ScalarEvolution.cpp revision 361e54d433e67db5d6b6455f7fd098de8c01f882
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 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 752 return getAddRecExpr(Operands, AddRec->getLoop()); 753 } 754 755 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)]; 756 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty); 757 return Result; 758} 759 760SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, 761 const Type *Ty) { 762 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 763 "This is not an extending conversion!"); 764 assert(isSCEVable(Ty) && 765 "This is not a conversion to a SCEVable type!"); 766 Ty = getEffectiveSCEVType(Ty); 767 768 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 769 const Type *IntTy = getEffectiveSCEVType(Ty); 770 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 771 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 772 return getUnknown(C); 773 } 774 775 // zext(zext(x)) --> zext(x) 776 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 777 return getZeroExtendExpr(SZ->getOperand(), Ty); 778 779 // If the input value is a chrec scev, and we can prove that the value 780 // did not overflow the old, smaller, value, we can zero extend all of the 781 // operands (often constants). This allows analysis of something like 782 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 783 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 784 if (AR->isAffine()) { 785 // Check whether the backedge-taken count is SCEVCouldNotCompute. 786 // Note that this serves two purposes: It filters out loops that are 787 // simply not analyzable, and it covers the case where this code is 788 // being called from within backedge-taken count analysis, such that 789 // attempting to ask for the backedge-taken count would likely result 790 // in infinite recursion. In the later case, the analysis code will 791 // cope with a conservative value, and it will take care to purge 792 // that value once it has finished. 793 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 794 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 795 // Manually compute the final value for AR, checking for 796 // overflow. 797 SCEVHandle Start = AR->getStart(); 798 SCEVHandle Step = AR->getStepRecurrence(*this); 799 800 // Check whether the backedge-taken count can be losslessly casted to 801 // the addrec's type. The count is always unsigned. 802 SCEVHandle CastedMaxBECount = 803 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 804 if (MaxBECount == 805 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 806 const Type *WideTy = 807 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 808 // Check whether Start+Step*MaxBECount has no unsigned overflow. 809 SCEVHandle ZMul = 810 getMulExpr(CastedMaxBECount, 811 getTruncateOrZeroExtend(Step, Start->getType())); 812 SCEVHandle Add = getAddExpr(Start, ZMul); 813 if (getZeroExtendExpr(Add, WideTy) == 814 getAddExpr(getZeroExtendExpr(Start, WideTy), 815 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 816 getZeroExtendExpr(Step, WideTy)))) 817 // Return the expression with the addrec on the outside. 818 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 819 getZeroExtendExpr(Step, Ty), 820 AR->getLoop()); 821 822 // Similar to above, only this time treat the step value as signed. 823 // This covers loops that count down. 824 SCEVHandle SMul = 825 getMulExpr(CastedMaxBECount, 826 getTruncateOrSignExtend(Step, Start->getType())); 827 Add = getAddExpr(Start, SMul); 828 if (getZeroExtendExpr(Add, WideTy) == 829 getAddExpr(getZeroExtendExpr(Start, WideTy), 830 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 831 getSignExtendExpr(Step, WideTy)))) 832 // Return the expression with the addrec on the outside. 833 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 834 getSignExtendExpr(Step, Ty), 835 AR->getLoop()); 836 } 837 } 838 } 839 840 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)]; 841 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty); 842 return Result; 843} 844 845SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, 846 const Type *Ty) { 847 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 848 "This is not an extending conversion!"); 849 assert(isSCEVable(Ty) && 850 "This is not a conversion to a SCEVable type!"); 851 Ty = getEffectiveSCEVType(Ty); 852 853 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 854 const Type *IntTy = getEffectiveSCEVType(Ty); 855 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 856 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 857 return getUnknown(C); 858 } 859 860 // sext(sext(x)) --> sext(x) 861 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 862 return getSignExtendExpr(SS->getOperand(), Ty); 863 864 // If the input value is a chrec scev, and we can prove that the value 865 // did not overflow the old, smaller, value, we can sign extend all of the 866 // operands (often constants). This allows analysis of something like 867 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 868 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 869 if (AR->isAffine()) { 870 // Check whether the backedge-taken count is SCEVCouldNotCompute. 871 // Note that this serves two purposes: It filters out loops that are 872 // simply not analyzable, and it covers the case where this code is 873 // being called from within backedge-taken count analysis, such that 874 // attempting to ask for the backedge-taken count would likely result 875 // in infinite recursion. In the later case, the analysis code will 876 // cope with a conservative value, and it will take care to purge 877 // that value once it has finished. 878 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 879 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 880 // Manually compute the final value for AR, checking for 881 // overflow. 882 SCEVHandle Start = AR->getStart(); 883 SCEVHandle Step = AR->getStepRecurrence(*this); 884 885 // Check whether the backedge-taken count can be losslessly casted to 886 // the addrec's type. The count is always unsigned. 887 SCEVHandle CastedMaxBECount = 888 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 889 if (MaxBECount == 890 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) { 891 const Type *WideTy = 892 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 893 // Check whether Start+Step*MaxBECount has no signed overflow. 894 SCEVHandle SMul = 895 getMulExpr(CastedMaxBECount, 896 getTruncateOrSignExtend(Step, Start->getType())); 897 SCEVHandle Add = getAddExpr(Start, SMul); 898 if (getSignExtendExpr(Add, WideTy) == 899 getAddExpr(getSignExtendExpr(Start, WideTy), 900 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 901 getSignExtendExpr(Step, WideTy)))) 902 // Return the expression with the addrec on the outside. 903 return getAddRecExpr(getSignExtendExpr(Start, Ty), 904 getSignExtendExpr(Step, Ty), 905 AR->getLoop()); 906 } 907 } 908 } 909 910 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)]; 911 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty); 912 return Result; 913} 914 915// get - Get a canonical add expression, or something simpler if possible. 916SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) { 917 assert(!Ops.empty() && "Cannot get empty add!"); 918 if (Ops.size() == 1) return Ops[0]; 919 920 // Sort by complexity, this groups all similar expression types together. 921 GroupByComplexity(Ops, LI); 922 923 // If there are any constants, fold them together. 924 unsigned Idx = 0; 925 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 926 ++Idx; 927 assert(Idx < Ops.size()); 928 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 929 // We found two constants, fold them together! 930 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() + 931 RHSC->getValue()->getValue()); 932 Ops[0] = getConstant(Fold); 933 Ops.erase(Ops.begin()+1); // Erase the folded element 934 if (Ops.size() == 1) return Ops[0]; 935 LHSC = cast<SCEVConstant>(Ops[0]); 936 } 937 938 // If we are left with a constant zero being added, strip it off. 939 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 940 Ops.erase(Ops.begin()); 941 --Idx; 942 } 943 } 944 945 if (Ops.size() == 1) return Ops[0]; 946 947 // Okay, check to see if the same value occurs in the operand list twice. If 948 // so, merge them together into an multiply expression. Since we sorted the 949 // list, these values are required to be adjacent. 950 const Type *Ty = Ops[0]->getType(); 951 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 952 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 953 // Found a match, merge the two values into a multiply, and add any 954 // remaining values to the result. 955 SCEVHandle Two = getIntegerSCEV(2, Ty); 956 SCEVHandle Mul = getMulExpr(Ops[i], Two); 957 if (Ops.size() == 2) 958 return Mul; 959 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 960 Ops.push_back(Mul); 961 return getAddExpr(Ops); 962 } 963 964 // Check for truncates. If all the operands are truncated from the same 965 // type, see if factoring out the truncate would permit the result to be 966 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 967 // if the contents of the resulting outer trunc fold to something simple. 968 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 969 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 970 const Type *DstType = Trunc->getType(); 971 const Type *SrcType = Trunc->getOperand()->getType(); 972 std::vector<SCEVHandle> LargeOps; 973 bool Ok = true; 974 // Check all the operands to see if they can be represented in the 975 // source type of the truncate. 976 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 977 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 978 if (T->getOperand()->getType() != SrcType) { 979 Ok = false; 980 break; 981 } 982 LargeOps.push_back(T->getOperand()); 983 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 984 // This could be either sign or zero extension, but sign extension 985 // is much more likely to be foldable here. 986 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 987 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 988 std::vector<SCEVHandle> LargeMulOps; 989 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 990 if (const SCEVTruncateExpr *T = 991 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 992 if (T->getOperand()->getType() != SrcType) { 993 Ok = false; 994 break; 995 } 996 LargeMulOps.push_back(T->getOperand()); 997 } else if (const SCEVConstant *C = 998 dyn_cast<SCEVConstant>(M->getOperand(j))) { 999 // This could be either sign or zero extension, but sign extension 1000 // is much more likely to be foldable here. 1001 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1002 } else { 1003 Ok = false; 1004 break; 1005 } 1006 } 1007 if (Ok) 1008 LargeOps.push_back(getMulExpr(LargeMulOps)); 1009 } else { 1010 Ok = false; 1011 break; 1012 } 1013 } 1014 if (Ok) { 1015 // Evaluate the expression in the larger type. 1016 SCEVHandle Fold = getAddExpr(LargeOps); 1017 // If it folds to something simple, use it. Otherwise, don't. 1018 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1019 return getTruncateExpr(Fold, DstType); 1020 } 1021 } 1022 1023 // Skip past any other cast SCEVs. 1024 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1025 ++Idx; 1026 1027 // If there are add operands they would be next. 1028 if (Idx < Ops.size()) { 1029 bool DeletedAdd = false; 1030 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1031 // If we have an add, expand the add operands onto the end of the operands 1032 // list. 1033 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1034 Ops.erase(Ops.begin()+Idx); 1035 DeletedAdd = true; 1036 } 1037 1038 // If we deleted at least one add, we added operands to the end of the list, 1039 // and they are not necessarily sorted. Recurse to resort and resimplify 1040 // any operands we just aquired. 1041 if (DeletedAdd) 1042 return getAddExpr(Ops); 1043 } 1044 1045 // Skip over the add expression until we get to a multiply. 1046 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1047 ++Idx; 1048 1049 // If we are adding something to a multiply expression, make sure the 1050 // something is not already an operand of the multiply. If so, merge it into 1051 // the multiply. 1052 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1053 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1054 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1055 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1056 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1057 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) { 1058 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1059 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0); 1060 if (Mul->getNumOperands() != 2) { 1061 // If the multiply has more than two operands, we must get the 1062 // Y*Z term. 1063 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 1064 MulOps.erase(MulOps.begin()+MulOp); 1065 InnerMul = getMulExpr(MulOps); 1066 } 1067 SCEVHandle One = getIntegerSCEV(1, Ty); 1068 SCEVHandle AddOne = getAddExpr(InnerMul, One); 1069 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1070 if (Ops.size() == 2) return OuterMul; 1071 if (AddOp < Idx) { 1072 Ops.erase(Ops.begin()+AddOp); 1073 Ops.erase(Ops.begin()+Idx-1); 1074 } else { 1075 Ops.erase(Ops.begin()+Idx); 1076 Ops.erase(Ops.begin()+AddOp-1); 1077 } 1078 Ops.push_back(OuterMul); 1079 return getAddExpr(Ops); 1080 } 1081 1082 // Check this multiply against other multiplies being added together. 1083 for (unsigned OtherMulIdx = Idx+1; 1084 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1085 ++OtherMulIdx) { 1086 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1087 // If MulOp occurs in OtherMul, we can fold the two multiplies 1088 // together. 