ScalarEvolution.cpp revision 6e70e31810464289a9e9b37e0345847e3ca5d5cf
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. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/LoopInfo.h" 73#include "llvm/Analysis/ValueTracking.h" 74#include "llvm/Assembly/Writer.h" 75#include "llvm/Target/TargetData.h" 76#include "llvm/Support/CommandLine.h" 77#include "llvm/Support/Compiler.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106static RegisterPass<ScalarEvolution> 107R("scalar-evolution", "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(errs()); 122 errs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeID(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 181 new (S) SCEVConstant(ID, V); 182 UniqueSCEVs.InsertNode(S, IP); 183 return S; 184} 185 186const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 187 return getConstant(ConstantInt::get(getContext(), Val)); 188} 189 190const SCEV * 191ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 192 return getConstant( 193 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 194} 195 196const Type *SCEVConstant::getType() const { return V->getType(); } 197 198void SCEVConstant::print(raw_ostream &OS) const { 199 WriteAsOperand(OS, V, false); 200} 201 202SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 203 unsigned SCEVTy, const SCEV *op, const Type *ty) 204 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 205 206bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 207 return Op->dominates(BB, DT); 208} 209 210bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 211 return Op->properlyDominates(BB, DT); 212} 213 214SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 215 const SCEV *op, const Type *ty) 216 : SCEVCastExpr(ID, scTruncate, op, ty) { 217 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 218 (Ty->isInteger() || isa<PointerType>(Ty)) && 219 "Cannot truncate non-integer value!"); 220} 221 222void SCEVTruncateExpr::print(raw_ostream &OS) const { 223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 224} 225 226SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 227 const SCEV *op, const Type *ty) 228 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 229 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 230 (Ty->isInteger() || isa<PointerType>(Ty)) && 231 "Cannot zero extend non-integer value!"); 232} 233 234void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 236} 237 238SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 239 const SCEV *op, const Type *ty) 240 : SCEVCastExpr(ID, scSignExtend, op, ty) { 241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 242 (Ty->isInteger() || isa<PointerType>(Ty)) && 243 "Cannot sign extend non-integer value!"); 244} 245 246void SCEVSignExtendExpr::print(raw_ostream &OS) const { 247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 248} 249 250void SCEVCommutativeExpr::print(raw_ostream &OS) const { 251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 252 const char *OpStr = getOperationStr(); 253 OS << "(" << *Operands[0]; 254 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 255 OS << OpStr << *Operands[i]; 256 OS << ")"; 257} 258 259bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 261 if (!getOperand(i)->dominates(BB, DT)) 262 return false; 263 } 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 269 if (!getOperand(i)->properlyDominates(BB, DT)) 270 return false; 271 } 272 return true; 273} 274 275bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 276 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 277} 278 279bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 280 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 281} 282 283void SCEVUDivExpr::print(raw_ostream &OS) const { 284 OS << "(" << *LHS << " /u " << *RHS << ")"; 285} 286 287const Type *SCEVUDivExpr::getType() const { 288 // In most cases the types of LHS and RHS will be the same, but in some 289 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 290 // depend on the type for correctness, but handling types carefully can 291 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 292 // a pointer type than the RHS, so use the RHS' type here. 293 return RHS->getType(); 294} 295 296bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 297 // Add recurrences are never invariant in the function-body (null loop). 298 if (!QueryLoop) 299 return false; 300 301 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 302 if (QueryLoop->contains(L->getHeader())) 303 return false; 304 305 // This recurrence is variant w.r.t. QueryLoop if any of its operands 306 // are variant. 307 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 308 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 309 return false; 310 311 // Otherwise it's loop-invariant. 312 return true; 313} 314 315void SCEVAddRecExpr::print(raw_ostream &OS) const { 316 OS << "{" << *Operands[0]; 317 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 318 OS << ",+," << *Operands[i]; 319 OS << "}<" << L->getHeader()->getName() + ">"; 320} 321 322void SCEVFieldOffsetExpr::print(raw_ostream &OS) const { 323 // LLVM struct fields don't have names, so just print the field number. 324 OS << "offsetof(" << *STy << ", " << FieldNo << ")"; 325} 326 327void SCEVAllocSizeExpr::print(raw_ostream &OS) const { 328 OS << "sizeof(" << *AllocTy << ")"; 329} 330 331bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 332 // All non-instruction values are loop invariant. All instructions are loop 333 // invariant if they are not contained in the specified loop. 334 // Instructions are never considered invariant in the function body 335 // (null loop) because they are defined within the "loop". 336 if (Instruction *I = dyn_cast<Instruction>(V)) 337 return L && !L->contains(I->getParent()); 338 return true; 339} 340 341bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 342 if (Instruction *I = dyn_cast<Instruction>(getValue())) 343 return DT->dominates(I->getParent(), BB); 344 return true; 345} 346 347bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 348 if (Instruction *I = dyn_cast<Instruction>(getValue())) 349 return DT->properlyDominates(I->getParent(), BB); 350 return true; 351} 352 353const Type *SCEVUnknown::getType() const { 354 return V->getType(); 355} 356 357void SCEVUnknown::print(raw_ostream &OS) const { 358 WriteAsOperand(OS, V, false); 359} 360 361//===----------------------------------------------------------------------===// 362// SCEV Utilities 363//===----------------------------------------------------------------------===// 364 365static bool CompareTypes(const Type *A, const Type *B) { 366 if (A->getTypeID() != B->getTypeID()) 367 return A->getTypeID() < B->getTypeID(); 368 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 369 const IntegerType *BI = cast<IntegerType>(B); 370 return AI->getBitWidth() < BI->getBitWidth(); 371 } 372 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 373 const PointerType *BI = cast<PointerType>(B); 374 return CompareTypes(AI->getElementType(), BI->getElementType()); 375 } 376 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 377 const ArrayType *BI = cast<ArrayType>(B); 378 if (AI->getNumElements() != BI->getNumElements()) 379 return AI->getNumElements() < BI->getNumElements(); 380 return CompareTypes(AI->getElementType(), BI->getElementType()); 381 } 382 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 383 const VectorType *BI = cast<VectorType>(B); 384 if (AI->getNumElements() != BI->getNumElements()) 385 return AI->getNumElements() < BI->getNumElements(); 386 return CompareTypes(AI->getElementType(), BI->getElementType()); 387 } 388 if (const StructType *AI = dyn_cast<StructType>(A)) { 389 const StructType *BI = cast<StructType>(B); 390 if (AI->getNumElements() != BI->getNumElements()) 391 return AI->getNumElements() < BI->getNumElements(); 392 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 393 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 394 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 395 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 396 } 397 return false; 398} 399 400namespace { 401 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 402 /// than the complexity of the RHS. This comparator is used to canonicalize 403 /// expressions. 404 class VISIBILITY_HIDDEN SCEVComplexityCompare { 405 LoopInfo *LI; 406 public: 407 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 408 409 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 410 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 411 if (LHS == RHS) 412 return false; 413 414 // Primarily, sort the SCEVs by their getSCEVType(). 415 if (LHS->getSCEVType() != RHS->getSCEVType()) 416 return LHS->getSCEVType() < RHS->getSCEVType(); 417 418 // Aside from the getSCEVType() ordering, the particular ordering 419 // isn't very important except that it's beneficial to be consistent, 420 // so that (a + b) and (b + a) don't end up as different expressions. 421 422 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 423 // not as complete as it could be. 424 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 425 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 426 427 // Order pointer values after integer values. This helps SCEVExpander 428 // form GEPs. 429 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 430 return false; 431 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 432 return true; 433 434 // Compare getValueID values. 435 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 436 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 437 438 // Sort arguments by their position. 439 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 440 const Argument *RA = cast<Argument>(RU->getValue()); 441 return LA->getArgNo() < RA->getArgNo(); 442 } 443 444 // For instructions, compare their loop depth, and their opcode. 445 // This is pretty loose. 446 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 447 Instruction *RV = cast<Instruction>(RU->getValue()); 448 449 // Compare loop depths. 450 if (LI->getLoopDepth(LV->getParent()) != 451 LI->getLoopDepth(RV->getParent())) 452 return LI->getLoopDepth(LV->getParent()) < 453 LI->getLoopDepth(RV->getParent()); 454 455 // Compare opcodes. 456 if (LV->getOpcode() != RV->getOpcode()) 457 return LV->getOpcode() < RV->getOpcode(); 458 459 // Compare the number of operands. 460 if (LV->getNumOperands() != RV->getNumOperands()) 461 return LV->getNumOperands() < RV->getNumOperands(); 462 } 463 464 return false; 465 } 466 467 // Compare constant values. 468 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 469 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 470 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 471 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 472 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 473 } 474 475 // Compare addrec loop depths. 476 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 477 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 478 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 479 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 480 } 481 482 // Lexicographically compare n-ary expressions. 483 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 484 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 485 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 486 if (i >= RC->getNumOperands()) 487 return false; 488 if (operator()(LC->getOperand(i), RC->getOperand(i))) 489 return true; 490 if (operator()(RC->getOperand(i), LC->getOperand(i))) 491 return false; 492 } 493 return LC->getNumOperands() < RC->getNumOperands(); 494 } 495 496 // Lexicographically compare udiv expressions. 497 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 498 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 499 if (operator()(LC->getLHS(), RC->getLHS())) 500 return true; 501 if (operator()(RC->getLHS(), LC->getLHS())) 502 return false; 503 if (operator()(LC->getRHS(), RC->getRHS())) 504 return true; 505 if (operator()(RC->getRHS(), LC->getRHS())) 506 return false; 507 return false; 508 } 509 510 // Compare cast expressions by operand. 511 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 512 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 513 return operator()(LC->getOperand(), RC->getOperand()); 514 } 515 516 // Compare offsetof expressions. 517 if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) { 518 const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS); 519 if (CompareTypes(LA->getStructType(), RA->getStructType()) || 520 CompareTypes(RA->getStructType(), LA->getStructType())) 521 return CompareTypes(LA->getStructType(), RA->getStructType()); 522 return LA->getFieldNo() < RA->getFieldNo(); 523 } 524 525 // Compare sizeof expressions by the allocation type. 526 if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) { 527 const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS); 528 return CompareTypes(LA->getAllocType(), RA->getAllocType()); 529 } 530 531 llvm_unreachable("Unknown SCEV kind!"); 532 return false; 533 } 534 }; 535} 536 537/// GroupByComplexity - Given a list of SCEV objects, order them by their 538/// complexity, and group objects of the same complexity together by value. 539/// When this routine is finished, we know that any duplicates in the vector are 540/// consecutive and that complexity is monotonically increasing. 541/// 542/// Note that we go take special precautions to ensure that we get determinstic 543/// results from this routine. In other words, we don't want the results of 544/// this to depend on where the addresses of various SCEV objects happened to 545/// land in memory. 546/// 547static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 548 LoopInfo *LI) { 549 if (Ops.size() < 2) return; // Noop 550 if (Ops.size() == 2) { 551 // This is the common case, which also happens to be trivially simple. 552 // Special case it. 553 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 554 std::swap(Ops[0], Ops[1]); 555 return; 556 } 557 558 // Do the rough sort by complexity. 559 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 560 561 // Now that we are sorted by complexity, group elements of the same 562 // complexity. Note that this is, at worst, N^2, but the vector is likely to 563 // be extremely short in practice. Note that we take this approach because we 564 // do not want to depend on the addresses of the objects we are grouping. 565 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 566 const SCEV *S = Ops[i]; 567 unsigned Complexity = S->getSCEVType(); 568 569 // If there are any objects of the same complexity and same value as this 570 // one, group them. 571 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 572 if (Ops[j] == S) { // Found a duplicate. 573 // Move it to immediately after i'th element. 574 std::swap(Ops[i+1], Ops[j]); 575 ++i; // no need to rescan it. 576 if (i == e-2) return; // Done! 577 } 578 } 579 } 580} 581 582 583 584//===----------------------------------------------------------------------===// 585// Simple SCEV method implementations 586//===----------------------------------------------------------------------===// 587 588/// BinomialCoefficient - Compute BC(It, K). The result has width W. 589/// Assume, K > 0. 590static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 591 ScalarEvolution &SE, 592 const Type* ResultTy) { 593 // Handle the simplest case efficiently. 594 if (K == 1) 595 return SE.getTruncateOrZeroExtend(It, ResultTy); 596 597 // We are using the following formula for BC(It, K): 598 // 599 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 600 // 601 // Suppose, W is the bitwidth of the return value. We must be prepared for 602 // overflow. Hence, we must assure that the result of our computation is 603 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 604 // safe in modular arithmetic. 605 // 606 // However, this code doesn't use exactly that formula; the formula it uses 607 // is something like the following, where T is the number of factors of 2 in 608 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 609 // exponentiation: 610 // 611 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 612 // 613 // This formula is trivially equivalent to the previous formula. However, 614 // this formula can be implemented much more efficiently. The trick is that 615 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 616 // arithmetic. To do exact division in modular arithmetic, all we have 617 // to do is multiply by the inverse. Therefore, this step can be done at 618 // width W. 619 // 620 // The next issue is how to safely do the division by 2^T. The way this 621 // is done is by doing the multiplication step at a width of at least W + T 622 // bits. This way, the bottom W+T bits of the product are accurate. Then, 623 // when we perform the division by 2^T (which is equivalent to a right shift 624 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 625 // truncated out after the division by 2^T. 626 // 627 // In comparison to just directly using the first formula, this technique 628 // is much more efficient; using the first formula requires W * K bits, 629 // but this formula less than W + K bits. Also, the first formula requires 630 // a division step, whereas this formula only requires multiplies and shifts. 631 // 632 // It doesn't matter whether the subtraction step is done in the calculation 633 // width or the input iteration count's width; if the subtraction overflows, 634 // the result must be zero anyway. We prefer here to do it in the width of 635 // the induction variable because it helps a lot for certain cases; CodeGen 636 // isn't smart enough to ignore the overflow, which leads to much less 637 // efficient code if the width of the subtraction is wider than the native 638 // register width. 639 // 640 // (It's possible to not widen at all by pulling out factors of 2 before 641 // the multiplication; for example, K=2 can be calculated as 642 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 643 // extra arithmetic, so it's not an obvious win, and it gets 644 // much more complicated for K > 3.) 645 646 // Protection from insane SCEVs; this bound is conservative, 647 // but it probably doesn't matter. 648 if (K > 1000) 649 return SE.getCouldNotCompute(); 650 651 unsigned W = SE.getTypeSizeInBits(ResultTy); 652 653 // Calculate K! / 2^T and T; we divide out the factors of two before 654 // multiplying for calculating K! / 2^T to avoid overflow. 655 // Other overflow doesn't matter because we only care about the bottom 656 // W bits of the result. 657 APInt OddFactorial(W, 1); 658 unsigned T = 1; 659 for (unsigned i = 3; i <= K; ++i) { 660 APInt Mult(W, i); 661 unsigned TwoFactors = Mult.countTrailingZeros(); 662 T += TwoFactors; 663 Mult = Mult.lshr(TwoFactors); 664 OddFactorial *= Mult; 665 } 666 667 // We need at least W + T bits for the multiplication step 668 unsigned CalculationBits = W + T; 669 670 // Calcuate 2^T, at width T+W. 671 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 672 673 // Calculate the multiplicative inverse of K! / 2^T; 674 // this multiplication factor will perform the exact division by 675 // K! / 2^T. 676 APInt Mod = APInt::getSignedMinValue(W+1); 677 APInt MultiplyFactor = OddFactorial.zext(W+1); 678 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 679 MultiplyFactor = MultiplyFactor.trunc(W); 680 681 // Calculate the product, at width T+W 682 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 683 CalculationBits); 684 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 685 for (unsigned i = 1; i != K; ++i) { 686 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 687 Dividend = SE.getMulExpr(Dividend, 688 SE.getTruncateOrZeroExtend(S, CalculationTy)); 689 } 690 691 // Divide by 2^T 692 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 693 694 // Truncate the result, and divide by K! / 2^T. 695 696 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 697 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 698} 699 700/// evaluateAtIteration - Return the value of this chain of recurrences at 701/// the specified iteration number. We can evaluate this recurrence by 702/// multiplying each element in the chain by the binomial coefficient 703/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 704/// 705/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 706/// 707/// where BC(It, k) stands for binomial coefficient. 708/// 709const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 710 ScalarEvolution &SE) const { 711 const SCEV *Result = getStart(); 712 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 713 // The computation is correct in the face of overflow provided that the 714 // multiplication is performed _after_ the evaluation of the binomial 715 // coefficient. 