Idx < Ops.size()) { 1471 bool DeletedSMax = false; 1472 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1473 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1474 Ops.erase(Ops.begin()+Idx); 1475 DeletedSMax = true; 1476 } 1477 1478 if (DeletedSMax) 1479 return getSMaxExpr(Ops); 1480 } 1481 1482 // Okay, check to see if the same value occurs in the operand list twice. If 1483 // so, delete one. Since we sorted the list, these values are required to 1484 // be adjacent. 1485 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1486 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1487 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1488 --i; --e; 1489 } 1490 1491 if (Ops.size() == 1) return Ops[0]; 1492 1493 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1494 1495 // Okay, it looks like we really DO need an smax expr. Check to see if we 1496 // already have one, otherwise create a new one. 1497 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1498 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1499 SCEVOps)]; 1500 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1501 return Result; 1502} 1503 1504SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1505 const SCEVHandle &RHS) { 1506 std::vector<SCEVHandle> Ops; 1507 Ops.push_back(LHS); 1508 Ops.push_back(RHS); 1509 return getUMaxExpr(Ops); 1510} 1511 1512SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1513 assert(!Ops.empty() && "Cannot get empty umax!"); 1514 if (Ops.size() == 1) return Ops[0]; 1515 1516 // Sort by complexity, this groups all similar expression types together. 1517 GroupByComplexity(Ops, LI); 1518 1519 // If there are any constants, fold them together. 1520 unsigned Idx = 0; 1521 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1522 ++Idx; 1523 assert(Idx < Ops.size()); 1524 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1525 // We found two constants, fold them together! 1526 ConstantInt *Fold = ConstantInt::get( 1527 APIntOps::umax(LHSC->getValue()->getValue(), 1528 RHSC->getValue()->getValue())); 1529 Ops[0] = getConstant(Fold); 1530 Ops.erase(Ops.begin()+1); // Erase the folded element 1531 if (Ops.size() == 1) return Ops[0]; 1532 LHSC = cast<SCEVConstant>(Ops[0]); 1533 } 1534 1535 // If we are left with a constant zero, strip it off. 1536 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1537 Ops.erase(Ops.begin()); 1538 --Idx; 1539 } 1540 } 1541 1542 if (Ops.size() == 1) return Ops[0]; 1543 1544 // Find the first UMax 1545 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1546 ++Idx; 1547 1548 // Check to see if one of the operands is a UMax. If so, expand its operands 1549 // onto our operand list, and recurse to simplify. 1550 if (Idx < Ops.size()) { 1551 bool DeletedUMax = false; 1552 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1553 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1554 Ops.erase(Ops.begin()+Idx); 1555 DeletedUMax = true; 1556 } 1557 1558 if (DeletedUMax) 1559 return getUMaxExpr(Ops); 1560 } 1561 1562 // Okay, check to see if the same value occurs in the operand list twice. If 1563 // so, delete one. Since we sorted the list, these values are required to 1564 // be adjacent. 1565 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1566 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1567 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1568 --i; --e; 1569 } 1570 1571 if (Ops.size() == 1) return Ops[0]; 1572 1573 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1574 1575 // Okay, it looks like we really DO need a umax expr. Check to see if we 1576 // already have one, otherwise create a new one. 1577 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1578 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1579 SCEVOps)]; 1580 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1581 return Result; 1582} 1583 1584SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1585 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1586 return getConstant(CI); 1587 if (isa<ConstantPointerNull>(V)) 1588 return getIntegerSCEV(0, V->getType()); 1589 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1590 if (Result == 0) Result = new SCEVUnknown(V); 1591 return Result; 1592} 1593 1594//===----------------------------------------------------------------------===// 1595// Basic SCEV Analysis and PHI Idiom Recognition Code 1596// 1597 1598/// isSCEVable - Test if values of the given type are analyzable within 1599/// the SCEV framework. This primarily includes integer types, and it 1600/// can optionally include pointer types if the ScalarEvolution class 1601/// has access to target-specific information. 1602bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1603 // Integers are always SCEVable. 1604 if (Ty->isInteger()) 1605 return true; 1606 1607 // Pointers are SCEVable if TargetData information is available 1608 // to provide pointer size information. 1609 if (isa<PointerType>(Ty)) 1610 return TD != NULL; 1611 1612 // Otherwise it's not SCEVable. 1613 return false; 1614} 1615 1616/// getTypeSizeInBits - Return the size in bits of the specified type, 1617/// for which isSCEVable must return true. 1618uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1619 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1620 1621 // If we have a TargetData, use it! 1622 if (TD) 1623 return TD->getTypeSizeInBits(Ty); 1624 1625 // Otherwise, we support only integer types. 1626 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1627 return Ty->getPrimitiveSizeInBits(); 1628} 1629 1630/// getEffectiveSCEVType - Return a type with the same bitwidth as 1631/// the given type and which represents how SCEV will treat the given 1632/// type, for which isSCEVable must return true. For pointer types, 1633/// this is the pointer-sized integer type. 1634const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1635 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1636 1637 if (Ty->isInteger()) 1638 return Ty; 1639 1640 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1641 return TD->getIntPtrType(); 1642} 1643 1644SCEVHandle ScalarEvolution::getCouldNotCompute() { 1645 return UnknownValue; 1646} 1647 1648/// hasSCEV - Return true if the SCEV for this value has already been 1649/// computed. 1650bool ScalarEvolution::hasSCEV(Value *V) const { 1651 return Scalars.count(V); 1652} 1653 1654/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1655/// expression and create a new one. 1656SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1657 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1658 1659 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V); 1660 if (I != Scalars.end()) return I->second; 1661 SCEVHandle S = createSCEV(V); 1662 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 1663 return S; 1664} 1665 1666/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1667/// specified signed integer value and return a SCEV for the constant. 1668SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 1669 Ty = getEffectiveSCEVType(Ty); 1670 Constant *C; 1671 if (Val == 0) 1672 C = Constant::getNullValue(Ty); 1673 else if (Ty->isFloatingPoint()) 1674 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1675 APFloat::IEEEdouble, Val)); 1676 else 1677 C = ConstantInt::get(Ty, Val); 1678 return getUnknown(C); 1679} 1680 1681/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1682/// 1683SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 1684 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1685 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 1686 1687 const Type *Ty = V->getType(); 1688 Ty = getEffectiveSCEVType(Ty); 1689 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 1690} 1691 1692/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1693SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 1694 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1695 return getUnknown(ConstantExpr::getNot(VC->getValue())); 1696 1697 const Type *Ty = V->getType(); 1698 Ty = getEffectiveSCEVType(Ty); 1699 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 1700 return getMinusSCEV(AllOnes, V); 1701} 1702 1703/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1704/// 1705SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 1706 const SCEVHandle &RHS) { 1707 // X - Y --> X + -Y 1708 return getAddExpr(LHS, getNegativeSCEV(RHS)); 1709} 1710 1711/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1712/// input value to the specified type. If the type must be extended, it is zero 1713/// extended. 1714SCEVHandle 1715ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 1716 const Type *Ty) { 1717 const Type *SrcTy = V->getType(); 1718 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1719 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1720 "Cannot truncate or zero extend with non-integer arguments!"); 1721 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1722 return V; // No conversion 1723 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1724 return getTruncateExpr(V, Ty); 1725 return getZeroExtendExpr(V, Ty); 1726} 1727 1728/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1729/// input value to the specified type. If the type must be extended, it is sign 1730/// extended. 1731SCEVHandle 1732ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 1733 const Type *Ty) { 1734 const Type *SrcTy = V->getType(); 1735 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1736 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1737 "Cannot truncate or zero extend with non-integer arguments!"); 1738 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1739 return V; // No conversion 1740 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1741 return getTruncateExpr(V, Ty); 1742 return getSignExtendExpr(V, Ty); 1743} 1744 1745/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1746/// the specified instruction and replaces any references to the symbolic value 1747/// SymName with the specified value. This is used during PHI resolution. 1748void ScalarEvolution:: 1749ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1750 const SCEVHandle &NewVal) { 1751 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI = 1752 Scalars.find(SCEVCallbackVH(I, this)); 1753 if (SI == Scalars.end()) return; 1754 1755 SCEVHandle NV = 1756 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 1757 if (NV == SI->second) return; // No change. 