ScalarEvolution.cpp revision ba70188f895647f0a56bd69717ec3a0f7ed717df
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/ErrorHandling.h" 79#include "llvm/Support/GetElementPtrTypeIterator.h" 80#include "llvm/Support/InstIterator.h" 81#include "llvm/Support/MathExtras.h" 82#include "llvm/Support/raw_ostream.h" 83#include "llvm/ADT/Statistic.h" 84#include "llvm/ADT/STLExtras.h" 85#include "llvm/ADT/SmallPtrSet.h" 86#include <algorithm> 87using namespace llvm; 88 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98static cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant " 102 "derived loop"), 103 cl::init(100)); 104 105static RegisterPass<ScalarEvolution> 106R("scalar-evolution", "Scalar Evolution Analysis", false, true); 107char ScalarEvolution::ID = 0; 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116 117SCEV::~SCEV() {} 118 119void SCEV::dump() const { 120 print(errs()); 121 errs() << '\n'; 122} 123 124void SCEV::print(std::ostream &o) const { 125 raw_os_ostream OS(o); 126 print(OS); 127} 128 129bool SCEV::isZero() const { 130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 131 return SC->getValue()->isZero(); 132 return false; 133} 134 135bool SCEV::isOne() const { 136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 137 return SC->getValue()->isOne(); 138 return false; 139} 140 141bool SCEV::isAllOnesValue() const { 142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 143 return SC->getValue()->isAllOnesValue(); 144 return false; 145} 146 147SCEVCouldNotCompute::SCEVCouldNotCompute() : 148 SCEV(FoldingSetNodeID(), scCouldNotCompute) {} 149 150bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 151 LLVM_UNREACHABLE("Attempt to use a SCEVCouldNotCompute object!"); 152 return false; 153} 154 155const Type *SCEVCouldNotCompute::getType() const { 156 LLVM_UNREACHABLE("Attempt to use a SCEVCouldNotCompute object!"); 157 return 0; 158} 159 160bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 161 LLVM_UNREACHABLE("Attempt to use a SCEVCouldNotCompute object!"); 162 return false; 163} 164 165const SCEV * 166SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete( 167 const SCEV *Sym, 168 const SCEV *Conc, 169 ScalarEvolution &SE) const { 170 return this; 171} 172 173void SCEVCouldNotCompute::print(raw_ostream &OS) const { 174 OS << "***COULDNOTCOMPUTE***"; 175} 176 177bool SCEVCouldNotCompute::classof(const SCEV *S) { 178 return S->getSCEVType() == scCouldNotCompute; 179} 180 181const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 182 FoldingSetNodeID ID; 183 ID.AddInteger(scConstant); 184 ID.AddPointer(V); 185 void *IP = 0; 186 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 187 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 188 new (S) SCEVConstant(ID, V); 189 UniqueSCEVs.InsertNode(S, IP); 190 return S; 191} 192 193const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 194 return getConstant(ConstantInt::get(Val)); 195} 196 197const SCEV * 198ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 199 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 200} 201 202const Type *SCEVConstant::getType() const { return V->getType(); } 203 204void SCEVConstant::print(raw_ostream &OS) const { 205 WriteAsOperand(OS, V, false); 206} 207 208SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 209 unsigned SCEVTy, const SCEV *op, const Type *ty) 210 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 211 212bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 213 return Op->dominates(BB, DT); 214} 215 216SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 217 const SCEV *op, const Type *ty) 218 : SCEVCastExpr(ID, scTruncate, op, ty) { 219 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 220 (Ty->isInteger() || isa<PointerType>(Ty)) && 221 "Cannot truncate non-integer value!"); 222} 223 224void SCEVTruncateExpr::print(raw_ostream &OS) const { 225 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 226} 227 228SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 229 const SCEV *op, const Type *ty) 230 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 231 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 232 (Ty->isInteger() || isa<PointerType>(Ty)) && 233 "Cannot zero extend non-integer value!"); 234} 235 236void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 237 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 238} 239 240SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 241 const SCEV *op, const Type *ty) 242 : SCEVCastExpr(ID, scSignExtend, op, ty) { 243 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 244 (Ty->isInteger() || isa<PointerType>(Ty)) && 245 "Cannot sign extend non-integer value!"); 246} 247 248void SCEVSignExtendExpr::print(raw_ostream &OS) const { 249 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 250} 251 252void SCEVCommutativeExpr::print(raw_ostream &OS) const { 253 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 254 const char *OpStr = getOperationStr(); 255 OS << "(" << *Operands[0]; 256 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 257 OS << OpStr << *Operands[i]; 258 OS << ")"; 259} 260 261const SCEV * 262SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete( 263 const SCEV *Sym, 264 const SCEV *Conc, 265 ScalarEvolution &SE) const { 266 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 267 const SCEV *H = 268 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 269 if (H != getOperand(i)) { 270 SmallVector<const SCEV *, 8> NewOps; 271 NewOps.reserve(getNumOperands()); 272 for (unsigned j = 0; j != i; ++j) 273 NewOps.push_back(getOperand(j)); 274 NewOps.push_back(H); 275 for (++i; i != e; ++i) 276 NewOps.push_back(getOperand(i)-> 277 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 278 279 if (isa<SCEVAddExpr>(this)) 280 return SE.getAddExpr(NewOps); 281 else if (isa<SCEVMulExpr>(this)) 282 return SE.getMulExpr(NewOps); 283 else if (isa<SCEVSMaxExpr>(this)) 284 return SE.getSMaxExpr(NewOps); 285 else if (isa<SCEVUMaxExpr>(this)) 286 return SE.getUMaxExpr(NewOps); 287 else 288 LLVM_UNREACHABLE("Unknown commutative expr!"); 289 } 290 } 291 return this; 292} 293 294bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 295 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 296 if (!getOperand(i)->dominates(BB, DT)) 297 return false; 298 } 299 return true; 300} 301 302bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 303 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 304} 305 306void SCEVUDivExpr::print(raw_ostream &OS) const { 307 OS << "(" << *LHS << " /u " << *RHS << ")"; 308} 309 310const Type *SCEVUDivExpr::getType() const { 311 // In most cases the types of LHS and RHS will be the same, but in some 312 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 313 // depend on the type for correctness, but handling types carefully can 314 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 315 // a pointer type than the RHS, so use the RHS' type here. 316 return RHS->getType(); 317} 318 319const SCEV * 320SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym, 321 const SCEV *Conc, 322 ScalarEvolution &SE) const { 323 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 324 const SCEV *H = 325 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE); 326 if (H != getOperand(i)) { 327 SmallVector<const SCEV *, 8> NewOps; 328 NewOps.reserve(getNumOperands()); 329 for (unsigned j = 0; j != i; ++j) 330 NewOps.push_back(getOperand(j)); 331 NewOps.push_back(H); 332 for (++i; i != e; ++i) 333 NewOps.push_back(getOperand(i)-> 334 replaceSymbolicValuesWithConcrete(Sym, Conc, SE)); 335 336 return SE.getAddRecExpr(NewOps, L); 337 } 338 } 339 return this; 340} 341 342 343bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 344 // Add recurrences are never invariant in the function-body (null loop). 345 if (!QueryLoop) 346 return false; 347 348 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 349 if (QueryLoop->contains(L->getHeader())) 350 return false; 351 352 // This recurrence is variant w.r.t. QueryLoop if any of its operands 353 // are variant. 354 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 355 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 356 return false; 357 358 // Otherwise it's loop-invariant. 359 return true; 360} 361 362void SCEVAddRecExpr::print(raw_ostream &OS) const { 363 OS << "{" << *Operands[0]; 364 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 365 OS << ",+," << *Operands[i]; 366 OS << "}<" << L->getHeader()->getName() + ">"; 367} 368 369bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 370 // All non-instruction values are loop invariant. All instructions are loop 371 // invariant if they are not contained in the specified loop. 372 // Instructions are never considered invariant in the function body 373 // (null loop) because they are defined within the "loop". 374 if (Instruction *I = dyn_cast<Instruction>(V)) 375 return L && !L->contains(I->getParent()); 376 return true; 377} 378 379bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 380 if (Instruction *I = dyn_cast<Instruction>(getValue())) 381 return DT->dominates(I->getParent(), BB); 382 return true; 383} 384 385const Type *SCEVUnknown::getType() const { 386 return V->getType(); 387} 388 389void SCEVUnknown::print(raw_ostream &OS) const { 390 WriteAsOperand(OS, V, false); 391} 392 393//===----------------------------------------------------------------------===// 394// SCEV Utilities 395//===----------------------------------------------------------------------===// 396 397namespace { 398 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 399 /// than the complexity of the RHS. This comparator is used to canonicalize 400 /// expressions. 401 class VISIBILITY_HIDDEN SCEVComplexityCompare { 402 LoopInfo *LI; 403 public: 404 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 405 406 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 407 // Primarily, sort the SCEVs by their getSCEVType(). 408 if (LHS->getSCEVType() != RHS->getSCEVType()) 409 return LHS->getSCEVType() < RHS->getSCEVType(); 410 411 // Aside from the getSCEVType() ordering, the particular ordering 412 // isn't very important except that it's beneficial to be consistent, 413 // so that (a + b) and (b + a) don't end up as different expressions. 414 415 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 416 // not as complete as it could be. 417 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 418 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 419 420 // Order pointer values after integer values. This helps SCEVExpander 421 // form GEPs. 422 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 423 return false; 424 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 425 return true; 426 427 // Compare getValueID values. 428 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 429 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 430 431 // Sort arguments by their position. 432 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 433 const Argument *RA = cast<Argument>(RU->getValue()); 434 return LA->getArgNo() < RA->getArgNo(); 435 } 436 437 // For instructions, compare their loop depth, and their opcode. 438 // This is pretty loose. 439 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 440 Instruction *RV = cast<Instruction>(RU->getValue()); 441 442 // Compare loop depths. 443 if (LI->getLoopDepth(LV->getParent()) != 444 LI->getLoopDepth(RV->getParent())) 445 return LI->getLoopDepth(LV->getParent()) < 446 LI->getLoopDepth(RV->getParent()); 447 448 // Compare opcodes. 449 if (LV->getOpcode() != RV->getOpcode()) 450 return LV->getOpcode() < RV->getOpcode(); 451 452 // Compare the number of operands. 453 if (LV->getNumOperands() != RV->getNumOperands()) 454 return LV->getNumOperands() < RV->getNumOperands(); 455 } 456 457 return false; 458 } 459 460 // Compare constant values. 461 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 462 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 463 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 464 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 465 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 466 } 467 468 // Compare addrec loop depths. 469 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 470 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 471 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 472 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 473 } 474 475 // Lexicographically compare n-ary expressions. 476 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 477 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 478 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 479 if (i >= RC->getNumOperands()) 480 return false; 481 if (operator()(LC->getOperand(i), RC->getOperand(i))) 482 return true; 483 if (operator()(RC->getOperand(i), LC->getOperand(i))) 484 return false; 485 } 486 return LC->getNumOperands() < RC->getNumOperands(); 487 } 488 489 // Lexicographically compare udiv expressions. 490 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 491 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 492 if (operator()(LC->getLHS(), RC->getLHS())) 493 return true; 494 if (operator()(RC->getLHS(), LC->getLHS())) 495 return false; 496 if (operator()(LC->getRHS(), RC->getRHS())) 497 return true; 498 if (operator()(RC->getRHS(), LC->getRHS())) 499 return false; 500 return false; 501 } 502 503 // Compare cast expressions by operand. 504 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 505 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 506 return operator()(LC->getOperand(), RC->getOperand()); 507 } 508 509 LLVM_UNREACHABLE("Unknown SCEV kind!"); 510 return false; 511 } 512 }; 513} 514 515/// GroupByComplexity - Given a list of SCEV objects, order them by their 516/// complexity, and group objects of the same complexity together by value. 517/// When this routine is finished, we know that any duplicates in the vector are 518/// consecutive and that complexity is monotonically increasing. 519/// 520/// Note that we go take special precautions to ensure that we get determinstic 521/// results from this routine. In other words, we don't want the results of 522/// this to depend on where the addresses of various SCEV objects happened to 523/// land in memory. 524/// 525static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 526 LoopInfo *LI) { 527 if (Ops.size() < 2) return; // Noop 528 if (Ops.size() == 2) { 529 // This is the common case, which also happens to be trivially simple. 530 // Special case it. 531 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 532 std::swap(Ops[0], Ops[1]); 533 return; 534 } 535 536 // Do the rough sort by complexity. 537 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 538 539 // Now that we are sorted by complexity, group elements of the same 540 // complexity. Note that this is, at worst, N^2, but the vector is likely to 541 // be extremely short in practice. Note that we take this approach because we 542 // do not want to depend on the addresses of the objects we are grouping. 543 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 544 const SCEV *S = Ops[i]; 545 unsigned Complexity = S->getSCEVType(); 546 547 // If there are any objects of the same complexity and same value as this 548 // one, group them. 549 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 550 if (Ops[j] == S) { // Found a duplicate. 551 // Move it to immediately after i'th element. 552 std::swap(Ops[i+1], Ops[j]); 553 ++i; // no need to rescan it. 554 if (i == e-2) return; // Done! 555 } 556 } 557 } 558} 559 560 561 562//===----------------------------------------------------------------------===// 563// Simple SCEV method implementations 564//===----------------------------------------------------------------------===// 565 566/// BinomialCoefficient - Compute BC(It, K). The result has width W. 567/// Assume, K > 0. 568static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 569 ScalarEvolution &SE, 570 const Type* ResultTy) { 571 // Handle the simplest case efficiently. 572 if (K == 1) 573 return SE.getTruncateOrZeroExtend(It, ResultTy); 574 575 // We are using the following formula for BC(It, K): 576 // 577 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 578 // 579 // Suppose, W is the bitwidth of the return value. We must be prepared for 580 // overflow. Hence, we must assure that the result of our computation is 581 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 582 // safe in modular arithmetic. 583 // 584 // However, this code doesn't use exactly that formula; the formula it uses 585 // is something like the following, where T is the number of factors of 2 in 586 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 587 // exponentiation: 588 // 589 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 590 // 591 // This formula is trivially equivalent to the previous formula. However, 592 // this formula can be implemented much more efficiently. The trick is that 593 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 594 // arithmetic. To do exact division in modular arithmetic, all we have 595 // to do is multiply by the inverse. Therefore, this step can be done at 596 // width W. 597 // 598 // The next issue is how to safely do the division by 2^T. The way this 599 // is done is by doing the multiplication step at a width of at least W + T 600 // bits. This way, the bottom W+T bits of the product are accurate. Then, 601 // when we perform the division by 2^T (which is equivalent to a right shift 602 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 603 // truncated out after the division by 2^T. 604 // 605 // In comparison to just directly using the first formula, this technique 606 // is much more efficient; using the first formula requires W * K bits, 607 // but this formula less than W + K bits. Also, the first formula requires 608 // a division step, whereas this formula only requires multiplies and shifts. 609 // 610 // It doesn't matter whether the subtraction step is done in the calculation 611 // width or the input iteration count's width; if the subtraction overflows, 612 // the result must be zero anyway. We prefer here to do it in the width of 613 // the induction variable because it helps a lot for certain cases; CodeGen 614 // isn't smart enough to ignore the overflow, which leads to much less 615 // efficient code if the width of the subtraction is wider than the native 616 // register width. 617 // 618 // (It's possible to not widen at all by pulling out factors of 2 before 619 // the multiplication; for example, K=2 can be calculated as 620 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 621 // extra arithmetic, so it's not an obvious win, and it gets 622 // much more complicated for K > 3.) 623 624 // Protection from insane SCEVs; this bound is conservative, 625 // but it probably doesn't matter. 626 if (K > 1000) 627 return SE.getCouldNotCompute(); 628 629 unsigned W = SE.getTypeSizeInBits(ResultTy); 630 631 // Calculate K! / 2^T and T; we divide out the factors of two before 632 // multiplying for calculating K! / 2^T to avoid overflow. 633 // Other overflow doesn't matter because we only care about the bottom 634 // W bits of the result. 635 APInt OddFactorial(W, 1); 636 unsigned T = 1; 637 for (unsigned i = 3; i <= K; ++i) { 638 APInt Mult(W, i); 639 unsigned TwoFactors = Mult.countTrailingZeros(); 640 T += TwoFactors; 641 Mult = Mult.lshr(TwoFactors); 642 OddFactorial *= Mult; 643 } 644 645 // We need at least W + T bits for the multiplication step 646 unsigned CalculationBits = W + T; 647 648 // Calcuate 2^T, at width T+W. 649 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 650 651 // Calculate the multiplicative inverse of K! / 2^T; 652 // this multiplication factor will perform the exact division by 653 // K! / 2^T. 654 APInt Mod = APInt::getSignedMinValue(W+1); 655 APInt MultiplyFactor = OddFactorial.zext(W+1); 656 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 657 MultiplyFactor = MultiplyFactor.trunc(W); 658 659 // Calculate the product, at width T+W 660 const IntegerType *CalculationTy = IntegerType::get(CalculationBits); 661 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 662 for (unsigned i = 1; i != K; ++i) { 663 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 664 Dividend = SE.getMulExpr(Dividend, 665 SE.getTruncateOrZeroExtend(S, CalculationTy)); 666 } 667 668 // Divide by 2^T 669 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 670 671 // Truncate the result, and divide by K! / 2^T. 672 673 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 674 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 675} 676 677/// evaluateAtIteration - Return the value of this chain of recurrences at 678/// the specified iteration number. We can evaluate this recurrence by 679/// multiplying each element in the chain by the binomial coefficient 680/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 681/// 682/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 683/// 684/// where BC(It, k) stands for binomial coefficient. 685/// 686const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 687 ScalarEvolution &SE) const { 688 const SCEV *Result = getStart(); 689 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 690 // The computation is correct in the face of overflow provided that the 691 // multiplication is performed _after_ the evaluation of the binomial 692 // coefficient. 693 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 694 if (isa<SCEVCouldNotCompute>(Coeff)) 695 return Coeff; 696 697 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 698 } 699 return Result; 700} 701 702//===----------------------------------------------------------------------===// 703// SCEV Expression folder implementations 704//===----------------------------------------------------------------------===// 705 706const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 707 const Type *Ty) { 708 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 709 "This is not a truncating conversion!"); 710 assert(isSCEVable(Ty) && 711 "This is not a conversion to a SCEVable type!"); 712 Ty = getEffectiveSCEVType(Ty); 713 714 FoldingSetNodeID ID; 715 ID.AddInteger(scTruncate); 716 ID.AddPointer(Op); 717 ID.AddPointer(Ty); 718 void *IP = 0; 719 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 720 721 // Fold if the operand is constant. 722 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 723 return getConstant( 724 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 725 726 // trunc(trunc(x)) --> trunc(x) 727 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 728 return getTruncateExpr(ST->getOperand(), Ty); 729 730 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 731 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 732 return getTruncateOrSignExtend(SS->getOperand(), Ty); 733 734 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 735 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 736 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 737 738 // If the input value is a chrec scev, truncate the chrec's operands. 