1089 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1090 OMulOp != e; ++OMulOp) 1091 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1092 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1093 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0); 1094 if (Mul->getNumOperands() != 2) { 1095 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end()); 1096 MulOps.erase(MulOps.begin()+MulOp); 1097 InnerMul1 = getMulExpr(MulOps); 1098 } 1099 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1100 if (OtherMul->getNumOperands() != 2) { 1101 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(), 1102 OtherMul->op_end()); 1103 MulOps.erase(MulOps.begin()+OMulOp); 1104 InnerMul2 = getMulExpr(MulOps); 1105 } 1106 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1107 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1108 if (Ops.size() == 2) return OuterMul; 1109 Ops.erase(Ops.begin()+Idx); 1110 Ops.erase(Ops.begin()+OtherMulIdx-1); 1111 Ops.push_back(OuterMul); 1112 return getAddExpr(Ops); 1113 } 1114 } 1115 } 1116 } 1117 1118 // If there are any add recurrences in the operands list, see if any other 1119 // added values are loop invariant. If so, we can fold them into the 1120 // recurrence. 1121 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1122 ++Idx; 1123 1124 // Scan over all recurrences, trying to fold loop invariants into them. 1125 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1126 // Scan all of the other operands to this add and add them to the vector if 1127 // they are loop invariant w.r.t. the recurrence. 1128 std::vector<SCEVHandle> LIOps; 1129 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1130 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1131 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1132 LIOps.push_back(Ops[i]); 1133 Ops.erase(Ops.begin()+i); 1134 --i; --e; 1135 } 1136 1137 // If we found some loop invariants, fold them into the recurrence. 1138 if (!LIOps.empty()) { 1139 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1140 LIOps.push_back(AddRec->getStart()); 1141 1142 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end()); 1143 AddRecOps[0] = getAddExpr(LIOps); 1144 1145 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1146 // If all of the other operands were loop invariant, we are done. 1147 if (Ops.size() == 1) return NewRec; 1148 1149 // Otherwise, add the folded AddRec by the non-liv parts. 1150 for (unsigned i = 0;; ++i) 1151 if (Ops[i] == AddRec) { 1152 Ops[i] = NewRec; 1153 break; 1154 } 1155 return getAddExpr(Ops); 1156 } 1157 1158 // Okay, if there weren't any loop invariants to be folded, check to see if 1159 // there are multiple AddRec's with the same loop induction variable being 1160 // added together. If so, we can fold them. 1161 for (unsigned OtherIdx = Idx+1; 1162 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1163 if (OtherIdx != Idx) { 1164 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1165 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1166 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1167 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end()); 1168 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1169 if (i >= NewOps.size()) { 1170 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1171 OtherAddRec->op_end()); 1172 break; 1173 } 1174 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1175 } 1176 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1177 1178 if (Ops.size() == 2) return NewAddRec; 1179 1180 Ops.erase(Ops.begin()+Idx); 1181 Ops.erase(Ops.begin()+OtherIdx-1); 1182 Ops.push_back(NewAddRec); 1183 return getAddExpr(Ops); 1184 } 1185 } 1186 1187 // Otherwise couldn't fold anything into this recurrence. Move onto the 1188 // next one. 1189 } 1190 1191 // Okay, it looks like we really DO need an add expr. Check to see if we 1192 // already have one, otherwise create a new one. 1193 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1194 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr, 1195 SCEVOps)]; 1196 if (Result == 0) Result = new SCEVAddExpr(Ops); 1197 return Result; 1198} 1199 1200 1201SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) { 1202 assert(!Ops.empty() && "Cannot get empty mul!"); 1203 1204 // Sort by complexity, this groups all similar expression types together. 1205 GroupByComplexity(Ops, LI); 1206 1207 // If there are any constants, fold them together. 1208 unsigned Idx = 0; 1209 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1210 1211 // C1*(C2+V) -> C1*C2 + C1*V 1212 if (Ops.size() == 2) 1213 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1214 if (Add->getNumOperands() == 2 && 1215 isa<SCEVConstant>(Add->getOperand(0))) 1216 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1217 getMulExpr(LHSC, Add->getOperand(1))); 1218 1219 1220 ++Idx; 1221 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1222 // We found two constants, fold them together! 1223 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1224 RHSC->getValue()->getValue()); 1225 Ops[0] = getConstant(Fold); 1226 Ops.erase(Ops.begin()+1); // Erase the folded element 1227 if (Ops.size() == 1) return Ops[0]; 1228 LHSC = cast<SCEVConstant>(Ops[0]); 1229 } 1230 1231 // If we are left with a constant one being multiplied, strip it off. 1232 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1233 Ops.erase(Ops.begin()); 1234 --Idx; 1235 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1236 // If we have a multiply of zero, it will always be zero. 1237 return Ops[0]; 1238 } 1239 } 1240 1241 // Skip over the add expression until we get to a multiply. 1242 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1243 ++Idx; 1244 1245 if (Ops.size() == 1) 1246 return Ops[0]; 1247 1248 // If there are mul operands inline them all into this expression. 1249 if (Idx < Ops.size()) { 1250 bool DeletedMul = false; 1251 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1252 // If we have an mul, expand the mul operands onto the end of the operands 1253 // list. 1254 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1255 Ops.erase(Ops.begin()+Idx); 1256 DeletedMul = true; 1257 } 1258 1259 // If we deleted at least one mul, we added operands to the end of the list, 1260 // and they are not necessarily sorted. Recurse to resort and resimplify 1261 // any operands we just aquired. 1262 if (DeletedMul) 1263 return getMulExpr(Ops); 1264 } 1265 1266 // If there are any add recurrences in the operands list, see if any other 1267 // added values are loop invariant. If so, we can fold them into the 1268 // recurrence. 1269 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1270 ++Idx; 1271 1272 // Scan over all recurrences, trying to fold loop invariants into them. 1273 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1274 // Scan all of the other operands to this mul and add them to the vector if 1275 // they are loop invariant w.r.t. the recurrence. 1276 std::vector<SCEVHandle> LIOps; 1277 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1278 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1279 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1280 LIOps.push_back(Ops[i]); 1281 Ops.erase(Ops.begin()+i); 1282 --i; --e; 1283 } 1284 1285 // If we found some loop invariants, fold them into the recurrence. 1286 if (!LIOps.empty()) { 1287 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1288 std::vector<SCEVHandle> NewOps; 1289 NewOps.reserve(AddRec->getNumOperands()); 1290 if (LIOps.size() == 1) { 1291 const SCEV *Scale = LIOps[0]; 1292 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1293 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1294 } else { 1295 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1296 std::vector<SCEVHandle> MulOps(LIOps); 1297 MulOps.push_back(AddRec->getOperand(i)); 1298 NewOps.push_back(getMulExpr(MulOps)); 1299 } 1300 } 1301 1302 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1303 1304 // If all of the other operands were loop invariant, we are done. 1305 if (Ops.size() == 1) return NewRec; 1306 1307 // Otherwise, multiply the folded AddRec by the non-liv parts. 1308 for (unsigned i = 0;; ++i) 1309 if (Ops[i] == AddRec) { 1310 Ops[i] = NewRec; 1311 break; 1312 } 1313 return getMulExpr(Ops); 1314 } 1315 1316 // Okay, if there weren't any loop invariants to be folded, check to see if 1317 // there are multiple AddRec's with the same loop induction variable being 1318 // multiplied together. If so, we can fold them. 1319 for (unsigned OtherIdx = Idx+1; 1320 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1321 if (OtherIdx != Idx) { 1322 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1323 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1324 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1325 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1326 SCEVHandle NewStart = getMulExpr(F->getStart(), 1327 G->getStart()); 1328 SCEVHandle B = F->getStepRecurrence(*this); 1329 SCEVHandle D = G->getStepRecurrence(*this); 1330 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D), 1331 getMulExpr(G, B), 1332 getMulExpr(B, D)); 1333 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep, 1334 F->getLoop()); 1335 if (Ops.size() == 2) return NewAddRec; 1336 1337 Ops.erase(Ops.begin()+Idx); 1338 Ops.erase(Ops.begin()+OtherIdx-1); 1339 Ops.push_back(NewAddRec); 1340 return getMulExpr(Ops); 1341 } 1342 } 1343 1344 // Otherwise couldn't fold anything into this recurrence. Move onto the 1345 // next one. 1346 } 1347 1348 // Okay, it looks like we really DO need an mul expr. Check to see if we 1349 // already have one, otherwise create a new one. 1350 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1351 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr, 1352 SCEVOps)]; 1353 if (Result == 0) 1354 Result = new SCEVMulExpr(Ops); 1355 return Result; 1356} 1357 1358SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, 1359 const SCEVHandle &RHS) { 1360 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1361 if (RHSC->getValue()->equalsInt(1)) 1362 return LHS; // X udiv 1 --> x 1363 if (RHSC->isZero()) 1364 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1365 1366 // Determine if the division can be folded into the operands of 1367 // its operands. 1368 // TODO: Generalize this to non-constants by using known-bits information. 1369 const Type *Ty = LHS->getType(); 1370 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1371 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1372 // For non-power-of-two values, effectively round the value up to the 1373 // nearest power of two. 1374 if (!RHSC->getValue()->getValue().isPowerOf2()) 1375 ++MaxShiftAmt; 1376 const IntegerType *ExtTy = 1377 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1378 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1379 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1380 if (const SCEVConstant *Step = 1381 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1382 if (!Step->getValue()->getValue() 1383 .urem(RHSC->getValue()->getValue()) && 1384 getZeroExtendExpr(AR, ExtTy) == 1385 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1386 getZeroExtendExpr(Step, ExtTy), 1387 AR->getLoop())) { 1388 std::vector<SCEVHandle> Operands; 1389 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1390 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1391 return getAddRecExpr(Operands, AR->getLoop()); 1392 } 1393 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1394 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1395 std::vector<SCEVHandle> Operands; 1396 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1397 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1398 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1399 // Find an operand that's safely divisible. 1400 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1401 SCEVHandle Op = M->getOperand(i); 1402 SCEVHandle Div = getUDivExpr(Op, RHSC); 1403 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1404 Operands = M->getOperands(); 1405 Operands[i] = Div; 1406 return getMulExpr(Operands); 1407 } 1408 } 1409 } 1410 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1411 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1412 std::vector<SCEVHandle> Operands; 1413 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1414 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1415 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1416 Operands.clear(); 1417 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1418 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS); 1419 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1420 break; 1421 Operands.push_back(Op); 1422 } 1423 if (Operands.size() == A->getNumOperands()) 1424 return getAddExpr(Operands); 1425 } 1426 } 1427 1428 // Fold if both operands are constant. 1429 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1430 Constant *LHSCV = LHSC->getValue(); 1431 Constant *RHSCV = RHSC->getValue(); 1432 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV)); 1433 } 1434 } 1435 1436 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)]; 1437 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS); 1438 return Result; 1439} 1440 1441 1442/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1443/// specified loop. Simplify the expression as much as possible. 1444SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start, 1445 const SCEVHandle &Step, const Loop *L) { 1446 std::vector<SCEVHandle> Operands; 1447 Operands.push_back(Start); 1448 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1449 if (StepChrec->getLoop() == L) { 1450 Operands.insert(Operands.end(), StepChrec->op_begin(), 1451 StepChrec->op_end()); 1452 return getAddRecExpr(Operands, L); 1453 } 1454 1455 Operands.push_back(Step); 1456 return getAddRecExpr(Operands, L); 1457} 1458 1459/// SCEVAddRecExpr::get - Get a add recurrence expression for the 1460/// specified loop. Simplify the expression as much as possible. 