ScalarEvolution.cpp revision 195340
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 const SCEV* 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/Analysis/ValueTracking.h" 72#include "llvm/Assembly/Writer.h" 73#include "llvm/Target/TargetData.h" 74#include "llvm/Support/CommandLine.h" 75#include "llvm/Support/Compiler.h" 76#include "llvm/Support/ConstantRange.h" 77#include "llvm/Support/GetElementPtrTypeIterator.h" 78#include "llvm/Support/InstIterator.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 <algorithm> 84using namespace llvm; 85 86STATISTIC(NumArrayLenItCounts, 87 "Number of trip counts computed with array length"); 88STATISTIC(NumTripCountsComputed, 89 "Number of loops with predictable loop counts"); 90STATISTIC(NumTripCountsNotComputed, 91 "Number of loops without predictable loop counts"); 92STATISTIC(NumBruteForceTripCountsComputed, 93 "Number of loops with trip counts computed by force"); 94 95static cl::opt<unsigned> 96MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 97 cl::desc("Maximum number of iterations SCEV will " 98 "symbolically execute a constant " 99 "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// 113 114SCEV::~SCEV() {} 115 116void SCEV::dump() const { 117 print(errs()); 118 errs() << '\n'; 119} 120 121void SCEV::print(std::ostream &o) const { 122 raw_os_ostream OS(o); 123 print(OS); 124} 125 126bool SCEV::isZero() const { 127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 128 return SC->getValue()->isZero(); 129 return false; 130} 131 132bool SCEV::isOne() const { 133 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 134 return SC->getValue()->isOne(); 135 return false; 136} 137 138bool SCEV::isAllOnesValue() const { 139 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 140 return SC->getValue()->isAllOnesValue(); 141 return false; 142} 143 144SCEVCouldNotCompute::SCEVCouldNotCompute() : 145 SCEV(scCouldNotCompute) {} 146 147void SCEVCouldNotCompute::Profile(FoldingSetNodeID &ID) const { 148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 149} 150 151bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 152 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 153 return false; 154} 155 156const Type *SCEVCouldNotCompute::getType() const { 157 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 158 return 0; 159} 160 161bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 162 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166const SCEV * 167SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete( 168 const SCEV *Sym, 169 const SCEV *Conc, 170 ScalarEvolution &SE) const { 171 return this; 172} 173 174void SCEVCouldNotCompute::print(raw_ostream &OS) const { 175 OS << "***COULDNOTCOMPUTE***"; 176} 177 178bool SCEVCouldNotCompute::classof(const SCEV *S) { 179 return S->getSCEVType() == scCouldNotCompute; 180} 181 182const SCEV* ScalarEvolution::getConstant(ConstantInt *V) { 183 FoldingSetNodeID ID; 184 ID.AddInteger(scConstant); 185 ID.AddPointer(V); 186 void *IP = 0; 187 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 188 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 189 new (S) SCEVConstant(V); 190 UniqueSCEVs.InsertNode(S, IP); 191 return S; 192} 193 194const SCEV* ScalarEvolution::getConstant(const APInt& Val) { 195 return getConstant(ConstantInt::get(Val)); 196} 197 198const SCEV* 199ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 200 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 201} 202 203void SCEVConstant::Profile(FoldingSetNodeID &ID) const { 204 ID.AddInteger(scConstant); 205 ID.AddPointer(V); 206} 207 208const Type *SCEVConstant::getType() const { return V->getType(); } 209 210void SCEVConstant::print(raw_ostream &OS) const { 211 WriteAsOperand(OS, V, false); 212} 213 214SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy, 215 const SCEV* op, const Type *ty) 216 : SCEV(SCEVTy), Op(op), Ty(ty) {} 217 218void SCEVCastExpr::Profile(FoldingSetNodeID &ID) const { 219 ID.AddInteger(getSCEVType()); 220 ID.AddPointer(Op); 221 ID.AddPointer(Ty); 222} 223 224bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 225 return Op->dominates(BB, DT); 226} 227 228SCEVTruncateExpr::SCEVTruncateExpr(const SCEV* op, const Type *ty) 229 : SCEVCastExpr(scTruncate, op, ty) { 230 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 231 (Ty->isInteger() || isa<PointerType>(Ty)) && 232 "Cannot truncate non-integer value!"); 233} 234 235void SCEVTruncateExpr::print(raw_ostream &OS) const { 236 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 237} 238 239SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEV* op, const Type *ty) 240 : SCEVCastExpr(scZeroExtend, op, ty) { 241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 242 (Ty->isInteger() || isa<PointerType>(Ty)) && 243 "Cannot zero extend non-integer value!"); 244} 245 246void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 247 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 248} 249 250SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEV* op, const Type *ty) 251 : SCEVCastExpr(scSignExtend, op, ty) { 252 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 253 (Ty->isInteger() || isa<PointerType>(Ty)) && 254 "Cannot sign extend non-integer value!"); 255} 256 257void SCEVSignExtendExpr::print(raw_ostream &OS) const { 258 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 259} 260 261void SCEVCommutativeExpr::print(raw_ostream &OS) const { 262 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 263 const char *OpStr = getOperationStr(); 264 OS << "(" << *Operands[0]; 265 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 266 OS << OpStr << *Operands[i]; 267 OS << ")"; 268} 269 270const SCEV * 271SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete( 272 const SCEV *Sym, 273 const SCEV *Conc, 274 ScalarEvolution &SE) const { 275 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 276 const SCEV* H = 277 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 278 if (H != getOperand(i)) { 279 SmallVector<const SCEV*, 8> NewOps; 280 NewOps.reserve(getNumOperands()); 281 for (unsigned j = 0; j != i; ++j) 282 NewOps.push_back(getOperand(j)); 283 NewOps.push_back(H); 284 for (++i; i != e; ++i) 285 NewOps.push_back(getOperand(i)-> 286 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 287 288 if (isa<SCEVAddExpr>(this)) 289 return SE.getAddExpr(NewOps); 290 else if (isa<SCEVMulExpr>(this)) 291 return SE.getMulExpr(NewOps); 292 else if (isa<SCEVSMaxExpr>(this)) 293 return SE.getSMaxExpr(NewOps); 294 else if (isa<SCEVUMaxExpr>(this)) 295 return SE.getUMaxExpr(NewOps); 296 else 297 assert(0 && "Unknown commutative expr!"); 298 } 299 } 300 return this; 301} 302 303void SCEVNAryExpr::Profile(FoldingSetNodeID &ID) const { 304 ID.AddInteger(getSCEVType()); 305 ID.AddInteger(Operands.size()); 306 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 307 ID.AddPointer(Operands[i]); 308} 309 310bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 311 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 312 if (!getOperand(i)->dominates(BB, DT)) 313 return false; 314 } 315 return true; 316} 317 318void SCEVUDivExpr::Profile(FoldingSetNodeID &ID) const { 319 ID.AddInteger(scUDivExpr); 320 ID.AddPointer(LHS); 321 ID.AddPointer(RHS); 322} 323 324bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 325 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 326} 327 328void SCEVUDivExpr::print(raw_ostream &OS) const { 329 OS << "(" << *LHS << " /u " << *RHS << ")"; 330} 331 332const Type *SCEVUDivExpr::getType() const { 333 // In most cases the types of LHS and RHS will be the same, but in some 334 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 335 // depend on the type for correctness, but handling types carefully can 336 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 337 // a pointer type than the RHS, so use the RHS' type here. 338 return RHS->getType(); 339} 340 341void SCEVAddRecExpr::Profile(FoldingSetNodeID &ID) const { 342 ID.AddInteger(scAddRecExpr); 343 ID.AddInteger(Operands.size()); 344 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 345 ID.AddPointer(Operands[i]); 346 ID.AddPointer(L); 347} 348 349const SCEV * 350SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym, 351 const SCEV *Conc, 352 ScalarEvolution &SE) const { 353 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 354 const SCEV* H = 355 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 356 if (H != getOperand(i)) { 357 SmallVector<const SCEV*, 8> NewOps; 358 NewOps.reserve(getNumOperands()); 359 for (unsigned j = 0; j != i; ++j) 360 NewOps.push_back(getOperand(j)); 361 NewOps.push_back(H); 362 for (++i; i != e; ++i) 363 NewOps.push_back(getOperand(i)-> 364 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 365 366 return SE.getAddRecExpr(NewOps, L); 367 } 368 } 369 return this; 370} 371 372 373bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 374 // Add recurrences are never invariant in the function-body (null loop). 375 if (!QueryLoop) 376 return false; 377 378 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 379 if (QueryLoop->contains(L->getHeader())) 380 return false; 381 382 // This recurrence is variant w.r.t. QueryLoop if any of its operands 383 // are variant. 384 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 385 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 386 return false; 387 388 // Otherwise it's loop-invariant. 389 return true; 390} 391 392void SCEVAddRecExpr::print(raw_ostream &OS) const { 393 OS << "{" << *Operands[0]; 394 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 395 OS << ",+," << *Operands[i]; 396 OS << "}<" << L->getHeader()->getName() + ">"; 397} 398 399void SCEVUnknown::Profile(FoldingSetNodeID &ID) const { 400 ID.AddInteger(scUnknown); 401 ID.AddPointer(V); 402} 403 404bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 405 // All non-instruction values are loop invariant. All instructions are loop 406 // invariant if they are not contained in the specified loop. 407 // Instructions are never considered invariant in the function body 408 // (null loop) because they are defined within the "loop". 409 if (Instruction *I = dyn_cast<Instruction>(V)) 410 return L && !L->contains(I->getParent()); 411 return true; 412} 413 414bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 415 if (Instruction *I = dyn_cast<Instruction>(getValue())) 416 return DT->dominates(I->getParent(), BB); 417 return true; 418} 419 420const Type *SCEVUnknown::getType() const { 421 return V->getType(); 422} 423 424void SCEVUnknown::print(raw_ostream &OS) const { 425 WriteAsOperand(OS, V, false); 426} 427 428//===----------------------------------------------------------------------===// 429// SCEV Utilities 430//===----------------------------------------------------------------------===// 431 432namespace { 433 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 434 /// than the complexity of the RHS. This comparator is used to canonicalize 435 /// expressions. 436 class VISIBILITY_HIDDEN SCEVComplexityCompare { 437 LoopInfo *LI; 438 public: 439 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 440 441 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 442 // Primarily, sort the SCEVs by their getSCEVType(). 443 if (LHS->getSCEVType() != RHS->getSCEVType()) 444 return LHS->getSCEVType() < RHS->getSCEVType(); 445 446 // Aside from the getSCEVType() ordering, the particular ordering 447 // isn't very important except that it's beneficial to be consistent, 448 // so that (a + b) and (b + a) don't end up as different expressions. 449 450 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 451 // not as complete as it could be. 452 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 453 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 454 455 // Order pointer values after integer values. This helps SCEVExpander 456 // form GEPs. 457 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 458 return false; 459 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 460 return true; 461 462 // Compare getValueID values. 463 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 464 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 465 466 // Sort arguments by their position. 467 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 468 const Argument *RA = cast<Argument>(RU->getValue()); 469 return LA->getArgNo() < RA->getArgNo(); 470 } 471 472 // For instructions, compare their loop depth, and their opcode. 473 // This is pretty loose. 474 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 475 Instruction *RV = cast<Instruction>(RU->getValue()); 476 477 // Compare loop depths. 478 if (LI->getLoopDepth(LV->getParent()) != 479 LI->getLoopDepth(RV->getParent())) 480 return LI->getLoopDepth(LV->getParent()) < 481 LI->getLoopDepth(RV->getParent()); 482 483 // Compare opcodes. 484 if (LV->getOpcode() != RV->getOpcode()) 485 return LV->getOpcode() < RV->getOpcode(); 486 487 // Compare the number of operands. 488 if (LV->getNumOperands() != RV->getNumOperands()) 489 return LV->getNumOperands() < RV->getNumOperands(); 490 } 491 492 return false; 493 } 494 495 // Compare constant values. 496 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 497 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 498 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 499 } 500 501 // Compare addrec loop depths. 502 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 503 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 504 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 505 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 506 } 507 508 // Lexicographically compare n-ary expressions. 509 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 510 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 511 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 512 if (i >= RC->getNumOperands()) 513 return false; 514 if (operator()(LC->getOperand(i), RC->getOperand(i))) 515 return true; 516 if (operator()(RC->getOperand(i), LC->getOperand(i))) 517 return false; 518 } 519 return LC->getNumOperands() < RC->getNumOperands(); 520 } 521 522 // Lexicographically compare udiv expressions. 523 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 524 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 525 if (operator()(LC->getLHS(), RC->getLHS())) 526 return true; 527 if (operator()(RC->getLHS(), LC->getLHS())) 528 return false; 529 if (operator()(LC->getRHS(), RC->getRHS())) 530 return true; 531 if (operator()(RC->getRHS(), LC->getRHS())) 532 return false; 533 return false; 534 } 535 536 // Compare cast expressions by operand. 537 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 538 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 539 return operator()(LC->getOperand(), RC->getOperand()); 540 } 541 542 assert(0 && "Unknown SCEV kind!"); 543 return false; 544 } 545 }; 546} 547 548/// GroupByComplexity - Given a list of SCEV objects, order them by their 549/// complexity, and group objects of the same complexity together by value. 550/// When this routine is finished, we know that any duplicates in the vector are 551/// consecutive and that complexity is monotonically increasing. 552/// 553/// Note that we go take special precautions to ensure that we get determinstic 554/// results from this routine. In other words, we don't want the results of 555/// this to depend on where the addresses of various SCEV objects happened to 556/// land in memory. 557/// 558static void GroupByComplexity(SmallVectorImpl<const SCEV*> &Ops, 559 LoopInfo *LI) { 560 if (Ops.size() < 2) return; // Noop 561 if (Ops.size() == 2) { 562 // This is the common case, which also happens to be trivially simple. 563 // Special case it. 564 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 565 std::swap(Ops[0], Ops[1]); 566 return; 567 } 568 569 // Do the rough sort by complexity. 570 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 571 572 // Now that we are sorted by complexity, group elements of the same 573 // complexity. Note that this is, at worst, N^2, but the vector is likely to 574 // be extremely short in practice. Note that we take this approach because we 575 // do not want to depend on the addresses of the objects we are grouping. 576 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 577 const SCEV *S = Ops[i]; 578 unsigned Complexity = S->getSCEVType(); 579 580 // If there are any objects of the same complexity and same value as this 581 // one, group them. 582 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 583 if (Ops[j] == S) { // Found a duplicate. 584 // Move it to immediately after i'th element. 585 std::swap(Ops[i+1], Ops[j]); 586 ++i; // no need to rescan it. 587 if (i == e-2) return; // Done! 588 } 589 } 590 } 591} 592 593 594 595//===----------------------------------------------------------------------===// 596// Simple SCEV method implementations 597//===----------------------------------------------------------------------===// 598 599/// BinomialCoefficient - Compute BC(It, K). The result has width W. 600/// Assume, K > 0. 601static const SCEV* BinomialCoefficient(const SCEV* It, unsigned K, 602 ScalarEvolution &SE, 603 const Type* ResultTy) { 604 // Handle the simplest case efficiently. 605 if (K == 1) 606 return SE.getTruncateOrZeroExtend(It, ResultTy); 607 608 // We are using the following formula for BC(It, K): 609 // 610 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 611 // 612 // Suppose, W is the bitwidth of the return value. We must be prepared for 613 // overflow. Hence, we must assure that the result of our computation is 614 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 615 // safe in modular arithmetic. 616 // 617 // However, this code doesn't use exactly that formula; the formula it uses 618 // is something like the following, where T is the number of factors of 2 in 619 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 620 // exponentiation: 621 // 622 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 623 // 624 // This formula is trivially equivalent to the previous formula. However, 625 // this formula can be implemented much more efficiently. The trick is that 626 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 627 // arithmetic. To do exact division in modular arithmetic, all we have 628 // to do is multiply by the inverse. Therefore, this step can be done at 629 // width W. 630 // 631 // The next issue is how to safely do the division by 2^T. The way this 632 // is done is by doing the multiplication step at a width of at least W + T 633 // bits. This way, the bottom W+T bits of the product are accurate. Then, 634 // when we perform the division by 2^T (which is equivalent to a right shift 635 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 636 // truncated out after the division by 2^T. 637 // 638 // In comparison to just directly using the first formula, this technique 639 // is much more efficient; using the first formula requires W * K bits, 640 // but this formula less than W + K bits. Also, the first formula requires 641 // a division step, whereas this formula only requires multiplies and shifts. 642 // 643 // It doesn't matter whether the subtraction step is done in the calculation 644 // width or the input iteration count's width; if the subtraction overflows, 645 // the result must be zero anyway. We prefer here to do it in the width of 646 // the induction variable because it helps a lot for certain cases; CodeGen 647 // isn't smart enough to ignore the overflow, which leads to much less 648 // efficient code if the width of the subtraction is wider than the native 649 // register width. 650 // 651 // (It's possible to not widen at all by pulling out factors of 2 before 652 // the multiplication; for example, K=2 can be calculated as 653 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 654 // extra arithmetic, so it's not an obvious win, and it gets 655 // much more complicated for K > 3.) 656 657 // Protection from insane SCEVs; this bound is conservative, 658 // but it probably doesn't matter. 659 if (K > 1000) 660 return SE.getCouldNotCompute(); 661 662 unsigned W = SE.getTypeSizeInBits(ResultTy); 663 664 // Calculate K! / 2^T and T; we divide out the factors of two before 665 // multiplying for calculating K! / 2^T to avoid overflow. 666 // Other overflow doesn't matter because we only care about the bottom 667 // W bits of the result. 