1758 1759 SI->second = NV; // Update the scalars map! 1760 1761 // Any instruction values that use this instruction might also need to be 1762 // updated! 1763 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1764 UI != E; ++UI) 1765 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1766} 1767 1768/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1769/// a loop header, making it a potential recurrence, or it doesn't. 1770/// 1771SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 1772 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1773 if (const Loop *L = LI->getLoopFor(PN->getParent())) 1774 if (L->getHeader() == PN->getParent()) { 1775 // If it lives in the loop header, it has two incoming values, one 1776 // from outside the loop, and one from inside. 1777 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1778 unsigned BackEdge = IncomingEdge^1; 1779 1780 // While we are analyzing this PHI node, handle its value symbolically. 1781 SCEVHandle SymbolicName = getUnknown(PN); 1782 assert(Scalars.find(PN) == Scalars.end() && 1783 "PHI node already processed?"); 1784 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 1785 1786 // Using this symbolic name for the PHI, analyze the value coming around 1787 // the back-edge. 1788 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1789 1790 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1791 // has a special value for the first iteration of the loop. 1792 1793 // If the value coming around the backedge is an add with the symbolic 1794 // value we just inserted, then we found a simple induction variable! 1795 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1796 // If there is a single occurrence of the symbolic value, replace it 1797 // with a recurrence. 1798 unsigned FoundIndex = Add->getNumOperands(); 1799 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1800 if (Add->getOperand(i) == SymbolicName) 1801 if (FoundIndex == e) { 1802 FoundIndex = i; 1803 break; 1804 } 1805 1806 if (FoundIndex != Add->getNumOperands()) { 1807 // Create an add with everything but the specified operand. 1808 std::vector<SCEVHandle> Ops; 1809 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1810 if (i != FoundIndex) 1811 Ops.push_back(Add->getOperand(i)); 1812 SCEVHandle Accum = getAddExpr(Ops); 1813 1814 // This is not a valid addrec if the step amount is varying each 1815 // loop iteration, but is not itself an addrec in this loop. 1816 if (Accum->isLoopInvariant(L) || 1817 (isa<SCEVAddRecExpr>(Accum) && 1818 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1819 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1820 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 1821 1822 // Okay, for the entire analysis of this edge we assumed the PHI 1823 // to be symbolic. We now need to go back and update all of the 1824 // entries for the scalars that use the PHI (except for the PHI 1825 // itself) to use the new analyzed value instead of the "symbolic" 1826 // value. 1827 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1828 return PHISCEV; 1829 } 1830 } 1831 } else if (const SCEVAddRecExpr *AddRec = 1832 dyn_cast<SCEVAddRecExpr>(BEValue)) { 1833 // Otherwise, this could be a loop like this: 1834 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1835 // In this case, j = {1,+,1} and BEValue is j. 1836 // Because the other in-value of i (0) fits the evolution of BEValue 1837 // i really is an addrec evolution. 1838 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1839 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1840 1841 // If StartVal = j.start - j.stride, we can use StartVal as the 1842 // initial step of the addrec evolution. 1843 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 1844 AddRec->getOperand(1))) { 1845 SCEVHandle PHISCEV = 1846 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1847 1848 // Okay, for the entire analysis of this edge we assumed the PHI 1849 // to be symbolic. We now need to go back and update all of the 1850 // entries for the scalars that use the PHI (except for the PHI 1851 // itself) to use the new analyzed value instead of the "symbolic" 1852 // value. 1853 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1854 return PHISCEV; 1855 } 1856 } 1857 } 1858 1859 return SymbolicName; 1860 } 1861 1862 // If it's not a loop phi, we can't handle it yet. 1863 return getUnknown(PN); 1864} 1865 1866/// createNodeForGEP - Expand GEP instructions into add and multiply 1867/// operations. This allows them to be analyzed by regular SCEV code. 1868/// 1869SCEVHandle ScalarEvolution::createNodeForGEP(GetElementPtrInst *GEP) { 1870 1871 const Type *IntPtrTy = TD->getIntPtrType(); 1872 Value *Base = GEP->getOperand(0); 1873 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1874 gep_type_iterator GTI = gep_type_begin(GEP); 1875 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 1876 E = GEP->op_end(); 1877 I != E; ++I) { 1878 Value *Index = *I; 1879 // Compute the (potentially symbolic) offset in bytes for this index. 1880 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1881 // For a struct, add the member offset. 1882 const StructLayout &SL = *TD->getStructLayout(STy); 1883 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1884 uint64_t Offset = SL.getElementOffset(FieldNo); 1885 TotalOffset = getAddExpr(TotalOffset, 1886 getIntegerSCEV(Offset, IntPtrTy)); 1887 } else { 1888 // For an array, add the element offset, explicitly scaled. 1889 SCEVHandle LocalOffset = getSCEV(Index); 1890 if (!isa<PointerType>(LocalOffset->getType())) 1891 // Getelementptr indicies are signed. 1892 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1893 IntPtrTy); 1894 LocalOffset = 1895 getMulExpr(LocalOffset, 1896 getIntegerSCEV(TD->getTypePaddedSize(*GTI), 1897 IntPtrTy)); 1898 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1899 } 1900 } 1901 return getAddExpr(getSCEV(Base), TotalOffset); 1902} 1903 1904/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1905/// guaranteed to end in (at every loop iteration). It is, at the same time, 1906/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1907/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1908static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) { 1909 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1910 return C->getValue()->getValue().countTrailingZeros(); 1911 1912 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1913 return std::min(GetMinTrailingZeros(T->getOperand(), SE), 1914 (uint32_t)SE.getTypeSizeInBits(T->getType())); 1915 1916 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1917 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1918 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1919 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1920 } 1921 1922 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1923 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1924 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1925 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1926 } 1927 1928 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1929 // The result is the min of all operands results. 1930 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1931 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1932 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1933 return MinOpRes; 1934 } 1935 1936 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 1937 // The result is the sum of all operands results. 1938 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1939 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType()); 1940 for (unsigned i = 1, e = M->getNumOperands(); 1941 SumOpRes != BitWidth && i != e; ++i) 1942 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE), 1943 BitWidth); 1944 return SumOpRes; 1945 } 1946 1947 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 1948 // The result is the min of all operands results. 1949 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1950 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 1951 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 1952 return MinOpRes; 1953 } 1954 1955 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 1956 // The result is the min of all operands results. 1957 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1958 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1959 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1960 return MinOpRes; 1961 } 1962 1963 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 1964 // The result is the min of all operands results. 1965 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 1966 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 1967 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 1968 return MinOpRes; 1969 } 1970 1971 // SCEVUDivExpr, SCEVUnknown 1972 return 0; 1973} 1974 1975/// createSCEV - We know that there is no SCEV for the specified value. 1976/// Analyze the expression. 1977/// 1978SCEVHandle ScalarEvolution::createSCEV(Value *V) { 1979 if (!isSCEVable(V->getType())) 1980 return getUnknown(V); 1981 1982 unsigned Opcode = Instruction::UserOp1; 1983 if (Instruction *I = dyn_cast<Instruction>(V)) 1984 Opcode = I->getOpcode(); 1985 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 1986 Opcode = CE->getOpcode(); 1987 else 1988 return getUnknown(V); 1989 1990 User *U = cast<User>(V); 1991 switch (Opcode) { 1992 case Instruction::Add: 1993 return getAddExpr(getSCEV(U->getOperand(0)), 1994 getSCEV(U->getOperand(1))); 1995 case Instruction::Mul: 1996 return getMulExpr(getSCEV(U->getOperand(0)), 1997 getSCEV(U->getOperand(1))); 1998 case Instruction::UDiv: 1999 return getUDivExpr(getSCEV(U->getOperand(0)), 2000 getSCEV(U->getOperand(1))); 2001 case Instruction::Sub: 2002 return getMinusSCEV(getSCEV(U->getOperand(0)), 2003 getSCEV(U->getOperand(1))); 2004 case Instruction::And: 2005 // For an expression like x&255 that merely masks off the high bits, 2006 // use zext(trunc(x)) as the SCEV expression. 