1461SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands, 1462 const Loop *L) { 1463 if (Operands.size() == 1) return Operands[0]; 1464 1465 if (Operands.back()->isZero()) { 1466 Operands.pop_back(); 1467 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1468 } 1469 1470 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1471 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1472 const Loop* NestedLoop = NestedAR->getLoop(); 1473 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1474 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(), 1475 NestedAR->op_end()); 1476 SCEVHandle NestedARHandle(NestedAR); 1477 Operands[0] = NestedAR->getStart(); 1478 NestedOperands[0] = getAddRecExpr(Operands, L); 1479 return getAddRecExpr(NestedOperands, NestedLoop); 1480 } 1481 } 1482 1483 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end()); 1484 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)]; 1485 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L); 1486 return Result; 1487} 1488 1489SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS, 1490 const SCEVHandle &RHS) { 1491 std::vector<SCEVHandle> Ops; 1492 Ops.push_back(LHS); 1493 Ops.push_back(RHS); 1494 return getSMaxExpr(Ops); 1495} 1496 1497SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) { 1498 assert(!Ops.empty() && "Cannot get empty smax!"); 1499 if (Ops.size() == 1) return Ops[0]; 1500 1501 // Sort by complexity, this groups all similar expression types together. 1502 GroupByComplexity(Ops, LI); 1503 1504 // If there are any constants, fold them together. 1505 unsigned Idx = 0; 1506 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1507 ++Idx; 1508 assert(Idx < Ops.size()); 1509 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1510 // We found two constants, fold them together! 1511 ConstantInt *Fold = ConstantInt::get( 1512 APIntOps::smax(LHSC->getValue()->getValue(), 1513 RHSC->getValue()->getValue())); 1514 Ops[0] = getConstant(Fold); 1515 Ops.erase(Ops.begin()+1); // Erase the folded element 1516 if (Ops.size() == 1) return Ops[0]; 1517 LHSC = cast<SCEVConstant>(Ops[0]); 1518 } 1519 1520 // If we are left with a constant -inf, strip it off. 1521 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1522 Ops.erase(Ops.begin()); 1523 --Idx; 1524 } 1525 } 1526 1527 if (Ops.size() == 1) return Ops[0]; 1528 1529 // Find the first SMax 1530 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1531 ++Idx; 1532 1533 // Check to see if one of the operands is an SMax. If so, expand its operands 1534 // onto our operand list, and recurse to simplify. 1535 if (Idx < Ops.size()) { 1536 bool DeletedSMax = false; 1537 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1538 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1539 Ops.erase(Ops.begin()+Idx); 1540 DeletedSMax = true; 1541 } 1542 1543 if (DeletedSMax) 1544 return getSMaxExpr(Ops); 1545 } 1546 1547 // Okay, check to see if the same value occurs in the operand list twice. If 1548 // so, delete one. Since we sorted the list, these values are required to 1549 // be adjacent. 1550 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1551 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1552 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1553 --i; --e; 1554 } 1555 1556 if (Ops.size() == 1) return Ops[0]; 1557 1558 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1559 1560 // Okay, it looks like we really DO need an smax expr. Check to see if we 1561 // already have one, otherwise create a new one. 1562 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1563 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr, 1564 SCEVOps)]; 1565 if (Result == 0) Result = new SCEVSMaxExpr(Ops); 1566 return Result; 1567} 1568 1569SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS, 1570 const SCEVHandle &RHS) { 1571 std::vector<SCEVHandle> Ops; 1572 Ops.push_back(LHS); 1573 Ops.push_back(RHS); 1574 return getUMaxExpr(Ops); 1575} 1576 1577SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) { 1578 assert(!Ops.empty() && "Cannot get empty umax!"); 1579 if (Ops.size() == 1) return Ops[0]; 1580 1581 // Sort by complexity, this groups all similar expression types together. 1582 GroupByComplexity(Ops, LI); 1583 1584 // If there are any constants, fold them together. 1585 unsigned Idx = 0; 1586 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1587 ++Idx; 1588 assert(Idx < Ops.size()); 1589 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1590 // We found two constants, fold them together! 1591 ConstantInt *Fold = ConstantInt::get( 1592 APIntOps::umax(LHSC->getValue()->getValue(), 1593 RHSC->getValue()->getValue())); 1594 Ops[0] = getConstant(Fold); 1595 Ops.erase(Ops.begin()+1); // Erase the folded element 1596 if (Ops.size() == 1) return Ops[0]; 1597 LHSC = cast<SCEVConstant>(Ops[0]); 1598 } 1599 1600 // If we are left with a constant zero, strip it off. 1601 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1602 Ops.erase(Ops.begin()); 1603 --Idx; 1604 } 1605 } 1606 1607 if (Ops.size() == 1) return Ops[0]; 1608 1609 // Find the first UMax 1610 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1611 ++Idx; 1612 1613 // Check to see if one of the operands is a UMax. If so, expand its operands 1614 // onto our operand list, and recurse to simplify. 1615 if (Idx < Ops.size()) { 1616 bool DeletedUMax = false; 1617 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1618 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1619 Ops.erase(Ops.begin()+Idx); 1620 DeletedUMax = true; 1621 } 1622 1623 if (DeletedUMax) 1624 return getUMaxExpr(Ops); 1625 } 1626 1627 // Okay, check to see if the same value occurs in the operand list twice. If 1628 // so, delete one. Since we sorted the list, these values are required to 1629 // be adjacent. 1630 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1631 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1632 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1633 --i; --e; 1634 } 1635 1636 if (Ops.size() == 1) return Ops[0]; 1637 1638 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1639 1640 // Okay, it looks like we really DO need a umax expr. Check to see if we 1641 // already have one, otherwise create a new one. 1642 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end()); 1643 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr, 1644 SCEVOps)]; 1645 if (Result == 0) Result = new SCEVUMaxExpr(Ops); 1646 return Result; 1647} 1648 1649SCEVHandle ScalarEvolution::getUnknown(Value *V) { 1650 if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 1651 return getConstant(CI); 1652 if (isa<ConstantPointerNull>(V)) 1653 return getIntegerSCEV(0, V->getType()); 1654 SCEVUnknown *&Result = (*SCEVUnknowns)[V]; 1655 if (Result == 0) Result = new SCEVUnknown(V); 1656 return Result; 1657} 1658 1659//===----------------------------------------------------------------------===// 1660// Basic SCEV Analysis and PHI Idiom Recognition Code 1661// 1662 1663/// isSCEVable - Test if values of the given type are analyzable within 1664/// the SCEV framework. This primarily includes integer types, and it 1665/// can optionally include pointer types if the ScalarEvolution class 1666/// has access to target-specific information. 1667bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1668 // Integers are always SCEVable. 1669 if (Ty->isInteger()) 1670 return true; 1671 1672 // Pointers are SCEVable if TargetData information is available 1673 // to provide pointer size information. 1674 if (isa<PointerType>(Ty)) 1675 return TD != NULL; 1676 1677 // Otherwise it's not SCEVable. 1678 return false; 1679} 1680 1681/// getTypeSizeInBits - Return the size in bits of the specified type, 1682/// for which isSCEVable must return true. 1683uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 1684 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1685 1686 // If we have a TargetData, use it! 1687 if (TD) 1688 return TD->getTypeSizeInBits(Ty); 1689 1690 // Otherwise, we support only integer types. 1691 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 1692 return Ty->getPrimitiveSizeInBits(); 1693} 1694 1695/// getEffectiveSCEVType - Return a type with the same bitwidth as 1696/// the given type and which represents how SCEV will treat the given 1697/// type, for which isSCEVable must return true. For pointer types, 1698/// this is the pointer-sized integer type. 1699const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 1700 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 1701 1702 if (Ty->isInteger()) 1703 return Ty; 1704 1705 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 1706 return TD->getIntPtrType(); 1707} 1708 1709SCEVHandle ScalarEvolution::getCouldNotCompute() { 1710 return UnknownValue; 1711} 1712 1713/// hasSCEV - Return true if the SCEV for this value has already been 1714/// computed. 1715bool ScalarEvolution::hasSCEV(Value *V) const { 1716 return Scalars.count(V); 1717} 1718 1719/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 1720/// expression and create a new one. 1721SCEVHandle ScalarEvolution::getSCEV(Value *V) { 1722 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 1723 1724 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V); 1725 if (I != Scalars.end()) return I->second; 1726 SCEVHandle S = createSCEV(V); 1727 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 1728 return S; 1729} 1730 1731/// getIntegerSCEV - Given an integer or FP type, create a constant for the 1732/// specified signed integer value and return a SCEV for the constant. 1733SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 1734 Ty = getEffectiveSCEVType(Ty); 1735 Constant *C; 1736 if (Val == 0) 1737 C = Constant::getNullValue(Ty); 1738 else if (Ty->isFloatingPoint()) 1739 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle : 1740 APFloat::IEEEdouble, Val)); 1741 else 1742 C = ConstantInt::get(Ty, Val); 1743 return getUnknown(C); 1744} 1745 1746/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 1747/// 1748SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) { 1749 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1750 return getUnknown(ConstantExpr::getNeg(VC->getValue())); 1751 1752 const Type *Ty = V->getType(); 1753 Ty = getEffectiveSCEVType(Ty); 1754 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 1755} 1756 1757/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 1758SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) { 1759 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 1760 return getUnknown(ConstantExpr::getNot(VC->getValue())); 1761 1762 const Type *Ty = V->getType(); 1763 Ty = getEffectiveSCEVType(Ty); 1764 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 1765 return getMinusSCEV(AllOnes, V); 1766} 1767 1768/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 1769/// 1770SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS, 1771 const SCEVHandle &RHS) { 1772 // X - Y --> X + -Y 1773 return getAddExpr(LHS, getNegativeSCEV(RHS)); 1774} 1775 1776/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 1777/// input value to the specified type. If the type must be extended, it is zero 1778/// extended. 1779SCEVHandle 1780ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V, 1781 const Type *Ty) { 1782 const Type *SrcTy = V->getType(); 1783 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1784 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1785 "Cannot truncate or zero extend with non-integer arguments!"); 1786 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1787 return V; // No conversion 1788 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1789 return getTruncateExpr(V, Ty); 1790 return getZeroExtendExpr(V, Ty); 1791} 1792 1793/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 1794/// input value to the specified type. If the type must be extended, it is sign 1795/// extended. 1796SCEVHandle 1797ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V, 1798 const Type *Ty) { 1799 const Type *SrcTy = V->getType(); 1800 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 1801 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 1802 "Cannot truncate or zero extend with non-integer arguments!"); 1803 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 1804 return V; // No conversion 1805 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 1806 return getTruncateExpr(V, Ty); 1807 return getSignExtendExpr(V, Ty); 1808} 1809 1810/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 1811/// the specified instruction and replaces any references to the symbolic value 1812/// SymName with the specified value. This is used during PHI resolution. 1813void ScalarEvolution:: 1814ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName, 1815 const SCEVHandle &NewVal) { 1816 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI = 1817 Scalars.find(SCEVCallbackVH(I, this)); 1818 if (SI == Scalars.end()) return; 1819 1820 SCEVHandle NV = 1821 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 1822 if (NV == SI->second) return; // No change. 1823 1824 SI->second = NV; // Update the scalars map! 1825 1826 // Any instruction values that use this instruction might also need to be 1827 // updated! 1828 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 1829 UI != E; ++UI) 1830 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 1831} 1832 1833/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 1834/// a loop header, making it a potential recurrence, or it doesn't. 1835/// 1836SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) { 1837 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 1838 if (const Loop *L = LI->getLoopFor(PN->getParent())) 1839 if (L->getHeader() == PN->getParent()) { 1840 // If it lives in the loop header, it has two incoming values, one 1841 // from outside the loop, and one from inside. 1842 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 1843 unsigned BackEdge = IncomingEdge^1; 1844 1845 // While we are analyzing this PHI node, handle its value symbolically. 1846 SCEVHandle SymbolicName = getUnknown(PN); 1847 assert(Scalars.find(PN) == Scalars.end() && 1848 "PHI node already processed?"); 1849 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 1850 1851 // Using this symbolic name for the PHI, analyze the value coming around 1852 // the back-edge. 1853 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 1854 1855 // NOTE: If BEValue is loop invariant, we know that the PHI node just 1856 // has a special value for the first iteration of the loop. 1857 1858 // If the value coming around the backedge is an add with the symbolic 1859 // value we just inserted, then we found a simple induction variable! 