668 APInt OddFactorial(W, 1); 669 unsigned T = 1; 670 for (unsigned i = 3; i <= K; ++i) { 671 APInt Mult(W, i); 672 unsigned TwoFactors = Mult.countTrailingZeros(); 673 T += TwoFactors; 674 Mult = Mult.lshr(TwoFactors); 675 OddFactorial *= Mult; 676 } 677 678 // We need at least W + T bits for the multiplication step 679 unsigned CalculationBits = W + T; 680 681 // Calcuate 2^T, at width T+W. 682 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 683 684 // Calculate the multiplicative inverse of K! / 2^T; 685 // this multiplication factor will perform the exact division by 686 // K! / 2^T. 687 APInt Mod = APInt::getSignedMinValue(W+1); 688 APInt MultiplyFactor = OddFactorial.zext(W+1); 689 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 690 MultiplyFactor = MultiplyFactor.trunc(W); 691 692 // Calculate the product, at width T+W 693 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 694 const SCEV* Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 695 for (unsigned i = 1; i != K; ++i) { 696 const SCEV* S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 697 Dividend = SE.getMulExpr(Dividend, 698 SE.getTruncateOrZeroExtend(S, CalculationTy)); 699 } 700 701 // Divide by 2^T 702 const SCEV* DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 703 704 // Truncate the result, and divide by K! / 2^T. 705 706 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 707 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 708} 709 710/// evaluateAtIteration - Return the value of this chain of recurrences at 711/// the specified iteration number. We can evaluate this recurrence by 712/// multiplying each element in the chain by the binomial coefficient 713/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 714/// 715/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 716/// 717/// where BC(It, k) stands for binomial coefficient. 718/// 719const SCEV* SCEVAddRecExpr::evaluateAtIteration(const SCEV* It, 720 ScalarEvolution &SE) const { 721 const SCEV* Result = getStart(); 722 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 723 // The computation is correct in the face of overflow provided that the 724 // multiplication is performed _after_ the evaluation of the binomial 725 // coefficient. 726 const SCEV* Coeff = BinomialCoefficient(It, i, SE, getType()); 727 if (isa<SCEVCouldNotCompute>(Coeff)) 728 return Coeff; 729 730 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 731 } 732 return Result; 733} 734 735//===----------------------------------------------------------------------===// 736// SCEV Expression folder implementations 737//===----------------------------------------------------------------------===// 738 739const SCEV* ScalarEvolution::getTruncateExpr(const SCEV* Op, 740 const Type *Ty) { 741 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 742 "This is not a truncating conversion!"); 743 assert(isSCEVable(Ty) && 744 "This is not a conversion to a SCEVable type!"); 745 Ty = getEffectiveSCEVType(Ty); 746 747 // Fold if the operand is constant. 748 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 749 return getConstant( 750 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 751 752 // trunc(trunc(x)) --> trunc(x) 753 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 754 return getTruncateExpr(ST->getOperand(), Ty); 755 756 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 757 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 758 return getTruncateOrSignExtend(SS->getOperand(), Ty); 759 760 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 761 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 762 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 763 764 // If the input value is a chrec scev, truncate the chrec's operands. 765 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 766 SmallVector<const SCEV*, 4> Operands; 767 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 768 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 769 return getAddRecExpr(Operands, AddRec->getLoop()); 770 } 771 772 FoldingSetNodeID ID; 773 ID.AddInteger(scTruncate); 774 ID.AddPointer(Op); 775 ID.AddPointer(Ty); 776 void *IP = 0; 777 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 778 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 779 new (S) SCEVTruncateExpr(Op, Ty); 780 UniqueSCEVs.InsertNode(S, IP); 781 return S; 782} 783 784const SCEV* ScalarEvolution::getZeroExtendExpr(const SCEV* Op, 785 const Type *Ty) { 786 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 787 "This is not an extending conversion!"); 788 assert(isSCEVable(Ty) && 789 "This is not a conversion to a SCEVable type!"); 790 Ty = getEffectiveSCEVType(Ty); 791 792 // Fold if the operand is constant. 793 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 794 const Type *IntTy = getEffectiveSCEVType(Ty); 795 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 796 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 797 return getConstant(cast<ConstantInt>(C)); 798 } 799 800 // zext(zext(x)) --> zext(x) 801 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 802 return getZeroExtendExpr(SZ->getOperand(), Ty); 803 804 // If the input value is a chrec scev, and we can prove that the value 805 // did not overflow the old, smaller, value, we can zero extend all of the 806 // operands (often constants). This allows analysis of something like 807 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 808 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 809 if (AR->isAffine()) { 810 // Check whether the backedge-taken count is SCEVCouldNotCompute. 811 // Note that this serves two purposes: It filters out loops that are 812 // simply not analyzable, and it covers the case where this code is 813 // being called from within backedge-taken count analysis, such that 814 // attempting to ask for the backedge-taken count would likely result 815 // in infinite recursion. In the later case, the analysis code will 816 // cope with a conservative value, and it will take care to purge 817 // that value once it has finished. 818 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 819 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 820 // Manually compute the final value for AR, checking for 821 // overflow. 822 const SCEV* Start = AR->getStart(); 823 const SCEV* Step = AR->getStepRecurrence(*this); 824 825 // Check whether the backedge-taken count can be losslessly casted to 826 // the addrec's type. The count is always unsigned. 827 const SCEV* CastedMaxBECount = 828 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 829 const SCEV* RecastedMaxBECount = 830 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 831 if (MaxBECount == RecastedMaxBECount) { 832 const Type *WideTy = 833 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 834 // Check whether Start+Step*MaxBECount has no unsigned overflow. 835 const SCEV* ZMul = 836 getMulExpr(CastedMaxBECount, 837 getTruncateOrZeroExtend(Step, Start->getType())); 838 const SCEV* Add = getAddExpr(Start, ZMul); 839 const SCEV* OperandExtendedAdd = 840 getAddExpr(getZeroExtendExpr(Start, WideTy), 841 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 842 getZeroExtendExpr(Step, WideTy))); 843 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 844 // Return the expression with the addrec on the outside. 845 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 846 getZeroExtendExpr(Step, Ty), 847 AR->getLoop()); 848 849 // Similar to above, only this time treat the step value as signed. 850 // This covers loops that count down. 851 const SCEV* SMul = 852 getMulExpr(CastedMaxBECount, 853 getTruncateOrSignExtend(Step, Start->getType())); 854 Add = getAddExpr(Start, SMul); 855 OperandExtendedAdd = 856 getAddExpr(getZeroExtendExpr(Start, WideTy), 857 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 858 getSignExtendExpr(Step, WideTy))); 859 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 860 // Return the expression with the addrec on the outside. 861 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 862 getSignExtendExpr(Step, Ty), 863 AR->getLoop()); 864 } 865 } 866 } 867 868 FoldingSetNodeID ID; 869 ID.AddInteger(scZeroExtend); 870 ID.AddPointer(Op); 871 ID.AddPointer(Ty); 872 void *IP = 0; 873 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 874 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 875 new (S) SCEVZeroExtendExpr(Op, Ty); 876 UniqueSCEVs.InsertNode(S, IP); 877 return S; 878} 879 880const SCEV* ScalarEvolution::getSignExtendExpr(const SCEV* Op, 881 const Type *Ty) { 882 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 883 "This is not an extending conversion!"); 884 assert(isSCEVable(Ty) && 885 "This is not a conversion to a SCEVable type!"); 886 Ty = getEffectiveSCEVType(Ty); 887 888 // Fold if the operand is constant. 889 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 890 const Type *IntTy = getEffectiveSCEVType(Ty); 891 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 892 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 893 return getConstant(cast<ConstantInt>(C)); 894 } 895 896 // sext(sext(x)) --> sext(x) 897 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 898 return getSignExtendExpr(SS->getOperand(), Ty); 899 900 // If the input value is a chrec scev, and we can prove that the value 901 // did not overflow the old, smaller, value, we can sign extend all of the 902 // operands (often constants). This allows analysis of something like 903 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 904 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 905 if (AR->isAffine()) { 906 // Check whether the backedge-taken count is SCEVCouldNotCompute. 907 // Note that this serves two purposes: It filters out loops that are 908 // simply not analyzable, and it covers the case where this code is 909 // being called from within backedge-taken count analysis, such that 910 // attempting to ask for the backedge-taken count would likely result 911 // in infinite recursion. In the later case, the analysis code will 912 // cope with a conservative value, and it will take care to purge 913 // that value once it has finished. 914 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 915 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 916 // Manually compute the final value for AR, checking for 917 // overflow. 918 const SCEV* Start = AR->getStart(); 919 const SCEV* Step = AR->getStepRecurrence(*this); 920 921 // Check whether the backedge-taken count can be losslessly casted to 922 // the addrec's type. The count is always unsigned. 923 const SCEV* CastedMaxBECount = 924 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 925 const SCEV* RecastedMaxBECount = 926 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 927 if (MaxBECount == RecastedMaxBECount) { 928 const Type *WideTy = 929 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 930 // Check whether Start+Step*MaxBECount has no signed overflow. 931 const SCEV* SMul = 932 getMulExpr(CastedMaxBECount, 933 getTruncateOrSignExtend(Step, Start->getType())); 934 const SCEV* Add = getAddExpr(Start, SMul); 935 const SCEV* OperandExtendedAdd = 936 getAddExpr(getSignExtendExpr(Start, WideTy), 937 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 938 getSignExtendExpr(Step, WideTy))); 939 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 940 // Return the expression with the addrec on the outside. 941 return getAddRecExpr(getSignExtendExpr(Start, Ty), 942 getSignExtendExpr(Step, Ty), 943 AR->getLoop()); 944 } 945 } 946 } 947 948 FoldingSetNodeID ID; 949 ID.AddInteger(scSignExtend); 950 ID.AddPointer(Op); 951 ID.AddPointer(Ty); 952 void *IP = 0; 953 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 954 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 955 new (S) SCEVSignExtendExpr(Op, Ty); 956 UniqueSCEVs.InsertNode(S, IP); 957 return S; 958} 959 960/// getAnyExtendExpr - Return a SCEV for the given operand extended with 961/// unspecified bits out to the given type. 962/// 963const SCEV* ScalarEvolution::getAnyExtendExpr(const SCEV* Op, 964 const Type *Ty) { 965 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 966 "This is not an extending conversion!"); 967 assert(isSCEVable(Ty) && 968 "This is not a conversion to a SCEVable type!"); 969 Ty = getEffectiveSCEVType(Ty); 970 971 // Sign-extend negative constants. 972 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 973 if (SC->getValue()->getValue().isNegative()) 974 return getSignExtendExpr(Op, Ty); 975 976 // Peel off a truncate cast. 977 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 978 const SCEV* NewOp = T->getOperand(); 979 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 980 return getAnyExtendExpr(NewOp, Ty); 981 return getTruncateOrNoop(NewOp, Ty); 982 } 983 984 // Next try a zext cast. If the cast is folded, use it. 985 const SCEV* ZExt = getZeroExtendExpr(Op, Ty); 986 if (!isa<SCEVZeroExtendExpr>(ZExt)) 987 return ZExt; 988 989 // Next try a sext cast. If the cast is folded, use it. 990 const SCEV* SExt = getSignExtendExpr(Op, Ty); 991 if (!isa<SCEVSignExtendExpr>(SExt)) 992 return SExt; 993 994 // If the expression is obviously signed, use the sext cast value. 995 if (isa<SCEVSMaxExpr>(Op)) 996 return SExt; 997 998 // Absent any other information, use the zext cast value. 999 return ZExt; 1000} 1001 1002/// CollectAddOperandsWithScales - Process the given Ops list, which is 1003/// a list of operands to be added under the given scale, update the given 1004/// map. This is a helper function for getAddRecExpr. As an example of 1005/// what it does, given a sequence of operands that would form an add 1006/// expression like this: 1007/// 1008/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1009/// 1010/// where A and B are constants, update the map with these values: 1011/// 1012/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1013/// 1014/// and add 13 + A*B*29 to AccumulatedConstant. 1015/// This will allow getAddRecExpr to produce this: 1016/// 1017/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1018/// 1019/// This form often exposes folding opportunities that are hidden in 1020/// the original operand list. 1021/// 1022/// Return true iff it appears that any interesting folding opportunities 1023/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1024/// the common case where no interesting opportunities are present, and 1025/// is also used as a check to avoid infinite recursion. 1026/// 1027static bool 1028CollectAddOperandsWithScales(DenseMap<const SCEV*, APInt> &M, 1029 SmallVector<const SCEV*, 8> &NewOps, 1030 APInt &AccumulatedConstant, 1031 const SmallVectorImpl<const SCEV*> &Ops, 1032 const APInt &Scale, 1033 ScalarEvolution &SE) { 1034 bool Interesting = false; 1035 1036 // Iterate over the add operands. 1037 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1038 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1039 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1040 APInt NewScale = 1041 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1042 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1043 // A multiplication of a constant with another add; recurse. 1044 Interesting |= 1045 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1046 cast<SCEVAddExpr>(Mul->getOperand(1)) 1047 ->getOperands(), 1048 NewScale, SE); 1049 } else { 1050 // A multiplication of a constant with some other value. Update 1051 // the map. 1052 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1053 const SCEV* Key = SE.getMulExpr(MulOps); 1054 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair = 1055 M.insert(std::make_pair(Key, NewScale)); 1056 if (Pair.second) { 1057 NewOps.push_back(Pair.first->first); 1058 } else { 1059 Pair.first->second += NewScale; 1060 // The map already had an entry for this value, which may indicate 1061 // a folding opportunity. 1062 Interesting = true; 1063 } 1064 } 1065 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1066 // Pull a buried constant out to the outside. 1067 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1068 Interesting = true; 1069 AccumulatedConstant += Scale * C->getValue()->getValue(); 1070 } else { 1071 // An ordinary operand. Update the map. 1072 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair = 1073 M.insert(std::make_pair(Ops[i], Scale)); 1074 if (Pair.second) { 1075 NewOps.push_back(Pair.first->first); 1076 } else { 1077 Pair.first->second += Scale; 1078 // The map already had an entry for this value, which may indicate 1079 // a folding opportunity. 1080 Interesting = true; 1081 } 1082 } 1083 } 1084 1085 return Interesting; 1086} 1087 1088namespace { 1089 struct APIntCompare { 1090 bool operator()(const APInt &LHS, const APInt &RHS) const { 1091 return LHS.ult(RHS); 1092 } 1093 }; 1094} 1095 1096/// getAddExpr - Get a canonical add expression, or something simpler if 1097/// possible. 1098const SCEV* ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV*> &Ops) { 1099 assert(!Ops.empty() && "Cannot get empty add!"); 1100 if (Ops.size() == 1) return Ops[0]; 1101#ifndef NDEBUG 1102 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1103 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1104 getEffectiveSCEVType(Ops[0]->getType()) && 1105 "SCEVAddExpr operand types don't match!"); 1106#endif 1107 1108 // Sort by complexity, this groups all similar expression types together. 1109 GroupByComplexity(Ops, LI); 1110 1111 // If there are any constants, fold them together. 1112 unsigned Idx = 0; 1113 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1114 ++Idx; 1115 assert(Idx < Ops.size()); 1116 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1117 // We found two constants, fold them together! 1118 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1119 RHSC->getValue()->getValue()); 1120 if (Ops.size() == 2) return Ops[0]; 1121 Ops.erase(Ops.begin()+1); // Erase the folded element 1122 LHSC = cast<SCEVConstant>(Ops[0]); 1123 } 1124 1125 // If we are left with a constant zero being added, strip it off. 1126 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1127 Ops.erase(Ops.begin()); 1128 --Idx; 1129 } 1130 } 1131 1132 if (Ops.size() == 1) return Ops[0]; 1133 1134 // Okay, check to see if the same value occurs in the operand list twice. If 1135 // so, merge them together into an multiply expression. Since we sorted the 1136 // list, these values are required to be adjacent. 1137 const Type *Ty = Ops[0]->getType(); 1138 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1139 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1140 // Found a match, merge the two values into a multiply, and add any 1141 // remaining values to the result. 1142 const SCEV* Two = getIntegerSCEV(2, Ty); 1143 const SCEV* Mul = getMulExpr(Ops[i], Two); 1144 if (Ops.size() == 2) 1145 return Mul; 1146 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1147 Ops.push_back(Mul); 1148 return getAddExpr(Ops); 1149 } 1150 1151 // Check for truncates. If all the operands are truncated from the same 1152 // type, see if factoring out the truncate would permit the result to be 1153 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1154 // if the contents of the resulting outer trunc fold to something simple. 1155 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1156 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1157 const Type *DstType = Trunc->getType(); 1158 const Type *SrcType = Trunc->getOperand()->getType(); 1159 SmallVector<const SCEV*, 8> LargeOps; 1160 bool Ok = true; 1161 // Check all the operands to see if they can be represented in the 1162 // source type of the truncate. 1163 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1164 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1165 if (T->getOperand()->getType() != SrcType) { 1166 Ok = false; 1167 break; 1168 } 1169 LargeOps.push_back(T->getOperand()); 1170 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1171 // This could be either sign or zero extension, but sign extension 1172 // is much more likely to be foldable here. 1173 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1174 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1175 SmallVector<const SCEV*, 8> LargeMulOps; 1176 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1177 if (const SCEVTruncateExpr *T = 1178 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1179 if (T->getOperand()->getType() != SrcType) { 1180 Ok = false; 1181 break; 1182 } 1183 LargeMulOps.push_back(T->getOperand()); 1184 } else if (const SCEVConstant *C = 1185 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1186 // This could be either sign or zero extension, but sign extension 1187 // is much more likely to be foldable here. 1188 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1189 } else { 1190 Ok = false; 1191 break; 1192 } 1193 } 1194 if (Ok) 1195 LargeOps.push_back(getMulExpr(LargeMulOps)); 1196 } else { 1197 Ok = false; 1198 break; 1199 } 1200 } 1201 if (Ok) { 1202 // Evaluate the expression in the larger type. 1203 const SCEV* Fold = getAddExpr(LargeOps); 1204 // If it folds to something simple, use it. Otherwise, don't. 1205 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1206 return getTruncateExpr(Fold, DstType); 1207 } 1208 } 1209 1210 // Skip past any other cast SCEVs. 1211 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1212 ++Idx; 1213 1214 // If there are add operands they would be next. 1215 if (Idx < Ops.size()) { 1216 bool DeletedAdd = false; 1217 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1218 // If we have an add, expand the add operands onto the end of the operands 1219 // list. 1220 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1221 Ops.erase(Ops.begin()+Idx); 1222 DeletedAdd = true; 1223 } 1224 1225 // If we deleted at least one add, we added operands to the end of the list, 1226 // and they are not necessarily sorted. Recurse to resort and resimplify 1227 // any operands we just aquired. 1228 if (DeletedAdd) 1229 return getAddExpr(Ops); 1230 } 1231 1232 // Skip over the add expression until we get to a multiply. 