739 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 740 SmallVector<const SCEV *, 4> Operands; 741 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 742 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 743 return getAddRecExpr(Operands, AddRec->getLoop()); 744 } 745 746 // The cast wasn't folded; create an explicit cast node. 747 // Recompute the insert position, as it may have been invalidated. 748 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 749 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 750 new (S) SCEVTruncateExpr(ID, Op, Ty); 751 UniqueSCEVs.InsertNode(S, IP); 752 return S; 753} 754 755const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 756 const Type *Ty) { 757 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 758 "This is not an extending conversion!"); 759 assert(isSCEVable(Ty) && 760 "This is not a conversion to a SCEVable type!"); 761 Ty = getEffectiveSCEVType(Ty); 762 763 // Fold if the operand is constant. 764 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 765 const Type *IntTy = getEffectiveSCEVType(Ty); 766 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 767 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 768 return getConstant(cast<ConstantInt>(C)); 769 } 770 771 // zext(zext(x)) --> zext(x) 772 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 773 return getZeroExtendExpr(SZ->getOperand(), Ty); 774 775 // Before doing any expensive analysis, check to see if we've already 776 // computed a SCEV for this Op and Ty. 777 FoldingSetNodeID ID; 778 ID.AddInteger(scZeroExtend); 779 ID.AddPointer(Op); 780 ID.AddPointer(Ty); 781 void *IP = 0; 782 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 783 784 // If the input value is a chrec scev, and we can prove that the value 785 // did not overflow the old, smaller, value, we can zero extend all of the 786 // operands (often constants). This allows analysis of something like 787 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 788 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 789 if (AR->isAffine()) { 790 const SCEV *Start = AR->getStart(); 791 const SCEV *Step = AR->getStepRecurrence(*this); 792 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 793 const Loop *L = AR->getLoop(); 794 795 // Check whether the backedge-taken count is SCEVCouldNotCompute. 796 // Note that this serves two purposes: It filters out loops that are 797 // simply not analyzable, and it covers the case where this code is 798 // being called from within backedge-taken count analysis, such that 799 // attempting to ask for the backedge-taken count would likely result 800 // in infinite recursion. In the later case, the analysis code will 801 // cope with a conservative value, and it will take care to purge 802 // that value once it has finished. 803 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 804 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 805 // Manually compute the final value for AR, checking for 806 // overflow. 807 808 // Check whether the backedge-taken count can be losslessly casted to 809 // the addrec's type. The count is always unsigned. 810 const SCEV *CastedMaxBECount = 811 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 812 const SCEV *RecastedMaxBECount = 813 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 814 if (MaxBECount == RecastedMaxBECount) { 815 const Type *WideTy = IntegerType::get(BitWidth * 2); 816 // Check whether Start+Step*MaxBECount has no unsigned overflow. 817 const SCEV *ZMul = 818 getMulExpr(CastedMaxBECount, 819 getTruncateOrZeroExtend(Step, Start->getType())); 820 const SCEV *Add = getAddExpr(Start, ZMul); 821 const SCEV *OperandExtendedAdd = 822 getAddExpr(getZeroExtendExpr(Start, WideTy), 823 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 824 getZeroExtendExpr(Step, WideTy))); 825 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 826 // Return the expression with the addrec on the outside. 827 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 828 getZeroExtendExpr(Step, Ty), 829 L); 830 831 // Similar to above, only this time treat the step value as signed. 832 // This covers loops that count down. 833 const SCEV *SMul = 834 getMulExpr(CastedMaxBECount, 835 getTruncateOrSignExtend(Step, Start->getType())); 836 Add = getAddExpr(Start, SMul); 837 OperandExtendedAdd = 838 getAddExpr(getZeroExtendExpr(Start, WideTy), 839 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 840 getSignExtendExpr(Step, WideTy))); 841 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 842 // Return the expression with the addrec on the outside. 843 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 844 getSignExtendExpr(Step, Ty), 845 L); 846 } 847 848 // If the backedge is guarded by a comparison with the pre-inc value 849 // the addrec is safe. Also, if the entry is guarded by a comparison 850 // with the start value and the backedge is guarded by a comparison 851 // with the post-inc value, the addrec is safe. 852 if (isKnownPositive(Step)) { 853 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 854 getUnsignedRange(Step).getUnsignedMax()); 855 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 856 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 857 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 858 AR->getPostIncExpr(*this), N))) 859 // Return the expression with the addrec on the outside. 860 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 861 getZeroExtendExpr(Step, Ty), 862 L); 863 } else if (isKnownNegative(Step)) { 864 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 865 getSignedRange(Step).getSignedMin()); 866 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 867 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 868 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 869 AR->getPostIncExpr(*this), N))) 870 // Return the expression with the addrec on the outside. 871 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 872 getSignExtendExpr(Step, Ty), 873 L); 874 } 875 } 876 } 877 878 // The cast wasn't folded; create an explicit cast node. 879 // Recompute the insert position, as it may have been invalidated. 880 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 881 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 882 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 883 UniqueSCEVs.InsertNode(S, IP); 884 return S; 885} 886 887const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 888 const Type *Ty) { 889 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 890 "This is not an extending conversion!"); 891 assert(isSCEVable(Ty) && 892 "This is not a conversion to a SCEVable type!"); 893 Ty = getEffectiveSCEVType(Ty); 894 895 // Fold if the operand is constant. 896 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 897 const Type *IntTy = getEffectiveSCEVType(Ty); 898 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 899 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 900 return getConstant(cast<ConstantInt>(C)); 901 } 902 903 // sext(sext(x)) --> sext(x) 904 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 905 return getSignExtendExpr(SS->getOperand(), Ty); 906 907 // Before doing any expensive analysis, check to see if we've already 908 // computed a SCEV for this Op and Ty. 909 FoldingSetNodeID ID; 910 ID.AddInteger(scSignExtend); 911 ID.AddPointer(Op); 912 ID.AddPointer(Ty); 913 void *IP = 0; 914 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 915 916 // If the input value is a chrec scev, and we can prove that the value 917 // did not overflow the old, smaller, value, we can sign extend all of the 918 // operands (often constants). This allows analysis of something like 919 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 920 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 921 if (AR->isAffine()) { 922 const SCEV *Start = AR->getStart(); 923 const SCEV *Step = AR->getStepRecurrence(*this); 924 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 925 const Loop *L = AR->getLoop(); 926 927 // Check whether the backedge-taken count is SCEVCouldNotCompute. 928 // Note that this serves two purposes: It filters out loops that are 929 // simply not analyzable, and it covers the case where this code is 930 // being called from within backedge-taken count analysis, such that 931 // attempting to ask for the backedge-taken count would likely result 932 // in infinite recursion. In the later case, the analysis code will 933 // cope with a conservative value, and it will take care to purge 934 // that value once it has finished. 935 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 936 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 937 // Manually compute the final value for AR, checking for 938 // overflow. 939 940 // Check whether the backedge-taken count can be losslessly casted to 941 // the addrec's type. The count is always unsigned. 942 const SCEV *CastedMaxBECount = 943 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 944 const SCEV *RecastedMaxBECount = 945 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 946 if (MaxBECount == RecastedMaxBECount) { 947 const Type *WideTy = IntegerType::get(BitWidth * 2); 948 // Check whether Start+Step*MaxBECount has no signed overflow. 949 const SCEV *SMul = 950 getMulExpr(CastedMaxBECount, 951 getTruncateOrSignExtend(Step, Start->getType())); 952 const SCEV *Add = getAddExpr(Start, SMul); 953 const SCEV *OperandExtendedAdd = 954 getAddExpr(getSignExtendExpr(Start, WideTy), 955 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 956 getSignExtendExpr(Step, WideTy))); 957 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 958 // Return the expression with the addrec on the outside. 959 return getAddRecExpr(getSignExtendExpr(Start, Ty), 960 getSignExtendExpr(Step, Ty), 961 L); 962 } 963 964 // If the backedge is guarded by a comparison with the pre-inc value 965 // the addrec is safe. Also, if the entry is guarded by a comparison 966 // with the start value and the backedge is guarded by a comparison 967 // with the post-inc value, the addrec is safe. 968 if (isKnownPositive(Step)) { 969 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 970 getSignedRange(Step).getSignedMax()); 971 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 972 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 973 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 974 AR->getPostIncExpr(*this), N))) 975 // Return the expression with the addrec on the outside. 976 return getAddRecExpr(getSignExtendExpr(Start, Ty), 977 getSignExtendExpr(Step, Ty), 978 L); 979 } else if (isKnownNegative(Step)) { 980 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 981 getSignedRange(Step).getSignedMin()); 982 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 983 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 984 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 985 AR->getPostIncExpr(*this), N))) 986 // Return the expression with the addrec on the outside. 987 return getAddRecExpr(getSignExtendExpr(Start, Ty), 988 getSignExtendExpr(Step, Ty), 989 L); 990 } 991 } 992 } 993 994 // The cast wasn't folded; create an explicit cast node. 995 // Recompute the insert position, as it may have been invalidated. 996 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 997 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 998 new (S) SCEVSignExtendExpr(ID, Op, Ty); 999 UniqueSCEVs.InsertNode(S, IP); 1000 return S; 1001} 1002 1003/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1004/// unspecified bits out to the given type. 1005/// 1006const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1007 const Type *Ty) { 1008 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1009 "This is not an extending conversion!"); 1010 assert(isSCEVable(Ty) && 1011 "This is not a conversion to a SCEVable type!"); 1012 Ty = getEffectiveSCEVType(Ty); 1013 1014 // Sign-extend negative constants. 1015 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1016 if (SC->getValue()->getValue().isNegative()) 1017 return getSignExtendExpr(Op, Ty); 1018 1019 // Peel off a truncate cast. 1020 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1021 const SCEV *NewOp = T->getOperand(); 1022 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1023 return getAnyExtendExpr(NewOp, Ty); 1024 return getTruncateOrNoop(NewOp, Ty); 1025 } 1026 1027 // Next try a zext cast. If the cast is folded, use it. 1028 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1029 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1030 return ZExt; 1031 1032 // Next try a sext cast. If the cast is folded, use it. 1033 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1034 if (!isa<SCEVSignExtendExpr>(SExt)) 1035 return SExt; 1036 1037 // If the expression is obviously signed, use the sext cast value. 1038 if (isa<SCEVSMaxExpr>(Op)) 1039 return SExt; 1040 1041 // Absent any other information, use the zext cast value. 1042 return ZExt; 1043} 1044 1045/// CollectAddOperandsWithScales - Process the given Ops list, which is 1046/// a list of operands to be added under the given scale, update the given 1047/// map. This is a helper function for getAddRecExpr. As an example of 1048/// what it does, given a sequence of operands that would form an add 1049/// expression like this: 1050/// 1051/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1052/// 1053/// where A and B are constants, update the map with these values: 1054/// 1055/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1056/// 1057/// and add 13 + A*B*29 to AccumulatedConstant. 1058/// This will allow getAddRecExpr to produce this: 1059/// 1060/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1061/// 1062/// This form often exposes folding opportunities that are hidden in 1063/// the original operand list. 1064/// 1065/// Return true iff it appears that any interesting folding opportunities 1066/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1067/// the common case where no interesting opportunities are present, and 1068/// is also used as a check to avoid infinite recursion. 1069/// 1070static bool 1071CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1072 SmallVector<const SCEV *, 8> &NewOps, 1073 APInt &AccumulatedConstant, 1074 const SmallVectorImpl<const SCEV *> &Ops, 1075 const APInt &Scale, 1076 ScalarEvolution &SE) { 1077 bool Interesting = false; 1078 1079 // Iterate over the add operands. 1080 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1081 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1082 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1083 APInt NewScale = 1084 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1085 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1086 // A multiplication of a constant with another add; recurse. 1087 Interesting |= 1088 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1089 cast<SCEVAddExpr>(Mul->getOperand(1)) 1090 ->getOperands(), 1091 NewScale, SE); 1092 } else { 1093 // A multiplication of a constant with some other value. Update 1094 // the map. 1095 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1096 const SCEV *Key = SE.getMulExpr(MulOps); 1097 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1098 M.insert(std::make_pair(Key, NewScale)); 1099 if (Pair.second) { 1100 NewOps.push_back(Pair.first->first); 1101 } else { 1102 Pair.first->second += NewScale; 1103 // The map already had an entry for this value, which may indicate 1104 // a folding opportunity. 1105 Interesting = true; 1106 } 1107 } 1108 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1109 // Pull a buried constant out to the outside. 1110 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1111 Interesting = true; 1112 AccumulatedConstant += Scale * C->getValue()->getValue(); 1113 } else { 1114 // An ordinary operand. Update the map. 1115 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1116 M.insert(std::make_pair(Ops[i], Scale)); 1117 if (Pair.second) { 1118 NewOps.push_back(Pair.first->first); 1119 } else { 1120 Pair.first->second += Scale; 1121 // The map already had an entry for this value, which may indicate 1122 // a folding opportunity. 1123 Interesting = true; 1124 } 1125 } 1126 } 1127 1128 return Interesting; 1129} 1130 1131namespace { 1132 struct APIntCompare { 1133 bool operator()(const APInt &LHS, const APInt &RHS) const { 1134 return LHS.ult(RHS); 1135 } 1136 }; 1137} 1138 1139/// getAddExpr - Get a canonical add expression, or something simpler if 1140/// possible. 1141const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) { 1142 assert(!Ops.empty() && "Cannot get empty add!"); 1143 if (Ops.size() == 1) return Ops[0]; 1144#ifndef NDEBUG 1145 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1146 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1147 getEffectiveSCEVType(Ops[0]->getType()) && 1148 "SCEVAddExpr operand types don't match!"); 1149#endif 1150 1151 // Sort by complexity, this groups all similar expression types together. 1152 GroupByComplexity(Ops, LI); 1153 1154 // If there are any constants, fold them together. 1155 unsigned Idx = 0; 1156 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1157 ++Idx; 1158 assert(Idx < Ops.size()); 1159 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1160 // We found two constants, fold them together! 1161 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1162 RHSC->getValue()->getValue()); 1163 if (Ops.size() == 2) return Ops[0]; 1164 Ops.erase(Ops.begin()+1); // Erase the folded element 1165 LHSC = cast<SCEVConstant>(Ops[0]); 1166 } 1167 1168 // If we are left with a constant zero being added, strip it off. 1169 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1170 Ops.erase(Ops.begin()); 1171 --Idx; 1172 } 1173 } 1174 1175 if (Ops.size() == 1) return Ops[0]; 1176 1177 // Okay, check to see if the same value occurs in the operand list twice. If 1178 // so, merge them together into an multiply expression. Since we sorted the 1179 // list, these values are required to be adjacent. 1180 const Type *Ty = Ops[0]->getType(); 1181 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1182 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1183 // Found a match, merge the two values into a multiply, and add any 1184 // remaining values to the result. 1185 const SCEV *Two = getIntegerSCEV(2, Ty); 1186 const SCEV *Mul = getMulExpr(Ops[i], Two); 1187 if (Ops.size() == 2) 1188 return Mul; 1189 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1190 Ops.push_back(Mul); 1191 return getAddExpr(Ops); 1192 } 1193 1194 // Check for truncates. If all the operands are truncated from the same 1195 // type, see if factoring out the truncate would permit the result to be 1196 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1197 // if the contents of the resulting outer trunc fold to something simple. 1198 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1199 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1200 const Type *DstType = Trunc->getType(); 1201 const Type *SrcType = Trunc->getOperand()->getType(); 1202 SmallVector<const SCEV *, 8> LargeOps; 1203 bool Ok = true; 1204 // Check all the operands to see if they can be represented in the 1205 // source type of the truncate. 1206 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1207 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1208 if (T->getOperand()->getType() != SrcType) { 1209 Ok = false; 1210 break; 1211 } 1212 LargeOps.push_back(T->getOperand()); 1213 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1214 // This could be either sign or zero extension, but sign extension 1215 // is much more likely to be foldable here. 1216 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1217 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1218 SmallVector<const SCEV *, 8> LargeMulOps; 1219 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1220 if (const SCEVTruncateExpr *T = 1221 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1222 if (T->getOperand()->getType() != SrcType) { 1223 Ok = false; 1224 break; 1225 } 1226 LargeMulOps.push_back(T->getOperand()); 1227 } else if (const SCEVConstant *C = 1228 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1229 // This could be either sign or zero extension, but sign extension 1230 // is much more likely to be foldable here. 1231 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1232 } else { 1233 Ok = false; 1234 break; 1235 } 1236 } 1237 if (Ok) 1238 LargeOps.push_back(getMulExpr(LargeMulOps)); 1239 } else { 1240 Ok = false; 1241 break; 1242 } 1243 } 1244 if (Ok) { 1245 // Evaluate the expression in the larger type. 1246 const SCEV *Fold = getAddExpr(LargeOps); 1247 // If it folds to something simple, use it. Otherwise, don't. 1248 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1249 return getTruncateExpr(Fold, DstType); 1250 } 1251 } 1252 1253 // Skip past any other cast SCEVs. 1254 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1255 ++Idx; 1256 1257 // If there are add operands they would be next. 1258 if (Idx < Ops.size()) { 1259 bool DeletedAdd = false; 1260 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1261 // If we have an add, expand the add operands onto the end of the operands 1262 // list. 1263 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1264 Ops.erase(Ops.begin()+Idx); 1265 DeletedAdd = true; 1266 } 1267 1268 // If we deleted at least one add, we added operands to the end of the list, 1269 // and they are not necessarily sorted. Recurse to resort and resimplify 1270 // any operands we just aquired. 1271 if (DeletedAdd) 1272 return getAddExpr(Ops); 1273 } 1274 1275 // Skip over the add expression until we get to a multiply. 1276 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1277 ++Idx; 1278 1279 // Check to see if there are any folding opportunities present with 1280 // operands multiplied by constant values. 1281 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1282 uint64_t BitWidth = getTypeSizeInBits(Ty); 1283 DenseMap<const SCEV *, APInt> M; 1284 SmallVector<const SCEV *, 8> NewOps; 1285 APInt AccumulatedConstant(BitWidth, 0); 1286 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1287 Ops, APInt(BitWidth, 1), *this)) { 1288 // Some interesting folding opportunity is present, so its worthwhile to 1289 // re-generate the operands list. Group the operands by constant scale, 1290 // to avoid multiplying by the same constant scale multiple times. 1291 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1292 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1293 E = NewOps.end(); I != E; ++I) 1294 MulOpLists[M.find(*I)->second].push_back(*I); 1295 // Re-generate the operands list. 1296 Ops.clear(); 1297 if (AccumulatedConstant != 0) 1298 Ops.push_back(getConstant(AccumulatedConstant)); 1299 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1300 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1301 if (I->first != 0) 1302 Ops.push_back(getMulExpr(getConstant(I->first), 1303 getAddExpr(I->second))); 1304 if (Ops.empty()) 1305 return getIntegerSCEV(0, Ty); 1306 if (Ops.size() == 1) 1307 return Ops[0]; 1308 return getAddExpr(Ops); 1309 } 1310 } 1311 1312 // If we are adding something to a multiply expression, make sure the 1313 // something is not already an operand of the multiply. If so, merge it into 1314 // the multiply. 