1860 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 1861 // If there is a single occurrence of the symbolic value, replace it 1862 // with a recurrence. 1863 unsigned FoundIndex = Add->getNumOperands(); 1864 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1865 if (Add->getOperand(i) == SymbolicName) 1866 if (FoundIndex == e) { 1867 FoundIndex = i; 1868 break; 1869 } 1870 1871 if (FoundIndex != Add->getNumOperands()) { 1872 // Create an add with everything but the specified operand. 1873 std::vector<SCEVHandle> Ops; 1874 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 1875 if (i != FoundIndex) 1876 Ops.push_back(Add->getOperand(i)); 1877 SCEVHandle Accum = getAddExpr(Ops); 1878 1879 // This is not a valid addrec if the step amount is varying each 1880 // loop iteration, but is not itself an addrec in this loop. 1881 if (Accum->isLoopInvariant(L) || 1882 (isa<SCEVAddRecExpr>(Accum) && 1883 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 1884 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1885 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L); 1886 1887 // Okay, for the entire analysis of this edge we assumed the PHI 1888 // to be symbolic. We now need to go back and update all of the 1889 // entries for the scalars that use the PHI (except for the PHI 1890 // itself) to use the new analyzed value instead of the "symbolic" 1891 // value. 1892 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1893 return PHISCEV; 1894 } 1895 } 1896 } else if (const SCEVAddRecExpr *AddRec = 1897 dyn_cast<SCEVAddRecExpr>(BEValue)) { 1898 // Otherwise, this could be a loop like this: 1899 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 1900 // In this case, j = {1,+,1} and BEValue is j. 1901 // Because the other in-value of i (0) fits the evolution of BEValue 1902 // i really is an addrec evolution. 1903 if (AddRec->getLoop() == L && AddRec->isAffine()) { 1904 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 1905 1906 // If StartVal = j.start - j.stride, we can use StartVal as the 1907 // initial step of the addrec evolution. 1908 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 1909 AddRec->getOperand(1))) { 1910 SCEVHandle PHISCEV = 1911 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 1912 1913 // Okay, for the entire analysis of this edge we assumed the PHI 1914 // to be symbolic. We now need to go back and update all of the 1915 // entries for the scalars that use the PHI (except for the PHI 1916 // itself) to use the new analyzed value instead of the "symbolic" 1917 // value. 1918 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 1919 return PHISCEV; 1920 } 1921 } 1922 } 1923 1924 return SymbolicName; 1925 } 1926 1927 // If it's not a loop phi, we can't handle it yet. 1928 return getUnknown(PN); 1929} 1930 1931/// createNodeForGEP - Expand GEP instructions into add and multiply 1932/// operations. This allows them to be analyzed by regular SCEV code. 1933/// 1934SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) { 1935 1936 const Type *IntPtrTy = TD->getIntPtrType(); 1937 Value *Base = GEP->getOperand(0); 1938 // Don't attempt to analyze GEPs over unsized objects. 1939 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 1940 return getUnknown(GEP); 1941 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy); 1942 gep_type_iterator GTI = gep_type_begin(GEP); 1943 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 1944 E = GEP->op_end(); 1945 I != E; ++I) { 1946 Value *Index = *I; 1947 // Compute the (potentially symbolic) offset in bytes for this index. 1948 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 1949 // For a struct, add the member offset. 1950 const StructLayout &SL = *TD->getStructLayout(STy); 1951 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 1952 uint64_t Offset = SL.getElementOffset(FieldNo); 1953 TotalOffset = getAddExpr(TotalOffset, 1954 getIntegerSCEV(Offset, IntPtrTy)); 1955 } else { 1956 // For an array, add the element offset, explicitly scaled. 1957 SCEVHandle LocalOffset = getSCEV(Index); 1958 if (!isa<PointerType>(LocalOffset->getType())) 1959 // Getelementptr indicies are signed. 1960 LocalOffset = getTruncateOrSignExtend(LocalOffset, 1961 IntPtrTy); 1962 LocalOffset = 1963 getMulExpr(LocalOffset, 1964 getIntegerSCEV(TD->getTypeAllocSize(*GTI), 1965 IntPtrTy)); 1966 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 1967 } 1968 } 1969 return getAddExpr(getSCEV(Base), TotalOffset); 1970} 1971 1972/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 1973/// guaranteed to end in (at every loop iteration). It is, at the same time, 1974/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 1975/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 1976static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) { 1977 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 1978 return C->getValue()->getValue().countTrailingZeros(); 1979 1980 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 1981 return std::min(GetMinTrailingZeros(T->getOperand(), SE), 1982 (uint32_t)SE.getTypeSizeInBits(T->getType())); 1983 1984 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 1985 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1986 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1987 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1988 } 1989 1990 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 1991 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE); 1992 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ? 1993 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes; 1994 } 1995 1996 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 1997 // The result is the min of all operands results. 1998 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 1999 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2000 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 2001 return MinOpRes; 2002 } 2003 2004 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2005 // The result is the sum of all operands results. 2006 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 2007 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType()); 2008 for (unsigned i = 1, e = M->getNumOperands(); 2009 SumOpRes != BitWidth && i != e; ++i) 2010 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE), 2011 BitWidth); 2012 return SumOpRes; 2013 } 2014 2015 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2016 // The result is the min of all operands results. 2017 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE); 2018 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2019 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE)); 2020 return MinOpRes; 2021 } 2022 2023 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2024 // The result is the min of all operands results. 2025 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 2026 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2027 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 2028 return MinOpRes; 2029 } 2030 2031 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2032 // The result is the min of all operands results. 2033 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE); 2034 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2035 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE)); 2036 return MinOpRes; 2037 } 2038 2039 // SCEVUDivExpr, SCEVUnknown 2040 return 0; 2041} 2042 2043/// createSCEV - We know that there is no SCEV for the specified value. 2044/// Analyze the expression. 2045/// 2046SCEVHandle ScalarEvolution::createSCEV(Value *V) { 2047 if (!isSCEVable(V->getType())) 2048 return getUnknown(V); 2049 2050 unsigned Opcode = Instruction::UserOp1; 2051 if (Instruction *I = dyn_cast<Instruction>(V)) 2052 Opcode = I->getOpcode(); 2053 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2054 Opcode = CE->getOpcode(); 2055 else 2056 return getUnknown(V); 2057 2058 User *U = cast<User>(V); 2059 switch (Opcode) { 2060 case Instruction::Add: 2061 return getAddExpr(getSCEV(U->getOperand(0)), 2062 getSCEV(U->getOperand(1))); 2063 case Instruction::Mul: 2064 return getMulExpr(getSCEV(U->getOperand(0)), 2065 getSCEV(U->getOperand(1))); 2066 case Instruction::UDiv: 2067 return getUDivExpr(getSCEV(U->getOperand(0)), 2068 getSCEV(U->getOperand(1))); 2069 case Instruction::Sub: 2070 return getMinusSCEV(getSCEV(U->getOperand(0)), 2071 getSCEV(U->getOperand(1))); 2072 case Instruction::And: 2073 // For an expression like x&255 that merely masks off the high bits, 2074 // use zext(trunc(x)) as the SCEV expression. 2075 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2076 if (CI->isNullValue()) 2077 return getSCEV(U->getOperand(1)); 2078 if (CI->isAllOnesValue()) 2079 return getSCEV(U->getOperand(0)); 2080 const APInt &A = CI->getValue(); 2081 unsigned Ones = A.countTrailingOnes(); 2082 if (APIntOps::isMask(Ones, A)) 2083 return 2084 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2085 IntegerType::get(Ones)), 2086 U->getType()); 2087 } 2088 break; 2089 case Instruction::Or: 2090 // If the RHS of the Or is a constant, we may have something like: 2091 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2092 // optimizations will transparently handle this case. 2093 // 2094 // In order for this transformation to be safe, the LHS must be of the 2095 // form X*(2^n) and the Or constant must be less than 2^n. 2096 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2097 SCEVHandle LHS = getSCEV(U->getOperand(0)); 2098 const APInt &CIVal = CI->getValue(); 2099 if (GetMinTrailingZeros(LHS, *this) >= 2100 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2101 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2102 } 2103 break; 2104 case Instruction::Xor: 2105 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2106 // If the RHS of the xor is a signbit, then this is just an add. 2107 // Instcombine turns add of signbit into xor as a strength reduction step. 2108 if (CI->getValue().isSignBit()) 2109 return getAddExpr(getSCEV(U->getOperand(0)), 2110 getSCEV(U->getOperand(1))); 2111 2112 // If the RHS of xor is -1, then this is a not operation. 2113 else if (CI->isAllOnesValue()) 2114 return getNotSCEV(getSCEV(U->getOperand(0))); 2115 } 2116 break; 2117 2118 case Instruction::Shl: 2119 // Turn shift left of a constant amount into a multiply. 2120 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2121 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2122 Constant *X = ConstantInt::get( 2123 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2124 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2125 } 2126 break; 2127 2128 case Instruction::LShr: 2129 // Turn logical shift right of a constant into a unsigned divide. 2130 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2131 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2132 Constant *X = ConstantInt::get( 2133 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2134 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2135 } 2136 break; 2137 2138 case Instruction::AShr: 2139 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2140 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2141 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2142 if (L->getOpcode() == Instruction::Shl && 2143 L->getOperand(1) == U->getOperand(1)) { 2144 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2145 uint64_t Amt = BitWidth - CI->getZExtValue(); 2146 if (Amt == BitWidth) 2147 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2148 if (Amt > BitWidth) 2149 return getIntegerSCEV(0, U->getType()); // value is undefined 2150 return 2151 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2152 IntegerType::get(Amt)), 2153 U->getType()); 2154 } 2155 break; 2156 2157 case Instruction::Trunc: 2158 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2159 2160 case Instruction::ZExt: 2161 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2162 2163 case Instruction::SExt: 2164 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2165 2166 case Instruction::BitCast: 2167 // BitCasts are no-op casts so we just eliminate the cast. 2168 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2169 return getSCEV(U->getOperand(0)); 2170 break; 2171 2172 case Instruction::IntToPtr: 2173 if (!TD) break; // Without TD we can't analyze pointers. 2174 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2175 TD->getIntPtrType()); 2176 2177 case Instruction::PtrToInt: 2178 if (!TD) break; // Without TD we can't analyze pointers. 2179 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2180 U->getType()); 2181 2182 case Instruction::GetElementPtr: 2183 if (!TD) break; // Without TD we can't analyze pointers. 2184 return createNodeForGEP(U); 2185 2186 case Instruction::PHI: 2187 return createNodeForPHI(cast<PHINode>(U)); 2188 2189 case Instruction::Select: 2190 // This could be a smax or umax that was lowered earlier. 2191 // Try to recover it. 2192 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2193 Value *LHS = ICI->getOperand(0); 2194 Value *RHS = ICI->getOperand(1); 2195 switch (ICI->getPredicate()) { 2196 case ICmpInst::ICMP_SLT: 2197 case ICmpInst::ICMP_SLE: 2198 std::swap(LHS, RHS); 2199 // fall through 2200 case ICmpInst::ICMP_SGT: 2201 case ICmpInst::ICMP_SGE: 2202 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2203 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2204 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2205 // ~smax(~x, ~y) == smin(x, y). 2206 return getNotSCEV(getSMaxExpr( 2207 getNotSCEV(getSCEV(LHS)), 2208 getNotSCEV(getSCEV(RHS)))); 2209 break; 2210 case ICmpInst::ICMP_ULT: 2211 case ICmpInst::ICMP_ULE: 2212 std::swap(LHS, RHS); 2213 // fall through 2214 case ICmpInst::ICMP_UGT: 2215 case ICmpInst::ICMP_UGE: 2216 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2217 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2218 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2219 // ~umax(~x, ~y) == umin(x, y) 2220 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)), 2221 getNotSCEV(getSCEV(RHS)))); 2222 break; 2223 default: 2224 break; 2225 } 2226 } 2227 2228 default: // We cannot analyze this expression. 