ScalarEvolution.cpp revision 73c6b7127aff4499e4d6a2edb219685aee178ee1
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 // Check whether the backedge-taken count is SCEVCouldNotCompute. 791 // Note that this serves two purposes: It filters out loops that are 792 // simply not analyzable, and it covers the case where this code is 793 // being called from within backedge-taken count analysis, such that 794 // attempting to ask for the backedge-taken count would likely result 795 // in infinite recursion. In the later case, the analysis code will 796 // cope with a conservative value, and it will take care to purge 797 // that value once it has finished. 798 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 799 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 800 // Manually compute the final value for AR, checking for 801 // overflow. 802 const SCEV *Start = AR->getStart(); 803 const SCEV *Step = AR->getStepRecurrence(*this); 804 805 // Check whether the backedge-taken count can be losslessly casted to 806 // the addrec's type. The count is always unsigned. 807 const SCEV *CastedMaxBECount = 808 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 809 const SCEV *RecastedMaxBECount = 810 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 811 if (MaxBECount == RecastedMaxBECount) { 812 const Type *WideTy = 813 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 814 // Check whether Start+Step*MaxBECount has no unsigned overflow. 815 const SCEV *ZMul = 816 getMulExpr(CastedMaxBECount, 817 getTruncateOrZeroExtend(Step, Start->getType())); 818 const SCEV *Add = getAddExpr(Start, ZMul); 819 const SCEV *OperandExtendedAdd = 820 getAddExpr(getZeroExtendExpr(Start, WideTy), 821 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 822 getZeroExtendExpr(Step, WideTy))); 823 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 824 // Return the expression with the addrec on the outside. 825 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 826 getZeroExtendExpr(Step, Ty), 827 AR->getLoop()); 828 829 // Similar to above, only this time treat the step value as signed. 830 // This covers loops that count down. 831 const SCEV *SMul = 832 getMulExpr(CastedMaxBECount, 833 getTruncateOrSignExtend(Step, Start->getType())); 834 Add = getAddExpr(Start, SMul); 835 OperandExtendedAdd = 836 getAddExpr(getZeroExtendExpr(Start, WideTy), 837 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 838 getSignExtendExpr(Step, WideTy))); 839 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 840 // Return the expression with the addrec on the outside. 841 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 842 getSignExtendExpr(Step, Ty), 843 AR->getLoop()); 844 } 845 } 846 } 847 848 // The cast wasn't folded; create an explicit cast node. 849 // Recompute the insert position, as it may have been invalidated. 850 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 851 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 852 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 853 UniqueSCEVs.InsertNode(S, IP); 854 return S; 855} 856 857const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 858 const Type *Ty) { 859 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 860 "This is not an extending conversion!"); 861 assert(isSCEVable(Ty) && 862 "This is not a conversion to a SCEVable type!"); 863 Ty = getEffectiveSCEVType(Ty); 864 865 // Fold if the operand is constant. 866 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 867 const Type *IntTy = getEffectiveSCEVType(Ty); 868 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 869 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 870 return getConstant(cast<ConstantInt>(C)); 871 } 872 873 // sext(sext(x)) --> sext(x) 874 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 875 return getSignExtendExpr(SS->getOperand(), Ty); 876 877 // Before doing any expensive analysis, check to see if we've already 878 // computed a SCEV for this Op and Ty. 879 FoldingSetNodeID ID; 880 ID.AddInteger(scSignExtend); 881 ID.AddPointer(Op); 882 ID.AddPointer(Ty); 883 void *IP = 0; 884 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 885 886 // If the input value is a chrec scev, and we can prove that the value 887 // did not overflow the old, smaller, value, we can sign extend all of the 888 // operands (often constants). This allows analysis of something like 889 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 890 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 891 if (AR->isAffine()) { 892 // Check whether the backedge-taken count is SCEVCouldNotCompute. 893 // Note that this serves two purposes: It filters out loops that are 894 // simply not analyzable, and it covers the case where this code is 895 // being called from within backedge-taken count analysis, such that 896 // attempting to ask for the backedge-taken count would likely result 897 // in infinite recursion. In the later case, the analysis code will 898 // cope with a conservative value, and it will take care to purge 899 // that value once it has finished. 900 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AR->getLoop()); 901 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 902 // Manually compute the final value for AR, checking for 903 // overflow. 904 const SCEV *Start = AR->getStart(); 905 const SCEV *Step = AR->getStepRecurrence(*this); 906 907 // Check whether the backedge-taken count can be losslessly casted to 908 // the addrec's type. The count is always unsigned. 909 const SCEV *CastedMaxBECount = 910 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 911 const SCEV *RecastedMaxBECount = 912 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 913 if (MaxBECount == RecastedMaxBECount) { 914 const Type *WideTy = 915 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2); 916 // Check whether Start+Step*MaxBECount has no signed overflow. 917 const SCEV *SMul = 918 getMulExpr(CastedMaxBECount, 919 getTruncateOrSignExtend(Step, Start->getType())); 920 const SCEV *Add = getAddExpr(Start, SMul); 921 const SCEV *OperandExtendedAdd = 922 getAddExpr(getSignExtendExpr(Start, WideTy), 923 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 924 getSignExtendExpr(Step, WideTy))); 925 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 926 // Return the expression with the addrec on the outside. 927 return getAddRecExpr(getSignExtendExpr(Start, Ty), 928 getSignExtendExpr(Step, Ty), 929 AR->getLoop()); 930 } 931 } 932 } 933 934 // The cast wasn't folded; create an explicit cast node. 935 // Recompute the insert position, as it may have been invalidated. 936 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 937 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 938 new (S) SCEVSignExtendExpr(ID, Op, Ty); 939 UniqueSCEVs.InsertNode(S, IP); 940 return S; 941} 942 943/// getAnyExtendExpr - Return a SCEV for the given operand extended with 944/// unspecified bits out to the given type. 945/// 946const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 947 const Type *Ty) { 948 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 949 "This is not an extending conversion!"); 950 assert(isSCEVable(Ty) && 951 "This is not a conversion to a SCEVable type!"); 952 Ty = getEffectiveSCEVType(Ty); 953 954 // Sign-extend negative constants. 955 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 956 if (SC->getValue()->getValue().isNegative()) 957 return getSignExtendExpr(Op, Ty); 958 959 // Peel off a truncate cast. 960 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 961 const SCEV *NewOp = T->getOperand(); 962 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 963 return getAnyExtendExpr(NewOp, Ty); 964 return getTruncateOrNoop(NewOp, Ty); 965 } 966 967 // Next try a zext cast. If the cast is folded, use it. 968 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 969 if (!isa<SCEVZeroExtendExpr>(ZExt)) 970 return ZExt; 971 972 // Next try a sext cast. If the cast is folded, use it. 973 const SCEV *SExt = getSignExtendExpr(Op, Ty); 974 if (!isa<SCEVSignExtendExpr>(SExt)) 975 return SExt; 976 977 // If the expression is obviously signed, use the sext cast value. 978 if (isa<SCEVSMaxExpr>(Op)) 979 return SExt; 980 981 // Absent any other information, use the zext cast value. 982 return ZExt; 983} 984 985/// CollectAddOperandsWithScales - Process the given Ops list, which is 986/// a list of operands to be added under the given scale, update the given 987/// map. This is a helper function for getAddRecExpr. As an example of 988/// what it does, given a sequence of operands that would form an add 989/// expression like this: 990/// 991/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 992/// 993/// where A and B are constants, update the map with these values: 994/// 995/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 996/// 997/// and add 13 + A*B*29 to AccumulatedConstant. 998/// This will allow getAddRecExpr to produce this: 999/// 1000/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1001/// 1002/// This form often exposes folding opportunities that are hidden in 1003/// the original operand list. 1004/// 1005/// Return true iff it appears that any interesting folding opportunities 1006/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1007/// the common case where no interesting opportunities are present, and 1008/// is also used as a check to avoid infinite recursion. 1009/// 1010static bool 1011CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1012 SmallVector<const SCEV *, 8> &NewOps, 1013 APInt &AccumulatedConstant, 1014 const SmallVectorImpl<const SCEV *> &Ops, 1015 const APInt &Scale, 1016 ScalarEvolution &SE) { 1017 bool Interesting = false; 1018 1019 // Iterate over the add operands. 1020 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1021 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1022 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1023 APInt NewScale = 1024 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1025 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1026 // A multiplication of a constant with another add; recurse. 1027 Interesting |= 1028 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1029 cast<SCEVAddExpr>(Mul->getOperand(1)) 1030 ->getOperands(), 1031 NewScale, SE); 1032 } else { 1033 // A multiplication of a constant with some other value. Update 1034 // the map. 1035 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1036 const SCEV *Key = SE.getMulExpr(MulOps); 1037 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1038 M.insert(std::make_pair(Key, NewScale)); 1039 if (Pair.second) { 1040 NewOps.push_back(Pair.first->first); 1041 } else { 1042 Pair.first->second += NewScale; 1043 // The map already had an entry for this value, which may indicate 1044 // a folding opportunity. 1045 Interesting = true; 1046 } 1047 } 1048 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1049 // Pull a buried constant out to the outside. 1050 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1051 Interesting = true; 1052 AccumulatedConstant += Scale * C->getValue()->getValue(); 1053 } else { 1054 // An ordinary operand. Update the map. 1055 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1056 M.insert(std::make_pair(Ops[i], Scale)); 1057 if (Pair.second) { 1058 NewOps.push_back(Pair.first->first); 1059 } else { 1060 Pair.first->second += Scale; 1061 // The map already had an entry for this value, which may indicate 1062 // a folding opportunity. 1063 Interesting = true; 1064 } 1065 } 1066 } 1067 1068 return Interesting; 1069} 1070 1071namespace { 1072 struct APIntCompare { 1073 bool operator()(const APInt &LHS, const APInt &RHS) const { 1074 return LHS.ult(RHS); 1075 } 1076 }; 1077} 1078 1079/// getAddExpr - Get a canonical add expression, or something simpler if 1080/// possible. 1081const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) { 1082 assert(!Ops.empty() && "Cannot get empty add!"); 1083 if (Ops.size() == 1) return Ops[0]; 1084#ifndef NDEBUG 1085 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1086 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1087 getEffectiveSCEVType(Ops[0]->getType()) && 1088 "SCEVAddExpr operand types don't match!"); 1089#endif 1090 1091 // Sort by complexity, this groups all similar expression types together. 1092 GroupByComplexity(Ops, LI); 1093 1094 // If there are any constants, fold them together. 1095 unsigned Idx = 0; 1096 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1097 ++Idx; 1098 assert(Idx < Ops.size()); 1099 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1100 // We found two constants, fold them together! 1101 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1102 RHSC->getValue()->getValue()); 1103 if (Ops.size() == 2) return Ops[0]; 1104 Ops.erase(Ops.begin()+1); // Erase the folded element 1105 LHSC = cast<SCEVConstant>(Ops[0]); 1106 } 1107 1108 // If we are left with a constant zero being added, strip it off. 1109 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1110 Ops.erase(Ops.begin()); 1111 --Idx; 1112 } 1113 } 1114 1115 if (Ops.size() == 1) return Ops[0]; 1116 1117 // Okay, check to see if the same value occurs in the operand list twice. If 1118 // so, merge them together into an multiply expression. Since we sorted the 1119 // list, these values are required to be adjacent. 1120 const Type *Ty = Ops[0]->getType(); 1121 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1122 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1123 // Found a match, merge the two values into a multiply, and add any 1124 // remaining values to the result. 1125 const SCEV *Two = getIntegerSCEV(2, Ty); 1126 const SCEV *Mul = getMulExpr(Ops[i], Two); 1127 if (Ops.size() == 2) 1128 return Mul; 1129 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1130 Ops.push_back(Mul); 1131 return getAddExpr(Ops); 1132 } 1133 1134 // Check for truncates. If all the operands are truncated from the same 1135 // type, see if factoring out the truncate would permit the result to be 1136 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1137 // if the contents of the resulting outer trunc fold to something simple. 1138 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1139 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1140 const Type *DstType = Trunc->getType(); 1141 const Type *SrcType = Trunc->getOperand()->getType(); 1142 SmallVector<const SCEV *, 8> LargeOps; 1143 bool Ok = true; 1144 // Check all the operands to see if they can be represented in the 1145 // source type of the truncate. 1146 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1147 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1148 if (T->getOperand()->getType() != SrcType) { 1149 Ok = false; 1150 break; 1151 } 1152 LargeOps.push_back(T->getOperand()); 1153 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1154 // This could be either sign or zero extension, but sign extension 1155 // is much more likely to be foldable here. 1156 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1157 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1158 SmallVector<const SCEV *, 8> LargeMulOps; 1159 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1160 if (const SCEVTruncateExpr *T = 1161 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1162 if (T->getOperand()->getType() != SrcType) { 1163 Ok = false; 1164 break; 1165 } 1166 LargeMulOps.push_back(T->getOperand()); 1167 } else if (const SCEVConstant *C = 1168 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1169 // This could be either sign or zero extension, but sign extension 1170 // is much more likely to be foldable here. 1171 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1172 } else { 1173 Ok = false; 1174 break; 1175 } 1176 } 1177 if (Ok) 1178 LargeOps.push_back(getMulExpr(LargeMulOps)); 1179 } else { 1180 Ok = false; 1181 break; 1182 } 1183 } 1184 if (Ok) { 1185 // Evaluate the expression in the larger type. 1186 const SCEV *Fold = getAddExpr(LargeOps); 1187 // If it folds to something simple, use it. Otherwise, don't. 1188 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1189 return getTruncateExpr(Fold, DstType); 1190 } 1191 } 1192 1193 // Skip past any other cast SCEVs. 1194 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1195 ++Idx; 1196 1197 // If there are add operands they would be next. 1198 if (Idx < Ops.size()) { 1199 bool DeletedAdd = false; 1200 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1201 // If we have an add, expand the add operands onto the end of the operands 1202 // list. 1203 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1204 Ops.erase(Ops.begin()+Idx); 1205 DeletedAdd = true; 1206 } 1207 1208 // If we deleted at least one add, we added operands to the end of the list, 1209 // and they are not necessarily sorted. Recurse to resort and resimplify 1210 // any operands we just aquired. 1211 if (DeletedAdd) 1212 return getAddExpr(Ops); 1213 } 1214 1215 // Skip over the add expression until we get to a multiply. 1216 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1217 ++Idx; 1218 1219 // Check to see if there are any folding opportunities present with 1220 // operands multiplied by constant values. 1221 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1222 uint64_t BitWidth = getTypeSizeInBits(Ty); 1223 DenseMap<const SCEV *, APInt> M; 1224 SmallVector<const SCEV *, 8> NewOps; 1225 APInt AccumulatedConstant(BitWidth, 0); 1226 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1227 Ops, APInt(BitWidth, 1), *this)) { 1228 // Some interesting folding opportunity is present, so its worthwhile to 1229 // re-generate the operands list. Group the operands by constant scale, 1230 // to avoid multiplying by the same constant scale multiple times. 