2007 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2008 if (CI->isNullValue()) 2009 return getSCEV(U->getOperand(1)); 2010 if (CI->isAllOnesValue()) 2011 return getSCEV(U->getOperand(0)); 2012 const APInt &A = CI->getValue(); 2013 unsigned Ones = A.countTrailingOnes(); 2014 if (APIntOps::isMask(Ones, A)) 2015 return 2016 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2017 IntegerType::get(Ones)), 2018 U->getType()); 2019 } 2020 break; 2021 case Instruction::Or: 2022 // If the RHS of the Or is a constant, we may have something like: 2023 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2024 // optimizations will transparently handle this case. 2025 // 2026 // In order for this transformation to be safe, the LHS must be of the 2027 // form X*(2^n) and the Or constant must be less than 2^n. 2028 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2029 SCEVHandle LHS = getSCEV(U->getOperand(0)); 2030 const APInt &CIVal = CI->getValue(); 2031 if (GetMinTrailingZeros(LHS, *this) >= 2032 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2033 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2034 } 2035 break; 2036 case Instruction::Xor: 2037 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2038 // If the RHS of the xor is a signbit, then this is just an add. 2039 // Instcombine turns add of signbit into xor as a strength reduction step. 2040 if (CI->getValue().isSignBit()) 2041 return getAddExpr(getSCEV(U->getOperand(0)), 2042 getSCEV(U->getOperand(1))); 2043 2044 // If the RHS of xor is -1, then this is a not operation. 2045 else if (CI->isAllOnesValue()) 2046 return getNotSCEV(getSCEV(U->getOperand(0))); 2047 } 2048 break; 2049 2050 case Instruction::Shl: 2051 // Turn shift left of a constant amount into a multiply. 2052 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2053 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2054 Constant *X = ConstantInt::get( 2055 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2056 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2057 } 2058 break; 2059 2060 case Instruction::LShr: 2061 // Turn logical shift right of a constant into a unsigned divide. 2062 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2063 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2064 Constant *X = ConstantInt::get( 2065 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2066 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2067 } 2068 break; 2069 2070 case Instruction::AShr: 2071 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2072 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2073 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2074 if (L->getOpcode() == Instruction::Shl && 2075 L->getOperand(1) == U->getOperand(1)) { 2076 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2077 uint64_t Amt = BitWidth - CI->getZExtValue(); 2078 if (Amt == BitWidth) 2079 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2080 if (Amt > BitWidth) 2081 return getIntegerSCEV(0, U->getType()); // value is undefined 2082 return 2083 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2084 IntegerType::get(Amt)), 2085 U->getType()); 2086 } 2087 break; 2088 2089 case Instruction::Trunc: 2090 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2091 2092 case Instruction::ZExt: 2093 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2094 2095 case Instruction::SExt: 2096 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2097 2098 case Instruction::BitCast: 2099 // BitCasts are no-op casts so we just eliminate the cast. 2100 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2101 return getSCEV(U->getOperand(0)); 2102 break; 2103 2104 case Instruction::IntToPtr: 2105 if (!TD) break; // Without TD we can't analyze pointers. 2106 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2107 TD->getIntPtrType()); 2108 2109 case Instruction::PtrToInt: 2110 if (!TD) break; // Without TD we can't analyze pointers. 2111 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2112 U->getType()); 2113 2114 case Instruction::GetElementPtr: 2115 if (!TD) break; // Without TD we can't analyze pointers. 2116 return createNodeForGEP(cast<GetElementPtrInst>(U)); 2117 2118 case Instruction::PHI: 2119 return createNodeForPHI(cast<PHINode>(U)); 2120 2121 case Instruction::Select: 2122 // This could be a smax or umax that was lowered earlier. 2123 // Try to recover it. 2124 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2125 Value *LHS = ICI->getOperand(0); 2126 Value *RHS = ICI->getOperand(1); 2127 switch (ICI->getPredicate()) { 2128 case ICmpInst::ICMP_SLT: 2129 case ICmpInst::ICMP_SLE: 2130 std::swap(LHS, RHS); 2131 // fall through 2132 case ICmpInst::ICMP_SGT: 2133 case ICmpInst::ICMP_SGE: 2134 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2135 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2136 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2137 // ~smax(~x, ~y) == smin(x, y). 2138 return getNotSCEV(getSMaxExpr( 2139 getNotSCEV(getSCEV(LHS)), 2140 getNotSCEV(getSCEV(RHS)))); 2141 break; 2142 case ICmpInst::ICMP_ULT: 2143 case ICmpInst::ICMP_ULE: 2144 std::swap(LHS, RHS); 2145 // fall through 2146 case ICmpInst::ICMP_UGT: 2147 case ICmpInst::ICMP_UGE: 2148 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2149 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2150 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2151 // ~umax(~x, ~y) == umin(x, y) 2152 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 2153 getNotSCEV(getSCEV(RHS)))); 2154 break; 2155 default: 2156 break; 2157 } 2158 } 2159 2160 default: // We cannot analyze this expression. 2161 break; 2162 } 2163 2164 return getUnknown(V); 2165} 2166 2167 2168 2169//===----------------------------------------------------------------------===// 2170// Iteration Count Computation Code 2171// 2172 2173/// getBackedgeTakenCount - If the specified loop has a predictable 2174/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2175/// object. The backedge-taken count is the number of times the loop header 2176/// will be branched to from within the loop. This is one less than the 2177/// trip count of the loop, since it doesn't count the first iteration, 2178/// when the header is branched to from outside the loop. 2179/// 2180/// Note that it is not valid to call this method on a loop without a 2181/// loop-invariant backedge-taken count (see 2182/// hasLoopInvariantBackedgeTakenCount). 2183/// 2184SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2185 return getBackedgeTakenInfo(L).Exact; 2186} 2187 2188/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2189/// return the least SCEV value that is known never to be less than the 2190/// actual backedge taken count. 2191SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2192 return getBackedgeTakenInfo(L).Max; 2193} 2194 2195const ScalarEvolution::BackedgeTakenInfo & 2196ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2197 // Initially insert a CouldNotCompute for this loop. If the insertion 2198 // succeeds, procede to actually compute a backedge-taken count and 2199 // update the value. The temporary CouldNotCompute value tells SCEV 2200 // code elsewhere that it shouldn't attempt to request a new 2201 // backedge-taken count, which could result in infinite recursion. 2202 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2203 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2204 if (Pair.second) { 2205 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2206 if (ItCount.Exact != UnknownValue) { 2207 assert(ItCount.Exact->isLoopInvariant(L) && 2208 ItCount.Max->isLoopInvariant(L) && 2209 "Computed trip count isn't loop invariant for loop!"); 2210 ++NumTripCountsComputed; 2211 2212 // Update the value in the map. 2213 Pair.first->second = ItCount; 2214 } else if (isa<PHINode>(L->getHeader()->begin())) { 2215 // Only count loops that have phi nodes as not being computable. 2216 ++NumTripCountsNotComputed; 2217 } 2218 2219 // Now that we know more about the trip count for this loop, forget any 2220 // existing SCEV values for PHI nodes in this loop since they are only 2221 // conservative estimates made without the benefit 2222 // of trip count information. 2223 if (ItCount.hasAnyInfo()) 2224 forgetLoopPHIs(L); 2225 } 2226 return Pair.first->second; 2227} 2228 2229/// forgetLoopBackedgeTakenCount - This method should be called by the 2230/// client when it has changed a loop in a way that may effect 2231/// ScalarEvolution's ability to compute a trip count, or if the loop 2232/// is deleted. 2233void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2234 BackedgeTakenCounts.erase(L); 2235 forgetLoopPHIs(L); 2236} 2237 2238/// forgetLoopPHIs - Delete the memoized SCEVs associated with the 2239/// PHI nodes in the given loop. This is used when the trip count of 2240/// the loop may have changed. 2241void ScalarEvolution::forgetLoopPHIs(const Loop *L) { 2242 BasicBlock *Header = L->getHeader(); 2243 2244 SmallVector<Instruction *, 16> Worklist; 2245 for (BasicBlock::iterator I = Header->begin(); 2246 PHINode *PN = dyn_cast<PHINode>(I); ++I) 2247 Worklist.push_back(PN); 2248 2249 while (!Worklist.empty()) { 2250 Instruction *I = Worklist.pop_back_val(); 2251 if (Scalars.erase(I)) 2252 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2253 UI != UE; ++UI) 2254 Worklist.push_back(cast<Instruction>(UI)); 2255 } 2256} 2257 2258/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2259/// of the specified loop will execute. 2260ScalarEvolution::BackedgeTakenInfo 2261ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2262 // If the loop has a non-one exit block count, we can't analyze it. 2263 SmallVector<BasicBlock*, 8> ExitBlocks; 2264 L->getExitBlocks(ExitBlocks); 2265 if (ExitBlocks.size() != 1) return UnknownValue; 2266 2267 // Okay, there is one exit block. Try to find the condition that causes the 2268 // loop to be exited. 2269 BasicBlock *ExitBlock = ExitBlocks[0]; 2270 2271 BasicBlock *ExitingBlock = 0; 2272 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 2273 PI != E; ++PI) 2274 if (L->contains(*PI)) { 2275 if (ExitingBlock == 0) 2276 ExitingBlock = *PI; 2277 else 2278 return UnknownValue; // More than one block exiting! 