ScalarEvolution.cpp revision 1b342583f6fc42f548912632f6aa24fc6e11986a
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/// hasSCEV - Return true if the SCEV for this value has already been 2124/// computed. 2125bool ScalarEvolution::hasSCEV(Value *V) const { 2126 return Scalars.count(V); 2127} 2128 2129/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2130/// expression and create a new one. 2131const SCEV *ScalarEvolution::getSCEV(Value *V) { 2132 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2133 2134 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2135 if (I != Scalars.end()) return I->second; 2136 const SCEV *S = createSCEV(V); 2137 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2138 return S; 2139} 2140 2141/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2142/// specified signed integer value and return a SCEV for the constant. 2143const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2144 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2145 return getConstant(ConstantInt::get(ITy, Val)); 2146} 2147 2148/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2149/// 2150const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2151 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2152 return getConstant(cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2153 2154 const Type *Ty = V->getType(); 2155 Ty = getEffectiveSCEVType(Ty); 2156 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty))); 2157} 2158 2159/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2160const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2161 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2162 return getConstant(cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2163 2164 const Type *Ty = V->getType(); 2165 Ty = getEffectiveSCEVType(Ty); 2166 const SCEV *AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty)); 2167 return getMinusSCEV(AllOnes, V); 2168} 2169 2170/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2171/// 2172const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2173 const SCEV *RHS) { 2174 // X - Y --> X + -Y 2175 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2176} 2177 2178/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2179/// input value to the specified type. If the type must be extended, it is zero 2180/// extended. 2181const SCEV * 2182ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2183 const Type *Ty) { 2184 const Type *SrcTy = V->getType(); 2185 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2186 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2187 "Cannot truncate or zero extend with non-integer arguments!"); 2188 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2189 return V; // No conversion 2190 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2191 return getTruncateExpr(V, Ty); 2192 return getZeroExtendExpr(V, Ty); 2193} 2194 2195/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2196/// input value to the specified type. If the type must be extended, it is sign 2197/// extended. 2198const SCEV * 2199ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2200 const Type *Ty) { 2201 const Type *SrcTy = V->getType(); 2202 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2203 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2204 "Cannot truncate or zero extend with non-integer arguments!"); 2205 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2206 return V; // No conversion 2207 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2208 return getTruncateExpr(V, Ty); 2209 return getSignExtendExpr(V, Ty); 2210} 2211 2212/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2213/// input value to the specified type. If the type must be extended, it is zero 2214/// extended. The conversion must not be narrowing. 2215const SCEV * 2216ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2217 const Type *SrcTy = V->getType(); 2218 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2219 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2220 "Cannot noop or zero extend with non-integer arguments!"); 2221 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2222 "getNoopOrZeroExtend cannot truncate!"); 2223 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2224 return V; // No conversion 2225 return getZeroExtendExpr(V, Ty); 2226} 2227 2228/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2229/// input value to the specified type. If the type must be extended, it is sign 2230/// extended. The conversion must not be narrowing. 2231const SCEV * 2232ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2233 const Type *SrcTy = V->getType(); 2234 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2235 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2236 "Cannot noop or sign extend with non-integer arguments!"); 2237 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2238 "getNoopOrSignExtend cannot truncate!"); 2239 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2240 return V; // No conversion 2241 return getSignExtendExpr(V, Ty); 2242} 2243 2244/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2245/// the input value to the specified type. If the type must be extended, 2246/// it is extended with unspecified bits. The conversion must not be 2247/// narrowing. 2248const SCEV * 2249ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2250 const Type *SrcTy = V->getType(); 2251 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2252 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2253 "Cannot noop or any extend with non-integer arguments!"); 2254 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2255 "getNoopOrAnyExtend cannot truncate!"); 2256 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2257 return V; // No conversion 2258 return getAnyExtendExpr(V, Ty); 2259} 2260 2261/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2262/// input value to the specified type. The conversion must not be widening. 2263const SCEV * 2264ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2265 const Type *SrcTy = V->getType(); 2266 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2267 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2268 "Cannot truncate or noop with non-integer arguments!"); 2269 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2270 "getTruncateOrNoop cannot extend!"); 2271 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2272 return V; // No conversion 2273 return getTruncateExpr(V, Ty); 2274} 2275 2276/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2277/// the types using zero-extension, and then perform a umax operation 2278/// with them. 2279const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2280 const SCEV *RHS) { 2281 const SCEV *PromotedLHS = LHS; 2282 const SCEV *PromotedRHS = RHS; 2283 2284 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2285 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2286 else 2287 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2288 2289 return getUMaxExpr(PromotedLHS, PromotedRHS); 2290} 2291 2292/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2293/// the types using zero-extension, and then perform a umin operation 2294/// with them. 2295const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2296 const SCEV *RHS) { 2297 const SCEV *PromotedLHS = LHS; 2298 const SCEV *PromotedRHS = RHS; 2299 2300 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2301 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2302 else 2303 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2304 2305 return getUMinExpr(PromotedLHS, PromotedRHS); 2306} 2307 2308/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2309/// the specified instruction and replaces any references to the symbolic value 2310/// SymName with the specified value. This is used during PHI resolution. 2311void 2312ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I, 2313 const SCEV *SymName, 2314 const SCEV *NewVal) { 2315 std::map<SCEVCallbackVH, const SCEV *>::iterator SI = 2316 Scalars.find(SCEVCallbackVH(I, this)); 2317 if (SI == Scalars.end()) return; 2318 2319 const SCEV *NV = 2320 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2321 if (NV == SI->second) return; // No change. 2322 2323 SI->second = NV; // Update the scalars map! 2324 2325 // Any instruction values that use this instruction might also need to be 2326 // updated! 2327 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2328 UI != E; ++UI) 2329 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2330} 2331 2332/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2333/// a loop header, making it a potential recurrence, or it doesn't. 2334/// 2335const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2336 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2337 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2338 if (L->getHeader() == PN->getParent()) { 2339 // If it lives in the loop header, it has two incoming values, one 2340 // from outside the loop, and one from inside. 2341 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2342 unsigned BackEdge = IncomingEdge^1; 2343 2344 // While we are analyzing this PHI node, handle its value symbolically. 2345 const SCEV *SymbolicName = getUnknown(PN); 2346 assert(Scalars.find(PN) == Scalars.end() && 2347 "PHI node already processed?"); 2348 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2349 2350 // Using this symbolic name for the PHI, analyze the value coming around 2351 // the back-edge. 2352 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2353 2354 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2355 // has a special value for the first iteration of the loop. 2356 2357 // If the value coming around the backedge is an add with the symbolic 2358 // value we just inserted, then we found a simple induction variable! 2359 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2360 // If there is a single occurrence of the symbolic value, replace it 2361 // with a recurrence. 2362 unsigned FoundIndex = Add->getNumOperands(); 2363 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2364 if (Add->getOperand(i) == SymbolicName) 2365 if (FoundIndex == e) { 2366 FoundIndex = i; 2367 break; 2368 } 2369 2370 if (FoundIndex != Add->getNumOperands()) { 2371 // Create an add with everything but the specified operand. 2372 SmallVector<const SCEV *, 8> Ops; 2373 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2374 if (i != FoundIndex) 2375 Ops.push_back(Add->getOperand(i)); 2376 const SCEV *Accum = getAddExpr(Ops); 2377 2378 // This is not a valid addrec if the step amount is varying each 2379 // loop iteration, but is not itself an addrec in this loop. 2380 if (Accum->isLoopInvariant(L) || 2381 (isa<SCEVAddRecExpr>(Accum) && 2382 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2383 const SCEV *StartVal = 2384 getSCEV(PN->getIncomingValue(IncomingEdge)); 2385 const SCEV *PHISCEV = 2386 getAddRecExpr(StartVal, Accum, L); 2387 2388 // Okay, for the entire analysis of this edge we assumed the PHI 2389 // to be symbolic. We now need to go back and update all of the 2390 // entries for the scalars that use the PHI (except for the PHI 2391 // itself) to use the new analyzed value instead of the "symbolic" 2392 // value. 2393 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2394 return PHISCEV; 2395 } 2396 } 2397 } else if (const SCEVAddRecExpr *AddRec = 2398 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2399 // Otherwise, this could be a loop like this: 2400 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2401 // In this case, j = {1,+,1} and BEValue is j. 2402 // Because the other in-value of i (0) fits the evolution of BEValue 2403 // i really is an addrec evolution. 2404 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2405 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2406 2407 // If StartVal = j.start - j.stride, we can use StartVal as the 2408 // initial step of the addrec evolution. 2409 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2410 AddRec->getOperand(1))) { 2411 const SCEV *PHISCEV = 2412 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2413 2414 // Okay, for the entire analysis of this edge we assumed the PHI 2415 // to be symbolic. We now need to go back and update all of the 2416 // entries for the scalars that use the PHI (except for the PHI 2417 // itself) to use the new analyzed value instead of the "symbolic" 2418 // value. 2419 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2420 return PHISCEV; 2421 } 2422 } 2423 } 2424 2425 return SymbolicName; 2426 } 2427 2428 // If it's not a loop phi, we can't handle it yet. 2429 return getUnknown(PN); 2430} 2431 2432/// createNodeForGEP - Expand GEP instructions into add and multiply 2433/// operations. This allows them to be analyzed by regular SCEV code. 2434/// 2435const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) { 2436 2437 const Type *IntPtrTy = TD->getIntPtrType(); 2438 Value *Base = GEP->getOperand(0); 2439 // Don't attempt to analyze GEPs over unsized objects. 2440 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2441 return getUnknown(GEP); 2442 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2443 gep_type_iterator GTI = gep_type_begin(GEP); 2444 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2445 E = GEP->op_end(); 2446 I != E; ++I) { 2447 Value *Index = *I; 2448 // Compute the (potentially symbolic) offset in bytes for this index. 2449 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2450 // For a struct, add the member offset. 2451 const StructLayout &SL = *TD->getStructLayout(STy); 2452 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2453 uint64_t Offset = SL.getElementOffset(FieldNo); 2454 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy)); 2455 } else { 2456 // For an array, add the element offset, explicitly scaled. 