716 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 717 if (isa<SCEVCouldNotCompute>(Coeff)) 718 return Coeff; 719 720 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 721 } 722 return Result; 723} 724 725//===----------------------------------------------------------------------===// 726// SCEV Expression folder implementations 727//===----------------------------------------------------------------------===// 728 729const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 730 const Type *Ty) { 731 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 732 "This is not a truncating conversion!"); 733 assert(isSCEVable(Ty) && 734 "This is not a conversion to a SCEVable type!"); 735 Ty = getEffectiveSCEVType(Ty); 736 737 FoldingSetNodeID ID; 738 ID.AddInteger(scTruncate); 739 ID.AddPointer(Op); 740 ID.AddPointer(Ty); 741 void *IP = 0; 742 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 743 744 // Fold if the operand is constant. 745 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 746 return getConstant( 747 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 748 749 // trunc(trunc(x)) --> trunc(x) 750 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 751 return getTruncateExpr(ST->getOperand(), Ty); 752 753 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 754 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 755 return getTruncateOrSignExtend(SS->getOperand(), Ty); 756 757 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 758 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 759 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 760 761 // If the input value is a chrec scev, truncate the chrec's operands. 762 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 763 SmallVector<const SCEV *, 4> Operands; 764 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 765 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 766 return getAddRecExpr(Operands, AddRec->getLoop()); 767 } 768 769 // The cast wasn't folded; create an explicit cast node. 770 // Recompute the insert position, as it may have been invalidated. 771 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 772 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 773 new (S) SCEVTruncateExpr(ID, Op, Ty); 774 UniqueSCEVs.InsertNode(S, IP); 775 return S; 776} 777 778const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 779 const Type *Ty) { 780 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 781 "This is not an extending conversion!"); 782 assert(isSCEVable(Ty) && 783 "This is not a conversion to a SCEVable type!"); 784 Ty = getEffectiveSCEVType(Ty); 785 786 // Fold if the operand is constant. 787 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 788 const Type *IntTy = getEffectiveSCEVType(Ty); 789 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 790 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 791 return getConstant(cast<ConstantInt>(C)); 792 } 793 794 // zext(zext(x)) --> zext(x) 795 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 796 return getZeroExtendExpr(SZ->getOperand(), Ty); 797 798 // Before doing any expensive analysis, check to see if we've already 799 // computed a SCEV for this Op and Ty. 800 FoldingSetNodeID ID; 801 ID.AddInteger(scZeroExtend); 802 ID.AddPointer(Op); 803 ID.AddPointer(Ty); 804 void *IP = 0; 805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 806 807 // If the input value is a chrec scev, and we can prove that the value 808 // did not overflow the old, smaller, value, we can zero extend all of the 809 // operands (often constants). This allows analysis of something like 810 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 811 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 812 if (AR->isAffine()) { 813 const SCEV *Start = AR->getStart(); 814 const SCEV *Step = AR->getStepRecurrence(*this); 815 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 816 const Loop *L = AR->getLoop(); 817 818 // If we have special knowledge that this addrec won't overflow, 819 // we don't need to do any further analysis. 820 if (AR->hasNoUnsignedWrap()) 821 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 822 getZeroExtendExpr(Step, Ty), 823 L); 824 825 // Check whether the backedge-taken count is SCEVCouldNotCompute. 826 // Note that this serves two purposes: It filters out loops that are 827 // simply not analyzable, and it covers the case where this code is 828 // being called from within backedge-taken count analysis, such that 829 // attempting to ask for the backedge-taken count would likely result 830 // in infinite recursion. In the later case, the analysis code will 831 // cope with a conservative value, and it will take care to purge 832 // that value once it has finished. 833 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 834 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 835 // Manually compute the final value for AR, checking for 836 // overflow. 837 838 // Check whether the backedge-taken count can be losslessly casted to 839 // the addrec's type. The count is always unsigned. 840 const SCEV *CastedMaxBECount = 841 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 842 const SCEV *RecastedMaxBECount = 843 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 844 if (MaxBECount == RecastedMaxBECount) { 845 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 846 // Check whether Start+Step*MaxBECount has no unsigned overflow. 847 const SCEV *ZMul = 848 getMulExpr(CastedMaxBECount, 849 getTruncateOrZeroExtend(Step, Start->getType())); 850 const SCEV *Add = getAddExpr(Start, ZMul); 851 const SCEV *OperandExtendedAdd = 852 getAddExpr(getZeroExtendExpr(Start, WideTy), 853 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 854 getZeroExtendExpr(Step, WideTy))); 855 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 856 // Return the expression with the addrec on the outside. 857 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 858 getZeroExtendExpr(Step, Ty), 859 L); 860 861 // Similar to above, only this time treat the step value as signed. 862 // This covers loops that count down. 863 const SCEV *SMul = 864 getMulExpr(CastedMaxBECount, 865 getTruncateOrSignExtend(Step, Start->getType())); 866 Add = getAddExpr(Start, SMul); 867 OperandExtendedAdd = 868 getAddExpr(getZeroExtendExpr(Start, WideTy), 869 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 870 getSignExtendExpr(Step, WideTy))); 871 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 872 // Return the expression with the addrec on the outside. 873 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 874 getSignExtendExpr(Step, Ty), 875 L); 876 } 877 878 // If the backedge is guarded by a comparison with the pre-inc value 879 // the addrec is safe. Also, if the entry is guarded by a comparison 880 // with the start value and the backedge is guarded by a comparison 881 // with the post-inc value, the addrec is safe. 882 if (isKnownPositive(Step)) { 883 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 884 getUnsignedRange(Step).getUnsignedMax()); 885 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 886 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 887 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 888 AR->getPostIncExpr(*this), N))) 889 // Return the expression with the addrec on the outside. 890 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 891 getZeroExtendExpr(Step, Ty), 892 L); 893 } else if (isKnownNegative(Step)) { 894 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 895 getSignedRange(Step).getSignedMin()); 896 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 897 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 898 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 899 AR->getPostIncExpr(*this), N))) 900 // Return the expression with the addrec on the outside. 901 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 902 getSignExtendExpr(Step, Ty), 903 L); 904 } 905 } 906 } 907 908 // The cast wasn't folded; create an explicit cast node. 909 // Recompute the insert position, as it may have been invalidated. 910 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 911 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 912 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 913 UniqueSCEVs.InsertNode(S, IP); 914 return S; 915} 916 917const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 918 const Type *Ty) { 919 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 920 "This is not an extending conversion!"); 921 assert(isSCEVable(Ty) && 922 "This is not a conversion to a SCEVable type!"); 923 Ty = getEffectiveSCEVType(Ty); 924 925 // Fold if the operand is constant. 926 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 927 const Type *IntTy = getEffectiveSCEVType(Ty); 928 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 929 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 930 return getConstant(cast<ConstantInt>(C)); 931 } 932 933 // sext(sext(x)) --> sext(x) 934 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 935 return getSignExtendExpr(SS->getOperand(), Ty); 936 937 // Before doing any expensive analysis, check to see if we've already 938 // computed a SCEV for this Op and Ty. 939 FoldingSetNodeID ID; 940 ID.AddInteger(scSignExtend); 941 ID.AddPointer(Op); 942 ID.AddPointer(Ty); 943 void *IP = 0; 944 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 945 946 // If the input value is a chrec scev, and we can prove that the value 947 // did not overflow the old, smaller, value, we can sign extend all of the 948 // operands (often constants). This allows analysis of something like 949 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 950 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 951 if (AR->isAffine()) { 952 const SCEV *Start = AR->getStart(); 953 const SCEV *Step = AR->getStepRecurrence(*this); 954 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 955 const Loop *L = AR->getLoop(); 956 957 // If we have special knowledge that this addrec won't overflow, 958 // we don't need to do any further analysis. 959 if (AR->hasNoSignedWrap()) 960 return getAddRecExpr(getSignExtendExpr(Start, Ty), 961 getSignExtendExpr(Step, Ty), 962 L); 963 964 // Check whether the backedge-taken count is SCEVCouldNotCompute. 965 // Note that this serves two purposes: It filters out loops that are 966 // simply not analyzable, and it covers the case where this code is 967 // being called from within backedge-taken count analysis, such that 968 // attempting to ask for the backedge-taken count would likely result 969 // in infinite recursion. In the later case, the analysis code will 970 // cope with a conservative value, and it will take care to purge 971 // that value once it has finished. 972 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 973 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 974 // Manually compute the final value for AR, checking for 975 // overflow. 976 977 // Check whether the backedge-taken count can be losslessly casted to 978 // the addrec's type. The count is always unsigned. 979 const SCEV *CastedMaxBECount = 980 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 981 const SCEV *RecastedMaxBECount = 982 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 983 if (MaxBECount == RecastedMaxBECount) { 984 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 985 // Check whether Start+Step*MaxBECount has no signed overflow. 986 const SCEV *SMul = 987 getMulExpr(CastedMaxBECount, 988 getTruncateOrSignExtend(Step, Start->getType())); 989 const SCEV *Add = getAddExpr(Start, SMul); 990 const SCEV *OperandExtendedAdd = 991 getAddExpr(getSignExtendExpr(Start, WideTy), 992 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 993 getSignExtendExpr(Step, WideTy))); 994 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 995 // Return the expression with the addrec on the outside. 996 return getAddRecExpr(getSignExtendExpr(Start, Ty), 997 getSignExtendExpr(Step, Ty), 998 L); 999 1000 // Similar to above, only this time treat the step value as unsigned. 1001 // This covers loops that count up with an unsigned step. 1002 const SCEV *UMul = 1003 getMulExpr(CastedMaxBECount, 1004 getTruncateOrZeroExtend(Step, Start->getType())); 1005 Add = getAddExpr(Start, UMul); 1006 OperandExtendedAdd = 1007 getAddExpr(getSignExtendExpr(Start, WideTy), 1008 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1009 getZeroExtendExpr(Step, WideTy))); 1010 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1011 // Return the expression with the addrec on the outside. 1012 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1013 getZeroExtendExpr(Step, Ty), 1014 L); 1015 } 1016 1017 // If the backedge is guarded by a comparison with the pre-inc value 1018 // the addrec is safe. Also, if the entry is guarded by a comparison 1019 // with the start value and the backedge is guarded by a comparison 1020 // with the post-inc value, the addrec is safe. 1021 if (isKnownPositive(Step)) { 1022 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1023 getSignedRange(Step).getSignedMax()); 1024 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1025 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1026 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1027 AR->getPostIncExpr(*this), N))) 1028 // Return the expression with the addrec on the outside. 1029 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1030 getSignExtendExpr(Step, Ty), 1031 L); 1032 } else if (isKnownNegative(Step)) { 1033 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1034 getSignedRange(Step).getSignedMin()); 1035 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1036 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1037 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1038 AR->getPostIncExpr(*this), N))) 1039 // Return the expression with the addrec on the outside. 1040 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1041 getSignExtendExpr(Step, Ty), 1042 L); 1043 } 1044 } 1045 } 1046 1047 // The cast wasn't folded; create an explicit cast node. 1048 // Recompute the insert position, as it may have been invalidated. 1049 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1050 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1051 new (S) SCEVSignExtendExpr(ID, Op, Ty); 1052 UniqueSCEVs.InsertNode(S, IP); 1053 return S; 1054} 1055 1056/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1057/// unspecified bits out to the given type. 1058/// 1059const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1060 const Type *Ty) { 1061 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1062 "This is not an extending conversion!"); 1063 assert(isSCEVable(Ty) && 1064 "This is not a conversion to a SCEVable type!"); 1065 Ty = getEffectiveSCEVType(Ty); 1066 1067 // Sign-extend negative constants. 1068 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1069 if (SC->getValue()->getValue().isNegative()) 1070 return getSignExtendExpr(Op, Ty); 1071 1072 // Peel off a truncate cast. 1073 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1074 const SCEV *NewOp = T->getOperand(); 1075 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1076 return getAnyExtendExpr(NewOp, Ty); 1077 return getTruncateOrNoop(NewOp, Ty); 1078 } 1079 1080 // Next try a zext cast. If the cast is folded, use it. 1081 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1082 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1083 return ZExt; 1084 1085 // Next try a sext cast. If the cast is folded, use it. 1086 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1087 if (!isa<SCEVSignExtendExpr>(SExt)) 1088 return SExt; 1089 1090 // If the expression is obviously signed, use the sext cast value. 1091 if (isa<SCEVSMaxExpr>(Op)) 1092 return SExt; 1093 1094 // Absent any other information, use the zext cast value. 1095 return ZExt; 1096} 1097 1098/// CollectAddOperandsWithScales - Process the given Ops list, which is 1099/// a list of operands to be added under the given scale, update the given 1100/// map. This is a helper function for getAddRecExpr. As an example of 1101/// what it does, given a sequence of operands that would form an add 1102/// expression like this: 1103/// 1104/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1105/// 1106/// where A and B are constants, update the map with these values: 1107/// 1108/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1109/// 1110/// and add 13 + A*B*29 to AccumulatedConstant. 1111/// This will allow getAddRecExpr to produce this: 1112/// 1113/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1114/// 1115/// This form often exposes folding opportunities that are hidden in 1116/// the original operand list. 1117/// 1118/// Return true iff it appears that any interesting folding opportunities 1119/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1120/// the common case where no interesting opportunities are present, and 1121/// is also used as a check to avoid infinite recursion. 1122/// 1123static bool 1124CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1125 SmallVector<const SCEV *, 8> &NewOps, 1126 APInt &AccumulatedConstant, 1127 const SmallVectorImpl<const SCEV *> &Ops, 1128 const APInt &Scale, 1129 ScalarEvolution &SE) { 1130 bool Interesting = false; 1131 1132 // Iterate over the add operands. 1133 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1134 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1135 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1136 APInt NewScale = 1137 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1138 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1139 // A multiplication of a constant with another add; recurse. 1140 Interesting |= 1141 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1142 cast<SCEVAddExpr>(Mul->getOperand(1)) 1143 ->getOperands(), 1144 NewScale, SE); 1145 } else { 1146 // A multiplication of a constant with some other value. Update 1147 // the map. 1148 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1149 const SCEV *Key = SE.getMulExpr(MulOps); 1150 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1151 M.insert(std::make_pair(Key, NewScale)); 1152 if (Pair.second) { 1153 NewOps.push_back(Pair.first->first); 1154 } else { 1155 Pair.first->second += NewScale; 1156 // The map already had an entry for this value, which may indicate 1157 // a folding opportunity. 1158 Interesting = true; 1159 } 1160 } 1161 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1162 // Pull a buried constant out to the outside. 1163 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1164 Interesting = true; 1165 AccumulatedConstant += Scale * C->getValue()->getValue(); 1166 } else { 1167 // An ordinary operand. Update the map. 1168 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1169 M.insert(std::make_pair(Ops[i], Scale)); 1170 if (Pair.second) { 1171 NewOps.push_back(Pair.first->first); 1172 } else { 1173 Pair.first->second += Scale; 1174 // The map already had an entry for this value, which may indicate 1175 // a folding opportunity. 1176 Interesting = true; 1177 } 1178 } 1179 } 1180 1181 return Interesting; 1182} 1183 1184namespace { 1185 struct APIntCompare { 1186 bool operator()(const APInt &LHS, const APInt &RHS) const { 1187 return LHS.ult(RHS); 1188 } 1189 }; 1190} 1191 1192/// getAddExpr - Get a canonical add expression, or something simpler if 1193/// possible. 1194const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) { 1195 assert(!Ops.empty() && "Cannot get empty add!"); 1196 if (Ops.size() == 1) return Ops[0]; 1197#ifndef NDEBUG 1198 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1199 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1200 getEffectiveSCEVType(Ops[0]->getType()) && 1201 "SCEVAddExpr operand types don't match!"); 1202#endif 1203 1204 // Sort by complexity, this groups all similar expression types together. 1205 GroupByComplexity(Ops, LI); 1206 1207 // If there are any constants, fold them together. 1208 unsigned Idx = 0; 1209 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1210 ++Idx; 1211 assert(Idx < Ops.size()); 1212 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1213 // We found two constants, fold them together! 1214 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1215 RHSC->getValue()->getValue()); 1216 if (Ops.size() == 2) return Ops[0]; 1217 Ops.erase(Ops.begin()+1); // Erase the folded element 1218 LHSC = cast<SCEVConstant>(Ops[0]); 1219 } 1220 1221 // If we are left with a constant zero being added, strip it off. 1222 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1223 Ops.erase(Ops.begin()); 1224 --Idx; 1225 } 1226 } 1227 1228 if (Ops.size() == 1) return Ops[0]; 1229 1230 // Okay, check to see if the same value occurs in the operand list twice. If 1231 // so, merge them together into an multiply expression. Since we sorted the 1232 // list, these values are required to be adjacent. 