2279 } 2280 assert(ExitingBlock && "No exits from loop, something is broken!"); 2281 2282 // Okay, we've computed the exiting block. See what condition causes us to 2283 // exit. 2284 // 2285 // FIXME: we should be able to handle switch instructions (with a single exit) 2286 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2287 if (ExitBr == 0) return UnknownValue; 2288 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2289 2290 // At this point, we know we have a conditional branch that determines whether 2291 // the loop is exited. However, we don't know if the branch is executed each 2292 // time through the loop. If not, then the execution count of the branch will 2293 // not be equal to the trip count of the loop. 2294 // 2295 // Currently we check for this by checking to see if the Exit branch goes to 2296 // the loop header. If so, we know it will always execute the same number of 2297 // times as the loop. We also handle the case where the exit block *is* the 2298 // loop header. This is common for un-rotated loops. More extensive analysis 2299 // could be done to handle more cases here. 2300 if (ExitBr->getSuccessor(0) != L->getHeader() && 2301 ExitBr->getSuccessor(1) != L->getHeader() && 2302 ExitBr->getParent() != L->getHeader()) 2303 return UnknownValue; 2304 2305 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2306 2307 // If it's not an integer comparison then compute it the hard way. 2308 // Note that ICmpInst deals with pointer comparisons too so we must check 2309 // the type of the operand. 2310 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType())) 2311 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2312 ExitBr->getSuccessor(0) == ExitBlock); 2313 2314 // If the condition was exit on true, convert the condition to exit on false 2315 ICmpInst::Predicate Cond; 2316 if (ExitBr->getSuccessor(1) == ExitBlock) 2317 Cond = ExitCond->getPredicate(); 2318 else 2319 Cond = ExitCond->getInversePredicate(); 2320 2321 // Handle common loops like: for (X = "string"; *X; ++X) 2322 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2323 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2324 SCEVHandle ItCnt = 2325 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2326 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2327 } 2328 2329 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2330 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2331 2332 // Try to evaluate any dependencies out of the loop. 2333 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2334 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2335 Tmp = getSCEVAtScope(RHS, L); 2336 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2337 2338 // At this point, we would like to compute how many iterations of the 2339 // loop the predicate will return true for these inputs. 2340 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2341 // If there is a loop-invariant, force it into the RHS. 2342 std::swap(LHS, RHS); 2343 Cond = ICmpInst::getSwappedPredicate(Cond); 2344 } 2345 2346 // If we have a comparison of a chrec against a constant, try to use value 2347 // ranges to answer this query. 2348 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2349 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2350 if (AddRec->getLoop() == L) { 2351 // Form the comparison range using the constant of the correct type so 2352 // that the ConstantRange class knows to do a signed or unsigned 2353 // comparison. 2354 ConstantInt *CompVal = RHSC->getValue(); 2355 const Type *RealTy = ExitCond->getOperand(0)->getType(); 2356 CompVal = dyn_cast<ConstantInt>( 2357 ConstantExpr::getBitCast(CompVal, RealTy)); 2358 if (CompVal) { 2359 // Form the constant range. 2360 ConstantRange CompRange( 2361 ICmpInst::makeConstantRange(Cond, CompVal->getValue())); 2362 2363 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2364 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2365 } 2366 } 2367 2368 switch (Cond) { 2369 case ICmpInst::ICMP_NE: { // while (X != Y) 2370 // Convert to: while (X-Y != 0) 2371 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2372 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2373 break; 2374 } 2375 case ICmpInst::ICMP_EQ: { 2376 // Convert to: while (X-Y == 0) // while (X == Y) 2377 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2378 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2379 break; 2380 } 2381 case ICmpInst::ICMP_SLT: { 2382 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 2383 if (BTI.hasAnyInfo()) return BTI; 2384 break; 2385 } 2386 case ICmpInst::ICMP_SGT: { 2387 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2388 getNotSCEV(RHS), L, true); 2389 if (BTI.hasAnyInfo()) return BTI; 2390 break; 2391 } 2392 case ICmpInst::ICMP_ULT: { 2393 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 2394 if (BTI.hasAnyInfo()) return BTI; 2395 break; 2396 } 2397 case ICmpInst::ICMP_UGT: { 2398 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2399 getNotSCEV(RHS), L, false); 2400 if (BTI.hasAnyInfo()) return BTI; 2401 break; 2402 } 2403 default: 2404#if 0 2405 errs() << "ComputeBackedgeTakenCount "; 2406 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2407 errs() << "[unsigned] "; 2408 errs() << *LHS << " " 2409 << Instruction::getOpcodeName(Instruction::ICmp) 2410 << " " << *RHS << "\n"; 2411#endif 2412 break; 2413 } 2414 return 2415 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2416 ExitBr->getSuccessor(0) == ExitBlock); 2417} 2418 2419static ConstantInt * 2420EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2421 ScalarEvolution &SE) { 2422 SCEVHandle InVal = SE.getConstant(C); 2423 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2424 assert(isa<SCEVConstant>(Val) && 2425 "Evaluation of SCEV at constant didn't fold correctly?"); 2426 return cast<SCEVConstant>(Val)->getValue(); 2427} 2428 2429/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2430/// and a GEP expression (missing the pointer index) indexing into it, return 2431/// the addressed element of the initializer or null if the index expression is 2432/// invalid. 2433static Constant * 2434GetAddressedElementFromGlobal(GlobalVariable *GV, 2435 const std::vector<ConstantInt*> &Indices) { 2436 Constant *Init = GV->getInitializer(); 2437 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2438 uint64_t Idx = Indices[i]->getZExtValue(); 2439 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2440 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2441 Init = cast<Constant>(CS->getOperand(Idx)); 2442 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2443 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2444 Init = cast<Constant>(CA->getOperand(Idx)); 2445 } else if (isa<ConstantAggregateZero>(Init)) { 2446 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2447 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2448 Init = Constant::getNullValue(STy->getElementType(Idx)); 2449 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2450 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2451 Init = Constant::getNullValue(ATy->getElementType()); 2452 } else { 2453 assert(0 && "Unknown constant aggregate type!"); 2454 } 2455 return 0; 2456 } else { 2457 return 0; // Unknown initializer type 2458 } 2459 } 2460 return Init; 2461} 2462 2463/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2464/// 'icmp op load X, cst', try to see if we can compute the backedge 2465/// execution count. 2466SCEVHandle ScalarEvolution:: 2467ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2468 const Loop *L, 2469 ICmpInst::Predicate predicate) { 2470 if (LI->isVolatile()) return UnknownValue; 2471 2472 // Check to see if the loaded pointer is a getelementptr of a global. 2473 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2474 if (!GEP) return UnknownValue; 2475 2476 // Make sure that it is really a constant global we are gepping, with an 2477 // initializer, and make sure the first IDX is really 0. 2478 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2479 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2480 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2481 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2482 return UnknownValue; 2483 2484 // Okay, we allow one non-constant index into the GEP instruction. 2485 Value *VarIdx = 0; 2486 std::vector<ConstantInt*> Indexes; 2487 unsigned VarIdxNum = 0; 2488 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2489 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2490 Indexes.push_back(CI); 2491 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2492 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2493 VarIdx = GEP->getOperand(i); 2494 VarIdxNum = i-2; 2495 Indexes.push_back(0); 2496 } 2497 2498 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2499 // Check to see if X is a loop variant variable value now. 2500 SCEVHandle Idx = getSCEV(VarIdx); 2501 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2502 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2503 2504 // We can only recognize very limited forms of loop index expressions, in 2505 // particular, only affine AddRec's like {C1,+,C2}. 2506 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2507 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2508 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2509 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2510 return UnknownValue; 2511 2512 unsigned MaxSteps = MaxBruteForceIterations; 2513 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2514 ConstantInt *ItCst = 2515 ConstantInt::get(IdxExpr->getType(), IterationNum); 2516 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2517 2518 // Form the GEP offset. 2519 Indexes[VarIdxNum] = Val; 2520 2521 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2522 if (Result == 0) break; // Cannot compute! 2523 2524 // Evaluate the condition for this iteration. 2525 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2526 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2527 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2528#if 0 2529 errs() << "\n***\n*** Computed loop count " << *ItCst 2530 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2531 << "***\n"; 2532#endif 2533 ++NumArrayLenItCounts; 2534 return getConstant(ItCst); // Found terminating iteration! 2535 } 2536 } 2537 return UnknownValue; 2538} 2539 2540 2541/// CanConstantFold - Return true if we can constant fold an instruction of the 2542/// specified type, assuming that all operands were constants. 