2229 break; 2230 } 2231 2232 return getUnknown(V); 2233} 2234 2235 2236 2237//===----------------------------------------------------------------------===// 2238// Iteration Count Computation Code 2239// 2240 2241/// getBackedgeTakenCount - If the specified loop has a predictable 2242/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2243/// object. The backedge-taken count is the number of times the loop header 2244/// will be branched to from within the loop. This is one less than the 2245/// trip count of the loop, since it doesn't count the first iteration, 2246/// when the header is branched to from outside the loop. 2247/// 2248/// Note that it is not valid to call this method on a loop without a 2249/// loop-invariant backedge-taken count (see 2250/// hasLoopInvariantBackedgeTakenCount). 2251/// 2252SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2253 return getBackedgeTakenInfo(L).Exact; 2254} 2255 2256/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2257/// return the least SCEV value that is known never to be less than the 2258/// actual backedge taken count. 2259SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2260 return getBackedgeTakenInfo(L).Max; 2261} 2262 2263const ScalarEvolution::BackedgeTakenInfo & 2264ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2265 // Initially insert a CouldNotCompute for this loop. If the insertion 2266 // succeeds, procede to actually compute a backedge-taken count and 2267 // update the value. The temporary CouldNotCompute value tells SCEV 2268 // code elsewhere that it shouldn't attempt to request a new 2269 // backedge-taken count, which could result in infinite recursion. 2270 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2271 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2272 if (Pair.second) { 2273 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2274 if (ItCount.Exact != UnknownValue) { 2275 assert(ItCount.Exact->isLoopInvariant(L) && 2276 ItCount.Max->isLoopInvariant(L) && 2277 "Computed trip count isn't loop invariant for loop!"); 2278 ++NumTripCountsComputed; 2279 2280 // Update the value in the map. 2281 Pair.first->second = ItCount; 2282 } else if (isa<PHINode>(L->getHeader()->begin())) { 2283 // Only count loops that have phi nodes as not being computable. 2284 ++NumTripCountsNotComputed; 2285 } 2286 2287 // Now that we know more about the trip count for this loop, forget any 2288 // existing SCEV values for PHI nodes in this loop since they are only 2289 // conservative estimates made without the benefit 2290 // of trip count information. 2291 if (ItCount.hasAnyInfo()) 2292 forgetLoopPHIs(L); 2293 } 2294 return Pair.first->second; 2295} 2296 2297/// forgetLoopBackedgeTakenCount - This method should be called by the 2298/// client when it has changed a loop in a way that may effect 2299/// ScalarEvolution's ability to compute a trip count, or if the loop 2300/// is deleted. 2301void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2302 BackedgeTakenCounts.erase(L); 2303 forgetLoopPHIs(L); 2304} 2305 2306/// forgetLoopPHIs - Delete the memoized SCEVs associated with the 2307/// PHI nodes in the given loop. This is used when the trip count of 2308/// the loop may have changed. 2309void ScalarEvolution::forgetLoopPHIs(const Loop *L) { 2310 BasicBlock *Header = L->getHeader(); 2311 2312 SmallVector<Instruction *, 16> Worklist; 2313 for (BasicBlock::iterator I = Header->begin(); 2314 PHINode *PN = dyn_cast<PHINode>(I); ++I) 2315 Worklist.push_back(PN); 2316 2317 while (!Worklist.empty()) { 2318 Instruction *I = Worklist.pop_back_val(); 2319 if (Scalars.erase(I)) 2320 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2321 UI != UE; ++UI) 2322 Worklist.push_back(cast<Instruction>(UI)); 2323 } 2324} 2325 2326/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2327/// of the specified loop will execute. 2328ScalarEvolution::BackedgeTakenInfo 2329ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2330 // If the loop has a non-one exit block count, we can't analyze it. 2331 SmallVector<BasicBlock*, 8> ExitBlocks; 2332 L->getExitBlocks(ExitBlocks); 2333 if (ExitBlocks.size() != 1) return UnknownValue; 2334 2335 // Okay, there is one exit block. Try to find the condition that causes the 2336 // loop to be exited. 2337 BasicBlock *ExitBlock = ExitBlocks[0]; 2338 2339 BasicBlock *ExitingBlock = 0; 2340 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock); 2341 PI != E; ++PI) 2342 if (L->contains(*PI)) { 2343 if (ExitingBlock == 0) 2344 ExitingBlock = *PI; 2345 else 2346 return UnknownValue; // More than one block exiting! 2347 } 2348 assert(ExitingBlock && "No exits from loop, something is broken!"); 2349 2350 // Okay, we've computed the exiting block. See what condition causes us to 2351 // exit. 2352 // 2353 // FIXME: we should be able to handle switch instructions (with a single exit) 2354 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2355 if (ExitBr == 0) return UnknownValue; 2356 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2357 2358 // At this point, we know we have a conditional branch that determines whether 2359 // the loop is exited. However, we don't know if the branch is executed each 2360 // time through the loop. If not, then the execution count of the branch will 2361 // not be equal to the trip count of the loop. 2362 // 2363 // Currently we check for this by checking to see if the Exit branch goes to 2364 // the loop header. If so, we know it will always execute the same number of 2365 // times as the loop. We also handle the case where the exit block *is* the 2366 // loop header. This is common for un-rotated loops. More extensive analysis 2367 // could be done to handle more cases here. 2368 if (ExitBr->getSuccessor(0) != L->getHeader() && 2369 ExitBr->getSuccessor(1) != L->getHeader() && 2370 ExitBr->getParent() != L->getHeader()) 2371 return UnknownValue; 2372 2373 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition()); 2374 2375 // If it's not an integer or pointer comparison then compute it the hard way. 2376 if (ExitCond == 0) 2377 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(), 2378 ExitBr->getSuccessor(0) == ExitBlock); 2379 2380 // If the condition was exit on true, convert the condition to exit on false 2381 ICmpInst::Predicate Cond; 2382 if (ExitBr->getSuccessor(1) == ExitBlock) 2383 Cond = ExitCond->getPredicate(); 2384 else 2385 Cond = ExitCond->getInversePredicate(); 2386 2387 // Handle common loops like: for (X = "string"; *X; ++X) 2388 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 2389 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 2390 SCEVHandle ItCnt = 2391 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 2392 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt; 2393 } 2394 2395 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0)); 2396 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1)); 2397 2398 // Try to evaluate any dependencies out of the loop. 2399 SCEVHandle Tmp = getSCEVAtScope(LHS, L); 2400 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp; 2401 Tmp = getSCEVAtScope(RHS, L); 2402 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp; 2403 2404 // At this point, we would like to compute how many iterations of the 2405 // loop the predicate will return true for these inputs. 2406 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 2407 // If there is a loop-invariant, force it into the RHS. 2408 std::swap(LHS, RHS); 2409 Cond = ICmpInst::getSwappedPredicate(Cond); 2410 } 2411 2412 // If we have a comparison of a chrec against a constant, try to use value 2413 // ranges to answer this query. 2414 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 2415 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 2416 if (AddRec->getLoop() == L) { 2417 // Form the constant range. 2418 ConstantRange CompRange( 2419 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 2420 2421 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this); 2422 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 2423 } 2424 2425 switch (Cond) { 2426 case ICmpInst::ICMP_NE: { // while (X != Y) 2427 // Convert to: while (X-Y != 0) 2428 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 2429 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2430 break; 2431 } 2432 case ICmpInst::ICMP_EQ: { 2433 // Convert to: while (X-Y == 0) // while (X == Y) 2434 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 2435 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 2436 break; 2437 } 2438 case ICmpInst::ICMP_SLT: { 2439 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 2440 if (BTI.hasAnyInfo()) return BTI; 2441 break; 2442 } 2443 case ICmpInst::ICMP_SGT: { 2444 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2445 getNotSCEV(RHS), L, true); 2446 if (BTI.hasAnyInfo()) return BTI; 2447 break; 2448 } 2449 case ICmpInst::ICMP_ULT: { 2450 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 2451 if (BTI.hasAnyInfo()) return BTI; 2452 break; 2453 } 2454 case ICmpInst::ICMP_UGT: { 2455 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 2456 getNotSCEV(RHS), L, false); 2457 if (BTI.hasAnyInfo()) return BTI; 2458 break; 2459 } 2460 default: 2461#if 0 2462 errs() << "ComputeBackedgeTakenCount "; 2463 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 2464 errs() << "[unsigned] "; 2465 errs() << *LHS << " " 2466 << Instruction::getOpcodeName(Instruction::ICmp) 2467 << " " << *RHS << "\n"; 2468#endif 2469 break; 2470 } 2471 return 2472 ComputeBackedgeTakenCountExhaustively(L, ExitCond, 2473 ExitBr->getSuccessor(0) == ExitBlock); 2474} 2475 2476static ConstantInt * 2477EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 2478 ScalarEvolution &SE) { 2479 SCEVHandle InVal = SE.getConstant(C); 2480 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE); 2481 assert(isa<SCEVConstant>(Val) && 2482 "Evaluation of SCEV at constant didn't fold correctly?"); 2483 return cast<SCEVConstant>(Val)->getValue(); 2484} 2485 2486/// GetAddressedElementFromGlobal - Given a global variable with an initializer 2487/// and a GEP expression (missing the pointer index) indexing into it, return 2488/// the addressed element of the initializer or null if the index expression is 2489/// invalid. 2490static Constant * 2491GetAddressedElementFromGlobal(GlobalVariable *GV, 2492 const std::vector<ConstantInt*> &Indices) { 2493 Constant *Init = GV->getInitializer(); 2494 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 2495 uint64_t Idx = Indices[i]->getZExtValue(); 2496 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 2497 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 2498 Init = cast<Constant>(CS->getOperand(Idx)); 2499 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 2500 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 2501 Init = cast<Constant>(CA->getOperand(Idx)); 2502 } else if (isa<ConstantAggregateZero>(Init)) { 2503 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 2504 assert(Idx < STy->getNumElements() && "Bad struct index!"); 2505 Init = Constant::getNullValue(STy->getElementType(Idx)); 2506 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 2507 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 2508 Init = Constant::getNullValue(ATy->getElementType()); 2509 } else { 2510 assert(0 && "Unknown constant aggregate type!"); 2511 } 2512 return 0; 2513 } else { 2514 return 0; // Unknown initializer type 2515 } 2516 } 2517 return Init; 2518} 2519 2520/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 2521/// 'icmp op load X, cst', try to see if we can compute the backedge 2522/// execution count. 2523SCEVHandle ScalarEvolution:: 2524ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS, 2525 const Loop *L, 2526 ICmpInst::Predicate predicate) { 2527 if (LI->isVolatile()) return UnknownValue; 2528 2529 // Check to see if the loaded pointer is a getelementptr of a global. 2530 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 2531 if (!GEP) return UnknownValue; 2532 2533 // Make sure that it is really a constant global we are gepping, with an 2534 // initializer, and make sure the first IDX is really 0. 2535 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 2536 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 2537 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 2538 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 2539 return UnknownValue; 2540 2541 // Okay, we allow one non-constant index into the GEP instruction. 2542 Value *VarIdx = 0; 2543 std::vector<ConstantInt*> Indexes; 2544 unsigned VarIdxNum = 0; 2545 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 2546 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 2547 Indexes.push_back(CI); 2548 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 2549 if (VarIdx) return UnknownValue; // Multiple non-constant idx's. 2550 VarIdx = GEP->getOperand(i); 2551 VarIdxNum = i-2; 2552 Indexes.push_back(0); 2553 } 2554 2555 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 2556 // Check to see if X is a loop variant variable value now. 2557 SCEVHandle Idx = getSCEV(VarIdx); 2558 SCEVHandle Tmp = getSCEVAtScope(Idx, L); 2559 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp; 2560 2561 // We can only recognize very limited forms of loop index expressions, in 2562 // particular, only affine AddRec's like {C1,+,C2}. 2563 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 2564 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 2565 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 2566 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 2567 return UnknownValue; 2568 2569 unsigned MaxSteps = MaxBruteForceIterations; 2570 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 2571 ConstantInt *ItCst = 2572 ConstantInt::get(IdxExpr->getType(), IterationNum); 2573 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 2574 2575 // Form the GEP offset. 2576 Indexes[VarIdxNum] = Val; 2577 2578 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 2579 if (Result == 0) break; // Cannot compute! 2580 2581 // Evaluate the condition for this iteration. 