ScalarEvolution.cpp revision 1afdc5f3565f09d33de888fede895540059dca4c
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/LLVMContext.h" 69#include "llvm/Analysis/ConstantFolding.h" 70#include "llvm/Analysis/Dominators.h" 71#include "llvm/Analysis/LoopInfo.h" 72#include "llvm/Analysis/ValueTracking.h" 73#include "llvm/Assembly/Writer.h" 74#include "llvm/Target/TargetData.h" 75#include "llvm/Support/CommandLine.h" 76#include "llvm/Support/Compiler.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/GetElementPtrTypeIterator.h" 79#include "llvm/Support/InstIterator.h" 80#include "llvm/Support/MathExtras.h" 81#include "llvm/Support/raw_ostream.h" 82#include "llvm/ADT/Statistic.h" 83#include "llvm/ADT/STLExtras.h" 84#include "llvm/ADT/SmallPtrSet.h" 85#include <algorithm> 86using namespace llvm; 87 88STATISTIC(NumArrayLenItCounts, 89 "Number of trip counts computed with array length"); 90STATISTIC(NumTripCountsComputed, 91 "Number of loops with predictable loop counts"); 92STATISTIC(NumTripCountsNotComputed, 93 "Number of loops without predictable loop counts"); 94STATISTIC(NumBruteForceTripCountsComputed, 95 "Number of loops with trip counts computed by force"); 96 97static cl::opt<unsigned> 98MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 99 cl::desc("Maximum number of iterations SCEV will " 100 "symbolically execute a constant " 101 "derived loop"), 102 cl::init(100)); 103 104static RegisterPass<ScalarEvolution> 105R("scalar-evolution", "Scalar Evolution Analysis", false, true); 106char ScalarEvolution::ID = 0; 107 108//===----------------------------------------------------------------------===// 109// SCEV class definitions 110//===----------------------------------------------------------------------===// 111 112//===----------------------------------------------------------------------===// 113// Implementation of the SCEV class. 114// 115 116SCEV::~SCEV() {} 117 118void SCEV::dump() const { 119 print(errs()); 120 errs() << '\n'; 121} 122 123void SCEV::print(std::ostream &o) const { 124 raw_os_ostream OS(o); 125 print(OS); 126} 127 128bool SCEV::isZero() const { 129 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 130 return SC->getValue()->isZero(); 131 return false; 132} 133 134bool SCEV::isOne() const { 135 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 136 return SC->getValue()->isOne(); 137 return false; 138} 139 140bool SCEV::isAllOnesValue() const { 141 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 142 return SC->getValue()->isAllOnesValue(); 143 return false; 144} 145 146SCEVCouldNotCompute::SCEVCouldNotCompute() : 147 SCEV(scCouldNotCompute) {} 148 149void SCEVCouldNotCompute::Profile(FoldingSetNodeID &ID) const { 150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 151} 152 153bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 154 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 155 return false; 156} 157 158const Type *SCEVCouldNotCompute::getType() const { 159 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 160 return 0; 161} 162 163bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 164 assert(0 && "Attempt to use a SCEVCouldNotCompute object!"); 165 return false; 166} 167 168const SCEV * 169SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete( 170 const SCEV *Sym, 171 const SCEV *Conc, 172 ScalarEvolution &SE) const { 173 return this; 174} 175 176void SCEVCouldNotCompute::print(raw_ostream &OS) const { 177 OS << "***COULDNOTCOMPUTE***"; 178} 179 180bool SCEVCouldNotCompute::classof(const SCEV *S) { 181 return S->getSCEVType() == scCouldNotCompute; 182} 183 184const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 185 FoldingSetNodeID ID; 186 ID.AddInteger(scConstant); 187 ID.AddPointer(V); 188 void *IP = 0; 189 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 190 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 191 new (S) SCEVConstant(V); 192 UniqueSCEVs.InsertNode(S, IP); 193 return S; 194} 195 196const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 197 return getConstant(ConstantInt::get(Val)); 198} 199 200const SCEV * 201ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 202 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 203} 204 205void SCEVConstant::Profile(FoldingSetNodeID &ID) const { 206 ID.AddInteger(scConstant); 207 ID.AddPointer(V); 208} 209 210const Type *SCEVConstant::getType() const { return V->getType(); } 211 212void SCEVConstant::print(raw_ostream &OS) const { 213 WriteAsOperand(OS, V, false); 214} 215 216SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy, 217 const SCEV *op, const Type *ty) 218 : SCEV(SCEVTy), Op(op), Ty(ty) {} 219 220void SCEVCastExpr::Profile(FoldingSetNodeID &ID) const { 221 ID.AddInteger(getSCEVType()); 222 ID.AddPointer(Op); 223 ID.AddPointer(Ty); 224} 225 226bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 227 return Op->dominates(BB, DT); 228} 229 230SCEVTruncateExpr::SCEVTruncateExpr(const SCEV *op, const Type *ty) 231 : SCEVCastExpr(scTruncate, op, ty) { 232 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 233 (Ty->isInteger() || isa<PointerType>(Ty)) && 234 "Cannot truncate non-integer value!"); 235} 236 237void SCEVTruncateExpr::print(raw_ostream &OS) const { 238 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 239} 240 241SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEV *op, const Type *ty) 242 : SCEVCastExpr(scZeroExtend, op, ty) { 243 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 244 (Ty->isInteger() || isa<PointerType>(Ty)) && 245 "Cannot zero extend non-integer value!"); 246} 247 248void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 249 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 250} 251 252SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEV *op, const Type *ty) 253 : SCEVCastExpr(scSignExtend, op, ty) { 254 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 255 (Ty->isInteger() || isa<PointerType>(Ty)) && 256 "Cannot sign extend non-integer value!"); 257} 258 259void SCEVSignExtendExpr::print(raw_ostream &OS) const { 260 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 261} 262 263void SCEVCommutativeExpr::print(raw_ostream &OS) const { 264 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 265 const char *OpStr = getOperationStr(); 266 OS << "(" << *Operands[0]; 267 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 268 OS << OpStr << *Operands[i]; 269 OS << ")"; 270} 271 272const SCEV * 273SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete( 274 const SCEV *Sym, 275 const SCEV *Conc, 276 ScalarEvolution &SE) const { 277 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 278 const SCEV *H = 279 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 280 if (H != getOperand(i)) { 281 SmallVector<const SCEV *, 8> NewOps; 282 NewOps.reserve(getNumOperands()); 283 for (unsigned j = 0; j != i; ++j) 284 NewOps.push_back(getOperand(j)); 285 NewOps.push_back(H); 286 for (++i; i != e; ++i) 287 NewOps.push_back(getOperand(i)-> 288 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 289 290 if (isa<SCEVAddExpr>(this)) 291 return SE.getAddExpr(NewOps); 292 else if (isa<SCEVMulExpr>(this)) 293 return SE.getMulExpr(NewOps); 294 else if (isa<SCEVSMaxExpr>(this)) 295 return SE.getSMaxExpr(NewOps); 296 else if (isa<SCEVUMaxExpr>(this)) 297 return SE.getUMaxExpr(NewOps); 298 else 299 assert(0 && "Unknown commutative expr!"); 300 } 301 } 302 return this; 303} 304 305void SCEVNAryExpr::Profile(FoldingSetNodeID &ID) const { 306 ID.AddInteger(getSCEVType()); 307 ID.AddInteger(Operands.size()); 308 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 309 ID.AddPointer(Operands[i]); 310} 311 312bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 313 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 314 if (!getOperand(i)->dominates(BB, DT)) 315 return false; 316 } 317 return true; 318} 319 320void SCEVUDivExpr::Profile(FoldingSetNodeID &ID) const { 321 ID.AddInteger(scUDivExpr); 322 ID.AddPointer(LHS); 323 ID.AddPointer(RHS); 324} 325 326bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 327 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 328} 329 330void SCEVUDivExpr::print(raw_ostream &OS) const { 331 OS << "(" << *LHS << " /u " << *RHS << ")"; 332} 333 334const Type *SCEVUDivExpr::getType() const { 335 // In most cases the types of LHS and RHS will be the same, but in some 336 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 337 // depend on the type for correctness, but handling types carefully can 338 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 339 // a pointer type than the RHS, so use the RHS' type here. 340 return RHS->getType(); 341} 342 343void SCEVAddRecExpr::Profile(FoldingSetNodeID &ID) const { 344 ID.AddInteger(scAddRecExpr); 345 ID.AddInteger(Operands.size()); 346 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 347 ID.AddPointer(Operands[i]); 348 ID.AddPointer(L); 349} 350 351const SCEV * 352SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym, 353 const SCEV *Conc, 354 ScalarEvolution &SE) const { 355 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 356 const SCEV *H = 357 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 358 if (H != getOperand(i)) { 359 SmallVector<const SCEV *, 8> NewOps; 360 NewOps.reserve(getNumOperands()); 361 for (unsigned j = 0; j != i; ++j) 362 NewOps.push_back(getOperand(j)); 363 NewOps.push_back(H); 364 for (++i; i != e; ++i) 365 NewOps.push_back(getOperand(i)-> 366 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 367 368 return SE.getAddRecExpr(NewOps, L); 369 } 370 } 371 return this; 372} 373 374 375bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 376 // Add recurrences are never invariant in the function-body (null loop). 377 if (!QueryLoop) 378 return false; 379 380 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 381 if (QueryLoop->contains(L->getHeader())) 382 return false; 383 384 // This recurrence is variant w.r.t. QueryLoop if any of its operands 385 // are variant. 386 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 387 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 388 return false; 389 390 // Otherwise it's loop-invariant. 391 return true; 392} 393 394void SCEVAddRecExpr::print(raw_ostream &OS) const { 395 OS << "{" << *Operands[0]; 396 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 397 OS << ",+," << *Operands[i]; 398 OS << "}<" << L->getHeader()->getName() + ">"; 399} 400 401void SCEVUnknown::Profile(FoldingSetNodeID &ID) const { 402 ID.AddInteger(scUnknown); 403 ID.AddPointer(V); 404} 405 406bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 407 // All non-instruction values are loop invariant. All instructions are loop 408 // invariant if they are not contained in the specified loop. 409 // Instructions are never considered invariant in the function body 410 // (null loop) because they are defined within the "loop". 411 if (Instruction *I = dyn_cast<Instruction>(V)) 412 return L && !L->contains(I->getParent()); 413 return true; 414} 415 416bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 417 if (Instruction *I = dyn_cast<Instruction>(getValue())) 418 return DT->dominates(I->getParent(), BB); 419 return true; 420} 421 422const Type *SCEVUnknown::getType() const { 423 return V->getType(); 424} 425 426void SCEVUnknown::print(raw_ostream &OS) const { 427 WriteAsOperand(OS, V, false); 428} 429 430//===----------------------------------------------------------------------===// 431// SCEV Utilities 432//===----------------------------------------------------------------------===// 433 434namespace { 435 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 436 /// than the complexity of the RHS. This comparator is used to canonicalize 437 /// expressions. 438 class VISIBILITY_HIDDEN SCEVComplexityCompare { 439 LoopInfo *LI; 440 public: 441 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 442 443 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 444 // Primarily, sort the SCEVs by their getSCEVType(). 445 if (LHS->getSCEVType() != RHS->getSCEVType()) 446 return LHS->getSCEVType() < RHS->getSCEVType(); 447 448 // Aside from the getSCEVType() ordering, the particular ordering 449 // isn't very important except that it's beneficial to be consistent, 450 // so that (a + b) and (b + a) don't end up as different expressions. 451 452 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 453 // not as complete as it could be. 454 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 455 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 456 457 // Order pointer values after integer values. This helps SCEVExpander 458 // form GEPs. 459 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 460 return false; 461 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 462 return true; 463 464 // Compare getValueID values. 465 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 466 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 467 468 // Sort arguments by their position. 469 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 470 const Argument *RA = cast<Argument>(RU->getValue()); 471 return LA->getArgNo() < RA->getArgNo(); 472 } 473 474 // For instructions, compare their loop depth, and their opcode. 475 // This is pretty loose. 476 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 477 Instruction *RV = cast<Instruction>(RU->getValue()); 478 479 // Compare loop depths. 480 if (LI->getLoopDepth(LV->getParent()) != 481 LI->getLoopDepth(RV->getParent())) 482 return LI->getLoopDepth(LV->getParent()) < 483 LI->getLoopDepth(RV->getParent()); 484 485 // Compare opcodes. 486 if (LV->getOpcode() != RV->getOpcode()) 487 return LV->getOpcode() < RV->getOpcode(); 488 489 // Compare the number of operands. 490 if (LV->getNumOperands() != RV->getNumOperands()) 491 return LV->getNumOperands() < RV->getNumOperands(); 492 } 493 494 return false; 495 } 496 497 // Compare constant values. 498 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 499 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 500 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 501 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 502 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 503 } 504 505 // Compare addrec loop depths. 506 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 507 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 508 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 509 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 510 } 511 512 // Lexicographically compare n-ary expressions. 513 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 514 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 515 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 516 if (i >= RC->getNumOperands()) 517 return false; 518 if (operator()(LC->getOperand(i), RC->getOperand(i))) 519 return true; 520 if (operator()(RC->getOperand(i), LC->getOperand(i))) 521 return false; 522 } 523 return LC->getNumOperands() < RC->getNumOperands(); 524 } 525 526 // Lexicographically compare udiv expressions. 527 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 528 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 529 if (operator()(LC->getLHS(), RC->getLHS())) 530 return true; 531 if (operator()(RC->getLHS(), LC->getLHS())) 532 return false; 533 if (operator()(LC->getRHS(), RC->getRHS())) 534 return true; 535 if (operator()(RC->getRHS(), LC->getRHS())) 536 return false; 537 return false; 538 } 539 540 // Compare cast expressions by operand. 541 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 542 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 543 return operator()(LC->getOperand(), RC->getOperand()); 544 } 545 546 assert(0 && "Unknown SCEV kind!"); 547 return false; 548 } 549 }; 550} 551 552/// GroupByComplexity - Given a list of SCEV objects, order them by their 553/// complexity, and group objects of the same complexity together by value. 554/// When this routine is finished, we know that any duplicates in the vector are 555/// consecutive and that complexity is monotonically increasing. 556/// 557/// Note that we go take special precautions to ensure that we get determinstic 558/// results from this routine. In other words, we don't want the results of 559/// this to depend on where the addresses of various SCEV objects happened to 560/// land in memory. 561/// 562static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 563 LoopInfo *LI) { 564 if (Ops.size() < 2) return; // Noop 565 if (Ops.size() == 2) { 566 // This is the common case, which also happens to be trivially simple. 567 // Special case it. 568 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 569 std::swap(Ops[0], Ops[1]); 570 return; 571 } 572 573 // Do the rough sort by complexity. 574 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 575 576 // Now that we are sorted by complexity, group elements of the same 577 // complexity. Note that this is, at worst, N^2, but the vector is likely to 578 // be extremely short in practice. Note that we take this approach because we 579 // do not want to depend on the addresses of the objects we are grouping. 580 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 581 const SCEV *S = Ops[i]; 582 unsigned Complexity = S->getSCEVType(); 583 584 // If there are any objects of the same complexity and same value as this 585 // one, group them. 586 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 587 if (Ops[j] == S) { // Found a duplicate. 588 // Move it to immediately after i'th element. 589 std::swap(Ops[i+1], Ops[j]); 590 ++i; // no need to rescan it. 591 if (i == e-2) return; // Done! 592 } 593 } 594 } 595} 596 597 598 599//===----------------------------------------------------------------------===// 600// Simple SCEV method implementations 601//===----------------------------------------------------------------------===// 602 603/// BinomialCoefficient - Compute BC(It, K). The result has width W. 604/// Assume, K > 0. 605static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 606 ScalarEvolution &SE, 607 const Type* ResultTy) { 608 // Handle the simplest case efficiently. 609 if (K == 1) 610 return SE.getTruncateOrZeroExtend(It, ResultTy); 611 612 // We are using the following formula for BC(It, K): 613 // 614 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 615 // 616 // Suppose, W is the bitwidth of the return value. We must be prepared for 617 // overflow. Hence, we must assure that the result of our computation is 618 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 619 // safe in modular arithmetic. 620 // 621 // However, this code doesn't use exactly that formula; the formula it uses 622 // is something like the following, where T is the number of factors of 2 in 623 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 624 // exponentiation: 625 // 626 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 627 // 628 // This formula is trivially equivalent to the previous formula. However, 629 // this formula can be implemented much more efficiently. The trick is that 630 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 631 // arithmetic. To do exact division in modular arithmetic, all we have 632 // to do is multiply by the inverse. Therefore, this step can be done at 633 // width W. 634 // 635 // The next issue is how to safely do the division by 2^T. The way this 636 // is done is by doing the multiplication step at a width of at least W + T 637 // bits. This way, the bottom W+T bits of the product are accurate. Then, 638 // when we perform the division by 2^T (which is equivalent to a right shift 639 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 640 // truncated out after the division by 2^T. 641 // 642 // In comparison to just directly using the first formula, this technique 643 // is much more efficient; using the first formula requires W * K bits, 644 // but this formula less than W + K bits. Also, the first formula requires 645 // a division step, whereas this formula only requires multiplies and shifts. 646 // 647 // It doesn't matter whether the subtraction step is done in the calculation 648 // width or the input iteration count's width; if the subtraction overflows, 649 // the result must be zero anyway. We prefer here to do it in the width of 650 // the induction variable because it helps a lot for certain cases; CodeGen 651 // isn't smart enough to ignore the overflow, which leads to much less 652 // efficient code if the width of the subtraction is wider than the native 653 // register width. 654 // 655 // (It's possible to not widen at all by pulling out factors of 2 before 656 // the multiplication; for example, K=2 can be calculated as 657 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 658 // extra arithmetic, so it's not an obvious win, and it gets 659 // much more complicated for K > 3.) 660 661 // Protection from insane SCEVs; this bound is conservative, 662 // but it probably doesn't matter. 663 if (K > 1000) 664 return SE.getCouldNotCompute(); 665 666 unsigned W = SE.getTypeSizeInBits(ResultTy); 667 668 // Calculate K! / 2^T and T; we divide out the factors of two before 669 // multiplying for calculating K! / 2^T to avoid overflow. 670 // Other overflow doesn't matter because we only care about the bottom 671 // W bits of the result. 672 APInt OddFactorial(W, 1); 673 unsigned T = 1; 674 for (unsigned i = 3; i <= K; ++i) { 675 APInt Mult(W, i); 676 unsigned TwoFactors = Mult.countTrailingZeros(); 677 T += TwoFactors; 678 Mult = Mult.lshr(TwoFactors); 679 OddFactorial *= Mult; 680 } 681 682 // We need at least W + T bits for the multiplication step 683 unsigned CalculationBits = W + T; 684 685 // Calcuate 2^T, at width T+W. 686 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 687 688 // Calculate the multiplicative inverse of K! / 2^T; 689 // this multiplication factor will perform the exact division by 690 // K! / 2^T. 691 APInt Mod = APInt::getSignedMinValue(W+1); 692 APInt MultiplyFactor = OddFactorial.zext(W+1); 693 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 694 MultiplyFactor = MultiplyFactor.trunc(W); 695 696 // Calculate the product, at width T+W 697 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 698 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 699 for (unsigned i = 1; i != K; ++i) { 700 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 701 Dividend = SE.getMulExpr(Dividend, 702 SE.getTruncateOrZeroExtend(S, CalculationTy)); 703 } 704 705 // Divide by 2^T 706 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 707 708 // Truncate the result, and divide by K! / 2^T. 709 710 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 711 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 712} 713 714/// evaluateAtIteration - Return the value of this chain of recurrences at 715/// the specified iteration number. We can evaluate this recurrence by 716/// multiplying each element in the chain by the binomial coefficient 717/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 718/// 719/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 720/// 721/// where BC(It, k) stands for binomial coefficient. 