1233 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1234 ++Idx; 1235 1236 // Check to see if there are any folding opportunities present with 1237 // operands multiplied by constant values. 1238 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1239 uint64_t BitWidth = getTypeSizeInBits(Ty); 1240 DenseMap<const SCEV*, APInt> M; 1241 SmallVector<const SCEV*, 8> NewOps; 1242 APInt AccumulatedConstant(BitWidth, 0); 1243 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1244 Ops, APInt(BitWidth, 1), *this)) { 1245 // Some interesting folding opportunity is present, so its worthwhile to 1246 // re-generate the operands list. Group the operands by constant scale, 1247 // to avoid multiplying by the same constant scale multiple times. 1248 std::map<APInt, SmallVector<const SCEV*, 4>, APIntCompare> MulOpLists; 1249 for (SmallVector<const SCEV*, 8>::iterator I = NewOps.begin(), 1250 E = NewOps.end(); I != E; ++I) 1251 MulOpLists[M.find(*I)->second].push_back(*I); 1252 // Re-generate the operands list. 1253 Ops.clear(); 1254 if (AccumulatedConstant != 0) 1255 Ops.push_back(getConstant(AccumulatedConstant)); 1256 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1257 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1258 if (I->first != 0) 1259 Ops.push_back(getMulExpr(getConstant(I->first), 1260 getAddExpr(I->second))); 1261 if (Ops.empty()) 1262 return getIntegerSCEV(0, Ty); 1263 if (Ops.size() == 1) 1264 return Ops[0]; 1265 return getAddExpr(Ops); 1266 } 1267 } 1268 1269 // If we are adding something to a multiply expression, make sure the 1270 // something is not already an operand of the multiply. If so, merge it into 1271 // the multiply. 1272 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1273 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1274 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1275 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1276 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1277 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1278 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1279 const SCEV* InnerMul = Mul->getOperand(MulOp == 0); 1280 if (Mul->getNumOperands() != 2) { 1281 // If the multiply has more than two operands, we must get the 1282 // Y*Z term. 1283 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1284 MulOps.erase(MulOps.begin()+MulOp); 1285 InnerMul = getMulExpr(MulOps); 1286 } 1287 const SCEV* One = getIntegerSCEV(1, Ty); 1288 const SCEV* AddOne = getAddExpr(InnerMul, One); 1289 const SCEV* OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1290 if (Ops.size() == 2) return OuterMul; 1291 if (AddOp < Idx) { 1292 Ops.erase(Ops.begin()+AddOp); 1293 Ops.erase(Ops.begin()+Idx-1); 1294 } else { 1295 Ops.erase(Ops.begin()+Idx); 1296 Ops.erase(Ops.begin()+AddOp-1); 1297 } 1298 Ops.push_back(OuterMul); 1299 return getAddExpr(Ops); 1300 } 1301 1302 // Check this multiply against other multiplies being added together. 1303 for (unsigned OtherMulIdx = Idx+1; 1304 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1305 ++OtherMulIdx) { 1306 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1307 // If MulOp occurs in OtherMul, we can fold the two multiplies 1308 // together. 1309 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1310 OMulOp != e; ++OMulOp) 1311 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1312 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1313 const SCEV* InnerMul1 = Mul->getOperand(MulOp == 0); 1314 if (Mul->getNumOperands() != 2) { 1315 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1316 Mul->op_end()); 1317 MulOps.erase(MulOps.begin()+MulOp); 1318 InnerMul1 = getMulExpr(MulOps); 1319 } 1320 const SCEV* InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1321 if (OtherMul->getNumOperands() != 2) { 1322 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1323 OtherMul->op_end()); 1324 MulOps.erase(MulOps.begin()+OMulOp); 1325 InnerMul2 = getMulExpr(MulOps); 1326 } 1327 const SCEV* InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1328 const SCEV* OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1329 if (Ops.size() == 2) return OuterMul; 1330 Ops.erase(Ops.begin()+Idx); 1331 Ops.erase(Ops.begin()+OtherMulIdx-1); 1332 Ops.push_back(OuterMul); 1333 return getAddExpr(Ops); 1334 } 1335 } 1336 } 1337 } 1338 1339 // If there are any add recurrences in the operands list, see if any other 1340 // added values are loop invariant. If so, we can fold them into the 1341 // recurrence. 1342 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1343 ++Idx; 1344 1345 // Scan over all recurrences, trying to fold loop invariants into them. 1346 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1347 // Scan all of the other operands to this add and add them to the vector if 1348 // they are loop invariant w.r.t. the recurrence. 1349 SmallVector<const SCEV*, 8> LIOps; 1350 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1351 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1352 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1353 LIOps.push_back(Ops[i]); 1354 Ops.erase(Ops.begin()+i); 1355 --i; --e; 1356 } 1357 1358 // If we found some loop invariants, fold them into the recurrence. 1359 if (!LIOps.empty()) { 1360 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1361 LIOps.push_back(AddRec->getStart()); 1362 1363 SmallVector<const SCEV*, 4> AddRecOps(AddRec->op_begin(), 1364 AddRec->op_end()); 1365 AddRecOps[0] = getAddExpr(LIOps); 1366 1367 const SCEV* NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1368 // If all of the other operands were loop invariant, we are done. 1369 if (Ops.size() == 1) return NewRec; 1370 1371 // Otherwise, add the folded AddRec by the non-liv parts. 1372 for (unsigned i = 0;; ++i) 1373 if (Ops[i] == AddRec) { 1374 Ops[i] = NewRec; 1375 break; 1376 } 1377 return getAddExpr(Ops); 1378 } 1379 1380 // Okay, if there weren't any loop invariants to be folded, check to see if 1381 // there are multiple AddRec's with the same loop induction variable being 1382 // added together. If so, we can fold them. 1383 for (unsigned OtherIdx = Idx+1; 1384 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1385 if (OtherIdx != Idx) { 1386 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1387 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1388 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1389 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1390 AddRec->op_end()); 1391 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1392 if (i >= NewOps.size()) { 1393 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1394 OtherAddRec->op_end()); 1395 break; 1396 } 1397 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1398 } 1399 const SCEV* NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1400 1401 if (Ops.size() == 2) return NewAddRec; 1402 1403 Ops.erase(Ops.begin()+Idx); 1404 Ops.erase(Ops.begin()+OtherIdx-1); 1405 Ops.push_back(NewAddRec); 1406 return getAddExpr(Ops); 1407 } 1408 } 1409 1410 // Otherwise couldn't fold anything into this recurrence. Move onto the 1411 // next one. 1412 } 1413 1414 // Okay, it looks like we really DO need an add expr. Check to see if we 1415 // already have one, otherwise create a new one. 1416 FoldingSetNodeID ID; 1417 ID.AddInteger(scAddExpr); 1418 ID.AddInteger(Ops.size()); 1419 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1420 ID.AddPointer(Ops[i]); 1421 void *IP = 0; 1422 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1423 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1424 new (S) SCEVAddExpr(Ops); 1425 UniqueSCEVs.InsertNode(S, IP); 1426 return S; 1427} 1428 1429 1430/// getMulExpr - Get a canonical multiply expression, or something simpler if 1431/// possible. 1432const SCEV* ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV*> &Ops) { 1433 assert(!Ops.empty() && "Cannot get empty mul!"); 1434#ifndef NDEBUG 1435 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1436 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1437 getEffectiveSCEVType(Ops[0]->getType()) && 1438 "SCEVMulExpr operand types don't match!"); 1439#endif 1440 1441 // Sort by complexity, this groups all similar expression types together. 1442 GroupByComplexity(Ops, LI); 1443 1444 // If there are any constants, fold them together. 1445 unsigned Idx = 0; 1446 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1447 1448 // C1*(C2+V) -> C1*C2 + C1*V 1449 if (Ops.size() == 2) 1450 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1451 if (Add->getNumOperands() == 2 && 1452 isa<SCEVConstant>(Add->getOperand(0))) 1453 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1454 getMulExpr(LHSC, Add->getOperand(1))); 1455 1456 1457 ++Idx; 1458 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1459 // We found two constants, fold them together! 1460 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1461 RHSC->getValue()->getValue()); 1462 Ops[0] = getConstant(Fold); 1463 Ops.erase(Ops.begin()+1); // Erase the folded element 1464 if (Ops.size() == 1) return Ops[0]; 1465 LHSC = cast<SCEVConstant>(Ops[0]); 1466 } 1467 1468 // If we are left with a constant one being multiplied, strip it off. 1469 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1470 Ops.erase(Ops.begin()); 1471 --Idx; 1472 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1473 // If we have a multiply of zero, it will always be zero. 1474 return Ops[0]; 1475 } 1476 } 1477 1478 // Skip over the add expression until we get to a multiply. 1479 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1480 ++Idx; 1481 1482 if (Ops.size() == 1) 1483 return Ops[0]; 1484 1485 // If there are mul operands inline them all into this expression. 1486 if (Idx < Ops.size()) { 1487 bool DeletedMul = false; 1488 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1489 // If we have an mul, expand the mul operands onto the end of the operands 1490 // list. 1491 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1492 Ops.erase(Ops.begin()+Idx); 1493 DeletedMul = true; 1494 } 1495 1496 // If we deleted at least one mul, we added operands to the end of the list, 1497 // and they are not necessarily sorted. Recurse to resort and resimplify 1498 // any operands we just aquired. 1499 if (DeletedMul) 1500 return getMulExpr(Ops); 1501 } 1502 1503 // If there are any add recurrences in the operands list, see if any other 1504 // added values are loop invariant. If so, we can fold them into the 1505 // recurrence. 1506 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1507 ++Idx; 1508 1509 // Scan over all recurrences, trying to fold loop invariants into them. 1510 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1511 // Scan all of the other operands to this mul and add them to the vector if 1512 // they are loop invariant w.r.t. the recurrence. 1513 SmallVector<const SCEV*, 8> LIOps; 1514 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1515 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1516 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1517 LIOps.push_back(Ops[i]); 1518 Ops.erase(Ops.begin()+i); 1519 --i; --e; 1520 } 1521 1522 // If we found some loop invariants, fold them into the recurrence. 1523 if (!LIOps.empty()) { 1524 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1525 SmallVector<const SCEV*, 4> NewOps; 1526 NewOps.reserve(AddRec->getNumOperands()); 1527 if (LIOps.size() == 1) { 1528 const SCEV *Scale = LIOps[0]; 1529 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1530 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1531 } else { 1532 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1533 SmallVector<const SCEV*, 4> MulOps(LIOps.begin(), LIOps.end()); 1534 MulOps.push_back(AddRec->getOperand(i)); 1535 NewOps.push_back(getMulExpr(MulOps)); 1536 } 1537 } 1538 1539 const SCEV* NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1540 1541 // If all of the other operands were loop invariant, we are done. 1542 if (Ops.size() == 1) return NewRec; 1543 1544 // Otherwise, multiply the folded AddRec by the non-liv parts. 1545 for (unsigned i = 0;; ++i) 1546 if (Ops[i] == AddRec) { 1547 Ops[i] = NewRec; 1548 break; 1549 } 1550 return getMulExpr(Ops); 1551 } 1552 1553 // Okay, if there weren't any loop invariants to be folded, check to see if 1554 // there are multiple AddRec's with the same loop induction variable being 1555 // multiplied together. If so, we can fold them. 1556 for (unsigned OtherIdx = Idx+1; 1557 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1558 if (OtherIdx != Idx) { 1559 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1560 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1561 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1562 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1563 const SCEV* NewStart = getMulExpr(F->getStart(), 1564 G->getStart()); 1565 const SCEV* B = F->getStepRecurrence(*this); 1566 const SCEV* D = G->getStepRecurrence(*this); 1567 const SCEV* NewStep = getAddExpr(getMulExpr(F, D), 1568 getMulExpr(G, B), 1569 getMulExpr(B, D)); 1570 const SCEV* NewAddRec = getAddRecExpr(NewStart, NewStep, 1571 F->getLoop()); 1572 if (Ops.size() == 2) return NewAddRec; 1573 1574 Ops.erase(Ops.begin()+Idx); 1575 Ops.erase(Ops.begin()+OtherIdx-1); 1576 Ops.push_back(NewAddRec); 1577 return getMulExpr(Ops); 1578 } 1579 } 1580 1581 // Otherwise couldn't fold anything into this recurrence. Move onto the 1582 // next one. 1583 } 1584 1585 // Okay, it looks like we really DO need an mul expr. Check to see if we 1586 // already have one, otherwise create a new one. 1587 FoldingSetNodeID ID; 1588 ID.AddInteger(scMulExpr); 1589 ID.AddInteger(Ops.size()); 1590 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1591 ID.AddPointer(Ops[i]); 1592 void *IP = 0; 1593 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1594 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1595 new (S) SCEVMulExpr(Ops); 1596 UniqueSCEVs.InsertNode(S, IP); 1597 return S; 1598} 1599 1600/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1601/// possible. 1602const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1603 const SCEV *RHS) { 1604 assert(getEffectiveSCEVType(LHS->getType()) == 1605 getEffectiveSCEVType(RHS->getType()) && 1606 "SCEVUDivExpr operand types don't match!"); 1607 1608 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1609 if (RHSC->getValue()->equalsInt(1)) 1610 return LHS; // X udiv 1 --> x 1611 if (RHSC->isZero()) 1612 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1613 1614 // Determine if the division can be folded into the operands of 1615 // its operands. 1616 // TODO: Generalize this to non-constants by using known-bits information. 1617 const Type *Ty = LHS->getType(); 1618 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1619 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1620 // For non-power-of-two values, effectively round the value up to the 1621 // nearest power of two. 1622 if (!RHSC->getValue()->getValue().isPowerOf2()) 1623 ++MaxShiftAmt; 1624 const IntegerType *ExtTy = 1625 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1626 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1627 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1628 if (const SCEVConstant *Step = 1629 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1630 if (!Step->getValue()->getValue() 1631 .urem(RHSC->getValue()->getValue()) && 1632 getZeroExtendExpr(AR, ExtTy) == 1633 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1634 getZeroExtendExpr(Step, ExtTy), 1635 AR->getLoop())) { 1636 SmallVector<const SCEV*, 4> Operands; 1637 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1638 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1639 return getAddRecExpr(Operands, AR->getLoop()); 1640 } 1641 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1642 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1643 SmallVector<const SCEV*, 4> Operands; 1644 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1645 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1646 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1647 // Find an operand that's safely divisible. 1648 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1649 const SCEV* Op = M->getOperand(i); 1650 const SCEV* Div = getUDivExpr(Op, RHSC); 1651 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1652 const SmallVectorImpl<const SCEV*> &MOperands = M->getOperands(); 1653 Operands = SmallVector<const SCEV*, 4>(MOperands.begin(), 1654 MOperands.end()); 1655 Operands[i] = Div; 1656 return getMulExpr(Operands); 1657 } 1658 } 1659 } 1660 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1661 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1662 SmallVector<const SCEV*, 4> Operands; 1663 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1664 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1665 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1666 Operands.clear(); 1667 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1668 const SCEV* Op = getUDivExpr(A->getOperand(i), RHS); 1669 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1670 break; 1671 Operands.push_back(Op); 1672 } 1673 if (Operands.size() == A->getNumOperands()) 1674 return getAddExpr(Operands); 1675 } 1676 } 1677 1678 // Fold if both operands are constant. 1679 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1680 Constant *LHSCV = LHSC->getValue(); 1681 Constant *RHSCV = RHSC->getValue(); 1682 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1683 RHSCV))); 1684 } 1685 } 1686 1687 FoldingSetNodeID ID; 1688 ID.AddInteger(scUDivExpr); 1689 ID.AddPointer(LHS); 1690 ID.AddPointer(RHS); 1691 void *IP = 0; 1692 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1693 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1694 new (S) SCEVUDivExpr(LHS, RHS); 1695 UniqueSCEVs.InsertNode(S, IP); 1696 return S; 1697} 1698 1699 1700/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1701/// Simplify the expression as much as possible. 1702const SCEV* ScalarEvolution::getAddRecExpr(const SCEV* Start, 1703 const SCEV* Step, const Loop *L) { 1704 SmallVector<const SCEV*, 4> Operands; 1705 Operands.push_back(Start); 1706 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1707 if (StepChrec->getLoop() == L) { 1708 Operands.insert(Operands.end(), StepChrec->op_begin(), 1709 StepChrec->op_end()); 1710 return getAddRecExpr(Operands, L); 1711 } 1712 1713 Operands.push_back(Step); 1714 return getAddRecExpr(Operands, L); 1715} 1716 1717/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1718/// Simplify the expression as much as possible. 1719const SCEV * 1720ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV*> &Operands, 1721 const Loop *L) { 1722 if (Operands.size() == 1) return Operands[0]; 1723#ifndef NDEBUG 1724 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1725 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1726 getEffectiveSCEVType(Operands[0]->getType()) && 1727 "SCEVAddRecExpr operand types don't match!"); 1728#endif 1729 1730 if (Operands.back()->isZero()) { 1731 Operands.pop_back(); 1732 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1733 } 1734 1735 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1736 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1737 const Loop* NestedLoop = NestedAR->getLoop(); 1738 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1739 SmallVector<const SCEV*, 4> NestedOperands(NestedAR->op_begin(), 1740 NestedAR->op_end()); 1741 Operands[0] = NestedAR->getStart(); 1742 // AddRecs require their operands be loop-invariant with respect to their 1743 // loops. Don't perform this transformation if it would break this 1744 // requirement. 1745 bool AllInvariant = true; 1746 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1747 if (!Operands[i]->isLoopInvariant(L)) { 1748 AllInvariant = false; 1749 break; 1750 } 1751 if (AllInvariant) { 1752 NestedOperands[0] = getAddRecExpr(Operands, L); 1753 AllInvariant = true; 1754 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1755 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1756 AllInvariant = false; 1757 break; 1758 } 1759 if (AllInvariant) 1760 // Ok, both add recurrences are valid after the transformation. 1761 return getAddRecExpr(NestedOperands, NestedLoop); 1762 } 1763 // Reset Operands to its original state. 1764 Operands[0] = NestedAR; 1765 } 1766 } 1767 1768 FoldingSetNodeID ID; 1769 ID.AddInteger(scAddRecExpr); 1770 ID.AddInteger(Operands.size()); 1771 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1772 ID.AddPointer(Operands[i]); 1773 ID.AddPointer(L); 1774 void *IP = 0; 1775 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1776 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1777 new (S) SCEVAddRecExpr(Operands, L); 1778 UniqueSCEVs.InsertNode(S, IP); 1779 return S; 1780} 1781 1782const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1783 const SCEV *RHS) { 1784 SmallVector<const SCEV*, 2> Ops; 1785 Ops.push_back(LHS); 1786 Ops.push_back(RHS); 1787 return getSMaxExpr(Ops); 1788} 1789 1790const SCEV* 1791ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV*> &Ops) { 1792 assert(!Ops.empty() && "Cannot get empty smax!"); 1793 if (Ops.size() == 1) return Ops[0]; 1794#ifndef NDEBUG 1795 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1796 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1797 getEffectiveSCEVType(Ops[0]->getType()) && 1798 "SCEVSMaxExpr operand types don't match!"); 1799#endif 1800 1801 // Sort by complexity, this groups all similar expression types together. 