1231 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1232 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1233 E = NewOps.end(); I != E; ++I) 1234 MulOpLists[M.find(*I)->second].push_back(*I); 1235 // Re-generate the operands list. 1236 Ops.clear(); 1237 if (AccumulatedConstant != 0) 1238 Ops.push_back(getConstant(AccumulatedConstant)); 1239 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1240 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1241 if (I->first != 0) 1242 Ops.push_back(getMulExpr(getConstant(I->first), 1243 getAddExpr(I->second))); 1244 if (Ops.empty()) 1245 return getIntegerSCEV(0, Ty); 1246 if (Ops.size() == 1) 1247 return Ops[0]; 1248 return getAddExpr(Ops); 1249 } 1250 } 1251 1252 // If we are adding something to a multiply expression, make sure the 1253 // something is not already an operand of the multiply. If so, merge it into 1254 // the multiply. 1255 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1256 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1257 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1258 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1259 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1260 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1261 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1262 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1263 if (Mul->getNumOperands() != 2) { 1264 // If the multiply has more than two operands, we must get the 1265 // Y*Z term. 1266 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1267 MulOps.erase(MulOps.begin()+MulOp); 1268 InnerMul = getMulExpr(MulOps); 1269 } 1270 const SCEV *One = getIntegerSCEV(1, Ty); 1271 const SCEV *AddOne = getAddExpr(InnerMul, One); 1272 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1273 if (Ops.size() == 2) return OuterMul; 1274 if (AddOp < Idx) { 1275 Ops.erase(Ops.begin()+AddOp); 1276 Ops.erase(Ops.begin()+Idx-1); 1277 } else { 1278 Ops.erase(Ops.begin()+Idx); 1279 Ops.erase(Ops.begin()+AddOp-1); 1280 } 1281 Ops.push_back(OuterMul); 1282 return getAddExpr(Ops); 1283 } 1284 1285 // Check this multiply against other multiplies being added together. 1286 for (unsigned OtherMulIdx = Idx+1; 1287 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1288 ++OtherMulIdx) { 1289 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1290 // If MulOp occurs in OtherMul, we can fold the two multiplies 1291 // together. 1292 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1293 OMulOp != e; ++OMulOp) 1294 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1295 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1296 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1297 if (Mul->getNumOperands() != 2) { 1298 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1299 Mul->op_end()); 1300 MulOps.erase(MulOps.begin()+MulOp); 1301 InnerMul1 = getMulExpr(MulOps); 1302 } 1303 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1304 if (OtherMul->getNumOperands() != 2) { 1305 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1306 OtherMul->op_end()); 1307 MulOps.erase(MulOps.begin()+OMulOp); 1308 InnerMul2 = getMulExpr(MulOps); 1309 } 1310 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1311 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1312 if (Ops.size() == 2) return OuterMul; 1313 Ops.erase(Ops.begin()+Idx); 1314 Ops.erase(Ops.begin()+OtherMulIdx-1); 1315 Ops.push_back(OuterMul); 1316 return getAddExpr(Ops); 1317 } 1318 } 1319 } 1320 } 1321 1322 // If there are any add recurrences in the operands list, see if any other 1323 // added values are loop invariant. If so, we can fold them into the 1324 // recurrence. 1325 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1326 ++Idx; 1327 1328 // Scan over all recurrences, trying to fold loop invariants into them. 1329 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1330 // Scan all of the other operands to this add and add them to the vector if 1331 // they are loop invariant w.r.t. the recurrence. 1332 SmallVector<const SCEV *, 8> LIOps; 1333 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1334 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1335 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1336 LIOps.push_back(Ops[i]); 1337 Ops.erase(Ops.begin()+i); 1338 --i; --e; 1339 } 1340 1341 // If we found some loop invariants, fold them into the recurrence. 1342 if (!LIOps.empty()) { 1343 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1344 LIOps.push_back(AddRec->getStart()); 1345 1346 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1347 AddRec->op_end()); 1348 AddRecOps[0] = getAddExpr(LIOps); 1349 1350 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1351 // If all of the other operands were loop invariant, we are done. 1352 if (Ops.size() == 1) return NewRec; 1353 1354 // Otherwise, add the folded AddRec by the non-liv parts. 1355 for (unsigned i = 0;; ++i) 1356 if (Ops[i] == AddRec) { 1357 Ops[i] = NewRec; 1358 break; 1359 } 1360 return getAddExpr(Ops); 1361 } 1362 1363 // Okay, if there weren't any loop invariants to be folded, check to see if 1364 // there are multiple AddRec's with the same loop induction variable being 1365 // added together. If so, we can fold them. 1366 for (unsigned OtherIdx = Idx+1; 1367 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1368 if (OtherIdx != Idx) { 1369 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1370 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1371 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1372 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1373 AddRec->op_end()); 1374 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1375 if (i >= NewOps.size()) { 1376 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1377 OtherAddRec->op_end()); 1378 break; 1379 } 1380 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1381 } 1382 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1383 1384 if (Ops.size() == 2) return NewAddRec; 1385 1386 Ops.erase(Ops.begin()+Idx); 1387 Ops.erase(Ops.begin()+OtherIdx-1); 1388 Ops.push_back(NewAddRec); 1389 return getAddExpr(Ops); 1390 } 1391 } 1392 1393 // Otherwise couldn't fold anything into this recurrence. Move onto the 1394 // next one. 1395 } 1396 1397 // Okay, it looks like we really DO need an add expr. Check to see if we 1398 // already have one, otherwise create a new one. 1399 FoldingSetNodeID ID; 1400 ID.AddInteger(scAddExpr); 1401 ID.AddInteger(Ops.size()); 1402 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1403 ID.AddPointer(Ops[i]); 1404 void *IP = 0; 1405 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1406 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1407 new (S) SCEVAddExpr(ID, Ops); 1408 UniqueSCEVs.InsertNode(S, IP); 1409 return S; 1410} 1411 1412 1413/// getMulExpr - Get a canonical multiply expression, or something simpler if 1414/// possible. 1415const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) { 1416 assert(!Ops.empty() && "Cannot get empty mul!"); 1417#ifndef NDEBUG 1418 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1419 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1420 getEffectiveSCEVType(Ops[0]->getType()) && 1421 "SCEVMulExpr operand types don't match!"); 1422#endif 1423 1424 // Sort by complexity, this groups all similar expression types together. 1425 GroupByComplexity(Ops, LI); 1426 1427 // If there are any constants, fold them together. 1428 unsigned Idx = 0; 1429 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1430 1431 // C1*(C2+V) -> C1*C2 + C1*V 1432 if (Ops.size() == 2) 1433 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1434 if (Add->getNumOperands() == 2 && 1435 isa<SCEVConstant>(Add->getOperand(0))) 1436 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1437 getMulExpr(LHSC, Add->getOperand(1))); 1438 1439 1440 ++Idx; 1441 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1442 // We found two constants, fold them together! 1443 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() * 1444 RHSC->getValue()->getValue()); 1445 Ops[0] = getConstant(Fold); 1446 Ops.erase(Ops.begin()+1); // Erase the folded element 1447 if (Ops.size() == 1) return Ops[0]; 1448 LHSC = cast<SCEVConstant>(Ops[0]); 1449 } 1450 1451 // If we are left with a constant one being multiplied, strip it off. 1452 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1453 Ops.erase(Ops.begin()); 1454 --Idx; 1455 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1456 // If we have a multiply of zero, it will always be zero. 1457 return Ops[0]; 1458 } 1459 } 1460 1461 // Skip over the add expression until we get to a multiply. 1462 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1463 ++Idx; 1464 1465 if (Ops.size() == 1) 1466 return Ops[0]; 1467 1468 // If there are mul operands inline them all into this expression. 1469 if (Idx < Ops.size()) { 1470 bool DeletedMul = false; 1471 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1472 // If we have an mul, expand the mul operands onto the end of the operands 1473 // list. 1474 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1475 Ops.erase(Ops.begin()+Idx); 1476 DeletedMul = true; 1477 } 1478 1479 // If we deleted at least one mul, we added operands to the end of the list, 1480 // and they are not necessarily sorted. Recurse to resort and resimplify 1481 // any operands we just aquired. 1482 if (DeletedMul) 1483 return getMulExpr(Ops); 1484 } 1485 1486 // If there are any add recurrences in the operands list, see if any other 1487 // added values are loop invariant. If so, we can fold them into the 1488 // recurrence. 1489 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1490 ++Idx; 1491 1492 // Scan over all recurrences, trying to fold loop invariants into them. 1493 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1494 // Scan all of the other operands to this mul and add them to the vector if 1495 // they are loop invariant w.r.t. the recurrence. 1496 SmallVector<const SCEV *, 8> LIOps; 1497 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1498 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1499 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1500 LIOps.push_back(Ops[i]); 1501 Ops.erase(Ops.begin()+i); 1502 --i; --e; 1503 } 1504 1505 // If we found some loop invariants, fold them into the recurrence. 1506 if (!LIOps.empty()) { 1507 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1508 SmallVector<const SCEV *, 4> NewOps; 1509 NewOps.reserve(AddRec->getNumOperands()); 1510 if (LIOps.size() == 1) { 1511 const SCEV *Scale = LIOps[0]; 1512 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1513 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1514 } else { 1515 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1516 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1517 MulOps.push_back(AddRec->getOperand(i)); 1518 NewOps.push_back(getMulExpr(MulOps)); 1519 } 1520 } 1521 1522 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1523 1524 // If all of the other operands were loop invariant, we are done. 1525 if (Ops.size() == 1) return NewRec; 1526 1527 // Otherwise, multiply the folded AddRec by the non-liv parts. 1528 for (unsigned i = 0;; ++i) 1529 if (Ops[i] == AddRec) { 1530 Ops[i] = NewRec; 1531 break; 1532 } 1533 return getMulExpr(Ops); 1534 } 1535 1536 // Okay, if there weren't any loop invariants to be folded, check to see if 1537 // there are multiple AddRec's with the same loop induction variable being 1538 // multiplied together. If so, we can fold them. 1539 for (unsigned OtherIdx = Idx+1; 1540 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1541 if (OtherIdx != Idx) { 1542 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1543 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1544 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1545 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1546 const SCEV *NewStart = getMulExpr(F->getStart(), 1547 G->getStart()); 1548 const SCEV *B = F->getStepRecurrence(*this); 1549 const SCEV *D = G->getStepRecurrence(*this); 1550 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1551 getMulExpr(G, B), 1552 getMulExpr(B, D)); 1553 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1554 F->getLoop()); 1555 if (Ops.size() == 2) return NewAddRec; 1556 1557 Ops.erase(Ops.begin()+Idx); 1558 Ops.erase(Ops.begin()+OtherIdx-1); 1559 Ops.push_back(NewAddRec); 1560 return getMulExpr(Ops); 1561 } 1562 } 1563 1564 // Otherwise couldn't fold anything into this recurrence. Move onto the 1565 // next one. 1566 } 1567 1568 // Okay, it looks like we really DO need an mul expr. Check to see if we 1569 // already have one, otherwise create a new one. 1570 FoldingSetNodeID ID; 1571 ID.AddInteger(scMulExpr); 1572 ID.AddInteger(Ops.size()); 1573 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1574 ID.AddPointer(Ops[i]); 1575 void *IP = 0; 1576 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1577 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1578 new (S) SCEVMulExpr(ID, Ops); 1579 UniqueSCEVs.InsertNode(S, IP); 1580 return S; 1581} 1582 1583/// getUDivExpr - Get a canonical multiply expression, or something simpler if 1584/// possible. 1585const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1586 const SCEV *RHS) { 1587 assert(getEffectiveSCEVType(LHS->getType()) == 1588 getEffectiveSCEVType(RHS->getType()) && 1589 "SCEVUDivExpr operand types don't match!"); 1590 1591 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1592 if (RHSC->getValue()->equalsInt(1)) 1593 return LHS; // X udiv 1 --> x 1594 if (RHSC->isZero()) 1595 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1596 1597 // Determine if the division can be folded into the operands of 1598 // its operands. 1599 // TODO: Generalize this to non-constants by using known-bits information. 1600 const Type *Ty = LHS->getType(); 1601 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1602 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1603 // For non-power-of-two values, effectively round the value up to the 1604 // nearest power of two. 1605 if (!RHSC->getValue()->getValue().isPowerOf2()) 1606 ++MaxShiftAmt; 1607 const IntegerType *ExtTy = 1608 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt); 1609 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1610 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1611 if (const SCEVConstant *Step = 1612 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1613 if (!Step->getValue()->getValue() 1614 .urem(RHSC->getValue()->getValue()) && 1615 getZeroExtendExpr(AR, ExtTy) == 1616 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1617 getZeroExtendExpr(Step, ExtTy), 1618 AR->getLoop())) { 1619 SmallVector<const SCEV *, 4> Operands; 1620 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1621 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1622 return getAddRecExpr(Operands, AR->getLoop()); 1623 } 1624 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1625 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1626 SmallVector<const SCEV *, 4> Operands; 1627 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1628 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1629 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1630 // Find an operand that's safely divisible. 1631 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1632 const SCEV *Op = M->getOperand(i); 1633 const SCEV *Div = getUDivExpr(Op, RHSC); 1634 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1635 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1636 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1637 MOperands.end()); 1638 Operands[i] = Div; 1639 return getMulExpr(Operands); 1640 } 1641 } 1642 } 1643 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1644 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1645 SmallVector<const SCEV *, 4> Operands; 1646 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1647 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1648 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1649 Operands.clear(); 1650 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1651 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1652 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1653 break; 1654 Operands.push_back(Op); 1655 } 1656 if (Operands.size() == A->getNumOperands()) 1657 return getAddExpr(Operands); 1658 } 1659 } 1660 1661 // Fold if both operands are constant. 1662 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1663 Constant *LHSCV = LHSC->getValue(); 1664 Constant *RHSCV = RHSC->getValue(); 1665 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1666 RHSCV))); 1667 } 1668 } 1669 1670 FoldingSetNodeID ID; 1671 ID.AddInteger(scUDivExpr); 1672 ID.AddPointer(LHS); 1673 ID.AddPointer(RHS); 1674 void *IP = 0; 1675 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1676 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1677 new (S) SCEVUDivExpr(ID, LHS, RHS); 1678 UniqueSCEVs.InsertNode(S, IP); 1679 return S; 1680} 1681 1682 1683/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1684/// Simplify the expression as much as possible. 1685const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1686 const SCEV *Step, const Loop *L) { 1687 SmallVector<const SCEV *, 4> Operands; 1688 Operands.push_back(Start); 1689 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1690 if (StepChrec->getLoop() == L) { 1691 Operands.insert(Operands.end(), StepChrec->op_begin(), 1692 StepChrec->op_end()); 1693 return getAddRecExpr(Operands, L); 1694 } 1695 1696 Operands.push_back(Step); 1697 return getAddRecExpr(Operands, L); 1698} 1699 1700/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1701/// Simplify the expression as much as possible. 1702const SCEV * 1703ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1704 const Loop *L) { 1705 if (Operands.size() == 1) return Operands[0]; 1706#ifndef NDEBUG 1707 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1708 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1709 getEffectiveSCEVType(Operands[0]->getType()) && 1710 "SCEVAddRecExpr operand types don't match!"); 1711#endif 1712 1713 if (Operands.back()->isZero()) { 1714 Operands.pop_back(); 1715 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1716 } 1717 1718 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1719 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1720 const Loop* NestedLoop = NestedAR->getLoop(); 1721 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1722 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1723 NestedAR->op_end()); 1724 Operands[0] = NestedAR->getStart(); 1725 // AddRecs require their operands be loop-invariant with respect to their 1726 // loops. Don't perform this transformation if it would break this 1727 // requirement. 