722/// 723const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 724 ScalarEvolution &SE) const { 725 const SCEV *Result = getStart(); 726 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 727 // The computation is correct in the face of overflow provided that the 728 // multiplication is performed _after_ the evaluation of the binomial 729 // coefficient. 730 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 731 if (isa<SCEVCouldNotCompute>(Coeff)) 732 return Coeff; 733 734 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 735 } 736 return Result; 737} 738 739//===----------------------------------------------------------------------===// 740// SCEV Expression folder implementations 741//===----------------------------------------------------------------------===// 742 743const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 744 const Type *Ty) { 745 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 746 "This is not a truncating conversion!"); 747 assert(isSCEVable(Ty) && 748 "This is not a conversion to a SCEVable type!"); 749 Ty = getEffectiveSCEVType(Ty); 750 751 // Fold if the operand is constant. 752 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 753 return getConstant( 754 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 755 756 // trunc(trunc(x)) --> trunc(x) 757 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 758 return getTruncateExpr(ST->getOperand(), Ty); 759 760 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 761 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 762 return getTruncateOrSignExtend(SS->getOperand(), Ty); 763 764 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 765 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 766 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 767 768 // If the input value is a chrec scev, truncate the chrec's operands. 769 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 770 SmallVector<const SCEV *, 4> Operands; 771 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 772 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 773 return getAddRecExpr(Operands, AddRec->getLoop()); 774 } 775 776 FoldingSetNodeID ID; 777 ID.AddInteger(scTruncate); 778 ID.AddPointer(Op); 779 ID.AddPointer(Ty); 780 void *IP = 0; 781 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 782 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 783 new (S) SCEVTruncateExpr(Op, Ty); 784 UniqueSCEVs.InsertNode(S, IP); 785 return S; 786} 787 788const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 789 const Type *Ty) { 790 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 791 "This is not an extending conversion!"); 792 assert(isSCEVable(Ty) && 793 "This is not a conversion to a SCEVable type!"); 794 Ty = getEffectiveSCEVType(Ty); 795 796 // Fold if the operand is constant. 797 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 798 const Type *IntTy = getEffectiveSCEVType(Ty); 799 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 800 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 801 return getConstant(cast<ConstantInt>(C)); 802 } 803 804 // zext(zext(x)) --> zext(x) 805 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 806 return getZeroExtendExpr(SZ->getOperand(), Ty); 807 808 // If the input value is a chrec scev, and we can prove that the value 809 // did not overflow the old, smaller, value, we can zero extend all of the 810 // operands (often constants). This allows analysis of something like 811 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 812 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 813 if (AR->isAffine()) { 814 const SCEV *Start = AR->getStart(); 815 const SCEV *Step = AR->getStepRecurrence(*this); 816 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 817 const Loop *L = AR->getLoop(); 818 819 // Check whether the backedge-taken count is SCEVCouldNotCompute. 820 // Note that this serves two purposes: It filters out loops that are 821 // simply not analyzable, and it covers the case where this code is 822 // being called from within backedge-taken count analysis, such that 823 // attempting to ask for the backedge-taken count would likely result 824 // in infinite recursion. In the later case, the analysis code will 825 // cope with a conservative value, and it will take care to purge 826 // that value once it has finished. 827 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 828 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 829 // Manually compute the final value for AR, checking for 830 // overflow. 831 832 // Check whether the backedge-taken count can be losslessly casted to 833 // the addrec's type. The count is always unsigned. 834 const SCEV *CastedMaxBECount = 835 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 836 const SCEV *RecastedMaxBECount = 837 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 838 if (MaxBECount == RecastedMaxBECount) { 839 const Type *WideTy = IntegerType::get(BitWidth * 2); 840 // Check whether Start+Step*MaxBECount has no unsigned overflow. 841 const SCEV *ZMul = 842 getMulExpr(CastedMaxBECount, 843 getTruncateOrZeroExtend(Step, Start->getType())); 844 const SCEV *Add = getAddExpr(Start, ZMul); 845 const SCEV *OperandExtendedAdd = 846 getAddExpr(getZeroExtendExpr(Start, WideTy), 847 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 848 getZeroExtendExpr(Step, WideTy))); 849 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 850 // Return the expression with the addrec on the outside. 851 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 852 getZeroExtendExpr(Step, Ty), 853 L); 854 855 // Similar to above, only this time treat the step value as signed. 856 // This covers loops that count down. 857 const SCEV *SMul = 858 getMulExpr(CastedMaxBECount, 859 getTruncateOrSignExtend(Step, Start->getType())); 860 Add = getAddExpr(Start, SMul); 861 OperandExtendedAdd = 862 getAddExpr(getZeroExtendExpr(Start, WideTy), 863 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 864 getSignExtendExpr(Step, WideTy))); 865 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 866 // Return the expression with the addrec on the outside. 867 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 868 getSignExtendExpr(Step, Ty), 869 L); 870 } 871 872 // If the backedge is guarded by a comparison with the pre-inc value 873 // the addrec is safe. Also, if the entry is guarded by a comparison 874 // with the start value and the backedge is guarded by a comparison 875 // with the post-inc value, the addrec is safe. 876 if (isKnownPositive(Step)) { 877 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 878 getUnsignedRange(Step).getUnsignedMax()); 879 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 880 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 881 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 882 AR->getPostIncExpr(*this), N))) 883 // Return the expression with the addrec on the outside. 884 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 885 getZeroExtendExpr(Step, Ty), 886 L); 887 } else if (isKnownNegative(Step)) { 888 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 889 getSignedRange(Step).getSignedMin()); 890 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 891 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 892 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 893 AR->getPostIncExpr(*this), N))) 894 // Return the expression with the addrec on the outside. 895 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 896 getSignExtendExpr(Step, Ty), 897 L); 898 } 899 } 900 } 901 902 FoldingSetNodeID ID; 903 ID.AddInteger(scZeroExtend); 904 ID.AddPointer(Op); 905 ID.AddPointer(Ty); 906 void *IP = 0; 907 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 908 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 909 new (S) SCEVZeroExtendExpr(Op, Ty); 910 UniqueSCEVs.InsertNode(S, IP); 911 return S; 912} 913 914const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 915 const Type *Ty) { 916 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 917 "This is not an extending conversion!"); 918 assert(isSCEVable(Ty) && 919 "This is not a conversion to a SCEVable type!"); 920 Ty = getEffectiveSCEVType(Ty); 921 922 // Fold if the operand is constant. 923 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 924 const Type *IntTy = getEffectiveSCEVType(Ty); 925 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 926 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 927 return getConstant(cast<ConstantInt>(C)); 928 } 929 930 // sext(sext(x)) --> sext(x) 931 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 932 return getSignExtendExpr(SS->getOperand(), Ty); 933 934 // If the input value is a chrec scev, and we can prove that the value 935 // did not overflow the old, smaller, value, we can sign extend all of the 936 // operands (often constants). This allows analysis of something like 937 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 938 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 939 if (AR->isAffine()) { 940 const SCEV *Start = AR->getStart(); 941 const SCEV *Step = AR->getStepRecurrence(*this); 942 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 943 const Loop *L = AR->getLoop(); 944 945 // Check whether the backedge-taken count is SCEVCouldNotCompute. 946 // Note that this serves two purposes: It filters out loops that are 947 // simply not analyzable, and it covers the case where this code is 948 // being called from within backedge-taken count analysis, such that 949 // attempting to ask for the backedge-taken count would likely result 950 // in infinite recursion. In the later case, the analysis code will 951 // cope with a conservative value, and it will take care to purge 952 // that value once it has finished. 953 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 954 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 955 // Manually compute the final value for AR, checking for 956 // overflow. 957 958 // Check whether the backedge-taken count can be losslessly casted to 959 // the addrec's type. The count is always unsigned. 960 const SCEV *CastedMaxBECount = 961 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 962 const SCEV *RecastedMaxBECount = 963 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 964 if (MaxBECount == RecastedMaxBECount) { 965 const Type *WideTy = IntegerType::get(BitWidth * 2); 966 // Check whether Start+Step*MaxBECount has no signed overflow. 967 const SCEV *SMul = 968 getMulExpr(CastedMaxBECount, 969 getTruncateOrSignExtend(Step, Start->getType())); 970 const SCEV *Add = getAddExpr(Start, SMul); 971 const SCEV *OperandExtendedAdd = 972 getAddExpr(getSignExtendExpr(Start, WideTy), 973 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 974 getSignExtendExpr(Step, WideTy))); 975 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 976 // Return the expression with the addrec on the outside. 977 return getAddRecExpr(getSignExtendExpr(Start, Ty), 978 getSignExtendExpr(Step, Ty), 979 L); 980 } 981 982 // If the backedge is guarded by a comparison with the pre-inc value 983 // the addrec is safe. Also, if the entry is guarded by a comparison 984 // with the start value and the backedge is guarded by a comparison 985 // with the post-inc value, the addrec is safe. 986 if (isKnownPositive(Step)) { 987 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 988 getSignedRange(Step).getSignedMax()); 989 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 990 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 991 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 992 AR->getPostIncExpr(*this), N))) 993 // Return the expression with the addrec on the outside. 994 return getAddRecExpr(getSignExtendExpr(Start, Ty), 995 getSignExtendExpr(Step, Ty), 996 L); 997 } else if (isKnownNegative(Step)) { 998 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 999 getSignedRange(Step).getSignedMin()); 1000 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1001 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1002 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1003 AR->getPostIncExpr(*this), N))) 1004 // Return the expression with the addrec on the outside. 1005 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1006 getSignExtendExpr(Step, Ty), 1007 L); 1008 } 1009 } 1010 } 1011 1012 FoldingSetNodeID ID; 1013 ID.AddInteger(scSignExtend); 1014 ID.AddPointer(Op); 1015 ID.AddPointer(Ty); 1016 void *IP = 0; 1017 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1018 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1019 new (S) SCEVSignExtendExpr(Op, Ty); 1020 UniqueSCEVs.InsertNode(S, IP); 1021 return S; 1022} 1023 1024/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1025/// unspecified bits out to the given type. 1026/// 1027const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1028 const Type *Ty) { 1029 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1030 "This is not an extending conversion!"); 1031 assert(isSCEVable(Ty) && 1032 "This is not a conversion to a SCEVable type!"); 1033 Ty = getEffectiveSCEVType(Ty); 1034 1035 // Sign-extend negative constants. 1036 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1037 if (SC->getValue()->getValue().isNegative()) 1038 return getSignExtendExpr(Op, Ty); 1039 1040 // Peel off a truncate cast. 1041 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1042 const SCEV *NewOp = T->getOperand(); 1043 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1044 return getAnyExtendExpr(NewOp, Ty); 1045 return getTruncateOrNoop(NewOp, Ty); 1046 } 1047 1048 // Next try a zext cast. If the cast is folded, use it. 1049 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1050 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1051 return ZExt; 1052 1053 // Next try a sext cast. If the cast is folded, use it. 1054 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1055 if (!isa<SCEVSignExtendExpr>(SExt)) 1056 return SExt; 1057 1058 // If the expression is obviously signed, use the sext cast value. 1059 if (isa<SCEVSMaxExpr>(Op)) 1060 return SExt; 1061 1062 // Absent any other information, use the zext cast value. 1063 return ZExt; 1064} 1065 1066/// CollectAddOperandsWithScales - Process the given Ops list, which is 1067/// a list of operands to be added under the given scale, update the given 1068/// map. This is a helper function for getAddRecExpr. As an example of 1069/// what it does, given a sequence of operands that would form an add 1070/// expression like this: 1071/// 1072/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1073/// 1074/// where A and B are constants, update the map with these values: 1075/// 1076/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1077/// 1078/// and add 13 + A*B*29 to AccumulatedConstant. 1079/// This will allow getAddRecExpr to produce this: 1080/// 1081/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1082/// 1083/// This form often exposes folding opportunities that are hidden in 1084/// the original operand list. 1085/// 1086/// Return true iff it appears that any interesting folding opportunities 1087/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1088/// the common case where no interesting opportunities are present, and 1089/// is also used as a check to avoid infinite recursion. 1090/// 1091static bool 1092CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1093 SmallVector<const SCEV *, 8> &NewOps, 1094 APInt &AccumulatedConstant, 1095 const SmallVectorImpl<const SCEV *> &Ops, 1096 const APInt &Scale, 1097 ScalarEvolution &SE) { 1098 bool Interesting = false; 1099 1100 // Iterate over the add operands. 1101 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1102 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1103 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1104 APInt NewScale = 1105 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1106 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1107 // A multiplication of a constant with another add; recurse. 1108 Interesting |= 1109 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1110 cast<SCEVAddExpr>(Mul->getOperand(1)) 1111 ->getOperands(), 1112 NewScale, SE); 1113 } else { 1114 // A multiplication of a constant with some other value. Update 1115 // the map. 1116 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1117 const SCEV *Key = SE.getMulExpr(MulOps); 1118 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1119 M.insert(std::make_pair(Key, NewScale)); 1120 if (Pair.second) { 1121 NewOps.push_back(Pair.first->first); 1122 } else { 1123 Pair.first->second += NewScale; 1124 // The map already had an entry for this value, which may indicate 1125 // a folding opportunity. 1126 Interesting = true; 1127 } 1128 } 1129 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1130 // Pull a buried constant out to the outside. 1131 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1132 Interesting = true; 1133 AccumulatedConstant += Scale * C->getValue()->getValue(); 1134 } else { 1135 // An ordinary operand. Update the map. 1136 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1137 M.insert(std::make_pair(Ops[i], Scale)); 1138 if (Pair.second) { 1139 NewOps.push_back(Pair.first->first); 1140 } else { 1141 Pair.first->second += Scale; 1142 // The map already had an entry for this value, which may indicate 1143 // a folding opportunity. 1144 Interesting = true; 1145 } 1146 } 1147 } 1148 1149 return Interesting; 1150} 1151 1152namespace { 1153 struct APIntCompare { 1154 bool operator()(const APInt &LHS, const APInt &RHS) const { 1155 return LHS.ult(RHS); 1156 } 1157 }; 1158} 1159 1160/// getAddExpr - Get a canonical add expression, or something simpler if 1161/// possible. 1162const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) { 1163 assert(!Ops.empty() && "Cannot get empty add!"); 1164 if (Ops.size() == 1) return Ops[0]; 1165#ifndef NDEBUG 1166 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1167 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1168 getEffectiveSCEVType(Ops[0]->getType()) && 1169 "SCEVAddExpr operand types don't match!"); 1170#endif 1171 1172 // Sort by complexity, this groups all similar expression types together. 1173 GroupByComplexity(Ops, LI); 1174 1175 // If there are any constants, fold them together. 1176 unsigned Idx = 0; 1177 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1178 ++Idx; 1179 assert(Idx < Ops.size()); 1180 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1181 // We found two constants, fold them together! 1182 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1183 RHSC->getValue()->getValue()); 1184 if (Ops.size() == 2) return Ops[0]; 1185 Ops.erase(Ops.begin()+1); // Erase the folded element 1186 LHSC = cast<SCEVConstant>(Ops[0]); 1187 } 1188 1189 // If we are left with a constant zero being added, strip it off. 1190 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1191 Ops.erase(Ops.begin()); 1192 --Idx; 1193 } 1194 } 1195 1196 if (Ops.size() == 1) return Ops[0]; 1197 1198 // Okay, check to see if the same value occurs in the operand list twice. If 1199 // so, merge them together into an multiply expression. Since we sorted the 1200 // list, these values are required to be adjacent. 1201 const Type *Ty = Ops[0]->getType(); 1202 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1203 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1204 // Found a match, merge the two values into a multiply, and add any 1205 // remaining values to the result. 1206 const SCEV *Two = getIntegerSCEV(2, Ty); 1207 const SCEV *Mul = getMulExpr(Ops[i], Two); 1208 if (Ops.size() == 2) 1209 return Mul; 1210 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1211 Ops.push_back(Mul); 1212 return getAddExpr(Ops); 1213 } 1214 1215 // Check for truncates. If all the operands are truncated from the same 1216 // type, see if factoring out the truncate would permit the result to be 1217 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1218 // if the contents of the resulting outer trunc fold to something simple. 1219 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1220 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1221 const Type *DstType = Trunc->getType(); 1222 const Type *SrcType = Trunc->getOperand()->getType(); 1223 SmallVector<const SCEV *, 8> LargeOps; 1224 bool Ok = true; 1225 // Check all the operands to see if they can be represented in the 1226 // source type of the truncate. 1227 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1228 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1229 if (T->getOperand()->getType() != SrcType) { 1230 Ok = false; 1231 break; 1232 } 1233 LargeOps.push_back(T->getOperand()); 1234 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1235 // This could be either sign or zero extension, but sign extension 1236 // is much more likely to be foldable here. 1237 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1238 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1239 SmallVector<const SCEV *, 8> LargeMulOps; 1240 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1241 if (const SCEVTruncateExpr *T = 1242 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1243 if (T->getOperand()->getType() != SrcType) { 1244 Ok = false; 1245 break; 1246 } 1247 LargeMulOps.push_back(T->getOperand()); 1248 } else if (const SCEVConstant *C = 1249 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1250 // This could be either sign or zero extension, but sign extension 1251 // is much more likely to be foldable here. 1252 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1253 } else { 1254 Ok = false; 1255 break; 1256 } 1257 } 1258 if (Ok) 1259 LargeOps.push_back(getMulExpr(LargeMulOps)); 1260 } else { 1261 Ok = false; 1262 break; 1263 } 1264 } 1265 if (Ok) { 1266 // Evaluate the expression in the larger type. 1267 const SCEV *Fold = getAddExpr(LargeOps); 1268 // If it folds to something simple, use it. Otherwise, don't. 1269 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1270 return getTruncateExpr(Fold, DstType); 1271 } 1272 } 1273 1274 // Skip past any other cast SCEVs. 1275 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1276 ++Idx; 1277 1278 // If there are add operands they would be next. 1279 if (Idx < Ops.size()) { 1280 bool DeletedAdd = false; 1281 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1282 // If we have an add, expand the add operands onto the end of the operands 1283 // list. 1284 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1285 Ops.erase(Ops.begin()+Idx); 1286 DeletedAdd = true; 1287 } 1288 1289 // If we deleted at least one add, we added operands to the end of the list, 1290 // and they are not necessarily sorted. Recurse to resort and resimplify 1291 // any operands we just aquired. 1292 if (DeletedAdd) 1293 return getAddExpr(Ops); 1294 } 1295 1296 // Skip over the add expression until we get to a multiply. 1297 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1298 ++Idx; 1299 1300 // Check to see if there are any folding opportunities present with 1301 // operands multiplied by constant values. 1302 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1303 uint64_t BitWidth = getTypeSizeInBits(Ty); 1304 DenseMap<const SCEV *, APInt> M; 1305 SmallVector<const SCEV *, 8> NewOps; 1306 APInt AccumulatedConstant(BitWidth, 0); 1307 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1308 Ops, APInt(BitWidth, 1), *this)) { 1309 // Some interesting folding opportunity is present, so its worthwhile to 1310 // re-generate the operands list. Group the operands by constant scale, 1311 // to avoid multiplying by the same constant scale multiple times. 