1802 GroupByComplexity(Ops, LI); 1803 1804 // If there are any constants, fold them together. 1805 unsigned Idx = 0; 1806 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1807 ++Idx; 1808 assert(Idx < Ops.size()); 1809 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1810 // We found two constants, fold them together! 1811 ConstantInt *Fold = ConstantInt::get( 1812 APIntOps::smax(LHSC->getValue()->getValue(), 1813 RHSC->getValue()->getValue())); 1814 Ops[0] = getConstant(Fold); 1815 Ops.erase(Ops.begin()+1); // Erase the folded element 1816 if (Ops.size() == 1) return Ops[0]; 1817 LHSC = cast<SCEVConstant>(Ops[0]); 1818 } 1819 1820 // If we are left with a constant minimum-int, strip it off. 1821 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1822 Ops.erase(Ops.begin()); 1823 --Idx; 1824 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1825 // If we have an smax with a constant maximum-int, it will always be 1826 // maximum-int. 1827 return Ops[0]; 1828 } 1829 } 1830 1831 if (Ops.size() == 1) return Ops[0]; 1832 1833 // Find the first SMax 1834 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1835 ++Idx; 1836 1837 // Check to see if one of the operands is an SMax. If so, expand its operands 1838 // onto our operand list, and recurse to simplify. 1839 if (Idx < Ops.size()) { 1840 bool DeletedSMax = false; 1841 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1842 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1843 Ops.erase(Ops.begin()+Idx); 1844 DeletedSMax = true; 1845 } 1846 1847 if (DeletedSMax) 1848 return getSMaxExpr(Ops); 1849 } 1850 1851 // Okay, check to see if the same value occurs in the operand list twice. If 1852 // so, delete one. Since we sorted the list, these values are required to 1853 // be adjacent. 1854 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1855 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1856 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1857 --i; --e; 1858 } 1859 1860 if (Ops.size() == 1) return Ops[0]; 1861 1862 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1863 1864 // Okay, it looks like we really DO need an smax expr. Check to see if we 1865 // already have one, otherwise create a new one. 1866 FoldingSetNodeID ID; 1867 ID.AddInteger(scSMaxExpr); 1868 ID.AddInteger(Ops.size()); 1869 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1870 ID.AddPointer(Ops[i]); 1871 void *IP = 0; 1872 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1873 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1874 new (S) SCEVSMaxExpr(Ops); 1875 UniqueSCEVs.InsertNode(S, IP); 1876 return S; 1877} 1878 1879const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1880 const SCEV *RHS) { 1881 SmallVector<const SCEV*, 2> Ops; 1882 Ops.push_back(LHS); 1883 Ops.push_back(RHS); 1884 return getUMaxExpr(Ops); 1885} 1886 1887const SCEV* 1888ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV*> &Ops) { 1889 assert(!Ops.empty() && "Cannot get empty umax!"); 1890 if (Ops.size() == 1) return Ops[0]; 1891#ifndef NDEBUG 1892 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1893 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1894 getEffectiveSCEVType(Ops[0]->getType()) && 1895 "SCEVUMaxExpr operand types don't match!"); 1896#endif 1897 1898 // Sort by complexity, this groups all similar expression types together. 1899 GroupByComplexity(Ops, LI); 1900 1901 // If there are any constants, fold them together. 1902 unsigned Idx = 0; 1903 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1904 ++Idx; 1905 assert(Idx < Ops.size()); 1906 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1907 // We found two constants, fold them together! 1908 ConstantInt *Fold = ConstantInt::get( 1909 APIntOps::umax(LHSC->getValue()->getValue(), 1910 RHSC->getValue()->getValue())); 1911 Ops[0] = getConstant(Fold); 1912 Ops.erase(Ops.begin()+1); // Erase the folded element 1913 if (Ops.size() == 1) return Ops[0]; 1914 LHSC = cast<SCEVConstant>(Ops[0]); 1915 } 1916 1917 // If we are left with a constant minimum-int, strip it off. 1918 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1919 Ops.erase(Ops.begin()); 1920 --Idx; 1921 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 1922 // If we have an umax with a constant maximum-int, it will always be 1923 // maximum-int. 1924 return Ops[0]; 1925 } 1926 } 1927 1928 if (Ops.size() == 1) return Ops[0]; 1929 1930 // Find the first UMax 1931 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1932 ++Idx; 1933 1934 // Check to see if one of the operands is a UMax. If so, expand its operands 1935 // onto our operand list, and recurse to simplify. 1936 if (Idx < Ops.size()) { 1937 bool DeletedUMax = false; 1938 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1939 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1940 Ops.erase(Ops.begin()+Idx); 1941 DeletedUMax = true; 1942 } 1943 1944 if (DeletedUMax) 1945 return getUMaxExpr(Ops); 1946 } 1947 1948 // Okay, check to see if the same value occurs in the operand list twice. If 1949 // so, delete one. Since we sorted the list, these values are required to 1950 // be adjacent. 1951 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1952 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1953 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1954 --i; --e; 1955 } 1956 1957 if (Ops.size() == 1) return Ops[0]; 1958 1959 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1960 1961 // Okay, it looks like we really DO need a umax expr. Check to see if we 1962 // already have one, otherwise create a new one. 1963 FoldingSetNodeID ID; 1964 ID.AddInteger(scUMaxExpr); 1965 ID.AddInteger(Ops.size()); 1966 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1967 ID.AddPointer(Ops[i]); 1968 void *IP = 0; 1969 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1970 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 1971 new (S) SCEVUMaxExpr(Ops); 1972 UniqueSCEVs.InsertNode(S, IP); 1973 return S; 1974} 1975 1976const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 1977 const SCEV *RHS) { 1978 // ~smax(~x, ~y) == smin(x, y). 1979 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1980} 1981 1982const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 1983 const SCEV *RHS) { 1984 // ~umax(~x, ~y) == umin(x, y) 1985 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1986} 1987 1988const SCEV* ScalarEvolution::getUnknown(Value *V) { 1989 // Don't attempt to do anything other than create a SCEVUnknown object 1990 // here. createSCEV only calls getUnknown after checking for all other 1991 // interesting possibilities, and any other code that calls getUnknown 1992 // is doing so in order to hide a value from SCEV canonicalization. 1993 1994 FoldingSetNodeID ID; 1995 ID.AddInteger(scUnknown); 1996 ID.AddPointer(V); 1997 void *IP = 0; 1998 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1999 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2000 new (S) SCEVUnknown(V); 2001 UniqueSCEVs.InsertNode(S, IP); 2002 return S; 2003} 2004 2005//===----------------------------------------------------------------------===// 2006// Basic SCEV Analysis and PHI Idiom Recognition Code 2007// 2008 2009/// isSCEVable - Test if values of the given type are analyzable within 2010/// the SCEV framework. This primarily includes integer types, and it 2011/// can optionally include pointer types if the ScalarEvolution class 2012/// has access to target-specific information. 2013bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2014 // Integers are always SCEVable. 2015 if (Ty->isInteger()) 2016 return true; 2017 2018 // Pointers are SCEVable if TargetData information is available 2019 // to provide pointer size information. 2020 if (isa<PointerType>(Ty)) 2021 return TD != NULL; 2022 2023 // Otherwise it's not SCEVable. 2024 return false; 2025} 2026 2027/// getTypeSizeInBits - Return the size in bits of the specified type, 2028/// for which isSCEVable must return true. 2029uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2030 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2031 2032 // If we have a TargetData, use it! 2033 if (TD) 2034 return TD->getTypeSizeInBits(Ty); 2035 2036 // Otherwise, we support only integer types. 2037 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 2038 return Ty->getPrimitiveSizeInBits(); 2039} 2040 2041/// getEffectiveSCEVType - Return a type with the same bitwidth as 2042/// the given type and which represents how SCEV will treat the given 2043/// type, for which isSCEVable must return true. For pointer types, 2044/// this is the pointer-sized integer type. 2045const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2046 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2047 2048 if (Ty->isInteger()) 2049 return Ty; 2050 2051 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2052 return TD->getIntPtrType(); 2053} 2054 2055const SCEV* ScalarEvolution::getCouldNotCompute() { 2056 return &CouldNotCompute; 2057} 2058 2059/// hasSCEV - Return true if the SCEV for this value has already been 2060/// computed. 2061bool ScalarEvolution::hasSCEV(Value *V) const { 2062 return Scalars.count(V); 2063} 2064 2065/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2066/// expression and create a new one. 2067const SCEV* ScalarEvolution::getSCEV(Value *V) { 2068 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2069 2070 std::map<SCEVCallbackVH, const SCEV*>::iterator I = Scalars.find(V); 2071 if (I != Scalars.end()) return I->second; 2072 const SCEV* S = createSCEV(V); 2073 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2074 return S; 2075} 2076 2077/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2078/// specified signed integer value and return a SCEV for the constant. 2079const SCEV* ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2080 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2081 return getConstant(ConstantInt::get(ITy, Val)); 2082} 2083 2084/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2085/// 2086const SCEV* ScalarEvolution::getNegativeSCEV(const SCEV* V) { 2087 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2088 return getConstant(cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2089 2090 const Type *Ty = V->getType(); 2091 Ty = getEffectiveSCEVType(Ty); 2092 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 2093} 2094 2095/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2096const SCEV* ScalarEvolution::getNotSCEV(const SCEV* V) { 2097 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2098 return getConstant(cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2099 2100 const Type *Ty = V->getType(); 2101 Ty = getEffectiveSCEVType(Ty); 2102 const SCEV* AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 2103 return getMinusSCEV(AllOnes, V); 2104} 2105 2106/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2107/// 2108const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2109 const SCEV *RHS) { 2110 // X - Y --> X + -Y 2111 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2112} 2113 2114/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2115/// input value to the specified type. If the type must be extended, it is zero 2116/// extended. 2117const SCEV* 2118ScalarEvolution::getTruncateOrZeroExtend(const SCEV* V, 2119 const Type *Ty) { 2120 const Type *SrcTy = V->getType(); 2121 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2122 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2123 "Cannot truncate or zero extend with non-integer arguments!"); 2124 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2125 return V; // No conversion 2126 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2127 return getTruncateExpr(V, Ty); 2128 return getZeroExtendExpr(V, Ty); 2129} 2130 2131/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2132/// input value to the specified type. If the type must be extended, it is sign 2133/// extended. 2134const SCEV* 2135ScalarEvolution::getTruncateOrSignExtend(const SCEV* V, 2136 const Type *Ty) { 2137 const Type *SrcTy = V->getType(); 2138 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2139 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2140 "Cannot truncate or zero extend with non-integer arguments!"); 2141 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2142 return V; // No conversion 2143 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2144 return getTruncateExpr(V, Ty); 2145 return getSignExtendExpr(V, Ty); 2146} 2147 2148/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2149/// input value to the specified type. If the type must be extended, it is zero 2150/// extended. The conversion must not be narrowing. 2151const SCEV* 2152ScalarEvolution::getNoopOrZeroExtend(const SCEV* V, const Type *Ty) { 2153 const Type *SrcTy = V->getType(); 2154 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2155 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2156 "Cannot noop or zero extend with non-integer arguments!"); 2157 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2158 "getNoopOrZeroExtend cannot truncate!"); 2159 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2160 return V; // No conversion 2161 return getZeroExtendExpr(V, Ty); 2162} 2163 2164/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2165/// input value to the specified type. If the type must be extended, it is sign 2166/// extended. The conversion must not be narrowing. 2167const SCEV* 2168ScalarEvolution::getNoopOrSignExtend(const SCEV* V, const Type *Ty) { 2169 const Type *SrcTy = V->getType(); 2170 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2171 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2172 "Cannot noop or sign extend with non-integer arguments!"); 2173 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2174 "getNoopOrSignExtend cannot truncate!"); 2175 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2176 return V; // No conversion 2177 return getSignExtendExpr(V, Ty); 2178} 2179 2180/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2181/// the input value to the specified type. If the type must be extended, 2182/// it is extended with unspecified bits. The conversion must not be 2183/// narrowing. 2184const SCEV* 2185ScalarEvolution::getNoopOrAnyExtend(const SCEV* V, const Type *Ty) { 2186 const Type *SrcTy = V->getType(); 2187 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2188 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2189 "Cannot noop or any extend with non-integer arguments!"); 2190 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2191 "getNoopOrAnyExtend cannot truncate!"); 2192 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2193 return V; // No conversion 2194 return getAnyExtendExpr(V, Ty); 2195} 2196 2197/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2198/// input value to the specified type. The conversion must not be widening. 2199const SCEV* 2200ScalarEvolution::getTruncateOrNoop(const SCEV* V, const Type *Ty) { 2201 const Type *SrcTy = V->getType(); 2202 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2203 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2204 "Cannot truncate or noop with non-integer arguments!"); 2205 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2206 "getTruncateOrNoop cannot extend!"); 2207 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2208 return V; // No conversion 2209 return getTruncateExpr(V, Ty); 2210} 2211 2212/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2213/// the types using zero-extension, and then perform a umax operation 2214/// with them. 2215const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2216 const SCEV *RHS) { 2217 const SCEV* PromotedLHS = LHS; 2218 const SCEV* PromotedRHS = RHS; 2219 2220 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2221 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2222 else 2223 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2224 2225 return getUMaxExpr(PromotedLHS, PromotedRHS); 2226} 2227 2228/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2229/// the types using zero-extension, and then perform a umin operation 2230/// with them. 2231const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2232 const SCEV *RHS) { 2233 const SCEV* PromotedLHS = LHS; 2234 const SCEV* PromotedRHS = RHS; 2235 2236 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2237 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2238 else 2239 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2240 2241 return getUMinExpr(PromotedLHS, PromotedRHS); 2242} 2243 2244/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2245/// the specified instruction and replaces any references to the symbolic value 2246/// SymName with the specified value. This is used during PHI resolution. 2247void 2248ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I, 2249 const SCEV *SymName, 2250 const SCEV *NewVal) { 2251 std::map<SCEVCallbackVH, const SCEV*>::iterator SI = 2252 Scalars.find(SCEVCallbackVH(I, this)); 2253 if (SI == Scalars.end()) return; 2254 2255 const SCEV* NV = 2256 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2257 if (NV == SI->second) return; // No change. 2258 2259 SI->second = NV; // Update the scalars map! 2260 2261 // Any instruction values that use this instruction might also need to be 2262 // updated! 2263 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2264 UI != E; ++UI) 2265 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2266} 2267 2268/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2269/// a loop header, making it a potential recurrence, or it doesn't. 2270/// 2271const SCEV* ScalarEvolution::createNodeForPHI(PHINode *PN) { 2272 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2273 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2274 if (L->getHeader() == PN->getParent()) { 2275 // If it lives in the loop header, it has two incoming values, one 2276 // from outside the loop, and one from inside. 2277 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2278 unsigned BackEdge = IncomingEdge^1; 2279 2280 // While we are analyzing this PHI node, handle its value symbolically. 2281 const SCEV* SymbolicName = getUnknown(PN); 2282 assert(Scalars.find(PN) == Scalars.end() && 2283 "PHI node already processed?"); 2284 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2285 2286 // Using this symbolic name for the PHI, analyze the value coming around 2287 // the back-edge. 2288 const SCEV* BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2289 2290 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2291 // has a special value for the first iteration of the loop. 2292 2293 // If the value coming around the backedge is an add with the symbolic 2294 // value we just inserted, then we found a simple induction variable! 2295 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2296 // If there is a single occurrence of the symbolic value, replace it 2297 // with a recurrence. 2298 unsigned FoundIndex = Add->getNumOperands(); 2299 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2300 if (Add->getOperand(i) == SymbolicName) 2301 if (FoundIndex == e) { 2302 FoundIndex = i; 2303 break; 2304 } 2305 2306 if (FoundIndex != Add->getNumOperands()) { 2307 // Create an add with everything but the specified operand. 2308 SmallVector<const SCEV*, 8> Ops; 2309 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2310 if (i != FoundIndex) 2311 Ops.push_back(Add->getOperand(i)); 2312 const SCEV* Accum = getAddExpr(Ops); 2313 2314 // This is not a valid addrec if the step amount is varying each 2315 // loop iteration, but is not itself an addrec in this loop. 2316 if (Accum->isLoopInvariant(L) || 2317 (isa<SCEVAddRecExpr>(Accum) && 2318 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2319 const SCEV *StartVal = 2320 getSCEV(PN->getIncomingValue(IncomingEdge)); 2321 const SCEV *PHISCEV = 2322 getAddRecExpr(StartVal, Accum, L); 2323 2324 // Okay, for the entire analysis of this edge we assumed the PHI 2325 // to be symbolic. We now need to go back and update all of the 2326 // entries for the scalars that use the PHI (except for the PHI 2327 // itself) to use the new analyzed value instead of the "symbolic" 2328 // value. 2329 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2330 return PHISCEV; 2331 } 2332 } 2333 } else if (const SCEVAddRecExpr *AddRec = 2334 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2335 // Otherwise, this could be a loop like this: 2336 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2337 // In this case, j = {1,+,1} and BEValue is j. 2338 // Because the other in-value of i (0) fits the evolution of BEValue 2339 // i really is an addrec evolution. 2340 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2341 const SCEV* StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2342 2343 // If StartVal = j.start - j.stride, we can use StartVal as the 2344 // initial step of the addrec evolution. 