1728 bool AllInvariant = true; 1729 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1730 if (!Operands[i]->isLoopInvariant(L)) { 1731 AllInvariant = false; 1732 break; 1733 } 1734 if (AllInvariant) { 1735 NestedOperands[0] = getAddRecExpr(Operands, L); 1736 AllInvariant = true; 1737 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1738 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1739 AllInvariant = false; 1740 break; 1741 } 1742 if (AllInvariant) 1743 // Ok, both add recurrences are valid after the transformation. 1744 return getAddRecExpr(NestedOperands, NestedLoop); 1745 } 1746 // Reset Operands to its original state. 1747 Operands[0] = NestedAR; 1748 } 1749 } 1750 1751 FoldingSetNodeID ID; 1752 ID.AddInteger(scAddRecExpr); 1753 ID.AddInteger(Operands.size()); 1754 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1755 ID.AddPointer(Operands[i]); 1756 ID.AddPointer(L); 1757 void *IP = 0; 1758 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1759 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1760 new (S) SCEVAddRecExpr(ID, Operands, L); 1761 UniqueSCEVs.InsertNode(S, IP); 1762 return S; 1763} 1764 1765const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1766 const SCEV *RHS) { 1767 SmallVector<const SCEV *, 2> Ops; 1768 Ops.push_back(LHS); 1769 Ops.push_back(RHS); 1770 return getSMaxExpr(Ops); 1771} 1772 1773const SCEV * 1774ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1775 assert(!Ops.empty() && "Cannot get empty smax!"); 1776 if (Ops.size() == 1) return Ops[0]; 1777#ifndef NDEBUG 1778 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1779 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1780 getEffectiveSCEVType(Ops[0]->getType()) && 1781 "SCEVSMaxExpr operand types don't match!"); 1782#endif 1783 1784 // Sort by complexity, this groups all similar expression types together. 1785 GroupByComplexity(Ops, LI); 1786 1787 // If there are any constants, fold them together. 1788 unsigned Idx = 0; 1789 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1790 ++Idx; 1791 assert(Idx < Ops.size()); 1792 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1793 // We found two constants, fold them together! 1794 ConstantInt *Fold = ConstantInt::get( 1795 APIntOps::smax(LHSC->getValue()->getValue(), 1796 RHSC->getValue()->getValue())); 1797 Ops[0] = getConstant(Fold); 1798 Ops.erase(Ops.begin()+1); // Erase the folded element 1799 if (Ops.size() == 1) return Ops[0]; 1800 LHSC = cast<SCEVConstant>(Ops[0]); 1801 } 1802 1803 // If we are left with a constant minimum-int, strip it off. 1804 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1805 Ops.erase(Ops.begin()); 1806 --Idx; 1807 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1808 // If we have an smax with a constant maximum-int, it will always be 1809 // maximum-int. 1810 return Ops[0]; 1811 } 1812 } 1813 1814 if (Ops.size() == 1) return Ops[0]; 1815 1816 // Find the first SMax 1817 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1818 ++Idx; 1819 1820 // Check to see if one of the operands is an SMax. If so, expand its operands 1821 // onto our operand list, and recurse to simplify. 1822 if (Idx < Ops.size()) { 1823 bool DeletedSMax = false; 1824 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1825 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1826 Ops.erase(Ops.begin()+Idx); 1827 DeletedSMax = true; 1828 } 1829 1830 if (DeletedSMax) 1831 return getSMaxExpr(Ops); 1832 } 1833 1834 // Okay, check to see if the same value occurs in the operand list twice. If 1835 // so, delete one. Since we sorted the list, these values are required to 1836 // be adjacent. 1837 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1838 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1839 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1840 --i; --e; 1841 } 1842 1843 if (Ops.size() == 1) return Ops[0]; 1844 1845 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1846 1847 // Okay, it looks like we really DO need an smax expr. Check to see if we 1848 // already have one, otherwise create a new one. 1849 FoldingSetNodeID ID; 1850 ID.AddInteger(scSMaxExpr); 1851 ID.AddInteger(Ops.size()); 1852 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1853 ID.AddPointer(Ops[i]); 1854 void *IP = 0; 1855 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1856 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1857 new (S) SCEVSMaxExpr(ID, Ops); 1858 UniqueSCEVs.InsertNode(S, IP); 1859 return S; 1860} 1861 1862const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1863 const SCEV *RHS) { 1864 SmallVector<const SCEV *, 2> Ops; 1865 Ops.push_back(LHS); 1866 Ops.push_back(RHS); 1867 return getUMaxExpr(Ops); 1868} 1869 1870const SCEV * 1871ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1872 assert(!Ops.empty() && "Cannot get empty umax!"); 1873 if (Ops.size() == 1) return Ops[0]; 1874#ifndef NDEBUG 1875 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1876 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1877 getEffectiveSCEVType(Ops[0]->getType()) && 1878 "SCEVUMaxExpr operand types don't match!"); 1879#endif 1880 1881 // Sort by complexity, this groups all similar expression types together. 1882 GroupByComplexity(Ops, LI); 1883 1884 // If there are any constants, fold them together. 1885 unsigned Idx = 0; 1886 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1887 ++Idx; 1888 assert(Idx < Ops.size()); 1889 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1890 // We found two constants, fold them together! 1891 ConstantInt *Fold = ConstantInt::get( 1892 APIntOps::umax(LHSC->getValue()->getValue(), 1893 RHSC->getValue()->getValue())); 1894 Ops[0] = getConstant(Fold); 1895 Ops.erase(Ops.begin()+1); // Erase the folded element 1896 if (Ops.size() == 1) return Ops[0]; 1897 LHSC = cast<SCEVConstant>(Ops[0]); 1898 } 1899 1900 // If we are left with a constant minimum-int, strip it off. 1901 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 1902 Ops.erase(Ops.begin()); 1903 --Idx; 1904 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 1905 // If we have an umax with a constant maximum-int, it will always be 1906 // maximum-int. 1907 return Ops[0]; 1908 } 1909 } 1910 1911 if (Ops.size() == 1) return Ops[0]; 1912 1913 // Find the first UMax 1914 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 1915 ++Idx; 1916 1917 // Check to see if one of the operands is a UMax. If so, expand its operands 1918 // onto our operand list, and recurse to simplify. 1919 if (Idx < Ops.size()) { 1920 bool DeletedUMax = false; 1921 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 1922 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 1923 Ops.erase(Ops.begin()+Idx); 1924 DeletedUMax = true; 1925 } 1926 1927 if (DeletedUMax) 1928 return getUMaxExpr(Ops); 1929 } 1930 1931 // Okay, check to see if the same value occurs in the operand list twice. If 1932 // so, delete one. Since we sorted the list, these values are required to 1933 // be adjacent. 1934 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1935 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 1936 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1937 --i; --e; 1938 } 1939 1940 if (Ops.size() == 1) return Ops[0]; 1941 1942 assert(!Ops.empty() && "Reduced umax down to nothing!"); 1943 1944 // Okay, it looks like we really DO need a umax expr. Check to see if we 1945 // already have one, otherwise create a new one. 1946 FoldingSetNodeID ID; 1947 ID.AddInteger(scUMaxExpr); 1948 ID.AddInteger(Ops.size()); 1949 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1950 ID.AddPointer(Ops[i]); 1951 void *IP = 0; 1952 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1953 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 1954 new (S) SCEVUMaxExpr(ID, Ops); 1955 UniqueSCEVs.InsertNode(S, IP); 1956 return S; 1957} 1958 1959const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 1960 const SCEV *RHS) { 1961 // ~smax(~x, ~y) == smin(x, y). 1962 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1963} 1964 1965const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 1966 const SCEV *RHS) { 1967 // ~umax(~x, ~y) == umin(x, y) 1968 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 1969} 1970 1971const SCEV *ScalarEvolution::getUnknown(Value *V) { 1972 // Don't attempt to do anything other than create a SCEVUnknown object 1973 // here. createSCEV only calls getUnknown after checking for all other 1974 // interesting possibilities, and any other code that calls getUnknown 1975 // is doing so in order to hide a value from SCEV canonicalization. 1976 1977 FoldingSetNodeID ID; 1978 ID.AddInteger(scUnknown); 1979 ID.AddPointer(V); 1980 void *IP = 0; 1981 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1982 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 1983 new (S) SCEVUnknown(ID, V); 1984 UniqueSCEVs.InsertNode(S, IP); 1985 return S; 1986} 1987 1988//===----------------------------------------------------------------------===// 1989// Basic SCEV Analysis and PHI Idiom Recognition Code 1990// 1991 1992/// isSCEVable - Test if values of the given type are analyzable within 1993/// the SCEV framework. This primarily includes integer types, and it 1994/// can optionally include pointer types if the ScalarEvolution class 1995/// has access to target-specific information. 1996bool ScalarEvolution::isSCEVable(const Type *Ty) const { 1997 // Integers are always SCEVable. 1998 if (Ty->isInteger()) 1999 return true; 2000 2001 // Pointers are SCEVable if TargetData information is available 2002 // to provide pointer size information. 2003 if (isa<PointerType>(Ty)) 2004 return TD != NULL; 2005 2006 // Otherwise it's not SCEVable. 2007 return false; 2008} 2009 2010/// getTypeSizeInBits - Return the size in bits of the specified type, 2011/// for which isSCEVable must return true. 2012uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2013 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2014 2015 // If we have a TargetData, use it! 2016 if (TD) 2017 return TD->getTypeSizeInBits(Ty); 2018 2019 // Otherwise, we support only integer types. 2020 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!"); 2021 return Ty->getPrimitiveSizeInBits(); 2022} 2023 2024/// getEffectiveSCEVType - Return a type with the same bitwidth as 2025/// the given type and which represents how SCEV will treat the given 2026/// type, for which isSCEVable must return true. For pointer types, 2027/// this is the pointer-sized integer type. 2028const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2029 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2030 2031 if (Ty->isInteger()) 2032 return Ty; 2033 2034 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2035 return TD->getIntPtrType(); 2036} 2037 2038const SCEV *ScalarEvolution::getCouldNotCompute() { 2039 return &CouldNotCompute; 2040} 2041 2042/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2043/// expression and create a new one. 2044const SCEV *ScalarEvolution::getSCEV(Value *V) { 2045 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2046 2047 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2048 if (I != Scalars.end()) return I->second; 2049 const SCEV *S = createSCEV(V); 2050 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2051 return S; 2052} 2053 2054/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2055/// specified signed integer value and return a SCEV for the constant. 2056const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2057 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2058 return getConstant(ConstantInt::get(ITy, Val)); 2059} 2060 2061/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2062/// 2063const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2064 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2065 return getConstant( 2066 cast<ConstantInt>(Context->getConstantExprNeg(VC->getValue()))); 2067 2068 const Type *Ty = V->getType(); 2069 Ty = getEffectiveSCEVType(Ty); 2070 return getMulExpr(V, 2071 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty)))); 2072} 2073 2074/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2075const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2076 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2077 return getConstant( 2078 cast<ConstantInt>(Context->getConstantExprNot(VC->getValue()))); 2079 2080 const Type *Ty = V->getType(); 2081 Ty = getEffectiveSCEVType(Ty); 2082 const SCEV *AllOnes = 2083 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty))); 2084 return getMinusSCEV(AllOnes, V); 2085} 2086 2087/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2088/// 2089const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2090 const SCEV *RHS) { 2091 // X - Y --> X + -Y 2092 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2093} 2094 2095/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2096/// input value to the specified type. If the type must be extended, it is zero 2097/// extended. 2098const SCEV * 2099ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2100 const Type *Ty) { 2101 const Type *SrcTy = V->getType(); 2102 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2103 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2104 "Cannot truncate or zero extend with non-integer arguments!"); 2105 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2106 return V; // No conversion 2107 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2108 return getTruncateExpr(V, Ty); 2109 return getZeroExtendExpr(V, Ty); 2110} 2111 2112/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2113/// input value to the specified type. If the type must be extended, it is sign 2114/// extended. 2115const SCEV * 2116ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2117 const Type *Ty) { 2118 const Type *SrcTy = V->getType(); 2119 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2120 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2121 "Cannot truncate or zero extend with non-integer arguments!"); 2122 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2123 return V; // No conversion 2124 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2125 return getTruncateExpr(V, Ty); 2126 return getSignExtendExpr(V, Ty); 2127} 2128 2129/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2130/// input value to the specified type. If the type must be extended, it is zero 2131/// extended. The conversion must not be narrowing. 2132const SCEV * 2133ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2134 const Type *SrcTy = V->getType(); 2135 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2136 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2137 "Cannot noop or zero extend with non-integer arguments!"); 2138 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2139 "getNoopOrZeroExtend cannot truncate!"); 2140 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2141 return V; // No conversion 2142 return getZeroExtendExpr(V, Ty); 2143} 2144 2145/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2146/// input value to the specified type. If the type must be extended, it is sign 2147/// extended. The conversion must not be narrowing. 2148const SCEV * 2149ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2150 const Type *SrcTy = V->getType(); 2151 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2152 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2153 "Cannot noop or sign extend with non-integer arguments!"); 2154 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2155 "getNoopOrSignExtend cannot truncate!"); 2156 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2157 return V; // No conversion 2158 return getSignExtendExpr(V, Ty); 2159} 2160 2161/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2162/// the input value to the specified type. If the type must be extended, 2163/// it is extended with unspecified bits. The conversion must not be 2164/// narrowing. 2165const SCEV * 2166ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2167 const Type *SrcTy = V->getType(); 2168 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2169 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2170 "Cannot noop or any extend with non-integer arguments!"); 2171 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2172 "getNoopOrAnyExtend cannot truncate!"); 2173 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2174 return V; // No conversion 2175 return getAnyExtendExpr(V, Ty); 2176} 2177 2178/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2179/// input value to the specified type. The conversion must not be widening. 2180const SCEV * 2181ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2182 const Type *SrcTy = V->getType(); 2183 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) && 2184 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) && 2185 "Cannot truncate or noop with non-integer arguments!"); 2186 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2187 "getTruncateOrNoop cannot extend!"); 2188 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2189 return V; // No conversion 2190 return getTruncateExpr(V, Ty); 2191} 2192 2193/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2194/// the types using zero-extension, and then perform a umax operation 2195/// with them. 2196const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2197 const SCEV *RHS) { 2198 const SCEV *PromotedLHS = LHS; 2199 const SCEV *PromotedRHS = RHS; 2200 2201 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2202 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2203 else 2204 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2205 2206 return getUMaxExpr(PromotedLHS, PromotedRHS); 2207} 2208 2209/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2210/// the types using zero-extension, and then perform a umin operation 2211/// with them. 2212const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2213 const SCEV *RHS) { 2214 const SCEV *PromotedLHS = LHS; 2215 const SCEV *PromotedRHS = RHS; 2216 2217 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2218 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2219 else 2220 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2221 2222 return getUMinExpr(PromotedLHS, PromotedRHS); 2223} 2224 2225/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for 2226/// the specified instruction and replaces any references to the symbolic value 2227/// SymName with the specified value. This is used during PHI resolution. 