1315 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1316 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1317 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1318 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1319 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1320 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1321 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1322 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1323 if (Mul->getNumOperands() != 2) { 1324 // If the multiply has more than two operands, we must get the 1325 // Y*Z term. 1326 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1327 MulOps.erase(MulOps.begin()+MulOp); 1328 InnerMul = getMulExpr(MulOps); 1329 } 1330 const SCEV *One = getIntegerSCEV(1, Ty); 1331 const SCEV *AddOne = getAddExpr(InnerMul, One); 1332 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1333 if (Ops.size() == 2) return OuterMul; 1334 if (AddOp < Idx) { 1335 Ops.erase(Ops.begin()+AddOp); 1336 Ops.erase(Ops.begin()+Idx-1); 1337 } else { 1338 Ops.erase(Ops.begin()+Idx); 1339 Ops.erase(Ops.begin()+AddOp-1); 1340 } 1341 Ops.push_back(OuterMul); 1342 return getAddExpr(Ops); 1343 } 1344 1345 // Check this multiply against other multiplies being added together. 1346 for (unsigned OtherMulIdx = Idx+1; 1347 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1348 ++OtherMulIdx) { 1349 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1350 // If MulOp occurs in OtherMul, we can fold the two multiplies 1351 // together. 1352 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1353 OMulOp != e; ++OMulOp) 1354 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1355 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1356 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1357 if (Mul->getNumOperands() != 2) { 1358 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1359 Mul->op_end()); 1360 MulOps.erase(MulOps.begin()+MulOp); 1361 InnerMul1 = getMulExpr(MulOps); 1362 } 1363 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1364 if (OtherMul->getNumOperands() != 2) { 1365 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1366 OtherMul->op_end()); 1367 MulOps.erase(MulOps.begin()+OMulOp); 1368 InnerMul2 = getMulExpr(MulOps); 1369 } 1370 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1371 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1372 if (Ops.size() == 2) return OuterMul; 1373 Ops.erase(Ops.begin()+Idx); 1374 Ops.erase(Ops.begin()+OtherMulIdx-1); 1375 Ops.push_back(OuterMul); 1376 return getAddExpr(Ops); 1377 } 1378 } 1379 } 1380 } 1381 1382 // If there are any add recurrences in the operands list, see if any other 1383 // added values are loop invariant. If so, we can fold them into the 1384 // recurrence. 1385 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1386 ++Idx; 1387 1388 // Scan over all recurrences, trying to fold loop invariants into them. 1389 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1390 // Scan all of the other operands to this add and add them to the vector if 1391 // they are loop invariant w.r.t. the recurrence. 1392 SmallVector<const SCEV *, 8> LIOps; 1393 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1394 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1395 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1396 LIOps.push_back(Ops[i]); 1397 Ops.erase(Ops.begin()+i); 1398 --i; --e; 1399 } 1400 1401 // If we found some loop invariants, fold them into the recurrence. 1402 if (!LIOps.empty()) { 1403 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1404 LIOps.push_back(AddRec->getStart()); 1405 1406 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1407 AddRec->op_end()); 1408 AddRecOps[0] = getAddExpr(LIOps); 1409 1410 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1411 // If all of the other operands were loop invariant, we are done. 1412 if (Ops.size() == 1) return NewRec; 1413 1414 // Otherwise, add the folded AddRec by the non-liv parts. 1415 for (unsigned i = 0;; ++i) 1416 if (Ops[i] == AddRec) { 1417 Ops[i] = NewRec; 1418 break; 1419 } 1420 return getAddExpr(Ops); 1421 } 1422 1423 // Okay, if there weren't any loop invariants to be folded, check to see if 1424 // there are multiple AddRec's with the same loop induction variable being 1425 // added together. If so, we can fold them. 1426 for (unsigned OtherIdx = Idx+1; 1427 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1428 if (OtherIdx != Idx) { 1429 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1430 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1431 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1432 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1433 AddRec->op_end()); 1434 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1435 if (i >= NewOps.size()) { 1436 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1437 OtherAddRec->op_end()); 1438 break; 1439 } 1440 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1441 } 1442 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1443 1444 if (Ops.size() == 2) return NewAddRec; 1445 1446 Ops.erase(Ops.begin()+Idx); 1447 Ops.erase(Ops.begin()+OtherIdx-1); 1448 Ops.push_back(NewAddRec); 1449 return getAddExpr(Ops); 1450 } 1451 } 1452 1453 // Otherwise couldn't fold anything into this recurrence. Move onto the 1454 // next one. 1455 } 1456 1457 // Okay, it looks like we really DO need an add expr. Check to see if we 1458 // already have one, otherwise create a new one. 1459 FoldingSetNodeID ID; 1460 ID.AddInteger(scAddExpr); 1461 ID.AddInteger(Ops.size()); 1462 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1463 ID.AddPointer(Ops[i]); 1464 void *IP = 0; 1465 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1466 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1467 new (S) SCEVAddExpr(ID, Ops); 1468 UniqueSCEVs.InsertNode(S, IP); 1469 return S; 1470} 1471 1472 1473/// getMulExpr - Get a canonical multiply expression, or something simpler if 1474/// possible. 1475const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) { 1476 assert(!Ops.empty() && "Cannot get empty mul!"); 1477#ifndef NDEBUG 1478 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1479 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1480 getEffectiveSCEVType(Ops[0]->getType()) && 1481 "SCEVMulExpr operand types don't match!"); 1482#endif 1483 1484 // Sort by complexity, this groups all similar expression types together. 1485 GroupByComplexity(Ops, LI); 1486 1487 // If there are any constants, fold them together. 1488 unsigned Idx = 0; 1489 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1490 1491 // C1*(C2+V) -> C1*C2 + C1*V 1492 if (Ops.size() == 2) 1493 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1494 if (Add->getNumOperands() == 2 && 1495 isa<SCEVConstant>(Add->getOperand(0))) 1496 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1497 getMulExpr(LHSC, Add->getOperand(1))); 1498 1499 1500 ++Idx; 1501 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1502 // We found two constants, fold them together! 1503 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1504 RHSC->getValue()->getValue()); 1505 Ops[0] = getConstant(Fold); 1506 Ops.erase(Ops.begin()+1); // Erase the folded element 1507 if (Ops.size() == 1) return Ops[0]; 1508 LHSC = cast<SCEVConstant>(Ops[0]); 1509 } 1510 1511 // If we are left with a constant one being multiplied, strip it off. 1512 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1513 Ops.erase(Ops.begin()); 1514 --Idx; 1515 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1516 // If we have a multiply of zero, it will always be zero. 1517 return Ops[0]; 1518 } 1519 } 1520 1521 // Skip over the add expression until we get to a multiply. 1522 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1523 ++Idx; 1524 1525 if (Ops.size() == 1) 1526 return Ops[0]; 1527 1528 // If there are mul operands inline them all into this expression. 1529 if (Idx < Ops.size()) { 1530 bool DeletedMul = false; 1531 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1532 // If we have an mul, expand the mul operands onto the end of the operands 1533 // list. 1534 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1535 Ops.erase(Ops.begin()+Idx); 1536 DeletedMul = true; 1537 } 1538 1539 // If we deleted at least one mul, we added operands to the end of the list, 1540 // and they are not necessarily sorted. Recurse to resort and resimplify 1541 // any operands we just aquired. 1542 if (DeletedMul) 1543 return getMulExpr(Ops); 1544 } 1545 1546 // If there are any add recurrences in the operands list, see if any other 1547 // added values are loop invariant. If so, we can fold them into the 1548 // recurrence. 1549 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1550 ++Idx; 1551 1552 // Scan over all recurrences, trying to fold loop invariants into them. 1553 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1554 // Scan all of the other operands to this mul and add them to the vector if 1555 // they are loop invariant w.r.t. the recurrence. 1556 SmallVector<const SCEV *, 8> LIOps; 1557 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1558 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1559 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1560 LIOps.push_back(Ops[i]); 1561 Ops.erase(Ops.begin()+i); 1562 --i; --e; 1563 } 1564 1565 // If we found some loop invariants, fold them into the recurrence. 1566 if (!LIOps.empty()) { 1567 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1568 SmallVector<const SCEV *, 4> NewOps; 1569 NewOps.reserve(AddRec->getNumOperands()); 1570 if (LIOps.size() == 1) { 1571 const SCEV *Scale = LIOps[0]; 1572 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1573 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1574 } else { 1575 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1576 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1577 MulOps.push_back(AddRec->getOperand(i)); 1578 NewOps.push_back(getMulExpr(MulOps)); 1579 } 1580 } 1581 1582 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1583 1584 // If all of the other operands were loop invariant, we are done. 1585 if (Ops.size() == 1) return NewRec; 1586 1587 // Otherwise, multiply the folded AddRec by the non-liv parts. 1588 for (unsigned i = 0;; ++i) 1589 if (Ops[i] == AddRec) { 1590 Ops[i] = NewRec; 1591 break; 1592 } 1593 return getMulExpr(Ops); 1594 } 1595 1596 // Okay, if there weren't any loop invariants to be folded, check to see if 1597 // there are multiple AddRec's with the same loop induction variable being 1598 // multiplied together. If so, we can fold them. 1599 for (unsigned OtherIdx = Idx+1; 1600 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1601 if (OtherIdx != Idx) { 1602 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1603 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1604 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1605 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1606 const SCEV *NewStart = getMulExpr(F->getStart(), 1607 G->getStart()); 1608 const SCEV *B = F->getStepRecurrence(*this); 1609 const SCEV *D = G->getStepRecurrence(*this); 1610 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1611 getMulExpr(G, B), 1612 getMulExpr(B, D)); 1613 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1614 F->getLoop()); 1615 if (Ops.size() == 2) return NewAddRec; 1616 1617 Ops.erase(Ops.begin()+Idx); 1618 Ops.erase(Ops.begin()+OtherIdx-1); 1619 Ops.push_back(NewAddRec); 1620 return getMulExpr(Ops); 1621 } 1622 } 1623 1624 // Otherwise couldn't fold anything into this recurrence. Move onto the 1625 // next one. 1626 } 1627 1628 // Okay, it looks like we really DO need an mul expr. Check to see if we 1629 // already have one, otherwise create a new one. 1630 FoldingSetNodeID ID; 1631 ID.AddInteger(scMulExpr); 1632 ID.AddInteger(Ops.size()); 1633 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1634 ID.AddPointer(Ops[i]); 1635 void *IP = 0; 1636 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1637 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1638 new (S) SCEVMulExpr(ID, Ops); 1639 UniqueSCEVs.InsertNode(S, IP); 1640 return S; 1641} 1642 1643/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1644/// possible. 1645const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1646 const SCEV *RHS) { 1647 assert(getEffectiveSCEVType(LHS->getType()) == 1648 getEffectiveSCEVType(RHS->getType()) && 1649 "SCEVUDivExpr operand types don't match!"); 1650 1651 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1652 if (RHSC->getValue()->equalsInt(1)) 1653 return LHS; // X udiv 1 --> x 1654 if (RHSC->isZero()) 1655 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1656 1657 // Determine if the division can be folded into the operands of 1658 // its operands. 1659 // TODO: Generalize this to non-constants by using known-bits information. 1660 const Type *Ty = LHS->getType(); 1661 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1662 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1663 // For non-power-of-two values, effectively round the value up to the 1664 // nearest power of two. 1665 if (!RHSC->getValue()->getValue().isPowerOf2()) 1666 ++MaxShiftAmt; 1667 const IntegerType *ExtTy = 1668 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1669 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1670 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1671 if (const SCEVConstant *Step = 1672 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1673 if (!Step->getValue()->getValue() 1674 .urem(RHSC->getValue()->getValue()) && 1675 getZeroExtendExpr(AR, ExtTy) == 1676 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1677 getZeroExtendExpr(Step, ExtTy), 1678 AR->getLoop())) { 1679 SmallVector<const SCEV *, 4> Operands; 1680 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1681 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1682 return getAddRecExpr(Operands, AR->getLoop()); 1683 } 1684 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1685 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1686 SmallVector<const SCEV *, 4> Operands; 1687 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1688 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1689 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1690 // Find an operand that's safely divisible. 1691 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1692 const SCEV *Op = M->getOperand(i); 1693 const SCEV *Div = getUDivExpr(Op, RHSC); 1694 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1695 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1696 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1697 MOperands.end()); 1698 Operands[i] = Div; 1699 return getMulExpr(Operands); 1700 } 1701 } 1702 } 1703 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1704 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1705 SmallVector<const SCEV *, 4> Operands; 1706 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1707 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1708 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1709 Operands.clear(); 1710 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1711 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1712 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1713 break; 1714 Operands.push_back(Op); 1715 } 1716 if (Operands.size() == A->getNumOperands()) 1717 return getAddExpr(Operands); 1718 } 1719 } 1720 1721 // Fold if both operands are constant. 1722 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1723 Constant *LHSCV = LHSC->getValue(); 1724 Constant *RHSCV = RHSC->getValue(); 1725 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1726 RHSCV))); 1727 } 1728 } 1729 1730 FoldingSetNodeID ID; 1731 ID.AddInteger(scUDivExpr); 1732 ID.AddPointer(LHS); 1733 ID.AddPointer(RHS); 1734 void *IP = 0; 1735 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1736 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1737 new (S) SCEVUDivExpr(ID, LHS, RHS); 1738 UniqueSCEVs.InsertNode(S, IP); 1739 return S; 1740} 1741 1742 1743/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1744/// Simplify the expression as much as possible. 1745const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1746 const SCEV *Step, const Loop *L) { 1747 SmallVector<const SCEV *, 4> Operands; 1748 Operands.push_back(Start); 1749 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1750 if (StepChrec->getLoop() == L) { 1751 Operands.insert(Operands.end(), StepChrec->op_begin(), 1752 StepChrec->op_end()); 1753 return getAddRecExpr(Operands, L); 1754 } 1755 1756 Operands.push_back(Step); 1757 return getAddRecExpr(Operands, L); 1758} 1759 1760/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1761/// Simplify the expression as much as possible. 1762const SCEV * 1763ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1764 const Loop *L) { 1765 if (Operands.size() == 1) return Operands[0]; 1766#ifndef NDEBUG 1767 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1768 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1769 getEffectiveSCEVType(Operands[0]->getType()) && 1770 "SCEVAddRecExpr operand types don't match!"); 1771#endif 1772 1773 if (Operands.back()->isZero()) { 1774 Operands.pop_back(); 1775 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1776 } 1777 1778 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1779 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1780 const Loop* NestedLoop = NestedAR->getLoop(); 1781 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1782 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1783 NestedAR->op_end()); 1784 Operands[0] = NestedAR->getStart(); 1785 // AddRecs require their operands be loop-invariant with respect to their 1786 // loops. Don't perform this transformation if it would break this 1787 // requirement. 1788 bool AllInvariant = true; 1789 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1790 if (!Operands[i]->isLoopInvariant(L)) { 1791 AllInvariant = false; 1792 break; 1793 } 1794 if (AllInvariant) { 1795 NestedOperands[0] = getAddRecExpr(Operands, L); 1796 AllInvariant = true; 1797 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1798 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1799 AllInvariant = false; 1800 break; 1801 } 1802 if (AllInvariant) 1803 // Ok, both add recurrences are valid after the transformation. 1804 return getAddRecExpr(NestedOperands, NestedLoop); 1805 } 1806 // Reset Operands to its original state. 1807 Operands[0] = NestedAR; 1808 } 1809 } 1810 1811 FoldingSetNodeID ID; 1812 ID.AddInteger(scAddRecExpr); 1813 ID.AddInteger(Operands.size()); 1814 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1815 ID.AddPointer(Operands[i]); 1816 ID.AddPointer(L); 1817 void *IP = 0; 1818 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1819 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1820 new (S) SCEVAddRecExpr(ID, Operands, L); 1821 UniqueSCEVs.InsertNode(S, IP); 1822 return S; 1823} 1824 1825const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1826 const SCEV *RHS) { 1827 SmallVector<const SCEV *, 2> Ops; 1828 Ops.push_back(LHS); 1829 Ops.push_back(RHS); 1830 return getSMaxExpr(Ops); 1831} 1832 1833const SCEV * 1834ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1835 assert(!Ops.empty() && "Cannot get empty smax!"); 1836 if (Ops.size() == 1) return Ops[0]; 1837#ifndef NDEBUG 1838 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1839 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1840 getEffectiveSCEVType(Ops[0]->getType()) && 1841 "SCEVSMaxExpr operand types don't match!"); 1842#endif 1843 1844 // Sort by complexity, this groups all similar expression types together. 1845 GroupByComplexity(Ops, LI); 1846 1847 // If there are any constants, fold them together. 1848 unsigned Idx = 0; 1849 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1850 ++Idx; 1851 assert(Idx < Ops.size()); 1852 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1853 // We found two constants, fold them together! 1854 ConstantInt *Fold = ConstantInt::get( 1855 APIntOps::smax(LHSC->getValue()->getValue(), 1856 RHSC->getValue()->getValue())); 1857 Ops[0] = getConstant(Fold); 1858 Ops.erase(Ops.begin()+1); // Erase the folded element 1859 if (Ops.size() == 1) return Ops[0]; 1860 LHSC = cast<SCEVConstant>(Ops[0]); 1861 } 1862 1863 // If we are left with a constant minimum-int, strip it off. 1864 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1865 Ops.erase(Ops.begin()); 1866 --Idx; 1867 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1868 // If we have an smax with a constant maximum-int, it will always be 1869 // maximum-int. 1870 return Ops[0]; 1871 } 1872 } 1873 1874 if (Ops.size() == 1) return Ops[0]; 1875 1876 // Find the first SMax 1877 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1878 ++Idx; 1879 1880 // Check to see if one of the operands is an SMax. If so, expand its operands 1881 // onto our operand list, and recurse to simplify. 1882 if (Idx < Ops.size()) { 1883 bool DeletedSMax = false; 1884 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1885 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1886 Ops.erase(Ops.begin()+Idx); 1887 DeletedSMax = true; 1888 } 1889 1890 if (DeletedSMax) 1891 return getSMaxExpr(Ops); 1892 } 1893 1894 // Okay, check to see if the same value occurs in the operand list twice. If 1895 // so, delete one. Since we sorted the list, these values are required to 1896 // be adjacent. 1897 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1898 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1899 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1900 --i; --e; 1901 } 1902 1903 if (Ops.size() == 1) return Ops[0]; 1904 1905 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1906 1907 // Okay, it looks like we really DO need an smax expr. Check to see if we 1908 // already have one, otherwise create a new one. 1909 FoldingSetNodeID ID; 1910 ID.AddInteger(scSMaxExpr); 1911 ID.AddInteger(Ops.size()); 1912 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1913 ID.AddPointer(Ops[i]); 1914 void *IP = 0; 1915 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1916 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1917 new (S) SCEVSMaxExpr(ID, Ops); 1918 UniqueSCEVs.InsertNode(S, IP); 1919 return S; 1920} 1921 1922const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1923 const SCEV *RHS) { 1924 SmallVector<const SCEV *, 2> Ops; 1925 Ops.push_back(LHS); 1926 Ops.push_back(RHS); 1927 return getUMaxExpr(Ops); 1928} 1929 1930const SCEV * 1931ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1932 assert(!Ops.empty() && "Cannot get empty umax!"); 1933 if (Ops.size() == 1) return Ops[0]; 1934#ifndef NDEBUG 1935 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1936 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1937 getEffectiveSCEVType(Ops[0]->getType()) && 1938 "SCEVUMaxExpr operand types don't match!"); 1939#endif 1940 1941 // Sort by complexity, this groups all similar expression types together. 1942 GroupByComplexity(Ops, LI); 1943 1944 // If there are any constants, fold them together. 