2345 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2346 AddRec->getOperand(1))) { 2347 const SCEV* PHISCEV = 2348 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2349 2350 // Okay, for the entire analysis of this edge we assumed the PHI 2351 // to be symbolic. We now need to go back and update all of the 2352 // entries for the scalars that use the PHI (except for the PHI 2353 // itself) to use the new analyzed value instead of the "symbolic" 2354 // value. 2355 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2356 return PHISCEV; 2357 } 2358 } 2359 } 2360 2361 return SymbolicName; 2362 } 2363 2364 // If it's not a loop phi, we can't handle it yet. 2365 return getUnknown(PN); 2366} 2367 2368/// createNodeForGEP - Expand GEP instructions into add and multiply 2369/// operations. This allows them to be analyzed by regular SCEV code. 2370/// 2371const SCEV* ScalarEvolution::createNodeForGEP(User *GEP) { 2372 2373 const Type *IntPtrTy = TD->getIntPtrType(); 2374 Value *Base = GEP->getOperand(0); 2375 // Don't attempt to analyze GEPs over unsized objects. 2376 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2377 return getUnknown(GEP); 2378 const SCEV* TotalOffset = getIntegerSCEV(0, IntPtrTy); 2379 gep_type_iterator GTI = gep_type_begin(GEP); 2380 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2381 E = GEP->op_end(); 2382 I != E; ++I) { 2383 Value *Index = *I; 2384 // Compute the (potentially symbolic) offset in bytes for this index. 2385 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2386 // For a struct, add the member offset. 2387 const StructLayout &SL = *TD->getStructLayout(STy); 2388 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2389 uint64_t Offset = SL.getElementOffset(FieldNo); 2390 TotalOffset = getAddExpr(TotalOffset, 2391 getIntegerSCEV(Offset, IntPtrTy)); 2392 } else { 2393 // For an array, add the element offset, explicitly scaled. 2394 const SCEV* LocalOffset = getSCEV(Index); 2395 if (!isa<PointerType>(LocalOffset->getType())) 2396 // Getelementptr indicies are signed. 2397 LocalOffset = getTruncateOrSignExtend(LocalOffset, 2398 IntPtrTy); 2399 LocalOffset = 2400 getMulExpr(LocalOffset, 2401 getIntegerSCEV(TD->getTypeAllocSize(*GTI), 2402 IntPtrTy)); 2403 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2404 } 2405 } 2406 return getAddExpr(getSCEV(Base), TotalOffset); 2407} 2408 2409/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2410/// guaranteed to end in (at every loop iteration). It is, at the same time, 2411/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2412/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2413uint32_t 2414ScalarEvolution::GetMinTrailingZeros(const SCEV* S) { 2415 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2416 return C->getValue()->getValue().countTrailingZeros(); 2417 2418 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2419 return std::min(GetMinTrailingZeros(T->getOperand()), 2420 (uint32_t)getTypeSizeInBits(T->getType())); 2421 2422 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2423 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2424 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2425 getTypeSizeInBits(E->getType()) : OpRes; 2426 } 2427 2428 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2429 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2430 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2431 getTypeSizeInBits(E->getType()) : OpRes; 2432 } 2433 2434 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2435 // The result is the min of all operands results. 2436 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2437 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2438 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2439 return MinOpRes; 2440 } 2441 2442 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2443 // The result is the sum of all operands results. 2444 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2445 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2446 for (unsigned i = 1, e = M->getNumOperands(); 2447 SumOpRes != BitWidth && i != e; ++i) 2448 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2449 BitWidth); 2450 return SumOpRes; 2451 } 2452 2453 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2454 // The result is the min of all operands results. 2455 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2456 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2457 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2458 return MinOpRes; 2459 } 2460 2461 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2462 // The result is the min of all operands results. 2463 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2464 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2465 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2466 return MinOpRes; 2467 } 2468 2469 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2470 // The result is the min of all operands results. 2471 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2472 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2473 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2474 return MinOpRes; 2475 } 2476 2477 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2478 // For a SCEVUnknown, ask ValueTracking. 2479 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2480 APInt Mask = APInt::getAllOnesValue(BitWidth); 2481 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2482 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2483 return Zeros.countTrailingOnes(); 2484 } 2485 2486 // SCEVUDivExpr 2487 return 0; 2488} 2489 2490uint32_t 2491ScalarEvolution::GetMinLeadingZeros(const SCEV* S) { 2492 // TODO: Handle other SCEV expression types here. 2493 2494 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2495 return C->getValue()->getValue().countLeadingZeros(); 2496 2497 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) { 2498 // A zero-extension cast adds zero bits. 2499 return GetMinLeadingZeros(C->getOperand()) + 2500 (getTypeSizeInBits(C->getType()) - 2501 getTypeSizeInBits(C->getOperand()->getType())); 2502 } 2503 2504 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2505 // For a SCEVUnknown, ask ValueTracking. 2506 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2507 APInt Mask = APInt::getAllOnesValue(BitWidth); 2508 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2509 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2510 return Zeros.countLeadingOnes(); 2511 } 2512 2513 return 1; 2514} 2515 2516uint32_t 2517ScalarEvolution::GetMinSignBits(const SCEV* S) { 2518 // TODO: Handle other SCEV expression types here. 2519 2520 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 2521 const APInt &A = C->getValue()->getValue(); 2522 return A.isNegative() ? A.countLeadingOnes() : 2523 A.countLeadingZeros(); 2524 } 2525 2526 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) { 2527 // A sign-extension cast adds sign bits. 2528 return GetMinSignBits(C->getOperand()) + 2529 (getTypeSizeInBits(C->getType()) - 2530 getTypeSizeInBits(C->getOperand()->getType())); 2531 } 2532 2533 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2534 unsigned BitWidth = getTypeSizeInBits(A->getType()); 2535 2536 // Special case decrementing a value (ADD X, -1): 2537 if (const SCEVConstant *CRHS = dyn_cast<SCEVConstant>(A->getOperand(0))) 2538 if (CRHS->isAllOnesValue()) { 2539 SmallVector<const SCEV *, 4> OtherOps(A->op_begin() + 1, A->op_end()); 2540 const SCEV *OtherOpsAdd = getAddExpr(OtherOps); 2541 unsigned LZ = GetMinLeadingZeros(OtherOpsAdd); 2542 2543 // If the input is known to be 0 or 1, the output is 0/-1, which is all 2544 // sign bits set. 2545 if (LZ == BitWidth - 1) 2546 return BitWidth; 2547 2548 // If we are subtracting one from a positive number, there is no carry 2549 // out of the result. 2550 if (LZ > 0) 2551 return GetMinSignBits(OtherOpsAdd); 2552 } 2553 2554 // Add can have at most one carry bit. Thus we know that the output 2555 // is, at worst, one more bit than the inputs. 2556 unsigned Min = BitWidth; 2557 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2558 unsigned N = GetMinSignBits(A->getOperand(i)); 2559 Min = std::min(Min, N) - 1; 2560 if (Min == 0) return 1; 2561 } 2562 return 1; 2563 } 2564 2565 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2566 // For a SCEVUnknown, ask ValueTracking. 2567 return ComputeNumSignBits(U->getValue(), TD); 2568 } 2569 2570 return 1; 2571} 2572 2573/// createSCEV - We know that there is no SCEV for the specified value. 2574/// Analyze the expression. 2575/// 2576const SCEV* ScalarEvolution::createSCEV(Value *V) { 2577 if (!isSCEVable(V->getType())) 2578 return getUnknown(V); 2579 2580 unsigned Opcode = Instruction::UserOp1; 2581 if (Instruction *I = dyn_cast<Instruction>(V)) 2582 Opcode = I->getOpcode(); 2583 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2584 Opcode = CE->getOpcode(); 2585 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2586 return getConstant(CI); 2587 else if (isa<ConstantPointerNull>(V)) 2588 return getIntegerSCEV(0, V->getType()); 2589 else if (isa<UndefValue>(V)) 2590 return getIntegerSCEV(0, V->getType()); 2591 else 2592 return getUnknown(V); 2593 2594 User *U = cast<User>(V); 2595 switch (Opcode) { 2596 case Instruction::Add: 2597 return getAddExpr(getSCEV(U->getOperand(0)), 2598 getSCEV(U->getOperand(1))); 2599 case Instruction::Mul: 2600 return getMulExpr(getSCEV(U->getOperand(0)), 2601 getSCEV(U->getOperand(1))); 2602 case Instruction::UDiv: 2603 return getUDivExpr(getSCEV(U->getOperand(0)), 2604 getSCEV(U->getOperand(1))); 2605 case Instruction::Sub: 2606 return getMinusSCEV(getSCEV(U->getOperand(0)), 2607 getSCEV(U->getOperand(1))); 2608 case Instruction::And: 2609 // For an expression like x&255 that merely masks off the high bits, 2610 // use zext(trunc(x)) as the SCEV expression. 2611 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2612 if (CI->isNullValue()) 2613 return getSCEV(U->getOperand(1)); 2614 if (CI->isAllOnesValue()) 2615 return getSCEV(U->getOperand(0)); 2616 const APInt &A = CI->getValue(); 2617 2618 // Instcombine's ShrinkDemandedConstant may strip bits out of 2619 // constants, obscuring what would otherwise be a low-bits mask. 2620 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2621 // knew about to reconstruct a low-bits mask value. 2622 unsigned LZ = A.countLeadingZeros(); 2623 unsigned BitWidth = A.getBitWidth(); 2624 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2625 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2626 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2627 2628 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2629 2630 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2631 return 2632 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2633 IntegerType::get(BitWidth - LZ)), 2634 U->getType()); 2635 } 2636 break; 2637 2638 case Instruction::Or: 2639 // If the RHS of the Or is a constant, we may have something like: 2640 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2641 // optimizations will transparently handle this case. 2642 // 2643 // In order for this transformation to be safe, the LHS must be of the 2644 // form X*(2^n) and the Or constant must be less than 2^n. 2645 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2646 const SCEV* LHS = getSCEV(U->getOperand(0)); 2647 const APInt &CIVal = CI->getValue(); 2648 if (GetMinTrailingZeros(LHS) >= 2649 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2650 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2651 } 2652 break; 2653 case Instruction::Xor: 2654 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2655 // If the RHS of the xor is a signbit, then this is just an add. 2656 // Instcombine turns add of signbit into xor as a strength reduction step. 2657 if (CI->getValue().isSignBit()) 2658 return getAddExpr(getSCEV(U->getOperand(0)), 2659 getSCEV(U->getOperand(1))); 2660 2661 // If the RHS of xor is -1, then this is a not operation. 2662 if (CI->isAllOnesValue()) 2663 return getNotSCEV(getSCEV(U->getOperand(0))); 2664 2665 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2666 // This is a variant of the check for xor with -1, and it handles 2667 // the case where instcombine has trimmed non-demanded bits out 2668 // of an xor with -1. 2669 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2670 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2671 if (BO->getOpcode() == Instruction::And && 2672 LCI->getValue() == CI->getValue()) 2673 if (const SCEVZeroExtendExpr *Z = 2674 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2675 const Type *UTy = U->getType(); 2676 const SCEV* Z0 = Z->getOperand(); 2677 const Type *Z0Ty = Z0->getType(); 2678 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2679 2680 // If C is a low-bits mask, the zero extend is zerving to 2681 // mask off the high bits. Complement the operand and 2682 // re-apply the zext. 2683 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2684 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2685 2686 // If C is a single bit, it may be in the sign-bit position 2687 // before the zero-extend. In this case, represent the xor 2688 // using an add, which is equivalent, and re-apply the zext. 2689 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2690 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2691 Trunc.isSignBit()) 2692 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2693 UTy); 2694 } 2695 } 2696 break; 2697 2698 case Instruction::Shl: 2699 // Turn shift left of a constant amount into a multiply. 2700 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2701 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2702 Constant *X = ConstantInt::get( 2703 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2704 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2705 } 2706 break; 2707 2708 case Instruction::LShr: 2709 // Turn logical shift right of a constant into a unsigned divide. 2710 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2711 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2712 Constant *X = ConstantInt::get( 2713 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2714 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2715 } 2716 break; 2717 2718 case Instruction::AShr: 2719 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2720 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2721 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2722 if (L->getOpcode() == Instruction::Shl && 2723 L->getOperand(1) == U->getOperand(1)) { 2724 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2725 uint64_t Amt = BitWidth - CI->getZExtValue(); 2726 if (Amt == BitWidth) 2727 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2728 if (Amt > BitWidth) 2729 return getIntegerSCEV(0, U->getType()); // value is undefined 2730 return 2731 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2732 IntegerType::get(Amt)), 2733 U->getType()); 2734 } 2735 break; 2736 2737 case Instruction::Trunc: 2738 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2739 2740 case Instruction::ZExt: 2741 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2742 2743 case Instruction::SExt: 2744 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2745 2746 case Instruction::BitCast: 2747 // BitCasts are no-op casts so we just eliminate the cast. 2748 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2749 return getSCEV(U->getOperand(0)); 2750 break; 2751 2752 case Instruction::IntToPtr: 2753 if (!TD) break; // Without TD we can't analyze pointers. 2754 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2755 TD->getIntPtrType()); 2756 2757 case Instruction::PtrToInt: 2758 if (!TD) break; // Without TD we can't analyze pointers. 2759 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2760 U->getType()); 2761 2762 case Instruction::GetElementPtr: 2763 if (!TD) break; // Without TD we can't analyze pointers. 2764 return createNodeForGEP(U); 2765 2766 case Instruction::PHI: 2767 return createNodeForPHI(cast<PHINode>(U)); 2768 2769 case Instruction::Select: 2770 // This could be a smax or umax that was lowered earlier. 2771 // Try to recover it. 2772 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2773 Value *LHS = ICI->getOperand(0); 2774 Value *RHS = ICI->getOperand(1); 2775 switch (ICI->getPredicate()) { 2776 case ICmpInst::ICMP_SLT: 2777 case ICmpInst::ICMP_SLE: 2778 std::swap(LHS, RHS); 2779 // fall through 2780 case ICmpInst::ICMP_SGT: 2781 case ICmpInst::ICMP_SGE: 2782 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2783 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2784 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2785 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2786 break; 2787 case ICmpInst::ICMP_ULT: 2788 case ICmpInst::ICMP_ULE: 2789 std::swap(LHS, RHS); 2790 // fall through 2791 case ICmpInst::ICMP_UGT: 2792 case ICmpInst::ICMP_UGE: 2793 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2794 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2795 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2796 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2797 break; 2798 case ICmpInst::ICMP_NE: 2799 // n != 0 ? n : 1 -> umax(n, 1) 2800 if (LHS == U->getOperand(1) && 2801 isa<ConstantInt>(U->getOperand(2)) && 2802 cast<ConstantInt>(U->getOperand(2))->isOne() && 2803 isa<ConstantInt>(RHS) && 2804 cast<ConstantInt>(RHS)->isZero()) 2805 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2806 break; 2807 case ICmpInst::ICMP_EQ: 2808 // n == 0 ? 1 : n -> umax(n, 1) 2809 if (LHS == U->getOperand(2) && 2810 isa<ConstantInt>(U->getOperand(1)) && 2811 cast<ConstantInt>(U->getOperand(1))->isOne() && 2812 isa<ConstantInt>(RHS) && 2813 cast<ConstantInt>(RHS)->isZero()) 2814 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 2815 break; 2816 default: 2817 break; 2818 } 2819 } 2820 2821 default: // We cannot analyze this expression. 2822 break; 2823 } 2824 2825 return getUnknown(V); 2826} 2827 2828 2829 2830//===----------------------------------------------------------------------===// 2831// Iteration Count Computation Code 2832// 2833 2834/// getBackedgeTakenCount - If the specified loop has a predictable 2835/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2836/// object. The backedge-taken count is the number of times the loop header 2837/// will be branched to from within the loop. This is one less than the 2838/// trip count of the loop, since it doesn't count the first iteration, 2839/// when the header is branched to from outside the loop. 2840/// 2841/// Note that it is not valid to call this method on a loop without a 2842/// loop-invariant backedge-taken count (see 2843/// hasLoopInvariantBackedgeTakenCount). 2844/// 2845const SCEV* ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2846 return getBackedgeTakenInfo(L).Exact; 2847} 2848 2849/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2850/// return the least SCEV value that is known never to be less than the 2851/// actual backedge taken count. 2852const SCEV* ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2853 return getBackedgeTakenInfo(L).Max; 2854} 2855 2856const ScalarEvolution::BackedgeTakenInfo & 2857ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2858 // Initially insert a CouldNotCompute for this loop. If the insertion 2859 // succeeds, procede to actually compute a backedge-taken count and 2860 // update the value. The temporary CouldNotCompute value tells SCEV 2861 // code elsewhere that it shouldn't attempt to request a new 2862 // backedge-taken count, which could result in infinite recursion. 2863 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2864 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2865 if (Pair.second) { 2866 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2867 if (ItCount.Exact != getCouldNotCompute()) { 2868 assert(ItCount.Exact->isLoopInvariant(L) && 2869 ItCount.Max->isLoopInvariant(L) && 2870 "Computed trip count isn't loop invariant for loop!"); 2871 ++NumTripCountsComputed; 2872 2873 // Update the value in the map. 2874 Pair.first->second = ItCount; 2875 } else { 2876 if (ItCount.Max != getCouldNotCompute()) 2877 // Update the value in the map. 2878 Pair.first->second = ItCount; 2879 if (isa<PHINode>(L->getHeader()->begin())) 2880 // Only count loops that have phi nodes as not being computable. 2881 ++NumTripCountsNotComputed; 2882 } 2883 2884 // Now that we know more about the trip count for this loop, forget any 2885 // existing SCEV values for PHI nodes in this loop since they are only 2886 // conservative estimates made without the benefit 2887 // of trip count information. 2888 if (ItCount.hasAnyInfo()) 2889 forgetLoopPHIs(L); 2890 } 2891 return Pair.first->second; 2892} 2893 2894/// forgetLoopBackedgeTakenCount - This method should be called by the 2895/// client when it has changed a loop in a way that may effect 2896/// ScalarEvolution's ability to compute a trip count, or if the loop 2897/// is deleted. 2898void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2899 BackedgeTakenCounts.erase(L); 2900 forgetLoopPHIs(L); 2901} 2902 2903/// forgetLoopPHIs - Delete the memoized SCEVs associated with the 2904/// PHI nodes in the given loop. This is used when the trip count of 2905/// the loop may have changed. 