1233 const Type *Ty = Ops[0]->getType(); 1234 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1235 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1236 // Found a match, merge the two values into a multiply, and add any 1237 // remaining values to the result. 1238 const SCEV *Two = getIntegerSCEV(2, Ty); 1239 const SCEV *Mul = getMulExpr(Ops[i], Two); 1240 if (Ops.size() == 2) 1241 return Mul; 1242 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1243 Ops.push_back(Mul); 1244 return getAddExpr(Ops); 1245 } 1246 1247 // Check for truncates. If all the operands are truncated from the same 1248 // type, see if factoring out the truncate would permit the result to be 1249 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1250 // if the contents of the resulting outer trunc fold to something simple. 1251 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1252 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1253 const Type *DstType = Trunc->getType(); 1254 const Type *SrcType = Trunc->getOperand()->getType(); 1255 SmallVector<const SCEV *, 8> LargeOps; 1256 bool Ok = true; 1257 // Check all the operands to see if they can be represented in the 1258 // source type of the truncate. 1259 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1260 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1261 if (T->getOperand()->getType() != SrcType) { 1262 Ok = false; 1263 break; 1264 } 1265 LargeOps.push_back(T->getOperand()); 1266 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1267 // This could be either sign or zero extension, but sign extension 1268 // is much more likely to be foldable here. 1269 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1270 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1271 SmallVector<const SCEV *, 8> LargeMulOps; 1272 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1273 if (const SCEVTruncateExpr *T = 1274 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1275 if (T->getOperand()->getType() != SrcType) { 1276 Ok = false; 1277 break; 1278 } 1279 LargeMulOps.push_back(T->getOperand()); 1280 } else if (const SCEVConstant *C = 1281 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1282 // This could be either sign or zero extension, but sign extension 1283 // is much more likely to be foldable here. 1284 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1285 } else { 1286 Ok = false; 1287 break; 1288 } 1289 } 1290 if (Ok) 1291 LargeOps.push_back(getMulExpr(LargeMulOps)); 1292 } else { 1293 Ok = false; 1294 break; 1295 } 1296 } 1297 if (Ok) { 1298 // Evaluate the expression in the larger type. 1299 const SCEV *Fold = getAddExpr(LargeOps); 1300 // If it folds to something simple, use it. Otherwise, don't. 1301 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1302 return getTruncateExpr(Fold, DstType); 1303 } 1304 } 1305 1306 // Skip past any other cast SCEVs. 1307 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1308 ++Idx; 1309 1310 // If there are add operands they would be next. 1311 if (Idx < Ops.size()) { 1312 bool DeletedAdd = false; 1313 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1314 // If we have an add, expand the add operands onto the end of the operands 1315 // list. 1316 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1317 Ops.erase(Ops.begin()+Idx); 1318 DeletedAdd = true; 1319 } 1320 1321 // If we deleted at least one add, we added operands to the end of the list, 1322 // and they are not necessarily sorted. Recurse to resort and resimplify 1323 // any operands we just aquired. 1324 if (DeletedAdd) 1325 return getAddExpr(Ops); 1326 } 1327 1328 // Skip over the add expression until we get to a multiply. 1329 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1330 ++Idx; 1331 1332 // Check to see if there are any folding opportunities present with 1333 // operands multiplied by constant values. 1334 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1335 uint64_t BitWidth = getTypeSizeInBits(Ty); 1336 DenseMap<const SCEV *, APInt> M; 1337 SmallVector<const SCEV *, 8> NewOps; 1338 APInt AccumulatedConstant(BitWidth, 0); 1339 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1340 Ops, APInt(BitWidth, 1), *this)) { 1341 // Some interesting folding opportunity is present, so its worthwhile to 1342 // re-generate the operands list. Group the operands by constant scale, 1343 // to avoid multiplying by the same constant scale multiple times. 1344 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1345 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1346 E = NewOps.end(); I != E; ++I) 1347 MulOpLists[M.find(*I)->second].push_back(*I); 1348 // Re-generate the operands list. 1349 Ops.clear(); 1350 if (AccumulatedConstant != 0) 1351 Ops.push_back(getConstant(AccumulatedConstant)); 1352 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1353 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1354 if (I->first != 0) 1355 Ops.push_back(getMulExpr(getConstant(I->first), 1356 getAddExpr(I->second))); 1357 if (Ops.empty()) 1358 return getIntegerSCEV(0, Ty); 1359 if (Ops.size() == 1) 1360 return Ops[0]; 1361 return getAddExpr(Ops); 1362 } 1363 } 1364 1365 // If we are adding something to a multiply expression, make sure the 1366 // something is not already an operand of the multiply. If so, merge it into 1367 // the multiply. 1368 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1369 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1370 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1371 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1372 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1373 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1374 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1375 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1376 if (Mul->getNumOperands() != 2) { 1377 // If the multiply has more than two operands, we must get the 1378 // Y*Z term. 1379 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1380 MulOps.erase(MulOps.begin()+MulOp); 1381 InnerMul = getMulExpr(MulOps); 1382 } 1383 const SCEV *One = getIntegerSCEV(1, Ty); 1384 const SCEV *AddOne = getAddExpr(InnerMul, One); 1385 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1386 if (Ops.size() == 2) return OuterMul; 1387 if (AddOp < Idx) { 1388 Ops.erase(Ops.begin()+AddOp); 1389 Ops.erase(Ops.begin()+Idx-1); 1390 } else { 1391 Ops.erase(Ops.begin()+Idx); 1392 Ops.erase(Ops.begin()+AddOp-1); 1393 } 1394 Ops.push_back(OuterMul); 1395 return getAddExpr(Ops); 1396 } 1397 1398 // Check this multiply against other multiplies being added together. 1399 for (unsigned OtherMulIdx = Idx+1; 1400 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1401 ++OtherMulIdx) { 1402 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1403 // If MulOp occurs in OtherMul, we can fold the two multiplies 1404 // together. 1405 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1406 OMulOp != e; ++OMulOp) 1407 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1408 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1409 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1410 if (Mul->getNumOperands() != 2) { 1411 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1412 Mul->op_end()); 1413 MulOps.erase(MulOps.begin()+MulOp); 1414 InnerMul1 = getMulExpr(MulOps); 1415 } 1416 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1417 if (OtherMul->getNumOperands() != 2) { 1418 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1419 OtherMul->op_end()); 1420 MulOps.erase(MulOps.begin()+OMulOp); 1421 InnerMul2 = getMulExpr(MulOps); 1422 } 1423 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1424 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1425 if (Ops.size() == 2) return OuterMul; 1426 Ops.erase(Ops.begin()+Idx); 1427 Ops.erase(Ops.begin()+OtherMulIdx-1); 1428 Ops.push_back(OuterMul); 1429 return getAddExpr(Ops); 1430 } 1431 } 1432 } 1433 } 1434 1435 // If there are any add recurrences in the operands list, see if any other 1436 // added values are loop invariant. If so, we can fold them into the 1437 // recurrence. 1438 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1439 ++Idx; 1440 1441 // Scan over all recurrences, trying to fold loop invariants into them. 1442 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1443 // Scan all of the other operands to this add and add them to the vector if 1444 // they are loop invariant w.r.t. the recurrence. 1445 SmallVector<const SCEV *, 8> LIOps; 1446 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1447 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1448 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1449 LIOps.push_back(Ops[i]); 1450 Ops.erase(Ops.begin()+i); 1451 --i; --e; 1452 } 1453 1454 // If we found some loop invariants, fold them into the recurrence. 1455 if (!LIOps.empty()) { 1456 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1457 LIOps.push_back(AddRec->getStart()); 1458 1459 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1460 AddRec->op_end()); 1461 AddRecOps[0] = getAddExpr(LIOps); 1462 1463 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1464 // If all of the other operands were loop invariant, we are done. 1465 if (Ops.size() == 1) return NewRec; 1466 1467 // Otherwise, add the folded AddRec by the non-liv parts. 1468 for (unsigned i = 0;; ++i) 1469 if (Ops[i] == AddRec) { 1470 Ops[i] = NewRec; 1471 break; 1472 } 1473 return getAddExpr(Ops); 1474 } 1475 1476 // Okay, if there weren't any loop invariants to be folded, check to see if 1477 // there are multiple AddRec's with the same loop induction variable being 1478 // added together. If so, we can fold them. 1479 for (unsigned OtherIdx = Idx+1; 1480 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1481 if (OtherIdx != Idx) { 1482 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1483 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1484 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1485 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1486 AddRec->op_end()); 1487 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1488 if (i >= NewOps.size()) { 1489 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1490 OtherAddRec->op_end()); 1491 break; 1492 } 1493 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1494 } 1495 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1496 1497 if (Ops.size() == 2) return NewAddRec; 1498 1499 Ops.erase(Ops.begin()+Idx); 1500 Ops.erase(Ops.begin()+OtherIdx-1); 1501 Ops.push_back(NewAddRec); 1502 return getAddExpr(Ops); 1503 } 1504 } 1505 1506 // Otherwise couldn't fold anything into this recurrence. Move onto the 1507 // next one. 1508 } 1509 1510 // Okay, it looks like we really DO need an add expr. Check to see if we 1511 // already have one, otherwise create a new one. 1512 FoldingSetNodeID ID; 1513 ID.AddInteger(scAddExpr); 1514 ID.AddInteger(Ops.size()); 1515 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1516 ID.AddPointer(Ops[i]); 1517 void *IP = 0; 1518 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1519 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1520 new (S) SCEVAddExpr(ID, Ops); 1521 UniqueSCEVs.InsertNode(S, IP); 1522 return S; 1523} 1524 1525 1526/// getMulExpr - Get a canonical multiply expression, or something simpler if 1527/// possible. 1528const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) { 1529 assert(!Ops.empty() && "Cannot get empty mul!"); 1530#ifndef NDEBUG 1531 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1532 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1533 getEffectiveSCEVType(Ops[0]->getType()) && 1534 "SCEVMulExpr operand types don't match!"); 1535#endif 1536 1537 // Sort by complexity, this groups all similar expression types together. 1538 GroupByComplexity(Ops, LI); 1539 1540 // If there are any constants, fold them together. 1541 unsigned Idx = 0; 1542 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1543 1544 // C1*(C2+V) -> C1*C2 + C1*V 1545 if (Ops.size() == 2) 1546 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1547 if (Add->getNumOperands() == 2 && 1548 isa<SCEVConstant>(Add->getOperand(0))) 1549 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1550 getMulExpr(LHSC, Add->getOperand(1))); 1551 1552 1553 ++Idx; 1554 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1555 // We found two constants, fold them together! 1556 ConstantInt *Fold = ConstantInt::get(getContext(), 1557 LHSC->getValue()->getValue() * 1558 RHSC->getValue()->getValue()); 1559 Ops[0] = getConstant(Fold); 1560 Ops.erase(Ops.begin()+1); // Erase the folded element 1561 if (Ops.size() == 1) return Ops[0]; 1562 LHSC = cast<SCEVConstant>(Ops[0]); 1563 } 1564 1565 // If we are left with a constant one being multiplied, strip it off. 1566 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1567 Ops.erase(Ops.begin()); 1568 --Idx; 1569 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1570 // If we have a multiply of zero, it will always be zero. 1571 return Ops[0]; 1572 } 1573 } 1574 1575 // Skip over the add expression until we get to a multiply. 1576 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1577 ++Idx; 1578 1579 if (Ops.size() == 1) 1580 return Ops[0]; 1581 1582 // If there are mul operands inline them all into this expression. 1583 if (Idx < Ops.size()) { 1584 bool DeletedMul = false; 1585 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1586 // If we have an mul, expand the mul operands onto the end of the operands 1587 // list. 1588 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1589 Ops.erase(Ops.begin()+Idx); 1590 DeletedMul = true; 1591 } 1592 1593 // If we deleted at least one mul, we added operands to the end of the list, 1594 // and they are not necessarily sorted. Recurse to resort and resimplify 1595 // any operands we just aquired. 1596 if (DeletedMul) 1597 return getMulExpr(Ops); 1598 } 1599 1600 // If there are any add recurrences in the operands list, see if any other 1601 // added values are loop invariant. If so, we can fold them into the 1602 // recurrence. 1603 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1604 ++Idx; 1605 1606 // Scan over all recurrences, trying to fold loop invariants into them. 1607 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1608 // Scan all of the other operands to this mul and add them to the vector if 1609 // they are loop invariant w.r.t. the recurrence. 1610 SmallVector<const SCEV *, 8> LIOps; 1611 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1612 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1613 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1614 LIOps.push_back(Ops[i]); 1615 Ops.erase(Ops.begin()+i); 1616 --i; --e; 1617 } 1618 1619 // If we found some loop invariants, fold them into the recurrence. 1620 if (!LIOps.empty()) { 1621 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1622 SmallVector<const SCEV *, 4> NewOps; 1623 NewOps.reserve(AddRec->getNumOperands()); 1624 if (LIOps.size() == 1) { 1625 const SCEV *Scale = LIOps[0]; 1626 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1627 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1628 } else { 1629 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1630 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1631 MulOps.push_back(AddRec->getOperand(i)); 1632 NewOps.push_back(getMulExpr(MulOps)); 1633 } 1634 } 1635 1636 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1637 1638 // If all of the other operands were loop invariant, we are done. 1639 if (Ops.size() == 1) return NewRec; 1640 1641 // Otherwise, multiply the folded AddRec by the non-liv parts. 1642 for (unsigned i = 0;; ++i) 1643 if (Ops[i] == AddRec) { 1644 Ops[i] = NewRec; 1645 break; 1646 } 1647 return getMulExpr(Ops); 1648 } 1649 1650 // Okay, if there weren't any loop invariants to be folded, check to see if 1651 // there are multiple AddRec's with the same loop induction variable being 1652 // multiplied together. If so, we can fold them. 1653 for (unsigned OtherIdx = Idx+1; 1654 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1655 if (OtherIdx != Idx) { 1656 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1657 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1658 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1659 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1660 const SCEV *NewStart = getMulExpr(F->getStart(), 1661 G->getStart()); 1662 const SCEV *B = F->getStepRecurrence(*this); 1663 const SCEV *D = G->getStepRecurrence(*this); 1664 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1665 getMulExpr(G, B), 1666 getMulExpr(B, D)); 1667 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1668 F->getLoop()); 1669 if (Ops.size() == 2) return NewAddRec; 1670 1671 Ops.erase(Ops.begin()+Idx); 1672 Ops.erase(Ops.begin()+OtherIdx-1); 1673 Ops.push_back(NewAddRec); 1674 return getMulExpr(Ops); 1675 } 1676 } 1677 1678 // Otherwise couldn't fold anything into this recurrence. Move onto the 1679 // next one. 1680 } 1681 1682 // Okay, it looks like we really DO need an mul expr. Check to see if we 1683 // already have one, otherwise create a new one. 1684 FoldingSetNodeID ID; 1685 ID.AddInteger(scMulExpr); 1686 ID.AddInteger(Ops.size()); 1687 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1688 ID.AddPointer(Ops[i]); 1689 void *IP = 0; 1690 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1691 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1692 new (S) SCEVMulExpr(ID, Ops); 1693 UniqueSCEVs.InsertNode(S, IP); 1694 return S; 1695} 1696 1697/// getUDivExpr - Get a canonical unsigned division expression, or something 1698/// simpler if possible. 1699const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1700 const SCEV *RHS) { 1701 assert(getEffectiveSCEVType(LHS->getType()) == 1702 getEffectiveSCEVType(RHS->getType()) && 1703 "SCEVUDivExpr operand types don't match!"); 1704 1705 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1706 if (RHSC->getValue()->equalsInt(1)) 1707 return LHS; // X udiv 1 --> x 1708 if (RHSC->isZero()) 1709 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1710 1711 // Determine if the division can be folded into the operands of 1712 // its operands. 1713 // TODO: Generalize this to non-constants by using known-bits information. 1714 const Type *Ty = LHS->getType(); 1715 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1716 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1717 // For non-power-of-two values, effectively round the value up to the 1718 // nearest power of two. 1719 if (!RHSC->getValue()->getValue().isPowerOf2()) 1720 ++MaxShiftAmt; 1721 const IntegerType *ExtTy = 1722 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1723 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1724 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1725 if (const SCEVConstant *Step = 1726 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1727 if (!Step->getValue()->getValue() 1728 .urem(RHSC->getValue()->getValue()) && 1729 getZeroExtendExpr(AR, ExtTy) == 1730 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1731 getZeroExtendExpr(Step, ExtTy), 1732 AR->getLoop())) { 1733 SmallVector<const SCEV *, 4> Operands; 1734 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1735 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1736 return getAddRecExpr(Operands, AR->getLoop()); 1737 } 1738 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1739 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1740 SmallVector<const SCEV *, 4> Operands; 1741 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1742 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1743 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1744 // Find an operand that's safely divisible. 1745 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1746 const SCEV *Op = M->getOperand(i); 1747 const SCEV *Div = getUDivExpr(Op, RHSC); 1748 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1749 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1750 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1751 MOperands.end()); 1752 Operands[i] = Div; 1753 return getMulExpr(Operands); 1754 } 1755 } 1756 } 1757 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1758 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1759 SmallVector<const SCEV *, 4> Operands; 1760 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1761 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1762 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1763 Operands.clear(); 1764 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1765 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1766 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1767 break; 1768 Operands.push_back(Op); 1769 } 1770 if (Operands.size() == A->getNumOperands()) 1771 return getAddExpr(Operands); 1772 } 1773 } 1774 1775 // Fold if both operands are constant. 