1945 unsigned Idx = 0; 1946 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1947 ++Idx; 1948 assert(Idx < Ops.size()); 1949 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1950 // We found two constants, fold them together! 1951 ConstantInt *Fold = ConstantInt::get( 1952 APIntOps::umax(LHSC->getValue()->getValue(), 1953 RHSC->getValue()->getValue())); 1954 Ops[0] = getConstant(Fold); 1955 Ops.erase(Ops.begin()+1); // Erase the folded element 1956 if (Ops.size() == 1) return Ops[0]; 1957 LHSC = cast<SCEVConstant>(Ops[0]); 1958 } 1959 1960 // If we are left with a constant minimum-int, strip it off. 1961 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1962 Ops.erase(Ops.begin()); 1963 --Idx; 1964 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 1965 // If we have an umax with a constant maximum-int, it will always be 1966 // maximum-int. 1967 return Ops[0]; 1968 } 1969 } 1970 1971 if (Ops.size() == 1) return Ops[0]; 1972 1973 // Find the first UMax 1974 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1975 ++Idx; 1976 1977 // Check to see if one of the operands is a UMax. If so, expand its operands 1978 // onto our operand list, and recurse to simplify. 1979 if (Idx < Ops.size()) { 1980 bool DeletedUMax = false; 1981 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1982 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1983 Ops.erase(Ops.begin()+Idx); 1984 DeletedUMax = true; 1985 } 1986 1987 if (DeletedUMax) 1988 return getUMaxExpr(Ops); 1989 } 1990 1991 // Okay, check to see if the same value occurs in the operand list twice. If 1992 // so, delete one. Since we sorted the list, these values are required to 1993 // be adjacent. 1994 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1995 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1996 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1997 --i; --e; 1998 } 1999 2000 if (Ops.size() == 1) return Ops[0]; 2001 2002 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2003 2004 // Okay, it looks like we really DO need a umax expr. Check to see if we 2005 // already have one, otherwise create a new one. 2006 FoldingSetNodeID ID; 2007 ID.AddInteger(scUMaxExpr); 2008 ID.AddInteger(Ops.size()); 2009 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2010 ID.AddPointer(Ops[i]); 2011 void *IP = 0; 2012 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2013 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2014 new (S) SCEVUMaxExpr(ID, Ops); 2015 UniqueSCEVs.InsertNode(S, IP); 2016 return S; 2017} 2018 2019const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2020 const SCEV *RHS) { 2021 // ~smax(~x, ~y) == smin(x, y). 2022 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2023} 2024 2025const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2026 const SCEV *RHS) { 2027 // ~umax(~x, ~y) == umin(x, y) 2028 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2029} 2030 2031const SCEV *ScalarEvolution::getUnknown(Value *V) { 2032 // Don't attempt to do anything other than create a SCEVUnknown object 2033 // here. createSCEV only calls getUnknown after checking for all other 2034 // interesting possibilities, and any other code that calls getUnknown 2035 // is doing so in order to hide a value from SCEV canonicalization. 2036 2037 FoldingSetNodeID ID; 2038 ID.AddInteger(scUnknown); 2039 ID.AddPointer(V); 2040 void *IP = 0; 2041 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2042 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2043 new (S) SCEVUnknown(ID, V); 2044 UniqueSCEVs.InsertNode(S, IP); 2045 return S; 2046} 2047 2048//===----------------------------------------------------------------------===// 2049// Basic SCEV Analysis and PHI Idiom Recognition Code 2050// 2051 2052/// isSCEVable - Test if values of the given type are analyzable within 2053/// the SCEV framework. This primarily includes integer types, and it 2054/// can optionally include pointer types if the ScalarEvolution class 2055/// has access to target-specific information. 2056bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2057 // Integers are always SCEVable. 2058 if (Ty->isInteger()) 2059 return true; 2060 2061 // Pointers are SCEVable if TargetData information is available 2062 // to provide pointer size information. 2063 if (isa<PointerType>(Ty)) 2064 return TD != NULL; 2065 2066 // Otherwise it's not SCEVable. 2067 return false; 2068} 2069 2070/// getTypeSizeInBits - Return the size in bits of the specified type, 2071/// for which isSCEVable must return true. 2072uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2073 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2074 2075 // If we have a TargetData, use it! 2076 if (TD) 2077 return TD->getTypeSizeInBits(Ty); 2078 2079 // Otherwise, we support only integer types. 2080 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 2081 return Ty->getPrimitiveSizeInBits(); 2082} 2083 2084/// getEffectiveSCEVType - Return a type with the same bitwidth as 2085/// the given type and which represents how SCEV will treat the given 2086/// type, for which isSCEVable must return true. For pointer types, 2087/// this is the pointer-sized integer type. 2088const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2089 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2090 2091 if (Ty->isInteger()) 2092 return Ty; 2093 2094 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2095 return TD->getIntPtrType(); 2096} 2097 2098const SCEV *ScalarEvolution::getCouldNotCompute() { 2099 return &CouldNotCompute; 2100} 2101 2102/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2103/// expression and create a new one. 2104const SCEV *ScalarEvolution::getSCEV(Value *V) { 2105 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2106 2107 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2108 if (I != Scalars.end()) return I->second; 2109 const SCEV *S = createSCEV(V); 2110 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2111 return S; 2112} 2113 2114/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2115/// specified signed integer value and return a SCEV for the constant. 2116const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2117 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2118 return getConstant(ConstantInt::get(ITy, Val)); 2119} 2120 2121/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2122/// 2123const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2124 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2125 return getConstant( 2126 cast<ConstantInt>(Context->getConstantExprNeg(VC->getValue()))); 2127 2128 const Type *Ty = V->getType(); 2129 Ty = getEffectiveSCEVType(Ty); 2130 return getMulExpr(V, 2131 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty)))); 2132} 2133 2134/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2135const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2136 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2137 return getConstant( 2138 cast<ConstantInt>(Context->getConstantExprNot(VC->getValue()))); 2139 2140 const Type *Ty = V->getType(); 2141 Ty = getEffectiveSCEVType(Ty); 2142 const SCEV *AllOnes = 2143 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty))); 2144 return getMinusSCEV(AllOnes, V); 2145} 2146 2147/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2148/// 2149const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2150 const SCEV *RHS) { 2151 // X - Y --> X + -Y 2152 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2153} 2154 2155/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2156/// input value to the specified type. If the type must be extended, it is zero 2157/// extended. 2158const SCEV * 2159ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2160 const Type *Ty) { 2161 const Type *SrcTy = V->getType(); 2162 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2163 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2164 "Cannot truncate or zero extend with non-integer arguments!"); 2165 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2166 return V; // No conversion 2167 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2168 return getTruncateExpr(V, Ty); 2169 return getZeroExtendExpr(V, Ty); 2170} 2171 2172/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2173/// input value to the specified type. If the type must be extended, it is sign 2174/// extended. 2175const SCEV * 2176ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2177 const Type *Ty) { 2178 const Type *SrcTy = V->getType(); 2179 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2180 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2181 "Cannot truncate or zero extend with non-integer arguments!"); 2182 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2183 return V; // No conversion 2184 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2185 return getTruncateExpr(V, Ty); 2186 return getSignExtendExpr(V, Ty); 2187} 2188 2189/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2190/// input value to the specified type. If the type must be extended, it is zero 2191/// extended. The conversion must not be narrowing. 2192const SCEV * 2193ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2194 const Type *SrcTy = V->getType(); 2195 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2196 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2197 "Cannot noop or zero extend with non-integer arguments!"); 2198 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2199 "getNoopOrZeroExtend cannot truncate!"); 2200 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2201 return V; // No conversion 2202 return getZeroExtendExpr(V, Ty); 2203} 2204 2205/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2206/// input value to the specified type. If the type must be extended, it is sign 2207/// extended. The conversion must not be narrowing. 2208const SCEV * 2209ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2210 const Type *SrcTy = V->getType(); 2211 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2212 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2213 "Cannot noop or sign extend with non-integer arguments!"); 2214 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2215 "getNoopOrSignExtend cannot truncate!"); 2216 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2217 return V; // No conversion 2218 return getSignExtendExpr(V, Ty); 2219} 2220 2221/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2222/// the input value to the specified type. If the type must be extended, 2223/// it is extended with unspecified bits. The conversion must not be 2224/// narrowing. 2225const SCEV * 2226ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2227 const Type *SrcTy = V->getType(); 2228 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2229 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2230 "Cannot noop or any extend with non-integer arguments!"); 2231 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2232 "getNoopOrAnyExtend cannot truncate!"); 2233 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2234 return V; // No conversion 2235 return getAnyExtendExpr(V, Ty); 2236} 2237 2238/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2239/// input value to the specified type. The conversion must not be widening. 2240const SCEV * 2241ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2242 const Type *SrcTy = V->getType(); 2243 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2244 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2245 "Cannot truncate or noop with non-integer arguments!"); 2246 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2247 "getTruncateOrNoop cannot extend!"); 2248 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2249 return V; // No conversion 2250 return getTruncateExpr(V, Ty); 2251} 2252 2253/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2254/// the types using zero-extension, and then perform a umax operation 2255/// with them. 2256const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2257 const SCEV *RHS) { 2258 const SCEV *PromotedLHS = LHS; 2259 const SCEV *PromotedRHS = RHS; 2260 2261 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2262 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2263 else 2264 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2265 2266 return getUMaxExpr(PromotedLHS, PromotedRHS); 2267} 2268 2269/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2270/// the types using zero-extension, and then perform a umin operation 2271/// with them. 2272const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2273 const SCEV *RHS) { 2274 const SCEV *PromotedLHS = LHS; 2275 const SCEV *PromotedRHS = RHS; 2276 2277 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2278 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2279 else 2280 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2281 2282 return getUMinExpr(PromotedLHS, PromotedRHS); 2283} 2284 2285/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2286/// the specified instruction and replaces any references to the symbolic value 2287/// SymName with the specified value. This is used during PHI resolution. 2288void 2289ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I, 2290 const SCEV *SymName, 2291 const SCEV *NewVal) { 2292 std::map<SCEVCallbackVH, const SCEV *>::iterator SI = 2293 Scalars.find(SCEVCallbackVH(I, this)); 2294 if (SI == Scalars.end()) return; 2295 2296 const SCEV *NV = 2297 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2298 if (NV == SI->second) return; // No change. 2299 2300 SI->second = NV; // Update the scalars map! 2301 2302 // Any instruction values that use this instruction might also need to be 2303 // updated! 2304 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2305 UI != E; ++UI) 2306 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2307} 2308 2309/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2310/// a loop header, making it a potential recurrence, or it doesn't. 2311/// 2312const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2313 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2314 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2315 if (L->getHeader() == PN->getParent()) { 2316 // If it lives in the loop header, it has two incoming values, one 2317 // from outside the loop, and one from inside. 2318 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2319 unsigned BackEdge = IncomingEdge^1; 2320 2321 // While we are analyzing this PHI node, handle its value symbolically. 2322 const SCEV *SymbolicName = getUnknown(PN); 2323 assert(Scalars.find(PN) == Scalars.end() && 2324 "PHI node already processed?"); 2325 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2326 2327 // Using this symbolic name for the PHI, analyze the value coming around 2328 // the back-edge. 2329 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2330 2331 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2332 // has a special value for the first iteration of the loop. 2333 2334 // If the value coming around the backedge is an add with the symbolic 2335 // value we just inserted, then we found a simple induction variable! 2336 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2337 // If there is a single occurrence of the symbolic value, replace it 2338 // with a recurrence. 2339 unsigned FoundIndex = Add->getNumOperands(); 2340 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2341 if (Add->getOperand(i) == SymbolicName) 2342 if (FoundIndex == e) { 2343 FoundIndex = i; 2344 break; 2345 } 2346 2347 if (FoundIndex != Add->getNumOperands()) { 2348 // Create an add with everything but the specified operand. 2349 SmallVector<const SCEV *, 8> Ops; 2350 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2351 if (i != FoundIndex) 2352 Ops.push_back(Add->getOperand(i)); 2353 const SCEV *Accum = getAddExpr(Ops); 2354 2355 // This is not a valid addrec if the step amount is varying each 2356 // loop iteration, but is not itself an addrec in this loop. 2357 if (Accum->isLoopInvariant(L) || 2358 (isa<SCEVAddRecExpr>(Accum) && 2359 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2360 const SCEV *StartVal = 2361 getSCEV(PN->getIncomingValue(IncomingEdge)); 2362 const SCEV *PHISCEV = 2363 getAddRecExpr(StartVal, Accum, L); 2364 2365 // Okay, for the entire analysis of this edge we assumed the PHI 2366 // to be symbolic. We now need to go back and update all of the 2367 // entries for the scalars that use the PHI (except for the PHI 2368 // itself) to use the new analyzed value instead of the "symbolic" 2369 // value. 2370 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2371 return PHISCEV; 2372 } 2373 } 2374 } else if (const SCEVAddRecExpr *AddRec = 2375 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2376 // Otherwise, this could be a loop like this: 2377 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2378 // In this case, j = {1,+,1} and BEValue is j. 2379 // Because the other in-value of i (0) fits the evolution of BEValue 2380 // i really is an addrec evolution. 2381 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2382 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2383 2384 // If StartVal = j.start - j.stride, we can use StartVal as the 2385 // initial step of the addrec evolution. 2386 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2387 AddRec->getOperand(1))) { 2388 const SCEV *PHISCEV = 2389 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2390 2391 // Okay, for the entire analysis of this edge we assumed the PHI 2392 // to be symbolic. We now need to go back and update all of the 2393 // entries for the scalars that use the PHI (except for the PHI 2394 // itself) to use the new analyzed value instead of the "symbolic" 2395 // value. 2396 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2397 return PHISCEV; 2398 } 2399 } 2400 } 2401 2402 return SymbolicName; 2403 } 2404 2405 // If it's not a loop phi, we can't handle it yet. 2406 return getUnknown(PN); 2407} 2408 2409/// createNodeForGEP - Expand GEP instructions into add and multiply 2410/// operations. This allows them to be analyzed by regular SCEV code. 2411/// 2412const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) { 2413 2414 const Type *IntPtrTy = TD->getIntPtrType(); 2415 Value *Base = GEP->getOperand(0); 2416 // Don't attempt to analyze GEPs over unsized objects. 2417 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2418 return getUnknown(GEP); 2419 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2420 gep_type_iterator GTI = gep_type_begin(GEP); 2421 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2422 E = GEP->op_end(); 2423 I != E; ++I) { 2424 Value *Index = *I; 2425 // Compute the (potentially symbolic) offset in bytes for this index. 2426 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2427 // For a struct, add the member offset. 2428 const StructLayout &SL = *TD->getStructLayout(STy); 2429 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2430 uint64_t Offset = SL.getElementOffset(FieldNo); 2431 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy)); 2432 } else { 2433 // For an array, add the element offset, explicitly scaled. 2434 const SCEV *LocalOffset = getSCEV(Index); 2435 if (!isa<PointerType>(LocalOffset->getType())) 2436 // Getelementptr indicies are signed. 2437 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2438 LocalOffset = 2439 getMulExpr(LocalOffset, 2440 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy)); 2441 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2442 } 2443 } 2444 return getAddExpr(getSCEV(Base), TotalOffset); 2445} 2446 2447/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2448/// guaranteed to end in (at every loop iteration). It is, at the same time, 2449/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2450/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2451uint32_t 2452ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2453 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2454 return C->getValue()->getValue().countTrailingZeros(); 2455 2456 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2457 return std::min(GetMinTrailingZeros(T->getOperand()), 2458 (uint32_t)getTypeSizeInBits(T->getType())); 2459 2460 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2461 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2462 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2463 getTypeSizeInBits(E->getType()) : OpRes; 2464 } 2465 2466 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2467 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2468 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2469 getTypeSizeInBits(E->getType()) : OpRes; 2470 } 2471 2472 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2473 // The result is the min of all operands results. 2474 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2475 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2476 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2477 return MinOpRes; 2478 } 2479 2480 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2481 // The result is the sum of all operands results. 2482 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2483 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2484 for (unsigned i = 1, e = M->getNumOperands(); 2485 SumOpRes != BitWidth && i != e; ++i) 2486 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2487 BitWidth); 2488 return SumOpRes; 2489 } 2490 2491 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2492 // The result is the min of all operands results. 2493 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2494 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2495 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2496 return MinOpRes; 2497 } 2498 2499 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2500 // The result is the min of all operands results. 2501 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2502 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2503 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2504 return MinOpRes; 2505 } 2506 2507 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2508 // The result is the min of all operands results. 2509 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2510 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2511 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2512 return MinOpRes; 2513 } 2514 2515 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2516 // For a SCEVUnknown, ask ValueTracking. 