2228void 2229ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I, 2230 const SCEV *SymName, 2231 const SCEV *NewVal) { 2232 std::map<SCEVCallbackVH, const SCEV *>::iterator SI = 2233 Scalars.find(SCEVCallbackVH(I, this)); 2234 if (SI == Scalars.end()) return; 2235 2236 const SCEV *NV = 2237 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this); 2238 if (NV == SI->second) return; // No change. 2239 2240 SI->second = NV; // Update the scalars map! 2241 2242 // Any instruction values that use this instruction might also need to be 2243 // updated! 2244 for (Value::use_iterator UI = I->use_begin(), E = I->use_end(); 2245 UI != E; ++UI) 2246 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal); 2247} 2248 2249/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2250/// a loop header, making it a potential recurrence, or it doesn't. 2251/// 2252const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2253 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2254 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2255 if (L->getHeader() == PN->getParent()) { 2256 // If it lives in the loop header, it has two incoming values, one 2257 // from outside the loop, and one from inside. 2258 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2259 unsigned BackEdge = IncomingEdge^1; 2260 2261 // While we are analyzing this PHI node, handle its value symbolically. 2262 const SCEV *SymbolicName = getUnknown(PN); 2263 assert(Scalars.find(PN) == Scalars.end() && 2264 "PHI node already processed?"); 2265 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2266 2267 // Using this symbolic name for the PHI, analyze the value coming around 2268 // the back-edge. 2269 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge)); 2270 2271 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2272 // has a special value for the first iteration of the loop. 2273 2274 // If the value coming around the backedge is an add with the symbolic 2275 // value we just inserted, then we found a simple induction variable! 2276 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2277 // If there is a single occurrence of the symbolic value, replace it 2278 // with a recurrence. 2279 unsigned FoundIndex = Add->getNumOperands(); 2280 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2281 if (Add->getOperand(i) == SymbolicName) 2282 if (FoundIndex == e) { 2283 FoundIndex = i; 2284 break; 2285 } 2286 2287 if (FoundIndex != Add->getNumOperands()) { 2288 // Create an add with everything but the specified operand. 2289 SmallVector<const SCEV *, 8> Ops; 2290 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2291 if (i != FoundIndex) 2292 Ops.push_back(Add->getOperand(i)); 2293 const SCEV *Accum = getAddExpr(Ops); 2294 2295 // This is not a valid addrec if the step amount is varying each 2296 // loop iteration, but is not itself an addrec in this loop. 2297 if (Accum->isLoopInvariant(L) || 2298 (isa<SCEVAddRecExpr>(Accum) && 2299 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2300 const SCEV *StartVal = 2301 getSCEV(PN->getIncomingValue(IncomingEdge)); 2302 const SCEV *PHISCEV = 2303 getAddRecExpr(StartVal, Accum, L); 2304 2305 // Okay, for the entire analysis of this edge we assumed the PHI 2306 // to be symbolic. We now need to go back and update all of the 2307 // entries for the scalars that use the PHI (except for the PHI 2308 // itself) to use the new analyzed value instead of the "symbolic" 2309 // value. 2310 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2311 return PHISCEV; 2312 } 2313 } 2314 } else if (const SCEVAddRecExpr *AddRec = 2315 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2316 // Otherwise, this could be a loop like this: 2317 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2318 // In this case, j = {1,+,1} and BEValue is j. 2319 // Because the other in-value of i (0) fits the evolution of BEValue 2320 // i really is an addrec evolution. 2321 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2322 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2323 2324 // If StartVal = j.start - j.stride, we can use StartVal as the 2325 // initial step of the addrec evolution. 2326 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2327 AddRec->getOperand(1))) { 2328 const SCEV *PHISCEV = 2329 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2330 2331 // Okay, for the entire analysis of this edge we assumed the PHI 2332 // to be symbolic. We now need to go back and update all of the 2333 // entries for the scalars that use the PHI (except for the PHI 2334 // itself) to use the new analyzed value instead of the "symbolic" 2335 // value. 2336 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV); 2337 return PHISCEV; 2338 } 2339 } 2340 } 2341 2342 return SymbolicName; 2343 } 2344 2345 // If it's not a loop phi, we can't handle it yet. 2346 return getUnknown(PN); 2347} 2348 2349/// createNodeForGEP - Expand GEP instructions into add and multiply 2350/// operations. This allows them to be analyzed by regular SCEV code. 2351/// 2352const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) { 2353 2354 const Type *IntPtrTy = TD->getIntPtrType(); 2355 Value *Base = GEP->getOperand(0); 2356 // Don't attempt to analyze GEPs over unsized objects. 2357 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2358 return getUnknown(GEP); 2359 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2360 gep_type_iterator GTI = gep_type_begin(GEP); 2361 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2362 E = GEP->op_end(); 2363 I != E; ++I) { 2364 Value *Index = *I; 2365 // Compute the (potentially symbolic) offset in bytes for this index. 2366 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2367 // For a struct, add the member offset. 2368 const StructLayout &SL = *TD->getStructLayout(STy); 2369 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2370 uint64_t Offset = SL.getElementOffset(FieldNo); 2371 TotalOffset = getAddExpr(TotalOffset, 2372 getIntegerSCEV(Offset, IntPtrTy)); 2373 } else { 2374 // For an array, add the element offset, explicitly scaled. 2375 const SCEV *LocalOffset = getSCEV(Index); 2376 if (!isa<PointerType>(LocalOffset->getType())) 2377 // Getelementptr indicies are signed. 2378 LocalOffset = getTruncateOrSignExtend(LocalOffset, 2379 IntPtrTy); 2380 LocalOffset = 2381 getMulExpr(LocalOffset, 2382 getIntegerSCEV(TD->getTypeAllocSize(*GTI), 2383 IntPtrTy)); 2384 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2385 } 2386 } 2387 return getAddExpr(getSCEV(Base), TotalOffset); 2388} 2389 2390/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2391/// guaranteed to end in (at every loop iteration). It is, at the same time, 2392/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2393/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2394uint32_t 2395ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2396 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2397 return C->getValue()->getValue().countTrailingZeros(); 2398 2399 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2400 return std::min(GetMinTrailingZeros(T->getOperand()), 2401 (uint32_t)getTypeSizeInBits(T->getType())); 2402 2403 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2404 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2405 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2406 getTypeSizeInBits(E->getType()) : OpRes; 2407 } 2408 2409 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2410 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2411 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2412 getTypeSizeInBits(E->getType()) : OpRes; 2413 } 2414 2415 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2416 // The result is the min of all operands results. 2417 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2418 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2419 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2420 return MinOpRes; 2421 } 2422 2423 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2424 // The result is the sum of all operands results. 2425 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2426 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2427 for (unsigned i = 1, e = M->getNumOperands(); 2428 SumOpRes != BitWidth && i != e; ++i) 2429 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2430 BitWidth); 2431 return SumOpRes; 2432 } 2433 2434 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2435 // The result is the min of all operands results. 2436 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2437 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2438 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2439 return MinOpRes; 2440 } 2441 2442 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2443 // The result is the min of all operands results. 2444 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2445 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2446 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2447 return MinOpRes; 2448 } 2449 2450 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2451 // The result is the min of all operands results. 2452 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2453 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2454 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2455 return MinOpRes; 2456 } 2457 2458 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2459 // For a SCEVUnknown, ask ValueTracking. 2460 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2461 APInt Mask = APInt::getAllOnesValue(BitWidth); 2462 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2463 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2464 return Zeros.countTrailingOnes(); 2465 } 2466 2467 // SCEVUDivExpr 2468 return 0; 2469} 2470 2471uint32_t 2472ScalarEvolution::GetMinLeadingZeros(const SCEV *S) { 2473 // TODO: Handle other SCEV expression types here. 2474 2475 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2476 return C->getValue()->getValue().countLeadingZeros(); 2477 2478 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) { 2479 // A zero-extension cast adds zero bits. 2480 return GetMinLeadingZeros(C->getOperand()) + 2481 (getTypeSizeInBits(C->getType()) - 2482 getTypeSizeInBits(C->getOperand()->getType())); 2483 } 2484 2485 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2486 // For a SCEVUnknown, ask ValueTracking. 2487 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2488 APInt Mask = APInt::getAllOnesValue(BitWidth); 2489 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2490 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2491 return Zeros.countLeadingOnes(); 2492 } 2493 2494 return 1; 2495} 2496 2497uint32_t 2498ScalarEvolution::GetMinSignBits(const SCEV *S) { 2499 // TODO: Handle other SCEV expression types here. 2500 2501 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) { 2502 const APInt &A = C->getValue()->getValue(); 2503 return A.isNegative() ? A.countLeadingOnes() : 2504 A.countLeadingZeros(); 2505 } 2506 2507 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) { 2508 // A sign-extension cast adds sign bits. 2509 return GetMinSignBits(C->getOperand()) + 2510 (getTypeSizeInBits(C->getType()) - 2511 getTypeSizeInBits(C->getOperand()->getType())); 2512 } 2513 2514 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2515 unsigned BitWidth = getTypeSizeInBits(A->getType()); 2516 2517 // Special case decrementing a value (ADD X, -1): 2518 if (const SCEVConstant *CRHS = dyn_cast<SCEVConstant>(A->getOperand(0))) 2519 if (CRHS->isAllOnesValue()) { 2520 SmallVector<const SCEV *, 4> OtherOps(A->op_begin() + 1, A->op_end()); 2521 const SCEV *OtherOpsAdd = getAddExpr(OtherOps); 2522 unsigned LZ = GetMinLeadingZeros(OtherOpsAdd); 2523 2524 // If the input is known to be 0 or 1, the output is 0/-1, which is all 2525 // sign bits set. 2526 if (LZ == BitWidth - 1) 2527 return BitWidth; 2528 2529 // If we are subtracting one from a positive number, there is no carry 2530 // out of the result. 2531 if (LZ > 0) 2532 return GetMinSignBits(OtherOpsAdd); 2533 } 2534 2535 // Add can have at most one carry bit. Thus we know that the output 2536 // is, at worst, one more bit than the inputs. 2537 unsigned Min = BitWidth; 2538 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2539 unsigned N = GetMinSignBits(A->getOperand(i)); 2540 Min = std::min(Min, N) - 1; 2541 if (Min == 0) return 1; 2542 } 2543 return 1; 2544 } 2545 2546 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2547 // For a SCEVUnknown, ask ValueTracking. 2548 return ComputeNumSignBits(U->getValue(), TD); 2549 } 2550 2551 return 1; 2552} 2553 2554/// createSCEV - We know that there is no SCEV for the specified value. 2555/// Analyze the expression. 2556/// 2557const SCEV *ScalarEvolution::createSCEV(Value *V) { 2558 if (!isSCEVable(V->getType())) 2559 return getUnknown(V); 2560 2561 unsigned Opcode = Instruction::UserOp1; 2562 if (Instruction *I = dyn_cast<Instruction>(V)) 2563 Opcode = I->getOpcode(); 2564 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2565 Opcode = CE->getOpcode(); 2566 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2567 return getConstant(CI); 2568 else if (isa<ConstantPointerNull>(V)) 2569 return getIntegerSCEV(0, V->getType()); 2570 else if (isa<UndefValue>(V)) 2571 return getIntegerSCEV(0, V->getType()); 2572 else 2573 return getUnknown(V); 2574 2575 User *U = cast<User>(V); 2576 switch (Opcode) { 2577 case Instruction::Add: 2578 return getAddExpr(getSCEV(U->getOperand(0)), 2579 getSCEV(U->getOperand(1))); 2580 case Instruction::Mul: 2581 return getMulExpr(getSCEV(U->getOperand(0)), 2582 getSCEV(U->getOperand(1))); 2583 case Instruction::UDiv: 2584 return getUDivExpr(getSCEV(U->getOperand(0)), 2585 getSCEV(U->getOperand(1))); 2586 case Instruction::Sub: 2587 return getMinusSCEV(getSCEV(U->getOperand(0)), 2588 getSCEV(U->getOperand(1))); 2589 case Instruction::And: 2590 // For an expression like x&255 that merely masks off the high bits, 2591 // use zext(trunc(x)) as the SCEV expression. 2592 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2593 if (CI->isNullValue()) 2594 return getSCEV(U->getOperand(1)); 2595 if (CI->isAllOnesValue()) 2596 return getSCEV(U->getOperand(0)); 2597 const APInt &A = CI->getValue(); 2598 2599 // Instcombine's ShrinkDemandedConstant may strip bits out of 2600 // constants, obscuring what would otherwise be a low-bits mask. 2601 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2602 // knew about to reconstruct a low-bits mask value. 2603 unsigned LZ = A.countLeadingZeros(); 2604 unsigned BitWidth = A.getBitWidth(); 2605 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2606 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2607 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2608 2609 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2610 2611 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2612 return 2613 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2614 IntegerType::get(BitWidth - LZ)), 2615 U->getType()); 2616 } 2617 break; 2618 2619 case Instruction::Or: 2620 // If the RHS of the Or is a constant, we may have something like: 2621 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2622 // optimizations will transparently handle this case. 2623 // 2624 // In order for this transformation to be safe, the LHS must be of the 2625 // form X*(2^n) and the Or constant must be less than 2^n. 2626 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2627 const SCEV *LHS = getSCEV(U->getOperand(0)); 2628 const APInt &CIVal = CI->getValue(); 2629 if (GetMinTrailingZeros(LHS) >= 2630 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) 2631 return getAddExpr(LHS, getSCEV(U->getOperand(1))); 2632 } 2633 break; 2634 case Instruction::Xor: 2635 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2636 // If the RHS of the xor is a signbit, then this is just an add. 2637 // Instcombine turns add of signbit into xor as a strength reduction step. 2638 if (CI->getValue().isSignBit()) 2639 return getAddExpr(getSCEV(U->getOperand(0)), 2640 getSCEV(U->getOperand(1))); 2641 2642 // If the RHS of xor is -1, then this is a not operation. 2643 if (CI->isAllOnesValue()) 2644 return getNotSCEV(getSCEV(U->getOperand(0))); 2645 2646 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 2647 // This is a variant of the check for xor with -1, and it handles 2648 // the case where instcombine has trimmed non-demanded bits out 2649 // of an xor with -1. 2650 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 2651 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 2652 if (BO->getOpcode() == Instruction::And && 2653 LCI->getValue() == CI->getValue()) 2654 if (const SCEVZeroExtendExpr *Z = 2655 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 2656 const Type *UTy = U->getType(); 2657 const SCEV *Z0 = Z->getOperand(); 2658 const Type *Z0Ty = Z0->getType(); 2659 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 2660 2661 // If C is a low-bits mask, the zero extend is zerving to 2662 // mask off the high bits. Complement the operand and 2663 // re-apply the zext. 2664 if (APIntOps::isMask(Z0TySize, CI->getValue())) 2665 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 2666 2667 // If C is a single bit, it may be in the sign-bit position 2668 // before the zero-extend. In this case, represent the xor 2669 // using an add, which is equivalent, and re-apply the zext. 2670 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 2671 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 2672 Trunc.isSignBit()) 2673 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 2674 UTy); 2675 } 2676 } 2677 break; 2678 2679 case Instruction::Shl: 2680 // Turn shift left of a constant amount into a multiply. 