2543static bool CanConstantFold(const Instruction *I) { 2544 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2545 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2546 return true; 2547 2548 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2549 if (const Function *F = CI->getCalledFunction()) 2550 return canConstantFoldCallTo(F); 2551 return false; 2552} 2553 2554/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2555/// in the loop that V is derived from. We allow arbitrary operations along the 2556/// way, but the operands of an operation must either be constants or a value 2557/// derived from a constant PHI. If this expression does not fit with these 2558/// constraints, return null. 2559static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2560 // If this is not an instruction, or if this is an instruction outside of the 2561 // loop, it can't be derived from a loop PHI. 2562 Instruction *I = dyn_cast<Instruction>(V); 2563 if (I == 0 || !L->contains(I->getParent())) return 0; 2564 2565 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2566 if (L->getHeader() == I->getParent()) 2567 return PN; 2568 else 2569 // We don't currently keep track of the control flow needed to evaluate 2570 // PHIs, so we cannot handle PHIs inside of loops. 2571 return 0; 2572 } 2573 2574 // If we won't be able to constant fold this expression even if the operands 2575 // are constants, return early. 2576 if (!CanConstantFold(I)) return 0; 2577 2578 // Otherwise, we can evaluate this instruction if all of its operands are 2579 // constant or derived from a PHI node themselves. 2580 PHINode *PHI = 0; 2581 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2582 if (!(isa<Constant>(I->getOperand(Op)) || 2583 isa<GlobalValue>(I->getOperand(Op)))) { 2584 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2585 if (P == 0) return 0; // Not evolving from PHI 2586 if (PHI == 0) 2587 PHI = P; 2588 else if (PHI != P) 2589 return 0; // Evolving from multiple different PHIs. 2590 } 2591 2592 // This is a expression evolving from a constant PHI! 2593 return PHI; 2594} 2595 2596/// EvaluateExpression - Given an expression that passes the 2597/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2598/// in the loop has the value PHIVal. If we can't fold this expression for some 2599/// reason, return null. 2600static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2601 if (isa<PHINode>(V)) return PHIVal; 2602 if (Constant *C = dyn_cast<Constant>(V)) return C; 2603 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2604 Instruction *I = cast<Instruction>(V); 2605 2606 std::vector<Constant*> Operands; 2607 Operands.resize(I->getNumOperands()); 2608 2609 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2610 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2611 if (Operands[i] == 0) return 0; 2612 } 2613 2614 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2615 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2616 &Operands[0], Operands.size()); 2617 else 2618 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2619 &Operands[0], Operands.size()); 2620} 2621 2622/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2623/// in the header of its containing loop, we know the loop executes a 2624/// constant number of times, and the PHI node is just a recurrence 2625/// involving constants, fold it. 2626Constant *ScalarEvolution:: 2627getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2628 std::map<PHINode*, Constant*>::iterator I = 2629 ConstantEvolutionLoopExitValue.find(PN); 2630 if (I != ConstantEvolutionLoopExitValue.end()) 2631 return I->second; 2632 2633 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2634 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2635 2636 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2637 2638 // Since the loop is canonicalized, the PHI node must have two entries. One 2639 // entry must be a constant (coming in from outside of the loop), and the 2640 // second must be derived from the same PHI. 2641 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2642 Constant *StartCST = 2643 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2644 if (StartCST == 0) 2645 return RetVal = 0; // Must be a constant. 2646 2647 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2648 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2649 if (PN2 != PN) 2650 return RetVal = 0; // Not derived from same PHI. 2651 2652 // Execute the loop symbolically to determine the exit value. 2653 if (BEs.getActiveBits() >= 32) 2654 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2655 2656 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2657 unsigned IterationNum = 0; 2658 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2659 if (IterationNum == NumIterations) 2660 return RetVal = PHIVal; // Got exit value! 2661 2662 // Compute the value of the PHI node for the next iteration. 2663 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2664 if (NextPHI == PHIVal) 2665 return RetVal = NextPHI; // Stopped evolving! 2666 if (NextPHI == 0) 2667 return 0; // Couldn't evaluate! 2668 PHIVal = NextPHI; 2669 } 2670} 2671 2672/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2673/// constant number of times (the condition evolves only from constants), 2674/// try to evaluate a few iterations of the loop until we get the exit 2675/// condition gets a value of ExitWhen (true or false). If we cannot 2676/// evaluate the trip count of the loop, return UnknownValue. 2677SCEVHandle ScalarEvolution:: 2678ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2679 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2680 if (PN == 0) return UnknownValue; 2681 2682 // Since the loop is canonicalized, the PHI node must have two entries. One 2683 // entry must be a constant (coming in from outside of the loop), and the 2684 // second must be derived from the same PHI. 2685 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2686 Constant *StartCST = 2687 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2688 if (StartCST == 0) return UnknownValue; // Must be a constant. 2689 2690 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2691 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2692 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2693 2694 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2695 // the loop symbolically to determine when the condition gets a value of 2696 // "ExitWhen". 2697 unsigned IterationNum = 0; 2698 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2699 for (Constant *PHIVal = StartCST; 2700 IterationNum != MaxIterations; ++IterationNum) { 2701 ConstantInt *CondVal = 2702 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2703 2704 // Couldn't symbolically evaluate. 2705 if (!CondVal) return UnknownValue; 2706 2707 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2708 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2709 ++NumBruteForceTripCountsComputed; 2710 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2711 } 2712 2713 // Compute the value of the PHI node for the next iteration. 2714 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2715 if (NextPHI == 0 || NextPHI == PHIVal) 2716 return UnknownValue; // Couldn't evaluate or not making progress... 2717 PHIVal = NextPHI; 2718 } 2719 2720 // Too many iterations were needed to evaluate. 2721 return UnknownValue; 2722} 2723 2724/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2725/// at the specified scope in the program. The L value specifies a loop 2726/// nest to evaluate the expression at, where null is the top-level or a 2727/// specified loop is immediately inside of the loop. 2728/// 2729/// This method can be used to compute the exit value for a variable defined 2730/// in a loop by querying what the value will hold in the parent loop. 2731/// 2732/// If this value is not computable at this scope, a SCEVCouldNotCompute 2733/// object is returned. 2734SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 2735 // FIXME: this should be turned into a virtual method on SCEV! 2736 2737 if (isa<SCEVConstant>(V)) return V; 2738 2739 // If this instruction is evolved from a constant-evolving PHI, compute the 2740 // exit value from the loop without using SCEVs. 2741 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2742 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2743 const Loop *LI = (*this->LI)[I->getParent()]; 2744 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2745 if (PHINode *PN = dyn_cast<PHINode>(I)) 2746 if (PN->getParent() == LI->getHeader()) { 2747 // Okay, there is no closed form solution for the PHI node. Check 2748 // to see if the loop that contains it has a known backedge-taken 2749 // count. If so, we may be able to force computation of the exit 2750 // value. 2751 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2752 if (const SCEVConstant *BTCC = 2753 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2754 // Okay, we know how many times the containing loop executes. If 2755 // this is a constant evolving PHI node, get the final value at 2756 // the specified iteration number. 2757 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2758 BTCC->getValue()->getValue(), 2759 LI); 2760 if (RV) return getUnknown(RV); 2761 } 2762 } 2763 2764 // Okay, this is an expression that we cannot symbolically evaluate 2765 // into a SCEV. Check to see if it's possible to symbolically evaluate 2766 // the arguments into constants, and if so, try to constant propagate the 2767 // result. This is particularly useful for computing loop exit values. 2768 if (CanConstantFold(I)) { 2769 std::vector<Constant*> Operands; 2770 Operands.reserve(I->getNumOperands()); 2771 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2772 Value *Op = I->getOperand(i); 2773 if (Constant *C = dyn_cast<Constant>(Op)) { 2774 Operands.push_back(C); 2775 } else { 2776 // If any of the operands is non-constant and if they are 2777 // non-integer and non-pointer, don't even try to analyze them 2778 // with scev techniques. 