2517 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2518 APInt Mask = APInt::getAllOnesValue(BitWidth); 2519 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2520 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2521 return Zeros.countTrailingOnes(); 2522 } 2523 2524 // SCEVUDivExpr 2525 return 0; 2526} 2527 2528/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2529/// 2530ConstantRange 2531ScalarEvolution::getUnsignedRange(const SCEV *S) { 2532 2533 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2534 return ConstantRange(C->getValue()->getValue()); 2535 2536 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2537 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2538 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2539 X = X.add(getUnsignedRange(Add->getOperand(i))); 2540 return X; 2541 } 2542 2543 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2544 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2545 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2546 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2547 return X; 2548 } 2549 2550 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2551 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2552 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2553 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2554 return X; 2555 } 2556 2557 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2558 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2559 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2560 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2561 return X; 2562 } 2563 2564 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2565 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2566 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2567 return X.udiv(Y); 2568 } 2569 2570 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2571 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2572 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2573 } 2574 2575 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2576 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2577 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2578 } 2579 2580 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2581 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2582 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2583 } 2584 2585 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2586 2587 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2588 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2589 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2590 if (!Trip) return FullSet; 2591 2592 // TODO: non-affine addrec 2593 if (AddRec->isAffine()) { 2594 const Type *Ty = AddRec->getType(); 2595 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2596 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2597 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2598 2599 const SCEV *Start = AddRec->getStart(); 2600 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2601 2602 // Check for overflow. 2603 if (!isKnownPredicate(ICmpInst::ICMP_ULE, Start, End)) 2604 return FullSet; 2605 2606 ConstantRange StartRange = getUnsignedRange(Start); 2607 ConstantRange EndRange = getUnsignedRange(End); 2608 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2609 EndRange.getUnsignedMin()); 2610 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2611 EndRange.getUnsignedMax()); 2612 if (Min.isMinValue() && Max.isMaxValue()) 2613 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2614 return ConstantRange(Min, Max+1); 2615 } 2616 } 2617 } 2618 2619 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2620 // For a SCEVUnknown, ask ValueTracking. 2621 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2622 APInt Mask = APInt::getAllOnesValue(BitWidth); 2623 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2624 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2625 return ConstantRange(Ones, ~Zeros); 2626 } 2627 2628 return FullSet; 2629} 2630 2631/// getSignedRange - Determine the signed range for a particular SCEV. 2632/// 2633ConstantRange 2634ScalarEvolution::getSignedRange(const SCEV *S) { 2635 2636 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2637 return ConstantRange(C->getValue()->getValue()); 2638 2639 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2640 ConstantRange X = getSignedRange(Add->getOperand(0)); 2641 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2642 X = X.add(getSignedRange(Add->getOperand(i))); 2643 return X; 2644 } 2645 2646 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2647 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2648 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2649 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2650 return X; 2651 } 2652 2653 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2654 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2655 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2656 X = X.smax(getSignedRange(SMax->getOperand(i))); 2657 return X; 2658 } 2659 2660 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2661 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2662 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2663 X = X.umax(getSignedRange(UMax->getOperand(i))); 2664 return X; 2665 } 2666 2667 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2668 ConstantRange X = getSignedRange(UDiv->getLHS()); 2669 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2670 return X.udiv(Y); 2671 } 2672 2673 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2674 ConstantRange X = getSignedRange(ZExt->getOperand()); 2675 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2676 } 2677 2678 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2679 ConstantRange X = getSignedRange(SExt->getOperand()); 2680 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2681 } 2682 2683 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2684 ConstantRange X = getSignedRange(Trunc->getOperand()); 2685 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2686 } 2687 2688 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2689 2690 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2691 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2692 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2693 if (!Trip) return FullSet; 2694 2695 // TODO: non-affine addrec 2696 if (AddRec->isAffine()) { 2697 const Type *Ty = AddRec->getType(); 2698 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2699 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2700 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2701 2702 const SCEV *Start = AddRec->getStart(); 2703 const SCEV *Step = AddRec->getStepRecurrence(*this); 2704 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2705 2706 // Check for overflow. 2707 if (!(isKnownPositive(Step) && 2708 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2709 !(isKnownNegative(Step) && 2710 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2711 return FullSet; 2712 2713 ConstantRange StartRange = getSignedRange(Start); 2714 ConstantRange EndRange = getSignedRange(End); 2715 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2716 EndRange.getSignedMin()); 2717 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2718 EndRange.getSignedMax()); 2719 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2720 return ConstantRange(Min.getBitWidth(), /*isFullSet=*/true); 2721 return ConstantRange(Min, Max+1); 2722 } 2723 } 2724 } 2725 2726 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2727 // For a SCEVUnknown, ask ValueTracking. 2728 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2729 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2730 if (NS == 1) 2731 return FullSet; 2732 return 2733 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2734 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2735 } 2736 2737 return FullSet; 2738} 2739 2740/// createSCEV - We know that there is no SCEV for the specified value. 2741/// Analyze the expression. 2742/// 2743const SCEV *ScalarEvolution::createSCEV(Value *V) { 2744 if (!isSCEVable(V->getType())) 2745 return getUnknown(V); 2746 2747 unsigned Opcode = Instruction::UserOp1; 2748 if (Instruction *I = dyn_cast<Instruction>(V)) 2749 Opcode = I->getOpcode(); 2750 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2751 Opcode = CE->getOpcode(); 2752 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2753 return getConstant(CI); 2754 else if (isa<ConstantPointerNull>(V)) 2755 return getIntegerSCEV(0, V->getType()); 2756 else if (isa<UndefValue>(V)) 2757 return getIntegerSCEV(0, V->getType()); 2758 else 2759 return getUnknown(V); 2760 2761 User *U = cast<User>(V); 2762 switch (Opcode) { 2763 case Instruction::Add: 2764 return getAddExpr(getSCEV(U->getOperand(0)), 2765 getSCEV(U->getOperand(1))); 2766 case Instruction::Mul: 2767 return getMulExpr(getSCEV(U->getOperand(0)), 2768 getSCEV(U->getOperand(1))); 2769 case Instruction::UDiv: 2770 return getUDivExpr(getSCEV(U->getOperand(0)), 2771 getSCEV(U->getOperand(1))); 2772 case Instruction::Sub: 2773 return getMinusSCEV(getSCEV(U->getOperand(0)), 2774 getSCEV(U->getOperand(1))); 2775 case Instruction::And: 2776 // For an expression like x&255 that merely masks off the high bits, 2777 // use zext(trunc(x)) as the SCEV expression. 2778 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2779 if (CI->isNullValue()) 2780 return getSCEV(U->getOperand(1)); 2781 if (CI->isAllOnesValue()) 2782 return getSCEV(U->getOperand(0)); 2783 const APInt &A = CI->getValue(); 2784 2785 // Instcombine's ShrinkDemandedConstant may strip bits out of 2786 // constants, obscuring what would otherwise be a low-bits mask. 2787 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2788 // knew about to reconstruct a low-bits mask value. 2789 unsigned LZ = A.countLeadingZeros(); 2790 unsigned BitWidth = A.getBitWidth(); 2791 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2792 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2793 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2794 2795 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2796 2797 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2798 return 2799 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2800 IntegerType::get(BitWidth - LZ)), 2801 U->getType()); 2802 } 2803 break; 2804 2805 case Instruction::Or: 2806 // If the RHS of the Or is a constant, we may have something like: 2807 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2808 // optimizations will transparently handle this case. 2809 // 2810 // In order for this transformation to be safe, the LHS must be of the 2811 // form X*(2^n) and the Or constant must be less than 2^n. 2812 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2813 const SCEV *LHS = getSCEV(U->getOperand(0)); 2814 const APInt &CIVal = CI->getValue(); 2815 if (GetMinTrailingZeros(LHS) >= 2816 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2817 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2818 } 2819 break; 2820 case Instruction::Xor: 2821 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2822 // If the RHS of the xor is a signbit, then this is just an add. 2823 // Instcombine turns add of signbit into xor as a strength reduction step. 2824 if (CI->getValue().isSignBit()) 2825 return getAddExpr(getSCEV(U->getOperand(0)), 2826 getSCEV(U->getOperand(1))); 2827 2828 // If the RHS of xor is -1, then this is a not operation. 2829 if (CI->isAllOnesValue()) 2830 return getNotSCEV(getSCEV(U->getOperand(0))); 2831 2832 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2833 // This is a variant of the check for xor with -1, and it handles 2834 // the case where instcombine has trimmed non-demanded bits out 2835 // of an xor with -1. 2836 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2837 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2838 if (BO->getOpcode() == Instruction::And && 2839 LCI->getValue() == CI->getValue()) 2840 if (const SCEVZeroExtendExpr *Z = 2841 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2842 const Type *UTy = U->getType(); 2843 const SCEV *Z0 = Z->getOperand(); 2844 const Type *Z0Ty = Z0->getType(); 2845 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2846 2847 // If C is a low-bits mask, the zero extend is zerving to 2848 // mask off the high bits. Complement the operand and 2849 // re-apply the zext. 2850 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2851 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2852 2853 // If C is a single bit, it may be in the sign-bit position 2854 // before the zero-extend. In this case, represent the xor 2855 // using an add, which is equivalent, and re-apply the zext. 2856 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2857 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2858 Trunc.isSignBit()) 2859 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2860 UTy); 2861 } 2862 } 2863 break; 2864 2865 case Instruction::Shl: 2866 // Turn shift left of a constant amount into a multiply. 2867 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2868 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2869 Constant *X = ConstantInt::get( 2870 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2871 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2872 } 2873 break; 2874 2875 case Instruction::LShr: 2876 // Turn logical shift right of a constant into a unsigned divide. 2877 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2878 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2879 Constant *X = ConstantInt::get( 2880 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2881 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2882 } 2883 break; 2884 2885 case Instruction::AShr: 2886 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2887 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2888 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2889 if (L->getOpcode() == Instruction::Shl && 2890 L->getOperand(1) == U->getOperand(1)) { 2891 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2892 uint64_t Amt = BitWidth - CI->getZExtValue(); 2893 if (Amt == BitWidth) 2894 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2895 if (Amt > BitWidth) 2896 return getIntegerSCEV(0, U->getType()); // value is undefined 2897 return 2898 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2899 IntegerType::get(Amt)), 2900 U->getType()); 2901 } 2902 break; 2903 2904 case Instruction::Trunc: 2905 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2906 2907 case Instruction::ZExt: 2908 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2909 2910 case Instruction::SExt: 2911 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2912 2913 case Instruction::BitCast: 2914 // BitCasts are no-op casts so we just eliminate the cast. 2915 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2916 return getSCEV(U->getOperand(0)); 2917 break; 2918 2919 case Instruction::IntToPtr: 2920 if (!TD) break; // Without TD we can't analyze pointers. 2921 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2922 TD->getIntPtrType()); 2923 2924 case Instruction::PtrToInt: 2925 if (!TD) break; // Without TD we can't analyze pointers. 2926 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2927 U->getType()); 2928 2929 case Instruction::GetElementPtr: 2930 if (!TD) break; // Without TD we can't analyze pointers. 2931 return createNodeForGEP(U); 2932 2933 case Instruction::PHI: 2934 return createNodeForPHI(cast<PHINode>(U)); 2935 2936 case Instruction::Select: 2937 // This could be a smax or umax that was lowered earlier. 2938 // Try to recover it. 2939 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2940 Value *LHS = ICI->getOperand(0); 2941 Value *RHS = ICI->getOperand(1); 2942 switch (ICI->getPredicate()) { 2943 case ICmpInst::ICMP_SLT: 2944 case ICmpInst::ICMP_SLE: 2945 std::swap(LHS, RHS); 2946 // fall through 2947 case ICmpInst::ICMP_SGT: 2948 case ICmpInst::ICMP_SGE: 2949 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2950 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2951 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2952 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2953 break; 2954 case ICmpInst::ICMP_ULT: 2955 case ICmpInst::ICMP_ULE: 2956 std::swap(LHS, RHS); 2957 // fall through 2958 case ICmpInst::ICMP_UGT: 2959 case ICmpInst::ICMP_UGE: 2960 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2961 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2962 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2963 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2964 break; 2965 case ICmpInst::ICMP_NE: 2966 // n != 0 ? n : 1 -> umax(n, 1) 2967 if (LHS == U->getOperand(1) && 2968 isa<ConstantInt>(U->getOperand(2)) && 2969 cast<ConstantInt>(U->getOperand(2))->isOne() && 2970 isa<ConstantInt>(RHS) && 2971 cast<ConstantInt>(RHS)->isZero()) 2972 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2973 break; 2974 case ICmpInst::ICMP_EQ: 2975 // n == 0 ? 1 : n -> umax(n, 1) 2976 if (LHS == U->getOperand(2) && 2977 isa<ConstantInt>(U->getOperand(1)) && 2978 cast<ConstantInt>(U->getOperand(1))->isOne() && 2979 isa<ConstantInt>(RHS) && 2980 cast<ConstantInt>(RHS)->isZero()) 2981 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 2982 break; 2983 default: 2984 break; 2985 } 2986 } 2987 2988 default: // We cannot analyze this expression. 2989 break; 2990 } 2991 2992 return getUnknown(V); 2993} 2994 2995 2996 2997//===----------------------------------------------------------------------===// 2998// Iteration Count Computation Code 2999// 3000 3001/// getBackedgeTakenCount - If the specified loop has a predictable 3002/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3003/// object. The backedge-taken count is the number of times the loop header 3004/// will be branched to from within the loop. This is one less than the 3005/// trip count of the loop, since it doesn't count the first iteration, 3006/// when the header is branched to from outside the loop. 3007/// 3008/// Note that it is not valid to call this method on a loop without a 3009/// loop-invariant backedge-taken count (see 3010/// hasLoopInvariantBackedgeTakenCount). 3011/// 3012const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3013 return getBackedgeTakenInfo(L).Exact; 3014} 3015 3016/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3017/// return the least SCEV value that is known never to be less than the 3018/// actual backedge taken count. 3019const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3020 return getBackedgeTakenInfo(L).Max; 3021} 3022 3023/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3024/// onto the given Worklist. 3025static void 3026PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3027 BasicBlock *Header = L->getHeader(); 3028 3029 // Push all Loop-header PHIs onto the Worklist stack. 3030 for (BasicBlock::iterator I = Header->begin(); 3031 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3032 Worklist.push_back(PN); 3033} 3034 3035/// PushDefUseChildren - Push users of the given Instruction 3036/// onto the given Worklist. 3037static void 3038PushDefUseChildren(Instruction *I, 3039 SmallVectorImpl<Instruction *> &Worklist) { 3040 // Push the def-use children onto the Worklist stack. 3041 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 3042 UI != UE; ++UI) 3043 Worklist.push_back(cast<Instruction>(UI)); 3044} 3045 3046const ScalarEvolution::BackedgeTakenInfo & 3047ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3048 // Initially insert a CouldNotCompute for this loop. If the insertion 3049 // succeeds, procede to actually compute a backedge-taken count and 3050 // update the value. The temporary CouldNotCompute value tells SCEV 3051 // code elsewhere that it shouldn't attempt to request a new 3052 // backedge-taken count, which could result in infinite recursion. 3053 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3054 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3055 if (Pair.second) { 3056 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3057 if (ItCount.Exact != getCouldNotCompute()) { 3058 assert(ItCount.Exact->isLoopInvariant(L) && 3059 ItCount.Max->isLoopInvariant(L) && 3060 "Computed trip count isn't loop invariant for loop!"); 3061 ++NumTripCountsComputed; 3062 3063 // Update the value in the map. 3064 Pair.first->second = ItCount; 3065 } else { 3066 if (ItCount.Max != getCouldNotCompute()) 3067 // Update the value in the map. 3068 Pair.first->second = ItCount; 3069 if (isa<PHINode>(L->getHeader()->begin())) 3070 // Only count loops that have phi nodes as not being computable. 3071 ++NumTripCountsNotComputed; 3072 } 3073 3074 // Now that we know more about the trip count for this loop, forget any 3075 // existing SCEV values for PHI nodes in this loop since they are only 3076 // conservative estimates made without the benefit of trip count 3077 // information. This is similar to the code in 3078 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3079 // nodes specially. 3080 if (ItCount.hasAnyInfo()) { 3081 SmallVector<Instruction *, 16> Worklist; 3082 PushLoopPHIs(L, Worklist); 3083 3084 SmallPtrSet<Instruction *, 8> Visited; 3085 while (!Worklist.empty()) { 3086 Instruction *I = Worklist.pop_back_val(); 3087 if (!Visited.insert(I)) continue; 3088 3089 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3090 Scalars.find(static_cast<Value *>(I)); 3091 if (It != Scalars.end()) { 3092 // SCEVUnknown for a PHI either means that it has an unrecognized 3093 // structure, or it's a PHI that's in the progress of being computed 3094 // by createNodeForPHI. In the former case, additional loop trip 3095 // count information isn't going to change anything. In the later 3096 // case, createNodeForPHI will perform the necessary updates on its 3097 // own when it gets to that point. 3098 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 3099 Scalars.erase(It); 3100 ValuesAtScopes.erase(I); 3101 if (PHINode *PN = dyn_cast<PHINode>(I)) 3102 ConstantEvolutionLoopExitValue.erase(PN); 3103 } 3104 3105 PushDefUseChildren(I, Worklist); 3106 } 3107 } 3108 } 3109 return Pair.first->second; 3110} 3111 3112/// forgetLoopBackedgeTakenCount - This method should be called by the 3113/// client when it has changed a loop in a way that may effect 3114/// ScalarEvolution's ability to compute a trip count, or if the loop 3115/// is deleted. 3116void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3117 BackedgeTakenCounts.erase(L); 3118 3119 SmallVector<Instruction *, 16> Worklist; 3120 PushLoopPHIs(L, Worklist); 3121 3122 SmallPtrSet<Instruction *, 8> Visited; 3123 while (!Worklist.empty()) { 3124 Instruction *I = Worklist.pop_back_val(); 3125 if (!Visited.insert(I)) continue; 3126 3127 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3128 Scalars.find(static_cast<Value *>(I)); 3129 if (It != Scalars.end()) { 3130 Scalars.erase(It); 3131 ValuesAtScopes.erase(I); 3132 if (PHINode *PN = dyn_cast<PHINode>(I)) 3133 ConstantEvolutionLoopExitValue.erase(PN); 3134 } 3135 3136 PushDefUseChildren(I, Worklist); 3137 } 3138} 3139 3140/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3141/// of the specified loop will execute. 3142ScalarEvolution::BackedgeTakenInfo 3143ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3144 SmallVector<BasicBlock*, 8> ExitingBlocks; 3145 L->getExitingBlocks(ExitingBlocks); 3146 3147 // Examine all exits and pick the most conservative values. 