2906void ScalarEvolution::forgetLoopPHIs(const Loop *L) { 2907 BasicBlock *Header = L->getHeader(); 2908 2909 // Push all Loop-header PHIs onto the Worklist stack, except those 2910 // that are presently represented via a SCEVUnknown. SCEVUnknown for 2911 // a PHI either means that it has an unrecognized structure, or it's 2912 // a PHI that's in the progress of being computed by createNodeForPHI. 2913 // In the former case, additional loop trip count information isn't 2914 // going to change anything. In the later case, createNodeForPHI will 2915 // perform the necessary updates on its own when it gets to that point. 2916 SmallVector<Instruction *, 16> Worklist; 2917 for (BasicBlock::iterator I = Header->begin(); 2918 PHINode *PN = dyn_cast<PHINode>(I); ++I) { 2919 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2920 Scalars.find((Value*)I); 2921 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second)) 2922 Worklist.push_back(PN); 2923 } 2924 2925 while (!Worklist.empty()) { 2926 Instruction *I = Worklist.pop_back_val(); 2927 if (Scalars.erase(I)) 2928 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2929 UI != UE; ++UI) 2930 Worklist.push_back(cast<Instruction>(UI)); 2931 } 2932} 2933 2934/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2935/// of the specified loop will execute. 2936ScalarEvolution::BackedgeTakenInfo 2937ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2938 SmallVector<BasicBlock*, 8> ExitingBlocks; 2939 L->getExitingBlocks(ExitingBlocks); 2940 2941 // Examine all exits and pick the most conservative values. 2942 const SCEV* BECount = getCouldNotCompute(); 2943 const SCEV* MaxBECount = getCouldNotCompute(); 2944 bool CouldNotComputeBECount = false; 2945 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 2946 BackedgeTakenInfo NewBTI = 2947 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 2948 2949 if (NewBTI.Exact == getCouldNotCompute()) { 2950 // We couldn't compute an exact value for this exit, so 2951 // we won't be able to compute an exact value for the loop. 2952 CouldNotComputeBECount = true; 2953 BECount = getCouldNotCompute(); 2954 } else if (!CouldNotComputeBECount) { 2955 if (BECount == getCouldNotCompute()) 2956 BECount = NewBTI.Exact; 2957 else 2958 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 2959 } 2960 if (MaxBECount == getCouldNotCompute()) 2961 MaxBECount = NewBTI.Max; 2962 else if (NewBTI.Max != getCouldNotCompute()) 2963 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 2964 } 2965 2966 return BackedgeTakenInfo(BECount, MaxBECount); 2967} 2968 2969/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 2970/// of the specified loop will execute if it exits via the specified block. 2971ScalarEvolution::BackedgeTakenInfo 2972ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 2973 BasicBlock *ExitingBlock) { 2974 2975 // Okay, we've chosen an exiting block. See what condition causes us to 2976 // exit at this block. 2977 // 2978 // FIXME: we should be able to handle switch instructions (with a single exit) 2979 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 2980 if (ExitBr == 0) return getCouldNotCompute(); 2981 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 2982 2983 // At this point, we know we have a conditional branch that determines whether 2984 // the loop is exited. However, we don't know if the branch is executed each 2985 // time through the loop. If not, then the execution count of the branch will 2986 // not be equal to the trip count of the loop. 2987 // 2988 // Currently we check for this by checking to see if the Exit branch goes to 2989 // the loop header. If so, we know it will always execute the same number of 2990 // times as the loop. We also handle the case where the exit block *is* the 2991 // loop header. This is common for un-rotated loops. 2992 // 2993 // If both of those tests fail, walk up the unique predecessor chain to the 2994 // header, stopping if there is an edge that doesn't exit the loop. If the 2995 // header is reached, the execution count of the branch will be equal to the 2996 // trip count of the loop. 2997 // 2998 // More extensive analysis could be done to handle more cases here. 2999 // 3000 if (ExitBr->getSuccessor(0) != L->getHeader() && 3001 ExitBr->getSuccessor(1) != L->getHeader() && 3002 ExitBr->getParent() != L->getHeader()) { 3003 // The simple checks failed, try climbing the unique predecessor chain 3004 // up to the header. 3005 bool Ok = false; 3006 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3007 BasicBlock *Pred = BB->getUniquePredecessor(); 3008 if (!Pred) 3009 return getCouldNotCompute(); 3010 TerminatorInst *PredTerm = Pred->getTerminator(); 3011 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3012 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3013 if (PredSucc == BB) 3014 continue; 3015 // If the predecessor has a successor that isn't BB and isn't 3016 // outside the loop, assume the worst. 3017 if (L->contains(PredSucc)) 3018 return getCouldNotCompute(); 3019 } 3020 if (Pred == L->getHeader()) { 3021 Ok = true; 3022 break; 3023 } 3024 BB = Pred; 3025 } 3026 if (!Ok) 3027 return getCouldNotCompute(); 3028 } 3029 3030 // Procede to the next level to examine the exit condition expression. 3031 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3032 ExitBr->getSuccessor(0), 3033 ExitBr->getSuccessor(1)); 3034} 3035 3036/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3037/// backedge of the specified loop will execute if its exit condition 3038/// were a conditional branch of ExitCond, TBB, and FBB. 3039ScalarEvolution::BackedgeTakenInfo 3040ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3041 Value *ExitCond, 3042 BasicBlock *TBB, 3043 BasicBlock *FBB) { 3044 // Check if the controlling expression for this loop is an And or Or. 3045 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3046 if (BO->getOpcode() == Instruction::And) { 3047 // Recurse on the operands of the and. 3048 BackedgeTakenInfo BTI0 = 3049 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3050 BackedgeTakenInfo BTI1 = 3051 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3052 const SCEV* BECount = getCouldNotCompute(); 3053 const SCEV* MaxBECount = getCouldNotCompute(); 3054 if (L->contains(TBB)) { 3055 // Both conditions must be true for the loop to continue executing. 3056 // Choose the less conservative count. 3057 if (BTI0.Exact == getCouldNotCompute() || 3058 BTI1.Exact == getCouldNotCompute()) 3059 BECount = getCouldNotCompute(); 3060 else 3061 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3062 if (BTI0.Max == getCouldNotCompute()) 3063 MaxBECount = BTI1.Max; 3064 else if (BTI1.Max == getCouldNotCompute()) 3065 MaxBECount = BTI0.Max; 3066 else 3067 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3068 } else { 3069 // Both conditions must be true for the loop to exit. 3070 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3071 if (BTI0.Exact != getCouldNotCompute() && 3072 BTI1.Exact != getCouldNotCompute()) 3073 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3074 if (BTI0.Max != getCouldNotCompute() && 3075 BTI1.Max != getCouldNotCompute()) 3076 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3077 } 3078 3079 return BackedgeTakenInfo(BECount, MaxBECount); 3080 } 3081 if (BO->getOpcode() == Instruction::Or) { 3082 // Recurse on the operands of the or. 3083 BackedgeTakenInfo BTI0 = 3084 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3085 BackedgeTakenInfo BTI1 = 3086 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3087 const SCEV* BECount = getCouldNotCompute(); 3088 const SCEV* MaxBECount = getCouldNotCompute(); 3089 if (L->contains(FBB)) { 3090 // Both conditions must be false for the loop to continue executing. 3091 // Choose the less conservative count. 3092 if (BTI0.Exact == getCouldNotCompute() || 3093 BTI1.Exact == getCouldNotCompute()) 3094 BECount = getCouldNotCompute(); 3095 else 3096 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3097 if (BTI0.Max == getCouldNotCompute()) 3098 MaxBECount = BTI1.Max; 3099 else if (BTI1.Max == getCouldNotCompute()) 3100 MaxBECount = BTI0.Max; 3101 else 3102 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3103 } else { 3104 // Both conditions must be false for the loop to exit. 3105 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3106 if (BTI0.Exact != getCouldNotCompute() && 3107 BTI1.Exact != getCouldNotCompute()) 3108 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3109 if (BTI0.Max != getCouldNotCompute() && 3110 BTI1.Max != getCouldNotCompute()) 3111 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3112 } 3113 3114 return BackedgeTakenInfo(BECount, MaxBECount); 3115 } 3116 } 3117 3118 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3119 // Procede to the next level to examine the icmp. 3120 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3121 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3122 3123 // If it's not an integer or pointer comparison then compute it the hard way. 3124 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3125} 3126 3127/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3128/// backedge of the specified loop will execute if its exit condition 3129/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3130ScalarEvolution::BackedgeTakenInfo 3131ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3132 ICmpInst *ExitCond, 3133 BasicBlock *TBB, 3134 BasicBlock *FBB) { 3135 3136 // If the condition was exit on true, convert the condition to exit on false 3137 ICmpInst::Predicate Cond; 3138 if (!L->contains(FBB)) 3139 Cond = ExitCond->getPredicate(); 3140 else 3141 Cond = ExitCond->getInversePredicate(); 3142 3143 // Handle common loops like: for (X = "string"; *X; ++X) 3144 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3145 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3146 const SCEV* ItCnt = 3147 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3148 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3149 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3150 return BackedgeTakenInfo(ItCnt, 3151 isa<SCEVConstant>(ItCnt) ? ItCnt : 3152 getConstant(APInt::getMaxValue(BitWidth)-1)); 3153 } 3154 } 3155 3156 const SCEV* LHS = getSCEV(ExitCond->getOperand(0)); 3157 const SCEV* RHS = getSCEV(ExitCond->getOperand(1)); 3158 3159 // Try to evaluate any dependencies out of the loop. 3160 LHS = getSCEVAtScope(LHS, L); 3161 RHS = getSCEVAtScope(RHS, L); 3162 3163 // At this point, we would like to compute how many iterations of the 3164 // loop the predicate will return true for these inputs. 3165 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3166 // If there is a loop-invariant, force it into the RHS. 3167 std::swap(LHS, RHS); 3168 Cond = ICmpInst::getSwappedPredicate(Cond); 3169 } 3170 3171 // If we have a comparison of a chrec against a constant, try to use value 3172 // ranges to answer this query. 3173 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3174 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3175 if (AddRec->getLoop() == L) { 3176 // Form the constant range. 3177 ConstantRange CompRange( 3178 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3179 3180 const SCEV* Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3181 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3182 } 3183 3184 switch (Cond) { 3185 case ICmpInst::ICMP_NE: { // while (X != Y) 3186 // Convert to: while (X-Y != 0) 3187 const SCEV* TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3188 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3189 break; 3190 } 3191 case ICmpInst::ICMP_EQ: { 3192 // Convert to: while (X-Y == 0) // while (X == Y) 3193 const SCEV* TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3194 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3195 break; 3196 } 3197 case ICmpInst::ICMP_SLT: { 3198 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3199 if (BTI.hasAnyInfo()) return BTI; 3200 break; 3201 } 3202 case ICmpInst::ICMP_SGT: { 3203 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3204 getNotSCEV(RHS), L, true); 3205 if (BTI.hasAnyInfo()) return BTI; 3206 break; 3207 } 3208 case ICmpInst::ICMP_ULT: { 3209 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3210 if (BTI.hasAnyInfo()) return BTI; 3211 break; 3212 } 3213 case ICmpInst::ICMP_UGT: { 3214 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3215 getNotSCEV(RHS), L, false); 3216 if (BTI.hasAnyInfo()) return BTI; 3217 break; 3218 } 3219 default: 3220#if 0 3221 errs() << "ComputeBackedgeTakenCount "; 3222 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3223 errs() << "[unsigned] "; 3224 errs() << *LHS << " " 3225 << Instruction::getOpcodeName(Instruction::ICmp) 3226 << " " << *RHS << "\n"; 3227#endif 3228 break; 3229 } 3230 return 3231 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3232} 3233 3234static ConstantInt * 3235EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3236 ScalarEvolution &SE) { 3237 const SCEV* InVal = SE.getConstant(C); 3238 const SCEV* Val = AddRec->evaluateAtIteration(InVal, SE); 3239 assert(isa<SCEVConstant>(Val) && 3240 "Evaluation of SCEV at constant didn't fold correctly?"); 3241 return cast<SCEVConstant>(Val)->getValue(); 3242} 3243 3244/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3245/// and a GEP expression (missing the pointer index) indexing into it, return 3246/// the addressed element of the initializer or null if the index expression is 3247/// invalid. 3248static Constant * 3249GetAddressedElementFromGlobal(GlobalVariable *GV, 3250 const std::vector<ConstantInt*> &Indices) { 3251 Constant *Init = GV->getInitializer(); 3252 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3253 uint64_t Idx = Indices[i]->getZExtValue(); 3254 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3255 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3256 Init = cast<Constant>(CS->getOperand(Idx)); 3257 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3258 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3259 Init = cast<Constant>(CA->getOperand(Idx)); 3260 } else if (isa<ConstantAggregateZero>(Init)) { 3261 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3262 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3263 Init = Constant::getNullValue(STy->getElementType(Idx)); 3264 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3265 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3266 Init = Constant::getNullValue(ATy->getElementType()); 3267 } else { 3268 assert(0 && "Unknown constant aggregate type!"); 3269 } 3270 return 0; 3271 } else { 3272 return 0; // Unknown initializer type 3273 } 3274 } 3275 return Init; 3276} 3277 3278/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3279/// 'icmp op load X, cst', try to see if we can compute the backedge 3280/// execution count. 3281const SCEV * 3282ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3283 LoadInst *LI, 3284 Constant *RHS, 3285 const Loop *L, 3286 ICmpInst::Predicate predicate) { 3287 if (LI->isVolatile()) return getCouldNotCompute(); 3288 3289 // Check to see if the loaded pointer is a getelementptr of a global. 3290 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3291 if (!GEP) return getCouldNotCompute(); 3292 3293 // Make sure that it is really a constant global we are gepping, with an 3294 // initializer, and make sure the first IDX is really 0. 3295 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3296 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3297 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3298 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3299 return getCouldNotCompute(); 3300 3301 // Okay, we allow one non-constant index into the GEP instruction. 3302 Value *VarIdx = 0; 3303 std::vector<ConstantInt*> Indexes; 3304 unsigned VarIdxNum = 0; 3305 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3306 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3307 Indexes.push_back(CI); 3308 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3309 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3310 VarIdx = GEP->getOperand(i); 3311 VarIdxNum = i-2; 3312 Indexes.push_back(0); 3313 } 3314 3315 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3316 // Check to see if X is a loop variant variable value now. 3317 const SCEV* Idx = getSCEV(VarIdx); 3318 Idx = getSCEVAtScope(Idx, L); 3319 3320 // We can only recognize very limited forms of loop index expressions, in 3321 // particular, only affine AddRec's like {C1,+,C2}. 3322 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3323 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3324 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3325 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3326 return getCouldNotCompute(); 3327 3328 unsigned MaxSteps = MaxBruteForceIterations; 3329 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3330 ConstantInt *ItCst = 3331 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3332 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3333 3334 // Form the GEP offset. 3335 Indexes[VarIdxNum] = Val; 3336 3337 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3338 if (Result == 0) break; // Cannot compute! 3339 3340 // Evaluate the condition for this iteration. 3341 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3342 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3343 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3344#if 0 3345 errs() << "\n***\n*** Computed loop count " << *ItCst 3346 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3347 << "***\n"; 3348#endif 3349 ++NumArrayLenItCounts; 3350 return getConstant(ItCst); // Found terminating iteration! 3351 } 3352 } 3353 return getCouldNotCompute(); 3354} 3355 3356 3357/// CanConstantFold - Return true if we can constant fold an instruction of the 3358/// specified type, assuming that all operands were constants. 3359static bool CanConstantFold(const Instruction *I) { 3360 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3361 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3362 return true; 3363 3364 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3365 if (const Function *F = CI->getCalledFunction()) 3366 return canConstantFoldCallTo(F); 3367 return false; 3368} 3369 3370/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3371/// in the loop that V is derived from. We allow arbitrary operations along the 3372/// way, but the operands of an operation must either be constants or a value 3373/// derived from a constant PHI. If this expression does not fit with these 3374/// constraints, return null. 3375static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3376 // If this is not an instruction, or if this is an instruction outside of the 3377 // loop, it can't be derived from a loop PHI. 3378 Instruction *I = dyn_cast<Instruction>(V); 3379 if (I == 0 || !L->contains(I->getParent())) return 0; 3380 3381 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3382 if (L->getHeader() == I->getParent()) 3383 return PN; 3384 else 3385 // We don't currently keep track of the control flow needed to evaluate 3386 // PHIs, so we cannot handle PHIs inside of loops. 3387 return 0; 3388 } 3389 3390 // If we won't be able to constant fold this expression even if the operands 3391 // are constants, return early. 3392 if (!CanConstantFold(I)) return 0; 3393 3394 // Otherwise, we can evaluate this instruction if all of its operands are 3395 // constant or derived from a PHI node themselves. 3396 PHINode *PHI = 0; 3397 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3398 if (!(isa<Constant>(I->getOperand(Op)) || 3399 isa<GlobalValue>(I->getOperand(Op)))) { 3400 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3401 if (P == 0) return 0; // Not evolving from PHI 3402 if (PHI == 0) 3403 PHI = P; 3404 else if (PHI != P) 3405 return 0; // Evolving from multiple different PHIs. 3406 } 3407 3408 // This is a expression evolving from a constant PHI! 3409 return PHI; 3410} 3411 3412/// EvaluateExpression - Given an expression that passes the 3413/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3414/// in the loop has the value PHIVal. If we can't fold this expression for some 3415/// reason, return null. 3416static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3417 if (isa<PHINode>(V)) return PHIVal; 3418 if (Constant *C = dyn_cast<Constant>(V)) return C; 3419 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3420 Instruction *I = cast<Instruction>(V); 3421 3422 std::vector<Constant*> Operands; 3423 Operands.resize(I->getNumOperands()); 3424 3425 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3426 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3427 if (Operands[i] == 0) return 0; 3428 } 3429 3430 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3431 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3432 &Operands[0], Operands.size()); 3433 else 3434 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3435 &Operands[0], Operands.size()); 3436} 3437 3438/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3439/// in the header of its containing loop, we know the loop executes a 3440/// constant number of times, and the PHI node is just a recurrence 3441/// involving constants, fold it. 3442Constant * 3443ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3444 const APInt& BEs, 3445 const Loop *L) { 3446 std::map<PHINode*, Constant*>::iterator I = 3447 ConstantEvolutionLoopExitValue.find(PN); 3448 if (I != ConstantEvolutionLoopExitValue.end()) 3449 return I->second; 3450 3451 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3452 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3453 3454 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3455 3456 // Since the loop is canonicalized, the PHI node must have two entries. One 3457 // entry must be a constant (coming in from outside of the loop), and the 3458 // second must be derived from the same PHI. 3459 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3460 Constant *StartCST = 3461 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3462 if (StartCST == 0) 3463 return RetVal = 0; // Must be a constant. 