1312 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1313 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1314 E = NewOps.end(); I != E; ++I) 1315 MulOpLists[M.find(*I)->second].push_back(*I); 1316 // Re-generate the operands list. 1317 Ops.clear(); 1318 if (AccumulatedConstant != 0) 1319 Ops.push_back(getConstant(AccumulatedConstant)); 1320 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1321 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1322 if (I->first != 0) 1323 Ops.push_back(getMulExpr(getConstant(I->first), 1324 getAddExpr(I->second))); 1325 if (Ops.empty()) 1326 return getIntegerSCEV(0, Ty); 1327 if (Ops.size() == 1) 1328 return Ops[0]; 1329 return getAddExpr(Ops); 1330 } 1331 } 1332 1333 // If we are adding something to a multiply expression, make sure the 1334 // something is not already an operand of the multiply. If so, merge it into 1335 // the multiply. 1336 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1337 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1338 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1339 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1340 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1341 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1342 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1343 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1344 if (Mul->getNumOperands() != 2) { 1345 // If the multiply has more than two operands, we must get the 1346 // Y*Z term. 1347 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1348 MulOps.erase(MulOps.begin()+MulOp); 1349 InnerMul = getMulExpr(MulOps); 1350 } 1351 const SCEV *One = getIntegerSCEV(1, Ty); 1352 const SCEV *AddOne = getAddExpr(InnerMul, One); 1353 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1354 if (Ops.size() == 2) return OuterMul; 1355 if (AddOp < Idx) { 1356 Ops.erase(Ops.begin()+AddOp); 1357 Ops.erase(Ops.begin()+Idx-1); 1358 } else { 1359 Ops.erase(Ops.begin()+Idx); 1360 Ops.erase(Ops.begin()+AddOp-1); 1361 } 1362 Ops.push_back(OuterMul); 1363 return getAddExpr(Ops); 1364 } 1365 1366 // Check this multiply against other multiplies being added together. 1367 for (unsigned OtherMulIdx = Idx+1; 1368 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1369 ++OtherMulIdx) { 1370 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1371 // If MulOp occurs in OtherMul, we can fold the two multiplies 1372 // together. 1373 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1374 OMulOp != e; ++OMulOp) 1375 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1376 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1377 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1378 if (Mul->getNumOperands() != 2) { 1379 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1380 Mul->op_end()); 1381 MulOps.erase(MulOps.begin()+MulOp); 1382 InnerMul1 = getMulExpr(MulOps); 1383 } 1384 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1385 if (OtherMul->getNumOperands() != 2) { 1386 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1387 OtherMul->op_end()); 1388 MulOps.erase(MulOps.begin()+OMulOp); 1389 InnerMul2 = getMulExpr(MulOps); 1390 } 1391 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1392 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1393 if (Ops.size() == 2) return OuterMul; 1394 Ops.erase(Ops.begin()+Idx); 1395 Ops.erase(Ops.begin()+OtherMulIdx-1); 1396 Ops.push_back(OuterMul); 1397 return getAddExpr(Ops); 1398 } 1399 } 1400 } 1401 } 1402 1403 // If there are any add recurrences in the operands list, see if any other 1404 // added values are loop invariant. If so, we can fold them into the 1405 // recurrence. 1406 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1407 ++Idx; 1408 1409 // Scan over all recurrences, trying to fold loop invariants into them. 1410 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1411 // Scan all of the other operands to this add and add them to the vector if 1412 // they are loop invariant w.r.t. the recurrence. 1413 SmallVector<const SCEV *, 8> LIOps; 1414 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1415 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1416 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1417 LIOps.push_back(Ops[i]); 1418 Ops.erase(Ops.begin()+i); 1419 --i; --e; 1420 } 1421 1422 // If we found some loop invariants, fold them into the recurrence. 1423 if (!LIOps.empty()) { 1424 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1425 LIOps.push_back(AddRec->getStart()); 1426 1427 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1428 AddRec->op_end()); 1429 AddRecOps[0] = getAddExpr(LIOps); 1430 1431 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1432 // If all of the other operands were loop invariant, we are done. 1433 if (Ops.size() == 1) return NewRec; 1434 1435 // Otherwise, add the folded AddRec by the non-liv parts. 1436 for (unsigned i = 0;; ++i) 1437 if (Ops[i] == AddRec) { 1438 Ops[i] = NewRec; 1439 break; 1440 } 1441 return getAddExpr(Ops); 1442 } 1443 1444 // Okay, if there weren't any loop invariants to be folded, check to see if 1445 // there are multiple AddRec's with the same loop induction variable being 1446 // added together. If so, we can fold them. 1447 for (unsigned OtherIdx = Idx+1; 1448 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1449 if (OtherIdx != Idx) { 1450 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1451 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1452 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1453 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1454 AddRec->op_end()); 1455 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1456 if (i >= NewOps.size()) { 1457 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1458 OtherAddRec->op_end()); 1459 break; 1460 } 1461 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1462 } 1463 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1464 1465 if (Ops.size() == 2) return NewAddRec; 1466 1467 Ops.erase(Ops.begin()+Idx); 1468 Ops.erase(Ops.begin()+OtherIdx-1); 1469 Ops.push_back(NewAddRec); 1470 return getAddExpr(Ops); 1471 } 1472 } 1473 1474 // Otherwise couldn't fold anything into this recurrence. Move onto the 1475 // next one. 1476 } 1477 1478 // Okay, it looks like we really DO need an add expr. Check to see if we 1479 // already have one, otherwise create a new one. 1480 FoldingSetNodeID ID; 1481 ID.AddInteger(scAddExpr); 1482 ID.AddInteger(Ops.size()); 1483 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1484 ID.AddPointer(Ops[i]); 1485 void *IP = 0; 1486 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1487 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1488 new (S) SCEVAddExpr(Ops); 1489 UniqueSCEVs.InsertNode(S, IP); 1490 return S; 1491} 1492 1493 1494/// getMulExpr - Get a canonical multiply expression, or something simpler if 1495/// possible. 1496const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) { 1497 assert(!Ops.empty() && "Cannot get empty mul!"); 1498#ifndef NDEBUG 1499 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1500 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1501 getEffectiveSCEVType(Ops[0]->getType()) && 1502 "SCEVMulExpr operand types don't match!"); 1503#endif 1504 1505 // Sort by complexity, this groups all similar expression types together. 1506 GroupByComplexity(Ops, LI); 1507 1508 // If there are any constants, fold them together. 1509 unsigned Idx = 0; 1510 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1511 1512 // C1*(C2+V) -> C1*C2 + C1*V 1513 if (Ops.size() == 2) 1514 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1515 if (Add->getNumOperands() == 2 && 1516 isa<SCEVConstant>(Add->getOperand(0))) 1517 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1518 getMulExpr(LHSC, Add->getOperand(1))); 1519 1520 1521 ++Idx; 1522 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1523 // We found two constants, fold them together! 1524 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1525 RHSC->getValue()->getValue()); 1526 Ops[0] = getConstant(Fold); 1527 Ops.erase(Ops.begin()+1); // Erase the folded element 1528 if (Ops.size() == 1) return Ops[0]; 1529 LHSC = cast<SCEVConstant>(Ops[0]); 1530 } 1531 1532 // If we are left with a constant one being multiplied, strip it off. 1533 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1534 Ops.erase(Ops.begin()); 1535 --Idx; 1536 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1537 // If we have a multiply of zero, it will always be zero. 1538 return Ops[0]; 1539 } 1540 } 1541 1542 // Skip over the add expression until we get to a multiply. 1543 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1544 ++Idx; 1545 1546 if (Ops.size() == 1) 1547 return Ops[0]; 1548 1549 // If there are mul operands inline them all into this expression. 1550 if (Idx < Ops.size()) { 1551 bool DeletedMul = false; 1552 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1553 // If we have an mul, expand the mul operands onto the end of the operands 1554 // list. 1555 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1556 Ops.erase(Ops.begin()+Idx); 1557 DeletedMul = true; 1558 } 1559 1560 // If we deleted at least one mul, we added operands to the end of the list, 1561 // and they are not necessarily sorted. Recurse to resort and resimplify 1562 // any operands we just aquired. 1563 if (DeletedMul) 1564 return getMulExpr(Ops); 1565 } 1566 1567 // If there are any add recurrences in the operands list, see if any other 1568 // added values are loop invariant. If so, we can fold them into the 1569 // recurrence. 1570 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1571 ++Idx; 1572 1573 // Scan over all recurrences, trying to fold loop invariants into them. 1574 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1575 // Scan all of the other operands to this mul and add them to the vector if 1576 // they are loop invariant w.r.t. the recurrence. 1577 SmallVector<const SCEV *, 8> LIOps; 1578 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1579 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1580 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1581 LIOps.push_back(Ops[i]); 1582 Ops.erase(Ops.begin()+i); 1583 --i; --e; 1584 } 1585 1586 // If we found some loop invariants, fold them into the recurrence. 1587 if (!LIOps.empty()) { 1588 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1589 SmallVector<const SCEV *, 4> NewOps; 1590 NewOps.reserve(AddRec->getNumOperands()); 1591 if (LIOps.size() == 1) { 1592 const SCEV *Scale = LIOps[0]; 1593 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1594 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1595 } else { 1596 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1597 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1598 MulOps.push_back(AddRec->getOperand(i)); 1599 NewOps.push_back(getMulExpr(MulOps)); 1600 } 1601 } 1602 1603 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1604 1605 // If all of the other operands were loop invariant, we are done. 1606 if (Ops.size() == 1) return NewRec; 1607 1608 // Otherwise, multiply the folded AddRec by the non-liv parts. 1609 for (unsigned i = 0;; ++i) 1610 if (Ops[i] == AddRec) { 1611 Ops[i] = NewRec; 1612 break; 1613 } 1614 return getMulExpr(Ops); 1615 } 1616 1617 // Okay, if there weren't any loop invariants to be folded, check to see if 1618 // there are multiple AddRec's with the same loop induction variable being 1619 // multiplied together. If so, we can fold them. 1620 for (unsigned OtherIdx = Idx+1; 1621 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1622 if (OtherIdx != Idx) { 1623 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1624 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1625 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1626 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1627 const SCEV *NewStart = getMulExpr(F->getStart(), 1628 G->getStart()); 1629 const SCEV *B = F->getStepRecurrence(*this); 1630 const SCEV *D = G->getStepRecurrence(*this); 1631 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1632 getMulExpr(G, B), 1633 getMulExpr(B, D)); 1634 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1635 F->getLoop()); 1636 if (Ops.size() == 2) return NewAddRec; 1637 1638 Ops.erase(Ops.begin()+Idx); 1639 Ops.erase(Ops.begin()+OtherIdx-1); 1640 Ops.push_back(NewAddRec); 1641 return getMulExpr(Ops); 1642 } 1643 } 1644 1645 // Otherwise couldn't fold anything into this recurrence. Move onto the 1646 // next one. 1647 } 1648 1649 // Okay, it looks like we really DO need an mul expr. Check to see if we 1650 // already have one, otherwise create a new one. 1651 FoldingSetNodeID ID; 1652 ID.AddInteger(scMulExpr); 1653 ID.AddInteger(Ops.size()); 1654 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1655 ID.AddPointer(Ops[i]); 1656 void *IP = 0; 1657 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1658 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1659 new (S) SCEVMulExpr(Ops); 1660 UniqueSCEVs.InsertNode(S, IP); 1661 return S; 1662} 1663 1664/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1665/// possible. 1666const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1667 const SCEV *RHS) { 1668 assert(getEffectiveSCEVType(LHS->getType()) == 1669 getEffectiveSCEVType(RHS->getType()) && 1670 "SCEVUDivExpr operand types don't match!"); 1671 1672 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1673 if (RHSC->getValue()->equalsInt(1)) 1674 return LHS; // X udiv 1 --> x 1675 if (RHSC->isZero()) 1676 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1677 1678 // Determine if the division can be folded into the operands of 1679 // its operands. 1680 // TODO: Generalize this to non-constants by using known-bits information. 1681 const Type *Ty = LHS->getType(); 1682 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1683 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1684 // For non-power-of-two values, effectively round the value up to the 1685 // nearest power of two. 1686 if (!RHSC->getValue()->getValue().isPowerOf2()) 1687 ++MaxShiftAmt; 1688 const IntegerType *ExtTy = 1689 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1690 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1691 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1692 if (const SCEVConstant *Step = 1693 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1694 if (!Step->getValue()->getValue() 1695 .urem(RHSC->getValue()->getValue()) && 1696 getZeroExtendExpr(AR, ExtTy) == 1697 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1698 getZeroExtendExpr(Step, ExtTy), 1699 AR->getLoop())) { 1700 SmallVector<const SCEV *, 4> Operands; 1701 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1702 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1703 return getAddRecExpr(Operands, AR->getLoop()); 1704 } 1705 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1706 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1707 SmallVector<const SCEV *, 4> Operands; 1708 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1709 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1710 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1711 // Find an operand that's safely divisible. 1712 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1713 const SCEV *Op = M->getOperand(i); 1714 const SCEV *Div = getUDivExpr(Op, RHSC); 1715 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1716 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1717 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1718 MOperands.end()); 1719 Operands[i] = Div; 1720 return getMulExpr(Operands); 1721 } 1722 } 1723 } 1724 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1725 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1726 SmallVector<const SCEV *, 4> Operands; 1727 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1728 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1729 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1730 Operands.clear(); 1731 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1732 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1733 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1734 break; 1735 Operands.push_back(Op); 1736 } 1737 if (Operands.size() == A->getNumOperands()) 1738 return getAddExpr(Operands); 1739 } 1740 } 1741 1742 // Fold if both operands are constant. 1743 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1744 Constant *LHSCV = LHSC->getValue(); 1745 Constant *RHSCV = RHSC->getValue(); 1746 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1747 RHSCV))); 1748 } 1749 } 1750 1751 FoldingSetNodeID ID; 1752 ID.AddInteger(scUDivExpr); 1753 ID.AddPointer(LHS); 1754 ID.AddPointer(RHS); 1755 void *IP = 0; 1756 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1757 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1758 new (S) SCEVUDivExpr(LHS, RHS); 1759 UniqueSCEVs.InsertNode(S, IP); 1760 return S; 1761} 1762 1763 1764/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1765/// Simplify the expression as much as possible. 1766const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1767 const SCEV *Step, const Loop *L) { 1768 SmallVector<const SCEV *, 4> Operands; 1769 Operands.push_back(Start); 1770 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1771 if (StepChrec->getLoop() == L) { 1772 Operands.insert(Operands.end(), StepChrec->op_begin(), 1773 StepChrec->op_end()); 1774 return getAddRecExpr(Operands, L); 1775 } 1776 1777 Operands.push_back(Step); 1778 return getAddRecExpr(Operands, L); 1779} 1780 1781/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1782/// Simplify the expression as much as possible. 1783const SCEV * 1784ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1785 const Loop *L) { 1786 if (Operands.size() == 1) return Operands[0]; 1787#ifndef NDEBUG 1788 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1789 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1790 getEffectiveSCEVType(Operands[0]->getType()) && 1791 "SCEVAddRecExpr operand types don't match!"); 1792#endif 1793 1794 if (Operands.back()->isZero()) { 1795 Operands.pop_back(); 1796 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1797 } 1798 1799 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1800 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1801 const Loop* NestedLoop = NestedAR->getLoop(); 1802 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1803 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1804 NestedAR->op_end()); 1805 Operands[0] = NestedAR->getStart(); 1806 // AddRecs require their operands be loop-invariant with respect to their 1807 // loops. Don't perform this transformation if it would break this 1808 // requirement. 1809 bool AllInvariant = true; 1810 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1811 if (!Operands[i]->isLoopInvariant(L)) { 1812 AllInvariant = false; 1813 break; 1814 } 1815 if (AllInvariant) { 1816 NestedOperands[0] = getAddRecExpr(Operands, L); 1817 AllInvariant = true; 1818 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1819 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1820 AllInvariant = false; 1821 break; 1822 } 1823 if (AllInvariant) 1824 // Ok, both add recurrences are valid after the transformation. 1825 return getAddRecExpr(NestedOperands, NestedLoop); 1826 } 1827 // Reset Operands to its original state. 1828 Operands[0] = NestedAR; 1829 } 1830 } 1831 1832 FoldingSetNodeID ID; 1833 ID.AddInteger(scAddRecExpr); 1834 ID.AddInteger(Operands.size()); 1835 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1836 ID.AddPointer(Operands[i]); 1837 ID.AddPointer(L); 1838 void *IP = 0; 1839 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1840 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1841 new (S) SCEVAddRecExpr(Operands, L); 1842 UniqueSCEVs.InsertNode(S, IP); 1843 return S; 1844} 1845 1846const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1847 const SCEV *RHS) { 1848 SmallVector<const SCEV *, 2> Ops; 1849 Ops.push_back(LHS); 1850 Ops.push_back(RHS); 1851 return getSMaxExpr(Ops); 1852} 1853 1854const SCEV * 1855ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1856 assert(!Ops.empty() && "Cannot get empty smax!"); 1857 if (Ops.size() == 1) return Ops[0]; 1858#ifndef NDEBUG 1859 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1860 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1861 getEffectiveSCEVType(Ops[0]->getType()) && 1862 "SCEVSMaxExpr operand types don't match!"); 1863#endif 1864 1865 // Sort by complexity, this groups all similar expression types together. 1866 GroupByComplexity(Ops, LI); 1867 1868 // If there are any constants, fold them together. 1869 unsigned Idx = 0; 1870 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1871 ++Idx; 1872 assert(Idx < Ops.size()); 1873 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1874 // We found two constants, fold them together! 1875 ConstantInt *Fold = ConstantInt::get( 1876 APIntOps::smax(LHSC->getValue()->getValue(), 1877 RHSC->getValue()->getValue())); 1878 Ops[0] = getConstant(Fold); 1879 Ops.erase(Ops.begin()+1); // Erase the folded element 1880 if (Ops.size() == 1) return Ops[0]; 1881 LHSC = cast<SCEVConstant>(Ops[0]); 1882 } 1883 1884 // If we are left with a constant minimum-int, strip it off. 1885 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1886 Ops.erase(Ops.begin()); 1887 --Idx; 1888 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1889 // If we have an smax with a constant maximum-int, it will always be 1890 // maximum-int. 1891 return Ops[0]; 1892 } 1893 } 1894 1895 if (Ops.size() == 1) return Ops[0]; 1896 1897 // Find the first SMax 1898 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1899 ++Idx; 1900 1901 // Check to see if one of the operands is an SMax. If so, expand its operands 1902 // onto our operand list, and recurse to simplify. 1903 if (Idx < Ops.size()) { 1904 bool DeletedSMax = false; 1905 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1906 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1907 Ops.erase(Ops.begin()+Idx); 1908 DeletedSMax = true; 1909 } 1910 1911 if (DeletedSMax) 1912 return getSMaxExpr(Ops); 1913 } 1914 1915 // Okay, check to see if the same value occurs in the operand list twice. If 1916 // so, delete one. Since we sorted the list, these values are required to 1917 // be adjacent. 