1776 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1777 Constant *LHSCV = LHSC->getValue(); 1778 Constant *RHSCV = RHSC->getValue(); 1779 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1780 RHSCV))); 1781 } 1782 } 1783 1784 FoldingSetNodeID ID; 1785 ID.AddInteger(scUDivExpr); 1786 ID.AddPointer(LHS); 1787 ID.AddPointer(RHS); 1788 void *IP = 0; 1789 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1790 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1791 new (S) SCEVUDivExpr(ID, LHS, RHS); 1792 UniqueSCEVs.InsertNode(S, IP); 1793 return S; 1794} 1795 1796 1797/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1798/// Simplify the expression as much as possible. 1799const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1800 const SCEV *Step, const Loop *L) { 1801 SmallVector<const SCEV *, 4> Operands; 1802 Operands.push_back(Start); 1803 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1804 if (StepChrec->getLoop() == L) { 1805 Operands.insert(Operands.end(), StepChrec->op_begin(), 1806 StepChrec->op_end()); 1807 return getAddRecExpr(Operands, L); 1808 } 1809 1810 Operands.push_back(Step); 1811 return getAddRecExpr(Operands, L); 1812} 1813 1814/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1815/// Simplify the expression as much as possible. 1816const SCEV * 1817ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1818 const Loop *L) { 1819 if (Operands.size() == 1) return Operands[0]; 1820#ifndef NDEBUG 1821 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1822 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1823 getEffectiveSCEVType(Operands[0]->getType()) && 1824 "SCEVAddRecExpr operand types don't match!"); 1825#endif 1826 1827 if (Operands.back()->isZero()) { 1828 Operands.pop_back(); 1829 return getAddRecExpr(Operands, L); // {X,+,0} --> X 1830 } 1831 1832 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1833 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1834 const Loop* NestedLoop = NestedAR->getLoop(); 1835 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1836 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1837 NestedAR->op_end()); 1838 Operands[0] = NestedAR->getStart(); 1839 // AddRecs require their operands be loop-invariant with respect to their 1840 // loops. Don't perform this transformation if it would break this 1841 // requirement. 1842 bool AllInvariant = true; 1843 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1844 if (!Operands[i]->isLoopInvariant(L)) { 1845 AllInvariant = false; 1846 break; 1847 } 1848 if (AllInvariant) { 1849 NestedOperands[0] = getAddRecExpr(Operands, L); 1850 AllInvariant = true; 1851 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1852 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1853 AllInvariant = false; 1854 break; 1855 } 1856 if (AllInvariant) 1857 // Ok, both add recurrences are valid after the transformation. 1858 return getAddRecExpr(NestedOperands, NestedLoop); 1859 } 1860 // Reset Operands to its original state. 1861 Operands[0] = NestedAR; 1862 } 1863 } 1864 1865 FoldingSetNodeID ID; 1866 ID.AddInteger(scAddRecExpr); 1867 ID.AddInteger(Operands.size()); 1868 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1869 ID.AddPointer(Operands[i]); 1870 ID.AddPointer(L); 1871 void *IP = 0; 1872 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1873 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1874 new (S) SCEVAddRecExpr(ID, Operands, L); 1875 UniqueSCEVs.InsertNode(S, IP); 1876 return S; 1877} 1878 1879const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1880 const SCEV *RHS) { 1881 SmallVector<const SCEV *, 2> Ops; 1882 Ops.push_back(LHS); 1883 Ops.push_back(RHS); 1884 return getSMaxExpr(Ops); 1885} 1886 1887const SCEV * 1888ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1889 assert(!Ops.empty() && "Cannot get empty smax!"); 1890 if (Ops.size() == 1) return Ops[0]; 1891#ifndef NDEBUG 1892 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1893 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1894 getEffectiveSCEVType(Ops[0]->getType()) && 1895 "SCEVSMaxExpr operand types don't match!"); 1896#endif 1897 1898 // Sort by complexity, this groups all similar expression types together. 1899 GroupByComplexity(Ops, LI); 1900 1901 // If there are any constants, fold them together. 1902 unsigned Idx = 0; 1903 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1904 ++Idx; 1905 assert(Idx < Ops.size()); 1906 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1907 // We found two constants, fold them together! 1908 ConstantInt *Fold = ConstantInt::get(getContext(), 1909 APIntOps::smax(LHSC->getValue()->getValue(), 1910 RHSC->getValue()->getValue())); 1911 Ops[0] = getConstant(Fold); 1912 Ops.erase(Ops.begin()+1); // Erase the folded element 1913 if (Ops.size() == 1) return Ops[0]; 1914 LHSC = cast<SCEVConstant>(Ops[0]); 1915 } 1916 1917 // If we are left with a constant minimum-int, strip it off. 1918 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1919 Ops.erase(Ops.begin()); 1920 --Idx; 1921 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1922 // If we have an smax with a constant maximum-int, it will always be 1923 // maximum-int. 1924 return Ops[0]; 1925 } 1926 } 1927 1928 if (Ops.size() == 1) return Ops[0]; 1929 1930 // Find the first SMax 1931 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1932 ++Idx; 1933 1934 // Check to see if one of the operands is an SMax. If so, expand its operands 1935 // onto our operand list, and recurse to simplify. 1936 if (Idx < Ops.size()) { 1937 bool DeletedSMax = false; 1938 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1939 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1940 Ops.erase(Ops.begin()+Idx); 1941 DeletedSMax = true; 1942 } 1943 1944 if (DeletedSMax) 1945 return getSMaxExpr(Ops); 1946 } 1947 1948 // Okay, check to see if the same value occurs in the operand list twice. If 1949 // so, delete one. Since we sorted the list, these values are required to 1950 // be adjacent. 1951 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1952 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1953 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1954 --i; --e; 1955 } 1956 1957 if (Ops.size() == 1) return Ops[0]; 1958 1959 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1960 1961 // Okay, it looks like we really DO need an smax expr. Check to see if we 1962 // already have one, otherwise create a new one. 1963 FoldingSetNodeID ID; 1964 ID.AddInteger(scSMaxExpr); 1965 ID.AddInteger(Ops.size()); 1966 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1967 ID.AddPointer(Ops[i]); 1968 void *IP = 0; 1969 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1970 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1971 new (S) SCEVSMaxExpr(ID, Ops); 1972 UniqueSCEVs.InsertNode(S, IP); 1973 return S; 1974} 1975 1976const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1977 const SCEV *RHS) { 1978 SmallVector<const SCEV *, 2> Ops; 1979 Ops.push_back(LHS); 1980 Ops.push_back(RHS); 1981 return getUMaxExpr(Ops); 1982} 1983 1984const SCEV * 1985ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1986 assert(!Ops.empty() && "Cannot get empty umax!"); 1987 if (Ops.size() == 1) return Ops[0]; 1988#ifndef NDEBUG 1989 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1990 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1991 getEffectiveSCEVType(Ops[0]->getType()) && 1992 "SCEVUMaxExpr operand types don't match!"); 1993#endif 1994 1995 // Sort by complexity, this groups all similar expression types together. 1996 GroupByComplexity(Ops, LI); 1997 1998 // If there are any constants, fold them together. 1999 unsigned Idx = 0; 2000 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2001 ++Idx; 2002 assert(Idx < Ops.size()); 2003 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2004 // We found two constants, fold them together! 2005 ConstantInt *Fold = ConstantInt::get(getContext(), 2006 APIntOps::umax(LHSC->getValue()->getValue(), 2007 RHSC->getValue()->getValue())); 2008 Ops[0] = getConstant(Fold); 2009 Ops.erase(Ops.begin()+1); // Erase the folded element 2010 if (Ops.size() == 1) return Ops[0]; 2011 LHSC = cast<SCEVConstant>(Ops[0]); 2012 } 2013 2014 // If we are left with a constant minimum-int, strip it off. 2015 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2016 Ops.erase(Ops.begin()); 2017 --Idx; 2018 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2019 // If we have an umax with a constant maximum-int, it will always be 2020 // maximum-int. 2021 return Ops[0]; 2022 } 2023 } 2024 2025 if (Ops.size() == 1) return Ops[0]; 2026 2027 // Find the first UMax 2028 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2029 ++Idx; 2030 2031 // Check to see if one of the operands is a UMax. If so, expand its operands 2032 // onto our operand list, and recurse to simplify. 2033 if (Idx < Ops.size()) { 2034 bool DeletedUMax = false; 2035 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2036 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2037 Ops.erase(Ops.begin()+Idx); 2038 DeletedUMax = true; 2039 } 2040 2041 if (DeletedUMax) 2042 return getUMaxExpr(Ops); 2043 } 2044 2045 // Okay, check to see if the same value occurs in the operand list twice. If 2046 // so, delete one. Since we sorted the list, these values are required to 2047 // be adjacent. 2048 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2049 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2050 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2051 --i; --e; 2052 } 2053 2054 if (Ops.size() == 1) return Ops[0]; 2055 2056 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2057 2058 // Okay, it looks like we really DO need a umax expr. Check to see if we 2059 // already have one, otherwise create a new one. 2060 FoldingSetNodeID ID; 2061 ID.AddInteger(scUMaxExpr); 2062 ID.AddInteger(Ops.size()); 2063 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2064 ID.AddPointer(Ops[i]); 2065 void *IP = 0; 2066 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2067 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2068 new (S) SCEVUMaxExpr(ID, Ops); 2069 UniqueSCEVs.InsertNode(S, IP); 2070 return S; 2071} 2072 2073const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2074 const SCEV *RHS) { 2075 // ~smax(~x, ~y) == smin(x, y). 2076 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2077} 2078 2079const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2080 const SCEV *RHS) { 2081 // ~umax(~x, ~y) == umin(x, y) 2082 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2083} 2084 2085const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy, 2086 unsigned FieldNo) { 2087 // If we have TargetData we can determine the constant offset. 2088 if (TD) { 2089 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2090 const StructLayout &SL = *TD->getStructLayout(STy); 2091 uint64_t Offset = SL.getElementOffset(FieldNo); 2092 return getIntegerSCEV(Offset, IntPtrTy); 2093 } 2094 2095 // Field 0 is always at offset 0. 2096 if (FieldNo == 0) { 2097 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2098 return getIntegerSCEV(0, Ty); 2099 } 2100 2101 // Okay, it looks like we really DO need an offsetof expr. Check to see if we 2102 // already have one, otherwise create a new one. 2103 FoldingSetNodeID ID; 2104 ID.AddInteger(scFieldOffset); 2105 ID.AddPointer(STy); 2106 ID.AddInteger(FieldNo); 2107 void *IP = 0; 2108 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2109 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>(); 2110 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2111 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo); 2112 UniqueSCEVs.InsertNode(S, IP); 2113 return S; 2114} 2115 2116const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) { 2117 // If we have TargetData we can determine the constant size. 2118 if (TD && AllocTy->isSized()) { 2119 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2120 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy); 2121 } 2122 2123 // Expand an array size into the element size times the number 2124 // of elements. 2125 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) { 2126 const SCEV *E = getAllocSizeExpr(ATy->getElementType()); 2127 return getMulExpr( 2128 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2129 ATy->getNumElements()))); 2130 } 2131 2132 // Expand a vector size into the element size times the number 2133 // of elements. 2134 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) { 2135 const SCEV *E = getAllocSizeExpr(VTy->getElementType()); 2136 return getMulExpr( 2137 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2138 VTy->getNumElements()))); 2139 } 2140 2141 // Okay, it looks like we really DO need a sizeof expr. Check to see if we 2142 // already have one, otherwise create a new one. 2143 FoldingSetNodeID ID; 2144 ID.AddInteger(scAllocSize); 2145 ID.AddPointer(AllocTy); 2146 void *IP = 0; 2147 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2148 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>(); 2149 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2150 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy); 2151 UniqueSCEVs.InsertNode(S, IP); 2152 return S; 2153} 2154 2155const SCEV *ScalarEvolution::getUnknown(Value *V) { 2156 // Don't attempt to do anything other than create a SCEVUnknown object 2157 // here. createSCEV only calls getUnknown after checking for all other 2158 // interesting possibilities, and any other code that calls getUnknown 2159 // is doing so in order to hide a value from SCEV canonicalization. 2160 2161 FoldingSetNodeID ID; 2162 ID.AddInteger(scUnknown); 2163 ID.AddPointer(V); 2164 void *IP = 0; 2165 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2166 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2167 new (S) SCEVUnknown(ID, V); 2168 UniqueSCEVs.InsertNode(S, IP); 2169 return S; 2170} 2171 2172//===----------------------------------------------------------------------===// 2173// Basic SCEV Analysis and PHI Idiom Recognition Code 2174// 2175 2176/// isSCEVable - Test if values of the given type are analyzable within 2177/// the SCEV framework. This primarily includes integer types, and it 2178/// can optionally include pointer types if the ScalarEvolution class 2179/// has access to target-specific information. 2180bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2181 // Integers and pointers are always SCEVable. 2182 return Ty->isInteger() || isa<PointerType>(Ty); 2183} 2184 2185/// getTypeSizeInBits - Return the size in bits of the specified type, 2186/// for which isSCEVable must return true. 2187uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2188 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2189 2190 // If we have a TargetData, use it! 2191 if (TD) 2192 return TD->getTypeSizeInBits(Ty); 2193 2194 // Integer types have fixed sizes. 2195 if (Ty->isInteger()) 2196 return Ty->getPrimitiveSizeInBits(); 2197 2198 // The only other support type is pointer. Without TargetData, conservatively 2199 // assume pointers are 64-bit. 2200 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!"); 2201 return 64; 2202} 2203 2204/// getEffectiveSCEVType - Return a type with the same bitwidth as 2205/// the given type and which represents how SCEV will treat the given 2206/// type, for which isSCEVable must return true. For pointer types, 2207/// this is the pointer-sized integer type. 2208const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2209 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2210 2211 if (Ty->isInteger()) 2212 return Ty; 2213 2214 // The only other support type is pointer. 2215 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2216 if (TD) return TD->getIntPtrType(getContext()); 2217 2218 // Without TargetData, conservatively assume pointers are 64-bit. 2219 return Type::getInt64Ty(getContext()); 2220} 2221 2222const SCEV *ScalarEvolution::getCouldNotCompute() { 2223 return &CouldNotCompute; 2224} 2225 2226/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2227/// expression and create a new one. 2228const SCEV *ScalarEvolution::getSCEV(Value *V) { 2229 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2230 2231 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2232 if (I != Scalars.end()) return I->second; 2233 const SCEV *S = createSCEV(V); 2234 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2235 return S; 2236} 2237 2238/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2239/// specified signed integer value and return a SCEV for the constant. 2240const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2241 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2242 return getConstant(ConstantInt::get(ITy, Val)); 2243} 2244 2245/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2246/// 2247const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2248 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2249 return getConstant( 2250 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2251 2252 const Type *Ty = V->getType(); 2253 Ty = getEffectiveSCEVType(Ty); 2254 return getMulExpr(V, 2255 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2256} 2257 2258/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2259const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2260 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2261 return getConstant( 2262 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2263 2264 const Type *Ty = V->getType(); 2265 Ty = getEffectiveSCEVType(Ty); 2266 const SCEV *AllOnes = 2267 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2268 return getMinusSCEV(AllOnes, V); 2269} 2270 2271/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2272/// 2273const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2274 const SCEV *RHS) { 2275 // X - Y --> X + -Y 2276 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2277} 2278 2279/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2280/// input value to the specified type. If the type must be extended, it is zero 2281/// extended. 2282const SCEV * 2283ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2284 const Type *Ty) { 2285 const Type *SrcTy = V->getType(); 2286 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2287 (Ty->isInteger() || isa<PointerType>(Ty)) && 2288 "Cannot truncate or zero extend with non-integer arguments!"); 2289 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2290 return V; // No conversion 2291 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2292 return getTruncateExpr(V, Ty); 2293 return getZeroExtendExpr(V, Ty); 2294} 2295 2296/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2297/// input value to the specified type. If the type must be extended, it is sign 2298/// extended. 2299const SCEV * 2300ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2301 const Type *Ty) { 2302 const Type *SrcTy = V->getType(); 2303 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2304 (Ty->isInteger() || isa<PointerType>(Ty)) && 2305 "Cannot truncate or zero extend with non-integer arguments!"); 2306 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2307 return V; // No conversion 2308 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2309 return getTruncateExpr(V, Ty); 2310 return getSignExtendExpr(V, Ty); 2311} 2312 2313/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2314/// input value to the specified type. If the type must be extended, it is zero 2315/// extended. The conversion must not be narrowing. 2316const SCEV * 2317ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2318 const Type *SrcTy = V->getType(); 2319 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2320 (Ty->isInteger() || isa<PointerType>(Ty)) && 2321 "Cannot noop or zero extend with non-integer arguments!"); 2322 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2323 "getNoopOrZeroExtend cannot truncate!"); 2324 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2325 return V; // No conversion 2326 return getZeroExtendExpr(V, Ty); 2327} 2328 2329/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2330/// input value to the specified type. If the type must be extended, it is sign 2331/// extended. The conversion must not be narrowing. 2332const SCEV * 2333ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2334 const Type *SrcTy = V->getType(); 2335 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2336 (Ty->isInteger() || isa<PointerType>(Ty)) && 2337 "Cannot noop or sign extend with non-integer arguments!"); 2338 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2339 "getNoopOrSignExtend cannot truncate!"); 2340 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2341 return V; // No conversion 2342 return getSignExtendExpr(V, Ty); 2343} 2344 2345/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2346/// the input value to the specified type. If the type must be extended, 2347/// it is extended with unspecified bits. The conversion must not be 2348/// narrowing. 