2457 const SCEV *LocalOffset = getSCEV(Index); 2458 if (!isa<PointerType>(LocalOffset->getType())) 2459 // Getelementptr indicies are signed. 2460 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2461 LocalOffset = 2462 getMulExpr(LocalOffset, 2463 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy)); 2464 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2465 } 2466 } 2467 return getAddExpr(getSCEV(Base), TotalOffset); 2468} 2469 2470/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2471/// guaranteed to end in (at every loop iteration). It is, at the same time, 2472/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2473/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2474uint32_t 2475ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2476 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2477 return C->getValue()->getValue().countTrailingZeros(); 2478 2479 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2480 return std::min(GetMinTrailingZeros(T->getOperand()), 2481 (uint32_t)getTypeSizeInBits(T->getType())); 2482 2483 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(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 SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2490 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2491 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2492 getTypeSizeInBits(E->getType()) : OpRes; 2493 } 2494 2495 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2496 // The result is the min of all operands results. 2497 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2498 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2499 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2500 return MinOpRes; 2501 } 2502 2503 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2504 // The result is the sum of all operands results. 2505 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2506 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2507 for (unsigned i = 1, e = M->getNumOperands(); 2508 SumOpRes != BitWidth && i != e; ++i) 2509 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2510 BitWidth); 2511 return SumOpRes; 2512 } 2513 2514 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2515 // The result is the min of all operands results. 2516 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2517 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2518 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2519 return MinOpRes; 2520 } 2521 2522 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2523 // The result is the min of all operands results. 2524 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2525 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2526 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2527 return MinOpRes; 2528 } 2529 2530 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2531 // The result is the min of all operands results. 2532 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2533 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2534 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2535 return MinOpRes; 2536 } 2537 2538 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2539 // For a SCEVUnknown, ask ValueTracking. 2540 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2541 APInt Mask = APInt::getAllOnesValue(BitWidth); 2542 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2543 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2544 return Zeros.countTrailingOnes(); 2545 } 2546 2547 // SCEVUDivExpr 2548 return 0; 2549} 2550 2551/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2552/// 2553ConstantRange 2554ScalarEvolution::getUnsignedRange(const SCEV *S) { 2555 2556 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2557 return ConstantRange(C->getValue()->getValue()); 2558 2559 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2560 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2561 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2562 X = X.add(getUnsignedRange(Add->getOperand(i))); 2563 return X; 2564 } 2565 2566 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2567 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2568 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2569 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2570 return X; 2571 } 2572 2573 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2574 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2575 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2576 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2577 return X; 2578 } 2579 2580 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2581 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2582 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2583 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2584 return X; 2585 } 2586 2587 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2588 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2589 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2590 return X.udiv(Y); 2591 } 2592 2593 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2594 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2595 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2596 } 2597 2598 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2599 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2600 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2601 } 2602 2603 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2604 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2605 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2606 } 2607 2608 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2609 2610 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2611 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2612 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2613 if (!Trip) return FullSet; 2614 2615 // TODO: non-affine addrec 2616 if (AddRec->isAffine()) { 2617 const Type *Ty = AddRec->getType(); 2618 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2619 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2620 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2621 2622 const SCEV *Start = AddRec->getStart(); 2623 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2624 2625 // Check for overflow. 2626 if (!isKnownPredicate(ICmpInst::ICMP_ULE, Start, End)) 2627 return FullSet; 2628 2629 ConstantRange StartRange = getUnsignedRange(Start); 2630 ConstantRange EndRange = getUnsignedRange(End); 2631 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2632 EndRange.getUnsignedMin()); 2633 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2634 EndRange.getUnsignedMax()); 2635 if (Min.isMinValue() && Max.isMaxValue()) 2636 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2637 return ConstantRange(Min, Max+1); 2638 } 2639 } 2640 } 2641 2642 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2643 // For a SCEVUnknown, ask ValueTracking. 2644 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2645 APInt Mask = APInt::getAllOnesValue(BitWidth); 2646 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2647 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2648 return ConstantRange(Ones, ~Zeros); 2649 } 2650 2651 return FullSet; 2652} 2653 2654/// getSignedRange - Determine the signed range for a particular SCEV. 2655/// 2656ConstantRange 2657ScalarEvolution::getSignedRange(const SCEV *S) { 2658 2659 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2660 return ConstantRange(C->getValue()->getValue()); 2661 2662 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2663 ConstantRange X = getSignedRange(Add->getOperand(0)); 2664 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2665 X = X.add(getSignedRange(Add->getOperand(i))); 2666 return X; 2667 } 2668 2669 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2670 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2671 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2672 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2673 return X; 2674 } 2675 2676 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2677 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2678 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2679 X = X.smax(getSignedRange(SMax->getOperand(i))); 2680 return X; 2681 } 2682 2683 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2684 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2685 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2686 X = X.umax(getSignedRange(UMax->getOperand(i))); 2687 return X; 2688 } 2689 2690 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2691 ConstantRange X = getSignedRange(UDiv->getLHS()); 2692 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2693 return X.udiv(Y); 2694 } 2695 2696 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2697 ConstantRange X = getSignedRange(ZExt->getOperand()); 2698 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2699 } 2700 2701 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2702 ConstantRange X = getSignedRange(SExt->getOperand()); 2703 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2704 } 2705 2706 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2707 ConstantRange X = getSignedRange(Trunc->getOperand()); 2708 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2709 } 2710 2711 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2712 2713 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2714 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2715 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2716 if (!Trip) return FullSet; 2717 2718 // TODO: non-affine addrec 2719 if (AddRec->isAffine()) { 2720 const Type *Ty = AddRec->getType(); 2721 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2722 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2723 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2724 2725 const SCEV *Start = AddRec->getStart(); 2726 const SCEV *Step = AddRec->getStepRecurrence(*this); 2727 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2728 2729 // Check for overflow. 2730 if (!(isKnownPositive(Step) && 2731 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2732 !(isKnownNegative(Step) && 2733 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2734 return FullSet; 2735 2736 ConstantRange StartRange = getSignedRange(Start); 2737 ConstantRange EndRange = getSignedRange(End); 2738 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2739 EndRange.getSignedMin()); 2740 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2741 EndRange.getSignedMax()); 2742 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2743 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2744 return ConstantRange(Min, Max+1); 2745 } 2746 } 2747 } 2748 2749 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2750 // For a SCEVUnknown, ask ValueTracking. 2751 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2752 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2753 if (NS == 1) 2754 return FullSet; 2755 return 2756 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2757 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2758 } 2759 2760 return FullSet; 2761} 2762 2763/// createSCEV - We know that there is no SCEV for the specified value. 2764/// Analyze the expression. 2765/// 2766const SCEV *ScalarEvolution::createSCEV(Value *V) { 2767 if (!isSCEVable(V->getType())) 2768 return getUnknown(V); 2769 2770 unsigned Opcode = Instruction::UserOp1; 2771 if (Instruction *I = dyn_cast<Instruction>(V)) 2772 Opcode = I->getOpcode(); 2773 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2774 Opcode = CE->getOpcode(); 2775 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2776 return getConstant(CI); 2777 else if (isa<ConstantPointerNull>(V)) 2778 return getIntegerSCEV(0, V->getType()); 2779 else if (isa<UndefValue>(V)) 2780 return getIntegerSCEV(0, V->getType()); 2781 else 2782 return getUnknown(V); 2783 2784 User *U = cast<User>(V); 2785 switch (Opcode) { 2786 case Instruction::Add: 2787 return getAddExpr(getSCEV(U->getOperand(0)), 2788 getSCEV(U->getOperand(1))); 2789 case Instruction::Mul: 2790 return getMulExpr(getSCEV(U->getOperand(0)), 2791 getSCEV(U->getOperand(1))); 2792 case Instruction::UDiv: 2793 return getUDivExpr(getSCEV(U->getOperand(0)), 2794 getSCEV(U->getOperand(1))); 2795 case Instruction::Sub: 2796 return getMinusSCEV(getSCEV(U->getOperand(0)), 2797 getSCEV(U->getOperand(1))); 2798 case Instruction::And: 2799 // For an expression like x&255 that merely masks off the high bits, 2800 // use zext(trunc(x)) as the SCEV expression. 2801 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2802 if (CI->isNullValue()) 2803 return getSCEV(U->getOperand(1)); 2804 if (CI->isAllOnesValue()) 2805 return getSCEV(U->getOperand(0)); 2806 const APInt &A = CI->getValue(); 2807 2808 // Instcombine's ShrinkDemandedConstant may strip bits out of 2809 // constants, obscuring what would otherwise be a low-bits mask. 2810 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2811 // knew about to reconstruct a low-bits mask value. 