3464 3465 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3466 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3467 if (PN2 != PN) 3468 return RetVal = 0; // Not derived from same PHI. 3469 3470 // Execute the loop symbolically to determine the exit value. 3471 if (BEs.getActiveBits() >= 32) 3472 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3473 3474 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3475 unsigned IterationNum = 0; 3476 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3477 if (IterationNum == NumIterations) 3478 return RetVal = PHIVal; // Got exit value! 3479 3480 // Compute the value of the PHI node for the next iteration. 3481 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3482 if (NextPHI == PHIVal) 3483 return RetVal = NextPHI; // Stopped evolving! 3484 if (NextPHI == 0) 3485 return 0; // Couldn't evaluate! 3486 PHIVal = NextPHI; 3487 } 3488} 3489 3490/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3491/// constant number of times (the condition evolves only from constants), 3492/// try to evaluate a few iterations of the loop until we get the exit 3493/// condition gets a value of ExitWhen (true or false). If we cannot 3494/// evaluate the trip count of the loop, return getCouldNotCompute(). 3495const SCEV * 3496ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3497 Value *Cond, 3498 bool ExitWhen) { 3499 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3500 if (PN == 0) return getCouldNotCompute(); 3501 3502 // Since the loop is canonicalized, the PHI node must have two entries. One 3503 // entry must be a constant (coming in from outside of the loop), and the 3504 // second must be derived from the same PHI. 3505 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3506 Constant *StartCST = 3507 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3508 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3509 3510 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3511 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3512 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3513 3514 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3515 // the loop symbolically to determine when the condition gets a value of 3516 // "ExitWhen". 3517 unsigned IterationNum = 0; 3518 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3519 for (Constant *PHIVal = StartCST; 3520 IterationNum != MaxIterations; ++IterationNum) { 3521 ConstantInt *CondVal = 3522 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3523 3524 // Couldn't symbolically evaluate. 3525 if (!CondVal) return getCouldNotCompute(); 3526 3527 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3528 ++NumBruteForceTripCountsComputed; 3529 return getConstant(Type::Int32Ty, IterationNum); 3530 } 3531 3532 // Compute the value of the PHI node for the next iteration. 3533 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3534 if (NextPHI == 0 || NextPHI == PHIVal) 3535 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3536 PHIVal = NextPHI; 3537 } 3538 3539 // Too many iterations were needed to evaluate. 3540 return getCouldNotCompute(); 3541} 3542 3543/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3544/// at the specified scope in the program. The L value specifies a loop 3545/// nest to evaluate the expression at, where null is the top-level or a 3546/// specified loop is immediately inside of the loop. 3547/// 3548/// This method can be used to compute the exit value for a variable defined 3549/// in a loop by querying what the value will hold in the parent loop. 3550/// 3551/// In the case that a relevant loop exit value cannot be computed, the 3552/// original value V is returned. 3553const SCEV* ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3554 // FIXME: this should be turned into a virtual method on SCEV! 3555 3556 if (isa<SCEVConstant>(V)) return V; 3557 3558 // If this instruction is evolved from a constant-evolving PHI, compute the 3559 // exit value from the loop without using SCEVs. 3560 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3561 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3562 const Loop *LI = (*this->LI)[I->getParent()]; 3563 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3564 if (PHINode *PN = dyn_cast<PHINode>(I)) 3565 if (PN->getParent() == LI->getHeader()) { 3566 // Okay, there is no closed form solution for the PHI node. Check 3567 // to see if the loop that contains it has a known backedge-taken 3568 // count. If so, we may be able to force computation of the exit 3569 // value. 3570 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(LI); 3571 if (const SCEVConstant *BTCC = 3572 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3573 // Okay, we know how many times the containing loop executes. If 3574 // this is a constant evolving PHI node, get the final value at 3575 // the specified iteration number. 3576 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3577 BTCC->getValue()->getValue(), 3578 LI); 3579 if (RV) return getSCEV(RV); 3580 } 3581 } 3582 3583 // Okay, this is an expression that we cannot symbolically evaluate 3584 // into a SCEV. Check to see if it's possible to symbolically evaluate 3585 // the arguments into constants, and if so, try to constant propagate the 3586 // result. This is particularly useful for computing loop exit values. 3587 if (CanConstantFold(I)) { 3588 // Check to see if we've folded this instruction at this loop before. 3589 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3590 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3591 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3592 if (!Pair.second) 3593 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3594 3595 std::vector<Constant*> Operands; 3596 Operands.reserve(I->getNumOperands()); 3597 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3598 Value *Op = I->getOperand(i); 3599 if (Constant *C = dyn_cast<Constant>(Op)) { 3600 Operands.push_back(C); 3601 } else { 3602 // If any of the operands is non-constant and if they are 3603 // non-integer and non-pointer, don't even try to analyze them 3604 // with scev techniques. 3605 if (!isSCEVable(Op->getType())) 3606 return V; 3607 3608 const SCEV* OpV = getSCEVAtScope(getSCEV(Op), L); 3609 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3610 Constant *C = SC->getValue(); 3611 if (C->getType() != Op->getType()) 3612 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3613 Op->getType(), 3614 false), 3615 C, Op->getType()); 3616 Operands.push_back(C); 3617 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3618 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3619 if (C->getType() != Op->getType()) 3620 C = 3621 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3622 Op->getType(), 3623 false), 3624 C, Op->getType()); 3625 Operands.push_back(C); 3626 } else 3627 return V; 3628 } else { 3629 return V; 3630 } 3631 } 3632 } 3633 3634 Constant *C; 3635 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3636 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3637 &Operands[0], Operands.size()); 3638 else 3639 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3640 &Operands[0], Operands.size()); 3641 Pair.first->second = C; 3642 return getSCEV(C); 3643 } 3644 } 3645 3646 // This is some other type of SCEVUnknown, just return it. 3647 return V; 3648 } 3649 3650 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3651 // Avoid performing the look-up in the common case where the specified 3652 // expression has no loop-variant portions. 3653 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3654 const SCEV* OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3655 if (OpAtScope != Comm->getOperand(i)) { 3656 // Okay, at least one of these operands is loop variant but might be 3657 // foldable. Build a new instance of the folded commutative expression. 3658 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3659 Comm->op_begin()+i); 3660 NewOps.push_back(OpAtScope); 3661 3662 for (++i; i != e; ++i) { 3663 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3664 NewOps.push_back(OpAtScope); 3665 } 3666 if (isa<SCEVAddExpr>(Comm)) 3667 return getAddExpr(NewOps); 3668 if (isa<SCEVMulExpr>(Comm)) 3669 return getMulExpr(NewOps); 3670 if (isa<SCEVSMaxExpr>(Comm)) 3671 return getSMaxExpr(NewOps); 3672 if (isa<SCEVUMaxExpr>(Comm)) 3673 return getUMaxExpr(NewOps); 3674 assert(0 && "Unknown commutative SCEV type!"); 3675 } 3676 } 3677 // If we got here, all operands are loop invariant. 3678 return Comm; 3679 } 3680 3681 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3682 const SCEV* LHS = getSCEVAtScope(Div->getLHS(), L); 3683 const SCEV* RHS = getSCEVAtScope(Div->getRHS(), L); 3684 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3685 return Div; // must be loop invariant 3686 return getUDivExpr(LHS, RHS); 3687 } 3688 3689 // If this is a loop recurrence for a loop that does not contain L, then we 3690 // are dealing with the final value computed by the loop. 3691 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3692 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3693 // To evaluate this recurrence, we need to know how many times the AddRec 3694 // loop iterates. Compute this now. 3695 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3696 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3697 3698 // Then, evaluate the AddRec. 3699 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3700 } 3701 return AddRec; 3702 } 3703 3704 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3705 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L); 3706 if (Op == Cast->getOperand()) 3707 return Cast; // must be loop invariant 3708 return getZeroExtendExpr(Op, Cast->getType()); 3709 } 3710 3711 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3712 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L); 3713 if (Op == Cast->getOperand()) 3714 return Cast; // must be loop invariant 3715 return getSignExtendExpr(Op, Cast->getType()); 3716 } 3717 3718 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3719 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L); 3720 if (Op == Cast->getOperand()) 3721 return Cast; // must be loop invariant 3722 return getTruncateExpr(Op, Cast->getType()); 3723 } 3724 3725 assert(0 && "Unknown SCEV type!"); 3726 return 0; 3727} 3728 3729/// getSCEVAtScope - This is a convenience function which does 3730/// getSCEVAtScope(getSCEV(V), L). 3731const SCEV* ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3732 return getSCEVAtScope(getSCEV(V), L); 3733} 3734 3735/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3736/// following equation: 3737/// 3738/// A * X = B (mod N) 3739/// 3740/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3741/// A and B isn't important. 3742/// 3743/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3744static const SCEV* SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3745 ScalarEvolution &SE) { 3746 uint32_t BW = A.getBitWidth(); 3747 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3748 assert(A != 0 && "A must be non-zero."); 3749 3750 // 1. D = gcd(A, N) 3751 // 3752 // The gcd of A and N may have only one prime factor: 2. The number of 3753 // trailing zeros in A is its multiplicity 3754 uint32_t Mult2 = A.countTrailingZeros(); 3755 // D = 2^Mult2 3756 3757 // 2. Check if B is divisible by D. 3758 // 3759 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3760 // is not less than multiplicity of this prime factor for D. 3761 if (B.countTrailingZeros() < Mult2) 3762 return SE.getCouldNotCompute(); 3763 3764 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3765 // modulo (N / D). 3766 // 3767 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3768 // bit width during computations. 3769 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3770 APInt Mod(BW + 1, 0); 3771 Mod.set(BW - Mult2); // Mod = N / D 3772 APInt I = AD.multiplicativeInverse(Mod); 3773 3774 // 4. Compute the minimum unsigned root of the equation: 3775 // I * (B / D) mod (N / D) 3776 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 3777 3778 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 3779 // bits. 3780 return SE.getConstant(Result.trunc(BW)); 3781} 3782 3783/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 3784/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 3785/// might be the same) or two SCEVCouldNotCompute objects. 3786/// 3787static std::pair<const SCEV*,const SCEV*> 3788SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 3789 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 3790 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 3791 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 3792 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 3793 3794 // We currently can only solve this if the coefficients are constants. 3795 if (!LC || !MC || !NC) { 3796 const SCEV *CNC = SE.getCouldNotCompute(); 3797 return std::make_pair(CNC, CNC); 3798 } 3799 3800 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 3801 const APInt &L = LC->getValue()->getValue(); 3802 const APInt &M = MC->getValue()->getValue(); 3803 const APInt &N = NC->getValue()->getValue(); 3804 APInt Two(BitWidth, 2); 3805 APInt Four(BitWidth, 4); 3806 3807 { 3808 using namespace APIntOps; 3809 const APInt& C = L; 3810 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 3811 // The B coefficient is M-N/2 3812 APInt B(M); 3813 B -= sdiv(N,Two); 3814 3815 // The A coefficient is N/2 3816 APInt A(N.sdiv(Two)); 3817 3818 // Compute the B^2-4ac term. 3819 APInt SqrtTerm(B); 3820 SqrtTerm *= B; 3821 SqrtTerm -= Four * (A * C); 3822 3823 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 3824 // integer value or else APInt::sqrt() will assert. 3825 APInt SqrtVal(SqrtTerm.sqrt()); 3826 3827 // Compute the two solutions for the quadratic formula. 3828 // The divisions must be performed as signed divisions. 3829 APInt NegB(-B); 3830 APInt TwoA( A << 1 ); 3831 if (TwoA.isMinValue()) { 3832 const SCEV *CNC = SE.getCouldNotCompute(); 3833 return std::make_pair(CNC, CNC); 3834 } 3835 3836 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA)); 3837 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA)); 3838 3839 return std::make_pair(SE.getConstant(Solution1), 3840 SE.getConstant(Solution2)); 3841 } // end APIntOps namespace 3842} 3843 3844/// HowFarToZero - Return the number of times a backedge comparing the specified 3845/// value to zero will execute. If not computable, return CouldNotCompute. 3846const SCEV* ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 3847 // If the value is a constant 3848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3849 // If the value is already zero, the branch will execute zero times. 3850 if (C->getValue()->isZero()) return C; 3851 return getCouldNotCompute(); // Otherwise it will loop infinitely. 3852 } 3853 3854 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 3855 if (!AddRec || AddRec->getLoop() != L) 3856 return getCouldNotCompute(); 3857 3858 if (AddRec->isAffine()) { 3859 // If this is an affine expression, the execution count of this branch is 3860 // the minimum unsigned root of the following equation: 3861 // 3862 // Start + Step*N = 0 (mod 2^BW) 3863 // 3864 // equivalent to: 3865 // 3866 // Step*N = -Start (mod 2^BW) 3867 // 3868 // where BW is the common bit width of Start and Step. 3869 3870 // Get the initial value for the loop. 3871 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 3872 L->getParentLoop()); 3873 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 3874 L->getParentLoop()); 3875 3876 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 3877 // For now we handle only constant steps. 3878 3879 // First, handle unitary steps. 3880 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 3881 return getNegativeSCEV(Start); // N = -Start (as unsigned) 3882 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 3883 return Start; // N = Start (as unsigned) 3884 3885 // Then, try to solve the above equation provided that Start is constant. 3886 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 3887 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 3888 -StartC->getValue()->getValue(), 3889 *this); 3890 } 3891 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 3892 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 3893 // the quadratic equation to solve it. 3894 std::pair<const SCEV*,const SCEV*> Roots = SolveQuadraticEquation(AddRec, 3895 *this); 3896 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3897 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3898 if (R1) { 3899#if 0 3900 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 3901 << " sol#2: " << *R2 << "\n"; 3902#endif 3903 // Pick the smallest positive root value. 3904 if (ConstantInt *CB = 3905 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 3906 R1->getValue(), R2->getValue()))) { 3907 if (CB->getZExtValue() == false) 3908 std::swap(R1, R2); // R1 is the minimum root now. 3909 3910 // We can only use this value if the chrec ends up with an exact zero 3911 // value at this index. When solving for "X*X != 5", for example, we 3912 // should not accept a root of 2. 3913 const SCEV* Val = AddRec->evaluateAtIteration(R1, *this); 3914 if (Val->isZero()) 3915 return R1; // We found a quadratic root! 3916 } 3917 } 3918 } 3919 3920 return getCouldNotCompute(); 3921} 3922 3923/// HowFarToNonZero - Return the number of times a backedge checking the 3924/// specified value for nonzero will execute. If not computable, return 3925/// CouldNotCompute 3926const SCEV* ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 3927 // Loops that look like: while (X == 0) are very strange indeed. We don't 3928 // handle them yet except for the trivial case. This could be expanded in the 3929 // future as needed. 3930 3931 // If the value is a constant, check to see if it is known to be non-zero 3932 // already. If so, the backedge will execute zero times. 3933 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3934 if (!C->getValue()->isNullValue()) 3935 return getIntegerSCEV(0, C->getType()); 3936 return getCouldNotCompute(); // Otherwise it will loop infinitely. 3937 } 3938 3939 // We could implement others, but I really doubt anyone writes loops like 3940 // this, and if they did, they would already be constant folded. 3941 return getCouldNotCompute(); 3942} 3943 3944/// getLoopPredecessor - If the given loop's header has exactly one unique 3945/// predecessor outside the loop, return it. Otherwise return null. 3946/// 3947BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 3948 BasicBlock *Header = L->getHeader(); 3949 BasicBlock *Pred = 0; 3950 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 3951 PI != E; ++PI) 3952 if (!L->contains(*PI)) { 3953 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 3954 Pred = *PI; 3955 } 3956 return Pred; 3957} 3958 3959/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 3960/// (which may not be an immediate predecessor) which has exactly one 3961/// successor from which BB is reachable, or null if no such block is 3962/// found. 3963/// 3964BasicBlock * 3965ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 3966 // If the block has a unique predecessor, then there is no path from the 3967 // predecessor to the block that does not go through the direct edge 3968 // from the predecessor to the block. 3969 if (BasicBlock *Pred = BB->getSinglePredecessor()) 3970 return Pred; 3971 3972 // A loop's header is defined to be a block that dominates the loop. 3973 // If the header has a unique predecessor outside the loop, it must be 3974 // a block that has exactly one successor that can reach the loop. 3975 if (Loop *L = LI->getLoopFor(BB)) 3976 return getLoopPredecessor(L); 3977 3978 return 0; 3979} 3980 3981/// HasSameValue - SCEV structural equivalence is usually sufficient for 3982/// testing whether two expressions are equal, however for the purposes of 3983/// looking for a condition guarding a loop, it can be useful to be a little 3984/// more general, since a front-end may have replicated the controlling 3985/// expression. 