2349const SCEV * 2350ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2351 const Type *SrcTy = V->getType(); 2352 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2353 (Ty->isInteger() || isa<PointerType>(Ty)) && 2354 "Cannot noop or any extend with non-integer arguments!"); 2355 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2356 "getNoopOrAnyExtend cannot truncate!"); 2357 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2358 return V; // No conversion 2359 return getAnyExtendExpr(V, Ty); 2360} 2361 2362/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2363/// input value to the specified type. The conversion must not be widening. 2364const SCEV * 2365ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2366 const Type *SrcTy = V->getType(); 2367 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2368 (Ty->isInteger() || isa<PointerType>(Ty)) && 2369 "Cannot truncate or noop with non-integer arguments!"); 2370 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2371 "getTruncateOrNoop cannot extend!"); 2372 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2373 return V; // No conversion 2374 return getTruncateExpr(V, Ty); 2375} 2376 2377/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2378/// the types using zero-extension, and then perform a umax operation 2379/// with them. 2380const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2381 const SCEV *RHS) { 2382 const SCEV *PromotedLHS = LHS; 2383 const SCEV *PromotedRHS = RHS; 2384 2385 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2386 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2387 else 2388 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2389 2390 return getUMaxExpr(PromotedLHS, PromotedRHS); 2391} 2392 2393/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2394/// the types using zero-extension, and then perform a umin operation 2395/// with them. 2396const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2397 const SCEV *RHS) { 2398 const SCEV *PromotedLHS = LHS; 2399 const SCEV *PromotedRHS = RHS; 2400 2401 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2402 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2403 else 2404 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2405 2406 return getUMinExpr(PromotedLHS, PromotedRHS); 2407} 2408 2409/// PushDefUseChildren - Push users of the given Instruction 2410/// onto the given Worklist. 2411static void 2412PushDefUseChildren(Instruction *I, 2413 SmallVectorImpl<Instruction *> &Worklist) { 2414 // Push the def-use children onto the Worklist stack. 2415 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2416 UI != UE; ++UI) 2417 Worklist.push_back(cast<Instruction>(UI)); 2418} 2419 2420/// ForgetSymbolicValue - This looks up computed SCEV values for all 2421/// instructions that depend on the given instruction and removes them from 2422/// the Scalars map if they reference SymName. This is used during PHI 2423/// resolution. 2424void 2425ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2426 SmallVector<Instruction *, 16> Worklist; 2427 PushDefUseChildren(I, Worklist); 2428 2429 SmallPtrSet<Instruction *, 8> Visited; 2430 Visited.insert(I); 2431 while (!Worklist.empty()) { 2432 Instruction *I = Worklist.pop_back_val(); 2433 if (!Visited.insert(I)) continue; 2434 2435 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2436 Scalars.find(static_cast<Value *>(I)); 2437 if (It != Scalars.end()) { 2438 // Short-circuit the def-use traversal if the symbolic name 2439 // ceases to appear in expressions. 2440 if (!It->second->hasOperand(SymName)) 2441 continue; 2442 2443 // SCEVUnknown for a PHI either means that it has an unrecognized 2444 // structure, or it's a PHI that's in the progress of being computed 2445 // by createNodeForPHI. In the former case, additional loop trip 2446 // count information isn't going to change anything. In the later 2447 // case, createNodeForPHI will perform the necessary updates on its 2448 // own when it gets to that point. 2449 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 2450 ValuesAtScopes.erase(It->second); 2451 Scalars.erase(It); 2452 } 2453 } 2454 2455 PushDefUseChildren(I, Worklist); 2456 } 2457} 2458 2459/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2460/// a loop header, making it a potential recurrence, or it doesn't. 2461/// 2462const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2463 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2464 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2465 if (L->getHeader() == PN->getParent()) { 2466 // If it lives in the loop header, it has two incoming values, one 2467 // from outside the loop, and one from inside. 2468 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2469 unsigned BackEdge = IncomingEdge^1; 2470 2471 // While we are analyzing this PHI node, handle its value symbolically. 2472 const SCEV *SymbolicName = getUnknown(PN); 2473 assert(Scalars.find(PN) == Scalars.end() && 2474 "PHI node already processed?"); 2475 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2476 2477 // Using this symbolic name for the PHI, analyze the value coming around 2478 // the back-edge. 2479 Value *BEValueV = PN->getIncomingValue(BackEdge); 2480 const SCEV *BEValue = getSCEV(BEValueV); 2481 2482 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2483 // has a special value for the first iteration of the loop. 2484 2485 // If the value coming around the backedge is an add with the symbolic 2486 // value we just inserted, then we found a simple induction variable! 2487 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2488 // If there is a single occurrence of the symbolic value, replace it 2489 // with a recurrence. 2490 unsigned FoundIndex = Add->getNumOperands(); 2491 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2492 if (Add->getOperand(i) == SymbolicName) 2493 if (FoundIndex == e) { 2494 FoundIndex = i; 2495 break; 2496 } 2497 2498 if (FoundIndex != Add->getNumOperands()) { 2499 // Create an add with everything but the specified operand. 2500 SmallVector<const SCEV *, 8> Ops; 2501 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2502 if (i != FoundIndex) 2503 Ops.push_back(Add->getOperand(i)); 2504 const SCEV *Accum = getAddExpr(Ops); 2505 2506 // This is not a valid addrec if the step amount is varying each 2507 // loop iteration, but is not itself an addrec in this loop. 2508 if (Accum->isLoopInvariant(L) || 2509 (isa<SCEVAddRecExpr>(Accum) && 2510 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2511 const SCEV *StartVal = 2512 getSCEV(PN->getIncomingValue(IncomingEdge)); 2513 const SCEVAddRecExpr *PHISCEV = 2514 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L)); 2515 2516 // If the increment doesn't overflow, then neither the addrec nor the 2517 // post-increment will overflow. 2518 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) 2519 if (OBO->getOperand(0) == PN && 2520 getSCEV(OBO->getOperand(1)) == 2521 PHISCEV->getStepRecurrence(*this)) { 2522 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this); 2523 if (OBO->hasNoUnsignedWrap()) { 2524 const_cast<SCEVAddRecExpr *>(PHISCEV) 2525 ->setHasNoUnsignedWrap(true); 2526 const_cast<SCEVAddRecExpr *>(PostInc) 2527 ->setHasNoUnsignedWrap(true); 2528 } 2529 if (OBO->hasNoSignedWrap()) { 2530 const_cast<SCEVAddRecExpr *>(PHISCEV) 2531 ->setHasNoSignedWrap(true); 2532 const_cast<SCEVAddRecExpr *>(PostInc) 2533 ->setHasNoSignedWrap(true); 2534 } 2535 } 2536 2537 // Okay, for the entire analysis of this edge we assumed the PHI 2538 // to be symbolic. We now need to go back and purge all of the 2539 // entries for the scalars that use the symbolic expression. 2540 ForgetSymbolicName(PN, SymbolicName); 2541 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2542 return PHISCEV; 2543 } 2544 } 2545 } else if (const SCEVAddRecExpr *AddRec = 2546 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2547 // Otherwise, this could be a loop like this: 2548 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2549 // In this case, j = {1,+,1} and BEValue is j. 2550 // Because the other in-value of i (0) fits the evolution of BEValue 2551 // i really is an addrec evolution. 2552 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2553 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2554 2555 // If StartVal = j.start - j.stride, we can use StartVal as the 2556 // initial step of the addrec evolution. 2557 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2558 AddRec->getOperand(1))) { 2559 const SCEV *PHISCEV = 2560 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2561 2562 // Okay, for the entire analysis of this edge we assumed the PHI 2563 // to be symbolic. We now need to go back and purge all of the 2564 // entries for the scalars that use the symbolic expression. 2565 ForgetSymbolicName(PN, SymbolicName); 2566 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2567 return PHISCEV; 2568 } 2569 } 2570 } 2571 2572 return SymbolicName; 2573 } 2574 2575 // It's tempting to recognize PHIs with a unique incoming value, however 2576 // this leads passes like indvars to break LCSSA form. Fortunately, such 2577 // PHIs are rare, as instcombine zaps them. 2578 2579 // If it's not a loop phi, we can't handle it yet. 2580 return getUnknown(PN); 2581} 2582 2583/// createNodeForGEP - Expand GEP instructions into add and multiply 2584/// operations. This allows them to be analyzed by regular SCEV code. 2585/// 2586const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) { 2587 2588 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2589 Value *Base = GEP->getOperand(0); 2590 // Don't attempt to analyze GEPs over unsized objects. 2591 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2592 return getUnknown(GEP); 2593 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2594 gep_type_iterator GTI = gep_type_begin(GEP); 2595 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2596 E = GEP->op_end(); 2597 I != E; ++I) { 2598 Value *Index = *I; 2599 // Compute the (potentially symbolic) offset in bytes for this index. 2600 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2601 // For a struct, add the member offset. 2602 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2603 TotalOffset = getAddExpr(TotalOffset, 2604 getFieldOffsetExpr(STy, FieldNo)); 2605 } else { 2606 // For an array, add the element offset, explicitly scaled. 2607 const SCEV *LocalOffset = getSCEV(Index); 2608 if (!isa<PointerType>(LocalOffset->getType())) 2609 // Getelementptr indicies are signed. 2610 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2611 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI)); 2612 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2613 } 2614 } 2615 return getAddExpr(getSCEV(Base), TotalOffset); 2616} 2617 2618/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2619/// guaranteed to end in (at every loop iteration). It is, at the same time, 2620/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2621/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2622uint32_t 2623ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2624 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2625 return C->getValue()->getValue().countTrailingZeros(); 2626 2627 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2628 return std::min(GetMinTrailingZeros(T->getOperand()), 2629 (uint32_t)getTypeSizeInBits(T->getType())); 2630 2631 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2632 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2633 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2634 getTypeSizeInBits(E->getType()) : OpRes; 2635 } 2636 2637 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2638 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2639 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2640 getTypeSizeInBits(E->getType()) : OpRes; 2641 } 2642 2643 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2644 // The result is the min of all operands results. 2645 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2646 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2647 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2648 return MinOpRes; 2649 } 2650 2651 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2652 // The result is the sum of all operands results. 2653 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2654 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2655 for (unsigned i = 1, e = M->getNumOperands(); 2656 SumOpRes != BitWidth && i != e; ++i) 2657 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2658 BitWidth); 2659 return SumOpRes; 2660 } 2661 2662 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2663 // The result is the min of all operands results. 2664 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2665 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2666 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2667 return MinOpRes; 2668 } 2669 2670 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2671 // The result is the min of all operands results. 2672 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2673 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2674 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2675 return MinOpRes; 2676 } 2677 2678 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2679 // The result is the min of all operands results. 2680 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2681 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2682 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2683 return MinOpRes; 2684 } 2685 2686 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2687 // For a SCEVUnknown, ask ValueTracking. 2688 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2689 APInt Mask = APInt::getAllOnesValue(BitWidth); 2690 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2691 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2692 return Zeros.countTrailingOnes(); 2693 } 2694 2695 // SCEVUDivExpr 2696 return 0; 2697} 2698 2699/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2700/// 2701ConstantRange 2702ScalarEvolution::getUnsignedRange(const SCEV *S) { 2703 2704 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2705 return ConstantRange(C->getValue()->getValue()); 2706 2707 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2708 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2709 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2710 X = X.add(getUnsignedRange(Add->getOperand(i))); 2711 return X; 2712 } 2713 2714 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2715 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2716 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2717 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2718 return X; 2719 } 2720 2721 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2722 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2723 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2724 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2725 return X; 2726 } 2727 2728 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2729 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2730 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2731 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2732 return X; 2733 } 2734 2735 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2736 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2737 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2738 return X.udiv(Y); 2739 } 2740 2741 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2742 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2743 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2744 } 2745 2746 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2747 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2748 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2749 } 2750 2751 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2752 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2753 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2754 } 2755 2756 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2757 2758 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2759 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2760 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2761 if (!Trip) return FullSet; 2762 2763 // TODO: non-affine addrec 2764 if (AddRec->isAffine()) { 2765 const Type *Ty = AddRec->getType(); 2766 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2767 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2768 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2769 2770 const SCEV *Start = AddRec->getStart(); 2771 const SCEV *Step = AddRec->getStepRecurrence(*this); 2772 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2773 2774 // Check for overflow. 2775 // TODO: This is very conservative. 2776 if (!(Step->isOne() && 2777 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) && 2778 !(Step->isAllOnesValue() && 2779 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End))) 2780 return FullSet; 2781 2782 ConstantRange StartRange = getUnsignedRange(Start); 2783 ConstantRange EndRange = getUnsignedRange(End); 2784 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2785 EndRange.getUnsignedMin()); 2786 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2787 EndRange.getUnsignedMax()); 2788 if (Min.isMinValue() && Max.isMaxValue()) 2789 return FullSet; 2790 return ConstantRange(Min, Max+1); 2791 } 2792 } 2793 } 2794 2795 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2796 // For a SCEVUnknown, ask ValueTracking. 2797 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2798 APInt Mask = APInt::getAllOnesValue(BitWidth); 2799 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2800 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2801 if (Ones == ~Zeros + 1) 2802 return FullSet; 2803 return ConstantRange(Ones, ~Zeros + 1); 2804 } 2805 2806 return FullSet; 2807} 2808 2809/// getSignedRange - Determine the signed range for a particular SCEV. 2810/// 2811ConstantRange 2812ScalarEvolution::getSignedRange(const SCEV *S) { 2813 2814 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2815 return ConstantRange(C->getValue()->getValue()); 2816 2817 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2818 ConstantRange X = getSignedRange(Add->getOperand(0)); 2819 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2820 X = X.add(getSignedRange(Add->getOperand(i))); 2821 return X; 2822 } 2823 2824 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2825 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2826 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2827 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2828 return X; 2829 } 2830 2831 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2832 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2833 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2834 X = X.smax(getSignedRange(SMax->getOperand(i))); 2835 return X; 2836 } 2837 2838 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2839 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2840 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2841 X = X.umax(getSignedRange(UMax->getOperand(i))); 2842 return X; 2843 } 2844 2845 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2846 ConstantRange X = getSignedRange(UDiv->getLHS()); 2847 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2848 return X.udiv(Y); 2849 } 2850 2851 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2852 ConstantRange X = getSignedRange(ZExt->getOperand()); 2853 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2854 } 2855 2856 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2857 ConstantRange X = getSignedRange(SExt->getOperand()); 2858 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2859 } 2860 2861 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2862 ConstantRange X = getSignedRange(Trunc->getOperand()); 2863 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2864 } 2865 2866 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2867 2868 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2869 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2870 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2871 if (!Trip) return FullSet; 2872 2873 // TODO: non-affine addrec 2874 if (AddRec->isAffine()) { 2875 const Type *Ty = AddRec->getType(); 2876 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2877 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2878 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2879 2880 const SCEV *Start = AddRec->getStart(); 2881 const SCEV *Step = AddRec->getStepRecurrence(*this); 2882 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2883 2884 // Check for overflow. 