2582 Result = ConstantExpr::getICmp(predicate, Result, RHS); 2583 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 2584 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 2585#if 0 2586 errs() << "\n***\n*** Computed loop count " << *ItCst 2587 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 2588 << "***\n"; 2589#endif 2590 ++NumArrayLenItCounts; 2591 return getConstant(ItCst); // Found terminating iteration! 2592 } 2593 } 2594 return UnknownValue; 2595} 2596 2597 2598/// CanConstantFold - Return true if we can constant fold an instruction of the 2599/// specified type, assuming that all operands were constants. 2600static bool CanConstantFold(const Instruction *I) { 2601 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 2602 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 2603 return true; 2604 2605 if (const CallInst *CI = dyn_cast<CallInst>(I)) 2606 if (const Function *F = CI->getCalledFunction()) 2607 return canConstantFoldCallTo(F); 2608 return false; 2609} 2610 2611/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 2612/// in the loop that V is derived from. We allow arbitrary operations along the 2613/// way, but the operands of an operation must either be constants or a value 2614/// derived from a constant PHI. If this expression does not fit with these 2615/// constraints, return null. 2616static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 2617 // If this is not an instruction, or if this is an instruction outside of the 2618 // loop, it can't be derived from a loop PHI. 2619 Instruction *I = dyn_cast<Instruction>(V); 2620 if (I == 0 || !L->contains(I->getParent())) return 0; 2621 2622 if (PHINode *PN = dyn_cast<PHINode>(I)) { 2623 if (L->getHeader() == I->getParent()) 2624 return PN; 2625 else 2626 // We don't currently keep track of the control flow needed to evaluate 2627 // PHIs, so we cannot handle PHIs inside of loops. 2628 return 0; 2629 } 2630 2631 // If we won't be able to constant fold this expression even if the operands 2632 // are constants, return early. 2633 if (!CanConstantFold(I)) return 0; 2634 2635 // Otherwise, we can evaluate this instruction if all of its operands are 2636 // constant or derived from a PHI node themselves. 2637 PHINode *PHI = 0; 2638 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 2639 if (!(isa<Constant>(I->getOperand(Op)) || 2640 isa<GlobalValue>(I->getOperand(Op)))) { 2641 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 2642 if (P == 0) return 0; // Not evolving from PHI 2643 if (PHI == 0) 2644 PHI = P; 2645 else if (PHI != P) 2646 return 0; // Evolving from multiple different PHIs. 2647 } 2648 2649 // This is a expression evolving from a constant PHI! 2650 return PHI; 2651} 2652 2653/// EvaluateExpression - Given an expression that passes the 2654/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 2655/// in the loop has the value PHIVal. If we can't fold this expression for some 2656/// reason, return null. 2657static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 2658 if (isa<PHINode>(V)) return PHIVal; 2659 if (Constant *C = dyn_cast<Constant>(V)) return C; 2660 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 2661 Instruction *I = cast<Instruction>(V); 2662 2663 std::vector<Constant*> Operands; 2664 Operands.resize(I->getNumOperands()); 2665 2666 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2667 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 2668 if (Operands[i] == 0) return 0; 2669 } 2670 2671 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2672 return ConstantFoldCompareInstOperands(CI->getPredicate(), 2673 &Operands[0], Operands.size()); 2674 else 2675 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2676 &Operands[0], Operands.size()); 2677} 2678 2679/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 2680/// in the header of its containing loop, we know the loop executes a 2681/// constant number of times, and the PHI node is just a recurrence 2682/// involving constants, fold it. 2683Constant *ScalarEvolution:: 2684getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){ 2685 std::map<PHINode*, Constant*>::iterator I = 2686 ConstantEvolutionLoopExitValue.find(PN); 2687 if (I != ConstantEvolutionLoopExitValue.end()) 2688 return I->second; 2689 2690 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 2691 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 2692 2693 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 2694 2695 // Since the loop is canonicalized, the PHI node must have two entries. One 2696 // entry must be a constant (coming in from outside of the loop), and the 2697 // second must be derived from the same PHI. 2698 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2699 Constant *StartCST = 2700 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2701 if (StartCST == 0) 2702 return RetVal = 0; // Must be a constant. 2703 2704 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2705 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2706 if (PN2 != PN) 2707 return RetVal = 0; // Not derived from same PHI. 2708 2709 // Execute the loop symbolically to determine the exit value. 2710 if (BEs.getActiveBits() >= 32) 2711 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 2712 2713 unsigned NumIterations = BEs.getZExtValue(); // must be in range 2714 unsigned IterationNum = 0; 2715 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 2716 if (IterationNum == NumIterations) 2717 return RetVal = PHIVal; // Got exit value! 2718 2719 // Compute the value of the PHI node for the next iteration. 2720 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2721 if (NextPHI == PHIVal) 2722 return RetVal = NextPHI; // Stopped evolving! 2723 if (NextPHI == 0) 2724 return 0; // Couldn't evaluate! 2725 PHIVal = NextPHI; 2726 } 2727} 2728 2729/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 2730/// constant number of times (the condition evolves only from constants), 2731/// try to evaluate a few iterations of the loop until we get the exit 2732/// condition gets a value of ExitWhen (true or false). If we cannot 2733/// evaluate the trip count of the loop, return UnknownValue. 2734SCEVHandle ScalarEvolution:: 2735ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { 2736 PHINode *PN = getConstantEvolvingPHI(Cond, L); 2737 if (PN == 0) return UnknownValue; 2738 2739 // Since the loop is canonicalized, the PHI node must have two entries. One 2740 // entry must be a constant (coming in from outside of the loop), and the 2741 // second must be derived from the same PHI. 2742 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 2743 Constant *StartCST = 2744 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 2745 if (StartCST == 0) return UnknownValue; // Must be a constant. 2746 2747 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 2748 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 2749 if (PN2 != PN) return UnknownValue; // Not derived from same PHI. 2750 2751 // Okay, we find a PHI node that defines the trip count of this loop. Execute 2752 // the loop symbolically to determine when the condition gets a value of 2753 // "ExitWhen". 2754 unsigned IterationNum = 0; 2755 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 2756 for (Constant *PHIVal = StartCST; 2757 IterationNum != MaxIterations; ++IterationNum) { 2758 ConstantInt *CondVal = 2759 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 2760 2761 // Couldn't symbolically evaluate. 2762 if (!CondVal) return UnknownValue; 2763 2764 if (CondVal->getValue() == uint64_t(ExitWhen)) { 2765 ConstantEvolutionLoopExitValue[PN] = PHIVal; 2766 ++NumBruteForceTripCountsComputed; 2767 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum)); 2768 } 2769 2770 // Compute the value of the PHI node for the next iteration. 2771 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 2772 if (NextPHI == 0 || NextPHI == PHIVal) 2773 return UnknownValue; // Couldn't evaluate or not making progress... 2774 PHIVal = NextPHI; 2775 } 2776 2777 // Too many iterations were needed to evaluate. 2778 return UnknownValue; 2779} 2780 2781/// getSCEVAtScope - Return a SCEV expression handle for the specified value 2782/// at the specified scope in the program. The L value specifies a loop 2783/// nest to evaluate the expression at, where null is the top-level or a 2784/// specified loop is immediately inside of the loop. 2785/// 2786/// This method can be used to compute the exit value for a variable defined 2787/// in a loop by querying what the value will hold in the parent loop. 2788/// 2789/// If this value is not computable at this scope, a SCEVCouldNotCompute 2790/// object is returned. 2791SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 2792 // FIXME: this should be turned into a virtual method on SCEV! 2793 2794 if (isa<SCEVConstant>(V)) return V; 2795 2796 // If this instruction is evolved from a constant-evolving PHI, compute the 2797 // exit value from the loop without using SCEVs. 2798 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 2799 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 2800 const Loop *LI = (*this->LI)[I->getParent()]; 2801 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 2802 if (PHINode *PN = dyn_cast<PHINode>(I)) 2803 if (PN->getParent() == LI->getHeader()) { 2804 // Okay, there is no closed form solution for the PHI node. Check 2805 // to see if the loop that contains it has a known backedge-taken 2806 // count. If so, we may be able to force computation of the exit 2807 // value. 2808 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI); 2809 if (const SCEVConstant *BTCC = 2810 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 2811 // Okay, we know how many times the containing loop executes. If 2812 // this is a constant evolving PHI node, get the final value at 2813 // the specified iteration number. 2814 Constant *RV = getConstantEvolutionLoopExitValue(PN, 2815 BTCC->getValue()->getValue(), 2816 LI); 2817 if (RV) return getUnknown(RV); 2818 } 2819 } 2820 2821 // Okay, this is an expression that we cannot symbolically evaluate 2822 // into a SCEV. Check to see if it's possible to symbolically evaluate 2823 // the arguments into constants, and if so, try to constant propagate the 2824 // result. This is particularly useful for computing loop exit values. 2825 if (CanConstantFold(I)) { 2826 // Check to see if we've folded this instruction at this loop before. 2827 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 2828 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 2829 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 2830 if (!Pair.second) 2831 return Pair.first->second ? &*getUnknown(Pair.first->second) : V; 2832 2833 std::vector<Constant*> Operands; 2834 Operands.reserve(I->getNumOperands()); 2835 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 2836 Value *Op = I->getOperand(i); 2837 if (Constant *C = dyn_cast<Constant>(Op)) { 2838 Operands.push_back(C); 2839 } else { 2840 // If any of the operands is non-constant and if they are 2841 // non-integer and non-pointer, don't even try to analyze them 2842 // with scev techniques. 2843 if (!isSCEVable(Op->getType())) 2844 return V; 2845 2846 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L); 2847 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 2848 Constant *C = SC->getValue(); 2849 if (C->getType() != Op->getType()) 2850 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2851 Op->getType(), 2852 false), 2853 C, Op->getType()); 2854 Operands.push_back(C); 2855 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 2856 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 2857 if (C->getType() != Op->getType()) 2858 C = 2859 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 2860 Op->getType(), 2861 false), 2862 C, Op->getType()); 2863 Operands.push_back(C); 2864 } else 2865 return V; 2866 } else { 2867 return V; 2868 } 2869 } 2870 } 2871 2872 Constant *C; 2873 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 2874 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 2875 &Operands[0], Operands.size()); 2876 else 2877 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 2878 &Operands[0], Operands.size()); 2879 Pair.first->second = C; 2880 return getUnknown(C); 2881 } 2882 } 2883 2884 // This is some other type of SCEVUnknown, just return it. 2885 return V; 2886 } 2887 2888 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 2889 // Avoid performing the look-up in the common case where the specified 2890 // expression has no loop-variant portions. 2891 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 2892 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2893 if (OpAtScope != Comm->getOperand(i)) { 2894 if (OpAtScope == UnknownValue) return UnknownValue; 2895 // Okay, at least one of these operands is loop variant but might be 2896 // foldable. Build a new instance of the folded commutative expression. 2897 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i); 2898 NewOps.push_back(OpAtScope); 2899 2900 for (++i; i != e; ++i) { 2901 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 2902 if (OpAtScope == UnknownValue) return UnknownValue; 2903 NewOps.push_back(OpAtScope); 2904 } 2905 if (isa<SCEVAddExpr>(Comm)) 2906 return getAddExpr(NewOps); 2907 if (isa<SCEVMulExpr>(Comm)) 2908 return getMulExpr(NewOps); 2909 if (isa<SCEVSMaxExpr>(Comm)) 2910 return getSMaxExpr(NewOps); 2911 if (isa<SCEVUMaxExpr>(Comm)) 2912 return getUMaxExpr(NewOps); 2913 assert(0 && "Unknown commutative SCEV type!"); 2914 } 2915 } 2916 // If we got here, all operands are loop invariant. 2917 return Comm; 2918 } 2919 2920 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 2921 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L); 2922 if (LHS == UnknownValue) return LHS; 2923 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L); 2924 if (RHS == UnknownValue) return RHS; 2925 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 2926 return Div; // must be loop invariant 2927 return getUDivExpr(LHS, RHS); 2928 } 2929 2930 // If this is a loop recurrence for a loop that does not contain L, then we 2931 // are dealing with the final value computed by the loop. 2932 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 2933 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 2934 // To evaluate this recurrence, we need to know how many times the AddRec 2935 // loop iterates. Compute this now. 2936 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 2937 if (BackedgeTakenCount == UnknownValue) return UnknownValue; 2938 2939 // Then, evaluate the AddRec. 