2812 unsigned LZ = A.countLeadingZeros(); 2813 unsigned BitWidth = A.getBitWidth(); 2814 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2815 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2816 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2817 2818 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2819 2820 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2821 return 2822 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2823 IntegerType::get(BitWidth - LZ)), 2824 U->getType()); 2825 } 2826 break; 2827 2828 case Instruction::Or: 2829 // If the RHS of the Or is a constant, we may have something like: 2830 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2831 // optimizations will transparently handle this case. 2832 // 2833 // In order for this transformation to be safe, the LHS must be of the 2834 // form X*(2^n) and the Or constant must be less than 2^n. 2835 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2836 const SCEV *LHS = getSCEV(U->getOperand(0)); 2837 const APInt &CIVal = CI->getValue(); 2838 if (GetMinTrailingZeros(LHS) >= 2839 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2840 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2841 } 2842 break; 2843 case Instruction::Xor: 2844 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2845 // If the RHS of the xor is a signbit, then this is just an add. 2846 // Instcombine turns add of signbit into xor as a strength reduction step. 2847 if (CI->getValue().isSignBit()) 2848 return getAddExpr(getSCEV(U->getOperand(0)), 2849 getSCEV(U->getOperand(1))); 2850 2851 // If the RHS of xor is -1, then this is a not operation. 2852 if (CI->isAllOnesValue()) 2853 return getNotSCEV(getSCEV(U->getOperand(0))); 2854 2855 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2856 // This is a variant of the check for xor with -1, and it handles 2857 // the case where instcombine has trimmed non-demanded bits out 2858 // of an xor with -1. 2859 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2860 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2861 if (BO->getOpcode() == Instruction::And && 2862 LCI->getValue() == CI->getValue()) 2863 if (const SCEVZeroExtendExpr *Z = 2864 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2865 const Type *UTy = U->getType(); 2866 const SCEV *Z0 = Z->getOperand(); 2867 const Type *Z0Ty = Z0->getType(); 2868 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2869 2870 // If C is a low-bits mask, the zero extend is zerving to 2871 // mask off the high bits. Complement the operand and 2872 // re-apply the zext. 2873 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2874 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2875 2876 // If C is a single bit, it may be in the sign-bit position 2877 // before the zero-extend. In this case, represent the xor 2878 // using an add, which is equivalent, and re-apply the zext. 2879 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2880 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2881 Trunc.isSignBit()) 2882 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2883 UTy); 2884 } 2885 } 2886 break; 2887 2888 case Instruction::Shl: 2889 // Turn shift left of a constant amount into a multiply. 2890 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2891 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2892 Constant *X = ConstantInt::get( 2893 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2894 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2895 } 2896 break; 2897 2898 case Instruction::LShr: 2899 // Turn logical shift right of a constant into a unsigned divide. 2900 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2901 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2902 Constant *X = ConstantInt::get( 2903 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2904 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2905 } 2906 break; 2907 2908 case Instruction::AShr: 2909 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2910 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2911 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2912 if (L->getOpcode() == Instruction::Shl && 2913 L->getOperand(1) == U->getOperand(1)) { 2914 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2915 uint64_t Amt = BitWidth - CI->getZExtValue(); 2916 if (Amt == BitWidth) 2917 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2918 if (Amt > BitWidth) 2919 return getIntegerSCEV(0, U->getType()); // value is undefined 2920 return 2921 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2922 IntegerType::get(Amt)), 2923 U->getType()); 2924 } 2925 break; 2926 2927 case Instruction::Trunc: 2928 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2929 2930 case Instruction::ZExt: 2931 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2932 2933 case Instruction::SExt: 2934 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2935 2936 case Instruction::BitCast: 2937 // BitCasts are no-op casts so we just eliminate the cast. 2938 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2939 return getSCEV(U->getOperand(0)); 2940 break; 2941 2942 case Instruction::IntToPtr: 2943 if (!TD) break; // Without TD we can't analyze pointers. 2944 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2945 TD->getIntPtrType()); 2946 2947 case Instruction::PtrToInt: 2948 if (!TD) break; // Without TD we can't analyze pointers. 2949 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2950 U->getType()); 2951 2952 case Instruction::GetElementPtr: 2953 if (!TD) break; // Without TD we can't analyze pointers. 2954 return createNodeForGEP(U); 2955 2956 case Instruction::PHI: 2957 return createNodeForPHI(cast<PHINode>(U)); 2958 2959 case Instruction::Select: 2960 // This could be a smax or umax that was lowered earlier. 2961 // Try to recover it. 2962 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2963 Value *LHS = ICI->getOperand(0); 2964 Value *RHS = ICI->getOperand(1); 2965 switch (ICI->getPredicate()) { 2966 case ICmpInst::ICMP_SLT: 2967 case ICmpInst::ICMP_SLE: 2968 std::swap(LHS, RHS); 2969 // fall through 2970 case ICmpInst::ICMP_SGT: 2971 case ICmpInst::ICMP_SGE: 2972 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2973 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2974 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2975 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2976 break; 2977 case ICmpInst::ICMP_ULT: 2978 case ICmpInst::ICMP_ULE: 2979 std::swap(LHS, RHS); 2980 // fall through 2981 case ICmpInst::ICMP_UGT: 2982 case ICmpInst::ICMP_UGE: 2983 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2984 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2985 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2986 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2987 break; 2988 case ICmpInst::ICMP_NE: 2989 // n != 0 ? n : 1 -> umax(n, 1) 2990 if (LHS == U->getOperand(1) && 2991 isa<ConstantInt>(U->getOperand(2)) && 2992 cast<ConstantInt>(U->getOperand(2))->isOne() && 2993 isa<ConstantInt>(RHS) && 2994 cast<ConstantInt>(RHS)->isZero()) 2995 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2996 break; 2997 case ICmpInst::ICMP_EQ: 2998 // n == 0 ? 1 : n -> umax(n, 1) 2999 if (LHS == U->getOperand(2) && 3000 isa<ConstantInt>(U->getOperand(1)) && 3001 cast<ConstantInt>(U->getOperand(1))->isOne() && 3002 isa<ConstantInt>(RHS) && 3003 cast<ConstantInt>(RHS)->isZero()) 3004 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3005 break; 3006 default: 3007 break; 3008 } 3009 } 3010 3011 default: // We cannot analyze this expression. 3012 break; 3013 } 3014 3015 return getUnknown(V); 3016} 3017 3018 3019 3020//===----------------------------------------------------------------------===// 3021// Iteration Count Computation Code 3022// 3023 3024/// getBackedgeTakenCount - If the specified loop has a predictable 3025/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3026/// object. The backedge-taken count is the number of times the loop header 3027/// will be branched to from within the loop. This is one less than the 3028/// trip count of the loop, since it doesn't count the first iteration, 3029/// when the header is branched to from outside the loop. 3030/// 3031/// Note that it is not valid to call this method on a loop without a 3032/// loop-invariant backedge-taken count (see 3033/// hasLoopInvariantBackedgeTakenCount). 3034/// 3035const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3036 return getBackedgeTakenInfo(L).Exact; 3037} 3038 3039/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3040/// return the least SCEV value that is known never to be less than the 3041/// actual backedge taken count. 3042const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3043 return getBackedgeTakenInfo(L).Max; 3044} 3045 3046/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3047/// onto the given Worklist. 3048static void 3049PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3050 BasicBlock *Header = L->getHeader(); 3051 3052 // Push all Loop-header PHIs onto the Worklist stack. 3053 for (BasicBlock::iterator I = Header->begin(); 3054 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3055 Worklist.push_back(PN); 3056} 3057 3058/// PushDefUseChildren - Push users of the given Instruction 3059/// onto the given Worklist. 3060static void 3061PushDefUseChildren(Instruction *I, 3062 SmallVectorImpl<Instruction *> &Worklist) { 3063 // Push the def-use children onto the Worklist stack. 3064 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 3065 UI != UE; ++UI) 3066 Worklist.push_back(cast<Instruction>(UI)); 3067} 3068 3069const ScalarEvolution::BackedgeTakenInfo & 3070ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3071 // Initially insert a CouldNotCompute for this loop. If the insertion 3072 // succeeds, procede to actually compute a backedge-taken count and 3073 // update the value. The temporary CouldNotCompute value tells SCEV 3074 // code elsewhere that it shouldn't attempt to request a new 3075 // backedge-taken count, which could result in infinite recursion. 3076 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3077 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3078 if (Pair.second) { 3079 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3080 if (ItCount.Exact != getCouldNotCompute()) { 3081 assert(ItCount.Exact->isLoopInvariant(L) && 3082 ItCount.Max->isLoopInvariant(L) && 3083 "Computed trip count isn't loop invariant for loop!"); 3084 ++NumTripCountsComputed; 3085 3086 // Update the value in the map. 3087 Pair.first->second = ItCount; 3088 } else { 3089 if (ItCount.Max != getCouldNotCompute()) 3090 // Update the value in the map. 3091 Pair.first->second = ItCount; 3092 if (isa<PHINode>(L->getHeader()->begin())) 3093 // Only count loops that have phi nodes as not being computable. 3094 ++NumTripCountsNotComputed; 3095 } 3096 3097 // Now that we know more about the trip count for this loop, forget any 3098 // existing SCEV values for PHI nodes in this loop since they are only 3099 // conservative estimates made without the benefit of trip count 3100 // information. This is similar to the code in 3101 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3102 // nodes specially. 3103 if (ItCount.hasAnyInfo()) { 3104 SmallVector<Instruction *, 16> Worklist; 3105 PushLoopPHIs(L, Worklist); 3106 3107 SmallPtrSet<Instruction *, 8> Visited; 3108 while (!Worklist.empty()) { 3109 Instruction *I = Worklist.pop_back_val(); 3110 if (!Visited.insert(I)) continue; 3111 3112 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3113 Scalars.find(static_cast<Value *>(I)); 3114 if (It != Scalars.end()) { 3115 // SCEVUnknown for a PHI either means that it has an unrecognized 3116 // structure, or it's a PHI that's in the progress of being computed 3117 // by createNodeForPHI. In the former case, additional loop trip count 3118 // information isn't going to change anything. In the later case, 3119 // createNodeForPHI will perform the necessary updates on its own when 3120 // it gets to that point. 3121 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 3122 Scalars.erase(It); 3123 ValuesAtScopes.erase(I); 3124 if (PHINode *PN = dyn_cast<PHINode>(I)) 3125 ConstantEvolutionLoopExitValue.erase(PN); 3126 } 3127 3128 PushDefUseChildren(I, Worklist); 3129 } 3130 } 3131 } 3132 return Pair.first->second; 3133} 3134 3135/// forgetLoopBackedgeTakenCount - This method should be called by the 3136/// client when it has changed a loop in a way that may effect 3137/// ScalarEvolution's ability to compute a trip count, or if the loop 3138/// is deleted. 3139void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3140 BackedgeTakenCounts.erase(L); 3141 3142 SmallVector<Instruction *, 16> Worklist; 3143 PushLoopPHIs(L, Worklist); 3144 3145 SmallPtrSet<Instruction *, 8> Visited; 3146 while (!Worklist.empty()) { 3147 Instruction *I = Worklist.pop_back_val(); 3148 if (!Visited.insert(I)) continue; 3149 3150 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3151 Scalars.find(static_cast<Value *>(I)); 3152 if (It != Scalars.end()) { 3153 Scalars.erase(It); 3154 ValuesAtScopes.erase(I); 3155 if (PHINode *PN = dyn_cast<PHINode>(I)) 3156 ConstantEvolutionLoopExitValue.erase(PN); 3157 } 3158 3159 PushDefUseChildren(I, Worklist); 3160 } 3161} 3162 3163/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3164/// of the specified loop will execute. 3165ScalarEvolution::BackedgeTakenInfo 3166ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3167 SmallVector<BasicBlock*, 8> ExitingBlocks; 3168 L->getExitingBlocks(ExitingBlocks); 3169 3170 // Examine all exits and pick the most conservative values. 3171 const SCEV *BECount = getCouldNotCompute(); 3172 const SCEV *MaxBECount = getCouldNotCompute(); 3173 bool CouldNotComputeBECount = false; 3174 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3175 BackedgeTakenInfo NewBTI = 3176 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3177 3178 if (NewBTI.Exact == getCouldNotCompute()) { 3179 // We couldn't compute an exact value for this exit, so 3180 // we won't be able to compute an exact value for the loop. 3181 CouldNotComputeBECount = true; 3182 BECount = getCouldNotCompute(); 3183 } else if (!CouldNotComputeBECount) { 3184 if (BECount == getCouldNotCompute()) 3185 BECount = NewBTI.Exact; 3186 else 3187 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3188 } 3189 if (MaxBECount == getCouldNotCompute()) 3190 MaxBECount = NewBTI.Max; 3191 else if (NewBTI.Max != getCouldNotCompute()) 3192 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3193 } 3194 3195 return BackedgeTakenInfo(BECount, MaxBECount); 3196} 3197 3198/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3199/// of the specified loop will execute if it exits via the specified block. 