2681 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2682 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2683 Constant *X = ConstantInt::get( 2684 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2685 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2686 } 2687 break; 2688 2689 case Instruction::LShr: 2690 // Turn logical shift right of a constant into a unsigned divide. 2691 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 2692 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 2693 Constant *X = ConstantInt::get( 2694 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 2695 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 2696 } 2697 break; 2698 2699 case Instruction::AShr: 2700 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 2701 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 2702 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 2703 if (L->getOpcode() == Instruction::Shl && 2704 L->getOperand(1) == U->getOperand(1)) { 2705 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2706 uint64_t Amt = BitWidth - CI->getZExtValue(); 2707 if (Amt == BitWidth) 2708 return getSCEV(L->getOperand(0)); // shift by zero --> noop 2709 if (Amt > BitWidth) 2710 return getIntegerSCEV(0, U->getType()); // value is undefined 2711 return 2712 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 2713 IntegerType::get(Amt)), 2714 U->getType()); 2715 } 2716 break; 2717 2718 case Instruction::Trunc: 2719 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 2720 2721 case Instruction::ZExt: 2722 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2723 2724 case Instruction::SExt: 2725 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 2726 2727 case Instruction::BitCast: 2728 // BitCasts are no-op casts so we just eliminate the cast. 2729 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 2730 return getSCEV(U->getOperand(0)); 2731 break; 2732 2733 case Instruction::IntToPtr: 2734 if (!TD) break; // Without TD we can't analyze pointers. 2735 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2736 TD->getIntPtrType()); 2737 2738 case Instruction::PtrToInt: 2739 if (!TD) break; // Without TD we can't analyze pointers. 2740 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)), 2741 U->getType()); 2742 2743 case Instruction::GetElementPtr: 2744 if (!TD) break; // Without TD we can't analyze pointers. 2745 return createNodeForGEP(U); 2746 2747 case Instruction::PHI: 2748 return createNodeForPHI(cast<PHINode>(U)); 2749 2750 case Instruction::Select: 2751 // This could be a smax or umax that was lowered earlier. 2752 // Try to recover it. 2753 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 2754 Value *LHS = ICI->getOperand(0); 2755 Value *RHS = ICI->getOperand(1); 2756 switch (ICI->getPredicate()) { 2757 case ICmpInst::ICMP_SLT: 2758 case ICmpInst::ICMP_SLE: 2759 std::swap(LHS, RHS); 2760 // fall through 2761 case ICmpInst::ICMP_SGT: 2762 case ICmpInst::ICMP_SGE: 2763 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2764 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2765 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2766 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 2767 break; 2768 case ICmpInst::ICMP_ULT: 2769 case ICmpInst::ICMP_ULE: 2770 std::swap(LHS, RHS); 2771 // fall through 2772 case ICmpInst::ICMP_UGT: 2773 case ICmpInst::ICMP_UGE: 2774 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 2775 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 2776 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 2777 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 2778 break; 2779 case ICmpInst::ICMP_NE: 2780 // n != 0 ? n : 1 -> umax(n, 1) 2781 if (LHS == U->getOperand(1) && 2782 isa<ConstantInt>(U->getOperand(2)) && 2783 cast<ConstantInt>(U->getOperand(2))->isOne() && 2784 isa<ConstantInt>(RHS) && 2785 cast<ConstantInt>(RHS)->isZero()) 2786 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 2787 break; 2788 case ICmpInst::ICMP_EQ: 2789 // n == 0 ? 1 : n -> umax(n, 1) 2790 if (LHS == U->getOperand(2) && 2791 isa<ConstantInt>(U->getOperand(1)) && 2792 cast<ConstantInt>(U->getOperand(1))->isOne() && 2793 isa<ConstantInt>(RHS) && 2794 cast<ConstantInt>(RHS)->isZero()) 2795 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 2796 break; 2797 default: 2798 break; 2799 } 2800 } 2801 2802 default: // We cannot analyze this expression. 2803 break; 2804 } 2805 2806 return getUnknown(V); 2807} 2808 2809 2810 2811//===----------------------------------------------------------------------===// 2812// Iteration Count Computation Code 2813// 2814 2815/// getBackedgeTakenCount - If the specified loop has a predictable 2816/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 2817/// object. The backedge-taken count is the number of times the loop header 2818/// will be branched to from within the loop. This is one less than the 2819/// trip count of the loop, since it doesn't count the first iteration, 2820/// when the header is branched to from outside the loop. 2821/// 2822/// Note that it is not valid to call this method on a loop without a 2823/// loop-invariant backedge-taken count (see 2824/// hasLoopInvariantBackedgeTakenCount). 2825/// 2826const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 2827 return getBackedgeTakenInfo(L).Exact; 2828} 2829 2830/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 2831/// return the least SCEV value that is known never to be less than the 2832/// actual backedge taken count. 2833const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 2834 return getBackedgeTakenInfo(L).Max; 2835} 2836 2837/// PushLoopPHIs - Push PHI nodes in the header of the given loop 2838/// onto the given Worklist. 2839static void 2840PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 2841 BasicBlock *Header = L->getHeader(); 2842 2843 // Push all Loop-header PHIs onto the Worklist stack. 2844 for (BasicBlock::iterator I = Header->begin(); 2845 PHINode *PN = dyn_cast<PHINode>(I); ++I) 2846 Worklist.push_back(PN); 2847} 2848 2849/// PushDefUseChildren - Push users of the given Instruction 2850/// onto the given Worklist. 2851static void 2852PushDefUseChildren(Instruction *I, 2853 SmallVectorImpl<Instruction *> &Worklist) { 2854 // Push the def-use children onto the Worklist stack. 2855 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2856 UI != UE; ++UI) 2857 Worklist.push_back(cast<Instruction>(UI)); 2858} 2859 2860const ScalarEvolution::BackedgeTakenInfo & 2861ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 2862 // Initially insert a CouldNotCompute for this loop. If the insertion 2863 // succeeds, procede to actually compute a backedge-taken count and 2864 // update the value. The temporary CouldNotCompute value tells SCEV 2865 // code elsewhere that it shouldn't attempt to request a new 2866 // backedge-taken count, which could result in infinite recursion. 2867 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 2868 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 2869 if (Pair.second) { 2870 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 2871 if (ItCount.Exact != getCouldNotCompute()) { 2872 assert(ItCount.Exact->isLoopInvariant(L) && 2873 ItCount.Max->isLoopInvariant(L) && 2874 "Computed trip count isn't loop invariant for loop!"); 2875 ++NumTripCountsComputed; 2876 2877 // Update the value in the map. 2878 Pair.first->second = ItCount; 2879 } else { 2880 if (ItCount.Max != getCouldNotCompute()) 2881 // Update the value in the map. 2882 Pair.first->second = ItCount; 2883 if (isa<PHINode>(L->getHeader()->begin())) 2884 // Only count loops that have phi nodes as not being computable. 2885 ++NumTripCountsNotComputed; 2886 } 2887 2888 // Now that we know more about the trip count for this loop, forget any 2889 // existing SCEV values for PHI nodes in this loop since they are only 2890 // conservative estimates made without the benefit of trip count 2891 // information. This is similar to the code in 2892 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 2893 // nodes specially. 2894 if (ItCount.hasAnyInfo()) { 2895 SmallVector<Instruction *, 16> Worklist; 2896 PushLoopPHIs(L, Worklist); 2897 2898 SmallPtrSet<Instruction *, 8> Visited; 2899 while (!Worklist.empty()) { 2900 Instruction *I = Worklist.pop_back_val(); 2901 if (!Visited.insert(I)) continue; 2902 2903 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2904 Scalars.find(static_cast<Value *>(I)); 2905 if (It != Scalars.end()) { 2906 // SCEVUnknown for a PHI either means that it has an unrecognized 2907 // structure, or it's a PHI that's in the progress of being computed 2908 // by createNodeForPHI. In the former case, additional loop trip count 2909 // information isn't going to change anything. In the later case, 2910 // createNodeForPHI will perform the necessary updates on its own when 2911 // it gets to that point. 2912 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) 2913 Scalars.erase(It); 2914 ValuesAtScopes.erase(I); 2915 if (PHINode *PN = dyn_cast<PHINode>(I)) 2916 ConstantEvolutionLoopExitValue.erase(PN); 2917 } 2918 2919 PushDefUseChildren(I, Worklist); 2920 } 2921 } 2922 } 2923 return Pair.first->second; 2924} 2925 2926/// forgetLoopBackedgeTakenCount - This method should be called by the 2927/// client when it has changed a loop in a way that may effect 2928/// ScalarEvolution's ability to compute a trip count, or if the loop 2929/// is deleted. 2930void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 2931 BackedgeTakenCounts.erase(L); 2932 2933 SmallVector<Instruction *, 16> Worklist; 2934 PushLoopPHIs(L, Worklist); 2935 2936 SmallPtrSet<Instruction *, 8> Visited; 2937 while (!Worklist.empty()) { 2938 Instruction *I = Worklist.pop_back_val(); 2939 if (!Visited.insert(I)) continue; 2940 2941 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2942 Scalars.find(static_cast<Value *>(I)); 2943 if (It != Scalars.end()) { 2944 Scalars.erase(It); 2945 ValuesAtScopes.erase(I); 2946 if (PHINode *PN = dyn_cast<PHINode>(I)) 2947 ConstantEvolutionLoopExitValue.erase(PN); 2948 } 2949 2950 PushDefUseChildren(I, Worklist); 2951 } 2952} 2953 2954/// ComputeBackedgeTakenCount - Compute the number of times the backedge 2955/// of the specified loop will execute. 2956ScalarEvolution::BackedgeTakenInfo 2957ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 2958 SmallVector<BasicBlock*, 8> ExitingBlocks; 2959 L->getExitingBlocks(ExitingBlocks); 2960 2961 // Examine all exits and pick the most conservative values. 2962 const SCEV *BECount = getCouldNotCompute(); 2963 const SCEV *MaxBECount = getCouldNotCompute(); 2964 bool CouldNotComputeBECount = false; 2965 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 2966 BackedgeTakenInfo NewBTI = 2967 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 2968 2969 if (NewBTI.Exact == getCouldNotCompute()) { 2970 // We couldn't compute an exact value for this exit, so 2971 // we won't be able to compute an exact value for the loop. 2972 CouldNotComputeBECount = true; 2973 BECount = getCouldNotCompute(); 2974 } else if (!CouldNotComputeBECount) { 2975 if (BECount == getCouldNotCompute()) 2976 BECount = NewBTI.Exact; 2977 else 2978 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 2979 } 2980 if (MaxBECount == getCouldNotCompute()) 2981 MaxBECount = NewBTI.Max; 2982 else if (NewBTI.Max != getCouldNotCompute()) 2983 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 2984 } 2985 2986 return BackedgeTakenInfo(BECount, MaxBECount); 2987} 2988 2989/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 2990/// of the specified loop will execute if it exits via the specified block. 2991ScalarEvolution::BackedgeTakenInfo 2992ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 2993 BasicBlock *ExitingBlock) { 2994 2995 // Okay, we've chosen an exiting block. See what condition causes us to 2996 // exit at this block. 2997 // 2998 // FIXME: we should be able to handle switch instructions (with a single exit) 2999 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3000 if (ExitBr == 0) return getCouldNotCompute(); 3001 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3002 3003 // At this point, we know we have a conditional branch that determines whether 3004 // the loop is exited. However, we don't know if the branch is executed each 3005 // time through the loop. If not, then the execution count of the branch will 3006 // not be equal to the trip count of the loop. 3007 // 3008 // Currently we check for this by checking to see if the Exit branch goes to 3009 // the loop header. If so, we know it will always execute the same number of 3010 // times as the loop. We also handle the case where the exit block *is* the 3011 // loop header. This is common for un-rotated loops. 3012 // 3013 // If both of those tests fail, walk up the unique predecessor chain to the 3014 // header, stopping if there is an edge that doesn't exit the loop. If the 3015 // header is reached, the execution count of the branch will be equal to the 3016 // trip count of the loop. 3017 // 3018 // More extensive analysis could be done to handle more cases here. 3019 // 3020 if (ExitBr->getSuccessor(0) != L->getHeader() && 3021 ExitBr->getSuccessor(1) != L->getHeader() && 3022 ExitBr->getParent() != L->getHeader()) { 3023 // The simple checks failed, try climbing the unique predecessor chain 3024 // up to the header. 3025 bool Ok = false; 3026 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3027 BasicBlock *Pred = BB->getUniquePredecessor(); 3028 if (!Pred) 3029 return getCouldNotCompute(); 3030 TerminatorInst *PredTerm = Pred->getTerminator(); 3031 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3032 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3033 if (PredSucc == BB) 3034 continue; 3035 // If the predecessor has a successor that isn't BB and isn't 3036 // outside the loop, assume the worst. 3037 if (L->contains(PredSucc)) 3038 return getCouldNotCompute(); 3039 } 3040 if (Pred == L->getHeader()) { 3041 Ok = true; 3042 break; 3043 } 3044 BB = Pred; 3045 } 3046 if (!Ok) 3047 return getCouldNotCompute(); 3048 } 3049 3050 // Procede to the next level to examine the exit condition expression. 3051 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3052 ExitBr->getSuccessor(0), 3053 ExitBr->getSuccessor(1)); 3054} 3055 3056/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3057/// backedge of the specified loop will execute if its exit condition 3058/// were a conditional branch of ExitCond, TBB, and FBB. 3059ScalarEvolution::BackedgeTakenInfo 3060ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3061 Value *ExitCond, 3062 BasicBlock *TBB, 3063 BasicBlock *FBB) { 3064 // Check if the controlling expression for this loop is an And or Or. 3065 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3066 if (BO->getOpcode() == Instruction::And) { 3067 // Recurse on the operands of the and. 3068 BackedgeTakenInfo BTI0 = 3069 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3070 BackedgeTakenInfo BTI1 = 3071 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3072 const SCEV *BECount = getCouldNotCompute(); 3073 const SCEV *MaxBECount = getCouldNotCompute(); 3074 if (L->contains(TBB)) { 3075 // Both conditions must be true for the loop to continue executing. 3076 // Choose the less conservative count. 3077 if (BTI0.Exact == getCouldNotCompute() || 3078 BTI1.Exact == getCouldNotCompute()) 3079 BECount = getCouldNotCompute(); 3080 else 3081 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3082 if (BTI0.Max == getCouldNotCompute()) 3083 MaxBECount = BTI1.Max; 3084 else if (BTI1.Max == getCouldNotCompute()) 3085 MaxBECount = BTI0.Max; 3086 else 3087 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3088 } else { 3089 // Both conditions must be true for the loop to exit. 3090 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3091 if (BTI0.Exact != getCouldNotCompute() && 3092 BTI1.Exact != getCouldNotCompute()) 3093 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3094 if (BTI0.Max != getCouldNotCompute() && 3095 BTI1.Max != getCouldNotCompute()) 3096 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3097 } 3098 3099 return BackedgeTakenInfo(BECount, MaxBECount); 3100 } 3101 if (BO->getOpcode() == Instruction::Or) { 3102 // Recurse on the operands of the or. 3103 BackedgeTakenInfo BTI0 = 3104 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3105 BackedgeTakenInfo BTI1 = 3106 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3107 const SCEV *BECount = getCouldNotCompute(); 3108 const SCEV *MaxBECount = getCouldNotCompute(); 3109 if (L->contains(FBB)) { 3110 // Both conditions must be false for the loop to continue executing. 3111 // Choose the less conservative count. 3112 if (BTI0.Exact == getCouldNotCompute() || 3113 BTI1.Exact == getCouldNotCompute()) 3114 BECount = getCouldNotCompute(); 3115 else 3116 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3117 if (BTI0.Max == getCouldNotCompute()) 3118 MaxBECount = BTI1.Max; 3119 else if (BTI1.Max == getCouldNotCompute()) 3120 MaxBECount = BTI0.Max; 3121 else 3122 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3123 } else { 3124 // Both conditions must be false for the loop to exit. 3125 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3126 if (BTI0.Exact != getCouldNotCompute() && 3127 BTI1.Exact != getCouldNotCompute()) 3128 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3129 if (BTI0.Max != getCouldNotCompute() && 3130 BTI1.Max != getCouldNotCompute()) 3131 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3132 } 3133 3134 return BackedgeTakenInfo(BECount, MaxBECount); 3135 } 3136 } 3137 3138 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3139 // Procede to the next level to examine the icmp. 3140 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3141 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3142 3143 // If it's not an integer or pointer comparison then compute it the hard way. 3144 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3145} 3146 3147/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3148/// backedge of the specified loop will execute if its exit condition 3149/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3150ScalarEvolution::BackedgeTakenInfo 3151ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3152 ICmpInst *ExitCond, 3153 BasicBlock *TBB, 3154 BasicBlock *FBB) { 3155 3156 // If the condition was exit on true, convert the condition to exit on false 3157 ICmpInst::Predicate Cond; 3158 if (!L->contains(FBB)) 3159 Cond = ExitCond->getPredicate(); 3160 else 3161 Cond = ExitCond->getInversePredicate(); 3162 3163 // Handle common loops like: for (X = "string"; *X; ++X) 3164 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3165 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3166 const SCEV *ItCnt = 3167 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3168 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3169 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3170 return BackedgeTakenInfo(ItCnt, 3171 isa<SCEVConstant>(ItCnt) ? ItCnt : 3172 getConstant(APInt::getMaxValue(BitWidth)-1)); 3173 } 3174 } 3175 3176 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3177 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3178 3179 // Try to evaluate any dependencies out of the loop. 3180 LHS = getSCEVAtScope(LHS, L); 3181 RHS = getSCEVAtScope(RHS, L); 3182 3183 // At this point, we would like to compute how many iterations of the 3184 // loop the predicate will return true for these inputs. 