3148 const SCEV *BECount = getCouldNotCompute(); 3149 const SCEV *MaxBECount = getCouldNotCompute(); 3150 bool CouldNotComputeBECount = false; 3151 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3152 BackedgeTakenInfo NewBTI = 3153 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3154 3155 if (NewBTI.Exact == getCouldNotCompute()) { 3156 // We couldn't compute an exact value for this exit, so 3157 // we won't be able to compute an exact value for the loop. 3158 CouldNotComputeBECount = true; 3159 BECount = getCouldNotCompute(); 3160 } else if (!CouldNotComputeBECount) { 3161 if (BECount == getCouldNotCompute()) 3162 BECount = NewBTI.Exact; 3163 else 3164 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3165 } 3166 if (MaxBECount == getCouldNotCompute()) 3167 MaxBECount = NewBTI.Max; 3168 else if (NewBTI.Max != getCouldNotCompute()) 3169 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3170 } 3171 3172 return BackedgeTakenInfo(BECount, MaxBECount); 3173} 3174 3175/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3176/// of the specified loop will execute if it exits via the specified block. 3177ScalarEvolution::BackedgeTakenInfo 3178ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3179 BasicBlock *ExitingBlock) { 3180 3181 // Okay, we've chosen an exiting block. See what condition causes us to 3182 // exit at this block. 3183 // 3184 // FIXME: we should be able to handle switch instructions (with a single exit) 3185 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3186 if (ExitBr == 0) return getCouldNotCompute(); 3187 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3188 3189 // At this point, we know we have a conditional branch that determines whether 3190 // the loop is exited. However, we don't know if the branch is executed each 3191 // time through the loop. If not, then the execution count of the branch will 3192 // not be equal to the trip count of the loop. 3193 // 3194 // Currently we check for this by checking to see if the Exit branch goes to 3195 // the loop header. If so, we know it will always execute the same number of 3196 // times as the loop. We also handle the case where the exit block *is* the 3197 // loop header. This is common for un-rotated loops. 3198 // 3199 // If both of those tests fail, walk up the unique predecessor chain to the 3200 // header, stopping if there is an edge that doesn't exit the loop. If the 3201 // header is reached, the execution count of the branch will be equal to the 3202 // trip count of the loop. 3203 // 3204 // More extensive analysis could be done to handle more cases here. 3205 // 3206 if (ExitBr->getSuccessor(0) != L->getHeader() && 3207 ExitBr->getSuccessor(1) != L->getHeader() && 3208 ExitBr->getParent() != L->getHeader()) { 3209 // The simple checks failed, try climbing the unique predecessor chain 3210 // up to the header. 3211 bool Ok = false; 3212 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3213 BasicBlock *Pred = BB->getUniquePredecessor(); 3214 if (!Pred) 3215 return getCouldNotCompute(); 3216 TerminatorInst *PredTerm = Pred->getTerminator(); 3217 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3218 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3219 if (PredSucc == BB) 3220 continue; 3221 // If the predecessor has a successor that isn't BB and isn't 3222 // outside the loop, assume the worst. 3223 if (L->contains(PredSucc)) 3224 return getCouldNotCompute(); 3225 } 3226 if (Pred == L->getHeader()) { 3227 Ok = true; 3228 break; 3229 } 3230 BB = Pred; 3231 } 3232 if (!Ok) 3233 return getCouldNotCompute(); 3234 } 3235 3236 // Procede to the next level to examine the exit condition expression. 3237 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3238 ExitBr->getSuccessor(0), 3239 ExitBr->getSuccessor(1)); 3240} 3241 3242/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3243/// backedge of the specified loop will execute if its exit condition 3244/// were a conditional branch of ExitCond, TBB, and FBB. 3245ScalarEvolution::BackedgeTakenInfo 3246ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3247 Value *ExitCond, 3248 BasicBlock *TBB, 3249 BasicBlock *FBB) { 3250 // Check if the controlling expression for this loop is an And or Or. 3251 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3252 if (BO->getOpcode() == Instruction::And) { 3253 // Recurse on the operands of the and. 3254 BackedgeTakenInfo BTI0 = 3255 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3256 BackedgeTakenInfo BTI1 = 3257 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3258 const SCEV *BECount = getCouldNotCompute(); 3259 const SCEV *MaxBECount = getCouldNotCompute(); 3260 if (L->contains(TBB)) { 3261 // Both conditions must be true for the loop to continue executing. 3262 // Choose the less conservative count. 3263 if (BTI0.Exact == getCouldNotCompute() || 3264 BTI1.Exact == getCouldNotCompute()) 3265 BECount = getCouldNotCompute(); 3266 else 3267 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3268 if (BTI0.Max == getCouldNotCompute()) 3269 MaxBECount = BTI1.Max; 3270 else if (BTI1.Max == getCouldNotCompute()) 3271 MaxBECount = BTI0.Max; 3272 else 3273 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3274 } else { 3275 // Both conditions must be true for the loop to exit. 3276 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3277 if (BTI0.Exact != getCouldNotCompute() && 3278 BTI1.Exact != getCouldNotCompute()) 3279 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3280 if (BTI0.Max != getCouldNotCompute() && 3281 BTI1.Max != getCouldNotCompute()) 3282 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3283 } 3284 3285 return BackedgeTakenInfo(BECount, MaxBECount); 3286 } 3287 if (BO->getOpcode() == Instruction::Or) { 3288 // Recurse on the operands of the or. 3289 BackedgeTakenInfo BTI0 = 3290 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3291 BackedgeTakenInfo BTI1 = 3292 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3293 const SCEV *BECount = getCouldNotCompute(); 3294 const SCEV *MaxBECount = getCouldNotCompute(); 3295 if (L->contains(FBB)) { 3296 // Both conditions must be false for the loop to continue executing. 3297 // Choose the less conservative count. 3298 if (BTI0.Exact == getCouldNotCompute() || 3299 BTI1.Exact == getCouldNotCompute()) 3300 BECount = getCouldNotCompute(); 3301 else 3302 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3303 if (BTI0.Max == getCouldNotCompute()) 3304 MaxBECount = BTI1.Max; 3305 else if (BTI1.Max == getCouldNotCompute()) 3306 MaxBECount = BTI0.Max; 3307 else 3308 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3309 } else { 3310 // Both conditions must be false for the loop to exit. 3311 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3312 if (BTI0.Exact != getCouldNotCompute() && 3313 BTI1.Exact != getCouldNotCompute()) 3314 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3315 if (BTI0.Max != getCouldNotCompute() && 3316 BTI1.Max != getCouldNotCompute()) 3317 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3318 } 3319 3320 return BackedgeTakenInfo(BECount, MaxBECount); 3321 } 3322 } 3323 3324 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3325 // Procede to the next level to examine the icmp. 3326 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3327 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3328 3329 // If it's not an integer or pointer comparison then compute it the hard way. 3330 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3331} 3332 3333/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3334/// backedge of the specified loop will execute if its exit condition 3335/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3336ScalarEvolution::BackedgeTakenInfo 3337ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3338 ICmpInst *ExitCond, 3339 BasicBlock *TBB, 3340 BasicBlock *FBB) { 3341 3342 // If the condition was exit on true, convert the condition to exit on false 3343 ICmpInst::Predicate Cond; 3344 if (!L->contains(FBB)) 3345 Cond = ExitCond->getPredicate(); 3346 else 3347 Cond = ExitCond->getInversePredicate(); 3348 3349 // Handle common loops like: for (X = "string"; *X; ++X) 3350 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3351 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3352 const SCEV *ItCnt = 3353 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3354 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3355 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3356 return BackedgeTakenInfo(ItCnt, 3357 isa<SCEVConstant>(ItCnt) ? ItCnt : 3358 getConstant(APInt::getMaxValue(BitWidth)-1)); 3359 } 3360 } 3361 3362 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3363 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3364 3365 // Try to evaluate any dependencies out of the loop. 3366 LHS = getSCEVAtScope(LHS, L); 3367 RHS = getSCEVAtScope(RHS, L); 3368 3369 // At this point, we would like to compute how many iterations of the 3370 // loop the predicate will return true for these inputs. 3371 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3372 // If there is a loop-invariant, force it into the RHS. 3373 std::swap(LHS, RHS); 3374 Cond = ICmpInst::getSwappedPredicate(Cond); 3375 } 3376 3377 // If we have a comparison of a chrec against a constant, try to use value 3378 // ranges to answer this query. 3379 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3380 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3381 if (AddRec->getLoop() == L) { 3382 // Form the constant range. 3383 ConstantRange CompRange( 3384 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3385 3386 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3387 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3388 } 3389 3390 switch (Cond) { 3391 case ICmpInst::ICMP_NE: { // while (X != Y) 3392 // Convert to: while (X-Y != 0) 3393 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3394 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3395 break; 3396 } 3397 case ICmpInst::ICMP_EQ: { 3398 // Convert to: while (X-Y == 0) // while (X == Y) 3399 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3400 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3401 break; 3402 } 3403 case ICmpInst::ICMP_SLT: { 3404 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3405 if (BTI.hasAnyInfo()) return BTI; 3406 break; 3407 } 3408 case ICmpInst::ICMP_SGT: { 3409 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3410 getNotSCEV(RHS), L, true); 3411 if (BTI.hasAnyInfo()) return BTI; 3412 break; 3413 } 3414 case ICmpInst::ICMP_ULT: { 3415 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3416 if (BTI.hasAnyInfo()) return BTI; 3417 break; 3418 } 3419 case ICmpInst::ICMP_UGT: { 3420 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3421 getNotSCEV(RHS), L, false); 3422 if (BTI.hasAnyInfo()) return BTI; 3423 break; 3424 } 3425 default: 3426#if 0 3427 errs() << "ComputeBackedgeTakenCount "; 3428 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3429 errs() << "[unsigned] "; 3430 errs() << *LHS << " " 3431 << Instruction::getOpcodeName(Instruction::ICmp) 3432 << " " << *RHS << "\n"; 3433#endif 3434 break; 3435 } 3436 return 3437 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3438} 3439 3440static ConstantInt * 3441EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3442 ScalarEvolution &SE) { 3443 const SCEV *InVal = SE.getConstant(C); 3444 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3445 assert(isa<SCEVConstant>(Val) && 3446 "Evaluation of SCEV at constant didn't fold correctly?"); 3447 return cast<SCEVConstant>(Val)->getValue(); 3448} 3449 3450/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3451/// and a GEP expression (missing the pointer index) indexing into it, return 3452/// the addressed element of the initializer or null if the index expression is 3453/// invalid. 3454static Constant * 3455GetAddressedElementFromGlobal(LLVMContext *Context, GlobalVariable *GV, 3456 const std::vector<ConstantInt*> &Indices) { 3457 Constant *Init = GV->getInitializer(); 3458 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3459 uint64_t Idx = Indices[i]->getZExtValue(); 3460 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3461 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3462 Init = cast<Constant>(CS->getOperand(Idx)); 3463 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3464 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3465 Init = cast<Constant>(CA->getOperand(Idx)); 3466 } else if (isa<ConstantAggregateZero>(Init)) { 3467 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3468 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3469 Init = Context->getNullValue(STy->getElementType(Idx)); 3470 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3471 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3472 Init = Context->getNullValue(ATy->getElementType()); 3473 } else { 3474 LLVM_UNREACHABLE("Unknown constant aggregate type!"); 3475 } 3476 return 0; 3477 } else { 3478 return 0; // Unknown initializer type 3479 } 3480 } 3481 return Init; 3482} 3483 3484/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3485/// 'icmp op load X, cst', try to see if we can compute the backedge 3486/// execution count. 3487const SCEV * 3488ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3489 LoadInst *LI, 3490 Constant *RHS, 3491 const Loop *L, 3492 ICmpInst::Predicate predicate) { 3493 if (LI->isVolatile()) return getCouldNotCompute(); 3494 3495 // Check to see if the loaded pointer is a getelementptr of a global. 3496 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3497 if (!GEP) return getCouldNotCompute(); 3498 3499 // Make sure that it is really a constant global we are gepping, with an 3500 // initializer, and make sure the first IDX is really 0. 3501 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3502 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3503 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3504 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3505 return getCouldNotCompute(); 3506 3507 // Okay, we allow one non-constant index into the GEP instruction. 3508 Value *VarIdx = 0; 3509 std::vector<ConstantInt*> Indexes; 3510 unsigned VarIdxNum = 0; 3511 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3512 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3513 Indexes.push_back(CI); 3514 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3515 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3516 VarIdx = GEP->getOperand(i); 3517 VarIdxNum = i-2; 3518 Indexes.push_back(0); 3519 } 3520 3521 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3522 // Check to see if X is a loop variant variable value now. 3523 const SCEV *Idx = getSCEV(VarIdx); 3524 Idx = getSCEVAtScope(Idx, L); 3525 3526 // We can only recognize very limited forms of loop index expressions, in 3527 // particular, only affine AddRec's like {C1,+,C2}. 3528 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3529 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3530 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3531 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3532 return getCouldNotCompute(); 3533 3534 unsigned MaxSteps = MaxBruteForceIterations; 3535 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3536 ConstantInt *ItCst = 3537 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3538 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3539 3540 // Form the GEP offset. 3541 Indexes[VarIdxNum] = Val; 3542 3543 Constant *Result = GetAddressedElementFromGlobal(Context, GV, Indexes); 3544 if (Result == 0) break; // Cannot compute! 3545 3546 // Evaluate the condition for this iteration. 3547 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3548 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3549 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3550#if 0 3551 errs() << "\n***\n*** Computed loop count " << *ItCst 3552 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3553 << "***\n"; 3554#endif 3555 ++NumArrayLenItCounts; 3556 return getConstant(ItCst); // Found terminating iteration! 3557 } 3558 } 3559 return getCouldNotCompute(); 3560} 3561 3562 3563/// CanConstantFold - Return true if we can constant fold an instruction of the 3564/// specified type, assuming that all operands were constants. 3565static bool CanConstantFold(const Instruction *I) { 3566 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3567 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3568 return true; 3569 3570 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3571 if (const Function *F = CI->getCalledFunction()) 3572 return canConstantFoldCallTo(F); 3573 return false; 3574} 3575 3576/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3577/// in the loop that V is derived from. We allow arbitrary operations along the 3578/// way, but the operands of an operation must either be constants or a value 3579/// derived from a constant PHI. If this expression does not fit with these 3580/// constraints, return null. 3581static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3582 // If this is not an instruction, or if this is an instruction outside of the 3583 // loop, it can't be derived from a loop PHI. 3584 Instruction *I = dyn_cast<Instruction>(V); 3585 if (I == 0 || !L->contains(I->getParent())) return 0; 3586 3587 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3588 if (L->getHeader() == I->getParent()) 3589 return PN; 3590 else 3591 // We don't currently keep track of the control flow needed to evaluate 3592 // PHIs, so we cannot handle PHIs inside of loops. 3593 return 0; 3594 } 3595 3596 // If we won't be able to constant fold this expression even if the operands 3597 // are constants, return early. 3598 if (!CanConstantFold(I)) return 0; 3599 3600 // Otherwise, we can evaluate this instruction if all of its operands are 3601 // constant or derived from a PHI node themselves. 3602 PHINode *PHI = 0; 3603 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3604 if (!(isa<Constant>(I->getOperand(Op)) || 3605 isa<GlobalValue>(I->getOperand(Op)))) { 3606 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3607 if (P == 0) return 0; // Not evolving from PHI 3608 if (PHI == 0) 3609 PHI = P; 3610 else if (PHI != P) 3611 return 0; // Evolving from multiple different PHIs. 3612 } 3613 3614 // This is a expression evolving from a constant PHI! 3615 return PHI; 3616} 3617 3618/// EvaluateExpression - Given an expression that passes the 3619/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3620/// in the loop has the value PHIVal. If we can't fold this expression for some 3621/// reason, return null. 3622static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3623 if (isa<PHINode>(V)) return PHIVal; 3624 if (Constant *C = dyn_cast<Constant>(V)) return C; 3625 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3626 Instruction *I = cast<Instruction>(V); 3627 LLVMContext *Context = I->getParent()->getContext(); 3628 3629 std::vector<Constant*> Operands; 3630 Operands.resize(I->getNumOperands()); 3631 3632 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3633 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3634 if (Operands[i] == 0) return 0; 3635 } 3636 3637 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3638 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3639 &Operands[0], Operands.size(), 3640 Context); 3641 else 3642 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3643 &Operands[0], Operands.size(), 3644 Context); 3645} 3646 3647/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3648/// in the header of its containing loop, we know the loop executes a 3649/// constant number of times, and the PHI node is just a recurrence 3650/// involving constants, fold it. 3651Constant * 3652ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3653 const APInt& BEs, 3654 const Loop *L) { 3655 std::map<PHINode*, Constant*>::iterator I = 3656 ConstantEvolutionLoopExitValue.find(PN); 3657 if (I != ConstantEvolutionLoopExitValue.end()) 3658 return I->second; 3659 3660 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3661 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3662 3663 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3664 3665 // Since the loop is canonicalized, the PHI node must have two entries. One 3666 // entry must be a constant (coming in from outside of the loop), and the 3667 // second must be derived from the same PHI. 3668 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3669 Constant *StartCST = 3670 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3671 if (StartCST == 0) 3672 return RetVal = 0; // Must be a constant. 3673 3674 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3675 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3676 if (PN2 != PN) 3677 return RetVal = 0; // Not derived from same PHI. 3678 3679 // Execute the loop symbolically to determine the exit value. 3680 if (BEs.getActiveBits() >= 32) 3681 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3682 3683 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3684 unsigned IterationNum = 0; 3685 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3686 if (IterationNum == NumIterations) 3687 return RetVal = PHIVal; // Got exit value! 3688 3689 // Compute the value of the PHI node for the next iteration. 3690 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3691 if (NextPHI == PHIVal) 3692 return RetVal = NextPHI; // Stopped evolving! 3693 if (NextPHI == 0) 3694 return 0; // Couldn't evaluate! 3695 PHIVal = NextPHI; 3696 } 3697} 3698 3699/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3700/// constant number of times (the condition evolves only from constants), 3701/// try to evaluate a few iterations of the loop until we get the exit 3702/// condition gets a value of ExitWhen (true or false). If we cannot 3703/// evaluate the trip count of the loop, return getCouldNotCompute(). 3704const SCEV * 3705ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3706 Value *Cond, 3707 bool ExitWhen) { 3708 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3709 if (PN == 0) return getCouldNotCompute(); 3710 3711 // Since the loop is canonicalized, the PHI node must have two entries. One 3712 // entry must be a constant (coming in from outside of the loop), and the 3713 // second must be derived from the same PHI. 3714 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3715 Constant *StartCST = 3716 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3717 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3718 3719 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3720 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3721 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3722 3723 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3724 // the loop symbolically to determine when the condition gets a value of 3725 // "ExitWhen". 3726 unsigned IterationNum = 0; 3727 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3728 for (Constant *PHIVal = StartCST; 3729 IterationNum != MaxIterations; ++IterationNum) { 3730 ConstantInt *CondVal = 3731 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3732 3733 // Couldn't symbolically evaluate. 3734 if (!CondVal) return getCouldNotCompute(); 3735 3736 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3737 ++NumBruteForceTripCountsComputed; 3738 return getConstant(Type::Int32Ty, IterationNum); 3739 } 3740 3741 // Compute the value of the PHI node for the next iteration. 