3200ScalarEvolution::BackedgeTakenInfo 3201ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3202 BasicBlock *ExitingBlock) { 3203 3204 // Okay, we've chosen an exiting block. See what condition causes us to 3205 // exit at this block. 3206 // 3207 // FIXME: we should be able to handle switch instructions (with a single exit) 3208 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3209 if (ExitBr == 0) return getCouldNotCompute(); 3210 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3211 3212 // At this point, we know we have a conditional branch that determines whether 3213 // the loop is exited. However, we don't know if the branch is executed each 3214 // time through the loop. If not, then the execution count of the branch will 3215 // not be equal to the trip count of the loop. 3216 // 3217 // Currently we check for this by checking to see if the Exit branch goes to 3218 // the loop header. If so, we know it will always execute the same number of 3219 // times as the loop. We also handle the case where the exit block *is* the 3220 // loop header. This is common for un-rotated loops. 3221 // 3222 // If both of those tests fail, walk up the unique predecessor chain to the 3223 // header, stopping if there is an edge that doesn't exit the loop. If the 3224 // header is reached, the execution count of the branch will be equal to the 3225 // trip count of the loop. 3226 // 3227 // More extensive analysis could be done to handle more cases here. 3228 // 3229 if (ExitBr->getSuccessor(0) != L->getHeader() && 3230 ExitBr->getSuccessor(1) != L->getHeader() && 3231 ExitBr->getParent() != L->getHeader()) { 3232 // The simple checks failed, try climbing the unique predecessor chain 3233 // up to the header. 3234 bool Ok = false; 3235 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3236 BasicBlock *Pred = BB->getUniquePredecessor(); 3237 if (!Pred) 3238 return getCouldNotCompute(); 3239 TerminatorInst *PredTerm = Pred->getTerminator(); 3240 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3241 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3242 if (PredSucc == BB) 3243 continue; 3244 // If the predecessor has a successor that isn't BB and isn't 3245 // outside the loop, assume the worst. 3246 if (L->contains(PredSucc)) 3247 return getCouldNotCompute(); 3248 } 3249 if (Pred == L->getHeader()) { 3250 Ok = true; 3251 break; 3252 } 3253 BB = Pred; 3254 } 3255 if (!Ok) 3256 return getCouldNotCompute(); 3257 } 3258 3259 // Procede to the next level to examine the exit condition expression. 3260 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3261 ExitBr->getSuccessor(0), 3262 ExitBr->getSuccessor(1)); 3263} 3264 3265/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3266/// backedge of the specified loop will execute if its exit condition 3267/// were a conditional branch of ExitCond, TBB, and FBB. 3268ScalarEvolution::BackedgeTakenInfo 3269ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3270 Value *ExitCond, 3271 BasicBlock *TBB, 3272 BasicBlock *FBB) { 3273 // Check if the controlling expression for this loop is an And or Or. 3274 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3275 if (BO->getOpcode() == Instruction::And) { 3276 // Recurse on the operands of the and. 3277 BackedgeTakenInfo BTI0 = 3278 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3279 BackedgeTakenInfo BTI1 = 3280 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3281 const SCEV *BECount = getCouldNotCompute(); 3282 const SCEV *MaxBECount = getCouldNotCompute(); 3283 if (L->contains(TBB)) { 3284 // Both conditions must be true for the loop to continue executing. 3285 // Choose the less conservative count. 3286 if (BTI0.Exact == getCouldNotCompute() || 3287 BTI1.Exact == getCouldNotCompute()) 3288 BECount = getCouldNotCompute(); 3289 else 3290 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3291 if (BTI0.Max == getCouldNotCompute()) 3292 MaxBECount = BTI1.Max; 3293 else if (BTI1.Max == getCouldNotCompute()) 3294 MaxBECount = BTI0.Max; 3295 else 3296 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3297 } else { 3298 // Both conditions must be true for the loop to exit. 3299 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3300 if (BTI0.Exact != getCouldNotCompute() && 3301 BTI1.Exact != getCouldNotCompute()) 3302 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3303 if (BTI0.Max != getCouldNotCompute() && 3304 BTI1.Max != getCouldNotCompute()) 3305 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3306 } 3307 3308 return BackedgeTakenInfo(BECount, MaxBECount); 3309 } 3310 if (BO->getOpcode() == Instruction::Or) { 3311 // Recurse on the operands of the or. 3312 BackedgeTakenInfo BTI0 = 3313 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3314 BackedgeTakenInfo BTI1 = 3315 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3316 const SCEV *BECount = getCouldNotCompute(); 3317 const SCEV *MaxBECount = getCouldNotCompute(); 3318 if (L->contains(FBB)) { 3319 // Both conditions must be false for the loop to continue executing. 3320 // Choose the less conservative count. 3321 if (BTI0.Exact == getCouldNotCompute() || 3322 BTI1.Exact == getCouldNotCompute()) 3323 BECount = getCouldNotCompute(); 3324 else 3325 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3326 if (BTI0.Max == getCouldNotCompute()) 3327 MaxBECount = BTI1.Max; 3328 else if (BTI1.Max == getCouldNotCompute()) 3329 MaxBECount = BTI0.Max; 3330 else 3331 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3332 } else { 3333 // Both conditions must be false for the loop to exit. 3334 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3335 if (BTI0.Exact != getCouldNotCompute() && 3336 BTI1.Exact != getCouldNotCompute()) 3337 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3338 if (BTI0.Max != getCouldNotCompute() && 3339 BTI1.Max != getCouldNotCompute()) 3340 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3341 } 3342 3343 return BackedgeTakenInfo(BECount, MaxBECount); 3344 } 3345 } 3346 3347 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3348 // Procede to the next level to examine the icmp. 3349 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3350 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3351 3352 // If it's not an integer or pointer comparison then compute it the hard way. 3353 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3354} 3355 3356/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3357/// backedge of the specified loop will execute if its exit condition 3358/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3359ScalarEvolution::BackedgeTakenInfo 3360ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3361 ICmpInst *ExitCond, 3362 BasicBlock *TBB, 3363 BasicBlock *FBB) { 3364 3365 // If the condition was exit on true, convert the condition to exit on false 3366 ICmpInst::Predicate Cond; 3367 if (!L->contains(FBB)) 3368 Cond = ExitCond->getPredicate(); 3369 else 3370 Cond = ExitCond->getInversePredicate(); 3371 3372 // Handle common loops like: for (X = "string"; *X; ++X) 3373 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3374 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3375 const SCEV *ItCnt = 3376 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3377 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3378 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3379 return BackedgeTakenInfo(ItCnt, 3380 isa<SCEVConstant>(ItCnt) ? ItCnt : 3381 getConstant(APInt::getMaxValue(BitWidth)-1)); 3382 } 3383 } 3384 3385 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3386 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3387 3388 // Try to evaluate any dependencies out of the loop. 3389 LHS = getSCEVAtScope(LHS, L); 3390 RHS = getSCEVAtScope(RHS, L); 3391 3392 // At this point, we would like to compute how many iterations of the 3393 // loop the predicate will return true for these inputs. 3394 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3395 // If there is a loop-invariant, force it into the RHS. 3396 std::swap(LHS, RHS); 3397 Cond = ICmpInst::getSwappedPredicate(Cond); 3398 } 3399 3400 // If we have a comparison of a chrec against a constant, try to use value 3401 // ranges to answer this query. 3402 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3403 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3404 if (AddRec->getLoop() == L) { 3405 // Form the constant range. 3406 ConstantRange CompRange( 3407 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3408 3409 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3410 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3411 } 3412 3413 switch (Cond) { 3414 case ICmpInst::ICMP_NE: { // while (X != Y) 3415 // Convert to: while (X-Y != 0) 3416 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3417 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3418 break; 3419 } 3420 case ICmpInst::ICMP_EQ: { 3421 // Convert to: while (X-Y == 0) // while (X == Y) 3422 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3423 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3424 break; 3425 } 3426 case ICmpInst::ICMP_SLT: { 3427 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3428 if (BTI.hasAnyInfo()) return BTI; 3429 break; 3430 } 3431 case ICmpInst::ICMP_SGT: { 3432 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3433 getNotSCEV(RHS), L, true); 3434 if (BTI.hasAnyInfo()) return BTI; 3435 break; 3436 } 3437 case ICmpInst::ICMP_ULT: { 3438 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3439 if (BTI.hasAnyInfo()) return BTI; 3440 break; 3441 } 3442 case ICmpInst::ICMP_UGT: { 3443 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3444 getNotSCEV(RHS), L, false); 3445 if (BTI.hasAnyInfo()) return BTI; 3446 break; 3447 } 3448 default: 3449#if 0 3450 errs() << "ComputeBackedgeTakenCount "; 3451 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3452 errs() << "[unsigned] "; 3453 errs() << *LHS << " " 3454 << Instruction::getOpcodeName(Instruction::ICmp) 3455 << " " << *RHS << "\n"; 3456#endif 3457 break; 3458 } 3459 return 3460 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3461} 3462 3463static ConstantInt * 3464EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3465 ScalarEvolution &SE) { 3466 const SCEV *InVal = SE.getConstant(C); 3467 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3468 assert(isa<SCEVConstant>(Val) && 3469 "Evaluation of SCEV at constant didn't fold correctly?"); 3470 return cast<SCEVConstant>(Val)->getValue(); 3471} 3472 3473/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3474/// and a GEP expression (missing the pointer index) indexing into it, return 3475/// the addressed element of the initializer or null if the index expression is 3476/// invalid. 3477static Constant * 3478GetAddressedElementFromGlobal(GlobalVariable *GV, 3479 const std::vector<ConstantInt*> &Indices) { 3480 Constant *Init = GV->getInitializer(); 3481 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3482 uint64_t Idx = Indices[i]->getZExtValue(); 3483 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3484 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3485 Init = cast<Constant>(CS->getOperand(Idx)); 3486 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3487 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3488 Init = cast<Constant>(CA->getOperand(Idx)); 3489 } else if (isa<ConstantAggregateZero>(Init)) { 3490 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3491 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3492 Init = Constant::getNullValue(STy->getElementType(Idx)); 3493 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3494 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3495 Init = Constant::getNullValue(ATy->getElementType()); 3496 } else { 3497 assert(0 && "Unknown constant aggregate type!"); 3498 } 3499 return 0; 3500 } else { 3501 return 0; // Unknown initializer type 3502 } 3503 } 3504 return Init; 3505} 3506 3507/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3508/// 'icmp op load X, cst', try to see if we can compute the backedge 3509/// execution count. 3510const SCEV * 3511ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3512 LoadInst *LI, 3513 Constant *RHS, 3514 const Loop *L, 3515 ICmpInst::Predicate predicate) { 3516 if (LI->isVolatile()) return getCouldNotCompute(); 3517 3518 // Check to see if the loaded pointer is a getelementptr of a global. 3519 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3520 if (!GEP) return getCouldNotCompute(); 3521 3522 // Make sure that it is really a constant global we are gepping, with an 3523 // initializer, and make sure the first IDX is really 0. 3524 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3525 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3526 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3527 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3528 return getCouldNotCompute(); 3529 3530 // Okay, we allow one non-constant index into the GEP instruction. 3531 Value *VarIdx = 0; 3532 std::vector<ConstantInt*> Indexes; 3533 unsigned VarIdxNum = 0; 3534 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3535 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3536 Indexes.push_back(CI); 3537 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3538 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3539 VarIdx = GEP->getOperand(i); 3540 VarIdxNum = i-2; 3541 Indexes.push_back(0); 3542 } 3543 3544 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3545 // Check to see if X is a loop variant variable value now. 3546 const SCEV *Idx = getSCEV(VarIdx); 3547 Idx = getSCEVAtScope(Idx, L); 3548 3549 // We can only recognize very limited forms of loop index expressions, in 3550 // particular, only affine AddRec's like {C1,+,C2}. 