3986/// 3987static bool HasSameValue(const SCEV* A, const SCEV* B) { 3988 // Quick check to see if they are the same SCEV. 3989 if (A == B) return true; 3990 3991 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 3992 // two different instructions with the same value. Check for this case. 3993 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 3994 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 3995 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 3996 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 3997 if (AI->isIdenticalTo(BI)) 3998 return true; 3999 4000 // Otherwise assume they may have a different value. 4001 return false; 4002} 4003 4004/// isLoopGuardedByCond - Test whether entry to the loop is protected by 4005/// a conditional between LHS and RHS. This is used to help avoid max 4006/// expressions in loop trip counts. 4007bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4008 ICmpInst::Predicate Pred, 4009 const SCEV *LHS, const SCEV *RHS) { 4010 // Interpret a null as meaning no loop, where there is obviously no guard 4011 // (interprocedural conditions notwithstanding). 4012 if (!L) return false; 4013 4014 BasicBlock *Predecessor = getLoopPredecessor(L); 4015 BasicBlock *PredecessorDest = L->getHeader(); 4016 4017 // Starting at the loop predecessor, climb up the predecessor chain, as long 4018 // as there are predecessors that can be found that have unique successors 4019 // leading to the original header. 4020 for (; Predecessor; 4021 PredecessorDest = Predecessor, 4022 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4023 4024 BranchInst *LoopEntryPredicate = 4025 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4026 if (!LoopEntryPredicate || 4027 LoopEntryPredicate->isUnconditional()) 4028 continue; 4029 4030 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4031 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4032 return true; 4033 } 4034 4035 return false; 4036} 4037 4038/// isNecessaryCond - Test whether the given CondValue value is a condition 4039/// which is at least as strict as the one described by Pred, LHS, and RHS. 4040bool ScalarEvolution::isNecessaryCond(Value *CondValue, 4041 ICmpInst::Predicate Pred, 4042 const SCEV *LHS, const SCEV *RHS, 4043 bool Inverse) { 4044 // Recursivly handle And and Or conditions. 4045 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4046 if (BO->getOpcode() == Instruction::And) { 4047 if (!Inverse) 4048 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4049 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4050 } else if (BO->getOpcode() == Instruction::Or) { 4051 if (Inverse) 4052 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4053 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4054 } 4055 } 4056 4057 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4058 if (!ICI) return false; 4059 4060 // Now that we found a conditional branch that dominates the loop, check to 4061 // see if it is the comparison we are looking for. 4062 Value *PreCondLHS = ICI->getOperand(0); 4063 Value *PreCondRHS = ICI->getOperand(1); 4064 ICmpInst::Predicate Cond; 4065 if (Inverse) 4066 Cond = ICI->getInversePredicate(); 4067 else 4068 Cond = ICI->getPredicate(); 4069 4070 if (Cond == Pred) 4071 ; // An exact match. 4072 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 4073 ; // The actual condition is beyond sufficient. 4074 else 4075 // Check a few special cases. 4076 switch (Cond) { 4077 case ICmpInst::ICMP_UGT: 4078 if (Pred == ICmpInst::ICMP_ULT) { 4079 std::swap(PreCondLHS, PreCondRHS); 4080 Cond = ICmpInst::ICMP_ULT; 4081 break; 4082 } 4083 return false; 4084 case ICmpInst::ICMP_SGT: 4085 if (Pred == ICmpInst::ICMP_SLT) { 4086 std::swap(PreCondLHS, PreCondRHS); 4087 Cond = ICmpInst::ICMP_SLT; 4088 break; 4089 } 4090 return false; 4091 case ICmpInst::ICMP_NE: 4092 // Expressions like (x >u 0) are often canonicalized to (x != 0), 4093 // so check for this case by checking if the NE is comparing against 4094 // a minimum or maximum constant. 4095 if (!ICmpInst::isTrueWhenEqual(Pred)) 4096 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 4097 const APInt &A = CI->getValue(); 4098 switch (Pred) { 4099 case ICmpInst::ICMP_SLT: 4100 if (A.isMaxSignedValue()) break; 4101 return false; 4102 case ICmpInst::ICMP_SGT: 4103 if (A.isMinSignedValue()) break; 4104 return false; 4105 case ICmpInst::ICMP_ULT: 4106 if (A.isMaxValue()) break; 4107 return false; 4108 case ICmpInst::ICMP_UGT: 4109 if (A.isMinValue()) break; 4110 return false; 4111 default: 4112 return false; 4113 } 4114 Cond = ICmpInst::ICMP_NE; 4115 // NE is symmetric but the original comparison may not be. Swap 4116 // the operands if necessary so that they match below. 4117 if (isa<SCEVConstant>(LHS)) 4118 std::swap(PreCondLHS, PreCondRHS); 4119 break; 4120 } 4121 return false; 4122 default: 4123 // We weren't able to reconcile the condition. 4124 return false; 4125 } 4126 4127 if (!PreCondLHS->getType()->isInteger()) return false; 4128 4129 const SCEV *PreCondLHSSCEV = getSCEV(PreCondLHS); 4130 const SCEV *PreCondRHSSCEV = getSCEV(PreCondRHS); 4131 return (HasSameValue(LHS, PreCondLHSSCEV) && 4132 HasSameValue(RHS, PreCondRHSSCEV)) || 4133 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) && 4134 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV))); 4135} 4136 4137/// getBECount - Subtract the end and start values and divide by the step, 4138/// rounding up, to get the number of times the backedge is executed. Return 4139/// CouldNotCompute if an intermediate computation overflows. 4140const SCEV* ScalarEvolution::getBECount(const SCEV* Start, 4141 const SCEV* End, 4142 const SCEV* Step) { 4143 const Type *Ty = Start->getType(); 4144 const SCEV* NegOne = getIntegerSCEV(-1, Ty); 4145 const SCEV* Diff = getMinusSCEV(End, Start); 4146 const SCEV* RoundUp = getAddExpr(Step, NegOne); 4147 4148 // Add an adjustment to the difference between End and Start so that 4149 // the division will effectively round up. 4150 const SCEV* Add = getAddExpr(Diff, RoundUp); 4151 4152 // Check Add for unsigned overflow. 4153 // TODO: More sophisticated things could be done here. 4154 const Type *WideTy = IntegerType::get(getTypeSizeInBits(Ty) + 1); 4155 const SCEV* OperandExtendedAdd = 4156 getAddExpr(getZeroExtendExpr(Diff, WideTy), 4157 getZeroExtendExpr(RoundUp, WideTy)); 4158 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4159 return getCouldNotCompute(); 4160 4161 return getUDivExpr(Add, Step); 4162} 4163 4164/// HowManyLessThans - Return the number of times a backedge containing the 4165/// specified less-than comparison will execute. If not computable, return 4166/// CouldNotCompute. 4167ScalarEvolution::BackedgeTakenInfo 4168ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4169 const Loop *L, bool isSigned) { 4170 // Only handle: "ADDREC < LoopInvariant". 4171 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4172 4173 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4174 if (!AddRec || AddRec->getLoop() != L) 4175 return getCouldNotCompute(); 4176 4177 if (AddRec->isAffine()) { 4178 // FORNOW: We only support unit strides. 4179 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4180 const SCEV* Step = AddRec->getStepRecurrence(*this); 4181 4182 // TODO: handle non-constant strides. 4183 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4184 if (!CStep || CStep->isZero()) 4185 return getCouldNotCompute(); 4186 if (CStep->isOne()) { 4187 // With unit stride, the iteration never steps past the limit value. 4188 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4189 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4190 // Test whether a positive iteration iteration can step past the limit 4191 // value and past the maximum value for its type in a single step. 4192 if (isSigned) { 4193 APInt Max = APInt::getSignedMaxValue(BitWidth); 4194 if ((Max - CStep->getValue()->getValue()) 4195 .slt(CLimit->getValue()->getValue())) 4196 return getCouldNotCompute(); 4197 } else { 4198 APInt Max = APInt::getMaxValue(BitWidth); 4199 if ((Max - CStep->getValue()->getValue()) 4200 .ult(CLimit->getValue()->getValue())) 4201 return getCouldNotCompute(); 4202 } 4203 } else 4204 // TODO: handle non-constant limit values below. 4205 return getCouldNotCompute(); 4206 } else 4207 // TODO: handle negative strides below. 4208 return getCouldNotCompute(); 4209 4210 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4211 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4212 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4213 // treat m-n as signed nor unsigned due to overflow possibility. 4214 4215 // First, we get the value of the LHS in the first iteration: n 4216 const SCEV* Start = AddRec->getOperand(0); 4217 4218 // Determine the minimum constant start value. 4219 const SCEV *MinStart = isa<SCEVConstant>(Start) ? Start : 4220 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 4221 APInt::getMinValue(BitWidth)); 4222 4223 // If we know that the condition is true in order to enter the loop, 4224 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4225 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4226 // the division must round up. 4227 const SCEV* End = RHS; 4228 if (!isLoopGuardedByCond(L, 4229 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 4230 getMinusSCEV(Start, Step), RHS)) 4231 End = isSigned ? getSMaxExpr(RHS, Start) 4232 : getUMaxExpr(RHS, Start); 4233 4234 // Determine the maximum constant end value. 4235 const SCEV* MaxEnd = 4236 isa<SCEVConstant>(End) ? End : 4237 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) 4238 .ashr(GetMinSignBits(End) - 1) : 4239 APInt::getMaxValue(BitWidth) 4240 .lshr(GetMinLeadingZeros(End))); 4241 4242 // Finally, we subtract these two values and divide, rounding up, to get 4243 // the number of times the backedge is executed. 4244 const SCEV* BECount = getBECount(Start, End, Step); 4245 4246 // The maximum backedge count is similar, except using the minimum start 4247 // value and the maximum end value. 4248 const SCEV* MaxBECount = getBECount(MinStart, MaxEnd, Step); 4249 4250 return BackedgeTakenInfo(BECount, MaxBECount); 4251 } 4252 4253 return getCouldNotCompute(); 4254} 4255 4256/// getNumIterationsInRange - Return the number of iterations of this loop that 4257/// produce values in the specified constant range. Another way of looking at 4258/// this is that it returns the first iteration number where the value is not in 4259/// the condition, thus computing the exit count. If the iteration count can't 4260/// be computed, an instance of SCEVCouldNotCompute is returned. 4261const SCEV* SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4262 ScalarEvolution &SE) const { 4263 if (Range.isFullSet()) // Infinite loop. 4264 return SE.getCouldNotCompute(); 4265 4266 // If the start is a non-zero constant, shift the range to simplify things. 4267 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4268 if (!SC->getValue()->isZero()) { 4269 SmallVector<const SCEV*, 4> Operands(op_begin(), op_end()); 4270 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4271 const SCEV* Shifted = SE.getAddRecExpr(Operands, getLoop()); 4272 if (const SCEVAddRecExpr *ShiftedAddRec = 4273 dyn_cast<SCEVAddRecExpr>(Shifted)) 4274 return ShiftedAddRec->getNumIterationsInRange( 4275 Range.subtract(SC->getValue()->getValue()), SE); 4276 // This is strange and shouldn't happen. 4277 return SE.getCouldNotCompute(); 4278 } 4279 4280 // The only time we can solve this is when we have all constant indices. 4281 // Otherwise, we cannot determine the overflow conditions. 4282 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4283 if (!isa<SCEVConstant>(getOperand(i))) 4284 return SE.getCouldNotCompute(); 4285 4286 4287 // Okay at this point we know that all elements of the chrec are constants and 4288 // that the start element is zero. 4289 4290 // First check to see if the range contains zero. If not, the first 4291 // iteration exits. 4292 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4293 if (!Range.contains(APInt(BitWidth, 0))) 4294 return SE.getIntegerSCEV(0, getType()); 4295 4296 if (isAffine()) { 4297 // If this is an affine expression then we have this situation: 4298 // Solve {0,+,A} in Range === Ax in Range 4299 4300 // We know that zero is in the range. If A is positive then we know that 4301 // the upper value of the range must be the first possible exit value. 4302 // If A is negative then the lower of the range is the last possible loop 4303 // value. Also note that we already checked for a full range. 4304 APInt One(BitWidth,1); 4305 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4306 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4307 4308 // The exit value should be (End+A)/A. 4309 APInt ExitVal = (End + A).udiv(A); 4310 ConstantInt *ExitValue = ConstantInt::get(ExitVal); 4311 4312 // Evaluate at the exit value. If we really did fall out of the valid 4313 // range, then we computed our trip count, otherwise wrap around or other 4314 // things must have happened. 4315 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4316 if (Range.contains(Val->getValue())) 4317 return SE.getCouldNotCompute(); // Something strange happened 4318 4319 // Ensure that the previous value is in the range. This is a sanity check. 4320 assert(Range.contains( 4321 EvaluateConstantChrecAtConstant(this, 4322 ConstantInt::get(ExitVal - One), SE)->getValue()) && 4323 "Linear scev computation is off in a bad way!"); 4324 return SE.getConstant(ExitValue); 4325 } else if (isQuadratic()) { 4326 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4327 // quadratic equation to solve it. To do this, we must frame our problem in 4328 // terms of figuring out when zero is crossed, instead of when 4329 // Range.getUpper() is crossed. 4330 SmallVector<const SCEV*, 4> NewOps(op_begin(), op_end()); 4331 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4332 const SCEV* NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4333 4334 // Next, solve the constructed addrec 4335 std::pair<const SCEV*,const SCEV*> Roots = 4336 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4337 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4338 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4339 if (R1) { 4340 // Pick the smallest positive root value. 4341 if (ConstantInt *CB = 4342 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4343 R1->getValue(), R2->getValue()))) { 4344 if (CB->getZExtValue() == false) 4345 std::swap(R1, R2); // R1 is the minimum root now. 4346 4347 // Make sure the root is not off by one. The returned iteration should 4348 // not be in the range, but the previous one should be. When solving 4349 // for "X*X < 5", for example, we should not return a root of 2. 4350 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4351 R1->getValue(), 4352 SE); 4353 if (Range.contains(R1Val->getValue())) { 4354 // The next iteration must be out of the range... 4355 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1); 4356 4357 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4358 if (!Range.contains(R1Val->getValue())) 4359 return SE.getConstant(NextVal); 4360 return SE.getCouldNotCompute(); // Something strange happened 4361 } 4362 4363 // If R1 was not in the range, then it is a good return value. Make 4364 // sure that R1-1 WAS in the range though, just in case. 4365 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1); 4366 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4367 if (Range.contains(R1Val->getValue())) 4368 return R1; 4369 return SE.getCouldNotCompute(); // Something strange happened 4370 } 4371 } 4372 } 4373 4374 return SE.getCouldNotCompute(); 4375} 4376 4377 4378 4379//===----------------------------------------------------------------------===// 4380// SCEVCallbackVH Class Implementation 4381//===----------------------------------------------------------------------===// 4382 4383void ScalarEvolution::SCEVCallbackVH::deleted() { 4384 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4385 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4386 SE->ConstantEvolutionLoopExitValue.erase(PN); 4387 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4388 SE->ValuesAtScopes.erase(I); 4389 SE->Scalars.erase(getValPtr()); 4390 // this now dangles! 4391} 4392 4393void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4394 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4395 4396 // Forget all the expressions associated with users of the old value, 4397 // so that future queries will recompute the expressions using the new 4398 // value. 4399 SmallVector<User *, 16> Worklist; 4400 Value *Old = getValPtr(); 4401 bool DeleteOld = false; 4402 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4403 UI != UE; ++UI) 4404 Worklist.push_back(*UI); 4405 while (!Worklist.empty()) { 4406 User *U = Worklist.pop_back_val(); 4407 // Deleting the Old value will cause this to dangle. Postpone 4408 // that until everything else is done. 4409 if (U == Old) { 4410 DeleteOld = true; 4411 continue; 4412 } 4413 if (PHINode *PN = dyn_cast<PHINode>(U)) 4414 SE->ConstantEvolutionLoopExitValue.erase(PN); 4415 if (Instruction *I = dyn_cast<Instruction>(U)) 4416 SE->ValuesAtScopes.erase(I); 4417 if (SE->Scalars.erase(U)) 4418 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4419 UI != UE; ++UI) 4420 Worklist.push_back(*UI); 4421 } 4422 if (DeleteOld) { 4423 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4424 SE->ConstantEvolutionLoopExitValue.erase(PN); 4425 if (Instruction *I = dyn_cast<Instruction>(Old)) 4426 SE->ValuesAtScopes.erase(I); 4427 SE->Scalars.erase(Old); 4428 // this now dangles! 4429 } 4430 // this may dangle! 4431} 4432 4433ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4434 : CallbackVH(V), SE(se) {} 4435 4436//===----------------------------------------------------------------------===// 4437// ScalarEvolution Class Implementation 4438//===----------------------------------------------------------------------===// 4439 4440ScalarEvolution::ScalarEvolution() 4441 : FunctionPass(&ID) { 4442} 4443 4444bool ScalarEvolution::runOnFunction(Function &F) { 4445 this->F = &F; 4446 LI = &getAnalysis<LoopInfo>(); 4447 TD = getAnalysisIfAvailable<TargetData>(); 4448 return false; 4449} 4450 4451void ScalarEvolution::releaseMemory() { 4452 Scalars.clear(); 4453 BackedgeTakenCounts.clear(); 4454 ConstantEvolutionLoopExitValue.clear(); 4455 ValuesAtScopes.clear(); 4456 UniqueSCEVs.clear(); 4457 SCEVAllocator.Reset(); 4458} 4459 4460void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4461 AU.setPreservesAll(); 4462 AU.addRequiredTransitive<LoopInfo>(); 4463} 4464 4465bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4466 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4467} 4468 4469static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4470 const Loop *L) { 4471 // Print all inner loops first 4472 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4473 PrintLoopInfo(OS, SE, *I); 4474 4475 OS << "Loop " << L->getHeader()->getName() << ": "; 4476 4477 SmallVector<BasicBlock*, 8> ExitBlocks; 4478 L->getExitBlocks(ExitBlocks); 4479 if (ExitBlocks.size() != 1) 4480 OS << "<multiple exits> "; 4481 4482 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4483 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4484 } else { 4485 OS << "Unpredictable backedge-taken count. "; 4486 } 4487 4488 OS << "\n"; 4489 OS << "Loop " << L->getHeader()->getName() << ": "; 4490 4491 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 4492 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 4493 } else { 4494 OS << "Unpredictable max backedge-taken count. "; 4495 } 4496 4497 OS << "\n"; 4498} 4499 4500void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4501 // ScalarEvolution's implementaiton of the print method is to print 4502 // out SCEV values of all instructions that are interesting. Doing 4503 // this potentially causes it to create new SCEV objects though, 4504 // which technically conflicts with the const qualifier. This isn't 4505 // observable from outside the class though (the hasSCEV function 4506 // notwithstanding), so casting away the const isn't dangerous. 4507 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4508 4509 OS << "Classifying expressions for: " << F->getName() << "\n"; 4510 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4511 if (isSCEVable(I->getType())) { 4512 OS << *I; 4513 OS << " --> "; 4514 const SCEV* SV = SE.getSCEV(&*I); 4515 SV->print(OS); 4516 4517 const Loop *L = LI->getLoopFor((*I).getParent()); 4518 4519 const SCEV* AtUse = SE.getSCEVAtScope(SV, L); 4520 if (AtUse != SV) { 4521 OS << " --> "; 4522 AtUse->print(OS); 4523 } 4524 4525 if (L) { 4526 OS << "\t\t" "Exits: "; 4527 const SCEV* ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4528 if (!ExitValue->isLoopInvariant(L)) { 4529 OS << "<<Unknown>>"; 4530 } else { 4531 OS << *ExitValue; 4532 } 4533 } 4534 4535 OS << "\n"; 4536 } 4537 4538 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 4539 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 4540 PrintLoopInfo(OS, &SE, *I); 4541} 4542 4543void ScalarEvolution::print(std::ostream &o, const Module *M) const { 4544 raw_os_ostream OS(o); 4545 print(OS, M); 4546} 4547