2940 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 2941 } 2942 return UnknownValue; 2943 } 2944 2945 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 2946 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2947 if (Op == UnknownValue) return Op; 2948 if (Op == Cast->getOperand()) 2949 return Cast; // must be loop invariant 2950 return getZeroExtendExpr(Op, Cast->getType()); 2951 } 2952 2953 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 2954 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2955 if (Op == UnknownValue) return Op; 2956 if (Op == Cast->getOperand()) 2957 return Cast; // must be loop invariant 2958 return getSignExtendExpr(Op, Cast->getType()); 2959 } 2960 2961 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 2962 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L); 2963 if (Op == UnknownValue) return Op; 2964 if (Op == Cast->getOperand()) 2965 return Cast; // must be loop invariant 2966 return getTruncateExpr(Op, Cast->getType()); 2967 } 2968 2969 assert(0 && "Unknown SCEV type!"); 2970} 2971 2972/// getSCEVAtScope - This is a convenience function which does 2973/// getSCEVAtScope(getSCEV(V), L). 2974SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 2975 return getSCEVAtScope(getSCEV(V), L); 2976} 2977 2978/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 2979/// following equation: 2980/// 2981/// A * X = B (mod N) 2982/// 2983/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 2984/// A and B isn't important. 2985/// 2986/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 2987static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 2988 ScalarEvolution &SE) { 2989 uint32_t BW = A.getBitWidth(); 2990 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 2991 assert(A != 0 && "A must be non-zero."); 2992 2993 // 1. D = gcd(A, N) 2994 // 2995 // The gcd of A and N may have only one prime factor: 2. The number of 2996 // trailing zeros in A is its multiplicity 2997 uint32_t Mult2 = A.countTrailingZeros(); 2998 // D = 2^Mult2 2999 3000 // 2. Check if B is divisible by D. 3001 // 3002 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3003 // is not less than multiplicity of this prime factor for D. 3004 if (B.countTrailingZeros() < Mult2) 3005 return SE.getCouldNotCompute(); 3006 3007 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3008 // modulo (N / D). 3009 // 3010 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3011 // bit width during computations. 3012 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3013 APInt Mod(BW + 1, 0); 3014 Mod.set(BW - Mult2); // Mod = N / D 3015 APInt I = AD.multiplicativeInverse(Mod); 3016 3017 // 4. Compute the minimum unsigned root of the equation: 3018 // I * (B / D) mod (N / D) 3019 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 3020 3021 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 3022 // bits. 3023 return SE.getConstant(Result.trunc(BW)); 3024} 3025 3026/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 3027/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 3028/// might be the same) or two SCEVCouldNotCompute objects. 3029/// 3030static std::pair<SCEVHandle,SCEVHandle> 3031SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 3032 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 3033 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 3034 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 3035 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 3036 3037 // We currently can only solve this if the coefficients are constants. 3038 if (!LC || !MC || !NC) { 3039 const SCEV *CNC = SE.getCouldNotCompute(); 3040 return std::make_pair(CNC, CNC); 3041 } 3042 3043 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 3044 const APInt &L = LC->getValue()->getValue(); 3045 const APInt &M = MC->getValue()->getValue(); 3046 const APInt &N = NC->getValue()->getValue(); 3047 APInt Two(BitWidth, 2); 3048 APInt Four(BitWidth, 4); 3049 3050 { 3051 using namespace APIntOps; 3052 const APInt& C = L; 3053 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 3054 // The B coefficient is M-N/2 3055 APInt B(M); 3056 B -= sdiv(N,Two); 3057 3058 // The A coefficient is N/2 3059 APInt A(N.sdiv(Two)); 3060 3061 // Compute the B^2-4ac term. 3062 APInt SqrtTerm(B); 3063 SqrtTerm *= B; 3064 SqrtTerm -= Four * (A * C); 3065 3066 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 3067 // integer value or else APInt::sqrt() will assert. 3068 APInt SqrtVal(SqrtTerm.sqrt()); 3069 3070 // Compute the two solutions for the quadratic formula. 3071 // The divisions must be performed as signed divisions. 3072 APInt NegB(-B); 3073 APInt TwoA( A << 1 ); 3074 if (TwoA.isMinValue()) { 3075 const SCEV *CNC = SE.getCouldNotCompute(); 3076 return std::make_pair(CNC, CNC); 3077 } 3078 3079 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 3080 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 3081 3082 return std::make_pair(SE.getConstant(Solution1), 3083 SE.getConstant(Solution2)); 3084 } // end APIntOps namespace 3085} 3086 3087/// HowFarToZero - Return the number of times a backedge comparing the specified 3088/// value to zero will execute. If not computable, return UnknownValue 3089SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 3090 // If the value is a constant 3091 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3092 // If the value is already zero, the branch will execute zero times. 3093 if (C->getValue()->isZero()) return C; 3094 return UnknownValue; // Otherwise it will loop infinitely. 3095 } 3096 3097 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 3098 if (!AddRec || AddRec->getLoop() != L) 3099 return UnknownValue; 3100 3101 if (AddRec->isAffine()) { 3102 // If this is an affine expression, the execution count of this branch is 3103 // the minimum unsigned root of the following equation: 3104 // 3105 // Start + Step*N = 0 (mod 2^BW) 3106 // 3107 // equivalent to: 3108 // 3109 // Step*N = -Start (mod 2^BW) 3110 // 3111 // where BW is the common bit width of Start and Step. 3112 3113 // Get the initial value for the loop. 3114 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 3115 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue; 3116 3117 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 3118 3119 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 3120 // For now we handle only constant steps. 3121 3122 // First, handle unitary steps. 3123 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 3124 return getNegativeSCEV(Start); // N = -Start (as unsigned) 3125 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 3126 return Start; // N = Start (as unsigned) 3127 3128 // Then, try to solve the above equation provided that Start is constant. 3129 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 3130 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 3131 -StartC->getValue()->getValue(), 3132 *this); 3133 } 3134 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 3135 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 3136 // the quadratic equation to solve it. 3137 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, 3138 *this); 3139 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3140 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3141 if (R1) { 3142#if 0 3143 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 3144 << " sol#2: " << *R2 << "\n"; 3145#endif 3146 // Pick the smallest positive root value. 3147 if (ConstantInt *CB = 3148 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3149 R1->getValue(), R2->getValue()))) { 3150 if (CB->getZExtValue() == false) 3151 std::swap(R1, R2); // R1 is the minimum root now. 3152 3153 // We can only use this value if the chrec ends up with an exact zero 3154 // value at this index. When solving for "X*X != 5", for example, we 3155 // should not accept a root of 2. 3156 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this); 3157 if (Val->isZero()) 3158 return R1; // We found a quadratic root! 3159 } 3160 } 3161 } 3162 3163 return UnknownValue; 3164} 3165 3166/// HowFarToNonZero - Return the number of times a backedge checking the 3167/// specified value for nonzero will execute. If not computable, return 3168/// UnknownValue 3169SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 3170 // Loops that look like: while (X == 0) are very strange indeed. We don't 3171 // handle them yet except for the trivial case. This could be expanded in the 3172 // future as needed. 3173 3174 // If the value is a constant, check to see if it is known to be non-zero 3175 // already. If so, the backedge will execute zero times. 3176 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3177 if (!C->getValue()->isNullValue()) 3178 return getIntegerSCEV(0, C->getType()); 3179 return UnknownValue; // Otherwise it will loop infinitely. 3180 } 3181 3182 // We could implement others, but I really doubt anyone writes loops like 3183 // this, and if they did, they would already be constant folded. 3184 return UnknownValue; 3185} 3186 3187/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 3188/// (which may not be an immediate predecessor) which has exactly one 3189/// successor from which BB is reachable, or null if no such block is 3190/// found. 3191/// 3192BasicBlock * 3193ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 3194 // If the block has a unique predecessor, then there is no path from the 3195 // predecessor to the block that does not go through the direct edge 3196 // from the predecessor to the block. 3197 if (BasicBlock *Pred = BB->getSinglePredecessor()) 3198 return Pred; 3199 3200 // A loop's header is defined to be a block that dominates the loop. 3201 // If the loop has a preheader, it must be a block that has exactly 3202 // one successor that can reach BB. This is slightly more strict 3203 // than necessary, but works if critical edges are split. 3204 if (Loop *L = LI->getLoopFor(BB)) 3205 return L->getLoopPreheader(); 3206 3207 return 0; 3208} 3209 3210/// isLoopGuardedByCond - Test whether entry to the loop is protected by 3211/// a conditional between LHS and RHS. This is used to help avoid max 3212/// expressions in loop trip counts. 3213bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 3214 ICmpInst::Predicate Pred, 3215 const SCEV *LHS, const SCEV *RHS) { 3216 BasicBlock *Preheader = L->getLoopPreheader(); 3217 BasicBlock *PreheaderDest = L->getHeader(); 3218 3219 // Starting at the preheader, climb up the predecessor chain, as long as 3220 // there are predecessors that can be found that have unique successors 3221 // leading to the original header. 3222 for (; Preheader; 3223 PreheaderDest = Preheader, 3224 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) { 3225 3226 BranchInst *LoopEntryPredicate = 3227 dyn_cast<BranchInst>(Preheader->getTerminator()); 3228 if (!LoopEntryPredicate || 3229 LoopEntryPredicate->isUnconditional()) 3230 continue; 3231 3232 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition()); 3233 if (!ICI) continue; 3234 3235 // Now that we found a conditional branch that dominates the loop, check to 3236 // see if it is the comparison we are looking for. 3237 Value *PreCondLHS = ICI->getOperand(0); 3238 Value *PreCondRHS = ICI->getOperand(1); 3239 ICmpInst::Predicate Cond; 3240 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest) 3241 Cond = ICI->getPredicate(); 3242 else 3243 Cond = ICI->getInversePredicate(); 3244 3245 if (Cond == Pred) 3246 ; // An exact match. 3247 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 3248 ; // The actual condition is beyond sufficient. 3249 else 3250 // Check a few special cases. 3251 switch (Cond) { 3252 case ICmpInst::ICMP_UGT: 3253 if (Pred == ICmpInst::ICMP_ULT) { 3254 std::swap(PreCondLHS, PreCondRHS); 3255 Cond = ICmpInst::ICMP_ULT; 3256 break; 3257 } 3258 continue; 3259 case ICmpInst::ICMP_SGT: 3260 if (Pred == ICmpInst::ICMP_SLT) { 3261 std::swap(PreCondLHS, PreCondRHS); 3262 Cond = ICmpInst::ICMP_SLT; 3263 break; 3264 } 3265 continue; 3266 case ICmpInst::ICMP_NE: 3267 // Expressions like (x >u 0) are often canonicalized to (x != 0), 3268 // so check for this case by checking if the NE is comparing against 3269 // a minimum or maximum constant. 3270 if (!ICmpInst::isTrueWhenEqual(Pred)) 3271 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 3272 const APInt &A = CI->getValue(); 3273 switch (Pred) { 3274 case ICmpInst::ICMP_SLT: 3275 if (A.isMaxSignedValue()) break; 3276 continue; 3277 case ICmpInst::ICMP_SGT: 3278 if (A.isMinSignedValue()) break; 3279 continue; 3280 case ICmpInst::ICMP_ULT: 3281 if (A.isMaxValue()) break; 3282 continue; 3283 case ICmpInst::ICMP_UGT: 3284 if (A.isMinValue()) break; 3285 continue; 3286 default: 3287 continue; 3288 } 3289 Cond = ICmpInst::ICMP_NE; 3290 // NE is symmetric but the original comparison may not be. Swap 3291 // the operands if necessary so that they match below. 3292 if (isa<SCEVConstant>(LHS)) 3293 std::swap(PreCondLHS, PreCondRHS); 3294 break; 3295 } 3296 continue; 3297 default: 3298 // We weren't able to reconcile the condition. 3299 continue; 3300 } 3301 3302 if (!PreCondLHS->getType()->isInteger()) continue; 3303 3304 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS); 3305 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS); 3306 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) || 3307 (LHS == getNotSCEV(PreCondRHSSCEV) && 3308 RHS == getNotSCEV(PreCondLHSSCEV))) 3309 return true; 3310 } 3311 3312 return false; 3313} 3314 3315/// HowManyLessThans - Return the number of times a backedge containing the 3316/// specified less-than comparison will execute. If not computable, return 3317/// UnknownValue. 3318ScalarEvolution::BackedgeTakenInfo ScalarEvolution:: 3319HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 3320 const Loop *L, bool isSigned) { 3321 // Only handle: "ADDREC < LoopInvariant". 