1918 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1919 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1920 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1921 --i; --e; 1922 } 1923 1924 if (Ops.size() == 1) return Ops[0]; 1925 1926 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1927 1928 // Okay, it looks like we really DO need an smax expr. Check to see if we 1929 // already have one, otherwise create a new one. 1930 FoldingSetNodeID ID; 1931 ID.AddInteger(scSMaxExpr); 1932 ID.AddInteger(Ops.size()); 1933 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1934 ID.AddPointer(Ops[i]); 1935 void *IP = 0; 1936 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1937 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1938 new (S) SCEVSMaxExpr(Ops); 1939 UniqueSCEVs.InsertNode(S, IP); 1940 return S; 1941} 1942 1943const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1944 const SCEV *RHS) { 1945 SmallVector<const SCEV *, 2> Ops; 1946 Ops.push_back(LHS); 1947 Ops.push_back(RHS); 1948 return getUMaxExpr(Ops); 1949} 1950 1951const SCEV * 1952ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1953 assert(!Ops.empty() && "Cannot get empty umax!"); 1954 if (Ops.size() == 1) return Ops[0]; 1955#ifndef NDEBUG 1956 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1957 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1958 getEffectiveSCEVType(Ops[0]->getType()) && 1959 "SCEVUMaxExpr operand types don't match!"); 1960#endif 1961 1962 // Sort by complexity, this groups all similar expression types together. 1963 GroupByComplexity(Ops, LI); 1964 1965 // If there are any constants, fold them together. 1966 unsigned Idx = 0; 1967 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1968 ++Idx; 1969 assert(Idx < Ops.size()); 1970 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1971 // We found two constants, fold them together! 1972 ConstantInt *Fold = ConstantInt::get( 1973 APIntOps::umax(LHSC->getValue()->getValue(), 1974 RHSC->getValue()->getValue())); 1975 Ops[0] = getConstant(Fold); 1976 Ops.erase(Ops.begin()+1); // Erase the folded element 1977 if (Ops.size() == 1) return Ops[0]; 1978 LHSC = cast<SCEVConstant>(Ops[0]); 1979 } 1980 1981 // If we are left with a constant minimum-int, strip it off. 1982 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1983 Ops.erase(Ops.begin()); 1984 --Idx; 1985 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 1986 // If we have an umax with a constant maximum-int, it will always be 1987 // maximum-int. 1988 return Ops[0]; 1989 } 1990 } 1991 1992 if (Ops.size() == 1) return Ops[0]; 1993 1994 // Find the first UMax 1995 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1996 ++Idx; 1997 1998 // Check to see if one of the operands is a UMax. If so, expand its operands 1999 // onto our operand list, and recurse to simplify. 2000 if (Idx < Ops.size()) { 2001 bool DeletedUMax = false; 2002 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2003 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2004 Ops.erase(Ops.begin()+Idx); 2005 DeletedUMax = true; 2006 } 2007 2008 if (DeletedUMax) 2009 return getUMaxExpr(Ops); 2010 } 2011 2012 // Okay, check to see if the same value occurs in the operand list twice. If 2013 // so, delete one. Since we sorted the list, these values are required to 2014 // be adjacent. 2015 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2016 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2017 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2018 --i; --e; 2019 } 2020 2021 if (Ops.size() == 1) return Ops[0]; 2022 2023 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2024 2025 // Okay, it looks like we really DO need a umax expr. Check to see if we 2026 // already have one, otherwise create a new one. 2027 FoldingSetNodeID ID; 2028 ID.AddInteger(scUMaxExpr); 2029 ID.AddInteger(Ops.size()); 2030 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2031 ID.AddPointer(Ops[i]); 2032 void *IP = 0; 2033 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2034 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2035 new (S) SCEVUMaxExpr(Ops); 2036 UniqueSCEVs.InsertNode(S, IP); 2037 return S; 2038} 2039 2040const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2041 const SCEV *RHS) { 2042 // ~smax(~x, ~y) == smin(x, y). 2043 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2044} 2045 2046const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2047 const SCEV *RHS) { 2048 // ~umax(~x, ~y) == umin(x, y) 2049 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2050} 2051 2052const SCEV *ScalarEvolution::getUnknown(Value *V) { 2053 // Don't attempt to do anything other than create a SCEVUnknown object 2054 // here. createSCEV only calls getUnknown after checking for all other 2055 // interesting possibilities, and any other code that calls getUnknown 2056 // is doing so in order to hide a value from SCEV canonicalization. 2057 2058 FoldingSetNodeID ID; 2059 ID.AddInteger(scUnknown); 2060 ID.AddPointer(V); 2061 void *IP = 0; 2062 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2063 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2064 new (S) SCEVUnknown(V); 2065 UniqueSCEVs.InsertNode(S, IP); 2066 return S; 2067} 2068 2069//===----------------------------------------------------------------------===// 2070// Basic SCEV Analysis and PHI Idiom Recognition Code 2071// 2072 2073/// isSCEVable - Test if values of the given type are analyzable within 2074/// the SCEV framework. This primarily includes integer types, and it 2075/// can optionally include pointer types if the ScalarEvolution class 2076/// has access to target-specific information. 2077bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2078 // Integers are always SCEVable. 2079 if (Ty->isInteger()) 2080 return true; 2081 2082 // Pointers are SCEVable if TargetData information is available 2083 // to provide pointer size information. 2084 if (isa<PointerType>(Ty)) 2085 return TD != NULL; 2086 2087 // Otherwise it's not SCEVable. 2088 return false; 2089} 2090 2091/// getTypeSizeInBits - Return the size in bits of the specified type, 2092/// for which isSCEVable must return true. 2093uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2094 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2095 2096 // If we have a TargetData, use it! 2097 if (TD) 2098 return TD->getTypeSizeInBits(Ty); 2099 2100 // Otherwise, we support only integer types. 2101 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 2102 return Ty->getPrimitiveSizeInBits(); 2103} 2104 2105/// getEffectiveSCEVType - Return a type with the same bitwidth as 2106/// the given type and which represents how SCEV will treat the given 2107/// type, for which isSCEVable must return true. For pointer types, 2108/// this is the pointer-sized integer type. 2109const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2110 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2111 2112 if (Ty->isInteger()) 2113 return Ty; 2114 2115 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2116 return TD->getIntPtrType(); 2117} 2118 2119const SCEV *ScalarEvolution::getCouldNotCompute() { 2120 return &CouldNotCompute; 2121} 2122 2123/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2124/// expression and create a new one. 2125const SCEV *ScalarEvolution::getSCEV(Value *V) { 2126 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2127 2128 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2129 if (I != Scalars.end()) return I->second; 2130 const SCEV *S = createSCEV(V); 2131 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2132 return S; 2133} 2134 2135/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2136/// specified signed integer value and return a SCEV for the constant. 2137const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2138 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2139 return getConstant(ConstantInt::get(ITy, Val)); 2140} 2141 2142/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2143/// 2144const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2145 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2146 return getConstant(cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2147 2148 const Type *Ty = V->getType(); 2149 Ty = getEffectiveSCEVType(Ty); 2150 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 2151} 2152 2153/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2154const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2155 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2156 return getConstant(cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2157 2158 const Type *Ty = V->getType(); 2159 Ty = getEffectiveSCEVType(Ty); 2160 const SCEV *AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 2161 return getMinusSCEV(AllOnes, V); 2162} 2163 2164/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2165/// 2166const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2167 const SCEV *RHS) { 2168 // X - Y --> X + -Y 2169 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2170} 2171 2172/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2173/// input value to the specified type. If the type must be extended, it is zero 2174/// extended. 2175const SCEV * 2176ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2177 const Type *Ty) { 2178 const Type *SrcTy = V->getType(); 2179 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2180 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2181 "Cannot truncate or zero extend with non-integer arguments!"); 2182 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2183 return V; // No conversion 2184 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2185 return getTruncateExpr(V, Ty); 2186 return getZeroExtendExpr(V, Ty); 2187} 2188 2189/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2190/// input value to the specified type. If the type must be extended, it is sign 2191/// extended. 2192const SCEV * 2193ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2194 const Type *Ty) { 2195 const Type *SrcTy = V->getType(); 2196 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2197 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2198 "Cannot truncate or zero extend with non-integer arguments!"); 2199 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2200 return V; // No conversion 2201 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2202 return getTruncateExpr(V, Ty); 2203 return getSignExtendExpr(V, Ty); 2204} 2205 2206/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2207/// input value to the specified type. If the type must be extended, it is zero 2208/// extended. The conversion must not be narrowing. 2209const SCEV * 2210ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2211 const Type *SrcTy = V->getType(); 2212 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2213 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2214 "Cannot noop or zero extend with non-integer arguments!"); 2215 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2216 "getNoopOrZeroExtend cannot truncate!"); 2217 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2218 return V; // No conversion 2219 return getZeroExtendExpr(V, Ty); 2220} 2221 2222/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2223/// input value to the specified type. If the type must be extended, it is sign 2224/// extended. The conversion must not be narrowing. 2225const SCEV * 2226ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2227 const Type *SrcTy = V->getType(); 2228 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2229 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2230 "Cannot noop or sign extend with non-integer arguments!"); 2231 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2232 "getNoopOrSignExtend cannot truncate!"); 2233 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2234 return V; // No conversion 2235 return getSignExtendExpr(V, Ty); 2236} 2237 2238/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2239/// the input value to the specified type. If the type must be extended, 2240/// it is extended with unspecified bits. The conversion must not be 2241/// narrowing. 2242const SCEV * 2243ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2244 const Type *SrcTy = V->getType(); 2245 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2246 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2247 "Cannot noop or any extend with non-integer arguments!"); 2248 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2249 "getNoopOrAnyExtend cannot truncate!"); 2250 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2251 return V; // No conversion 2252 return getAnyExtendExpr(V, Ty); 2253} 2254 2255/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2256/// input value to the specified type. The conversion must not be widening. 2257const SCEV * 2258ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2259 const Type *SrcTy = V->getType(); 2260 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2261 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2262 "Cannot truncate or noop with non-integer arguments!"); 2263 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2264 "getTruncateOrNoop cannot extend!"); 2265 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2266 return V; // No conversion 2267 return getTruncateExpr(V, Ty); 2268} 2269 2270/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2271/// the types using zero-extension, and then perform a umax operation 2272/// with them. 2273const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2274 const SCEV *RHS) { 2275 const SCEV *PromotedLHS = LHS; 2276 const SCEV *PromotedRHS = RHS; 2277 2278 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2279 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2280 else 2281 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2282 2283 return getUMaxExpr(PromotedLHS, PromotedRHS); 2284} 2285 2286/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2287/// the types using zero-extension, and then perform a umin operation 2288/// with them. 2289const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2290 const SCEV *RHS) { 2291 const SCEV *PromotedLHS = LHS; 2292 const SCEV *PromotedRHS = RHS; 2293 2294 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2295 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2296 else 2297 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2298 2299 return getUMinExpr(PromotedLHS, PromotedRHS); 2300} 2301 2302/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2303/// the specified instruction and replaces any references to the symbolic value 2304/// SymName with the specified value. This is used during PHI resolution. 2305void 2306ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I, 2307 const SCEV *SymName, 2308 const SCEV *NewVal) { 2309 std::map<SCEVCallbackVH, const SCEV *>::iterator SI = 2310 Scalars.find(SCEVCallbackVH(I, this)); 2311 if (SI == Scalars.end()) return; 2312 2313 const SCEV *NV = 2314 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2315 if (NV == SI->second) return; // No change. 2316 2317 SI->second = NV; // Update the scalars map! 2318 2319 // Any instruction values that use this instruction might also need to be 2320 // updated! 2321 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2322 UI != E; ++UI) 2323 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2324} 2325 2326/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2327/// a loop header, making it a potential recurrence, or it doesn't. 2328/// 2329const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2330 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2331 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2332 if (L->getHeader() == PN->getParent()) { 2333 // If it lives in the loop header, it has two incoming values, one 2334 // from outside the loop, and one from inside. 2335 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2336 unsigned BackEdge = IncomingEdge^1; 2337 2338 // While we are analyzing this PHI node, handle its value symbolically. 2339 const SCEV *SymbolicName = getUnknown(PN); 2340 assert(Scalars.find(PN) == Scalars.end() && 2341 "PHI node already processed?"); 2342 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2343 2344 // Using this symbolic name for the PHI, analyze the value coming around 2345 // the back-edge. 2346 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2347 2348 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2349 // has a special value for the first iteration of the loop. 2350 2351 // If the value coming around the backedge is an add with the symbolic 2352 // value we just inserted, then we found a simple induction variable! 2353 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2354 // If there is a single occurrence of the symbolic value, replace it 2355 // with a recurrence. 2356 unsigned FoundIndex = Add->getNumOperands(); 2357 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2358 if (Add->getOperand(i) == SymbolicName) 2359 if (FoundIndex == e) { 2360 FoundIndex = i; 2361 break; 2362 } 2363 2364 if (FoundIndex != Add->getNumOperands()) { 2365 // Create an add with everything but the specified operand. 2366 SmallVector<const SCEV *, 8> Ops; 2367 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2368 if (i != FoundIndex) 2369 Ops.push_back(Add->getOperand(i)); 2370 const SCEV *Accum = getAddExpr(Ops); 2371 2372 // This is not a valid addrec if the step amount is varying each 2373 // loop iteration, but is not itself an addrec in this loop. 2374 if (Accum->isLoopInvariant(L) || 2375 (isa<SCEVAddRecExpr>(Accum) && 2376 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2377 const SCEV *StartVal = 2378 getSCEV(PN->getIncomingValue(IncomingEdge)); 2379 const SCEV *PHISCEV = 2380 getAddRecExpr(StartVal, Accum, L); 2381 2382 // Okay, for the entire analysis of this edge we assumed the PHI 2383 // to be symbolic. We now need to go back and update all of the 2384 // entries for the scalars that use the PHI (except for the PHI 2385 // itself) to use the new analyzed value instead of the "symbolic" 2386 // value. 2387 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2388 return PHISCEV; 2389 } 2390 } 2391 } else if (const SCEVAddRecExpr *AddRec = 2392 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2393 // Otherwise, this could be a loop like this: 2394 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2395 // In this case, j = {1,+,1} and BEValue is j. 2396 // Because the other in-value of i (0) fits the evolution of BEValue 2397 // i really is an addrec evolution. 2398 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2399 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2400 2401 // If StartVal = j.start - j.stride, we can use StartVal as the 2402 // initial step of the addrec evolution. 2403 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2404 AddRec->getOperand(1))) { 2405 const SCEV *PHISCEV = 2406 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2407 2408 // Okay, for the entire analysis of this edge we assumed the PHI 2409 // to be symbolic. We now need to go back and update all of the 2410 // entries for the scalars that use the PHI (except for the PHI 2411 // itself) to use the new analyzed value instead of the "symbolic" 2412 // value. 2413 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2414 return PHISCEV; 2415 } 2416 } 2417 } 2418 2419 return SymbolicName; 2420 } 2421 2422 // If it's not a loop phi, we can't handle it yet. 2423 return getUnknown(PN); 2424} 2425 2426/// createNodeForGEP - Expand GEP instructions into add and multiply 2427/// operations. This allows them to be analyzed by regular SCEV code. 2428/// 2429const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) { 2430 2431 const Type *IntPtrTy = TD->getIntPtrType(); 2432 Value *Base = GEP->getOperand(0); 2433 // Don't attempt to analyze GEPs over unsized objects. 2434 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2435 return getUnknown(GEP); 2436 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2437 gep_type_iterator GTI = gep_type_begin(GEP); 2438 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2439 E = GEP->op_end(); 2440 I != E; ++I) { 2441 Value *Index = *I; 2442 // Compute the (potentially symbolic) offset in bytes for this index. 2443 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2444 // For a struct, add the member offset. 2445 const StructLayout &SL = *TD->getStructLayout(STy); 2446 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2447 uint64_t Offset = SL.getElementOffset(FieldNo); 2448 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy)); 2449 } else { 2450 // For an array, add the element offset, explicitly scaled. 2451 const SCEV *LocalOffset = getSCEV(Index); 2452 if (!isa<PointerType>(LocalOffset->getType())) 2453 // Getelementptr indicies are signed. 2454 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2455 LocalOffset = 2456 getMulExpr(LocalOffset, 2457 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy)); 2458 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2459 } 2460 } 2461 return getAddExpr(getSCEV(Base), TotalOffset); 2462} 2463 2464/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2465/// guaranteed to end in (at every loop iteration). It is, at the same time, 2466/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2467/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2468uint32_t 2469ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2470 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2471 return C->getValue()->getValue().countTrailingZeros(); 2472 2473 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2474 return std::min(GetMinTrailingZeros(T->getOperand()), 2475 (uint32_t)getTypeSizeInBits(T->getType())); 2476 2477 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2478 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2479 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2480 getTypeSizeInBits(E->getType()) : OpRes; 2481 } 2482 2483 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2484 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2485 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2486 getTypeSizeInBits(E->getType()) : OpRes; 2487 } 2488 2489 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2490 // The result is the min of all operands results. 2491 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2492 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2493 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2494 return MinOpRes; 2495 } 2496 2497 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2498 // The result is the sum of all operands results. 2499 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2500 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2501 for (unsigned i = 1, e = M->getNumOperands(); 2502 SumOpRes != BitWidth && i != e; ++i) 2503 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2504 BitWidth); 2505 return SumOpRes; 2506 } 2507 2508 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2509 // The result is the min of all operands results. 2510 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2511 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2512 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2513 return MinOpRes; 2514 } 2515 2516 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2517 // The result is the min of all operands results. 2518 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2519 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2520 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2521 return MinOpRes; 2522 } 2523 2524 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2525 // The result is the min of all operands results. 2526 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2527 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2528 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2529 return MinOpRes; 2530 } 2531 2532 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2533 // For a SCEVUnknown, ask ValueTracking. 