3742 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3743 if (NextPHI == 0 || NextPHI == PHIVal) 3744 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3745 PHIVal = NextPHI; 3746 } 3747 3748 // Too many iterations were needed to evaluate. 3749 return getCouldNotCompute(); 3750} 3751 3752/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3753/// at the specified scope in the program. The L value specifies a loop 3754/// nest to evaluate the expression at, where null is the top-level or a 3755/// specified loop is immediately inside of the loop. 3756/// 3757/// This method can be used to compute the exit value for a variable defined 3758/// in a loop by querying what the value will hold in the parent loop. 3759/// 3760/// In the case that a relevant loop exit value cannot be computed, the 3761/// original value V is returned. 3762const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3763 // FIXME: this should be turned into a virtual method on SCEV! 3764 3765 if (isa<SCEVConstant>(V)) return V; 3766 3767 // If this instruction is evolved from a constant-evolving PHI, compute the 3768 // exit value from the loop without using SCEVs. 3769 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3770 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3771 const Loop *LI = (*this->LI)[I->getParent()]; 3772 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3773 if (PHINode *PN = dyn_cast<PHINode>(I)) 3774 if (PN->getParent() == LI->getHeader()) { 3775 // Okay, there is no closed form solution for the PHI node. Check 3776 // to see if the loop that contains it has a known backedge-taken 3777 // count. If so, we may be able to force computation of the exit 3778 // value. 3779 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3780 if (const SCEVConstant *BTCC = 3781 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3782 // Okay, we know how many times the containing loop executes. If 3783 // this is a constant evolving PHI node, get the final value at 3784 // the specified iteration number. 3785 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3786 BTCC->getValue()->getValue(), 3787 LI); 3788 if (RV) return getSCEV(RV); 3789 } 3790 } 3791 3792 // Okay, this is an expression that we cannot symbolically evaluate 3793 // into a SCEV. Check to see if it's possible to symbolically evaluate 3794 // the arguments into constants, and if so, try to constant propagate the 3795 // result. This is particularly useful for computing loop exit values. 3796 if (CanConstantFold(I)) { 3797 // Check to see if we've folded this instruction at this loop before. 3798 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3799 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3800 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3801 if (!Pair.second) 3802 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3803 3804 std::vector<Constant*> Operands; 3805 Operands.reserve(I->getNumOperands()); 3806 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3807 Value *Op = I->getOperand(i); 3808 if (Constant *C = dyn_cast<Constant>(Op)) { 3809 Operands.push_back(C); 3810 } else { 3811 // If any of the operands is non-constant and if they are 3812 // non-integer and non-pointer, don't even try to analyze them 3813 // with scev techniques. 3814 if (!isSCEVable(Op->getType())) 3815 return V; 3816 3817 const SCEV* OpV = getSCEVAtScope(Op, L); 3818 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3819 Constant *C = SC->getValue(); 3820 if (C->getType() != Op->getType()) 3821 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3822 Op->getType(), 3823 false), 3824 C, Op->getType()); 3825 Operands.push_back(C); 3826 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3827 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3828 if (C->getType() != Op->getType()) 3829 C = 3830 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3831 Op->getType(), 3832 false), 3833 C, Op->getType()); 3834 Operands.push_back(C); 3835 } else 3836 return V; 3837 } else { 3838 return V; 3839 } 3840 } 3841 } 3842 3843 Constant *C; 3844 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3845 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3846 &Operands[0], Operands.size(), 3847 Context); 3848 else 3849 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3850 &Operands[0], Operands.size(), Context); 3851 Pair.first->second = C; 3852 return getSCEV(C); 3853 } 3854 } 3855 3856 // This is some other type of SCEVUnknown, just return it. 3857 return V; 3858 } 3859 3860 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3861 // Avoid performing the look-up in the common case where the specified 3862 // expression has no loop-variant portions. 3863 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3864 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3865 if (OpAtScope != Comm->getOperand(i)) { 3866 // Okay, at least one of these operands is loop variant but might be 3867 // foldable. Build a new instance of the folded commutative expression. 3868 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3869 Comm->op_begin()+i); 3870 NewOps.push_back(OpAtScope); 3871 3872 for (++i; i != e; ++i) { 3873 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3874 NewOps.push_back(OpAtScope); 3875 } 3876 if (isa<SCEVAddExpr>(Comm)) 3877 return getAddExpr(NewOps); 3878 if (isa<SCEVMulExpr>(Comm)) 3879 return getMulExpr(NewOps); 3880 if (isa<SCEVSMaxExpr>(Comm)) 3881 return getSMaxExpr(NewOps); 3882 if (isa<SCEVUMaxExpr>(Comm)) 3883 return getUMaxExpr(NewOps); 3884 LLVM_UNREACHABLE("Unknown commutative SCEV type!"); 3885 } 3886 } 3887 // If we got here, all operands are loop invariant. 3888 return Comm; 3889 } 3890 3891 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3892 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 3893 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 3894 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3895 return Div; // must be loop invariant 3896 return getUDivExpr(LHS, RHS); 3897 } 3898 3899 // If this is a loop recurrence for a loop that does not contain L, then we 3900 // are dealing with the final value computed by the loop. 3901 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3902 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3903 // To evaluate this recurrence, we need to know how many times the AddRec 3904 // loop iterates. Compute this now. 3905 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3906 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3907 3908 // Then, evaluate the AddRec. 3909 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3910 } 3911 return AddRec; 3912 } 3913 3914 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3915 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3916 if (Op == Cast->getOperand()) 3917 return Cast; // must be loop invariant 3918 return getZeroExtendExpr(Op, Cast->getType()); 3919 } 3920 3921 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3922 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3923 if (Op == Cast->getOperand()) 3924 return Cast; // must be loop invariant 3925 return getSignExtendExpr(Op, Cast->getType()); 3926 } 3927 3928 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3929 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3930 if (Op == Cast->getOperand()) 3931 return Cast; // must be loop invariant 3932 return getTruncateExpr(Op, Cast->getType()); 3933 } 3934 3935 LLVM_UNREACHABLE("Unknown SCEV type!"); 3936 return 0; 3937} 3938 3939/// getSCEVAtScope - This is a convenience function which does 3940/// getSCEVAtScope(getSCEV(V), L). 3941const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3942 return getSCEVAtScope(getSCEV(V), L); 3943} 3944 3945/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3946/// following equation: 3947/// 3948/// A * X = B (mod N) 3949/// 3950/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3951/// A and B isn't important. 3952/// 3953/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3954static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3955 ScalarEvolution &SE) { 3956 uint32_t BW = A.getBitWidth(); 3957 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3958 assert(A != 0 && "A must be non-zero."); 3959 3960 // 1. D = gcd(A, N) 3961 // 3962 // The gcd of A and N may have only one prime factor: 2. The number of 3963 // trailing zeros in A is its multiplicity 3964 uint32_t Mult2 = A.countTrailingZeros(); 3965 // D = 2^Mult2 3966 3967 // 2. Check if B is divisible by D. 3968 // 3969 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3970 // is not less than multiplicity of this prime factor for D. 3971 if (B.countTrailingZeros() < Mult2) 3972 return SE.getCouldNotCompute(); 3973 3974 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3975 // modulo (N / D). 3976 // 3977 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3978 // bit width during computations. 3979 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3980 APInt Mod(BW + 1, 0); 3981 Mod.set(BW - Mult2); // Mod = N / D 3982 APInt I = AD.multiplicativeInverse(Mod); 3983 3984 // 4. Compute the minimum unsigned root of the equation: 3985 // I * (B / D) mod (N / D) 3986 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 3987 3988 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 3989 // bits. 3990 return SE.getConstant(Result.trunc(BW)); 3991} 3992 3993/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 3994/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 3995/// might be the same) or two SCEVCouldNotCompute objects. 3996/// 3997static std::pair<const SCEV *,const SCEV *> 3998SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 3999 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4000 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4001 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4002 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4003 4004 // We currently can only solve this if the coefficients are constants. 4005 if (!LC || !MC || !NC) { 4006 const SCEV *CNC = SE.getCouldNotCompute(); 4007 return std::make_pair(CNC, CNC); 4008 } 4009 4010 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4011 const APInt &L = LC->getValue()->getValue(); 4012 const APInt &M = MC->getValue()->getValue(); 4013 const APInt &N = NC->getValue()->getValue(); 4014 APInt Two(BitWidth, 2); 4015 APInt Four(BitWidth, 4); 4016 4017 { 4018 using namespace APIntOps; 4019 const APInt& C = L; 4020 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4021 // The B coefficient is M-N/2 4022 APInt B(M); 4023 B -= sdiv(N,Two); 4024 4025 // The A coefficient is N/2 4026 APInt A(N.sdiv(Two)); 4027 4028 // Compute the B^2-4ac term. 4029 APInt SqrtTerm(B); 4030 SqrtTerm *= B; 4031 SqrtTerm -= Four * (A * C); 4032 4033 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4034 // integer value or else APInt::sqrt() will assert. 4035 APInt SqrtVal(SqrtTerm.sqrt()); 4036 4037 // Compute the two solutions for the quadratic formula. 4038 // The divisions must be performed as signed divisions. 4039 APInt NegB(-B); 4040 APInt TwoA( A << 1 ); 4041 if (TwoA.isMinValue()) { 4042 const SCEV *CNC = SE.getCouldNotCompute(); 4043 return std::make_pair(CNC, CNC); 4044 } 4045 4046 LLVMContext *Context = SE.getContext(); 4047 4048 ConstantInt *Solution1 = 4049 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA)); 4050 ConstantInt *Solution2 = 4051 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA)); 4052 4053 return std::make_pair(SE.getConstant(Solution1), 4054 SE.getConstant(Solution2)); 4055 } // end APIntOps namespace 4056} 4057 4058/// HowFarToZero - Return the number of times a backedge comparing the specified 4059/// value to zero will execute. If not computable, return CouldNotCompute. 4060const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4061 // If the value is a constant 4062 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4063 // If the value is already zero, the branch will execute zero times. 4064 if (C->getValue()->isZero()) return C; 4065 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4066 } 4067 4068 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4069 if (!AddRec || AddRec->getLoop() != L) 4070 return getCouldNotCompute(); 4071 4072 if (AddRec->isAffine()) { 4073 // If this is an affine expression, the execution count of this branch is 4074 // the minimum unsigned root of the following equation: 4075 // 4076 // Start + Step*N = 0 (mod 2^BW) 4077 // 4078 // equivalent to: 4079 // 4080 // Step*N = -Start (mod 2^BW) 4081 // 4082 // where BW is the common bit width of Start and Step. 4083 4084 // Get the initial value for the loop. 4085 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4086 L->getParentLoop()); 4087 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4088 L->getParentLoop()); 4089 4090 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4091 // For now we handle only constant steps. 4092 4093 // First, handle unitary steps. 4094 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4095 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4096 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4097 return Start; // N = Start (as unsigned) 4098 4099 // Then, try to solve the above equation provided that Start is constant. 4100 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4101 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4102 -StartC->getValue()->getValue(), 4103 *this); 4104 } 4105 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4106 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4107 // the quadratic equation to solve it. 4108 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4109 *this); 4110 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4111 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4112 if (R1) { 4113#if 0 4114 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4115 << " sol#2: " << *R2 << "\n"; 4116#endif 4117 // Pick the smallest positive root value. 4118 if (ConstantInt *CB = 4119 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT, 4120 R1->getValue(), R2->getValue()))) { 4121 if (CB->getZExtValue() == false) 4122 std::swap(R1, R2); // R1 is the minimum root now. 4123 4124 // We can only use this value if the chrec ends up with an exact zero 4125 // value at this index. When solving for "X*X != 5", for example, we 4126 // should not accept a root of 2. 4127 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4128 if (Val->isZero()) 4129 return R1; // We found a quadratic root! 4130 } 4131 } 4132 } 4133 4134 return getCouldNotCompute(); 4135} 4136 4137/// HowFarToNonZero - Return the number of times a backedge checking the 4138/// specified value for nonzero will execute. If not computable, return 4139/// CouldNotCompute 4140const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4141 // Loops that look like: while (X == 0) are very strange indeed. We don't 4142 // handle them yet except for the trivial case. This could be expanded in the 4143 // future as needed. 4144 4145 // If the value is a constant, check to see if it is known to be non-zero 4146 // already. If so, the backedge will execute zero times. 4147 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4148 if (!C->getValue()->isNullValue()) 4149 return getIntegerSCEV(0, C->getType()); 4150 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4151 } 4152 4153 // We could implement others, but I really doubt anyone writes loops like 4154 // this, and if they did, they would already be constant folded. 4155 return getCouldNotCompute(); 4156} 4157 4158/// getLoopPredecessor - If the given loop's header has exactly one unique 4159/// predecessor outside the loop, return it. Otherwise return null. 4160/// 4161BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4162 BasicBlock *Header = L->getHeader(); 4163 BasicBlock *Pred = 0; 4164 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4165 PI != E; ++PI) 4166 if (!L->contains(*PI)) { 4167 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4168 Pred = *PI; 4169 } 4170 return Pred; 4171} 4172 4173/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4174/// (which may not be an immediate predecessor) which has exactly one 4175/// successor from which BB is reachable, or null if no such block is 4176/// found. 4177/// 4178BasicBlock * 4179ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4180 // If the block has a unique predecessor, then there is no path from the 4181 // predecessor to the block that does not go through the direct edge 4182 // from the predecessor to the block. 4183 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4184 return Pred; 4185 4186 // A loop's header is defined to be a block that dominates the loop. 4187 // If the header has a unique predecessor outside the loop, it must be 4188 // a block that has exactly one successor that can reach the loop. 4189 if (Loop *L = LI->getLoopFor(BB)) 4190 return getLoopPredecessor(L); 4191 4192 return 0; 4193} 4194 4195/// HasSameValue - SCEV structural equivalence is usually sufficient for 4196/// testing whether two expressions are equal, however for the purposes of 4197/// looking for a condition guarding a loop, it can be useful to be a little 4198/// more general, since a front-end may have replicated the controlling 4199/// expression. 4200/// 4201static bool HasSameValue(const SCEV *A, const SCEV *B) { 4202 // Quick check to see if they are the same SCEV. 4203 if (A == B) return true; 4204 4205 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4206 // two different instructions with the same value. Check for this case. 4207 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4208 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4209 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4210 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4211 if (AI->isIdenticalTo(BI)) 4212 return true; 4213 4214 // Otherwise assume they may have a different value. 4215 return false; 4216} 4217 4218bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4219 return getSignedRange(S).getSignedMax().isNegative(); 4220} 4221 4222bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4223 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4224} 4225 4226bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4227 return !getSignedRange(S).getSignedMin().isNegative(); 4228} 4229 4230bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4231 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4232} 4233 4234bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4235 return isKnownNegative(S) || isKnownPositive(S); 4236} 4237 4238bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4239 const SCEV *LHS, const SCEV *RHS) { 4240 4241 if (HasSameValue(LHS, RHS)) 4242 return ICmpInst::isTrueWhenEqual(Pred); 4243 4244 switch (Pred) { 4245 default: 4246 assert(0 && "Unexpected ICmpInst::Predicate value!"); 4247 break; 4248 case ICmpInst::ICMP_SGT: 4249 Pred = ICmpInst::ICMP_SLT; 4250 std::swap(LHS, RHS); 4251 case ICmpInst::ICMP_SLT: { 4252 ConstantRange LHSRange = getSignedRange(LHS); 4253 ConstantRange RHSRange = getSignedRange(RHS); 4254 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4255 return true; 4256 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4257 return false; 4258 4259 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4260 ConstantRange DiffRange = getUnsignedRange(Diff); 4261 if (isKnownNegative(Diff)) { 4262 if (DiffRange.getUnsignedMax().ult(LHSRange.getUnsignedMin())) 4263 return true; 4264 if (DiffRange.getUnsignedMin().uge(LHSRange.getUnsignedMax())) 4265 return false; 4266 } else if (isKnownPositive(Diff)) { 4267 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4268 return true; 4269 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4270 return false; 4271 } 4272 break; 4273 } 4274 case ICmpInst::ICMP_SGE: 4275 Pred = ICmpInst::ICMP_SLE; 4276 std::swap(LHS, RHS); 4277 case ICmpInst::ICMP_SLE: { 4278 ConstantRange LHSRange = getSignedRange(LHS); 4279 ConstantRange RHSRange = getSignedRange(RHS); 4280 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4281 return true; 4282 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4283 return false; 4284 4285 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4286 ConstantRange DiffRange = getUnsignedRange(Diff); 4287 if (isKnownNonPositive(Diff)) { 4288 if (DiffRange.getUnsignedMax().ule(LHSRange.getUnsignedMin())) 4289 return true; 4290 if (DiffRange.getUnsignedMin().ugt(LHSRange.getUnsignedMax())) 4291 return false; 4292 } else if (isKnownNonNegative(Diff)) { 4293 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4294 return true; 4295 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4296 return false; 4297 } 4298 break; 4299 } 4300 case ICmpInst::ICMP_UGT: 4301 Pred = ICmpInst::ICMP_ULT; 4302 std::swap(LHS, RHS); 4303 case ICmpInst::ICMP_ULT: { 4304 ConstantRange LHSRange = getUnsignedRange(LHS); 4305 ConstantRange RHSRange = getUnsignedRange(RHS); 4306 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4307 return true; 4308 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4309 return false; 4310 4311 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4312 ConstantRange DiffRange = getUnsignedRange(Diff); 4313 if (LHSRange.getUnsignedMax().ult(DiffRange.getUnsignedMin())) 4314 return true; 4315 if (LHSRange.getUnsignedMin().uge(DiffRange.getUnsignedMax())) 4316 return false; 4317 break; 4318 } 4319 case ICmpInst::ICMP_UGE: 4320 Pred = ICmpInst::ICMP_ULE; 4321 std::swap(LHS, RHS); 4322 case ICmpInst::ICMP_ULE: { 4323 ConstantRange LHSRange = getUnsignedRange(LHS); 4324 ConstantRange RHSRange = getUnsignedRange(RHS); 4325 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4326 return true; 4327 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4328 return false; 4329 4330 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4331 ConstantRange DiffRange = getUnsignedRange(Diff); 4332 if (LHSRange.getUnsignedMax().ule(DiffRange.getUnsignedMin())) 4333 return true; 4334 if (LHSRange.getUnsignedMin().ugt(DiffRange.getUnsignedMax())) 4335 return false; 4336 break; 4337 } 4338 case ICmpInst::ICMP_NE: { 4339 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4340 return true; 4341 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4342 return true; 4343 4344 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4345 if (isKnownNonZero(Diff)) 4346 return true; 4347 break; 4348 } 4349 case ICmpInst::ICMP_EQ: 4350 break; 4351 } 4352 return false; 4353} 4354 4355/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4356/// protected by a conditional between LHS and RHS. This is used to 4357/// to eliminate casts. 4358bool 4359ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4360 ICmpInst::Predicate Pred, 4361 const SCEV *LHS, const SCEV *RHS) { 4362 // Interpret a null as meaning no loop, where there is obviously no guard 4363 // (interprocedural conditions notwithstanding). 