3551 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3552 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3553 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3554 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3555 return getCouldNotCompute(); 3556 3557 unsigned MaxSteps = MaxBruteForceIterations; 3558 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3559 ConstantInt *ItCst = 3560 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3561 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3562 3563 // Form the GEP offset. 3564 Indexes[VarIdxNum] = Val; 3565 3566 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3567 if (Result == 0) break; // Cannot compute! 3568 3569 // Evaluate the condition for this iteration. 3570 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3571 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3572 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3573#if 0 3574 errs() << "\n***\n*** Computed loop count " << *ItCst 3575 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3576 << "***\n"; 3577#endif 3578 ++NumArrayLenItCounts; 3579 return getConstant(ItCst); // Found terminating iteration! 3580 } 3581 } 3582 return getCouldNotCompute(); 3583} 3584 3585 3586/// CanConstantFold - Return true if we can constant fold an instruction of the 3587/// specified type, assuming that all operands were constants. 3588static bool CanConstantFold(const Instruction *I) { 3589 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3590 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3591 return true; 3592 3593 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3594 if (const Function *F = CI->getCalledFunction()) 3595 return canConstantFoldCallTo(F); 3596 return false; 3597} 3598 3599/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3600/// in the loop that V is derived from. We allow arbitrary operations along the 3601/// way, but the operands of an operation must either be constants or a value 3602/// derived from a constant PHI. If this expression does not fit with these 3603/// constraints, return null. 3604static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3605 // If this is not an instruction, or if this is an instruction outside of the 3606 // loop, it can't be derived from a loop PHI. 3607 Instruction *I = dyn_cast<Instruction>(V); 3608 if (I == 0 || !L->contains(I->getParent())) return 0; 3609 3610 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3611 if (L->getHeader() == I->getParent()) 3612 return PN; 3613 else 3614 // We don't currently keep track of the control flow needed to evaluate 3615 // PHIs, so we cannot handle PHIs inside of loops. 3616 return 0; 3617 } 3618 3619 // If we won't be able to constant fold this expression even if the operands 3620 // are constants, return early. 3621 if (!CanConstantFold(I)) return 0; 3622 3623 // Otherwise, we can evaluate this instruction if all of its operands are 3624 // constant or derived from a PHI node themselves. 3625 PHINode *PHI = 0; 3626 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3627 if (!(isa<Constant>(I->getOperand(Op)) || 3628 isa<GlobalValue>(I->getOperand(Op)))) { 3629 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3630 if (P == 0) return 0; // Not evolving from PHI 3631 if (PHI == 0) 3632 PHI = P; 3633 else if (PHI != P) 3634 return 0; // Evolving from multiple different PHIs. 3635 } 3636 3637 // This is a expression evolving from a constant PHI! 3638 return PHI; 3639} 3640 3641/// EvaluateExpression - Given an expression that passes the 3642/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3643/// in the loop has the value PHIVal. If we can't fold this expression for some 3644/// reason, return null. 3645static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3646 if (isa<PHINode>(V)) return PHIVal; 3647 if (Constant *C = dyn_cast<Constant>(V)) return C; 3648 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3649 Instruction *I = cast<Instruction>(V); 3650 LLVMContext *Context = I->getParent()->getContext(); 3651 3652 std::vector<Constant*> Operands; 3653 Operands.resize(I->getNumOperands()); 3654 3655 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3656 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3657 if (Operands[i] == 0) return 0; 3658 } 3659 3660 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3661 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3662 &Operands[0], Operands.size(), 3663 Context); 3664 else 3665 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3666 &Operands[0], Operands.size(), 3667 Context); 3668} 3669 3670/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3671/// in the header of its containing loop, we know the loop executes a 3672/// constant number of times, and the PHI node is just a recurrence 3673/// involving constants, fold it. 3674Constant * 3675ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3676 const APInt& BEs, 3677 const Loop *L) { 3678 std::map<PHINode*, Constant*>::iterator I = 3679 ConstantEvolutionLoopExitValue.find(PN); 3680 if (I != ConstantEvolutionLoopExitValue.end()) 3681 return I->second; 3682 3683 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3684 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3685 3686 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3687 3688 // Since the loop is canonicalized, the PHI node must have two entries. One 3689 // entry must be a constant (coming in from outside of the loop), and the 3690 // second must be derived from the same PHI. 3691 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3692 Constant *StartCST = 3693 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3694 if (StartCST == 0) 3695 return RetVal = 0; // Must be a constant. 3696 3697 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3698 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3699 if (PN2 != PN) 3700 return RetVal = 0; // Not derived from same PHI. 3701 3702 // Execute the loop symbolically to determine the exit value. 3703 if (BEs.getActiveBits() >= 32) 3704 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3705 3706 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3707 unsigned IterationNum = 0; 3708 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3709 if (IterationNum == NumIterations) 3710 return RetVal = PHIVal; // Got exit value! 3711 3712 // Compute the value of the PHI node for the next iteration. 3713 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3714 if (NextPHI == PHIVal) 3715 return RetVal = NextPHI; // Stopped evolving! 3716 if (NextPHI == 0) 3717 return 0; // Couldn't evaluate! 3718 PHIVal = NextPHI; 3719 } 3720} 3721 3722/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3723/// constant number of times (the condition evolves only from constants), 3724/// try to evaluate a few iterations of the loop until we get the exit 3725/// condition gets a value of ExitWhen (true or false). If we cannot 3726/// evaluate the trip count of the loop, return getCouldNotCompute(). 3727const SCEV * 3728ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3729 Value *Cond, 3730 bool ExitWhen) { 3731 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3732 if (PN == 0) return getCouldNotCompute(); 3733 3734 // Since the loop is canonicalized, the PHI node must have two entries. One 3735 // entry must be a constant (coming in from outside of the loop), and the 3736 // second must be derived from the same PHI. 3737 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3738 Constant *StartCST = 3739 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3740 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3741 3742 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3743 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3744 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3745 3746 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3747 // the loop symbolically to determine when the condition gets a value of 3748 // "ExitWhen". 3749 unsigned IterationNum = 0; 3750 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3751 for (Constant *PHIVal = StartCST; 3752 IterationNum != MaxIterations; ++IterationNum) { 3753 ConstantInt *CondVal = 3754 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3755 3756 // Couldn't symbolically evaluate. 3757 if (!CondVal) return getCouldNotCompute(); 3758 3759 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3760 ++NumBruteForceTripCountsComputed; 3761 return getConstant(Type::Int32Ty, IterationNum); 3762 } 3763 3764 // Compute the value of the PHI node for the next iteration. 3765 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3766 if (NextPHI == 0 || NextPHI == PHIVal) 3767 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3768 PHIVal = NextPHI; 3769 } 3770 3771 // Too many iterations were needed to evaluate. 3772 return getCouldNotCompute(); 3773} 3774 3775/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3776/// at the specified scope in the program. The L value specifies a loop 3777/// nest to evaluate the expression at, where null is the top-level or a 3778/// specified loop is immediately inside of the loop. 3779/// 3780/// This method can be used to compute the exit value for a variable defined 3781/// in a loop by querying what the value will hold in the parent loop. 3782/// 3783/// In the case that a relevant loop exit value cannot be computed, the 3784/// original value V is returned. 3785const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3786 // FIXME: this should be turned into a virtual method on SCEV! 3787 3788 if (isa<SCEVConstant>(V)) return V; 3789 3790 // If this instruction is evolved from a constant-evolving PHI, compute the 3791 // exit value from the loop without using SCEVs. 3792 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3793 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3794 const Loop *LI = (*this->LI)[I->getParent()]; 3795 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3796 if (PHINode *PN = dyn_cast<PHINode>(I)) 3797 if (PN->getParent() == LI->getHeader()) { 3798 // Okay, there is no closed form solution for the PHI node. Check 3799 // to see if the loop that contains it has a known backedge-taken 3800 // count. If so, we may be able to force computation of the exit 3801 // value. 3802 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3803 if (const SCEVConstant *BTCC = 3804 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3805 // Okay, we know how many times the containing loop executes. If 3806 // this is a constant evolving PHI node, get the final value at 3807 // the specified iteration number. 3808 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3809 BTCC->getValue()->getValue(), 3810 LI); 3811 if (RV) return getSCEV(RV); 3812 } 3813 } 3814 3815 // Okay, this is an expression that we cannot symbolically evaluate 3816 // into a SCEV. Check to see if it's possible to symbolically evaluate 3817 // the arguments into constants, and if so, try to constant propagate the 3818 // result. This is particularly useful for computing loop exit values. 3819 if (CanConstantFold(I)) { 3820 // Check to see if we've folded this instruction at this loop before. 3821 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3822 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3823 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3824 if (!Pair.second) 3825 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3826 3827 std::vector<Constant*> Operands; 3828 Operands.reserve(I->getNumOperands()); 3829 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3830 Value *Op = I->getOperand(i); 3831 if (Constant *C = dyn_cast<Constant>(Op)) { 3832 Operands.push_back(C); 3833 } else { 3834 // If any of the operands is non-constant and if they are 3835 // non-integer and non-pointer, don't even try to analyze them 3836 // with scev techniques. 3837 if (!isSCEVable(Op->getType())) 3838 return V; 3839 3840 const SCEV* OpV = getSCEVAtScope(Op, L); 3841 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3842 Constant *C = SC->getValue(); 3843 if (C->getType() != Op->getType()) 3844 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3845 Op->getType(), 3846 false), 3847 C, Op->getType()); 3848 Operands.push_back(C); 3849 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3850 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3851 if (C->getType() != Op->getType()) 3852 C = 3853 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3854 Op->getType(), 3855 false), 3856 C, Op->getType()); 3857 Operands.push_back(C); 3858 } else 3859 return V; 3860 } else { 3861 return V; 3862 } 3863 } 3864 } 3865 3866 Constant *C; 3867 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3868 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3869 &Operands[0], Operands.size(), 3870 Context); 3871 else 3872 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3873 &Operands[0], Operands.size(), Context); 3874 Pair.first->second = C; 3875 return getSCEV(C); 3876 } 3877 } 3878 3879 // This is some other type of SCEVUnknown, just return it. 3880 return V; 3881 } 3882 3883 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3884 // Avoid performing the look-up in the common case where the specified 3885 // expression has no loop-variant portions. 