2534 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2535 APInt Mask = APInt::getAllOnesValue(BitWidth); 2536 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2537 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2538 return Zeros.countTrailingOnes(); 2539 } 2540 2541 // SCEVUDivExpr 2542 return 0; 2543} 2544 2545/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2546/// 2547ConstantRange 2548ScalarEvolution::getUnsignedRange(const SCEV *S) { 2549 2550 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2551 return ConstantRange(C->getValue()->getValue()); 2552 2553 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2554 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2555 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2556 X = X.add(getUnsignedRange(Add->getOperand(i))); 2557 return X; 2558 } 2559 2560 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2561 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2562 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2563 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2564 return X; 2565 } 2566 2567 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2568 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2569 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2570 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2571 return X; 2572 } 2573 2574 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2575 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2576 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2577 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2578 return X; 2579 } 2580 2581 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2582 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2583 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2584 return X.udiv(Y); 2585 } 2586 2587 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2588 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2589 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2590 } 2591 2592 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2593 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2594 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2595 } 2596 2597 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2598 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2599 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2600 } 2601 2602 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2603 2604 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2605 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2606 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2607 if (!Trip) return FullSet; 2608 2609 // TODO: non-affine addrec 2610 if (AddRec->isAffine()) { 2611 const Type *Ty = AddRec->getType(); 2612 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2613 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2614 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2615 2616 const SCEV *Start = AddRec->getStart(); 2617 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2618 2619 // Check for overflow. 2620 if (!isKnownPredicate(ICmpInst::ICMP_ULE, Start, End)) 2621 return FullSet; 2622 2623 ConstantRange StartRange = getUnsignedRange(Start); 2624 ConstantRange EndRange = getUnsignedRange(End); 2625 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2626 EndRange.getUnsignedMin()); 2627 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2628 EndRange.getUnsignedMax()); 2629 if (Min.isMinValue() && Max.isMaxValue()) 2630 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2631 return ConstantRange(Min, Max+1); 2632 } 2633 } 2634 } 2635 2636 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2637 // For a SCEVUnknown, ask ValueTracking. 2638 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2639 APInt Mask = APInt::getAllOnesValue(BitWidth); 2640 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2641 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2642 return ConstantRange(Ones, ~Zeros); 2643 } 2644 2645 return FullSet; 2646} 2647 2648/// getSignedRange - Determine the signed range for a particular SCEV. 2649/// 2650ConstantRange 2651ScalarEvolution::getSignedRange(const SCEV *S) { 2652 2653 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2654 return ConstantRange(C->getValue()->getValue()); 2655 2656 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2657 ConstantRange X = getSignedRange(Add->getOperand(0)); 2658 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2659 X = X.add(getSignedRange(Add->getOperand(i))); 2660 return X; 2661 } 2662 2663 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2664 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2665 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2666 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2667 return X; 2668 } 2669 2670 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2671 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2672 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2673 X = X.smax(getSignedRange(SMax->getOperand(i))); 2674 return X; 2675 } 2676 2677 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2678 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2679 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2680 X = X.umax(getSignedRange(UMax->getOperand(i))); 2681 return X; 2682 } 2683 2684 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2685 ConstantRange X = getSignedRange(UDiv->getLHS()); 2686 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2687 return X.udiv(Y); 2688 } 2689 2690 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2691 ConstantRange X = getSignedRange(ZExt->getOperand()); 2692 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2693 } 2694 2695 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2696 ConstantRange X = getSignedRange(SExt->getOperand()); 2697 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2698 } 2699 2700 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2701 ConstantRange X = getSignedRange(Trunc->getOperand()); 2702 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2703 } 2704 2705 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2706 2707 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2708 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2709 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2710 if (!Trip) return FullSet; 2711 2712 // TODO: non-affine addrec 2713 if (AddRec->isAffine()) { 2714 const Type *Ty = AddRec->getType(); 2715 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2716 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2717 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2718 2719 const SCEV *Start = AddRec->getStart(); 2720 const SCEV *Step = AddRec->getStepRecurrence(*this); 2721 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2722 2723 // Check for overflow. 2724 if (!(isKnownPositive(Step) && 2725 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2726 !(isKnownNegative(Step) && 2727 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2728 return FullSet; 2729 2730 ConstantRange StartRange = getSignedRange(Start); 2731 ConstantRange EndRange = getSignedRange(End); 2732 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2733 EndRange.getSignedMin()); 2734 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2735 EndRange.getSignedMax()); 2736 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2737 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2738 return ConstantRange(Min, Max+1); 2739 } 2740 } 2741 } 2742 2743 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2744 // For a SCEVUnknown, ask ValueTracking. 2745 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2746 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2747 if (NS == 1) 2748 return FullSet; 2749 return 2750 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2751 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2752 } 2753 2754 return FullSet; 2755} 2756 2757/// createSCEV - We know that there is no SCEV for the specified value. 2758/// Analyze the expression. 2759/// 2760const SCEV *ScalarEvolution::createSCEV(Value *V) { 2761 if (!isSCEVable(V->getType())) 2762 return getUnknown(V); 2763 2764 unsigned Opcode = Instruction::UserOp1; 2765 if (Instruction *I = dyn_cast<Instruction>(V)) 2766 Opcode = I->getOpcode(); 2767 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2768 Opcode = CE->getOpcode(); 2769 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2770 return getConstant(CI); 2771 else if (isa<ConstantPointerNull>(V)) 2772 return getIntegerSCEV(0, V->getType()); 2773 else if (isa<UndefValue>(V)) 2774 return getIntegerSCEV(0, V->getType()); 2775 else 2776 return getUnknown(V); 2777 2778 User *U = cast<User>(V); 2779 switch (Opcode) { 2780 case Instruction::Add: 2781 return getAddExpr(getSCEV(U->getOperand(0)), 2782 getSCEV(U->getOperand(1))); 2783 case Instruction::Mul: 2784 return getMulExpr(getSCEV(U->getOperand(0)), 2785 getSCEV(U->getOperand(1))); 2786 case Instruction::UDiv: 2787 return getUDivExpr(getSCEV(U->getOperand(0)), 2788 getSCEV(U->getOperand(1))); 2789 case Instruction::Sub: 2790 return getMinusSCEV(getSCEV(U->getOperand(0)), 2791 getSCEV(U->getOperand(1))); 2792 case Instruction::And: 2793 // For an expression like x&255 that merely masks off the high bits, 2794 // use zext(trunc(x)) as the SCEV expression. 2795 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2796 if (CI->isNullValue()) 2797 return getSCEV(U->getOperand(1)); 2798 if (CI->isAllOnesValue()) 2799 return getSCEV(U->getOperand(0)); 2800 const APInt &A = CI->getValue(); 2801 2802 // Instcombine's ShrinkDemandedConstant may strip bits out of 2803 // constants, obscuring what would otherwise be a low-bits mask. 2804 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2805 // knew about to reconstruct a low-bits mask value. 2806 unsigned LZ = A.countLeadingZeros(); 2807 unsigned BitWidth = A.getBitWidth(); 2808 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2809 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2810 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2811 2812 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2813 2814 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2815 return 2816 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2817 IntegerType::get(BitWidth - LZ)), 2818 U->getType()); 2819 } 2820 break; 2821 2822 case Instruction::Or: 2823 // If the RHS of the Or is a constant, we may have something like: 2824 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2825 // optimizations will transparently handle this case. 2826 // 2827 // In order for this transformation to be safe, the LHS must be of the 2828 // form X*(2^n) and the Or constant must be less than 2^n. 2829 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2830 const SCEV *LHS = getSCEV(U->getOperand(0)); 2831 const APInt &CIVal = CI->getValue(); 2832 if (GetMinTrailingZeros(LHS) >= 2833 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2834 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2835 } 2836 break; 2837 case Instruction::Xor: 2838 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2839 // If the RHS of the xor is a signbit, then this is just an add. 2840 // Instcombine turns add of signbit into xor as a strength reduction step. 2841 if (CI->getValue().isSignBit()) 2842 return getAddExpr(getSCEV(U->getOperand(0)), 2843 getSCEV(U->getOperand(1))); 2844 2845 // If the RHS of xor is -1, then this is a not operation. 2846 if (CI->isAllOnesValue()) 2847 return getNotSCEV(getSCEV(U->getOperand(0))); 2848 2849 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2850 // This is a variant of the check for xor with -1, and it handles 2851 // the case where instcombine has trimmed non-demanded bits out 2852 // of an xor with -1. 2853 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2854 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2855 if (BO->getOpcode() == Instruction::And && 2856 LCI->getValue() == CI->getValue()) 2857 if (const SCEVZeroExtendExpr *Z = 2858 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2859 const Type *UTy = U->getType(); 2860 const SCEV *Z0 = Z->getOperand(); 2861 const Type *Z0Ty = Z0->getType(); 2862 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2863 2864 // If C is a low-bits mask, the zero extend is zerving to 2865 // mask off the high bits. Complement the operand and 2866 // re-apply the zext. 2867 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2868 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2869 2870 // If C is a single bit, it may be in the sign-bit position 2871 // before the zero-extend. In this case, represent the xor 2872 // using an add, which is equivalent, and re-apply the zext. 2873 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2874 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2875 Trunc.isSignBit()) 2876 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2877 UTy); 2878 } 2879 } 2880 break; 2881 2882 case Instruction::Shl: 2883 // Turn shift left of a constant amount into a multiply. 2884 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2885 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2886 Constant *X = ConstantInt::get( 2887 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2888 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2889 } 2890 break; 2891 2892 case Instruction::LShr: 2893 // Turn logical shift right of a constant into a unsigned divide. 2894 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2895 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2896 Constant *X = ConstantInt::get( 2897 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2898 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2899 } 2900 break; 2901 2902 case Instruction::AShr: 2903 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2904 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2905 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2906 if (L->getOpcode() == Instruction::Shl && 2907 L->getOperand(1) == U->getOperand(1)) { 2908 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2909 uint64_t Amt = BitWidth - CI->getZExtValue(); 2910 if (Amt == BitWidth) 2911 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2912 if (Amt > BitWidth) 2913 return getIntegerSCEV(0, U->getType()); // value is undefined 2914 return 2915 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2916 IntegerType::get(Amt)), 2917 U->getType()); 2918 } 2919 break; 2920 2921 case Instruction::Trunc: 2922 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2923 2924 case Instruction::ZExt: 2925 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2926 2927 case Instruction::SExt: 2928 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2929 2930 case Instruction::BitCast: 2931 // BitCasts are no-op casts so we just eliminate the cast. 2932 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2933 return getSCEV(U->getOperand(0)); 2934 break; 2935 2936 case Instruction::IntToPtr: 2937 if (!TD) break; // Without TD we can't analyze pointers. 2938 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2939 TD->getIntPtrType()); 2940 2941 case Instruction::PtrToInt: 2942 if (!TD) break; // Without TD we can't analyze pointers. 2943 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2944 U->getType()); 2945 2946 case Instruction::GetElementPtr: 2947 if (!TD) break; // Without TD we can't analyze pointers. 2948 return createNodeForGEP(U); 2949 2950 case Instruction::PHI: 2951 return createNodeForPHI(cast<PHINode>(U)); 2952 2953 case Instruction::Select: 2954 // This could be a smax or umax that was lowered earlier. 2955 // Try to recover it. 2956 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2957 Value *LHS = ICI->getOperand(0); 2958 Value *RHS = ICI->getOperand(1); 2959 switch (ICI->getPredicate()) { 2960 case ICmpInst::ICMP_SLT: 2961 case ICmpInst::ICMP_SLE: 2962 std::swap(LHS, RHS); 2963 // fall through 2964 case ICmpInst::ICMP_SGT: 2965 case ICmpInst::ICMP_SGE: 2966 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2967 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2968 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2969 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2970 break; 2971 case ICmpInst::ICMP_ULT: 2972 case ICmpInst::ICMP_ULE: 2973 std::swap(LHS, RHS); 2974 // fall through 2975 case ICmpInst::ICMP_UGT: 2976 case ICmpInst::ICMP_UGE: 2977 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2978 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2979 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2980 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2981 break; 2982 case ICmpInst::ICMP_NE: 2983 // n != 0 ? n : 1 -> umax(n, 1) 2984 if (LHS == U->getOperand(1) && 2985 isa<ConstantInt>(U->getOperand(2)) && 2986 cast<ConstantInt>(U->getOperand(2))->isOne() && 2987 isa<ConstantInt>(RHS) && 2988 cast<ConstantInt>(RHS)->isZero()) 2989 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2990 break; 2991 case ICmpInst::ICMP_EQ: 2992 // n == 0 ? 1 : n -> umax(n, 1) 2993 if (LHS == U->getOperand(2) && 2994 isa<ConstantInt>(U->getOperand(1)) && 2995 cast<ConstantInt>(U->getOperand(1))->isOne() && 2996 isa<ConstantInt>(RHS) && 2997 cast<ConstantInt>(RHS)->isZero()) 2998 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 2999 break; 3000 default: 3001 break; 3002 } 3003 } 3004 3005 default: // We cannot analyze this expression. 3006 break; 3007 } 3008 3009 return getUnknown(V); 3010} 3011 3012 3013 3014//===----------------------------------------------------------------------===// 3015// Iteration Count Computation Code 3016// 3017 3018/// getBackedgeTakenCount - If the specified loop has a predictable 3019/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3020/// object. The backedge-taken count is the number of times the loop header 3021/// will be branched to from within the loop. This is one less than the 3022/// trip count of the loop, since it doesn't count the first iteration, 3023/// when the header is branched to from outside the loop. 3024/// 3025/// Note that it is not valid to call this method on a loop without a 3026/// loop-invariant backedge-taken count (see 3027/// hasLoopInvariantBackedgeTakenCount). 3028/// 3029const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3030 return getBackedgeTakenInfo(L).Exact; 3031} 3032 3033/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3034/// return the least SCEV value that is known never to be less than the 3035/// actual backedge taken count. 3036const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3037 return getBackedgeTakenInfo(L).Max; 3038} 3039 3040/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3041/// onto the given Worklist. 3042static void 3043PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3044 BasicBlock *Header = L->getHeader(); 3045 3046 // Push all Loop-header PHIs onto the Worklist stack. 3047 for (BasicBlock::iterator I = Header->begin(); 3048 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3049 Worklist.push_back(PN); 3050} 3051 3052/// PushDefUseChildren - Push users of the given Instruction 3053/// onto the given Worklist. 3054static void 3055PushDefUseChildren(Instruction *I, 3056 SmallVectorImpl<Instruction *> &Worklist) { 3057 // Push the def-use children onto the Worklist stack. 3058 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 3059 UI != UE; ++UI) 3060 Worklist.push_back(cast<Instruction>(UI)); 3061} 3062 3063const ScalarEvolution::BackedgeTakenInfo & 3064ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3065 // Initially insert a CouldNotCompute for this loop. If the insertion 3066 // succeeds, procede to actually compute a backedge-taken count and 3067 // update the value. The temporary CouldNotCompute value tells SCEV 3068 // code elsewhere that it shouldn't attempt to request a new 3069 // backedge-taken count, which could result in infinite recursion. 3070 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3071 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3072 if (Pair.second) { 3073 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3074 if (ItCount.Exact != getCouldNotCompute()) { 3075 assert(ItCount.Exact->isLoopInvariant(L) && 3076 ItCount.Max->isLoopInvariant(L) && 3077 "Computed trip count isn't loop invariant for loop!"); 3078 ++NumTripCountsComputed; 3079 3080 // Update the value in the map. 3081 Pair.first->second = ItCount; 3082 } else { 3083 if (ItCount.Max != getCouldNotCompute()) 3084 // Update the value in the map. 3085 Pair.first->second = ItCount; 3086 if (isa<PHINode>(L->getHeader()->begin())) 3087 // Only count loops that have phi nodes as not being computable. 3088 ++NumTripCountsNotComputed; 3089 } 3090 3091 // Now that we know more about the trip count for this loop, forget any 3092 // existing SCEV values for PHI nodes in this loop since they are only 3093 // conservative estimates made without the benefit of trip count 3094 // information. This is similar to the code in 3095 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3096 // nodes specially. 3097 if (ItCount.hasAnyInfo()) { 3098 SmallVector<Instruction *, 16> Worklist; 3099 PushLoopPHIs(L, Worklist); 3100 3101 SmallPtrSet<Instruction *, 8> Visited; 3102 while (!Worklist.empty()) { 3103 Instruction *I = Worklist.pop_back_val(); 3104 if (!Visited.insert(I)) continue; 3105 3106 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3107 Scalars.find(static_cast<Value *>(I)); 3108 if (It != Scalars.end()) { 3109 // SCEVUnknown for a PHI either means that it has an unrecognized 3110 // structure, or it's a PHI that's in the progress of being computed 3111 // by createNodeForPHI. In the former case, additional loop trip count 3112 // information isn't going to change anything. In the later case, 3113 // createNodeForPHI will perform the necessary updates on its own when 3114 // it gets to that point. 3115 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 3116 Scalars.erase(It); 3117 ValuesAtScopes.erase(I); 3118 if (PHINode *PN = dyn_cast<PHINode>(I)) 3119 ConstantEvolutionLoopExitValue.erase(PN); 3120 } 3121 3122 PushDefUseChildren(I, Worklist); 3123 } 3124 } 3125 } 3126 return Pair.first->second; 3127} 3128 3129/// forgetLoopBackedgeTakenCount - This method should be called by the 3130/// client when it has changed a loop in a way that may effect 3131/// ScalarEvolution's ability to compute a trip count, or if the loop 3132/// is deleted. 3133void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3134 BackedgeTakenCounts.erase(L); 3135 3136 SmallVector<Instruction *, 16> Worklist; 3137 PushLoopPHIs(L, Worklist); 3138 3139 SmallPtrSet<Instruction *, 8> Visited; 3140 while (!Worklist.empty()) { 3141 Instruction *I = Worklist.pop_back_val(); 3142 if (!Visited.insert(I)) continue; 3143 3144 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3145 Scalars.find(static_cast<Value *>(I)); 3146 if (It != Scalars.end()) { 3147 Scalars.erase(It); 3148 ValuesAtScopes.erase(I); 3149 if (PHINode *PN = dyn_cast<PHINode>(I)) 3150 ConstantEvolutionLoopExitValue.erase(PN); 3151 } 3152 3153 PushDefUseChildren(I, Worklist); 3154 } 3155} 3156 3157/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3158/// of the specified loop will execute. 