4364 if (!L) return true; 4365 4366 BasicBlock *Latch = L->getLoopLatch(); 4367 if (!Latch) 4368 return false; 4369 4370 BranchInst *LoopContinuePredicate = 4371 dyn_cast<BranchInst>(Latch->getTerminator()); 4372 if (!LoopContinuePredicate || 4373 LoopContinuePredicate->isUnconditional()) 4374 return false; 4375 4376 return 4377 isNecessaryCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4378 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4379} 4380 4381/// isLoopGuardedByCond - Test whether entry to the loop is protected 4382/// by a conditional between LHS and RHS. This is used to help avoid max 4383/// expressions in loop trip counts, and to eliminate casts. 4384bool 4385ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4386 ICmpInst::Predicate Pred, 4387 const SCEV *LHS, const SCEV *RHS) { 4388 // Interpret a null as meaning no loop, where there is obviously no guard 4389 // (interprocedural conditions notwithstanding). 4390 if (!L) return false; 4391 4392 BasicBlock *Predecessor = getLoopPredecessor(L); 4393 BasicBlock *PredecessorDest = L->getHeader(); 4394 4395 // Starting at the loop predecessor, climb up the predecessor chain, as long 4396 // as there are predecessors that can be found that have unique successors 4397 // leading to the original header. 4398 for (; Predecessor; 4399 PredecessorDest = Predecessor, 4400 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4401 4402 BranchInst *LoopEntryPredicate = 4403 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4404 if (!LoopEntryPredicate || 4405 LoopEntryPredicate->isUnconditional()) 4406 continue; 4407 4408 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4409 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4410 return true; 4411 } 4412 4413 return false; 4414} 4415 4416/// isNecessaryCond - Test whether the condition described by Pred, LHS, 4417/// and RHS is a necessary condition for the given Cond value to evaluate 4418/// to true. 4419bool ScalarEvolution::isNecessaryCond(Value *CondValue, 4420 ICmpInst::Predicate Pred, 4421 const SCEV *LHS, const SCEV *RHS, 4422 bool Inverse) { 4423 // Recursivly handle And and Or conditions. 4424 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4425 if (BO->getOpcode() == Instruction::And) { 4426 if (!Inverse) 4427 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4428 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4429 } else if (BO->getOpcode() == Instruction::Or) { 4430 if (Inverse) 4431 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4432 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4433 } 4434 } 4435 4436 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4437 if (!ICI) return false; 4438 4439 // Now that we found a conditional branch that dominates the loop, check to 4440 // see if it is the comparison we are looking for. 4441 Value *PreCondLHS = ICI->getOperand(0); 4442 Value *PreCondRHS = ICI->getOperand(1); 4443 ICmpInst::Predicate FoundPred; 4444 if (Inverse) 4445 FoundPred = ICI->getInversePredicate(); 4446 else 4447 FoundPred = ICI->getPredicate(); 4448 4449 if (FoundPred == Pred) 4450 ; // An exact match. 4451 else if (!ICmpInst::isTrueWhenEqual(FoundPred) && Pred == ICmpInst::ICMP_NE) { 4452 // The actual condition is beyond sufficient. 4453 FoundPred = ICmpInst::ICMP_NE; 4454 // NE is symmetric but the original comparison may not be. Swap 4455 // the operands if necessary so that they match below. 4456 if (isa<SCEVConstant>(LHS)) 4457 std::swap(PreCondLHS, PreCondRHS); 4458 } else 4459 // Check a few special cases. 4460 switch (FoundPred) { 4461 case ICmpInst::ICMP_UGT: 4462 if (Pred == ICmpInst::ICMP_ULT) { 4463 std::swap(PreCondLHS, PreCondRHS); 4464 FoundPred = ICmpInst::ICMP_ULT; 4465 break; 4466 } 4467 return false; 4468 case ICmpInst::ICMP_SGT: 4469 if (Pred == ICmpInst::ICMP_SLT) { 4470 std::swap(PreCondLHS, PreCondRHS); 4471 FoundPred = ICmpInst::ICMP_SLT; 4472 break; 4473 } 4474 return false; 4475 case ICmpInst::ICMP_NE: 4476 // Expressions like (x >u 0) are often canonicalized to (x != 0), 4477 // so check for this case by checking if the NE is comparing against 4478 // a minimum or maximum constant. 4479 if (!ICmpInst::isTrueWhenEqual(Pred)) 4480 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(RHS)) { 4481 const APInt &A = C->getValue()->getValue(); 4482 switch (Pred) { 4483 case ICmpInst::ICMP_SLT: 4484 if (A.isMaxSignedValue()) break; 4485 return false; 4486 case ICmpInst::ICMP_SGT: 4487 if (A.isMinSignedValue()) break; 4488 return false; 4489 case ICmpInst::ICMP_ULT: 4490 if (A.isMaxValue()) break; 4491 return false; 4492 case ICmpInst::ICMP_UGT: 4493 if (A.isMinValue()) break; 4494 return false; 4495 default: 4496 return false; 4497 } 4498 FoundPred = Pred; 4499 // NE is symmetric but the original comparison may not be. Swap 4500 // the operands if necessary so that they match below. 4501 if (isa<SCEVConstant>(LHS)) 4502 std::swap(PreCondLHS, PreCondRHS); 4503 break; 4504 } 4505 return false; 4506 default: 4507 // We weren't able to reconcile the condition. 4508 return false; 4509 } 4510 4511 assert(Pred == FoundPred && "Conditions were not reconciled!"); 4512 4513 // Bail if the ICmp's operands' types are wider than the needed type 4514 // before attempting to call getSCEV on them. This avoids infinite 4515 // recursion, since the analysis of widening casts can require loop 4516 // exit condition information for overflow checking, which would 4517 // lead back here. 4518 if (getTypeSizeInBits(LHS->getType()) < 4519 getTypeSizeInBits(PreCondLHS->getType())) 4520 return false; 4521 4522 const SCEV *FoundLHS = getSCEV(PreCondLHS); 4523 const SCEV *FoundRHS = getSCEV(PreCondRHS); 4524 4525 // Balance the types. The case where FoundLHS' type is wider than 4526 // LHS' type is checked for above. 4527 if (getTypeSizeInBits(LHS->getType()) > 4528 getTypeSizeInBits(FoundLHS->getType())) { 4529 if (CmpInst::isSigned(Pred)) { 4530 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4531 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4532 } else { 4533 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4534 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4535 } 4536 } 4537 4538 return isNecessaryCondOperands(Pred, LHS, RHS, 4539 FoundLHS, FoundRHS) || 4540 // ~x < ~y --> x > y 4541 isNecessaryCondOperands(Pred, LHS, RHS, 4542 getNotSCEV(FoundRHS), getNotSCEV(FoundLHS)); 4543} 4544 4545/// isNecessaryCondOperands - Test whether the condition described by Pred, 4546/// LHS, and RHS is a necessary condition for the condition described by 4547/// Pred, FoundLHS, and FoundRHS to evaluate to true. 4548bool 4549ScalarEvolution::isNecessaryCondOperands(ICmpInst::Predicate Pred, 4550 const SCEV *LHS, const SCEV *RHS, 4551 const SCEV *FoundLHS, 4552 const SCEV *FoundRHS) { 4553 switch (Pred) { 4554 default: break; 4555 case ICmpInst::ICMP_SLT: 4556 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4557 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4558 return true; 4559 break; 4560 case ICmpInst::ICMP_SGT: 4561 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4562 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4563 return true; 4564 break; 4565 case ICmpInst::ICMP_ULT: 4566 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4567 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4568 return true; 4569 break; 4570 case ICmpInst::ICMP_UGT: 4571 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4572 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4573 return true; 4574 break; 4575 } 4576 4577 return false; 4578} 4579 4580/// getBECount - Subtract the end and start values and divide by the step, 4581/// rounding up, to get the number of times the backedge is executed. Return 4582/// CouldNotCompute if an intermediate computation overflows. 4583const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4584 const SCEV *End, 4585 const SCEV *Step) { 4586 const Type *Ty = Start->getType(); 4587 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4588 const SCEV *Diff = getMinusSCEV(End, Start); 4589 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4590 4591 // Add an adjustment to the difference between End and Start so that 4592 // the division will effectively round up. 4593 const SCEV *Add = getAddExpr(Diff, RoundUp); 4594 4595 // Check Add for unsigned overflow. 4596 // TODO: More sophisticated things could be done here. 4597 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1); 4598 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 4599 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 4600 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 4601 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4602 return getCouldNotCompute(); 4603 4604 return getUDivExpr(Add, Step); 4605} 4606 4607/// HowManyLessThans - Return the number of times a backedge containing the 4608/// specified less-than comparison will execute. If not computable, return 4609/// CouldNotCompute. 4610ScalarEvolution::BackedgeTakenInfo 4611ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4612 const Loop *L, bool isSigned) { 4613 // Only handle: "ADDREC < LoopInvariant". 4614 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4615 4616 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4617 if (!AddRec || AddRec->getLoop() != L) 4618 return getCouldNotCompute(); 4619 4620 if (AddRec->isAffine()) { 4621 // FORNOW: We only support unit strides. 4622 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4623 const SCEV *Step = AddRec->getStepRecurrence(*this); 4624 4625 // TODO: handle non-constant strides. 4626 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4627 if (!CStep || CStep->isZero()) 4628 return getCouldNotCompute(); 4629 if (CStep->isOne()) { 4630 // With unit stride, the iteration never steps past the limit value. 4631 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4632 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4633 // Test whether a positive iteration iteration can step past the limit 4634 // value and past the maximum value for its type in a single step. 4635 if (isSigned) { 4636 APInt Max = APInt::getSignedMaxValue(BitWidth); 4637 if ((Max - CStep->getValue()->getValue()) 4638 .slt(CLimit->getValue()->getValue())) 4639 return getCouldNotCompute(); 4640 } else { 4641 APInt Max = APInt::getMaxValue(BitWidth); 4642 if ((Max - CStep->getValue()->getValue()) 4643 .ult(CLimit->getValue()->getValue())) 4644 return getCouldNotCompute(); 4645 } 4646 } else 4647 // TODO: handle non-constant limit values below. 4648 return getCouldNotCompute(); 4649 } else 4650 // TODO: handle negative strides below. 4651 return getCouldNotCompute(); 4652 4653 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4654 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4655 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4656 // treat m-n as signed nor unsigned due to overflow possibility. 4657 4658 // First, we get the value of the LHS in the first iteration: n 4659 const SCEV *Start = AddRec->getOperand(0); 4660 4661 // Determine the minimum constant start value. 4662 const SCEV *MinStart = getConstant(isSigned ? 4663 getSignedRange(Start).getSignedMin() : 4664 getUnsignedRange(Start).getUnsignedMin()); 4665 4666 // If we know that the condition is true in order to enter the loop, 4667 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4668 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4669 // the division must round up. 4670 const SCEV *End = RHS; 4671 if (!isLoopGuardedByCond(L, 4672 isSigned ? ICmpInst::ICMP_SLT : 4673 ICmpInst::ICMP_ULT, 4674 getMinusSCEV(Start, Step), RHS)) 4675 End = isSigned ? getSMaxExpr(RHS, Start) 4676 : getUMaxExpr(RHS, Start); 4677 4678 // Determine the maximum constant end value. 4679 const SCEV *MaxEnd = getConstant(isSigned ? 4680 getSignedRange(End).getSignedMax() : 4681 getUnsignedRange(End).getUnsignedMax()); 4682 4683 // Finally, we subtract these two values and divide, rounding up, to get 4684 // the number of times the backedge is executed. 4685 const SCEV *BECount = getBECount(Start, End, Step); 4686 4687 // The maximum backedge count is similar, except using the minimum start 4688 // value and the maximum end value. 4689 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step); 4690 4691 return BackedgeTakenInfo(BECount, MaxBECount); 4692 } 4693 4694 return getCouldNotCompute(); 4695} 4696 4697/// getNumIterationsInRange - Return the number of iterations of this loop that 4698/// produce values in the specified constant range. Another way of looking at 4699/// this is that it returns the first iteration number where the value is not in 4700/// the condition, thus computing the exit count. If the iteration count can't 4701/// be computed, an instance of SCEVCouldNotCompute is returned. 4702const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4703 ScalarEvolution &SE) const { 4704 if (Range.isFullSet()) // Infinite loop. 4705 return SE.getCouldNotCompute(); 4706 4707 // If the start is a non-zero constant, shift the range to simplify things. 4708 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4709 if (!SC->getValue()->isZero()) { 4710 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4711 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4712 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4713 if (const SCEVAddRecExpr *ShiftedAddRec = 4714 dyn_cast<SCEVAddRecExpr>(Shifted)) 4715 return ShiftedAddRec->getNumIterationsInRange( 4716 Range.subtract(SC->getValue()->getValue()), SE); 4717 // This is strange and shouldn't happen. 4718 return SE.getCouldNotCompute(); 4719 } 4720 4721 // The only time we can solve this is when we have all constant indices. 4722 // Otherwise, we cannot determine the overflow conditions. 4723 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4724 if (!isa<SCEVConstant>(getOperand(i))) 4725 return SE.getCouldNotCompute(); 4726 4727 4728 // Okay at this point we know that all elements of the chrec are constants and 4729 // that the start element is zero. 4730 4731 // First check to see if the range contains zero. If not, the first 4732 // iteration exits. 4733 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4734 if (!Range.contains(APInt(BitWidth, 0))) 4735 return SE.getIntegerSCEV(0, getType()); 4736 4737 if (isAffine()) { 4738 // If this is an affine expression then we have this situation: 4739 // Solve {0,+,A} in Range === Ax in Range 4740 4741 // We know that zero is in the range. If A is positive then we know that 4742 // the upper value of the range must be the first possible exit value. 4743 // If A is negative then the lower of the range is the last possible loop 4744 // value. Also note that we already checked for a full range. 4745 APInt One(BitWidth,1); 4746 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4747 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4748 4749 // The exit value should be (End+A)/A. 4750 APInt ExitVal = (End + A).udiv(A); 4751 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal); 4752 4753 // Evaluate at the exit value. If we really did fall out of the valid 4754 // range, then we computed our trip count, otherwise wrap around or other 4755 // things must have happened. 4756 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4757 if (Range.contains(Val->getValue())) 4758 return SE.getCouldNotCompute(); // Something strange happened 4759 4760 // Ensure that the previous value is in the range. This is a sanity check. 4761 assert(Range.contains( 4762 EvaluateConstantChrecAtConstant(this, 4763 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) && 4764 "Linear scev computation is off in a bad way!"); 4765 return SE.getConstant(ExitValue); 4766 } else if (isQuadratic()) { 4767 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4768 // quadratic equation to solve it. To do this, we must frame our problem in 4769 // terms of figuring out when zero is crossed, instead of when 4770 // Range.getUpper() is crossed. 4771 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 4772 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4773 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4774 4775 // Next, solve the constructed addrec 4776 std::pair<const SCEV *,const SCEV *> Roots = 4777 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4778 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4779 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4780 if (R1) { 4781 // Pick the smallest positive root value. 4782 if (ConstantInt *CB = 4783 dyn_cast<ConstantInt>( 4784 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT, 4785 R1->getValue(), R2->getValue()))) { 4786 if (CB->getZExtValue() == false) 4787 std::swap(R1, R2); // R1 is the minimum root now. 4788 4789 // Make sure the root is not off by one. The returned iteration should 4790 // not be in the range, but the previous one should be. When solving 4791 // for "X*X < 5", for example, we should not return a root of 2. 4792 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4793 R1->getValue(), 4794 SE); 4795 if (Range.contains(R1Val->getValue())) { 4796 // The next iteration must be out of the range... 4797 ConstantInt *NextVal = 4798 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1); 4799 4800 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4801 if (!Range.contains(R1Val->getValue())) 4802 return SE.getConstant(NextVal); 4803 return SE.getCouldNotCompute(); // Something strange happened 4804 } 4805 4806 // If R1 was not in the range, then it is a good return value. Make 4807 // sure that R1-1 WAS in the range though, just in case. 4808 ConstantInt *NextVal = 4809 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1); 4810 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4811 if (Range.contains(R1Val->getValue())) 4812 return R1; 4813 return SE.getCouldNotCompute(); // Something strange happened 4814 } 4815 } 4816 } 4817 4818 return SE.getCouldNotCompute(); 4819} 4820 4821 4822 4823//===----------------------------------------------------------------------===// 4824// SCEVCallbackVH Class Implementation 4825//===----------------------------------------------------------------------===// 4826 4827void ScalarEvolution::SCEVCallbackVH::deleted() { 4828 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4829 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4830 SE->ConstantEvolutionLoopExitValue.erase(PN); 4831 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4832 SE->ValuesAtScopes.erase(I); 4833 SE->Scalars.erase(getValPtr()); 4834 // this now dangles! 4835} 4836 4837void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4838 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4839 4840 // Forget all the expressions associated with users of the old value, 4841 // so that future queries will recompute the expressions using the new 4842 // value. 4843 SmallVector<User *, 16> Worklist; 4844 Value *Old = getValPtr(); 4845 bool DeleteOld = false; 4846 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4847 UI != UE; ++UI) 4848 Worklist.push_back(*UI); 4849 while (!Worklist.empty()) { 4850 User *U = Worklist.pop_back_val(); 4851 // Deleting the Old value will cause this to dangle. Postpone 4852 // that until everything else is done. 4853 if (U == Old) { 4854 DeleteOld = true; 4855 continue; 4856 } 4857 if (PHINode *PN = dyn_cast<PHINode>(U)) 4858 SE->ConstantEvolutionLoopExitValue.erase(PN); 4859 if (Instruction *I = dyn_cast<Instruction>(U)) 4860 SE->ValuesAtScopes.erase(I); 4861 if (SE->Scalars.erase(U)) 4862 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4863 UI != UE; ++UI) 4864 Worklist.push_back(*UI); 4865 } 4866 if (DeleteOld) { 4867 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4868 SE->ConstantEvolutionLoopExitValue.erase(PN); 4869 if (Instruction *I = dyn_cast<Instruction>(Old)) 4870 SE->ValuesAtScopes.erase(I); 4871 SE->Scalars.erase(Old); 4872 // this now dangles! 4873 } 4874 // this may dangle! 4875} 4876 4877ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4878 : CallbackVH(V), SE(se) {} 4879 4880//===----------------------------------------------------------------------===// 4881// ScalarEvolution Class Implementation 4882//===----------------------------------------------------------------------===// 4883 4884ScalarEvolution::ScalarEvolution() 4885 : FunctionPass(&ID) { 4886} 4887 4888bool ScalarEvolution::runOnFunction(Function &F) { 4889 this->F = &F; 4890 LI = &getAnalysis<LoopInfo>(); 4891 TD = getAnalysisIfAvailable<TargetData>(); 4892 return false; 4893} 4894 4895void ScalarEvolution::releaseMemory() { 4896 Scalars.clear(); 4897 BackedgeTakenCounts.clear(); 4898 ConstantEvolutionLoopExitValue.clear(); 4899 ValuesAtScopes.clear(); 4900 UniqueSCEVs.clear(); 4901 SCEVAllocator.Reset(); 4902} 4903 4904void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4905 AU.setPreservesAll(); 4906 AU.addRequiredTransitive<LoopInfo>(); 4907} 4908 4909bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4910 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4911} 4912 4913static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4914 const Loop *L) { 4915 // Print all inner loops first 4916 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4917 PrintLoopInfo(OS, SE, *I); 4918 4919 OS << "Loop " << L->getHeader()->getName() << ": "; 4920 4921 SmallVector<BasicBlock*, 8> ExitBlocks; 4922 L->getExitBlocks(ExitBlocks); 4923 if (ExitBlocks.size() != 1) 4924 OS << "<multiple exits> "; 4925 4926 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4927 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4928 } else { 4929 OS << "Unpredictable backedge-taken count. "; 4930 } 4931 4932 OS << "\n"; 4933 OS << "Loop " << L->getHeader()->getName() << ": "; 4934 4935 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 4936 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 4937 } else { 4938 OS << "Unpredictable max backedge-taken count. "; 4939 } 4940 4941 OS << "\n"; 4942} 4943 4944void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4945 // ScalarEvolution's implementaiton of the print method is to print 4946 // out SCEV values of all instructions that are interesting. Doing 4947 // this potentially causes it to create new SCEV objects though, 4948 // which technically conflicts with the const qualifier. This isn't 4949 // observable from outside the class though, so casting away the 4950 // const isn't dangerous. 4951 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4952 4953 OS << "Classifying expressions for: " << F->getName() << "\n"; 4954 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4955 if (isSCEVable(I->getType())) { 4956 OS << *I; 4957 OS << " --> "; 4958 const SCEV *SV = SE.getSCEV(&*I); 4959 SV->print(OS); 4960 4961 const Loop *L = LI->getLoopFor((*I).getParent()); 4962 4963 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 4964 if (AtUse != SV) { 4965 OS << " --> "; 4966 AtUse->print(OS); 4967 } 4968 4969 if (L) { 4970 OS << "\t\t" "Exits: "; 4971 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4972 if (!ExitValue->isLoopInvariant(L)) { 4973 OS << "<<Unknown>>"; 4974 } else { 4975 OS << *ExitValue; 4976 } 4977 } 4978 4979 OS << "\n"; 4980 } 4981 4982 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 4983 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 4984 PrintLoopInfo(OS, &SE, *I); 4985} 4986 4987void ScalarEvolution::print(std::ostream &o, const Module *M) const { 4988 raw_os_ostream OS(o); 4989 print(OS, M); 4990} 4991