2885 // TODO: This is very conservative. 2886 if (!(Step->isOne() && 2887 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2888 !(Step->isAllOnesValue() && 2889 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2890 return FullSet; 2891 2892 ConstantRange StartRange = getSignedRange(Start); 2893 ConstantRange EndRange = getSignedRange(End); 2894 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2895 EndRange.getSignedMin()); 2896 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2897 EndRange.getSignedMax()); 2898 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2899 return FullSet; 2900 return ConstantRange(Min, Max+1); 2901 } 2902 } 2903 } 2904 2905 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2906 // For a SCEVUnknown, ask ValueTracking. 2907 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2908 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2909 if (NS == 1) 2910 return FullSet; 2911 return 2912 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2913 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2914 } 2915 2916 return FullSet; 2917} 2918 2919/// createSCEV - We know that there is no SCEV for the specified value. 2920/// Analyze the expression. 2921/// 2922const SCEV *ScalarEvolution::createSCEV(Value *V) { 2923 if (!isSCEVable(V->getType())) 2924 return getUnknown(V); 2925 2926 unsigned Opcode = Instruction::UserOp1; 2927 if (Instruction *I = dyn_cast<Instruction>(V)) 2928 Opcode = I->getOpcode(); 2929 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2930 Opcode = CE->getOpcode(); 2931 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2932 return getConstant(CI); 2933 else if (isa<ConstantPointerNull>(V)) 2934 return getIntegerSCEV(0, V->getType()); 2935 else if (isa<UndefValue>(V)) 2936 return getIntegerSCEV(0, V->getType()); 2937 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 2938 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 2939 else 2940 return getUnknown(V); 2941 2942 Operator *U = cast<Operator>(V); 2943 switch (Opcode) { 2944 case Instruction::Add: 2945 return getAddExpr(getSCEV(U->getOperand(0)), 2946 getSCEV(U->getOperand(1))); 2947 case Instruction::Mul: 2948 return getMulExpr(getSCEV(U->getOperand(0)), 2949 getSCEV(U->getOperand(1))); 2950 case Instruction::UDiv: 2951 return getUDivExpr(getSCEV(U->getOperand(0)), 2952 getSCEV(U->getOperand(1))); 2953 case Instruction::Sub: 2954 return getMinusSCEV(getSCEV(U->getOperand(0)), 2955 getSCEV(U->getOperand(1))); 2956 case Instruction::And: 2957 // For an expression like x&255 that merely masks off the high bits, 2958 // use zext(trunc(x)) as the SCEV expression. 2959 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2960 if (CI->isNullValue()) 2961 return getSCEV(U->getOperand(1)); 2962 if (CI->isAllOnesValue()) 2963 return getSCEV(U->getOperand(0)); 2964 const APInt &A = CI->getValue(); 2965 2966 // Instcombine's ShrinkDemandedConstant may strip bits out of 2967 // constants, obscuring what would otherwise be a low-bits mask. 2968 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2969 // knew about to reconstruct a low-bits mask value. 2970 unsigned LZ = A.countLeadingZeros(); 2971 unsigned BitWidth = A.getBitWidth(); 2972 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2973 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2974 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2975 2976 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2977 2978 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2979 return 2980 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2981 IntegerType::get(getContext(), BitWidth - LZ)), 2982 U->getType()); 2983 } 2984 break; 2985 2986 case Instruction::Or: 2987 // If the RHS of the Or is a constant, we may have something like: 2988 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 2989 // optimizations will transparently handle this case. 2990 // 2991 // In order for this transformation to be safe, the LHS must be of the 2992 // form X*(2^n) and the Or constant must be less than 2^n. 2993 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2994 const SCEV *LHS = getSCEV(U->getOperand(0)); 2995 const APInt &CIVal = CI->getValue(); 2996 if (GetMinTrailingZeros(LHS) >= 2997 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 2998 // Build a plain add SCEV. 2999 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3000 // If the LHS of the add was an addrec and it has no-wrap flags, 3001 // transfer the no-wrap flags, since an or won't introduce a wrap. 3002 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3003 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3004 if (OldAR->hasNoUnsignedWrap()) 3005 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3006 if (OldAR->hasNoSignedWrap()) 3007 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3008 } 3009 return S; 3010 } 3011 } 3012 break; 3013 case Instruction::Xor: 3014 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3015 // If the RHS of the xor is a signbit, then this is just an add. 3016 // Instcombine turns add of signbit into xor as a strength reduction step. 3017 if (CI->getValue().isSignBit()) 3018 return getAddExpr(getSCEV(U->getOperand(0)), 3019 getSCEV(U->getOperand(1))); 3020 3021 // If the RHS of xor is -1, then this is a not operation. 3022 if (CI->isAllOnesValue()) 3023 return getNotSCEV(getSCEV(U->getOperand(0))); 3024 3025 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3026 // This is a variant of the check for xor with -1, and it handles 3027 // the case where instcombine has trimmed non-demanded bits out 3028 // of an xor with -1. 3029 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3030 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3031 if (BO->getOpcode() == Instruction::And && 3032 LCI->getValue() == CI->getValue()) 3033 if (const SCEVZeroExtendExpr *Z = 3034 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3035 const Type *UTy = U->getType(); 3036 const SCEV *Z0 = Z->getOperand(); 3037 const Type *Z0Ty = Z0->getType(); 3038 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3039 3040 // If C is a low-bits mask, the zero extend is zerving to 3041 // mask off the high bits. Complement the operand and 3042 // re-apply the zext. 3043 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3044 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3045 3046 // If C is a single bit, it may be in the sign-bit position 3047 // before the zero-extend. In this case, represent the xor 3048 // using an add, which is equivalent, and re-apply the zext. 3049 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3050 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3051 Trunc.isSignBit()) 3052 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3053 UTy); 3054 } 3055 } 3056 break; 3057 3058 case Instruction::Shl: 3059 // Turn shift left of a constant amount into a multiply. 3060 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3061 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3062 Constant *X = ConstantInt::get(getContext(), 3063 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3064 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3065 } 3066 break; 3067 3068 case Instruction::LShr: 3069 // Turn logical shift right of a constant into a unsigned divide. 3070 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3071 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3072 Constant *X = ConstantInt::get(getContext(), 3073 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3074 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3075 } 3076 break; 3077 3078 case Instruction::AShr: 3079 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3080 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3081 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3082 if (L->getOpcode() == Instruction::Shl && 3083 L->getOperand(1) == U->getOperand(1)) { 3084 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3085 uint64_t Amt = BitWidth - CI->getZExtValue(); 3086 if (Amt == BitWidth) 3087 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3088 if (Amt > BitWidth) 3089 return getIntegerSCEV(0, U->getType()); // value is undefined 3090 return 3091 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3092 IntegerType::get(getContext(), Amt)), 3093 U->getType()); 3094 } 3095 break; 3096 3097 case Instruction::Trunc: 3098 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3099 3100 case Instruction::ZExt: 3101 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3102 3103 case Instruction::SExt: 3104 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3105 3106 case Instruction::BitCast: 3107 // BitCasts are no-op casts so we just eliminate the cast. 3108 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3109 return getSCEV(U->getOperand(0)); 3110 break; 3111 3112 // It's tempting to handle inttoptr and ptrtoint, however this can 3113 // lead to pointer expressions which cannot be expanded to GEPs 3114 // (because they may overflow). For now, the only pointer-typed 3115 // expressions we handle are GEPs and address literals. 3116 3117 case Instruction::GetElementPtr: 3118 return createNodeForGEP(U); 3119 3120 case Instruction::PHI: 3121 return createNodeForPHI(cast<PHINode>(U)); 3122 3123 case Instruction::Select: 3124 // This could be a smax or umax that was lowered earlier. 3125 // Try to recover it. 3126 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3127 Value *LHS = ICI->getOperand(0); 3128 Value *RHS = ICI->getOperand(1); 3129 switch (ICI->getPredicate()) { 3130 case ICmpInst::ICMP_SLT: 3131 case ICmpInst::ICMP_SLE: 3132 std::swap(LHS, RHS); 3133 // fall through 3134 case ICmpInst::ICMP_SGT: 3135 case ICmpInst::ICMP_SGE: 3136 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3137 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3138 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3139 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3140 break; 3141 case ICmpInst::ICMP_ULT: 3142 case ICmpInst::ICMP_ULE: 3143 std::swap(LHS, RHS); 3144 // fall through 3145 case ICmpInst::ICMP_UGT: 3146 case ICmpInst::ICMP_UGE: 3147 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3148 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3149 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3150 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3151 break; 3152 case ICmpInst::ICMP_NE: 3153 // n != 0 ? n : 1 -> umax(n, 1) 3154 if (LHS == U->getOperand(1) && 3155 isa<ConstantInt>(U->getOperand(2)) && 3156 cast<ConstantInt>(U->getOperand(2))->isOne() && 3157 isa<ConstantInt>(RHS) && 3158 cast<ConstantInt>(RHS)->isZero()) 3159 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3160 break; 3161 case ICmpInst::ICMP_EQ: 3162 // n == 0 ? 1 : n -> umax(n, 1) 3163 if (LHS == U->getOperand(2) && 3164 isa<ConstantInt>(U->getOperand(1)) && 3165 cast<ConstantInt>(U->getOperand(1))->isOne() && 3166 isa<ConstantInt>(RHS) && 3167 cast<ConstantInt>(RHS)->isZero()) 3168 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3169 break; 3170 default: 3171 break; 3172 } 3173 } 3174 3175 default: // We cannot analyze this expression. 3176 break; 3177 } 3178 3179 return getUnknown(V); 3180} 3181 3182 3183 3184//===----------------------------------------------------------------------===// 3185// Iteration Count Computation Code 3186// 3187 3188/// getBackedgeTakenCount - If the specified loop has a predictable 3189/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3190/// object. The backedge-taken count is the number of times the loop header 3191/// will be branched to from within the loop. This is one less than the 3192/// trip count of the loop, since it doesn't count the first iteration, 3193/// when the header is branched to from outside the loop. 3194/// 3195/// Note that it is not valid to call this method on a loop without a 3196/// loop-invariant backedge-taken count (see 3197/// hasLoopInvariantBackedgeTakenCount). 3198/// 3199const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3200 return getBackedgeTakenInfo(L).Exact; 3201} 3202 3203/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3204/// return the least SCEV value that is known never to be less than the 3205/// actual backedge taken count. 3206const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3207 return getBackedgeTakenInfo(L).Max; 3208} 3209 3210/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3211/// onto the given Worklist. 3212static void 3213PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3214 BasicBlock *Header = L->getHeader(); 3215 3216 // Push all Loop-header PHIs onto the Worklist stack. 3217 for (BasicBlock::iterator I = Header->begin(); 3218 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3219 Worklist.push_back(PN); 3220} 3221 3222const ScalarEvolution::BackedgeTakenInfo & 3223ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3224 // Initially insert a CouldNotCompute for this loop. If the insertion 3225 // succeeds, procede to actually compute a backedge-taken count and 3226 // update the value. The temporary CouldNotCompute value tells SCEV 3227 // code elsewhere that it shouldn't attempt to request a new 3228 // backedge-taken count, which could result in infinite recursion. 3229 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3230 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3231 if (Pair.second) { 3232 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3233 if (ItCount.Exact != getCouldNotCompute()) { 3234 assert(ItCount.Exact->isLoopInvariant(L) && 3235 ItCount.Max->isLoopInvariant(L) && 3236 "Computed trip count isn't loop invariant for loop!"); 3237 ++NumTripCountsComputed; 3238 3239 // Update the value in the map. 3240 Pair.first->second = ItCount; 3241 } else { 3242 if (ItCount.Max != getCouldNotCompute()) 3243 // Update the value in the map. 3244 Pair.first->second = ItCount; 3245 if (isa<PHINode>(L->getHeader()->begin())) 3246 // Only count loops that have phi nodes as not being computable. 3247 ++NumTripCountsNotComputed; 3248 } 3249 3250 // Now that we know more about the trip count for this loop, forget any 3251 // existing SCEV values for PHI nodes in this loop since they are only 3252 // conservative estimates made without the benefit of trip count 3253 // information. This is similar to the code in 3254 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3255 // nodes specially. 3256 if (ItCount.hasAnyInfo()) { 3257 SmallVector<Instruction *, 16> Worklist; 3258 PushLoopPHIs(L, Worklist); 3259 3260 SmallPtrSet<Instruction *, 8> Visited; 3261 while (!Worklist.empty()) { 3262 Instruction *I = Worklist.pop_back_val(); 3263 if (!Visited.insert(I)) continue; 3264 3265 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3266 Scalars.find(static_cast<Value *>(I)); 3267 if (It != Scalars.end()) { 3268 // SCEVUnknown for a PHI either means that it has an unrecognized 3269 // structure, or it's a PHI that's in the progress of being computed 3270 // by createNodeForPHI. In the former case, additional loop trip 3271 // count information isn't going to change anything. In the later 3272 // case, createNodeForPHI will perform the necessary updates on its 3273 // own when it gets to that point. 3274 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3275 ValuesAtScopes.erase(It->second); 3276 Scalars.erase(It); 3277 } 3278 if (PHINode *PN = dyn_cast<PHINode>(I)) 3279 ConstantEvolutionLoopExitValue.erase(PN); 3280 } 3281 3282 PushDefUseChildren(I, Worklist); 3283 } 3284 } 3285 } 3286 return Pair.first->second; 3287} 3288 3289/// forgetLoopBackedgeTakenCount - This method should be called by the 3290/// client when it has changed a loop in a way that may effect 3291/// ScalarEvolution's ability to compute a trip count, or if the loop 3292/// is deleted. 3293void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3294 BackedgeTakenCounts.erase(L); 3295 3296 SmallVector<Instruction *, 16> Worklist; 3297 PushLoopPHIs(L, Worklist); 3298 3299 SmallPtrSet<Instruction *, 8> Visited; 3300 while (!Worklist.empty()) { 3301 Instruction *I = Worklist.pop_back_val(); 3302 if (!Visited.insert(I)) continue; 3303 3304 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3305 Scalars.find(static_cast<Value *>(I)); 3306 if (It != Scalars.end()) { 3307 ValuesAtScopes.erase(It->second); 3308 Scalars.erase(It); 3309 if (PHINode *PN = dyn_cast<PHINode>(I)) 3310 ConstantEvolutionLoopExitValue.erase(PN); 3311 } 3312 3313 PushDefUseChildren(I, Worklist); 3314 } 3315} 3316 3317/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3318/// of the specified loop will execute. 3319ScalarEvolution::BackedgeTakenInfo 3320ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3321 SmallVector<BasicBlock*, 8> ExitingBlocks; 3322 L->getExitingBlocks(ExitingBlocks); 3323 3324 // Examine all exits and pick the most conservative values. 3325 const SCEV *BECount = getCouldNotCompute(); 3326 const SCEV *MaxBECount = getCouldNotCompute(); 3327 bool CouldNotComputeBECount = false; 3328 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3329 BackedgeTakenInfo NewBTI = 3330 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3331 3332 if (NewBTI.Exact == getCouldNotCompute()) { 3333 // We couldn't compute an exact value for this exit, so 3334 // we won't be able to compute an exact value for the loop. 3335 CouldNotComputeBECount = true; 3336 BECount = getCouldNotCompute(); 3337 } else if (!CouldNotComputeBECount) { 3338 if (BECount == getCouldNotCompute()) 3339 BECount = NewBTI.Exact; 3340 else 3341 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3342 } 3343 if (MaxBECount == getCouldNotCompute()) 3344 MaxBECount = NewBTI.Max; 3345 else if (NewBTI.Max != getCouldNotCompute()) 3346 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3347 } 3348 3349 return BackedgeTakenInfo(BECount, MaxBECount); 3350} 3351 3352/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3353/// of the specified loop will execute if it exits via the specified block. 3354ScalarEvolution::BackedgeTakenInfo 3355ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3356 BasicBlock *ExitingBlock) { 3357 3358 // Okay, we've chosen an exiting block. See what condition causes us to 3359 // exit at this block. 3360 // 3361 // FIXME: we should be able to handle switch instructions (with a single exit) 3362 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3363 if (ExitBr == 0) return getCouldNotCompute(); 3364 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3365 3366 // At this point, we know we have a conditional branch that determines whether 3367 // the loop is exited. However, we don't know if the branch is executed each 3368 // time through the loop. If not, then the execution count of the branch will 3369 // not be equal to the trip count of the loop. 3370 // 3371 // Currently we check for this by checking to see if the Exit branch goes to 3372 // the loop header. If so, we know it will always execute the same number of 3373 // times as the loop. We also handle the case where the exit block *is* the 3374 // loop header. This is common for un-rotated loops. 3375 // 3376 // If both of those tests fail, walk up the unique predecessor chain to the 3377 // header, stopping if there is an edge that doesn't exit the loop. If the 3378 // header is reached, the execution count of the branch will be equal to the 3379 // trip count of the loop. 3380 // 3381 // More extensive analysis could be done to handle more cases here. 3382 // 3383 if (ExitBr->getSuccessor(0) != L->getHeader() && 3384 ExitBr->getSuccessor(1) != L->getHeader() && 3385 ExitBr->getParent() != L->getHeader()) { 3386 // The simple checks failed, try climbing the unique predecessor chain 3387 // up to the header. 3388 bool Ok = false; 3389 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3390 BasicBlock *Pred = BB->getUniquePredecessor(); 3391 if (!Pred) 3392 return getCouldNotCompute(); 3393 TerminatorInst *PredTerm = Pred->getTerminator(); 3394 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3395 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3396 if (PredSucc == BB) 3397 continue; 3398 // If the predecessor has a successor that isn't BB and isn't 3399 // outside the loop, assume the worst. 3400 if (L->contains(PredSucc)) 3401 return getCouldNotCompute(); 3402 } 3403 if (Pred == L->getHeader()) { 3404 Ok = true; 3405 break; 3406 } 3407 BB = Pred; 3408 } 3409 if (!Ok) 3410 return getCouldNotCompute(); 3411 } 3412 3413 // Procede to the next level to examine the exit condition expression. 