3159ScalarEvolution::BackedgeTakenInfo 3160ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3161 SmallVector<BasicBlock*, 8> ExitingBlocks; 3162 L->getExitingBlocks(ExitingBlocks); 3163 3164 // Examine all exits and pick the most conservative values. 3165 const SCEV *BECount = getCouldNotCompute(); 3166 const SCEV *MaxBECount = getCouldNotCompute(); 3167 bool CouldNotComputeBECount = false; 3168 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3169 BackedgeTakenInfo NewBTI = 3170 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3171 3172 if (NewBTI.Exact == getCouldNotCompute()) { 3173 // We couldn't compute an exact value for this exit, so 3174 // we won't be able to compute an exact value for the loop. 3175 CouldNotComputeBECount = true; 3176 BECount = getCouldNotCompute(); 3177 } else if (!CouldNotComputeBECount) { 3178 if (BECount == getCouldNotCompute()) 3179 BECount = NewBTI.Exact; 3180 else 3181 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3182 } 3183 if (MaxBECount == getCouldNotCompute()) 3184 MaxBECount = NewBTI.Max; 3185 else if (NewBTI.Max != getCouldNotCompute()) 3186 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3187 } 3188 3189 return BackedgeTakenInfo(BECount, MaxBECount); 3190} 3191 3192/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3193/// of the specified loop will execute if it exits via the specified block. 3194ScalarEvolution::BackedgeTakenInfo 3195ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3196 BasicBlock *ExitingBlock) { 3197 3198 // Okay, we've chosen an exiting block. See what condition causes us to 3199 // exit at this block. 3200 // 3201 // FIXME: we should be able to handle switch instructions (with a single exit) 3202 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3203 if (ExitBr == 0) return getCouldNotCompute(); 3204 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3205 3206 // At this point, we know we have a conditional branch that determines whether 3207 // the loop is exited. However, we don't know if the branch is executed each 3208 // time through the loop. If not, then the execution count of the branch will 3209 // not be equal to the trip count of the loop. 3210 // 3211 // Currently we check for this by checking to see if the Exit branch goes to 3212 // the loop header. If so, we know it will always execute the same number of 3213 // times as the loop. We also handle the case where the exit block *is* the 3214 // loop header. This is common for un-rotated loops. 3215 // 3216 // If both of those tests fail, walk up the unique predecessor chain to the 3217 // header, stopping if there is an edge that doesn't exit the loop. If the 3218 // header is reached, the execution count of the branch will be equal to the 3219 // trip count of the loop. 3220 // 3221 // More extensive analysis could be done to handle more cases here. 3222 // 3223 if (ExitBr->getSuccessor(0) != L->getHeader() && 3224 ExitBr->getSuccessor(1) != L->getHeader() && 3225 ExitBr->getParent() != L->getHeader()) { 3226 // The simple checks failed, try climbing the unique predecessor chain 3227 // up to the header. 3228 bool Ok = false; 3229 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3230 BasicBlock *Pred = BB->getUniquePredecessor(); 3231 if (!Pred) 3232 return getCouldNotCompute(); 3233 TerminatorInst *PredTerm = Pred->getTerminator(); 3234 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3235 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3236 if (PredSucc == BB) 3237 continue; 3238 // If the predecessor has a successor that isn't BB and isn't 3239 // outside the loop, assume the worst. 3240 if (L->contains(PredSucc)) 3241 return getCouldNotCompute(); 3242 } 3243 if (Pred == L->getHeader()) { 3244 Ok = true; 3245 break; 3246 } 3247 BB = Pred; 3248 } 3249 if (!Ok) 3250 return getCouldNotCompute(); 3251 } 3252 3253 // Procede to the next level to examine the exit condition expression. 3254 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3255 ExitBr->getSuccessor(0), 3256 ExitBr->getSuccessor(1)); 3257} 3258 3259/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3260/// backedge of the specified loop will execute if its exit condition 3261/// were a conditional branch of ExitCond, TBB, and FBB. 3262ScalarEvolution::BackedgeTakenInfo 3263ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3264 Value *ExitCond, 3265 BasicBlock *TBB, 3266 BasicBlock *FBB) { 3267 // Check if the controlling expression for this loop is an And or Or. 3268 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3269 if (BO->getOpcode() == Instruction::And) { 3270 // Recurse on the operands of the and. 3271 BackedgeTakenInfo BTI0 = 3272 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3273 BackedgeTakenInfo BTI1 = 3274 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3275 const SCEV *BECount = getCouldNotCompute(); 3276 const SCEV *MaxBECount = getCouldNotCompute(); 3277 if (L->contains(TBB)) { 3278 // Both conditions must be true for the loop to continue executing. 3279 // Choose the less conservative count. 3280 if (BTI0.Exact == getCouldNotCompute() || 3281 BTI1.Exact == getCouldNotCompute()) 3282 BECount = getCouldNotCompute(); 3283 else 3284 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3285 if (BTI0.Max == getCouldNotCompute()) 3286 MaxBECount = BTI1.Max; 3287 else if (BTI1.Max == getCouldNotCompute()) 3288 MaxBECount = BTI0.Max; 3289 else 3290 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3291 } else { 3292 // Both conditions must be true for the loop to exit. 3293 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3294 if (BTI0.Exact != getCouldNotCompute() && 3295 BTI1.Exact != getCouldNotCompute()) 3296 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3297 if (BTI0.Max != getCouldNotCompute() && 3298 BTI1.Max != getCouldNotCompute()) 3299 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3300 } 3301 3302 return BackedgeTakenInfo(BECount, MaxBECount); 3303 } 3304 if (BO->getOpcode() == Instruction::Or) { 3305 // Recurse on the operands of the or. 3306 BackedgeTakenInfo BTI0 = 3307 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3308 BackedgeTakenInfo BTI1 = 3309 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3310 const SCEV *BECount = getCouldNotCompute(); 3311 const SCEV *MaxBECount = getCouldNotCompute(); 3312 if (L->contains(FBB)) { 3313 // Both conditions must be false for the loop to continue executing. 3314 // Choose the less conservative count. 3315 if (BTI0.Exact == getCouldNotCompute() || 3316 BTI1.Exact == getCouldNotCompute()) 3317 BECount = getCouldNotCompute(); 3318 else 3319 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3320 if (BTI0.Max == getCouldNotCompute()) 3321 MaxBECount = BTI1.Max; 3322 else if (BTI1.Max == getCouldNotCompute()) 3323 MaxBECount = BTI0.Max; 3324 else 3325 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3326 } else { 3327 // Both conditions must be false for the loop to exit. 3328 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3329 if (BTI0.Exact != getCouldNotCompute() && 3330 BTI1.Exact != getCouldNotCompute()) 3331 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3332 if (BTI0.Max != getCouldNotCompute() && 3333 BTI1.Max != getCouldNotCompute()) 3334 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3335 } 3336 3337 return BackedgeTakenInfo(BECount, MaxBECount); 3338 } 3339 } 3340 3341 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3342 // Procede to the next level to examine the icmp. 3343 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3344 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3345 3346 // If it's not an integer or pointer comparison then compute it the hard way. 3347 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3348} 3349 3350/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3351/// backedge of the specified loop will execute if its exit condition 3352/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3353ScalarEvolution::BackedgeTakenInfo 3354ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3355 ICmpInst *ExitCond, 3356 BasicBlock *TBB, 3357 BasicBlock *FBB) { 3358 3359 // If the condition was exit on true, convert the condition to exit on false 3360 ICmpInst::Predicate Cond; 3361 if (!L->contains(FBB)) 3362 Cond = ExitCond->getPredicate(); 3363 else 3364 Cond = ExitCond->getInversePredicate(); 3365 3366 // Handle common loops like: for (X = "string"; *X; ++X) 3367 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3368 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3369 const SCEV *ItCnt = 3370 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3371 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3372 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3373 return BackedgeTakenInfo(ItCnt, 3374 isa<SCEVConstant>(ItCnt) ? ItCnt : 3375 getConstant(APInt::getMaxValue(BitWidth)-1)); 3376 } 3377 } 3378 3379 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3380 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3381 3382 // Try to evaluate any dependencies out of the loop. 3383 LHS = getSCEVAtScope(LHS, L); 3384 RHS = getSCEVAtScope(RHS, L); 3385 3386 // At this point, we would like to compute how many iterations of the 3387 // loop the predicate will return true for these inputs. 3388 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3389 // If there is a loop-invariant, force it into the RHS. 3390 std::swap(LHS, RHS); 3391 Cond = ICmpInst::getSwappedPredicate(Cond); 3392 } 3393 3394 // If we have a comparison of a chrec against a constant, try to use value 3395 // ranges to answer this query. 3396 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3397 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3398 if (AddRec->getLoop() == L) { 3399 // Form the constant range. 3400 ConstantRange CompRange( 3401 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3402 3403 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3404 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3405 } 3406 3407 switch (Cond) { 3408 case ICmpInst::ICMP_NE: { // while (X != Y) 3409 // Convert to: while (X-Y != 0) 3410 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3411 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3412 break; 3413 } 3414 case ICmpInst::ICMP_EQ: { 3415 // Convert to: while (X-Y == 0) // while (X == Y) 3416 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3417 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3418 break; 3419 } 3420 case ICmpInst::ICMP_SLT: { 3421 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3422 if (BTI.hasAnyInfo()) return BTI; 3423 break; 3424 } 3425 case ICmpInst::ICMP_SGT: { 3426 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3427 getNotSCEV(RHS), L, true); 3428 if (BTI.hasAnyInfo()) return BTI; 3429 break; 3430 } 3431 case ICmpInst::ICMP_ULT: { 3432 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3433 if (BTI.hasAnyInfo()) return BTI; 3434 break; 3435 } 3436 case ICmpInst::ICMP_UGT: { 3437 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3438 getNotSCEV(RHS), L, false); 3439 if (BTI.hasAnyInfo()) return BTI; 3440 break; 3441 } 3442 default: 3443#if 0 3444 errs() << "ComputeBackedgeTakenCount "; 3445 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3446 errs() << "[unsigned] "; 3447 errs() << *LHS << " " 3448 << Instruction::getOpcodeName(Instruction::ICmp) 3449 << " " << *RHS << "\n"; 3450#endif 3451 break; 3452 } 3453 return 3454 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3455} 3456 3457static ConstantInt * 3458EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3459 ScalarEvolution &SE) { 3460 const SCEV *InVal = SE.getConstant(C); 3461 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3462 assert(isa<SCEVConstant>(Val) && 3463 "Evaluation of SCEV at constant didn't fold correctly?"); 3464 return cast<SCEVConstant>(Val)->getValue(); 3465} 3466 3467/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3468/// and a GEP expression (missing the pointer index) indexing into it, return 3469/// the addressed element of the initializer or null if the index expression is 3470/// invalid. 3471static Constant * 3472GetAddressedElementFromGlobal(GlobalVariable *GV, 3473 const std::vector<ConstantInt*> &Indices) { 3474 Constant *Init = GV->getInitializer(); 3475 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3476 uint64_t Idx = Indices[i]->getZExtValue(); 3477 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3478 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3479 Init = cast<Constant>(CS->getOperand(Idx)); 3480 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3481 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3482 Init = cast<Constant>(CA->getOperand(Idx)); 3483 } else if (isa<ConstantAggregateZero>(Init)) { 3484 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3485 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3486 Init = Constant::getNullValue(STy->getElementType(Idx)); 3487 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3488 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3489 Init = Constant::getNullValue(ATy->getElementType()); 3490 } else { 3491 assert(0 && "Unknown constant aggregate type!"); 3492 } 3493 return 0; 3494 } else { 3495 return 0; // Unknown initializer type 3496 } 3497 } 3498 return Init; 3499} 3500 3501/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3502/// 'icmp op load X, cst', try to see if we can compute the backedge 3503/// execution count. 3504const SCEV * 3505ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3506 LoadInst *LI, 3507 Constant *RHS, 3508 const Loop *L, 3509 ICmpInst::Predicate predicate) { 3510 if (LI->isVolatile()) return getCouldNotCompute(); 3511 3512 // Check to see if the loaded pointer is a getelementptr of a global. 3513 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3514 if (!GEP) return getCouldNotCompute(); 3515 3516 // Make sure that it is really a constant global we are gepping, with an 3517 // initializer, and make sure the first IDX is really 0. 3518 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3519 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3520 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3521 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3522 return getCouldNotCompute(); 3523 3524 // Okay, we allow one non-constant index into the GEP instruction. 3525 Value *VarIdx = 0; 3526 std::vector<ConstantInt*> Indexes; 3527 unsigned VarIdxNum = 0; 3528 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3529 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3530 Indexes.push_back(CI); 3531 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3532 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3533 VarIdx = GEP->getOperand(i); 3534 VarIdxNum = i-2; 3535 Indexes.push_back(0); 3536 } 3537 3538 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3539 // Check to see if X is a loop variant variable value now. 3540 const SCEV *Idx = getSCEV(VarIdx); 3541 Idx = getSCEVAtScope(Idx, L); 3542 3543 // We can only recognize very limited forms of loop index expressions, in 3544 // particular, only affine AddRec's like {C1,+,C2}. 3545 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3546 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3547 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3548 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3549 return getCouldNotCompute(); 3550 3551 unsigned MaxSteps = MaxBruteForceIterations; 3552 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3553 ConstantInt *ItCst = 3554 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3555 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3556 3557 // Form the GEP offset. 3558 Indexes[VarIdxNum] = Val; 3559 3560 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3561 if (Result == 0) break; // Cannot compute! 3562 3563 // Evaluate the condition for this iteration. 3564 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3565 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3566 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3567#if 0 3568 errs() << "\n***\n*** Computed loop count " << *ItCst 3569 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3570 << "***\n"; 3571#endif 3572 ++NumArrayLenItCounts; 3573 return getConstant(ItCst); // Found terminating iteration! 3574 } 3575 } 3576 return getCouldNotCompute(); 3577} 3578 3579 3580/// CanConstantFold - Return true if we can constant fold an instruction of the 3581/// specified type, assuming that all operands were constants. 3582static bool CanConstantFold(const Instruction *I) { 3583 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3584 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3585 return true; 3586 3587 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3588 if (const Function *F = CI->getCalledFunction()) 3589 return canConstantFoldCallTo(F); 3590 return false; 3591} 3592 3593/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3594/// in the loop that V is derived from. We allow arbitrary operations along the 3595/// way, but the operands of an operation must either be constants or a value 3596/// derived from a constant PHI. If this expression does not fit with these 3597/// constraints, return null. 3598static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3599 // If this is not an instruction, or if this is an instruction outside of the 3600 // loop, it can't be derived from a loop PHI. 3601 Instruction *I = dyn_cast<Instruction>(V); 3602 if (I == 0 || !L->contains(I->getParent())) return 0; 3603 3604 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3605 if (L->getHeader() == I->getParent()) 3606 return PN; 3607 else 3608 // We don't currently keep track of the control flow needed to evaluate 3609 // PHIs, so we cannot handle PHIs inside of loops. 3610 return 0; 3611 } 3612 3613 // If we won't be able to constant fold this expression even if the operands 3614 // are constants, return early. 3615 if (!CanConstantFold(I)) return 0; 3616 3617 // Otherwise, we can evaluate this instruction if all of its operands are 3618 // constant or derived from a PHI node themselves. 3619 PHINode *PHI = 0; 3620 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3621 if (!(isa<Constant>(I->getOperand(Op)) || 3622 isa<GlobalValue>(I->getOperand(Op)))) { 3623 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3624 if (P == 0) return 0; // Not evolving from PHI 3625 if (PHI == 0) 3626 PHI = P; 3627 else if (PHI != P) 3628 return 0; // Evolving from multiple different PHIs. 3629 } 3630 3631 // This is a expression evolving from a constant PHI! 3632 return PHI; 3633} 3634 3635/// EvaluateExpression - Given an expression that passes the 3636/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3637/// in the loop has the value PHIVal. If we can't fold this expression for some 3638/// reason, return null. 3639static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3640 if (isa<PHINode>(V)) return PHIVal; 3641 if (Constant *C = dyn_cast<Constant>(V)) return C; 3642 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3643 Instruction *I = cast<Instruction>(V); 3644 LLVMContext *Context = I->getParent()->getContext(); 3645 3646 std::vector<Constant*> Operands; 3647 Operands.resize(I->getNumOperands()); 3648 3649 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3650 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3651 if (Operands[i] == 0) return 0; 3652 } 3653 3654 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3655 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3656 &Operands[0], Operands.size(), 3657 Context); 3658 else 3659 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3660 &Operands[0], Operands.size(), 3661 Context); 3662} 3663 3664/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3665/// in the header of its containing loop, we know the loop executes a 3666/// constant number of times, and the PHI node is just a recurrence 3667/// involving constants, fold it. 3668Constant * 3669ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3670 const APInt& BEs, 3671 const Loop *L) { 3672 std::map<PHINode*, Constant*>::iterator I = 3673 ConstantEvolutionLoopExitValue.find(PN); 3674 if (I != ConstantEvolutionLoopExitValue.end()) 3675 return I->second; 3676 3677 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3678 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3679 3680 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3681 3682 // Since the loop is canonicalized, the PHI node must have two entries. One 3683 // entry must be a constant (coming in from outside of the loop), and the 3684 // second must be derived from the same PHI. 3685 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3686 Constant *StartCST = 3687 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3688 if (StartCST == 0) 3689 return RetVal = 0; // Must be a constant. 3690 3691 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3692 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3693 if (PN2 != PN) 3694 return RetVal = 0; // Not derived from same PHI. 3695 3696 // Execute the loop symbolically to determine the exit value. 3697 if (BEs.getActiveBits() >= 32) 3698 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3699 3700 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3701 unsigned IterationNum = 0; 3702 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3703 if (IterationNum == NumIterations) 3704 return RetVal = PHIVal; // Got exit value! 3705 3706 // Compute the value of the PHI node for the next iteration. 3707 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3708 if (NextPHI == PHIVal) 3709 return RetVal = NextPHI; // Stopped evolving! 3710 if (NextPHI == 0) 3711 return 0; // Couldn't evaluate! 3712 PHIVal = NextPHI; 3713 } 3714} 3715 3716/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3717/// constant number of times (the condition evolves only from constants), 3718/// try to evaluate a few iterations of the loop until we get the exit 3719/// condition gets a value of ExitWhen (true or false). If we cannot 3720/// evaluate the trip count of the loop, return getCouldNotCompute(). 3721const SCEV * 3722ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3723 Value *Cond, 3724 bool ExitWhen) { 3725 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3726 if (PN == 0) return getCouldNotCompute(); 3727 3728 // Since the loop is canonicalized, the PHI node must have two entries. One 3729 // entry must be a constant (coming in from outside of the loop), and the 3730 // second must be derived from the same PHI. 3731 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3732 Constant *StartCST = 3733 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3734 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3735 3736 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3737 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3738 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3739 3740 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3741 // the loop symbolically to determine when the condition gets a value of 3742 // "ExitWhen". 