3185 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3186 // If there is a loop-invariant, force it into the RHS. 3187 std::swap(LHS, RHS); 3188 Cond = ICmpInst::getSwappedPredicate(Cond); 3189 } 3190 3191 // If we have a comparison of a chrec against a constant, try to use value 3192 // ranges to answer this query. 3193 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3194 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3195 if (AddRec->getLoop() == L) { 3196 // Form the constant range. 3197 ConstantRange CompRange( 3198 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3199 3200 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3201 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3202 } 3203 3204 switch (Cond) { 3205 case ICmpInst::ICMP_NE: { // while (X != Y) 3206 // Convert to: while (X-Y != 0) 3207 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3208 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3209 break; 3210 } 3211 case ICmpInst::ICMP_EQ: { 3212 // Convert to: while (X-Y == 0) // while (X == Y) 3213 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3214 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3215 break; 3216 } 3217 case ICmpInst::ICMP_SLT: { 3218 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3219 if (BTI.hasAnyInfo()) return BTI; 3220 break; 3221 } 3222 case ICmpInst::ICMP_SGT: { 3223 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3224 getNotSCEV(RHS), L, true); 3225 if (BTI.hasAnyInfo()) return BTI; 3226 break; 3227 } 3228 case ICmpInst::ICMP_ULT: { 3229 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3230 if (BTI.hasAnyInfo()) return BTI; 3231 break; 3232 } 3233 case ICmpInst::ICMP_UGT: { 3234 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3235 getNotSCEV(RHS), L, false); 3236 if (BTI.hasAnyInfo()) return BTI; 3237 break; 3238 } 3239 default: 3240#if 0 3241 errs() << "ComputeBackedgeTakenCount "; 3242 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3243 errs() << "[unsigned] "; 3244 errs() << *LHS << " " 3245 << Instruction::getOpcodeName(Instruction::ICmp) 3246 << " " << *RHS << "\n"; 3247#endif 3248 break; 3249 } 3250 return 3251 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3252} 3253 3254static ConstantInt * 3255EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3256 ScalarEvolution &SE) { 3257 const SCEV *InVal = SE.getConstant(C); 3258 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3259 assert(isa<SCEVConstant>(Val) && 3260 "Evaluation of SCEV at constant didn't fold correctly?"); 3261 return cast<SCEVConstant>(Val)->getValue(); 3262} 3263 3264/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3265/// and a GEP expression (missing the pointer index) indexing into it, return 3266/// the addressed element of the initializer or null if the index expression is 3267/// invalid. 3268static Constant * 3269GetAddressedElementFromGlobal(LLVMContext *Context, GlobalVariable *GV, 3270 const std::vector<ConstantInt*> &Indices) { 3271 Constant *Init = GV->getInitializer(); 3272 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3273 uint64_t Idx = Indices[i]->getZExtValue(); 3274 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3275 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3276 Init = cast<Constant>(CS->getOperand(Idx)); 3277 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3278 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3279 Init = cast<Constant>(CA->getOperand(Idx)); 3280 } else if (isa<ConstantAggregateZero>(Init)) { 3281 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3282 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3283 Init = Context->getNullValue(STy->getElementType(Idx)); 3284 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3285 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3286 Init = Context->getNullValue(ATy->getElementType()); 3287 } else { 3288 LLVM_UNREACHABLE("Unknown constant aggregate type!"); 3289 } 3290 return 0; 3291 } else { 3292 return 0; // Unknown initializer type 3293 } 3294 } 3295 return Init; 3296} 3297 3298/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3299/// 'icmp op load X, cst', try to see if we can compute the backedge 3300/// execution count. 3301const SCEV * 3302ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3303 LoadInst *LI, 3304 Constant *RHS, 3305 const Loop *L, 3306 ICmpInst::Predicate predicate) { 3307 if (LI->isVolatile()) return getCouldNotCompute(); 3308 3309 // Check to see if the loaded pointer is a getelementptr of a global. 3310 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3311 if (!GEP) return getCouldNotCompute(); 3312 3313 // Make sure that it is really a constant global we are gepping, with an 3314 // initializer, and make sure the first IDX is really 0. 3315 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3316 if (!GV || !GV->isConstant() || !GV->hasInitializer() || 3317 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3318 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3319 return getCouldNotCompute(); 3320 3321 // Okay, we allow one non-constant index into the GEP instruction. 3322 Value *VarIdx = 0; 3323 std::vector<ConstantInt*> Indexes; 3324 unsigned VarIdxNum = 0; 3325 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3326 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3327 Indexes.push_back(CI); 3328 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3329 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3330 VarIdx = GEP->getOperand(i); 3331 VarIdxNum = i-2; 3332 Indexes.push_back(0); 3333 } 3334 3335 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3336 // Check to see if X is a loop variant variable value now. 3337 const SCEV *Idx = getSCEV(VarIdx); 3338 Idx = getSCEVAtScope(Idx, L); 3339 3340 // We can only recognize very limited forms of loop index expressions, in 3341 // particular, only affine AddRec's like {C1,+,C2}. 3342 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3343 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3344 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3345 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3346 return getCouldNotCompute(); 3347 3348 unsigned MaxSteps = MaxBruteForceIterations; 3349 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3350 ConstantInt *ItCst = 3351 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum); 3352 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3353 3354 // Form the GEP offset. 3355 Indexes[VarIdxNum] = Val; 3356 3357 Constant *Result = GetAddressedElementFromGlobal(Context, GV, Indexes); 3358 if (Result == 0) break; // Cannot compute! 3359 3360 // Evaluate the condition for this iteration. 3361 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3362 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3363 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3364#if 0 3365 errs() << "\n***\n*** Computed loop count " << *ItCst 3366 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3367 << "***\n"; 3368#endif 3369 ++NumArrayLenItCounts; 3370 return getConstant(ItCst); // Found terminating iteration! 3371 } 3372 } 3373 return getCouldNotCompute(); 3374} 3375 3376 3377/// CanConstantFold - Return true if we can constant fold an instruction of the 3378/// specified type, assuming that all operands were constants. 3379static bool CanConstantFold(const Instruction *I) { 3380 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3381 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3382 return true; 3383 3384 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3385 if (const Function *F = CI->getCalledFunction()) 3386 return canConstantFoldCallTo(F); 3387 return false; 3388} 3389 3390/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3391/// in the loop that V is derived from. We allow arbitrary operations along the 3392/// way, but the operands of an operation must either be constants or a value 3393/// derived from a constant PHI. If this expression does not fit with these 3394/// constraints, return null. 3395static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3396 // If this is not an instruction, or if this is an instruction outside of the 3397 // loop, it can't be derived from a loop PHI. 3398 Instruction *I = dyn_cast<Instruction>(V); 3399 if (I == 0 || !L->contains(I->getParent())) return 0; 3400 3401 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3402 if (L->getHeader() == I->getParent()) 3403 return PN; 3404 else 3405 // We don't currently keep track of the control flow needed to evaluate 3406 // PHIs, so we cannot handle PHIs inside of loops. 3407 return 0; 3408 } 3409 3410 // If we won't be able to constant fold this expression even if the operands 3411 // are constants, return early. 3412 if (!CanConstantFold(I)) return 0; 3413 3414 // Otherwise, we can evaluate this instruction if all of its operands are 3415 // constant or derived from a PHI node themselves. 3416 PHINode *PHI = 0; 3417 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3418 if (!(isa<Constant>(I->getOperand(Op)) || 3419 isa<GlobalValue>(I->getOperand(Op)))) { 3420 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3421 if (P == 0) return 0; // Not evolving from PHI 3422 if (PHI == 0) 3423 PHI = P; 3424 else if (PHI != P) 3425 return 0; // Evolving from multiple different PHIs. 3426 } 3427 3428 // This is a expression evolving from a constant PHI! 3429 return PHI; 3430} 3431 3432/// EvaluateExpression - Given an expression that passes the 3433/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3434/// in the loop has the value PHIVal. If we can't fold this expression for some 3435/// reason, return null. 3436static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3437 if (isa<PHINode>(V)) return PHIVal; 3438 if (Constant *C = dyn_cast<Constant>(V)) return C; 3439 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3440 Instruction *I = cast<Instruction>(V); 3441 LLVMContext *Context = I->getParent()->getContext(); 3442 3443 std::vector<Constant*> Operands; 3444 Operands.resize(I->getNumOperands()); 3445 3446 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3447 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3448 if (Operands[i] == 0) return 0; 3449 } 3450 3451 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3452 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3453 &Operands[0], Operands.size(), 3454 Context); 3455 else 3456 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3457 &Operands[0], Operands.size(), 3458 Context); 3459} 3460 3461/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3462/// in the header of its containing loop, we know the loop executes a 3463/// constant number of times, and the PHI node is just a recurrence 3464/// involving constants, fold it. 3465Constant * 3466ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3467 const APInt& BEs, 3468 const Loop *L) { 3469 std::map<PHINode*, Constant*>::iterator I = 3470 ConstantEvolutionLoopExitValue.find(PN); 3471 if (I != ConstantEvolutionLoopExitValue.end()) 3472 return I->second; 3473 3474 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3475 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3476 3477 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3478 3479 // Since the loop is canonicalized, the PHI node must have two entries. One 3480 // entry must be a constant (coming in from outside of the loop), and the 3481 // second must be derived from the same PHI. 3482 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3483 Constant *StartCST = 3484 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3485 if (StartCST == 0) 3486 return RetVal = 0; // Must be a constant. 3487 3488 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3489 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3490 if (PN2 != PN) 3491 return RetVal = 0; // Not derived from same PHI. 3492 3493 // Execute the loop symbolically to determine the exit value. 3494 if (BEs.getActiveBits() >= 32) 3495 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3496 3497 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3498 unsigned IterationNum = 0; 3499 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3500 if (IterationNum == NumIterations) 3501 return RetVal = PHIVal; // Got exit value! 3502 3503 // Compute the value of the PHI node for the next iteration. 3504 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3505 if (NextPHI == PHIVal) 3506 return RetVal = NextPHI; // Stopped evolving! 3507 if (NextPHI == 0) 3508 return 0; // Couldn't evaluate! 3509 PHIVal = NextPHI; 3510 } 3511} 3512 3513/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a 3514/// constant number of times (the condition evolves only from constants), 3515/// try to evaluate a few iterations of the loop until we get the exit 3516/// condition gets a value of ExitWhen (true or false). If we cannot 3517/// evaluate the trip count of the loop, return getCouldNotCompute(). 3518const SCEV * 3519ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3520 Value *Cond, 3521 bool ExitWhen) { 3522 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3523 if (PN == 0) return getCouldNotCompute(); 3524 3525 // Since the loop is canonicalized, the PHI node must have two entries. One 3526 // entry must be a constant (coming in from outside of the loop), and the 3527 // second must be derived from the same PHI. 3528 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3529 Constant *StartCST = 3530 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3531 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3532 3533 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3534 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3535 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3536 3537 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3538 // the loop symbolically to determine when the condition gets a value of 3539 // "ExitWhen". 3540 unsigned IterationNum = 0; 3541 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3542 for (Constant *PHIVal = StartCST; 3543 IterationNum != MaxIterations; ++IterationNum) { 3544 ConstantInt *CondVal = 3545 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3546 3547 // Couldn't symbolically evaluate. 3548 if (!CondVal) return getCouldNotCompute(); 3549 3550 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3551 ++NumBruteForceTripCountsComputed; 3552 return getConstant(Type::Int32Ty, IterationNum); 3553 } 3554 3555 // Compute the value of the PHI node for the next iteration. 3556 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3557 if (NextPHI == 0 || NextPHI == PHIVal) 3558 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3559 PHIVal = NextPHI; 3560 } 3561 3562 // Too many iterations were needed to evaluate. 3563 return getCouldNotCompute(); 3564} 3565 3566/// getSCEVAtScope - Return a SCEV expression handle for the specified value 3567/// at the specified scope in the program. The L value specifies a loop 3568/// nest to evaluate the expression at, where null is the top-level or a 3569/// specified loop is immediately inside of the loop. 3570/// 3571/// This method can be used to compute the exit value for a variable defined 3572/// in a loop by querying what the value will hold in the parent loop. 3573/// 3574/// In the case that a relevant loop exit value cannot be computed, the 3575/// original value V is returned. 3576const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3577 // FIXME: this should be turned into a virtual method on SCEV! 3578 3579 if (isa<SCEVConstant>(V)) return V; 3580 3581 // If this instruction is evolved from a constant-evolving PHI, compute the 3582 // exit value from the loop without using SCEVs. 3583 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3584 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3585 const Loop *LI = (*this->LI)[I->getParent()]; 3586 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3587 if (PHINode *PN = dyn_cast<PHINode>(I)) 3588 if (PN->getParent() == LI->getHeader()) { 3589 // Okay, there is no closed form solution for the PHI node. Check 3590 // to see if the loop that contains it has a known backedge-taken 3591 // count. If so, we may be able to force computation of the exit 3592 // value. 3593 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3594 if (const SCEVConstant *BTCC = 3595 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3596 // Okay, we know how many times the containing loop executes. If 3597 // this is a constant evolving PHI node, get the final value at 3598 // the specified iteration number. 3599 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3600 BTCC->getValue()->getValue(), 3601 LI); 3602 if (RV) return getSCEV(RV); 3603 } 3604 } 3605 3606 // Okay, this is an expression that we cannot symbolically evaluate 3607 // into a SCEV. Check to see if it's possible to symbolically evaluate 3608 // the arguments into constants, and if so, try to constant propagate the 3609 // result. This is particularly useful for computing loop exit values. 