3414 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3415 ExitBr->getSuccessor(0), 3416 ExitBr->getSuccessor(1)); 3417} 3418 3419/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3420/// backedge of the specified loop will execute if its exit condition 3421/// were a conditional branch of ExitCond, TBB, and FBB. 3422ScalarEvolution::BackedgeTakenInfo 3423ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3424 Value *ExitCond, 3425 BasicBlock *TBB, 3426 BasicBlock *FBB) { 3427 // Check if the controlling expression for this loop is an And or Or. 3428 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3429 if (BO->getOpcode() == Instruction::And) { 3430 // Recurse on the operands of the and. 3431 BackedgeTakenInfo BTI0 = 3432 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3433 BackedgeTakenInfo BTI1 = 3434 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3435 const SCEV *BECount = getCouldNotCompute(); 3436 const SCEV *MaxBECount = getCouldNotCompute(); 3437 if (L->contains(TBB)) { 3438 // Both conditions must be true for the loop to continue executing. 3439 // Choose the less conservative count. 3440 if (BTI0.Exact == getCouldNotCompute() || 3441 BTI1.Exact == getCouldNotCompute()) 3442 BECount = getCouldNotCompute(); 3443 else 3444 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3445 if (BTI0.Max == getCouldNotCompute()) 3446 MaxBECount = BTI1.Max; 3447 else if (BTI1.Max == getCouldNotCompute()) 3448 MaxBECount = BTI0.Max; 3449 else 3450 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3451 } else { 3452 // Both conditions must be true for the loop to exit. 3453 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3454 if (BTI0.Exact != getCouldNotCompute() && 3455 BTI1.Exact != getCouldNotCompute()) 3456 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3457 if (BTI0.Max != getCouldNotCompute() && 3458 BTI1.Max != getCouldNotCompute()) 3459 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3460 } 3461 3462 return BackedgeTakenInfo(BECount, MaxBECount); 3463 } 3464 if (BO->getOpcode() == Instruction::Or) { 3465 // Recurse on the operands of the or. 3466 BackedgeTakenInfo BTI0 = 3467 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3468 BackedgeTakenInfo BTI1 = 3469 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3470 const SCEV *BECount = getCouldNotCompute(); 3471 const SCEV *MaxBECount = getCouldNotCompute(); 3472 if (L->contains(FBB)) { 3473 // Both conditions must be false for the loop to continue executing. 3474 // Choose the less conservative count. 3475 if (BTI0.Exact == getCouldNotCompute() || 3476 BTI1.Exact == getCouldNotCompute()) 3477 BECount = getCouldNotCompute(); 3478 else 3479 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3480 if (BTI0.Max == getCouldNotCompute()) 3481 MaxBECount = BTI1.Max; 3482 else if (BTI1.Max == getCouldNotCompute()) 3483 MaxBECount = BTI0.Max; 3484 else 3485 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3486 } else { 3487 // Both conditions must be false for the loop to exit. 3488 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3489 if (BTI0.Exact != getCouldNotCompute() && 3490 BTI1.Exact != getCouldNotCompute()) 3491 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3492 if (BTI0.Max != getCouldNotCompute() && 3493 BTI1.Max != getCouldNotCompute()) 3494 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3495 } 3496 3497 return BackedgeTakenInfo(BECount, MaxBECount); 3498 } 3499 } 3500 3501 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3502 // Procede to the next level to examine the icmp. 3503 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3504 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3505 3506 // If it's not an integer or pointer comparison then compute it the hard way. 3507 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3508} 3509 3510/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3511/// backedge of the specified loop will execute if its exit condition 3512/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3513ScalarEvolution::BackedgeTakenInfo 3514ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3515 ICmpInst *ExitCond, 3516 BasicBlock *TBB, 3517 BasicBlock *FBB) { 3518 3519 // If the condition was exit on true, convert the condition to exit on false 3520 ICmpInst::Predicate Cond; 3521 if (!L->contains(FBB)) 3522 Cond = ExitCond->getPredicate(); 3523 else 3524 Cond = ExitCond->getInversePredicate(); 3525 3526 // Handle common loops like: for (X = "string"; *X; ++X) 3527 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3528 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3529 const SCEV *ItCnt = 3530 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3531 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3532 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3533 return BackedgeTakenInfo(ItCnt, 3534 isa<SCEVConstant>(ItCnt) ? ItCnt : 3535 getConstant(APInt::getMaxValue(BitWidth)-1)); 3536 } 3537 } 3538 3539 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3540 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3541 3542 // Try to evaluate any dependencies out of the loop. 3543 LHS = getSCEVAtScope(LHS, L); 3544 RHS = getSCEVAtScope(RHS, L); 3545 3546 // At this point, we would like to compute how many iterations of the 3547 // loop the predicate will return true for these inputs. 3548 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3549 // If there is a loop-invariant, force it into the RHS. 3550 std::swap(LHS, RHS); 3551 Cond = ICmpInst::getSwappedPredicate(Cond); 3552 } 3553 3554 // If we have a comparison of a chrec against a constant, try to use value 3555 // ranges to answer this query. 3556 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3557 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3558 if (AddRec->getLoop() == L) { 3559 // Form the constant range. 3560 ConstantRange CompRange( 3561 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3562 3563 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3564 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3565 } 3566 3567 switch (Cond) { 3568 case ICmpInst::ICMP_NE: { // while (X != Y) 3569 // Convert to: while (X-Y != 0) 3570 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3571 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3572 break; 3573 } 3574 case ICmpInst::ICMP_EQ: { // while (X == Y) 3575 // Convert to: while (X-Y == 0) 3576 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3577 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3578 break; 3579 } 3580 case ICmpInst::ICMP_SLT: { 3581 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3582 if (BTI.hasAnyInfo()) return BTI; 3583 break; 3584 } 3585 case ICmpInst::ICMP_SGT: { 3586 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3587 getNotSCEV(RHS), L, true); 3588 if (BTI.hasAnyInfo()) return BTI; 3589 break; 3590 } 3591 case ICmpInst::ICMP_ULT: { 3592 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3593 if (BTI.hasAnyInfo()) return BTI; 3594 break; 3595 } 3596 case ICmpInst::ICMP_UGT: { 3597 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3598 getNotSCEV(RHS), L, false); 3599 if (BTI.hasAnyInfo()) return BTI; 3600 break; 3601 } 3602 default: 3603#if 0 3604 errs() << "ComputeBackedgeTakenCount "; 3605 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3606 errs() << "[unsigned] "; 3607 errs() << *LHS << " " 3608 << Instruction::getOpcodeName(Instruction::ICmp) 3609 << " " << *RHS << "\n"; 3610#endif 3611 break; 3612 } 3613 return 3614 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3615} 3616 3617static ConstantInt * 3618EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3619 ScalarEvolution &SE) { 3620 const SCEV *InVal = SE.getConstant(C); 3621 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3622 assert(isa<SCEVConstant>(Val) && 3623 "Evaluation of SCEV at constant didn't fold correctly?"); 3624 return cast<SCEVConstant>(Val)->getValue(); 3625} 3626 3627/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3628/// and a GEP expression (missing the pointer index) indexing into it, return 3629/// the addressed element of the initializer or null if the index expression is 3630/// invalid. 3631static Constant * 3632GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV, 3633 const std::vector<ConstantInt*> &Indices) { 3634 Constant *Init = GV->getInitializer(); 3635 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3636 uint64_t Idx = Indices[i]->getZExtValue(); 3637 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3638 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3639 Init = cast<Constant>(CS->getOperand(Idx)); 3640 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3641 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3642 Init = cast<Constant>(CA->getOperand(Idx)); 3643 } else if (isa<ConstantAggregateZero>(Init)) { 3644 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3645 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3646 Init = Constant::getNullValue(STy->getElementType(Idx)); 3647 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3648 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3649 Init = Constant::getNullValue(ATy->getElementType()); 3650 } else { 3651 llvm_unreachable("Unknown constant aggregate type!"); 3652 } 3653 return 0; 3654 } else { 3655 return 0; // Unknown initializer type 3656 } 3657 } 3658 return Init; 3659} 3660 3661/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3662/// 'icmp op load X, cst', try to see if we can compute the backedge 3663/// execution count. 3664const SCEV * 3665ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3666 LoadInst *LI, 3667 Constant *RHS, 3668 const Loop *L, 3669 ICmpInst::Predicate predicate) { 3670 if (LI->isVolatile()) return getCouldNotCompute(); 3671 3672 // Check to see if the loaded pointer is a getelementptr of a global. 3673 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3674 if (!GEP) return getCouldNotCompute(); 3675 3676 // Make sure that it is really a constant global we are gepping, with an 3677 // initializer, and make sure the first IDX is really 0. 3678 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3679 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3680 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3681 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3682 return getCouldNotCompute(); 3683 3684 // Okay, we allow one non-constant index into the GEP instruction. 3685 Value *VarIdx = 0; 3686 std::vector<ConstantInt*> Indexes; 3687 unsigned VarIdxNum = 0; 3688 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3689 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3690 Indexes.push_back(CI); 3691 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3692 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3693 VarIdx = GEP->getOperand(i); 3694 VarIdxNum = i-2; 3695 Indexes.push_back(0); 3696 } 3697 3698 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3699 // Check to see if X is a loop variant variable value now. 3700 const SCEV *Idx = getSCEV(VarIdx); 3701 Idx = getSCEVAtScope(Idx, L); 3702 3703 // We can only recognize very limited forms of loop index expressions, in 3704 // particular, only affine AddRec's like {C1,+,C2}. 3705 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3706 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3707 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3708 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3709 return getCouldNotCompute(); 3710 3711 unsigned MaxSteps = MaxBruteForceIterations; 3712 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3713 ConstantInt *ItCst = ConstantInt::get( 3714 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3715 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3716 3717 // Form the GEP offset. 3718 Indexes[VarIdxNum] = Val; 3719 3720 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes); 3721 if (Result == 0) break; // Cannot compute! 3722 3723 // Evaluate the condition for this iteration. 3724 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3725 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3726 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3727#if 0 3728 errs() << "\n***\n*** Computed loop count " << *ItCst 3729 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3730 << "***\n"; 3731#endif 3732 ++NumArrayLenItCounts; 3733 return getConstant(ItCst); // Found terminating iteration! 3734 } 3735 } 3736 return getCouldNotCompute(); 3737} 3738 3739 3740/// CanConstantFold - Return true if we can constant fold an instruction of the 3741/// specified type, assuming that all operands were constants. 3742static bool CanConstantFold(const Instruction *I) { 3743 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3744 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3745 return true; 3746 3747 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3748 if (const Function *F = CI->getCalledFunction()) 3749 return canConstantFoldCallTo(F); 3750 return false; 3751} 3752 3753/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3754/// in the loop that V is derived from. We allow arbitrary operations along the 3755/// way, but the operands of an operation must either be constants or a value 3756/// derived from a constant PHI. If this expression does not fit with these 3757/// constraints, return null. 3758static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3759 // If this is not an instruction, or if this is an instruction outside of the 3760 // loop, it can't be derived from a loop PHI. 3761 Instruction *I = dyn_cast<Instruction>(V); 3762 if (I == 0 || !L->contains(I->getParent())) return 0; 3763 3764 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3765 if (L->getHeader() == I->getParent()) 3766 return PN; 3767 else 3768 // We don't currently keep track of the control flow needed to evaluate 3769 // PHIs, so we cannot handle PHIs inside of loops. 3770 return 0; 3771 } 3772 3773 // If we won't be able to constant fold this expression even if the operands 3774 // are constants, return early. 3775 if (!CanConstantFold(I)) return 0; 3776 3777 // Otherwise, we can evaluate this instruction if all of its operands are 3778 // constant or derived from a PHI node themselves. 3779 PHINode *PHI = 0; 3780 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3781 if (!(isa<Constant>(I->getOperand(Op)) || 3782 isa<GlobalValue>(I->getOperand(Op)))) { 3783 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3784 if (P == 0) return 0; // Not evolving from PHI 3785 if (PHI == 0) 3786 PHI = P; 3787 else if (PHI != P) 3788 return 0; // Evolving from multiple different PHIs. 3789 } 3790 3791 // This is a expression evolving from a constant PHI! 3792 return PHI; 3793} 3794 3795/// EvaluateExpression - Given an expression that passes the 3796/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3797/// in the loop has the value PHIVal. If we can't fold this expression for some 3798/// reason, return null. 3799static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3800 if (isa<PHINode>(V)) return PHIVal; 3801 if (Constant *C = dyn_cast<Constant>(V)) return C; 3802 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3803 Instruction *I = cast<Instruction>(V); 3804 LLVMContext &Context = I->getParent()->getContext(); 3805 3806 std::vector<Constant*> Operands; 3807 Operands.resize(I->getNumOperands()); 3808 3809 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3810 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3811 if (Operands[i] == 0) return 0; 3812 } 3813 3814 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3815 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3816 &Operands[0], Operands.size(), 3817 Context); 3818 else 3819 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3820 &Operands[0], Operands.size(), 3821 Context); 3822} 3823 3824/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3825/// in the header of its containing loop, we know the loop executes a 3826/// constant number of times, and the PHI node is just a recurrence 3827/// involving constants, fold it. 3828Constant * 3829ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3830 const APInt& BEs, 3831 const Loop *L) { 3832 std::map<PHINode*, Constant*>::iterator I = 3833 ConstantEvolutionLoopExitValue.find(PN); 3834 if (I != ConstantEvolutionLoopExitValue.end()) 3835 return I->second; 3836 3837 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3838 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3839 3840 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3841 3842 // Since the loop is canonicalized, the PHI node must have two entries. One 3843 // entry must be a constant (coming in from outside of the loop), and the 3844 // second must be derived from the same PHI. 3845 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3846 Constant *StartCST = 3847 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3848 if (StartCST == 0) 3849 return RetVal = 0; // Must be a constant. 3850 3851 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3852 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3853 if (PN2 != PN) 3854 return RetVal = 0; // Not derived from same PHI. 3855 3856 // Execute the loop symbolically to determine the exit value. 3857 if (BEs.getActiveBits() >= 32) 3858 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3859 3860 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3861 unsigned IterationNum = 0; 3862 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3863 if (IterationNum == NumIterations) 3864 return RetVal = PHIVal; // Got exit value! 3865 3866 // Compute the value of the PHI node for the next iteration. 3867 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3868 if (NextPHI == PHIVal) 3869 return RetVal = NextPHI; // Stopped evolving! 3870 if (NextPHI == 0) 3871 return 0; // Couldn't evaluate! 3872 PHIVal = NextPHI; 3873 } 3874} 3875 3876/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 3877/// constant number of times (the condition evolves only from constants), 3878/// try to evaluate a few iterations of the loop until we get the exit 3879/// condition gets a value of ExitWhen (true or false). If we cannot 3880/// evaluate the trip count of the loop, return getCouldNotCompute(). 3881const SCEV * 3882ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3883 Value *Cond, 3884 bool ExitWhen) { 3885 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3886 if (PN == 0) return getCouldNotCompute(); 3887 3888 // Since the loop is canonicalized, the PHI node must have two entries. One 3889 // entry must be a constant (coming in from outside of the loop), and the 3890 // second must be derived from the same PHI. 3891 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3892 Constant *StartCST = 3893 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3894 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3895 3896 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3897 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3898 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3899 3900 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3901 // the loop symbolically to determine when the condition gets a value of 3902 // "ExitWhen". 3903 unsigned IterationNum = 0; 3904 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3905 for (Constant *PHIVal = StartCST; 3906 IterationNum != MaxIterations; ++IterationNum) { 3907 ConstantInt *CondVal = 3908 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3909 3910 // Couldn't symbolically evaluate. 3911 if (!CondVal) return getCouldNotCompute(); 3912 3913 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3914 ++NumBruteForceTripCountsComputed; 3915 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 3916 } 3917 3918 // Compute the value of the PHI node for the next iteration. 3919 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3920 if (NextPHI == 0 || NextPHI == PHIVal) 3921 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3922 PHIVal = NextPHI; 3923 } 3924 3925 // Too many iterations were needed to evaluate. 3926 return getCouldNotCompute(); 3927} 3928 3929/// getSCEVAtScope - Return a SCEV expression for the specified value 3930/// at the specified scope in the program. The L value specifies a loop 3931/// nest to evaluate the expression at, where null is the top-level or a 3932/// specified loop is immediately inside of the loop. 3933/// 3934/// This method can be used to compute the exit value for a variable defined 3935/// in a loop by querying what the value will hold in the parent loop. 3936/// 3937/// In the case that a relevant loop exit value cannot be computed, the 3938/// original value V is returned. 3939const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3940 // Check to see if we've folded this expression at this loop before. 3941 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 3942 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 3943 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 3944 if (!Pair.second) 3945 return Pair.first->second ? Pair.first->second : V; 3946 3947 // Otherwise compute it. 3948 const SCEV *C = computeSCEVAtScope(V, L); 3949 ValuesAtScopes[V][L] = C; 3950 return C; 3951} 3952 3953const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 3954 if (isa<SCEVConstant>(V)) return V; 3955 3956 // If this instruction is evolved from a constant-evolving PHI, compute the 3957 // exit value from the loop without using SCEVs. 