3886 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3887 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3888 if (OpAtScope != Comm->getOperand(i)) { 3889 // Okay, at least one of these operands is loop variant but might be 3890 // foldable. Build a new instance of the folded commutative expression. 3891 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3892 Comm->op_begin()+i); 3893 NewOps.push_back(OpAtScope); 3894 3895 for (++i; i != e; ++i) { 3896 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3897 NewOps.push_back(OpAtScope); 3898 } 3899 if (isa<SCEVAddExpr>(Comm)) 3900 return getAddExpr(NewOps); 3901 if (isa<SCEVMulExpr>(Comm)) 3902 return getMulExpr(NewOps); 3903 if (isa<SCEVSMaxExpr>(Comm)) 3904 return getSMaxExpr(NewOps); 3905 if (isa<SCEVUMaxExpr>(Comm)) 3906 return getUMaxExpr(NewOps); 3907 assert(0 && "Unknown commutative SCEV type!"); 3908 } 3909 } 3910 // If we got here, all operands are loop invariant. 3911 return Comm; 3912 } 3913 3914 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3915 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 3916 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 3917 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3918 return Div; // must be loop invariant 3919 return getUDivExpr(LHS, RHS); 3920 } 3921 3922 // If this is a loop recurrence for a loop that does not contain L, then we 3923 // are dealing with the final value computed by the loop. 3924 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3925 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3926 // To evaluate this recurrence, we need to know how many times the AddRec 3927 // loop iterates. Compute this now. 3928 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3929 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3930 3931 // Then, evaluate the AddRec. 3932 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3933 } 3934 return AddRec; 3935 } 3936 3937 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3938 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3939 if (Op == Cast->getOperand()) 3940 return Cast; // must be loop invariant 3941 return getZeroExtendExpr(Op, Cast->getType()); 3942 } 3943 3944 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3945 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3946 if (Op == Cast->getOperand()) 3947 return Cast; // must be loop invariant 3948 return getSignExtendExpr(Op, Cast->getType()); 3949 } 3950 3951 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3952 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3953 if (Op == Cast->getOperand()) 3954 return Cast; // must be loop invariant 3955 return getTruncateExpr(Op, Cast->getType()); 3956 } 3957 3958 assert(0 && "Unknown SCEV type!"); 3959 return 0; 3960} 3961 3962/// getSCEVAtScope - This is a convenience function which does 3963/// getSCEVAtScope(getSCEV(V), L). 3964const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3965 return getSCEVAtScope(getSCEV(V), L); 3966} 3967 3968/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3969/// following equation: 3970/// 3971/// A * X = B (mod N) 3972/// 3973/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3974/// A and B isn't important. 3975/// 3976/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3977static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3978 ScalarEvolution &SE) { 3979 uint32_t BW = A.getBitWidth(); 3980 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3981 assert(A != 0 && "A must be non-zero."); 3982 3983 // 1. D = gcd(A, N) 3984 // 3985 // The gcd of A and N may have only one prime factor: 2. The number of 3986 // trailing zeros in A is its multiplicity 3987 uint32_t Mult2 = A.countTrailingZeros(); 3988 // D = 2^Mult2 3989 3990 // 2. Check if B is divisible by D. 3991 // 3992 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3993 // is not less than multiplicity of this prime factor for D. 3994 if (B.countTrailingZeros() < Mult2) 3995 return SE.getCouldNotCompute(); 3996 3997 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3998 // modulo (N / D). 3999 // 4000 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4001 // bit width during computations. 4002 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4003 APInt Mod(BW + 1, 0); 4004 Mod.set(BW - Mult2); // Mod = N / D 4005 APInt I = AD.multiplicativeInverse(Mod); 4006 4007 // 4. Compute the minimum unsigned root of the equation: 4008 // I * (B / D) mod (N / D) 4009 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4010 4011 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4012 // bits. 4013 return SE.getConstant(Result.trunc(BW)); 4014} 4015 4016/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4017/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4018/// might be the same) or two SCEVCouldNotCompute objects. 4019/// 4020static std::pair<const SCEV *,const SCEV *> 4021SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4022 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4023 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4024 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4025 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4026 4027 // We currently can only solve this if the coefficients are constants. 4028 if (!LC || !MC || !NC) { 4029 const SCEV *CNC = SE.getCouldNotCompute(); 4030 return std::make_pair(CNC, CNC); 4031 } 4032 4033 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4034 const APInt &L = LC->getValue()->getValue(); 4035 const APInt &M = MC->getValue()->getValue(); 4036 const APInt &N = NC->getValue()->getValue(); 4037 APInt Two(BitWidth, 2); 4038 APInt Four(BitWidth, 4); 4039 4040 { 4041 using namespace APIntOps; 4042 const APInt& C = L; 4043 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4044 // The B coefficient is M-N/2 4045 APInt B(M); 4046 B -= sdiv(N,Two); 4047 4048 // The A coefficient is N/2 4049 APInt A(N.sdiv(Two)); 4050 4051 // Compute the B^2-4ac term. 4052 APInt SqrtTerm(B); 4053 SqrtTerm *= B; 4054 SqrtTerm -= Four * (A * C); 4055 4056 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4057 // integer value or else APInt::sqrt() will assert. 4058 APInt SqrtVal(SqrtTerm.sqrt()); 4059 4060 // Compute the two solutions for the quadratic formula. 4061 // The divisions must be performed as signed divisions. 4062 APInt NegB(-B); 4063 APInt TwoA( A << 1 ); 4064 if (TwoA.isMinValue()) { 4065 const SCEV *CNC = SE.getCouldNotCompute(); 4066 return std::make_pair(CNC, CNC); 4067 } 4068 4069 LLVMContext *Context = SE.getContext(); 4070 4071 ConstantInt *Solution1 = 4072 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA)); 4073 ConstantInt *Solution2 = 4074 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA)); 4075 4076 return std::make_pair(SE.getConstant(Solution1), 4077 SE.getConstant(Solution2)); 4078 } // end APIntOps namespace 4079} 4080 4081/// HowFarToZero - Return the number of times a backedge comparing the specified 4082/// value to zero will execute. If not computable, return CouldNotCompute. 4083const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4084 // If the value is a constant 4085 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4086 // If the value is already zero, the branch will execute zero times. 4087 if (C->getValue()->isZero()) return C; 4088 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4089 } 4090 4091 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4092 if (!AddRec || AddRec->getLoop() != L) 4093 return getCouldNotCompute(); 4094 4095 if (AddRec->isAffine()) { 4096 // If this is an affine expression, the execution count of this branch is 4097 // the minimum unsigned root of the following equation: 4098 // 4099 // Start + Step*N = 0 (mod 2^BW) 4100 // 4101 // equivalent to: 4102 // 4103 // Step*N = -Start (mod 2^BW) 4104 // 4105 // where BW is the common bit width of Start and Step. 4106 4107 // Get the initial value for the loop. 4108 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4109 L->getParentLoop()); 4110 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4111 L->getParentLoop()); 4112 4113 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4114 // For now we handle only constant steps. 4115 4116 // First, handle unitary steps. 4117 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4118 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4119 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4120 return Start; // N = Start (as unsigned) 4121 4122 // Then, try to solve the above equation provided that Start is constant. 4123 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4124 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4125 -StartC->getValue()->getValue(), 4126 *this); 4127 } 4128 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4129 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4130 // the quadratic equation to solve it. 4131 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4132 *this); 4133 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4134 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4135 if (R1) { 4136#if 0 4137 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4138 << " sol#2: " << *R2 << "\n"; 4139#endif 4140 // Pick the smallest positive root value. 4141 if (ConstantInt *CB = 4142 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT, 4143 R1->getValue(), R2->getValue()))) { 4144 if (CB->getZExtValue() == false) 4145 std::swap(R1, R2); // R1 is the minimum root now. 4146 4147 // We can only use this value if the chrec ends up with an exact zero 4148 // value at this index. When solving for "X*X != 5", for example, we 4149 // should not accept a root of 2. 4150 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4151 if (Val->isZero()) 4152 return R1; // We found a quadratic root! 4153 } 4154 } 4155 } 4156 4157 return getCouldNotCompute(); 4158} 4159 4160/// HowFarToNonZero - Return the number of times a backedge checking the 4161/// specified value for nonzero will execute. If not computable, return 4162/// CouldNotCompute 4163const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4164 // Loops that look like: while (X == 0) are very strange indeed. We don't 4165 // handle them yet except for the trivial case. This could be expanded in the 4166 // future as needed. 4167 4168 // If the value is a constant, check to see if it is known to be non-zero 4169 // already. If so, the backedge will execute zero times. 4170 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4171 if (!C->getValue()->isNullValue()) 4172 return getIntegerSCEV(0, C->getType()); 4173 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4174 } 4175 4176 // We could implement others, but I really doubt anyone writes loops like 4177 // this, and if they did, they would already be constant folded. 4178 return getCouldNotCompute(); 4179} 4180 4181/// getLoopPredecessor - If the given loop's header has exactly one unique 4182/// predecessor outside the loop, return it. Otherwise return null. 4183/// 4184BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4185 BasicBlock *Header = L->getHeader(); 4186 BasicBlock *Pred = 0; 4187 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4188 PI != E; ++PI) 4189 if (!L->contains(*PI)) { 4190 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4191 Pred = *PI; 4192 } 4193 return Pred; 4194} 4195 4196/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4197/// (which may not be an immediate predecessor) which has exactly one 4198/// successor from which BB is reachable, or null if no such block is 4199/// found. 4200/// 4201BasicBlock * 4202ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4203 // If the block has a unique predecessor, then there is no path from the 4204 // predecessor to the block that does not go through the direct edge 4205 // from the predecessor to the block. 4206 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4207 return Pred; 4208 4209 // A loop's header is defined to be a block that dominates the loop. 4210 // If the header has a unique predecessor outside the loop, it must be 4211 // a block that has exactly one successor that can reach the loop. 4212 if (Loop *L = LI->getLoopFor(BB)) 4213 return getLoopPredecessor(L); 4214 4215 return 0; 4216} 4217 4218/// HasSameValue - SCEV structural equivalence is usually sufficient for 4219/// testing whether two expressions are equal, however for the purposes of 4220/// looking for a condition guarding a loop, it can be useful to be a little 4221/// more general, since a front-end may have replicated the controlling 4222/// expression. 4223/// 4224static bool HasSameValue(const SCEV *A, const SCEV *B) { 4225 // Quick check to see if they are the same SCEV. 4226 if (A == B) return true; 4227 4228 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4229 // two different instructions with the same value. Check for this case. 4230 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4231 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4232 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4233 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4234 if (AI->isIdenticalTo(BI)) 4235 return true; 4236 4237 // Otherwise assume they may have a different value. 