2779 if (!isSCEVable(Op->getType())) 2780 return V; 2781 2782 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2783 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 2784 Constant *C = SC->getValue(); 2785 if (C->getType() != Op->getType()) 2786 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2787 Op->getType(), 2788 false), 2789 C, Op->getType()); 2790 Operands.push_back(C); 2791 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2792 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 2793 if (C->getType() != Op->getType()) 2794 C = 2795 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2796 Op->getType(), 2797 false), 2798 C, Op->getType()); 2799 Operands.push_back(C); 2800 } else 2801 return V; 2802 } else { 2803 return V; 2804 } 2805 } 2806 } 2807 2808 Constant *C; 2809 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2810 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2811 &Operands[0], Operands.size()); 2812 else 2813 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2814 &Operands[0], Operands.size()); 2815 return getUnknown(C); 2816 } 2817 } 2818 2819 // This is some other type of SCEVUnknown, just return it. 2820 return V; 2821 } 2822 2823 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2824 // Avoid performing the look-up in the common case where the specified 2825 // expression has no loop-variant portions. 2826 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2827 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2828 if (OpAtScope != Comm->getOperand(i)) { 2829 if (OpAtScope == UnknownValue) return UnknownValue; 2830 // Okay, at least one of these operands is loop variant but might be 2831 // foldable. Build a new instance of the folded commutative expression. 2832 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2833 NewOps.push_back(OpAtScope); 2834 2835 for (++i; i != e; ++i) { 2836 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2837 if (OpAtScope == UnknownValue) return UnknownValue; 2838 NewOps.push_back(OpAtScope); 2839 } 2840 if (isa<SCEVAddExpr>(Comm)) 2841 return getAddExpr(NewOps); 2842 if (isa<SCEVMulExpr>(Comm)) 2843 return getMulExpr(NewOps); 2844 if (isa<SCEVSMaxExpr>(Comm)) 2845 return getSMaxExpr(NewOps); 2846 if (isa<SCEVUMaxExpr>(Comm)) 2847 return getUMaxExpr(NewOps); 2848 assert(0 && "Unknown commutative SCEV type!"); 2849 } 2850 } 2851 // If we got here, all operands are loop invariant. 2852 return Comm; 2853 } 2854 2855 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2856 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2857 if (LHS == UnknownValue) return LHS; 2858 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2859 if (RHS == UnknownValue) return RHS; 2860 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2861 return Div; // must be loop invariant 2862 return getUDivExpr(LHS, RHS); 2863 } 2864 2865 // If this is a loop recurrence for a loop that does not contain L, then we 2866 // are dealing with the final value computed by the loop. 2867 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2868 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2869 // To evaluate this recurrence, we need to know how many times the AddRec 2870 // loop iterates. Compute this now. 2871 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2872 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2873 2874 // Then, evaluate the AddRec. 2875 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2876 } 2877 return UnknownValue; 2878 } 2879 2880 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 2881 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2882 if (Op == UnknownValue) return Op; 2883 if (Op == Cast->getOperand()) 2884 return Cast; // must be loop invariant 2885 return getZeroExtendExpr(Op, Cast->getType()); 2886 } 2887 2888 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 2889 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2890 if (Op == UnknownValue) return Op; 2891 if (Op == Cast->getOperand()) 2892 return Cast; // must be loop invariant 2893 return getSignExtendExpr(Op, Cast->getType()); 2894 } 2895 2896 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 2897 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2898 if (Op == UnknownValue) return Op; 2899 if (Op == Cast->getOperand()) 2900 return Cast; // must be loop invariant 2901 return getTruncateExpr(Op, Cast->getType()); 2902 } 2903 2904 assert(0 && "Unknown SCEV type!"); 2905} 2906 2907/// getSCEVAtScope - This is a convenience function which does 2908/// getSCEVAtScope(getSCEV(V), L). 2909SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2910 return getSCEVAtScope(getSCEV(V), L); 2911} 2912 2913/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2914/// following equation: 2915/// 2916/// A * X = B (mod N) 2917/// 2918/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2919/// A and B isn't important. 2920/// 2921/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2922static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2923 ScalarEvolution &SE) { 2924 uint32_t BW = A.getBitWidth(); 2925 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2926 assert(A != 0 && "A must be non-zero."); 2927 2928 // 1. D = gcd(A, N) 2929 // 2930 // The gcd of A and N may have only one prime factor: 2. The number of 2931 // trailing zeros in A is its multiplicity 2932 uint32_t Mult2 = A.countTrailingZeros(); 2933 // D = 2^Mult2 2934 2935 // 2. Check if B is divisible by D. 2936 // 2937 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 2938 // is not less than multiplicity of this prime factor for D. 2939 if (B.countTrailingZeros() < Mult2) 2940 return SE.getCouldNotCompute(); 2941 2942 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 2943 // modulo (N / D). 2944 // 2945 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 2946 // bit width during computations. 2947 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 2948 APInt Mod(BW + 1, 0); 2949 Mod.set(BW - Mult2); // Mod = N / D 2950 APInt I = AD.multiplicativeInverse(Mod); 2951 2952 // 4. Compute the minimum unsigned root of the equation: 2953 // I * (B / D) mod (N / D) 2954 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 2955 2956 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 2957 // bits. 2958 return SE.getConstant(Result.trunc(BW)); 2959} 2960 2961/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 2962/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 2963/// might be the same) or two SCEVCouldNotCompute objects. 2964/// 2965static std::pair<SCEVHandle,SCEVHandle> 2966SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 2967 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 2968 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 2969 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 2970 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 2971 2972 // We currently can only solve this if the coefficients are constants. 2973 if (!LC || !MC || !NC) { 2974 const SCEV *CNC = SE.getCouldNotCompute(); 2975 return std::make_pair(CNC, CNC); 2976 } 2977 2978 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 2979 const APInt &L = LC->getValue()->getValue(); 2980 const APInt &M = MC->getValue()->getValue(); 2981 const APInt &N = NC->getValue()->getValue(); 2982 APInt Two(BitWidth, 2); 2983 APInt Four(BitWidth, 4); 2984 2985 { 2986 using namespace APIntOps; 2987 const APInt& C = L; 2988 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 2989 // The B coefficient is M-N/2 2990 APInt B(M); 2991 B -= sdiv(N,Two); 2992 2993 // The A coefficient is N/2 2994 APInt A(N.sdiv(Two)); 2995 2996 // Compute the B^2-4ac term. 2997 APInt SqrtTerm(B); 2998 SqrtTerm *= B; 2999 SqrtTerm -= Four * (A * C); 3000 3001 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 3002 // integer value or else APInt::sqrt() will assert. 3003 APInt SqrtVal(SqrtTerm.sqrt()); 3004 3005 // Compute the two solutions for the quadratic formula. 3006 // The divisions must be performed as signed divisions. 3007 APInt NegB(-B); 3008 APInt TwoA( A << 1 ); 3009 if (TwoA.isMinValue()) { 3010 const SCEV *CNC = SE.getCouldNotCompute(); 3011 return std::make_pair(CNC, CNC); 3012 } 3013 3014 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 3015 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 3016 3017 return std::make_pair(SE.getConstant(Solution1), 3018 SE.getConstant(Solution2)); 3019 } // end APIntOps namespace 3020} 3021 3022/// HowFarToZero - Return the number of times a backedge comparing the specified 3023/// value to zero will execute. If not computable, return UnknownValue 3024SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 3025 // If the value is a constant 3026 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3027 // If the value is already zero, the branch will execute zero times. 3028 if (C->getValue()->isZero()) return C; 3029 return UnknownValue; // Otherwise it will loop infinitely. 3030 } 3031 3032 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 3033 if (!AddRec || AddRec->getLoop() != L) 3034 return UnknownValue; 3035 3036 if (AddRec->isAffine()) { 3037 // If this is an affine expression, the execution count of this branch is 3038 // the minimum unsigned root of the following equation: 3039 // 3040 // Start + Step*N = 0 (mod 2^BW) 3041 // 3042 // equivalent to: 3043 // 3044 // Step*N = -Start (mod 2^BW) 3045 // 3046 // where BW is the common bit width of Start and Step. 3047 3048 // Get the initial value for the loop. 3049 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 3050 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 3051 3052 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 3053 3054 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 3055 // For now we handle only constant steps. 3056 3057 // First, handle unitary steps. 3058 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 3059 return getNegativeSCEV(Start); // N = -Start (as unsigned) 3060 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 3061 return Start; // N = Start (as unsigned) 3062 3063 // Then, try to solve the above equation provided that Start is constant. 