3743 unsigned IterationNum = 0; 3744 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3745 for (Constant *PHIVal = StartCST; 3746 IterationNum != MaxIterations; ++IterationNum) { 3747 ConstantInt *CondVal = 3748 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3749 3750 // Couldn't symbolically evaluate. 3751 if (!CondVal) return getCouldNotCompute(); 3752 3753 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3754 ++NumBruteForceTripCountsComputed; 3755 return getConstant(Type::Int32Ty, IterationNum); 3756 } 3757 3758 // Compute the value of the PHI node for the next iteration. 3759 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3760 if (NextPHI == 0 || NextPHI == PHIVal) 3761 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3762 PHIVal = NextPHI; 3763 } 3764 3765 // Too many iterations were needed to evaluate. 3766 return getCouldNotCompute(); 3767} 3768 3769/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3770/// at the specified scope in the program. The L value specifies a loop 3771/// nest to evaluate the expression at, where null is the top-level or a 3772/// specified loop is immediately inside of the loop. 3773/// 3774/// This method can be used to compute the exit value for a variable defined 3775/// in a loop by querying what the value will hold in the parent loop. 3776/// 3777/// In the case that a relevant loop exit value cannot be computed, the 3778/// original value V is returned. 3779const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3780 // FIXME: this should be turned into a virtual method on SCEV! 3781 3782 if (isa<SCEVConstant>(V)) return V; 3783 3784 // If this instruction is evolved from a constant-evolving PHI, compute the 3785 // exit value from the loop without using SCEVs. 3786 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3787 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3788 const Loop *LI = (*this->LI)[I->getParent()]; 3789 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3790 if (PHINode *PN = dyn_cast<PHINode>(I)) 3791 if (PN->getParent() == LI->getHeader()) { 3792 // Okay, there is no closed form solution for the PHI node. Check 3793 // to see if the loop that contains it has a known backedge-taken 3794 // count. If so, we may be able to force computation of the exit 3795 // value. 3796 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3797 if (const SCEVConstant *BTCC = 3798 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3799 // Okay, we know how many times the containing loop executes. If 3800 // this is a constant evolving PHI node, get the final value at 3801 // the specified iteration number. 3802 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3803 BTCC->getValue()->getValue(), 3804 LI); 3805 if (RV) return getSCEV(RV); 3806 } 3807 } 3808 3809 // Okay, this is an expression that we cannot symbolically evaluate 3810 // into a SCEV. Check to see if it's possible to symbolically evaluate 3811 // the arguments into constants, and if so, try to constant propagate the 3812 // result. This is particularly useful for computing loop exit values. 3813 if (CanConstantFold(I)) { 3814 // Check to see if we've folded this instruction at this loop before. 3815 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3816 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3817 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3818 if (!Pair.second) 3819 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3820 3821 std::vector<Constant*> Operands; 3822 Operands.reserve(I->getNumOperands()); 3823 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3824 Value *Op = I->getOperand(i); 3825 if (Constant *C = dyn_cast<Constant>(Op)) { 3826 Operands.push_back(C); 3827 } else { 3828 // If any of the operands is non-constant and if they are 3829 // non-integer and non-pointer, don't even try to analyze them 3830 // with scev techniques. 3831 if (!isSCEVable(Op->getType())) 3832 return V; 3833 3834 const SCEV* OpV = getSCEVAtScope(Op, L); 3835 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3836 Constant *C = SC->getValue(); 3837 if (C->getType() != Op->getType()) 3838 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3839 Op->getType(), 3840 false), 3841 C, Op->getType()); 3842 Operands.push_back(C); 3843 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3844 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3845 if (C->getType() != Op->getType()) 3846 C = 3847 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3848 Op->getType(), 3849 false), 3850 C, Op->getType()); 3851 Operands.push_back(C); 3852 } else 3853 return V; 3854 } else { 3855 return V; 3856 } 3857 } 3858 } 3859 3860 Constant *C; 3861 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3862 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3863 &Operands[0], Operands.size(), 3864 Context); 3865 else 3866 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3867 &Operands[0], Operands.size(), Context); 3868 Pair.first->second = C; 3869 return getSCEV(C); 3870 } 3871 } 3872 3873 // This is some other type of SCEVUnknown, just return it. 3874 return V; 3875 } 3876 3877 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3878 // Avoid performing the look-up in the common case where the specified 3879 // expression has no loop-variant portions. 3880 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3881 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3882 if (OpAtScope != Comm->getOperand(i)) { 3883 // Okay, at least one of these operands is loop variant but might be 3884 // foldable. Build a new instance of the folded commutative expression. 3885 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3886 Comm->op_begin()+i); 3887 NewOps.push_back(OpAtScope); 3888 3889 for (++i; i != e; ++i) { 3890 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3891 NewOps.push_back(OpAtScope); 3892 } 3893 if (isa<SCEVAddExpr>(Comm)) 3894 return getAddExpr(NewOps); 3895 if (isa<SCEVMulExpr>(Comm)) 3896 return getMulExpr(NewOps); 3897 if (isa<SCEVSMaxExpr>(Comm)) 3898 return getSMaxExpr(NewOps); 3899 if (isa<SCEVUMaxExpr>(Comm)) 3900 return getUMaxExpr(NewOps); 3901 assert(0 && "Unknown commutative SCEV type!"); 3902 } 3903 } 3904 // If we got here, all operands are loop invariant. 3905 return Comm; 3906 } 3907 3908 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3909 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 3910 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 3911 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3912 return Div; // must be loop invariant 3913 return getUDivExpr(LHS, RHS); 3914 } 3915 3916 // If this is a loop recurrence for a loop that does not contain L, then we 3917 // are dealing with the final value computed by the loop. 3918 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3919 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3920 // To evaluate this recurrence, we need to know how many times the AddRec 3921 // loop iterates. Compute this now. 3922 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3923 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3924 3925 // Then, evaluate the AddRec. 3926 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3927 } 3928 return AddRec; 3929 } 3930 3931 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3932 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3933 if (Op == Cast->getOperand()) 3934 return Cast; // must be loop invariant 3935 return getZeroExtendExpr(Op, Cast->getType()); 3936 } 3937 3938 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3939 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3940 if (Op == Cast->getOperand()) 3941 return Cast; // must be loop invariant 3942 return getSignExtendExpr(Op, Cast->getType()); 3943 } 3944 3945 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3946 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3947 if (Op == Cast->getOperand()) 3948 return Cast; // must be loop invariant 3949 return getTruncateExpr(Op, Cast->getType()); 3950 } 3951 3952 assert(0 && "Unknown SCEV type!"); 3953 return 0; 3954} 3955 3956/// getSCEVAtScope - This is a convenience function which does 3957/// getSCEVAtScope(getSCEV(V), L). 3958const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3959 return getSCEVAtScope(getSCEV(V), L); 3960} 3961 3962/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3963/// following equation: 3964/// 3965/// A * X = B (mod N) 3966/// 3967/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3968/// A and B isn't important. 3969/// 3970/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3971static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3972 ScalarEvolution &SE) { 3973 uint32_t BW = A.getBitWidth(); 3974 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3975 assert(A != 0 && "A must be non-zero."); 3976 3977 // 1. D = gcd(A, N) 3978 // 3979 // The gcd of A and N may have only one prime factor: 2. The number of 3980 // trailing zeros in A is its multiplicity 3981 uint32_t Mult2 = A.countTrailingZeros(); 3982 // D = 2^Mult2 3983 3984 // 2. Check if B is divisible by D. 3985 // 3986 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3987 // is not less than multiplicity of this prime factor for D. 3988 if (B.countTrailingZeros() < Mult2) 3989 return SE.getCouldNotCompute(); 3990 3991 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3992 // modulo (N / D). 3993 // 3994 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3995 // bit width during computations. 3996 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3997 APInt Mod(BW + 1, 0); 3998 Mod.set(BW - Mult2); // Mod = N / D 3999 APInt I = AD.multiplicativeInverse(Mod); 4000 4001 // 4. Compute the minimum unsigned root of the equation: 4002 // I * (B / D) mod (N / D) 4003 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4004 4005 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4006 // bits. 4007 return SE.getConstant(Result.trunc(BW)); 4008} 4009 4010/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4011/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4012/// might be the same) or two SCEVCouldNotCompute objects. 4013/// 4014static std::pair<const SCEV *,const SCEV *> 4015SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4016 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4017 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4018 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4019 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4020 4021 // We currently can only solve this if the coefficients are constants. 4022 if (!LC || !MC || !NC) { 4023 const SCEV *CNC = SE.getCouldNotCompute(); 4024 return std::make_pair(CNC, CNC); 4025 } 4026 4027 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4028 const APInt &L = LC->getValue()->getValue(); 4029 const APInt &M = MC->getValue()->getValue(); 4030 const APInt &N = NC->getValue()->getValue(); 4031 APInt Two(BitWidth, 2); 4032 APInt Four(BitWidth, 4); 4033 4034 { 4035 using namespace APIntOps; 4036 const APInt& C = L; 4037 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4038 // The B coefficient is M-N/2 4039 APInt B(M); 4040 B -= sdiv(N,Two); 4041 4042 // The A coefficient is N/2 4043 APInt A(N.sdiv(Two)); 4044 4045 // Compute the B^2-4ac term. 4046 APInt SqrtTerm(B); 4047 SqrtTerm *= B; 4048 SqrtTerm -= Four * (A * C); 4049 4050 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4051 // integer value or else APInt::sqrt() will assert. 4052 APInt SqrtVal(SqrtTerm.sqrt()); 4053 4054 // Compute the two solutions for the quadratic formula. 4055 // The divisions must be performed as signed divisions. 4056 APInt NegB(-B); 4057 APInt TwoA( A << 1 ); 4058 if (TwoA.isMinValue()) { 4059 const SCEV *CNC = SE.getCouldNotCompute(); 4060 return std::make_pair(CNC, CNC); 4061 } 4062 4063 LLVMContext *Context = SE.getContext(); 4064 4065 ConstantInt *Solution1 = 4066 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA)); 4067 ConstantInt *Solution2 = 4068 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA)); 4069 4070 return std::make_pair(SE.getConstant(Solution1), 4071 SE.getConstant(Solution2)); 4072 } // end APIntOps namespace 4073} 4074 4075/// HowFarToZero - Return the number of times a backedge comparing the specified 4076/// value to zero will execute. If not computable, return CouldNotCompute. 4077const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4078 // If the value is a constant 4079 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4080 // If the value is already zero, the branch will execute zero times. 4081 if (C->getValue()->isZero()) return C; 4082 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4083 } 4084 4085 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4086 if (!AddRec || AddRec->getLoop() != L) 4087 return getCouldNotCompute(); 4088 4089 if (AddRec->isAffine()) { 4090 // If this is an affine expression, the execution count of this branch is 4091 // the minimum unsigned root of the following equation: 4092 // 4093 // Start + Step*N = 0 (mod 2^BW) 4094 // 4095 // equivalent to: 4096 // 4097 // Step*N = -Start (mod 2^BW) 4098 // 4099 // where BW is the common bit width of Start and Step. 4100 4101 // Get the initial value for the loop. 4102 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4103 L->getParentLoop()); 4104 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4105 L->getParentLoop()); 4106 4107 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4108 // For now we handle only constant steps. 4109 4110 // First, handle unitary steps. 4111 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4112 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4113 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4114 return Start; // N = Start (as unsigned) 4115 4116 // Then, try to solve the above equation provided that Start is constant. 4117 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4118 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4119 -StartC->getValue()->getValue(), 4120 *this); 4121 } 4122 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4123 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4124 // the quadratic equation to solve it. 4125 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4126 *this); 4127 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4128 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4129 if (R1) { 4130#if 0 4131 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4132 << " sol#2: " << *R2 << "\n"; 4133#endif 4134 // Pick the smallest positive root value. 4135 if (ConstantInt *CB = 4136 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT, 4137 R1->getValue(), R2->getValue()))) { 4138 if (CB->getZExtValue() == false) 4139 std::swap(R1, R2); // R1 is the minimum root now. 4140 4141 // We can only use this value if the chrec ends up with an exact zero 4142 // value at this index. When solving for "X*X != 5", for example, we 4143 // should not accept a root of 2. 4144 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4145 if (Val->isZero()) 4146 return R1; // We found a quadratic root! 4147 } 4148 } 4149 } 4150 4151 return getCouldNotCompute(); 4152} 4153 4154/// HowFarToNonZero - Return the number of times a backedge checking the 4155/// specified value for nonzero will execute. If not computable, return 4156/// CouldNotCompute 4157const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4158 // Loops that look like: while (X == 0) are very strange indeed. We don't 4159 // handle them yet except for the trivial case. This could be expanded in the 4160 // future as needed. 4161 4162 // If the value is a constant, check to see if it is known to be non-zero 4163 // already. If so, the backedge will execute zero times. 4164 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4165 if (!C->getValue()->isNullValue()) 4166 return getIntegerSCEV(0, C->getType()); 4167 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4168 } 4169 4170 // We could implement others, but I really doubt anyone writes loops like 4171 // this, and if they did, they would already be constant folded. 4172 return getCouldNotCompute(); 4173} 4174 4175/// getLoopPredecessor - If the given loop's header has exactly one unique 4176/// predecessor outside the loop, return it. Otherwise return null. 4177/// 4178BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4179 BasicBlock *Header = L->getHeader(); 4180 BasicBlock *Pred = 0; 4181 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4182 PI != E; ++PI) 4183 if (!L->contains(*PI)) { 4184 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4185 Pred = *PI; 4186 } 4187 return Pred; 4188} 4189 4190/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4191/// (which may not be an immediate predecessor) which has exactly one 4192/// successor from which BB is reachable, or null if no such block is 4193/// found. 4194/// 4195BasicBlock * 4196ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4197 // If the block has a unique predecessor, then there is no path from the 4198 // predecessor to the block that does not go through the direct edge 4199 // from the predecessor to the block. 4200 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4201 return Pred; 4202 4203 // A loop's header is defined to be a block that dominates the loop. 4204 // If the header has a unique predecessor outside the loop, it must be 4205 // a block that has exactly one successor that can reach the loop. 4206 if (Loop *L = LI->getLoopFor(BB)) 4207 return getLoopPredecessor(L); 4208 4209 return 0; 4210} 4211 4212/// HasSameValue - SCEV structural equivalence is usually sufficient for 4213/// testing whether two expressions are equal, however for the purposes of 4214/// looking for a condition guarding a loop, it can be useful to be a little 4215/// more general, since a front-end may have replicated the controlling 4216/// expression. 4217/// 4218static bool HasSameValue(const SCEV *A, const SCEV *B) { 4219 // Quick check to see if they are the same SCEV. 4220 if (A == B) return true; 4221 4222 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4223 // two different instructions with the same value. Check for this case. 4224 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4225 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4226 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4227 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4228 if (AI->isIdenticalTo(BI)) 4229 return true; 4230 4231 // Otherwise assume they may have a different value. 4232 return false; 4233} 4234 4235bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4236 return getSignedRange(S).getSignedMax().isNegative(); 4237} 4238 4239bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4240 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4241} 4242 4243bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4244 return !getSignedRange(S).getSignedMin().isNegative(); 4245} 4246 4247bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4248 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4249} 4250 4251bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4252 return isKnownNegative(S) || isKnownPositive(S); 4253} 4254 4255bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4256 const SCEV *LHS, const SCEV *RHS) { 4257 4258 if (HasSameValue(LHS, RHS)) 4259 return ICmpInst::isTrueWhenEqual(Pred); 4260 4261 switch (Pred) { 4262 default: 4263 assert(0 && "Unexpected ICmpInst::Predicate value!"); 4264 break; 4265 case ICmpInst::ICMP_SGT: 4266 Pred = ICmpInst::ICMP_SLT; 4267 std::swap(LHS, RHS); 4268 case ICmpInst::ICMP_SLT: { 4269 ConstantRange LHSRange = getSignedRange(LHS); 4270 ConstantRange RHSRange = getSignedRange(RHS); 4271 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4272 return true; 4273 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4274 return false; 4275 4276 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4277 ConstantRange DiffRange = getUnsignedRange(Diff); 4278 if (isKnownNegative(Diff)) { 4279 if (DiffRange.getUnsignedMax().ult(LHSRange.getUnsignedMin())) 4280 return true; 4281 if (DiffRange.getUnsignedMin().uge(LHSRange.getUnsignedMax())) 4282 return false; 4283 } else if (isKnownPositive(Diff)) { 4284 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4285 return true; 4286 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4287 return false; 4288 } 4289 break; 4290 } 4291 case ICmpInst::ICMP_SGE: 4292 Pred = ICmpInst::ICMP_SLE; 4293 std::swap(LHS, RHS); 4294 case ICmpInst::ICMP_SLE: { 4295 ConstantRange LHSRange = getSignedRange(LHS); 4296 ConstantRange RHSRange = getSignedRange(RHS); 4297 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4298 return true; 4299 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4300 return false; 4301 4302 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4303 ConstantRange DiffRange = getUnsignedRange(Diff); 4304 if (isKnownNonPositive(Diff)) { 4305 if (DiffRange.getUnsignedMax().ule(LHSRange.getUnsignedMin())) 4306 return true; 4307 if (DiffRange.getUnsignedMin().ugt(LHSRange.getUnsignedMax())) 4308 return false; 4309 } else if (isKnownNonNegative(Diff)) { 4310 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4311 return true; 4312 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4313 return false; 4314 } 4315 break; 4316 } 4317 case ICmpInst::ICMP_UGT: 4318 Pred = ICmpInst::ICMP_ULT; 4319 std::swap(LHS, RHS); 4320 case ICmpInst::ICMP_ULT: { 4321 ConstantRange LHSRange = getUnsignedRange(LHS); 4322 ConstantRange RHSRange = getUnsignedRange(RHS); 4323 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4324 return true; 4325 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4326 return false; 4327 4328 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4329 ConstantRange DiffRange = getUnsignedRange(Diff); 4330 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4331 return true; 4332 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4333 return false; 4334 break; 4335 } 4336 case ICmpInst::ICMP_UGE: 4337 Pred = ICmpInst::ICMP_ULE; 4338 std::swap(LHS, RHS); 4339 case ICmpInst::ICMP_ULE: { 4340 ConstantRange LHSRange = getUnsignedRange(LHS); 4341 ConstantRange RHSRange = getUnsignedRange(RHS); 4342 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4343 return true; 4344 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4345 return false; 4346 4347 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4348 ConstantRange DiffRange = getUnsignedRange(Diff); 4349 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4350 return true; 4351 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4352 return false; 4353 break; 4354 } 4355 case ICmpInst::ICMP_NE: { 4356 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4357 return true; 4358 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4359 return true; 4360 4361 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4362 if (isKnownNonZero(Diff)) 4363 return true; 4364 break; 4365 } 4366 case ICmpInst::ICMP_EQ: 4367 break; 4368 } 4369 return false; 4370} 4371 4372/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4373/// protected by a conditional between LHS and RHS. This is used to 4374/// to eliminate casts. 4375bool 4376ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4377 ICmpInst::Predicate Pred, 4378 const SCEV *LHS, const SCEV *RHS) { 4379 // Interpret a null as meaning no loop, where there is obviously no guard 4380 // (interprocedural conditions notwithstanding). 