4238 return false; 4239} 4240 4241bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4242 return getSignedRange(S).getSignedMax().isNegative(); 4243} 4244 4245bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4246 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4247} 4248 4249bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4250 return !getSignedRange(S).getSignedMin().isNegative(); 4251} 4252 4253bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4254 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4255} 4256 4257bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4258 return isKnownNegative(S) || isKnownPositive(S); 4259} 4260 4261bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4262 const SCEV *LHS, const SCEV *RHS) { 4263 4264 if (HasSameValue(LHS, RHS)) 4265 return ICmpInst::isTrueWhenEqual(Pred); 4266 4267 switch (Pred) { 4268 default: 4269 assert(0 && "Unexpected ICmpInst::Predicate value!"); 4270 break; 4271 case ICmpInst::ICMP_SGT: 4272 Pred = ICmpInst::ICMP_SLT; 4273 std::swap(LHS, RHS); 4274 case ICmpInst::ICMP_SLT: { 4275 ConstantRange LHSRange = getSignedRange(LHS); 4276 ConstantRange RHSRange = getSignedRange(RHS); 4277 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4278 return true; 4279 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4280 return false; 4281 4282 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4283 ConstantRange DiffRange = getUnsignedRange(Diff); 4284 if (isKnownNegative(Diff)) { 4285 if (DiffRange.getUnsignedMax().ult(LHSRange.getUnsignedMin())) 4286 return true; 4287 if (DiffRange.getUnsignedMin().uge(LHSRange.getUnsignedMax())) 4288 return false; 4289 } else if (isKnownPositive(Diff)) { 4290 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4291 return true; 4292 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4293 return false; 4294 } 4295 break; 4296 } 4297 case ICmpInst::ICMP_SGE: 4298 Pred = ICmpInst::ICMP_SLE; 4299 std::swap(LHS, RHS); 4300 case ICmpInst::ICMP_SLE: { 4301 ConstantRange LHSRange = getSignedRange(LHS); 4302 ConstantRange RHSRange = getSignedRange(RHS); 4303 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4304 return true; 4305 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4306 return false; 4307 4308 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4309 ConstantRange DiffRange = getUnsignedRange(Diff); 4310 if (isKnownNonPositive(Diff)) { 4311 if (DiffRange.getUnsignedMax().ule(LHSRange.getUnsignedMin())) 4312 return true; 4313 if (DiffRange.getUnsignedMin().ugt(LHSRange.getUnsignedMax())) 4314 return false; 4315 } else if (isKnownNonNegative(Diff)) { 4316 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4317 return true; 4318 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4319 return false; 4320 } 4321 break; 4322 } 4323 case ICmpInst::ICMP_UGT: 4324 Pred = ICmpInst::ICMP_ULT; 4325 std::swap(LHS, RHS); 4326 case ICmpInst::ICMP_ULT: { 4327 ConstantRange LHSRange = getUnsignedRange(LHS); 4328 ConstantRange RHSRange = getUnsignedRange(RHS); 4329 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4330 return true; 4331 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4332 return false; 4333 4334 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4335 ConstantRange DiffRange = getUnsignedRange(Diff); 4336 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4337 return true; 4338 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4339 return false; 4340 break; 4341 } 4342 case ICmpInst::ICMP_UGE: 4343 Pred = ICmpInst::ICMP_ULE; 4344 std::swap(LHS, RHS); 4345 case ICmpInst::ICMP_ULE: { 4346 ConstantRange LHSRange = getUnsignedRange(LHS); 4347 ConstantRange RHSRange = getUnsignedRange(RHS); 4348 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4349 return true; 4350 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4351 return false; 4352 4353 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4354 ConstantRange DiffRange = getUnsignedRange(Diff); 4355 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4356 return true; 4357 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4358 return false; 4359 break; 4360 } 4361 case ICmpInst::ICMP_NE: { 4362 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4363 return true; 4364 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4365 return true; 4366 4367 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4368 if (isKnownNonZero(Diff)) 4369 return true; 4370 break; 4371 } 4372 case ICmpInst::ICMP_EQ: 4373 break; 4374 } 4375 return false; 4376} 4377 4378/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4379/// protected by a conditional between LHS and RHS. This is used to 4380/// to eliminate casts. 4381bool 4382ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4383 ICmpInst::Predicate Pred, 4384 const SCEV *LHS, const SCEV *RHS) { 4385 // Interpret a null as meaning no loop, where there is obviously no guard 4386 // (interprocedural conditions notwithstanding). 4387 if (!L) return true; 4388 4389 BasicBlock *Latch = L->getLoopLatch(); 4390 if (!Latch) 4391 return false; 4392 4393 BranchInst *LoopContinuePredicate = 4394 dyn_cast<BranchInst>(Latch->getTerminator()); 4395 if (!LoopContinuePredicate || 4396 LoopContinuePredicate->isUnconditional()) 4397 return false; 4398 4399 return 4400 isNecessaryCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4401 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4402} 4403 4404/// isLoopGuardedByCond - Test whether entry to the loop is protected 4405/// by a conditional between LHS and RHS. This is used to help avoid max 4406/// expressions in loop trip counts, and to eliminate casts. 4407bool 4408ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4409 ICmpInst::Predicate Pred, 4410 const SCEV *LHS, const SCEV *RHS) { 4411 // Interpret a null as meaning no loop, where there is obviously no guard 4412 // (interprocedural conditions notwithstanding). 4413 if (!L) return false; 4414 4415 BasicBlock *Predecessor = getLoopPredecessor(L); 4416 BasicBlock *PredecessorDest = L->getHeader(); 4417 4418 // Starting at the loop predecessor, climb up the predecessor chain, as long 4419 // as there are predecessors that can be found that have unique successors 4420 // leading to the original header. 4421 for (; Predecessor; 4422 PredecessorDest = Predecessor, 4423 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4424 4425 BranchInst *LoopEntryPredicate = 4426 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4427 if (!LoopEntryPredicate || 4428 LoopEntryPredicate->isUnconditional()) 4429 continue; 4430 4431 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4432 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4433 return true; 4434 } 4435 4436 return false; 4437} 4438 4439/// isNecessaryCond - Test whether the condition described by Pred, LHS, 4440/// and RHS is a necessary condition for the given Cond value to evaluate 4441/// to true. 4442bool ScalarEvolution::isNecessaryCond(Value *CondValue, 4443 ICmpInst::Predicate Pred, 4444 const SCEV *LHS, const SCEV *RHS, 4445 bool Inverse) { 4446 // Recursivly handle And and Or conditions. 4447 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4448 if (BO->getOpcode() == Instruction::And) { 4449 if (!Inverse) 4450 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4451 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4452 } else if (BO->getOpcode() == Instruction::Or) { 4453 if (Inverse) 4454 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4455 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4456 } 4457 } 4458 4459 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4460 if (!ICI) return false; 4461 4462 // Now that we found a conditional branch that dominates the loop, check to 4463 // see if it is the comparison we are looking for. 4464 Value *PreCondLHS = ICI->getOperand(0); 4465 Value *PreCondRHS = ICI->getOperand(1); 4466 ICmpInst::Predicate FoundPred; 4467 if (Inverse) 4468 FoundPred = ICI->getInversePredicate(); 4469 else 4470 FoundPred = ICI->getPredicate(); 4471 4472 if (FoundPred == Pred) 4473 ; // An exact match. 4474 else if (!ICmpInst::isTrueWhenEqual(FoundPred) && Pred == ICmpInst::ICMP_NE) { 4475 // The actual condition is beyond sufficient. 4476 FoundPred = ICmpInst::ICMP_NE; 4477 // NE is symmetric but the original comparison may not be. Swap 4478 // the operands if necessary so that they match below. 4479 if (isa<SCEVConstant>(LHS)) 4480 std::swap(PreCondLHS, PreCondRHS); 4481 } else 4482 // Check a few special cases. 4483 switch (FoundPred) { 4484 case ICmpInst::ICMP_UGT: 4485 if (Pred == ICmpInst::ICMP_ULT) { 4486 std::swap(PreCondLHS, PreCondRHS); 4487 FoundPred = ICmpInst::ICMP_ULT; 4488 break; 4489 } 4490 return false; 4491 case ICmpInst::ICMP_SGT: 4492 if (Pred == ICmpInst::ICMP_SLT) { 4493 std::swap(PreCondLHS, PreCondRHS); 4494 FoundPred = ICmpInst::ICMP_SLT; 4495 break; 4496 } 4497 return false; 4498 case ICmpInst::ICMP_NE: 4499 // Expressions like (x >u 0) are often canonicalized to (x != 0), 4500 // so check for this case by checking if the NE is comparing against 4501 // a minimum or maximum constant. 4502 if (!ICmpInst::isTrueWhenEqual(Pred)) 4503 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(RHS)) { 4504 const APInt &A = C->getValue()->getValue(); 4505 switch (Pred) { 4506 case ICmpInst::ICMP_SLT: 4507 if (A.isMaxSignedValue()) break; 4508 return false; 4509 case ICmpInst::ICMP_SGT: 4510 if (A.isMinSignedValue()) break; 4511 return false; 4512 case ICmpInst::ICMP_ULT: 4513 if (A.isMaxValue()) break; 4514 return false; 4515 case ICmpInst::ICMP_UGT: 4516 if (A.isMinValue()) break; 4517 return false; 4518 default: 4519 return false; 4520 } 4521 FoundPred = Pred; 4522 // NE is symmetric but the original comparison may not be. Swap 4523 // the operands if necessary so that they match below. 4524 if (isa<SCEVConstant>(LHS)) 4525 std::swap(PreCondLHS, PreCondRHS); 4526 break; 4527 } 4528 return false; 4529 default: 4530 // We weren't able to reconcile the condition. 4531 return false; 4532 } 4533 4534 assert(Pred == FoundPred && "Conditions were not reconciled!"); 4535 4536 const SCEV *FoundLHS = getSCEV(PreCondLHS); 4537 const SCEV *FoundRHS = getSCEV(PreCondRHS); 4538 4539 // Balance the types. 4540 if (getTypeSizeInBits(LHS->getType()) > 4541 getTypeSizeInBits(FoundLHS->getType())) { 4542 if (CmpInst::isSigned(Pred)) { 4543 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4544 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4545 } else { 4546 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4547 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4548 } 4549 } else if (getTypeSizeInBits(LHS->getType()) < 4550 getTypeSizeInBits(FoundLHS->getType())) { 4551 // TODO: Cast LHS and RHS to FoundLHS' type. Currently this can 4552 // result in infinite recursion since the code to construct 4553 // cast expressions may want to know things about the loop 4554 // iteration in order to do simplifications. 4555 return false; 4556 } 4557 4558 return isNecessaryCondOperands(Pred, LHS, RHS, 4559 FoundLHS, FoundRHS) || 4560 // ~x < ~y --> x > y 4561 isNecessaryCondOperands(Pred, LHS, RHS, 4562 getNotSCEV(FoundRHS), getNotSCEV(FoundLHS)); 4563} 4564 4565/// isNecessaryCondOperands - Test whether the condition described by Pred, 4566/// LHS, and RHS is a necessary condition for the condition described by 4567/// Pred, FoundLHS, and FoundRHS to evaluate to true. 4568bool 4569ScalarEvolution::isNecessaryCondOperands(ICmpInst::Predicate Pred, 4570 const SCEV *LHS, const SCEV *RHS, 4571 const SCEV *FoundLHS, 4572 const SCEV *FoundRHS) { 4573 switch (Pred) { 4574 default: break; 4575 case ICmpInst::ICMP_SLT: 4576 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4577 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4578 return true; 4579 break; 4580 case ICmpInst::ICMP_SGT: 4581 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4582 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4583 return true; 4584 break; 4585 case ICmpInst::ICMP_ULT: 4586 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4587 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4588 return true; 4589 break; 4590 case ICmpInst::ICMP_UGT: 4591 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4592 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4593 return true; 4594 break; 4595 } 4596 4597 return false; 4598} 4599 4600/// getBECount - Subtract the end and start values and divide by the step, 4601/// rounding up, to get the number of times the backedge is executed. Return 4602/// CouldNotCompute if an intermediate computation overflows. 4603const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4604 const SCEV *End, 4605 const SCEV *Step) { 4606 const Type *Ty = Start->getType(); 4607 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4608 const SCEV *Diff = getMinusSCEV(End, Start); 4609 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4610 4611 // Add an adjustment to the difference between End and Start so that 4612 // the division will effectively round up. 4613 const SCEV *Add = getAddExpr(Diff, RoundUp); 4614 4615 // Check Add for unsigned overflow. 4616 // TODO: More sophisticated things could be done here. 4617 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1); 4618 const SCEV *OperandExtendedAdd = 4619 getAddExpr(getZeroExtendExpr(Diff, WideTy), 4620 getZeroExtendExpr(RoundUp, WideTy)); 4621 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4622 return getCouldNotCompute(); 4623 4624 return getUDivExpr(Add, Step); 4625} 4626 4627/// HowManyLessThans - Return the number of times a backedge containing the 4628/// specified less-than comparison will execute. If not computable, return 4629/// CouldNotCompute. 4630ScalarEvolution::BackedgeTakenInfo 4631ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4632 const Loop *L, bool isSigned) { 4633 // Only handle: "ADDREC < LoopInvariant". 4634 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4635 4636 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4637 if (!AddRec || AddRec->getLoop() != L) 4638 return getCouldNotCompute(); 4639 4640 if (AddRec->isAffine()) { 4641 // FORNOW: We only support unit strides. 4642 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4643 const SCEV *Step = AddRec->getStepRecurrence(*this); 4644 4645 // TODO: handle non-constant strides. 4646 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4647 if (!CStep || CStep->isZero()) 4648 return getCouldNotCompute(); 4649 if (CStep->isOne()) { 4650 // With unit stride, the iteration never steps past the limit value. 