3064 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 3065 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 3066 -StartC->getValue()->getValue(), 3067 *this); 3068 } 3069 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 3070 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 3071 // the quadratic equation to solve it. 3072 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 3073 *this); 3074 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3075 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3076 if (R1) { 3077#if 0 3078 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 3079 << " sol#2: " << *R2 << "\n"; 3080#endif 3081 // Pick the smallest positive root value. 3082 if (ConstantInt *CB = 3083 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3084 R1->getValue(), R2->getValue()))) { 3085 if (CB->getZExtValue() == false) 3086 std::swap(R1, R2); // R1 is the minimum root now. 3087 3088 // We can only use this value if the chrec ends up with an exact zero 3089 // value at this index. When solving for "X*X != 5", for example, we 3090 // should not accept a root of 2. 3091 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 3092 if (Val->isZero()) 3093 return R1; // We found a quadratic root! 3094 } 3095 } 3096 } 3097 3098 return UnknownValue; 3099} 3100 3101/// HowFarToNonZero - Return the number of times a backedge checking the 3102/// specified value for nonzero will execute. If not computable, return 3103/// UnknownValue 3104SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 3105 // Loops that look like: while (X == 0) are very strange indeed. We don't 3106 // handle them yet except for the trivial case. This could be expanded in the 3107 // future as needed. 3108 3109 // If the value is a constant, check to see if it is known to be non-zero 3110 // already. If so, the backedge will execute zero times. 3111 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3112 if (!C->getValue()->isNullValue()) 3113 return getIntegerSCEV(0, C->getType()); 3114 return UnknownValue; // Otherwise it will loop infinitely. 3115 } 3116 3117 // We could implement others, but I really doubt anyone writes loops like 3118 // this, and if they did, they would already be constant folded. 3119 return UnknownValue; 3120} 3121 3122/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 3123/// (which may not be an immediate predecessor) which has exactly one 3124/// successor from which BB is reachable, or null if no such block is 3125/// found. 3126/// 3127BasicBlock * 3128ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 3129 // If the block has a unique predecessor, then there is no path from the 3130 // predecessor to the block that does not go through the direct edge 3131 // from the predecessor to the block. 3132 if (BasicBlock *Pred = BB->getSinglePredecessor()) 3133 return Pred; 3134 3135 // A loop's header is defined to be a block that dominates the loop. 3136 // If the loop has a preheader, it must be a block that has exactly 3137 // one successor that can reach BB. This is slightly more strict 3138 // than necessary, but works if critical edges are split. 3139 if (Loop *L = LI->getLoopFor(BB)) 3140 return L->getLoopPreheader(); 3141 3142 return 0; 3143} 3144 3145/// isLoopGuardedByCond - Test whether entry to the loop is protected by 3146/// a conditional between LHS and RHS. This is used to help avoid max 3147/// expressions in loop trip counts. 3148bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 3149 ICmpInst::Predicate Pred, 3150 const SCEV *LHS, const SCEV *RHS) { 3151 BasicBlock *Preheader = L->getLoopPreheader(); 3152 BasicBlock *PreheaderDest = L->getHeader(); 3153 3154 // Starting at the preheader, climb up the predecessor chain, as long as 3155 // there are predecessors that can be found that have unique successors 3156 // leading to the original header. 3157 for (; Preheader; 3158 PreheaderDest = Preheader, 3159 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 3160 3161 BranchInst *LoopEntryPredicate = 3162 dyn_cast<BranchInst>(Preheader->getTerminator()); 3163 if (!LoopEntryPredicate || 3164 LoopEntryPredicate->isUnconditional()) 3165 continue; 3166 3167 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 3168 if (!ICI) continue; 3169 3170 // Now that we found a conditional branch that dominates the loop, check to 3171 // see if it is the comparison we are looking for. 3172 Value *PreCondLHS = ICI->getOperand(0); 3173 Value *PreCondRHS = ICI->getOperand(1); 3174 ICmpInst::Predicate Cond; 3175 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 3176 Cond = ICI->getPredicate(); 3177 else 3178 Cond = ICI->getInversePredicate(); 3179 3180 if (Cond == Pred) 3181 ; // An exact match. 3182 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 3183 ; // The actual condition is beyond sufficient. 3184 else 3185 // Check a few special cases. 3186 switch (Cond) { 3187 case ICmpInst::ICMP_UGT: 3188 if (Pred == ICmpInst::ICMP_ULT) { 3189 std::swap(PreCondLHS, PreCondRHS); 3190 Cond = ICmpInst::ICMP_ULT; 3191 break; 3192 } 3193 continue; 3194 case ICmpInst::ICMP_SGT: 3195 if (Pred == ICmpInst::ICMP_SLT) { 3196 std::swap(PreCondLHS, PreCondRHS); 3197 Cond = ICmpInst::ICMP_SLT; 3198 break; 3199 } 3200 continue; 3201 case ICmpInst::ICMP_NE: 3202 // Expressions like (x >u 0) are often canonicalized to (x != 0), 3203 // so check for this case by checking if the NE is comparing against 3204 // a minimum or maximum constant. 3205 if (!ICmpInst::isTrueWhenEqual(Pred)) 3206 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 3207 const APInt &A = CI->getValue(); 3208 switch (Pred) { 3209 case ICmpInst::ICMP_SLT: 3210 if (A.isMaxSignedValue()) break; 3211 continue; 3212 case ICmpInst::ICMP_SGT: 3213 if (A.isMinSignedValue()) break; 3214 continue; 3215 case ICmpInst::ICMP_ULT: 3216 if (A.isMaxValue()) break; 3217 continue; 3218 case ICmpInst::ICMP_UGT: 3219 if (A.isMinValue()) break; 3220 continue; 3221 default: 3222 continue; 3223 } 3224 Cond = ICmpInst::ICMP_NE; 3225 // NE is symmetric but the original comparison may not be. Swap 3226 // the operands if necessary so that they match below. 3227 if (isa<SCEVConstant>(LHS)) 3228 std::swap(PreCondLHS, PreCondRHS); 3229 break; 3230 } 3231 continue; 3232 default: 3233 // We weren't able to reconcile the condition. 3234 continue; 3235 } 3236 3237 if (!PreCondLHS->getType()->isInteger()) continue; 3238 3239 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 3240 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 3241 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 3242 (LHS == getNotSCEV(PreCondRHSSCEV) && 3243 RHS == getNotSCEV(PreCondLHSSCEV))) 3244 return true; 3245 } 3246 3247 return false; 3248} 3249 3250/// HowManyLessThans - Return the number of times a backedge containing the 3251/// specified less-than comparison will execute. If not computable, return 3252/// UnknownValue. 3253ScalarEvolution::BackedgeTakenInfo ScalarEvolution:: 3254HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 3255 const Loop *L, bool isSigned) { 3256 // Only handle: "ADDREC < LoopInvariant". 3257 if (!RHS->isLoopInvariant(L)) return UnknownValue; 3258 3259 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 3260 if (!AddRec || AddRec->getLoop() != L) 3261 return UnknownValue; 3262 3263 if (AddRec->isAffine()) { 3264 // FORNOW: We only support unit strides. 3265 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 3266 SCEVHandle Step = AddRec->getStepRecurrence(*this); 3267 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType()); 3268 3269 // TODO: handle non-constant strides. 3270 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 3271 if (!CStep || CStep->isZero()) 3272 return UnknownValue; 3273 if (CStep->getValue()->getValue() == 1) { 3274 // With unit stride, the iteration never steps past the limit value. 3275 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 3276 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 3277 // Test whether a positive iteration iteration can step past the limit 3278 // value and past the maximum value for its type in a single step. 3279 if (isSigned) { 3280 APInt Max = APInt::getSignedMaxValue(BitWidth); 3281 if ((Max - CStep->getValue()->getValue()) 3282 .slt(CLimit->getValue()->getValue())) 3283 return UnknownValue; 3284 } else { 3285 APInt Max = APInt::getMaxValue(BitWidth); 3286 if ((Max - CStep->getValue()->getValue()) 3287 .ult(CLimit->getValue()->getValue())) 3288 return UnknownValue; 3289 } 3290 } else 3291 // TODO: handle non-constant limit values below. 3292 return UnknownValue; 3293 } else 3294 // TODO: handle negative strides below. 3295 return UnknownValue; 3296 3297 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 3298 // m. So, we count the number of iterations in which {n,+,s} < m is true. 3299 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 3300 // treat m-n as signed nor unsigned due to overflow possibility. 3301 3302 // First, we get the value of the LHS in the first iteration: n 3303 SCEVHandle Start = AddRec->getOperand(0); 3304 3305 // Determine the minimum constant start value. 3306 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start : 3307 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 3308 APInt::getMinValue(BitWidth)); 3309 3310 // If we know that the condition is true in order to enter the loop, 3311 // then we know that it will run exactly (m-n)/s times. Otherwise, we 3312 // only know if will execute (max(m,n)-n)/s times. In both cases, the 3313 // division must round up. 3314 SCEVHandle End = RHS; 3315 if (!isLoopGuardedByCond(L, 3316 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 3317 getMinusSCEV(Start, Step), RHS)) 3318 End = isSigned ? getSMaxExpr(RHS, Start) 3319 : getUMaxExpr(RHS, Start); 3320 3321 // Determine the maximum constant end value. 3322 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End : 3323 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) : 3324 APInt::getMaxValue(BitWidth)); 3325 3326 // Finally, we subtract these two values and divide, rounding up, to get 3327 // the number of times the backedge is executed. 3328 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start), 3329 getAddExpr(Step, NegOne)), 3330 Step); 3331 3332 // The maximum backedge count is similar, except using the minimum start 3333 // value and the maximum end value. 