4381 if (!L) return true; 4382 4383 BasicBlock *Latch = L->getLoopLatch(); 4384 if (!Latch) 4385 return false; 4386 4387 BranchInst *LoopContinuePredicate = 4388 dyn_cast<BranchInst>(Latch->getTerminator()); 4389 if (!LoopContinuePredicate || 4390 LoopContinuePredicate->isUnconditional()) 4391 return false; 4392 4393 return 4394 isNecessaryCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4395 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4396} 4397 4398/// isLoopGuardedByCond - Test whether entry to the loop is protected 4399/// by a conditional between LHS and RHS. This is used to help avoid max 4400/// expressions in loop trip counts, and to eliminate casts. 4401bool 4402ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4403 ICmpInst::Predicate Pred, 4404 const SCEV *LHS, const SCEV *RHS) { 4405 // Interpret a null as meaning no loop, where there is obviously no guard 4406 // (interprocedural conditions notwithstanding). 4407 if (!L) return false; 4408 4409 BasicBlock *Predecessor = getLoopPredecessor(L); 4410 BasicBlock *PredecessorDest = L->getHeader(); 4411 4412 // Starting at the loop predecessor, climb up the predecessor chain, as long 4413 // as there are predecessors that can be found that have unique successors 4414 // leading to the original header. 4415 for (; Predecessor; 4416 PredecessorDest = Predecessor, 4417 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4418 4419 BranchInst *LoopEntryPredicate = 4420 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4421 if (!LoopEntryPredicate || 4422 LoopEntryPredicate->isUnconditional()) 4423 continue; 4424 4425 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4426 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4427 return true; 4428 } 4429 4430 return false; 4431} 4432 4433/// isNecessaryCond - Test whether the condition described by Pred, LHS, 4434/// and RHS is a necessary condition for the given Cond value to evaluate 4435/// to true. 4436bool ScalarEvolution::isNecessaryCond(Value *CondValue, 4437 ICmpInst::Predicate Pred, 4438 const SCEV *LHS, const SCEV *RHS, 4439 bool Inverse) { 4440 // Recursivly handle And and Or conditions. 4441 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4442 if (BO->getOpcode() == Instruction::And) { 4443 if (!Inverse) 4444 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4445 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4446 } else if (BO->getOpcode() == Instruction::Or) { 4447 if (Inverse) 4448 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4449 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4450 } 4451 } 4452 4453 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4454 if (!ICI) return false; 4455 4456 // Now that we found a conditional branch that dominates the loop, check to 4457 // see if it is the comparison we are looking for. 4458 Value *PreCondLHS = ICI->getOperand(0); 4459 Value *PreCondRHS = ICI->getOperand(1); 4460 ICmpInst::Predicate FoundPred; 4461 if (Inverse) 4462 FoundPred = ICI->getInversePredicate(); 4463 else 4464 FoundPred = ICI->getPredicate(); 4465 4466 if (FoundPred == Pred) 4467 ; // An exact match. 4468 else if (!ICmpInst::isTrueWhenEqual(FoundPred) && Pred == ICmpInst::ICMP_NE) { 4469 // The actual condition is beyond sufficient. 4470 FoundPred = ICmpInst::ICMP_NE; 4471 // NE is symmetric but the original comparison may not be. Swap 4472 // the operands if necessary so that they match below. 4473 if (isa<SCEVConstant>(LHS)) 4474 std::swap(PreCondLHS, PreCondRHS); 4475 } else 4476 // Check a few special cases. 4477 switch (FoundPred) { 4478 case ICmpInst::ICMP_UGT: 4479 if (Pred == ICmpInst::ICMP_ULT) { 4480 std::swap(PreCondLHS, PreCondRHS); 4481 FoundPred = ICmpInst::ICMP_ULT; 4482 break; 4483 } 4484 return false; 4485 case ICmpInst::ICMP_SGT: 4486 if (Pred == ICmpInst::ICMP_SLT) { 4487 std::swap(PreCondLHS, PreCondRHS); 4488 FoundPred = ICmpInst::ICMP_SLT; 4489 break; 4490 } 4491 return false; 4492 case ICmpInst::ICMP_NE: 4493 // Expressions like (x >u 0) are often canonicalized to (x != 0), 4494 // so check for this case by checking if the NE is comparing against 4495 // a minimum or maximum constant. 4496 if (!ICmpInst::isTrueWhenEqual(Pred)) 4497 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(RHS)) { 4498 const APInt &A = C->getValue()->getValue(); 4499 switch (Pred) { 4500 case ICmpInst::ICMP_SLT: 4501 if (A.isMaxSignedValue()) break; 4502 return false; 4503 case ICmpInst::ICMP_SGT: 4504 if (A.isMinSignedValue()) break; 4505 return false; 4506 case ICmpInst::ICMP_ULT: 4507 if (A.isMaxValue()) break; 4508 return false; 4509 case ICmpInst::ICMP_UGT: 4510 if (A.isMinValue()) break; 4511 return false; 4512 default: 4513 return false; 4514 } 4515 FoundPred = Pred; 4516 // NE is symmetric but the original comparison may not be. Swap 4517 // the operands if necessary so that they match below. 4518 if (isa<SCEVConstant>(LHS)) 4519 std::swap(PreCondLHS, PreCondRHS); 4520 break; 4521 } 4522 return false; 4523 default: 4524 // We weren't able to reconcile the condition. 4525 return false; 4526 } 4527 4528 assert(Pred == FoundPred && "Conditions were not reconciled!"); 4529 4530 const SCEV *FoundLHS = getSCEV(PreCondLHS); 4531 const SCEV *FoundRHS = getSCEV(PreCondRHS); 4532 4533 // Balance the types. 4534 if (getTypeSizeInBits(LHS->getType()) > 4535 getTypeSizeInBits(FoundLHS->getType())) { 4536 if (CmpInst::isSigned(Pred)) { 4537 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4538 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4539 } else { 4540 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4541 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4542 } 4543 } else if (getTypeSizeInBits(LHS->getType()) < 4544 getTypeSizeInBits(FoundLHS->getType())) { 4545 // TODO: Cast LHS and RHS to FoundLHS' type. Currently this can 4546 // result in infinite recursion since the code to construct 4547 // cast expressions may want to know things about the loop 4548 // iteration in order to do simplifications. 4549 return false; 4550 } 4551 4552 return isNecessaryCondOperands(Pred, LHS, RHS, 4553 FoundLHS, FoundRHS) || 4554 // ~x < ~y --> x > y 4555 isNecessaryCondOperands(Pred, LHS, RHS, 4556 getNotSCEV(FoundRHS), getNotSCEV(FoundLHS)); 4557} 4558 4559/// isNecessaryCondOperands - Test whether the condition described by Pred, 4560/// LHS, and RHS is a necessary condition for the condition described by 4561/// Pred, FoundLHS, and FoundRHS to evaluate to true. 4562bool 4563ScalarEvolution::isNecessaryCondOperands(ICmpInst::Predicate Pred, 4564 const SCEV *LHS, const SCEV *RHS, 4565 const SCEV *FoundLHS, 4566 const SCEV *FoundRHS) { 4567 switch (Pred) { 4568 default: break; 4569 case ICmpInst::ICMP_SLT: 4570 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4571 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4572 return true; 4573 break; 4574 case ICmpInst::ICMP_SGT: 4575 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4576 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4577 return true; 4578 break; 4579 case ICmpInst::ICMP_ULT: 4580 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4581 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4582 return true; 4583 break; 4584 case ICmpInst::ICMP_UGT: 4585 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4586 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4587 return true; 4588 break; 4589 } 4590 4591 return false; 4592} 4593 4594/// getBECount - Subtract the end and start values and divide by the step, 4595/// rounding up, to get the number of times the backedge is executed. Return 4596/// CouldNotCompute if an intermediate computation overflows. 4597const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4598 const SCEV *End, 4599 const SCEV *Step) { 4600 const Type *Ty = Start->getType(); 4601 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4602 const SCEV *Diff = getMinusSCEV(End, Start); 4603 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4604 4605 // Add an adjustment to the difference between End and Start so that 4606 // the division will effectively round up. 4607 const SCEV *Add = getAddExpr(Diff, RoundUp); 4608 4609 // Check Add for unsigned overflow. 4610 // TODO: More sophisticated things could be done here. 4611 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1); 4612 const SCEV *OperandExtendedAdd = 4613 getAddExpr(getZeroExtendExpr(Diff, WideTy), 4614 getZeroExtendExpr(RoundUp, WideTy)); 4615 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4616 return getCouldNotCompute(); 4617 4618 return getUDivExpr(Add, Step); 4619} 4620 4621/// HowManyLessThans - Return the number of times a backedge containing the 4622/// specified less-than comparison will execute. If not computable, return 4623/// CouldNotCompute. 4624ScalarEvolution::BackedgeTakenInfo 4625ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4626 const Loop *L, bool isSigned) { 4627 // Only handle: "ADDREC < LoopInvariant". 4628 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4629 4630 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4631 if (!AddRec || AddRec->getLoop() != L) 4632 return getCouldNotCompute(); 4633 4634 if (AddRec->isAffine()) { 4635 // FORNOW: We only support unit strides. 4636 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4637 const SCEV *Step = AddRec->getStepRecurrence(*this); 4638 4639 // TODO: handle non-constant strides. 4640 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4641 if (!CStep || CStep->isZero()) 4642 return getCouldNotCompute(); 4643 if (CStep->isOne()) { 4644 // With unit stride, the iteration never steps past the limit value. 4645 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4646 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4647 // Test whether a positive iteration iteration can step past the limit 4648 // value and past the maximum value for its type in a single step. 4649 if (isSigned) { 4650 APInt Max = APInt::getSignedMaxValue(BitWidth); 4651 if ((Max - CStep->getValue()->getValue()) 4652 .slt(CLimit->getValue()->getValue())) 4653 return getCouldNotCompute(); 4654 } else { 4655 APInt Max = APInt::getMaxValue(BitWidth); 4656 if ((Max - CStep->getValue()->getValue()) 4657 .ult(CLimit->getValue()->getValue())) 4658 return getCouldNotCompute(); 4659 } 4660 } else 4661 // TODO: handle non-constant limit values below. 4662 return getCouldNotCompute(); 4663 } else 4664 // TODO: handle negative strides below. 4665 return getCouldNotCompute(); 4666 4667 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4668 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4669 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4670 // treat m-n as signed nor unsigned due to overflow possibility. 4671 4672 // First, we get the value of the LHS in the first iteration: n 4673 const SCEV *Start = AddRec->getOperand(0); 4674 4675 // Determine the minimum constant start value. 4676 const SCEV *MinStart = getConstant(isSigned ? 4677 getSignedRange(Start).getSignedMin() : 4678 getUnsignedRange(Start).getUnsignedMin()); 4679 4680 // If we know that the condition is true in order to enter the loop, 4681 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4682 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4683 // the division must round up. 4684 const SCEV *End = RHS; 4685 if (!isLoopGuardedByCond(L, 4686 isSigned ? ICmpInst::ICMP_SLT : 4687 ICmpInst::ICMP_ULT, 4688 getMinusSCEV(Start, Step), RHS)) 4689 End = isSigned ? getSMaxExpr(RHS, Start) 4690 : getUMaxExpr(RHS, Start); 4691 4692 // Determine the maximum constant end value. 4693 const SCEV *MaxEnd = getConstant(isSigned ? 4694 getSignedRange(End).getSignedMax() : 4695 getUnsignedRange(End).getUnsignedMax()); 4696 4697 // Finally, we subtract these two values and divide, rounding up, to get 4698 // the number of times the backedge is executed. 4699 const SCEV *BECount = getBECount(Start, End, Step); 4700 4701 // The maximum backedge count is similar, except using the minimum start 4702 // value and the maximum end value. 4703 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step); 4704 4705 return BackedgeTakenInfo(BECount, MaxBECount); 4706 } 4707 4708 return getCouldNotCompute(); 4709} 4710 4711/// getNumIterationsInRange - Return the number of iterations of this loop that 4712/// produce values in the specified constant range. Another way of looking at 4713/// this is that it returns the first iteration number where the value is not in 4714/// the condition, thus computing the exit count. If the iteration count can't 4715/// be computed, an instance of SCEVCouldNotCompute is returned. 4716const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4717 ScalarEvolution &SE) const { 4718 if (Range.isFullSet()) // Infinite loop. 4719 return SE.getCouldNotCompute(); 4720 4721 // If the start is a non-zero constant, shift the range to simplify things. 4722 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4723 if (!SC->getValue()->isZero()) { 4724 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4725 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4726 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4727 if (const SCEVAddRecExpr *ShiftedAddRec = 4728 dyn_cast<SCEVAddRecExpr>(Shifted)) 4729 return ShiftedAddRec->getNumIterationsInRange( 4730 Range.subtract(SC->getValue()->getValue()), SE); 4731 // This is strange and shouldn't happen. 4732 return SE.getCouldNotCompute(); 4733 } 4734 4735 // The only time we can solve this is when we have all constant indices. 4736 // Otherwise, we cannot determine the overflow conditions. 4737 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4738 if (!isa<SCEVConstant>(getOperand(i))) 4739 return SE.getCouldNotCompute(); 4740 4741 4742 // Okay at this point we know that all elements of the chrec are constants and 4743 // that the start element is zero. 4744 4745 // First check to see if the range contains zero. If not, the first 4746 // iteration exits. 4747 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4748 if (!Range.contains(APInt(BitWidth, 0))) 4749 return SE.getIntegerSCEV(0, getType()); 4750 4751 if (isAffine()) { 4752 // If this is an affine expression then we have this situation: 4753 // Solve {0,+,A} in Range === Ax in Range 4754 4755 // We know that zero is in the range. If A is positive then we know that 4756 // the upper value of the range must be the first possible exit value. 4757 // If A is negative then the lower of the range is the last possible loop 4758 // value. Also note that we already checked for a full range. 4759 APInt One(BitWidth,1); 4760 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4761 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4762 4763 // The exit value should be (End+A)/A. 4764 APInt ExitVal = (End + A).udiv(A); 4765 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal); 4766 4767 // Evaluate at the exit value. If we really did fall out of the valid 4768 // range, then we computed our trip count, otherwise wrap around or other 4769 // things must have happened. 4770 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4771 if (Range.contains(Val->getValue())) 4772 return SE.getCouldNotCompute(); // Something strange happened 4773 4774 // Ensure that the previous value is in the range. This is a sanity check. 4775 assert(Range.contains( 4776 EvaluateConstantChrecAtConstant(this, 4777 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) && 4778 "Linear scev computation is off in a bad way!"); 4779 return SE.getConstant(ExitValue); 4780 } else if (isQuadratic()) { 4781 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4782 // quadratic equation to solve it. To do this, we must frame our problem in 4783 // terms of figuring out when zero is crossed, instead of when 4784 // Range.getUpper() is crossed. 4785 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 4786 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4787 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4788 4789 // Next, solve the constructed addrec 4790 std::pair<const SCEV *,const SCEV *> Roots = 4791 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4792 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4793 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4794 if (R1) { 4795 // Pick the smallest positive root value. 4796 if (ConstantInt *CB = 4797 dyn_cast<ConstantInt>( 4798 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT, 4799 R1->getValue(), R2->getValue()))) { 4800 if (CB->getZExtValue() == false) 4801 std::swap(R1, R2); // R1 is the minimum root now. 4802 4803 // Make sure the root is not off by one. The returned iteration should 4804 // not be in the range, but the previous one should be. When solving 4805 // for "X*X < 5", for example, we should not return a root of 2. 4806 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4807 R1->getValue(), 4808 SE); 4809 if (Range.contains(R1Val->getValue())) { 4810 // The next iteration must be out of the range... 4811 ConstantInt *NextVal = 4812 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1); 4813 4814 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4815 if (!Range.contains(R1Val->getValue())) 4816 return SE.getConstant(NextVal); 4817 return SE.getCouldNotCompute(); // Something strange happened 4818 } 4819 4820 // If R1 was not in the range, then it is a good return value. Make 4821 // sure that R1-1 WAS in the range though, just in case. 4822 ConstantInt *NextVal = 4823 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1); 4824 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4825 if (Range.contains(R1Val->getValue())) 4826 return R1; 4827 return SE.getCouldNotCompute(); // Something strange happened 4828 } 4829 } 4830 } 4831 4832 return SE.getCouldNotCompute(); 4833} 4834 4835 4836 4837//===----------------------------------------------------------------------===// 4838// SCEVCallbackVH Class Implementation 4839//===----------------------------------------------------------------------===// 4840 4841void ScalarEvolution::SCEVCallbackVH::deleted() { 4842 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4843 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4844 SE->ConstantEvolutionLoopExitValue.erase(PN); 4845 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4846 SE->ValuesAtScopes.erase(I); 4847 SE->Scalars.erase(getValPtr()); 4848 // this now dangles! 4849} 4850 4851void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4852 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4853 4854 // Forget all the expressions associated with users of the old value, 4855 // so that future queries will recompute the expressions using the new 4856 // value. 4857 SmallVector<User *, 16> Worklist; 4858 Value *Old = getValPtr(); 4859 bool DeleteOld = false; 4860 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4861 UI != UE; ++UI) 4862 Worklist.push_back(*UI); 4863 while (!Worklist.empty()) { 4864 User *U = Worklist.pop_back_val(); 4865 // Deleting the Old value will cause this to dangle. Postpone 4866 // that until everything else is done. 4867 if (U == Old) { 4868 DeleteOld = true; 4869 continue; 4870 } 4871 if (PHINode *PN = dyn_cast<PHINode>(U)) 4872 SE->ConstantEvolutionLoopExitValue.erase(PN); 4873 if (Instruction *I = dyn_cast<Instruction>(U)) 4874 SE->ValuesAtScopes.erase(I); 4875 if (SE->Scalars.erase(U)) 4876 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4877 UI != UE; ++UI) 4878 Worklist.push_back(*UI); 4879 } 4880 if (DeleteOld) { 4881 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4882 SE->ConstantEvolutionLoopExitValue.erase(PN); 4883 if (Instruction *I = dyn_cast<Instruction>(Old)) 4884 SE->ValuesAtScopes.erase(I); 4885 SE->Scalars.erase(Old); 4886 // this now dangles! 4887 } 4888 // this may dangle! 4889} 4890 4891ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4892 : CallbackVH(V), SE(se) {} 4893 4894//===----------------------------------------------------------------------===// 4895// ScalarEvolution Class Implementation 4896//===----------------------------------------------------------------------===// 4897 4898ScalarEvolution::ScalarEvolution() 4899 : FunctionPass(&ID) { 4900} 4901 4902bool ScalarEvolution::runOnFunction(Function &F) { 4903 this->F = &F; 4904 LI = &getAnalysis<LoopInfo>(); 4905 TD = getAnalysisIfAvailable<TargetData>(); 4906 return false; 4907} 4908 4909void ScalarEvolution::releaseMemory() { 4910 Scalars.clear(); 4911 BackedgeTakenCounts.clear(); 4912 ConstantEvolutionLoopExitValue.clear(); 4913 ValuesAtScopes.clear(); 4914 UniqueSCEVs.clear(); 4915 SCEVAllocator.Reset(); 4916} 4917 4918void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4919 AU.setPreservesAll(); 4920 AU.addRequiredTransitive<LoopInfo>(); 4921} 4922 4923bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4924 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4925} 4926 4927static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4928 const Loop *L) { 4929 // Print all inner loops first 4930 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4931 PrintLoopInfo(OS, SE, *I); 4932 4933 OS << "Loop " << L->getHeader()->getName() << ": "; 4934 4935 SmallVector<BasicBlock*, 8> ExitBlocks; 4936 L->getExitBlocks(ExitBlocks); 4937 if (ExitBlocks.size() != 1) 4938 OS << "<multiple exits> "; 4939 4940 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4941 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4942 } else { 4943 OS << "Unpredictable backedge-taken count. "; 4944 } 4945 4946 OS << "\n"; 4947 OS << "Loop " << L->getHeader()->getName() << ": "; 4948 4949 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 4950 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 4951 } else { 4952 OS << "Unpredictable max backedge-taken count. "; 4953 } 4954 4955 OS << "\n"; 4956} 4957 4958void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4959 // ScalarEvolution's implementaiton of the print method is to print 4960 // out SCEV values of all instructions that are interesting. Doing 4961 // this potentially causes it to create new SCEV objects though, 4962 // which technically conflicts with the const qualifier. This isn't 4963 // observable from outside the class though, so casting away the 4964 // const isn't dangerous. 4965 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4966 4967 OS << "Classifying expressions for: " << F->getName() << "\n"; 4968 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4969 if (isSCEVable(I->getType())) { 4970 OS << *I; 4971 OS << " --> "; 4972 const SCEV *SV = SE.getSCEV(&*I); 4973 SV->print(OS); 4974 4975 const Loop *L = LI->getLoopFor((*I).getParent()); 4976 4977 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 4978 if (AtUse != SV) { 4979 OS << " --> "; 4980 AtUse->print(OS); 4981 } 4982 4983 if (L) { 4984 OS << "\t\t" "Exits: "; 4985 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4986 if (!ExitValue->isLoopInvariant(L)) { 4987 OS << "<<Unknown>>"; 4988 } else { 4989 OS << *ExitValue; 4990 } 4991 } 4992 4993 OS << "\n"; 4994 } 4995 4996 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 4997 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 4998 PrintLoopInfo(OS, &SE, *I); 4999} 5000 5001void ScalarEvolution::print(std::ostream &o, const Module *M) const { 5002 raw_os_ostream OS(o); 5003 print(OS, M); 5004} 5005