3610 if (CanConstantFold(I)) { 3611 // Check to see if we've folded this instruction at this loop before. 3612 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I]; 3613 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair = 3614 Values.insert(std::make_pair(L, static_cast<Constant *>(0))); 3615 if (!Pair.second) 3616 return Pair.first->second ? &*getSCEV(Pair.first->second) : V; 3617 3618 std::vector<Constant*> Operands; 3619 Operands.reserve(I->getNumOperands()); 3620 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3621 Value *Op = I->getOperand(i); 3622 if (Constant *C = dyn_cast<Constant>(Op)) { 3623 Operands.push_back(C); 3624 } else { 3625 // If any of the operands is non-constant and if they are 3626 // non-integer and non-pointer, don't even try to analyze them 3627 // with scev techniques. 3628 if (!isSCEVable(Op->getType())) 3629 return V; 3630 3631 const SCEV *OpV = getSCEVAtScope(getSCEV(Op), L); 3632 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 3633 Constant *C = SC->getValue(); 3634 if (C->getType() != Op->getType()) 3635 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3636 Op->getType(), 3637 false), 3638 C, Op->getType()); 3639 Operands.push_back(C); 3640 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 3641 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 3642 if (C->getType() != Op->getType()) 3643 C = 3644 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 3645 Op->getType(), 3646 false), 3647 C, Op->getType()); 3648 Operands.push_back(C); 3649 } else 3650 return V; 3651 } else { 3652 return V; 3653 } 3654 } 3655 } 3656 3657 Constant *C; 3658 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3659 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 3660 &Operands[0], Operands.size(), 3661 Context); 3662 else 3663 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3664 &Operands[0], Operands.size(), Context); 3665 Pair.first->second = C; 3666 return getSCEV(C); 3667 } 3668 } 3669 3670 // This is some other type of SCEVUnknown, just return it. 3671 return V; 3672 } 3673 3674 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 3675 // Avoid performing the look-up in the common case where the specified 3676 // expression has no loop-variant portions. 3677 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 3678 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3679 if (OpAtScope != Comm->getOperand(i)) { 3680 // Okay, at least one of these operands is loop variant but might be 3681 // foldable. Build a new instance of the folded commutative expression. 3682 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 3683 Comm->op_begin()+i); 3684 NewOps.push_back(OpAtScope); 3685 3686 for (++i; i != e; ++i) { 3687 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 3688 NewOps.push_back(OpAtScope); 3689 } 3690 if (isa<SCEVAddExpr>(Comm)) 3691 return getAddExpr(NewOps); 3692 if (isa<SCEVMulExpr>(Comm)) 3693 return getMulExpr(NewOps); 3694 if (isa<SCEVSMaxExpr>(Comm)) 3695 return getSMaxExpr(NewOps); 3696 if (isa<SCEVUMaxExpr>(Comm)) 3697 return getUMaxExpr(NewOps); 3698 LLVM_UNREACHABLE("Unknown commutative SCEV type!"); 3699 } 3700 } 3701 // If we got here, all operands are loop invariant. 3702 return Comm; 3703 } 3704 3705 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 3706 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 3707 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 3708 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 3709 return Div; // must be loop invariant 3710 return getUDivExpr(LHS, RHS); 3711 } 3712 3713 // If this is a loop recurrence for a loop that does not contain L, then we 3714 // are dealing with the final value computed by the loop. 3715 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 3716 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 3717 // To evaluate this recurrence, we need to know how many times the AddRec 3718 // loop iterates. Compute this now. 3719 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 3720 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 3721 3722 // Then, evaluate the AddRec. 3723 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 3724 } 3725 return AddRec; 3726 } 3727 3728 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 3729 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3730 if (Op == Cast->getOperand()) 3731 return Cast; // must be loop invariant 3732 return getZeroExtendExpr(Op, Cast->getType()); 3733 } 3734 3735 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 3736 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3737 if (Op == Cast->getOperand()) 3738 return Cast; // must be loop invariant 3739 return getSignExtendExpr(Op, Cast->getType()); 3740 } 3741 3742 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 3743 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 3744 if (Op == Cast->getOperand()) 3745 return Cast; // must be loop invariant 3746 return getTruncateExpr(Op, Cast->getType()); 3747 } 3748 3749 LLVM_UNREACHABLE("Unknown SCEV type!"); 3750 return 0; 3751} 3752 3753/// getSCEVAtScope - This is a convenience function which does 3754/// getSCEVAtScope(getSCEV(V), L). 3755const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 3756 return getSCEVAtScope(getSCEV(V), L); 3757} 3758 3759/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 3760/// following equation: 3761/// 3762/// A * X = B (mod N) 3763/// 3764/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 3765/// A and B isn't important. 3766/// 3767/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 3768static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 3769 ScalarEvolution &SE) { 3770 uint32_t BW = A.getBitWidth(); 3771 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 3772 assert(A != 0 && "A must be non-zero."); 3773 3774 // 1. D = gcd(A, N) 3775 // 3776 // The gcd of A and N may have only one prime factor: 2. The number of 3777 // trailing zeros in A is its multiplicity 3778 uint32_t Mult2 = A.countTrailingZeros(); 3779 // D = 2^Mult2 3780 3781 // 2. Check if B is divisible by D. 3782 // 3783 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 3784 // is not less than multiplicity of this prime factor for D. 3785 if (B.countTrailingZeros() < Mult2) 3786 return SE.getCouldNotCompute(); 3787 3788 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 3789 // modulo (N / D). 3790 // 3791 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 3792 // bit width during computations. 3793 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 3794 APInt Mod(BW + 1, 0); 3795 Mod.set(BW - Mult2); // Mod = N / D 3796 APInt I = AD.multiplicativeInverse(Mod); 3797 3798 // 4. Compute the minimum unsigned root of the equation: 3799 // I * (B / D) mod (N / D) 3800 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 3801 3802 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 3803 // bits. 3804 return SE.getConstant(Result.trunc(BW)); 3805} 3806 3807/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 3808/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 3809/// might be the same) or two SCEVCouldNotCompute objects. 3810/// 3811static std::pair<const SCEV *,const SCEV *> 3812SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 3813 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 3814 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 3815 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 3816 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 3817 3818 // We currently can only solve this if the coefficients are constants. 3819 if (!LC || !MC || !NC) { 3820 const SCEV *CNC = SE.getCouldNotCompute(); 3821 return std::make_pair(CNC, CNC); 3822 } 3823 3824 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 3825 const APInt &L = LC->getValue()->getValue(); 3826 const APInt &M = MC->getValue()->getValue(); 3827 const APInt &N = NC->getValue()->getValue(); 3828 APInt Two(BitWidth, 2); 3829 APInt Four(BitWidth, 4); 3830 3831 { 3832 using namespace APIntOps; 3833 const APInt& C = L; 3834 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 3835 // The B coefficient is M-N/2 3836 APInt B(M); 3837 B -= sdiv(N,Two); 3838 3839 // The A coefficient is N/2 3840 APInt A(N.sdiv(Two)); 3841 3842 // Compute the B^2-4ac term. 3843 APInt SqrtTerm(B); 3844 SqrtTerm *= B; 3845 SqrtTerm -= Four * (A * C); 3846 3847 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 3848 // integer value or else APInt::sqrt() will assert. 3849 APInt SqrtVal(SqrtTerm.sqrt()); 3850 3851 // Compute the two solutions for the quadratic formula. 3852 // The divisions must be performed as signed divisions. 3853 APInt NegB(-B); 3854 APInt TwoA( A << 1 ); 3855 if (TwoA.isMinValue()) { 3856 const SCEV *CNC = SE.getCouldNotCompute(); 3857 return std::make_pair(CNC, CNC); 3858 } 3859 3860 LLVMContext *Context = SE.getContext(); 3861 3862 ConstantInt *Solution1 = 3863 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA)); 3864 ConstantInt *Solution2 = 3865 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA)); 3866 3867 return std::make_pair(SE.getConstant(Solution1), 3868 SE.getConstant(Solution2)); 3869 } // end APIntOps namespace 3870} 3871 3872/// HowFarToZero - Return the number of times a backedge comparing the specified 3873/// value to zero will execute. If not computable, return CouldNotCompute. 3874const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 3875 // If the value is a constant 3876 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3877 // If the value is already zero, the branch will execute zero times. 3878 if (C->getValue()->isZero()) return C; 3879 return getCouldNotCompute(); // Otherwise it will loop infinitely. 3880 } 3881 3882 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 3883 if (!AddRec || AddRec->getLoop() != L) 3884 return getCouldNotCompute(); 3885 3886 if (AddRec->isAffine()) { 3887 // If this is an affine expression, the execution count of this branch is 3888 // the minimum unsigned root of the following equation: 3889 // 3890 // Start + Step*N = 0 (mod 2^BW) 3891 // 3892 // equivalent to: 3893 // 3894 // Step*N = -Start (mod 2^BW) 3895 // 3896 // where BW is the common bit width of Start and Step. 3897 3898 // Get the initial value for the loop. 3899 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 3900 L->getParentLoop()); 3901 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 3902 L->getParentLoop()); 3903 3904 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 3905 // For now we handle only constant steps. 3906 3907 // First, handle unitary steps. 3908 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 3909 return getNegativeSCEV(Start); // N = -Start (as unsigned) 3910 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 3911 return Start; // N = Start (as unsigned) 3912 3913 // Then, try to solve the above equation provided that Start is constant. 3914 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 3915 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 3916 -StartC->getValue()->getValue(), 3917 *this); 3918 } 3919 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 3920 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 3921 // the quadratic equation to solve it. 3922 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 3923 *this); 3924 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 3925 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 3926 if (R1) { 3927#if 0 3928 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 3929 << " sol#2: " << *R2 << "\n"; 3930#endif 3931 // Pick the smallest positive root value. 3932 if (ConstantInt *CB = 3933 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT, 3934 R1->getValue(), R2->getValue()))) { 3935 if (CB->getZExtValue() == false) 3936 std::swap(R1, R2); // R1 is the minimum root now. 3937 3938 // We can only use this value if the chrec ends up with an exact zero 3939 // value at this index. When solving for "X*X != 5", for example, we 3940 // should not accept a root of 2. 3941 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 3942 if (Val->isZero()) 3943 return R1; // We found a quadratic root! 3944 } 3945 } 3946 } 3947 3948 return getCouldNotCompute(); 3949} 3950 3951/// HowFarToNonZero - Return the number of times a backedge checking the 3952/// specified value for nonzero will execute. If not computable, return 3953/// CouldNotCompute 3954const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 3955 // Loops that look like: while (X == 0) are very strange indeed. We don't 3956 // handle them yet except for the trivial case. This could be expanded in the 3957 // future as needed. 3958 3959 // If the value is a constant, check to see if it is known to be non-zero 3960 // already. If so, the backedge will execute zero times. 3961 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 3962 if (!C->getValue()->isNullValue()) 3963 return getIntegerSCEV(0, C->getType()); 3964 return getCouldNotCompute(); // Otherwise it will loop infinitely. 3965 } 3966 3967 // We could implement others, but I really doubt anyone writes loops like 3968 // this, and if they did, they would already be constant folded. 3969 return getCouldNotCompute(); 3970} 3971 3972/// getLoopPredecessor - If the given loop's header has exactly one unique 3973/// predecessor outside the loop, return it. Otherwise return null. 3974/// 3975BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 3976 BasicBlock *Header = L->getHeader(); 3977 BasicBlock *Pred = 0; 3978 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 3979 PI != E; ++PI) 3980 if (!L->contains(*PI)) { 3981 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 3982 Pred = *PI; 3983 } 3984 return Pred; 3985} 3986 3987/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 3988/// (which may not be an immediate predecessor) which has exactly one 3989/// successor from which BB is reachable, or null if no such block is 3990/// found. 3991/// 3992BasicBlock * 3993ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 3994 // If the block has a unique predecessor, then there is no path from the 3995 // predecessor to the block that does not go through the direct edge 3996 // from the predecessor to the block. 3997 if (BasicBlock *Pred = BB->getSinglePredecessor()) 3998 return Pred; 3999 4000 // A loop's header is defined to be a block that dominates the loop. 4001 // If the header has a unique predecessor outside the loop, it must be 4002 // a block that has exactly one successor that can reach the loop. 4003 if (Loop *L = LI->getLoopFor(BB)) 4004 return getLoopPredecessor(L); 4005 4006 return 0; 4007} 4008 4009/// HasSameValue - SCEV structural equivalence is usually sufficient for 4010/// testing whether two expressions are equal, however for the purposes of 4011/// looking for a condition guarding a loop, it can be useful to be a little 4012/// more general, since a front-end may have replicated the controlling 4013/// expression. 4014/// 4015static bool HasSameValue(const SCEV *A, const SCEV *B) { 4016 // Quick check to see if they are the same SCEV. 4017 if (A == B) return true; 4018 4019 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4020 // two different instructions with the same value. Check for this case. 4021 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4022 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4023 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4024 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4025 if (AI->isIdenticalTo(BI)) 4026 return true; 4027 4028 // Otherwise assume they may have a different value. 4029 return false; 4030} 4031 4032/// isLoopGuardedByCond - Test whether entry to the loop is protected by 4033/// a conditional between LHS and RHS. This is used to help avoid max 4034/// expressions in loop trip counts. 4035bool ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4036 ICmpInst::Predicate Pred, 4037 const SCEV *LHS, const SCEV *RHS) { 4038 // Interpret a null as meaning no loop, where there is obviously no guard 4039 // (interprocedural conditions notwithstanding). 4040 if (!L) return false; 4041 4042 BasicBlock *Predecessor = getLoopPredecessor(L); 4043 BasicBlock *PredecessorDest = L->getHeader(); 4044 4045 // Starting at the loop predecessor, climb up the predecessor chain, as long 4046 // as there are predecessors that can be found that have unique successors 4047 // leading to the original header. 4048 for (; Predecessor; 4049 PredecessorDest = Predecessor, 4050 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4051 4052 BranchInst *LoopEntryPredicate = 4053 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4054 if (!LoopEntryPredicate || 4055 LoopEntryPredicate->isUnconditional()) 4056 continue; 4057 4058 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4059 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4060 return true; 4061 } 4062 4063 return false; 4064} 4065 4066/// isNecessaryCond - Test whether the given CondValue value is a condition 4067/// which is at least as strict as the one described by Pred, LHS, and RHS. 4068bool ScalarEvolution::isNecessaryCond(Value *CondValue, 4069 ICmpInst::Predicate Pred, 4070 const SCEV *LHS, const SCEV *RHS, 4071 bool Inverse) { 4072 // Recursivly handle And and Or conditions. 4073 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4074 if (BO->getOpcode() == Instruction::And) { 4075 if (!Inverse) 4076 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4077 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4078 } else if (BO->getOpcode() == Instruction::Or) { 4079 if (Inverse) 4080 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4081 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4082 } 4083 } 4084 4085 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4086 if (!ICI) return false; 4087 4088 // Now that we found a conditional branch that dominates the loop, check to 4089 // see if it is the comparison we are looking for. 4090 Value *PreCondLHS = ICI->getOperand(0); 4091 Value *PreCondRHS = ICI->getOperand(1); 4092 ICmpInst::Predicate Cond; 4093 if (Inverse) 4094 Cond = ICI->getInversePredicate(); 4095 else 4096 Cond = ICI->getPredicate(); 4097 4098 if (Cond == Pred) 4099 ; // An exact match. 