3322 if (!RHS->isLoopInvariant(L)) return UnknownValue; 3323 3324 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 3325 if (!AddRec || AddRec->getLoop() != L) 3326 return UnknownValue; 3327 3328 if (AddRec->isAffine()) { 3329 // FORNOW: We only support unit strides. 3330 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 3331 SCEVHandle Step = AddRec->getStepRecurrence(*this); 3332 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType()); 3333 3334 // TODO: handle non-constant strides. 3335 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 3336 if (!CStep || CStep->isZero()) 3337 return UnknownValue; 3338 if (CStep->getValue()->getValue() == 1) { 3339 // With unit stride, the iteration never steps past the limit value. 3340 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 3341 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 3342 // Test whether a positive iteration iteration can step past the limit 3343 // value and past the maximum value for its type in a single step. 3344 if (isSigned) { 3345 APInt Max = APInt::getSignedMaxValue(BitWidth); 3346 if ((Max - CStep->getValue()->getValue()) 3347 .slt(CLimit->getValue()->getValue())) 3348 return UnknownValue; 3349 } else { 3350 APInt Max = APInt::getMaxValue(BitWidth); 3351 if ((Max - CStep->getValue()->getValue()) 3352 .ult(CLimit->getValue()->getValue())) 3353 return UnknownValue; 3354 } 3355 } else 3356 // TODO: handle non-constant limit values below. 3357 return UnknownValue; 3358 } else 3359 // TODO: handle negative strides below. 3360 return UnknownValue; 3361 3362 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 3363 // m. So, we count the number of iterations in which {n,+,s} < m is true. 3364 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 3365 // treat m-n as signed nor unsigned due to overflow possibility. 3366 3367 // First, we get the value of the LHS in the first iteration: n 3368 SCEVHandle Start = AddRec->getOperand(0); 3369 3370 // Determine the minimum constant start value. 3371 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start : 3372 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 3373 APInt::getMinValue(BitWidth)); 3374 3375 // If we know that the condition is true in order to enter the loop, 3376 // then we know that it will run exactly (m-n)/s times. Otherwise, we 3377 // only know if will execute (max(m,n)-n)/s times. In both cases, the 3378 // division must round up. 3379 SCEVHandle End = RHS; 3380 if (!isLoopGuardedByCond(L, 3381 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 3382 getMinusSCEV(Start, Step), RHS)) 3383 End = isSigned ? getSMaxExpr(RHS, Start) 3384 : getUMaxExpr(RHS, Start); 3385 3386 // Determine the maximum constant end value. 3387 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End : 3388 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) : 3389 APInt::getMaxValue(BitWidth)); 3390 3391 // Finally, we subtract these two values and divide, rounding up, to get 3392 // the number of times the backedge is executed. 3393 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start), 3394 getAddExpr(Step, NegOne)), 3395 Step); 3396 3397 // The maximum backedge count is similar, except using the minimum start 3398 // value and the maximum end value. 3399 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd, 3400 MinStart), 3401 getAddExpr(Step, NegOne)), 3402 Step); 3403 3404 return BackedgeTakenInfo(BECount, MaxBECount); 3405 } 3406 3407 return UnknownValue; 3408} 3409 3410/// getNumIterationsInRange - Return the number of iterations of this loop that 3411/// produce values in the specified constant range. Another way of looking at 3412/// this is that it returns the first iteration number where the value is not in 3413/// the condition, thus computing the exit count. If the iteration count can't 3414/// be computed, an instance of SCEVCouldNotCompute is returned. 3415SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 3416 ScalarEvolution &SE) const { 3417 if (Range.isFullSet()) // Infinite loop. 3418 return SE.getCouldNotCompute(); 3419 3420 // If the start is a non-zero constant, shift the range to simplify things. 3421 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 3422 if (!SC->getValue()->isZero()) { 3423 std::vector<SCEVHandle> Operands(op_begin(), op_end()); 3424 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 3425 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop()); 3426 if (const SCEVAddRecExpr *ShiftedAddRec = 3427 dyn_cast<SCEVAddRecExpr>(Shifted)) 3428 return ShiftedAddRec->getNumIterationsInRange( 3429 Range.subtract(SC->getValue()->getValue()), SE); 3430 // This is strange and shouldn't happen. 3431 return SE.getCouldNotCompute(); 3432 } 3433 3434 // The only time we can solve this is when we have all constant indices. 3435 // Otherwise, we cannot determine the overflow conditions. 3436 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 3437 if (!isa<SCEVConstant>(getOperand(i))) 3438 return SE.getCouldNotCompute(); 3439 3440 3441 // Okay at this point we know that all elements of the chrec are constants and 3442 // that the start element is zero. 3443 3444 // First check to see if the range contains zero. If not, the first 3445 // iteration exits. 3446 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 3447 if (!Range.contains(APInt(BitWidth, 0))) 3448 return SE.getConstant(ConstantInt::get(getType(),0)); 3449 3450 if (isAffine()) { 3451 // If this is an affine expression then we have this situation: 3452 // Solve {0,+,A} in Range === Ax in Range 3453 3454 // We know that zero is in the range. If A is positive then we know that 3455 // the upper value of the range must be the first possible exit value. 3456 // If A is negative then the lower of the range is the last possible loop 3457 // value. Also note that we already checked for a full range. 3458 APInt One(BitWidth,1); 3459 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 3460 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 3461 3462 // The exit value should be (End+A)/A. 3463 APInt ExitVal = (End + A).udiv(A); 3464 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 3465 3466 // Evaluate at the exit value. If we really did fall out of the valid 3467 // range, then we computed our trip count, otherwise wrap around or other 3468 // things must have happened. 3469 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 3470 if (Range.contains(Val->getValue())) 3471 return SE.getCouldNotCompute(); // Something strange happened 3472 3473 // Ensure that the previous value is in the range. This is a sanity check. 3474 assert(Range.contains( 3475 EvaluateConstantChrecAtConstant(this, 3476 ConstantInt::get(ExitVal - One), SE)->getValue()) && 3477 "Linear scev computation is off in a bad way!"); 3478 return SE.getConstant(ExitValue); 3479 } else if (isQuadratic()) { 3480 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 3481 // quadratic equation to solve it. To do this, we must frame our problem in 3482 // terms of figuring out when zero is crossed, instead of when 3483 // Range.getUpper() is crossed. 3484 std::vector<SCEVHandle> NewOps(op_begin(), op_end()); 3485 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 3486 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 3487 3488 // Next, solve the constructed addrec 3489 std::pair<SCEVHandle,SCEVHandle> Roots = 3490 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 3491 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3492 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3493 if (R1) { 3494 // Pick the smallest positive root value. 3495 if (ConstantInt *CB = 3496 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3497 R1->getValue(), R2->getValue()))) { 3498 if (CB->getZExtValue() == false) 3499 std::swap(R1, R2); // R1 is the minimum root now. 3500 3501 // Make sure the root is not off by one. The returned iteration should 3502 // not be in the range, but the previous one should be. When solving 3503 // for "X*X < 5", for example, we should not return a root of 2. 3504 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 3505 R1->getValue(), 3506 SE); 3507 if (Range.contains(R1Val->getValue())) { 3508 // The next iteration must be out of the range... 3509 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 3510 3511 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3512 if (!Range.contains(R1Val->getValue())) 3513 return SE.getConstant(NextVal); 3514 return SE.getCouldNotCompute(); // Something strange happened 3515 } 3516 3517 // If R1 was not in the range, then it is a good return value. Make 3518 // sure that R1-1 WAS in the range though, just in case. 3519 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 3520 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 3521 if (Range.contains(R1Val->getValue())) 3522 return R1; 3523 return SE.getCouldNotCompute(); // Something strange happened 3524 } 3525 } 3526 } 3527 3528 return SE.getCouldNotCompute(); 3529} 3530 3531 3532 3533//===----------------------------------------------------------------------===// 3534// SCEVCallbackVH Class Implementation 3535//===----------------------------------------------------------------------===// 3536 3537void SCEVCallbackVH::deleted() { 3538 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 3539 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 3540 SE->ConstantEvolutionLoopExitValue.erase(PN); 3541 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 3542 SE->ValuesAtScopes.erase(I); 3543 SE->Scalars.erase(getValPtr()); 3544 // this now dangles! 3545} 3546 3547void SCEVCallbackVH::allUsesReplacedWith(Value *) { 3548 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 3549 3550 // Forget all the expressions associated with users of the old value, 3551 // so that future queries will recompute the expressions using the new 3552 // value. 3553 SmallVector<User *, 16> Worklist; 3554 Value *Old = getValPtr(); 3555 bool DeleteOld = false; 3556 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 3557 UI != UE; ++UI) 3558 Worklist.push_back(*UI); 3559 while (!Worklist.empty()) { 3560 User *U = Worklist.pop_back_val(); 3561 // Deleting the Old value will cause this to dangle. Postpone 3562 // that until everything else is done. 3563 if (U == Old) { 3564 DeleteOld = true; 3565 continue; 3566 } 3567 if (PHINode *PN = dyn_cast<PHINode>(U)) 3568 SE->ConstantEvolutionLoopExitValue.erase(PN); 3569 if (Instruction *I = dyn_cast<Instruction>(U)) 3570 SE->ValuesAtScopes.erase(I); 3571 if (SE->Scalars.erase(U)) 3572 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 3573 UI != UE; ++UI) 3574 Worklist.push_back(*UI); 3575 } 3576 if (DeleteOld) { 3577 if (PHINode *PN = dyn_cast<PHINode>(Old)) 3578 SE->ConstantEvolutionLoopExitValue.erase(PN); 3579 if (Instruction *I = dyn_cast<Instruction>(Old)) 3580 SE->ValuesAtScopes.erase(I); 3581 SE->Scalars.erase(Old); 3582 // this now dangles! 3583 } 3584 // this may dangle! 3585} 3586 3587SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 3588 : CallbackVH(V), SE(se) {} 3589 3590//===----------------------------------------------------------------------===// 3591// ScalarEvolution Class Implementation 3592//===----------------------------------------------------------------------===// 3593 3594ScalarEvolution::ScalarEvolution() 3595 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) { 3596} 3597 3598bool ScalarEvolution::runOnFunction(Function &F) { 3599 this->F = &F; 3600 LI = &getAnalysis<LoopInfo>(); 3601 TD = getAnalysisIfAvailable<TargetData>(); 3602 return false; 3603} 3604 3605void ScalarEvolution::releaseMemory() { 3606 Scalars.clear(); 3607 BackedgeTakenCounts.clear(); 3608 ConstantEvolutionLoopExitValue.clear(); 3609 ValuesAtScopes.clear(); 3610} 3611 3612void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 3613 AU.setPreservesAll(); 3614 AU.addRequiredTransitive<LoopInfo>(); 3615} 3616 3617bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 3618 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 3619} 3620 3621static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 3622 const Loop *L) { 3623 // Print all inner loops first 3624 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3625 PrintLoopInfo(OS, SE, *I); 3626 3627 OS << "Loop " << L->getHeader()->getName() << ": "; 3628 3629 SmallVector<BasicBlock*, 8> ExitBlocks; 3630 L->getExitBlocks(ExitBlocks); 3631 if (ExitBlocks.size() != 1) 3632 OS << "<multiple exits> "; 3633 3634 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 3635 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 3636 } else { 3637 OS << "Unpredictable backedge-taken count. "; 3638 } 3639 3640 OS << "\n"; 3641} 3642 3643void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 3644 // ScalarEvolution's implementaiton of the print method is to print 3645 // out SCEV values of all instructions that are interesting. Doing 3646 // this potentially causes it to create new SCEV objects though, 3647 // which technically conflicts with the const qualifier. This isn't 3648 // observable from outside the class though (the hasSCEV function 3649 // notwithstanding), so casting away the const isn't dangerous. 3650 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 3651 3652 OS << "Classifying expressions for: " << F->getName() << "\n"; 3653 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 3654 if (isSCEVable(I->getType())) { 3655 OS << *I; 3656 OS << " --> "; 3657 SCEVHandle SV = SE.getSCEV(&*I); 3658 SV->print(OS); 3659 OS << "\t\t"; 3660 3661 if (const Loop *L = LI->getLoopFor((*I).getParent())) { 3662 OS << "Exits: "; 3663 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop()); 3664 if (isa<SCEVCouldNotCompute>(ExitValue)) { 3665 OS << "<<Unknown>>"; 3666 } else { 3667 OS << *ExitValue; 3668 } 3669 } 3670 3671 3672 OS << "\n"; 3673 } 3674 3675 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 3676 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 3677 PrintLoopInfo(OS, &SE, *I); 3678} 3679 3680void ScalarEvolution::print(std::ostream &o, const Module *M) const { 3681 raw_os_ostream OS(o); 3682 print(OS, M); 3683} 3684