3334 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd, 3335 MinStart), 3336 getAddExpr(Step, NegOne)), 3337 Step); 3338 3339 return BackedgeTakenInfo(BECount, MaxBECount); 3340 } 3341 3342 return UnknownValue; 3343} 3344 3345/// getNumIterationsInRange - Return the number of iterations of this loop that 3346/// produce values in the specified constant range. Another way of looking at 3347/// this is that it returns the first iteration number where the value is not in 3348/// the condition, thus computing the exit count. If the iteration count can't 3349/// be computed, an instance of SCEVCouldNotCompute is returned. 3350SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 3351 ScalarEvolution &SE) const { 3352 if (Range.isFullSet()) // Infinite loop. 3353 return SE.getCouldNotCompute(); 3354 3355 // If the start is a non-zero constant, shift the range to simplify things. 3356 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 3357 if (!SC->getValue()->isZero()) { 3358 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3359 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3360 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3361 if (const SCEVAddRecExpr *ShiftedAddRec = 3362 dyn_cast<SCEVAddRecExpr>(Shifted)) 3363 return ShiftedAddRec->getNumIterationsInRange( 3364 Range.subtract(SC->getValue()->getValue()), SE); 3365 // This is strange and shouldn't happen. 3366 return SE.getCouldNotCompute(); 3367 } 3368 3369 // The only time we can solve this is when we have all constant indices. 3370 // Otherwise, we cannot determine the overflow conditions. 3371 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3372 if (!isa<SCEVConstant>(getOperand(i))) 3373 return SE.getCouldNotCompute(); 3374 3375 3376 // Okay at this point we know that all elements of the chrec are constants and 3377 // that the start element is zero. 3378 3379 // First check to see if the range contains zero. If not, the first 3380 // iteration exits. 3381 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3382 if (!Range.contains(APInt(BitWidth, 0))) 3383 return SE.getConstant(ConstantInt::get(getType(),0)); 3384 3385 if (isAffine()) { 3386 // If this is an affine expression then we have this situation: 3387 // Solve {0,+,A} in Range === Ax in Range 3388 3389 // We know that zero is in the range. If A is positive then we know that 3390 // the upper value of the range must be the first possible exit value. 3391 // If A is negative then the lower of the range is the last possible loop 3392 // value. Also note that we already checked for a full range. 3393 APInt One(BitWidth,1); 3394 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3395 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3396 3397 // The exit value should be (End+A)/A. 3398 APInt ExitVal = (End + A).udiv(A); 3399 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3400 3401 // Evaluate at the exit value. If we really did fall out of the valid 3402 // range, then we computed our trip count, otherwise wrap around or other 3403 // things must have happened. 3404 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3405 if (Range.contains(Val->getValue())) 3406 return SE.getCouldNotCompute(); // Something strange happened 3407 3408 // Ensure that the previous value is in the range. This is a sanity check. 3409 assert(Range.contains( 3410 EvaluateConstantChrecAtConstant(this, 3411 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3412 "Linear scev computation is off in a bad way!"); 3413 return SE.getConstant(ExitValue); 3414 } else if (isQuadratic()) { 3415 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3416 // quadratic equation to solve it. To do this, we must frame our problem in 3417 // terms of figuring out when zero is crossed, instead of when 3418 // Range.getUpper() is crossed. 3419 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3420 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3421 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3422 3423 // Next, solve the constructed addrec 3424 std::pair<SCEVHandle,SCEVHandle> Roots = 3425 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3426 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3427 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3428 if (R1) { 3429 // Pick the smallest positive root value. 3430 if (ConstantInt *CB = 3431 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3432 R1->getValue(), R2->getValue()))) { 3433 if (CB->getZExtValue() == false) 3434 std::swap(R1, R2); // R1 is the minimum root now. 3435 3436 // Make sure the root is not off by one. The returned iteration should 3437 // not be in the range, but the previous one should be. When solving 3438 // for "X*X < 5", for example, we should not return a root of 2. 3439 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3440 R1->getValue(), 3441 SE); 3442 if (Range.contains(R1Val->getValue())) { 3443 // The next iteration must be out of the range... 3444 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3445 3446 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3447 if (!Range.contains(R1Val->getValue())) 3448 return SE.getConstant(NextVal); 3449 return SE.getCouldNotCompute(); // Something strange happened 3450 } 3451 3452 // If R1 was not in the range, then it is a good return value. Make 3453 // sure that R1-1 WAS in the range though, just in case. 3454 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3455 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3456 if (Range.contains(R1Val->getValue())) 3457 return R1; 3458 return SE.getCouldNotCompute(); // Something strange happened 3459 } 3460 } 3461 } 3462 3463 return SE.getCouldNotCompute(); 3464} 3465 3466 3467 3468//===----------------------------------------------------------------------===// 3469// SCEVCallbackVH Class Implementation 3470//===----------------------------------------------------------------------===// 3471 3472void SCEVCallbackVH::deleted() { 3473 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 3474 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 3475 SE->ConstantEvolutionLoopExitValue.erase(PN); 3476 SE->Scalars.erase(getValPtr()); 3477 // this now dangles! 3478} 3479 3480void SCEVCallbackVH::allUsesReplacedWith(Value *) { 3481 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 3482 3483 // Forget all the expressions associated with users of the old value, 3484 // so that future queries will recompute the expressions using the new 3485 // value. 3486 SmallVector<User *, 16> Worklist; 3487 Value *Old = getValPtr(); 3488 bool DeleteOld = false; 3489 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 3490 UI != UE; ++UI) 3491 Worklist.push_back(*UI); 3492 while (!Worklist.empty()) { 3493 User *U = Worklist.pop_back_val(); 3494 // Deleting the Old value will cause this to dangle. Postpone 3495 // that until everything else is done. 3496 if (U == Old) { 3497 DeleteOld = true; 3498 continue; 3499 } 3500 if (PHINode *PN = dyn_cast<PHINode>(U)) 3501 SE->ConstantEvolutionLoopExitValue.erase(PN); 3502 if (SE->Scalars.erase(U)) 3503 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 3504 UI != UE; ++UI) 3505 Worklist.push_back(*UI); 3506 } 3507 if (DeleteOld) { 3508 if (PHINode *PN = dyn_cast<PHINode>(Old)) 3509 SE->ConstantEvolutionLoopExitValue.erase(PN); 3510 SE->Scalars.erase(Old); 3511 // this now dangles! 3512 } 3513 // this may dangle! 3514} 3515 3516SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 3517 : CallbackVH(V), SE(se) {} 3518 3519//===----------------------------------------------------------------------===// 3520// ScalarEvolution Class Implementation 3521//===----------------------------------------------------------------------===// 3522 3523ScalarEvolution::ScalarEvolution() 3524 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3525} 3526 3527bool ScalarEvolution::runOnFunction(Function &F) { 3528 this->F = &F; 3529 LI = &getAnalysis<LoopInfo>(); 3530 TD = getAnalysisIfAvailable<TargetData>(); 3531 return false; 3532} 3533 3534void ScalarEvolution::releaseMemory() { 3535 Scalars.clear(); 3536 BackedgeTakenCounts.clear(); 3537 ConstantEvolutionLoopExitValue.clear(); 3538} 3539 3540void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3541 AU.setPreservesAll(); 3542 AU.addRequiredTransitive<LoopInfo>(); 3543} 3544 3545bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3546 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3547} 3548 3549static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3550 const Loop *L) { 3551 // Print all inner loops first 3552 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3553 PrintLoopInfo(OS, SE, *I); 3554 3555 OS << "Loop " << L->getHeader()->getName() << ": "; 3556 3557 SmallVector<BasicBlock*, 8> ExitBlocks; 3558 L->getExitBlocks(ExitBlocks); 3559 if (ExitBlocks.size() != 1) 3560 OS << "<multiple exits> "; 3561 3562 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3563 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3564 } else { 3565 OS << "Unpredictable backedge-taken count. "; 3566 } 3567 3568 OS << "\n"; 3569} 3570 3571void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3572 // ScalarEvolution's implementaiton of the print method is to print 3573 // out SCEV values of all instructions that are interesting. Doing 3574 // this potentially causes it to create new SCEV objects though, 3575 // which technically conflicts with the const qualifier. This isn't 3576 // observable from outside the class though (the hasSCEV function 3577 // notwithstanding), so casting away the const isn't dangerous. 3578 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3579 3580 OS << "Classifying expressions for: " << F->getName() << "\n"; 3581 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3582 if (isSCEVable(I->getType())) { 3583 OS << *I; 3584 OS << " --> "; 3585 SCEVHandle SV = SE.getSCEV(&*I); 3586 SV->print(OS); 3587 OS << "\t\t"; 3588 3589 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3590 OS << "Exits: "; 3591 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3592 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3593 OS << "<<Unknown>>"; 3594 } else { 3595 OS << *ExitValue; 3596 } 3597 } 3598 3599 3600 OS << "\n"; 3601 } 3602 3603 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3604 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3605 PrintLoopInfo(OS, &SE, *I); 3606} 3607 3608void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3609 raw_os_ostream OS(o); 3610 print(OS, M); 3611} 3612