4100 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE) 4101 ; // The actual condition is beyond sufficient. 4102 else 4103 // Check a few special cases. 4104 switch (Cond) { 4105 case ICmpInst::ICMP_UGT: 4106 if (Pred == ICmpInst::ICMP_ULT) { 4107 std::swap(PreCondLHS, PreCondRHS); 4108 Cond = ICmpInst::ICMP_ULT; 4109 break; 4110 } 4111 return false; 4112 case ICmpInst::ICMP_SGT: 4113 if (Pred == ICmpInst::ICMP_SLT) { 4114 std::swap(PreCondLHS, PreCondRHS); 4115 Cond = ICmpInst::ICMP_SLT; 4116 break; 4117 } 4118 return false; 4119 case ICmpInst::ICMP_NE: 4120 // Expressions like (x >u 0) are often canonicalized to (x != 0), 4121 // so check for this case by checking if the NE is comparing against 4122 // a minimum or maximum constant. 4123 if (!ICmpInst::isTrueWhenEqual(Pred)) 4124 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) { 4125 const APInt &A = CI->getValue(); 4126 switch (Pred) { 4127 case ICmpInst::ICMP_SLT: 4128 if (A.isMaxSignedValue()) break; 4129 return false; 4130 case ICmpInst::ICMP_SGT: 4131 if (A.isMinSignedValue()) break; 4132 return false; 4133 case ICmpInst::ICMP_ULT: 4134 if (A.isMaxValue()) break; 4135 return false; 4136 case ICmpInst::ICMP_UGT: 4137 if (A.isMinValue()) break; 4138 return false; 4139 default: 4140 return false; 4141 } 4142 Cond = ICmpInst::ICMP_NE; 4143 // NE is symmetric but the original comparison may not be. Swap 4144 // the operands if necessary so that they match below. 4145 if (isa<SCEVConstant>(LHS)) 4146 std::swap(PreCondLHS, PreCondRHS); 4147 break; 4148 } 4149 return false; 4150 default: 4151 // We weren't able to reconcile the condition. 4152 return false; 4153 } 4154 4155 if (!PreCondLHS->getType()->isInteger()) return false; 4156 4157 const SCEV *PreCondLHSSCEV = getSCEV(PreCondLHS); 4158 const SCEV *PreCondRHSSCEV = getSCEV(PreCondRHS); 4159 return (HasSameValue(LHS, PreCondLHSSCEV) && 4160 HasSameValue(RHS, PreCondRHSSCEV)) || 4161 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) && 4162 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV))); 4163} 4164 4165/// getBECount - Subtract the end and start values and divide by the step, 4166/// rounding up, to get the number of times the backedge is executed. Return 4167/// CouldNotCompute if an intermediate computation overflows. 4168const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4169 const SCEV *End, 4170 const SCEV *Step) { 4171 const Type *Ty = Start->getType(); 4172 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4173 const SCEV *Diff = getMinusSCEV(End, Start); 4174 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4175 4176 // Add an adjustment to the difference between End and Start so that 4177 // the division will effectively round up. 4178 const SCEV *Add = getAddExpr(Diff, RoundUp); 4179 4180 // Check Add for unsigned overflow. 4181 // TODO: More sophisticated things could be done here. 4182 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1); 4183 const SCEV *OperandExtendedAdd = 4184 getAddExpr(getZeroExtendExpr(Diff, WideTy), 4185 getZeroExtendExpr(RoundUp, WideTy)); 4186 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4187 return getCouldNotCompute(); 4188 4189 return getUDivExpr(Add, Step); 4190} 4191 4192/// HowManyLessThans - Return the number of times a backedge containing the 4193/// specified less-than comparison will execute. If not computable, return 4194/// CouldNotCompute. 4195ScalarEvolution::BackedgeTakenInfo 4196ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4197 const Loop *L, bool isSigned) { 4198 // Only handle: "ADDREC < LoopInvariant". 4199 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4200 4201 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4202 if (!AddRec || AddRec->getLoop() != L) 4203 return getCouldNotCompute(); 4204 4205 if (AddRec->isAffine()) { 4206 // FORNOW: We only support unit strides. 4207 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4208 const SCEV *Step = AddRec->getStepRecurrence(*this); 4209 4210 // TODO: handle non-constant strides. 4211 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4212 if (!CStep || CStep->isZero()) 4213 return getCouldNotCompute(); 4214 if (CStep->isOne()) { 4215 // With unit stride, the iteration never steps past the limit value. 4216 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4217 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4218 // Test whether a positive iteration iteration can step past the limit 4219 // value and past the maximum value for its type in a single step. 4220 if (isSigned) { 4221 APInt Max = APInt::getSignedMaxValue(BitWidth); 4222 if ((Max - CStep->getValue()->getValue()) 4223 .slt(CLimit->getValue()->getValue())) 4224 return getCouldNotCompute(); 4225 } else { 4226 APInt Max = APInt::getMaxValue(BitWidth); 4227 if ((Max - CStep->getValue()->getValue()) 4228 .ult(CLimit->getValue()->getValue())) 4229 return getCouldNotCompute(); 4230 } 4231 } else 4232 // TODO: handle non-constant limit values below. 4233 return getCouldNotCompute(); 4234 } else 4235 // TODO: handle negative strides below. 4236 return getCouldNotCompute(); 4237 4238 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4239 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4240 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4241 // treat m-n as signed nor unsigned due to overflow possibility. 4242 4243 // First, we get the value of the LHS in the first iteration: n 4244 const SCEV *Start = AddRec->getOperand(0); 4245 4246 // Determine the minimum constant start value. 4247 const SCEV *MinStart = isa<SCEVConstant>(Start) ? Start : 4248 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) : 4249 APInt::getMinValue(BitWidth)); 4250 4251 // If we know that the condition is true in order to enter the loop, 4252 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4253 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4254 // the division must round up. 4255 const SCEV *End = RHS; 4256 if (!isLoopGuardedByCond(L, 4257 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, 4258 getMinusSCEV(Start, Step), RHS)) 4259 End = isSigned ? getSMaxExpr(RHS, Start) 4260 : getUMaxExpr(RHS, Start); 4261 4262 // Determine the maximum constant end value. 4263 const SCEV *MaxEnd = 4264 isa<SCEVConstant>(End) ? End : 4265 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) 4266 .ashr(GetMinSignBits(End) - 1) : 4267 APInt::getMaxValue(BitWidth) 4268 .lshr(GetMinLeadingZeros(End))); 4269 4270 // Finally, we subtract these two values and divide, rounding up, to get 4271 // the number of times the backedge is executed. 4272 const SCEV *BECount = getBECount(Start, End, Step); 4273 4274 // The maximum backedge count is similar, except using the minimum start 4275 // value and the maximum end value. 4276 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step); 4277 4278 return BackedgeTakenInfo(BECount, MaxBECount); 4279 } 4280 4281 return getCouldNotCompute(); 4282} 4283 4284/// getNumIterationsInRange - Return the number of iterations of this loop that 4285/// produce values in the specified constant range. Another way of looking at 4286/// this is that it returns the first iteration number where the value is not in 4287/// the condition, thus computing the exit count. If the iteration count can't 4288/// be computed, an instance of SCEVCouldNotCompute is returned. 4289const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4290 ScalarEvolution &SE) const { 4291 if (Range.isFullSet()) // Infinite loop. 4292 return SE.getCouldNotCompute(); 4293 4294 // If the start is a non-zero constant, shift the range to simplify things. 4295 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4296 if (!SC->getValue()->isZero()) { 4297 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4298 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4299 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4300 if (const SCEVAddRecExpr *ShiftedAddRec = 4301 dyn_cast<SCEVAddRecExpr>(Shifted)) 4302 return ShiftedAddRec->getNumIterationsInRange( 4303 Range.subtract(SC->getValue()->getValue()), SE); 4304 // This is strange and shouldn't happen. 4305 return SE.getCouldNotCompute(); 4306 } 4307 4308 // The only time we can solve this is when we have all constant indices. 4309 // Otherwise, we cannot determine the overflow conditions. 4310 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4311 if (!isa<SCEVConstant>(getOperand(i))) 4312 return SE.getCouldNotCompute(); 4313 4314 4315 // Okay at this point we know that all elements of the chrec are constants and 4316 // that the start element is zero. 4317 4318 // First check to see if the range contains zero. If not, the first 4319 // iteration exits. 4320 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4321 if (!Range.contains(APInt(BitWidth, 0))) 4322 return SE.getIntegerSCEV(0, getType()); 4323 4324 if (isAffine()) { 4325 // If this is an affine expression then we have this situation: 4326 // Solve {0,+,A} in Range === Ax in Range 4327 4328 // We know that zero is in the range. If A is positive then we know that 4329 // the upper value of the range must be the first possible exit value. 4330 // If A is negative then the lower of the range is the last possible loop 4331 // value. Also note that we already checked for a full range. 4332 APInt One(BitWidth,1); 4333 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 4334 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 4335 4336 // The exit value should be (End+A)/A. 4337 APInt ExitVal = (End + A).udiv(A); 4338 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal); 4339 4340 // Evaluate at the exit value. If we really did fall out of the valid 4341 // range, then we computed our trip count, otherwise wrap around or other 4342 // things must have happened. 4343 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 4344 if (Range.contains(Val->getValue())) 4345 return SE.getCouldNotCompute(); // Something strange happened 4346 4347 // Ensure that the previous value is in the range. This is a sanity check. 4348 assert(Range.contains( 4349 EvaluateConstantChrecAtConstant(this, 4350 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) && 4351 "Linear scev computation is off in a bad way!"); 4352 return SE.getConstant(ExitValue); 4353 } else if (isQuadratic()) { 4354 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 4355 // quadratic equation to solve it. To do this, we must frame our problem in 4356 // terms of figuring out when zero is crossed, instead of when 4357 // Range.getUpper() is crossed. 4358 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 4359 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 4360 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 4361 4362 // Next, solve the constructed addrec 4363 std::pair<const SCEV *,const SCEV *> Roots = 4364 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 4365 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4366 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4367 if (R1) { 4368 // Pick the smallest positive root value. 4369 if (ConstantInt *CB = 4370 dyn_cast<ConstantInt>( 4371 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT, 4372 R1->getValue(), R2->getValue()))) { 4373 if (CB->getZExtValue() == false) 4374 std::swap(R1, R2); // R1 is the minimum root now. 4375 4376 // Make sure the root is not off by one. The returned iteration should 4377 // not be in the range, but the previous one should be. When solving 4378 // for "X*X < 5", for example, we should not return a root of 2. 4379 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 4380 R1->getValue(), 4381 SE); 4382 if (Range.contains(R1Val->getValue())) { 4383 // The next iteration must be out of the range... 4384 ConstantInt *NextVal = 4385 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1); 4386 4387 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4388 if (!Range.contains(R1Val->getValue())) 4389 return SE.getConstant(NextVal); 4390 return SE.getCouldNotCompute(); // Something strange happened 4391 } 4392 4393 // If R1 was not in the range, then it is a good return value. Make 4394 // sure that R1-1 WAS in the range though, just in case. 4395 ConstantInt *NextVal = 4396 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1); 4397 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 4398 if (Range.contains(R1Val->getValue())) 4399 return R1; 4400 return SE.getCouldNotCompute(); // Something strange happened 4401 } 4402 } 4403 } 4404 4405 return SE.getCouldNotCompute(); 4406} 4407 4408 4409 4410//===----------------------------------------------------------------------===// 4411// SCEVCallbackVH Class Implementation 4412//===----------------------------------------------------------------------===// 4413 4414void ScalarEvolution::SCEVCallbackVH::deleted() { 4415 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4416 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 4417 SE->ConstantEvolutionLoopExitValue.erase(PN); 4418 if (Instruction *I = dyn_cast<Instruction>(getValPtr())) 4419 SE->ValuesAtScopes.erase(I); 4420 SE->Scalars.erase(getValPtr()); 4421 // this now dangles! 4422} 4423 4424void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 4425 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!"); 4426 4427 // Forget all the expressions associated with users of the old value, 4428 // so that future queries will recompute the expressions using the new 4429 // value. 4430 SmallVector<User *, 16> Worklist; 4431 Value *Old = getValPtr(); 4432 bool DeleteOld = false; 4433 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 4434 UI != UE; ++UI) 4435 Worklist.push_back(*UI); 4436 while (!Worklist.empty()) { 4437 User *U = Worklist.pop_back_val(); 4438 // Deleting the Old value will cause this to dangle. Postpone 4439 // that until everything else is done. 4440 if (U == Old) { 4441 DeleteOld = true; 4442 continue; 4443 } 4444 if (PHINode *PN = dyn_cast<PHINode>(U)) 4445 SE->ConstantEvolutionLoopExitValue.erase(PN); 4446 if (Instruction *I = dyn_cast<Instruction>(U)) 4447 SE->ValuesAtScopes.erase(I); 4448 if (SE->Scalars.erase(U)) 4449 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 4450 UI != UE; ++UI) 4451 Worklist.push_back(*UI); 4452 } 4453 if (DeleteOld) { 4454 if (PHINode *PN = dyn_cast<PHINode>(Old)) 4455 SE->ConstantEvolutionLoopExitValue.erase(PN); 4456 if (Instruction *I = dyn_cast<Instruction>(Old)) 4457 SE->ValuesAtScopes.erase(I); 4458 SE->Scalars.erase(Old); 4459 // this now dangles! 4460 } 4461 // this may dangle! 4462} 4463 4464ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 4465 : CallbackVH(V), SE(se) {} 4466 4467//===----------------------------------------------------------------------===// 4468// ScalarEvolution Class Implementation 4469//===----------------------------------------------------------------------===// 4470 4471ScalarEvolution::ScalarEvolution() 4472 : FunctionPass(&ID) { 4473} 4474 4475bool ScalarEvolution::runOnFunction(Function &F) { 4476 this->F = &F; 4477 LI = &getAnalysis<LoopInfo>(); 4478 TD = getAnalysisIfAvailable<TargetData>(); 4479 return false; 4480} 4481 4482void ScalarEvolution::releaseMemory() { 4483 Scalars.clear(); 4484 BackedgeTakenCounts.clear(); 4485 ConstantEvolutionLoopExitValue.clear(); 4486 ValuesAtScopes.clear(); 4487 UniqueSCEVs.clear(); 4488 SCEVAllocator.Reset(); 4489} 4490 4491void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 4492 AU.setPreservesAll(); 4493 AU.addRequiredTransitive<LoopInfo>(); 4494} 4495 4496bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 4497 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 4498} 4499 4500static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 4501 const Loop *L) { 4502 // Print all inner loops first 4503 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4504 PrintLoopInfo(OS, SE, *I); 4505 4506 OS << "Loop " << L->getHeader()->getName() << ": "; 4507 4508 SmallVector<BasicBlock*, 8> ExitBlocks; 4509 L->getExitBlocks(ExitBlocks); 4510 if (ExitBlocks.size() != 1) 4511 OS << "<multiple exits> "; 4512 4513 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 4514 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 4515 } else { 4516 OS << "Unpredictable backedge-taken count. "; 4517 } 4518 4519 OS << "\n"; 4520 OS << "Loop " << L->getHeader()->getName() << ": "; 4521 4522 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 4523 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 4524 } else { 4525 OS << "Unpredictable max backedge-taken count. "; 4526 } 4527 4528 OS << "\n"; 4529} 4530 4531void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 4532 // ScalarEvolution's implementaiton of the print method is to print 4533 // out SCEV values of all instructions that are interesting. Doing 4534 // this potentially causes it to create new SCEV objects though, 4535 // which technically conflicts with the const qualifier. This isn't 4536 // observable from outside the class though, so casting away the 4537 // const isn't dangerous. 4538 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 4539 4540 OS << "Classifying expressions for: " << F->getName() << "\n"; 4541 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 4542 if (isSCEVable(I->getType())) { 4543 OS << *I; 4544 OS << " --> "; 4545 const SCEV *SV = SE.getSCEV(&*I); 4546 SV->print(OS); 4547 4548 const Loop *L = LI->getLoopFor((*I).getParent()); 4549 4550 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 4551 if (AtUse != SV) { 4552 OS << " --> "; 4553 AtUse->print(OS); 4554 } 4555 4556 if (L) { 4557 OS << "\t\t" "Exits: "; 4558 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 4559 if (!ExitValue->isLoopInvariant(L)) { 4560 OS << "<<Unknown>>"; 4561 } else { 4562 OS << *ExitValue; 4563 } 4564 } 4565 4566 OS << "\n"; 4567 } 4568 4569 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 4570 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 4571 PrintLoopInfo(OS, &SE, *I); 4572} 4573 4574void ScalarEvolution::print(std::ostream &o, const Module *M) const { 4575 raw_os_ostream OS(o); 4576 print(OS, M); 4577} 4578