4651 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4652 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4653 // Test whether a positive iteration iteration can step past the limit 4654 // value and past the maximum value for its type in a single step. 4655 if (isSigned) { 4656 APInt Max = APInt::getSignedMaxValue(BitWidth); 4657 if ((Max - CStep->getValue()->getValue()) 4658 .slt(CLimit->getValue()->getValue())) 4659 return getCouldNotCompute(); 4660 } else { 4661 APInt Max = APInt::getMaxValue(BitWidth); 4662 if ((Max - CStep->getValue()->getValue()) 4663 .ult(CLimit->getValue()->getValue())) 4664 return getCouldNotCompute(); 4665 } 4666 } else 4667 // TODO: handle non-constant limit values below. 4668 return getCouldNotCompute(); 4669 } else 4670 // TODO: handle negative strides below. 4671 return getCouldNotCompute(); 4672 4673 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4674 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4675 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4676 // treat m-n as signed nor unsigned due to overflow possibility. 4677 4678 // First, we get the value of the LHS in the first iteration: n 4679 const SCEV *Start = AddRec->getOperand(0); 4680 4681 // Determine the minimum constant start value. 4682 const SCEV *MinStart = getConstant(isSigned ? 4683 getSignedRange(Start).getSignedMin() : 4684 getUnsignedRange(Start).getUnsignedMin()); 4685 4686 // If we know that the condition is true in order to enter the loop, 4687 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4688 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4689 // the division must round up. 4690 const SCEV *End = RHS; 4691 if (!isLoopGuardedByCond(L, 4692 isSigned ? ICmpInst::ICMP_SLT : 4693 ICmpInst::ICMP_ULT, 4694 getMinusSCEV(Start, Step), RHS)) 4695 End = isSigned ? getSMaxExpr(RHS, Start) 4696 : getUMaxExpr(RHS, Start); 4697 4698 // Determine the maximum constant end value. 4699 const SCEV *MaxEnd = getConstant(isSigned ? 4700 getSignedRange(End).getSignedMax() : 4701 getUnsignedRange(End).getUnsignedMax()); 4702 4703 // Finally, we subtract these two values and divide, rounding up, to get 4704 // the number of times the backedge is executed. 4705 const SCEV *BECount = getBECount(Start, End, Step); 4706 4707 // The maximum backedge count is similar, except using the minimum start 4708 // value and the maximum end value. 4709 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step); 4710 4711 return BackedgeTakenInfo(BECount, MaxBECount); 4712 } 4713 4714 return getCouldNotCompute(); 4715} 4716 4717/// getNumIterationsInRange - Return the number of iterations of this loop that 4718/// produce values in the specified constant range. Another way of looking at 4719/// this is that it returns the first iteration number where the value is not in 4720/// the condition, thus computing the exit count. If the iteration count can't 4721/// be computed, an instance of SCEVCouldNotCompute is returned. 4722const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4723 ScalarEvolution &SE) const { 4724 if (Range.isFullSet()) // Infinite loop. 4725 return SE.getCouldNotCompute(); 4726 4727 // If the start is a non-zero constant, shift the range to simplify things. 4728 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4729 if (!SC->getValue()->isZero()) { 4730 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4731 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4732 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4733 if (const SCEVAddRecExpr *ShiftedAddRec = 4734 dyn_cast<SCEVAddRecExpr>(Shifted)) 4735 return ShiftedAddRec->getNumIterationsInRange( 4736 Range.subtract(SC->getValue()->getValue()), SE); 4737 // This is strange and shouldn't happen. 4738 return SE.getCouldNotCompute(); 4739 } 4740 4741 // The only time we can solve this is when we have all constant indices. 4742 // Otherwise, we cannot determine the overflow conditions. 4743 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4744 if (!isa<SCEVConstant>(getOperand(i))) 4745 return SE.getCouldNotCompute(); 4746 4747 4748 // Okay at this point we know that all elements of the chrec are constants and 4749 // that the start element is zero. 4750 4751 // First check to see if the range contains zero. If not, the first 4752 // iteration exits. 4753 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4754 if (!Range.contains(APInt(BitWidth, 0))) 4755 return SE.getIntegerSCEV(0, getType()); 4756 4757 if (isAffine()) { 4758 // If this is an affine expression then we have this situation: 4759 // Solve {0,+,A} in Range === Ax in Range 4760 4761 // We know that zero is in the range. If A is positive then we know that 4762 // the upper value of the range must be the first possible exit value. 4763 // If A is negative then the lower of the range is the last possible loop 4764 // value. Also note that we already checked for a full range. 4765 APInt One(BitWidth,1); 4766 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4767 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4768 4769 // The exit value should be (End+A)/A. 4770 APInt ExitVal = (End + A).udiv(A); 4771 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal); 4772 4773 // Evaluate at the exit value. If we really did fall out of the valid 4774 // range, then we computed our trip count, otherwise wrap around or other 4775 // things must have happened. 4776 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4777 if (Range.contains(Val->getValue())) 4778 return SE.getCouldNotCompute(); // Something strange happened 4779 4780 // Ensure that the previous value is in the range. This is a sanity check. 4781 assert(Range.contains( 4782 EvaluateConstantChrecAtConstant(this, 4783 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) && 4784 "Linear scev computation is off in a bad way!"); 4785 return SE.getConstant(ExitValue); 4786 } else if (isQuadratic()) { 4787 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4788 // quadratic equation to solve it. To do this, we must frame our problem in 4789 // terms of figuring out when zero is crossed, instead of when 4790 // Range.getUpper() is crossed. 4791 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 4792 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4793 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4794 4795 // Next, solve the constructed addrec 4796 std::pair<const SCEV *,const SCEV *> Roots = 4797 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4798 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4799 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4800 if (R1) { 4801 // Pick the smallest positive root value. 4802 if (ConstantInt *CB = 4803 dyn_cast<ConstantInt>( 4804 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT, 4805 R1->getValue(), R2->getValue()))) { 4806 if (CB->getZExtValue() == false) 4807 std::swap(R1, R2); // R1 is the minimum root now. 4808 4809 // Make sure the root is not off by one. The returned iteration should 4810 // not be in the range, but the previous one should be. When solving 4811 // for "X*X < 5", for example, we should not return a root of 2. 4812 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4813 R1->getValue(), 4814 SE); 4815 if (Range.contains(R1Val->getValue())) { 4816 // The next iteration must be out of the range... 4817 ConstantInt *NextVal = 4818 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1); 4819 4820 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4821 if (!Range.contains(R1Val->getValue())) 4822 return SE.getConstant(NextVal); 4823 return SE.getCouldNotCompute(); // Something strange happened 4824 } 4825 4826 // If R1 was not in the range, then it is a good return value. Make 4827 // sure that R1-1 WAS in the range though, just in case. 4828 ConstantInt *NextVal = 4829 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1); 4830 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4831 if (Range.contains(R1Val->getValue())) 4832 return R1; 4833 return SE.getCouldNotCompute(); // Something strange happened 4834 } 4835 } 4836 } 4837 4838 return SE.getCouldNotCompute(); 4839} 4840 4841 4842 4843//===----------------------------------------------------------------------===// 4844// SCEVCallbackVH Class Implementation 4845//===----------------------------------------------------------------------===// 4846 4847void ScalarEvolution::SCEVCallbackVH::deleted() { 4848 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4849 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4850 SE->ConstantEvolutionLoopExitValue.erase(PN); 4851 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4852 SE->ValuesAtScopes.erase(I); 4853 SE->Scalars.erase(getValPtr()); 4854 // this now dangles! 4855} 4856 4857void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4858 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4859 4860 // Forget all the expressions associated with users of the old value, 4861 // so that future queries will recompute the expressions using the new 4862 // value. 4863 SmallVector<User *, 16> Worklist; 4864 Value *Old = getValPtr(); 4865 bool DeleteOld = false; 4866 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4867 UI != UE; ++UI) 4868 Worklist.push_back(*UI); 4869 while (!Worklist.empty()) { 4870 User *U = Worklist.pop_back_val(); 4871 // Deleting the Old value will cause this to dangle. Postpone 4872 // that until everything else is done. 4873 if (U == Old) { 4874 DeleteOld = true; 4875 continue; 4876 } 4877 if (PHINode *PN = dyn_cast<PHINode>(U)) 4878 SE->ConstantEvolutionLoopExitValue.erase(PN); 4879 if (Instruction *I = dyn_cast<Instruction>(U)) 4880 SE->ValuesAtScopes.erase(I); 4881 if (SE->Scalars.erase(U)) 4882 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4883 UI != UE; ++UI) 4884 Worklist.push_back(*UI); 4885 } 4886 if (DeleteOld) { 4887 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4888 SE->ConstantEvolutionLoopExitValue.erase(PN); 4889 if (Instruction *I = dyn_cast<Instruction>(Old)) 4890 SE->ValuesAtScopes.erase(I); 4891 SE->Scalars.erase(Old); 4892 // this now dangles! 4893 } 4894 // this may dangle! 4895} 4896 4897ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4898 : CallbackVH(V), SE(se) {} 4899 4900//===----------------------------------------------------------------------===// 4901// ScalarEvolution Class Implementation 4902//===----------------------------------------------------------------------===// 4903 4904ScalarEvolution::ScalarEvolution() 4905 : FunctionPass(&ID) { 4906} 4907 4908bool ScalarEvolution::runOnFunction(Function &F) { 4909 this->F = &F; 4910 LI = &getAnalysis<LoopInfo>(); 4911 TD = getAnalysisIfAvailable<TargetData>(); 4912 return false; 4913} 4914 4915void ScalarEvolution::releaseMemory() { 4916 Scalars.clear(); 4917 BackedgeTakenCounts.clear(); 4918 ConstantEvolutionLoopExitValue.clear(); 4919 ValuesAtScopes.clear(); 4920 UniqueSCEVs.clear(); 4921 SCEVAllocator.Reset(); 4922} 4923 4924void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4925 AU.setPreservesAll(); 4926 AU.addRequiredTransitive<LoopInfo>(); 4927} 4928 4929bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4930 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4931} 4932 4933static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4934 const Loop *L) { 4935 // Print all inner loops first 4936 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4937 PrintLoopInfo(OS, SE, *I); 4938 4939 OS << "Loop " << L->getHeader()->getName() << ": "; 4940 4941 SmallVector<BasicBlock*, 8> ExitBlocks; 4942 L->getExitBlocks(ExitBlocks); 4943 if (ExitBlocks.size() != 1) 4944 OS << "<multiple exits> "; 4945 4946 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4947 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4948 } else { 4949 OS << "Unpredictable backedge-taken count. "; 4950 } 4951 4952 OS << "\n"; 4953 OS << "Loop " << L->getHeader()->getName() << ": "; 4954 4955 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 4956 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 4957 } else { 4958 OS << "Unpredictable max backedge-taken count. "; 4959 } 4960 4961 OS << "\n"; 4962} 4963 4964void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4965 // ScalarEvolution's implementaiton of the print method is to print 4966 // out SCEV values of all instructions that are interesting. Doing 4967 // this potentially causes it to create new SCEV objects though, 4968 // which technically conflicts with the const qualifier. This isn't 4969 // observable from outside the class though (the hasSCEV function 4970 // notwithstanding), so casting away the const isn't dangerous. 4971 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4972 4973 OS << "Classifying expressions for: " << F->getName() << "\n"; 4974 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4975 if (isSCEVable(I->getType())) { 4976 OS << *I; 4977 OS << " --> "; 4978 const SCEV *SV = SE.getSCEV(&*I); 4979 SV->print(OS); 4980 4981 const Loop *L = LI->getLoopFor((*I).getParent()); 4982 4983 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 4984 if (AtUse != SV) { 4985 OS << " --> "; 4986 AtUse->print(OS); 4987 } 4988 4989 if (L) { 4990 OS << "\t\t" "Exits: "; 4991 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4992 if (!ExitValue->isLoopInvariant(L)) { 4993 OS << "<<Unknown>>"; 4994 } else { 4995 OS << *ExitValue; 4996 } 4997 } 4998 4999 OS << "\n"; 5000 } 5001 5002 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 5003 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5004 PrintLoopInfo(OS, &SE, *I); 5005} 5006 5007void ScalarEvolution::print(std::ostream &o, const Module *M) const { 5008 raw_os_ostream OS(o); 5009 print(OS, M); 5010} 5011