3958 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3959 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3960 const Loop *LI = (*this->LI)[I->getParent()]; 3961 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3962 if (PHINode *PN = dyn_cast<PHINode>(I)) 3963 if (PN->getParent() == LI->getHeader()) { 3964 // Okay, there is no closed form solution for the PHI node. Check 3965 // to see if the loop that contains it has a known backedge-taken 3966 // count. If so, we may be able to force computation of the exit 3967 // value. 3968 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3969 if (const SCEVConstant *BTCC = 3970 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3971 // Okay, we know how many times the containing loop executes. If 3972 // this is a constant evolving PHI node, get the final value at 3973 // the specified iteration number. 3974 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3975 BTCC->getValue()->getValue(), 3976 LI); 3977 if (RV) return getSCEV(RV); 3978 } 3979 } 3980 3981 // Okay, this is an expression that we cannot symbolically evaluate 3982 // into a SCEV. Check to see if it's possible to symbolically evaluate 3983 // the arguments into constants, and if so, try to constant propagate the 3984 // result. This is particularly useful for computing loop exit values. 3985 if (CanConstantFold(I)) { 3986 std::vector<Constant*> Operands; 3987 Operands.reserve(I->getNumOperands()); 3988 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3989 Value *Op = I->getOperand(i); 3990 if (Constant *C = dyn_cast<Constant>(Op)) { 3991 Operands.push_back(C); 3992 } else { 3993 // If any of the operands is non-constant and if they are 3994 // non-integer and non-pointer, don't even try to analyze them 3995 // with scev techniques. 3996 if (!isSCEVable(Op->getType())) 3997 return V; 3998 3999 const SCEV* OpV = getSCEVAtScope(Op, L); 4000 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4001 Constant *C = SC->getValue(); 4002 if (C->getType() != Op->getType()) 4003 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4004 Op->getType(), 4005 false), 4006 C, Op->getType()); 4007 Operands.push_back(C); 4008 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4009 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4010 if (C->getType() != Op->getType()) 4011 C = 4012 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4013 Op->getType(), 4014 false), 4015 C, Op->getType()); 4016 Operands.push_back(C); 4017 } else 4018 return V; 4019 } else { 4020 return V; 4021 } 4022 } 4023 } 4024 4025 Constant *C; 4026 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4027 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4028 &Operands[0], Operands.size(), 4029 getContext()); 4030 else 4031 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4032 &Operands[0], Operands.size(), 4033 getContext()); 4034 return getSCEV(C); 4035 } 4036 } 4037 4038 // This is some other type of SCEVUnknown, just return it. 4039 return V; 4040 } 4041 4042 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4043 // Avoid performing the look-up in the common case where the specified 4044 // expression has no loop-variant portions. 4045 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4046 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4047 if (OpAtScope != Comm->getOperand(i)) { 4048 // Okay, at least one of these operands is loop variant but might be 4049 // foldable. Build a new instance of the folded commutative expression. 4050 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4051 Comm->op_begin()+i); 4052 NewOps.push_back(OpAtScope); 4053 4054 for (++i; i != e; ++i) { 4055 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4056 NewOps.push_back(OpAtScope); 4057 } 4058 if (isa<SCEVAddExpr>(Comm)) 4059 return getAddExpr(NewOps); 4060 if (isa<SCEVMulExpr>(Comm)) 4061 return getMulExpr(NewOps); 4062 if (isa<SCEVSMaxExpr>(Comm)) 4063 return getSMaxExpr(NewOps); 4064 if (isa<SCEVUMaxExpr>(Comm)) 4065 return getUMaxExpr(NewOps); 4066 llvm_unreachable("Unknown commutative SCEV type!"); 4067 } 4068 } 4069 // If we got here, all operands are loop invariant. 4070 return Comm; 4071 } 4072 4073 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4074 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4075 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4076 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4077 return Div; // must be loop invariant 4078 return getUDivExpr(LHS, RHS); 4079 } 4080 4081 // If this is a loop recurrence for a loop that does not contain L, then we 4082 // are dealing with the final value computed by the loop. 4083 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4084 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 4085 // To evaluate this recurrence, we need to know how many times the AddRec 4086 // loop iterates. Compute this now. 4087 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4088 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4089 4090 // Then, evaluate the AddRec. 4091 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4092 } 4093 return AddRec; 4094 } 4095 4096 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4097 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4098 if (Op == Cast->getOperand()) 4099 return Cast; // must be loop invariant 4100 return getZeroExtendExpr(Op, Cast->getType()); 4101 } 4102 4103 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4104 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4105 if (Op == Cast->getOperand()) 4106 return Cast; // must be loop invariant 4107 return getSignExtendExpr(Op, Cast->getType()); 4108 } 4109 4110 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4111 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4112 if (Op == Cast->getOperand()) 4113 return Cast; // must be loop invariant 4114 return getTruncateExpr(Op, Cast->getType()); 4115 } 4116 4117 if (isa<SCEVTargetDataConstant>(V)) 4118 return V; 4119 4120 llvm_unreachable("Unknown SCEV type!"); 4121 return 0; 4122} 4123 4124/// getSCEVAtScope - This is a convenience function which does 4125/// getSCEVAtScope(getSCEV(V), L). 4126const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4127 return getSCEVAtScope(getSCEV(V), L); 4128} 4129 4130/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4131/// following equation: 4132/// 4133/// A * X = B (mod N) 4134/// 4135/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4136/// A and B isn't important. 4137/// 4138/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4139static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4140 ScalarEvolution &SE) { 4141 uint32_t BW = A.getBitWidth(); 4142 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4143 assert(A != 0 && "A must be non-zero."); 4144 4145 // 1. D = gcd(A, N) 4146 // 4147 // The gcd of A and N may have only one prime factor: 2. The number of 4148 // trailing zeros in A is its multiplicity 4149 uint32_t Mult2 = A.countTrailingZeros(); 4150 // D = 2^Mult2 4151 4152 // 2. Check if B is divisible by D. 4153 // 4154 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4155 // is not less than multiplicity of this prime factor for D. 4156 if (B.countTrailingZeros() < Mult2) 4157 return SE.getCouldNotCompute(); 4158 4159 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4160 // modulo (N / D). 4161 // 4162 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4163 // bit width during computations. 4164 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4165 APInt Mod(BW + 1, 0); 4166 Mod.set(BW - Mult2); // Mod = N / D 4167 APInt I = AD.multiplicativeInverse(Mod); 4168 4169 // 4. Compute the minimum unsigned root of the equation: 4170 // I * (B / D) mod (N / D) 4171 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4172 4173 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4174 // bits. 4175 return SE.getConstant(Result.trunc(BW)); 4176} 4177 4178/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4179/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4180/// might be the same) or two SCEVCouldNotCompute objects. 4181/// 4182static std::pair<const SCEV *,const SCEV *> 4183SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4184 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4185 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4186 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4187 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4188 4189 // We currently can only solve this if the coefficients are constants. 4190 if (!LC || !MC || !NC) { 4191 const SCEV *CNC = SE.getCouldNotCompute(); 4192 return std::make_pair(CNC, CNC); 4193 } 4194 4195 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4196 const APInt &L = LC->getValue()->getValue(); 4197 const APInt &M = MC->getValue()->getValue(); 4198 const APInt &N = NC->getValue()->getValue(); 4199 APInt Two(BitWidth, 2); 4200 APInt Four(BitWidth, 4); 4201 4202 { 4203 using namespace APIntOps; 4204 const APInt& C = L; 4205 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4206 // The B coefficient is M-N/2 4207 APInt B(M); 4208 B -= sdiv(N,Two); 4209 4210 // The A coefficient is N/2 4211 APInt A(N.sdiv(Two)); 4212 4213 // Compute the B^2-4ac term. 4214 APInt SqrtTerm(B); 4215 SqrtTerm *= B; 4216 SqrtTerm -= Four * (A * C); 4217 4218 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4219 // integer value or else APInt::sqrt() will assert. 4220 APInt SqrtVal(SqrtTerm.sqrt()); 4221 4222 // Compute the two solutions for the quadratic formula. 4223 // The divisions must be performed as signed divisions. 4224 APInt NegB(-B); 4225 APInt TwoA( A << 1 ); 4226 if (TwoA.isMinValue()) { 4227 const SCEV *CNC = SE.getCouldNotCompute(); 4228 return std::make_pair(CNC, CNC); 4229 } 4230 4231 LLVMContext &Context = SE.getContext(); 4232 4233 ConstantInt *Solution1 = 4234 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4235 ConstantInt *Solution2 = 4236 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4237 4238 return std::make_pair(SE.getConstant(Solution1), 4239 SE.getConstant(Solution2)); 4240 } // end APIntOps namespace 4241} 4242 4243/// HowFarToZero - Return the number of times a backedge comparing the specified 4244/// value to zero will execute. If not computable, return CouldNotCompute. 4245const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4246 // If the value is a constant 4247 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4248 // If the value is already zero, the branch will execute zero times. 4249 if (C->getValue()->isZero()) return C; 4250 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4251 } 4252 4253 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4254 if (!AddRec || AddRec->getLoop() != L) 4255 return getCouldNotCompute(); 4256 4257 if (AddRec->isAffine()) { 4258 // If this is an affine expression, the execution count of this branch is 4259 // the minimum unsigned root of the following equation: 4260 // 4261 // Start + Step*N = 0 (mod 2^BW) 4262 // 4263 // equivalent to: 4264 // 4265 // Step*N = -Start (mod 2^BW) 4266 // 4267 // where BW is the common bit width of Start and Step. 4268 4269 // Get the initial value for the loop. 4270 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4271 L->getParentLoop()); 4272 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4273 L->getParentLoop()); 4274 4275 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4276 // For now we handle only constant steps. 4277 4278 // First, handle unitary steps. 4279 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4280 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4281 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4282 return Start; // N = Start (as unsigned) 4283 4284 // Then, try to solve the above equation provided that Start is constant. 4285 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4286 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4287 -StartC->getValue()->getValue(), 4288 *this); 4289 } 4290 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4291 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4292 // the quadratic equation to solve it. 4293 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4294 *this); 4295 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4296 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4297 if (R1) { 4298#if 0 4299 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4300 << " sol#2: " << *R2 << "\n"; 4301#endif 4302 // Pick the smallest positive root value. 4303 if (ConstantInt *CB = 4304 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4305 R1->getValue(), R2->getValue()))) { 4306 if (CB->getZExtValue() == false) 4307 std::swap(R1, R2); // R1 is the minimum root now. 4308 4309 // We can only use this value if the chrec ends up with an exact zero 4310 // value at this index. When solving for "X*X != 5", for example, we 4311 // should not accept a root of 2. 4312 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4313 if (Val->isZero()) 4314 return R1; // We found a quadratic root! 4315 } 4316 } 4317 } 4318 4319 return getCouldNotCompute(); 4320} 4321 4322/// HowFarToNonZero - Return the number of times a backedge checking the 4323/// specified value for nonzero will execute. If not computable, return 4324/// CouldNotCompute 4325const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4326 // Loops that look like: while (X == 0) are very strange indeed. We don't 4327 // handle them yet except for the trivial case. This could be expanded in the 4328 // future as needed. 4329 4330 // If the value is a constant, check to see if it is known to be non-zero 4331 // already. If so, the backedge will execute zero times. 4332 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4333 if (!C->getValue()->isNullValue()) 4334 return getIntegerSCEV(0, C->getType()); 4335 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4336 } 4337 4338 // We could implement others, but I really doubt anyone writes loops like 4339 // this, and if they did, they would already be constant folded. 4340 return getCouldNotCompute(); 4341} 4342 4343/// getLoopPredecessor - If the given loop's header has exactly one unique 4344/// predecessor outside the loop, return it. Otherwise return null. 4345/// 4346BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4347 BasicBlock *Header = L->getHeader(); 4348 BasicBlock *Pred = 0; 4349 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4350 PI != E; ++PI) 4351 if (!L->contains(*PI)) { 4352 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4353 Pred = *PI; 4354 } 4355 return Pred; 4356} 4357 4358/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4359/// (which may not be an immediate predecessor) which has exactly one 4360/// successor from which BB is reachable, or null if no such block is 4361/// found. 4362/// 4363BasicBlock * 4364ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4365 // If the block has a unique predecessor, then there is no path from the 4366 // predecessor to the block that does not go through the direct edge 4367 // from the predecessor to the block. 4368 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4369 return Pred; 4370 4371 // A loop's header is defined to be a block that dominates the loop. 4372 // If the header has a unique predecessor outside the loop, it must be 4373 // a block that has exactly one successor that can reach the loop. 4374 if (Loop *L = LI->getLoopFor(BB)) 4375 return getLoopPredecessor(L); 4376 4377 return 0; 4378} 4379 4380/// HasSameValue - SCEV structural equivalence is usually sufficient for 4381/// testing whether two expressions are equal, however for the purposes of 4382/// looking for a condition guarding a loop, it can be useful to be a little 4383/// more general, since a front-end may have replicated the controlling 4384/// expression. 4385/// 4386static bool HasSameValue(const SCEV *A, const SCEV *B) { 4387 // Quick check to see if they are the same SCEV. 4388 if (A == B) return true; 4389 4390 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4391 // two different instructions with the same value. Check for this case. 4392 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4393 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4394 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4395 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4396 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4397 return true; 4398 4399 // Otherwise assume they may have a different value. 4400 return false; 4401} 4402 4403bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4404 return getSignedRange(S).getSignedMax().isNegative(); 4405} 4406 4407bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4408 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4409} 4410 4411bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4412 return !getSignedRange(S).getSignedMin().isNegative(); 4413} 4414 4415bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4416 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4417} 4418 4419bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4420 return isKnownNegative(S) || isKnownPositive(S); 4421} 4422 4423bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4424 const SCEV *LHS, const SCEV *RHS) { 4425 4426 if (HasSameValue(LHS, RHS)) 4427 return ICmpInst::isTrueWhenEqual(Pred); 4428 4429 switch (Pred) { 4430 default: 4431 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4432 break; 4433 case ICmpInst::ICMP_SGT: 4434 Pred = ICmpInst::ICMP_SLT; 4435 std::swap(LHS, RHS); 4436 case ICmpInst::ICMP_SLT: { 4437 ConstantRange LHSRange = getSignedRange(LHS); 4438 ConstantRange RHSRange = getSignedRange(RHS); 4439 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4440 return true; 4441 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4442 return false; 4443 break; 4444 } 4445 case ICmpInst::ICMP_SGE: 4446 Pred = ICmpInst::ICMP_SLE; 4447 std::swap(LHS, RHS); 4448 case ICmpInst::ICMP_SLE: { 4449 ConstantRange LHSRange = getSignedRange(LHS); 4450 ConstantRange RHSRange = getSignedRange(RHS); 4451 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4452 return true; 4453 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4454 return false; 4455 break; 4456 } 4457 case ICmpInst::ICMP_UGT: 4458 Pred = ICmpInst::ICMP_ULT; 4459 std::swap(LHS, RHS); 4460 case ICmpInst::ICMP_ULT: { 4461 ConstantRange LHSRange = getUnsignedRange(LHS); 4462 ConstantRange RHSRange = getUnsignedRange(RHS); 4463 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4464 return true; 4465 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4466 return false; 4467 break; 4468 } 4469 case ICmpInst::ICMP_UGE: 4470 Pred = ICmpInst::ICMP_ULE; 4471 std::swap(LHS, RHS); 4472 case ICmpInst::ICMP_ULE: { 4473 ConstantRange LHSRange = getUnsignedRange(LHS); 4474 ConstantRange RHSRange = getUnsignedRange(RHS); 4475 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4476 return true; 4477 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4478 return false; 4479 break; 4480 } 4481 case ICmpInst::ICMP_NE: { 4482 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4483 return true; 4484 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4485 return true; 4486 4487 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4488 if (isKnownNonZero(Diff)) 4489 return true; 4490 break; 4491 } 4492 case ICmpInst::ICMP_EQ: 4493 // The check at the top of the function catches the case where 4494 // the values are known to be equal. 4495 break; 4496 } 4497 return false; 4498} 4499 4500/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4501/// protected by a conditional between LHS and RHS. This is used to 4502/// to eliminate casts. 4503bool 4504ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4505 ICmpInst::Predicate Pred, 4506 const SCEV *LHS, const SCEV *RHS) { 4507 // Interpret a null as meaning no loop, where there is obviously no guard 4508 // (interprocedural conditions notwithstanding). 4509 if (!L) return true; 4510 4511 BasicBlock *Latch = L->getLoopLatch(); 4512 if (!Latch) 4513 return false; 4514 4515 BranchInst *LoopContinuePredicate = 4516 dyn_cast<BranchInst>(Latch->getTerminator()); 4517 if (!LoopContinuePredicate || 4518 LoopContinuePredicate->isUnconditional()) 4519 return false; 4520 4521 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4522 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4523} 4524 4525/// isLoopGuardedByCond - Test whether entry to the loop is protected 4526/// by a conditional between LHS and RHS. This is used to help avoid max 4527/// expressions in loop trip counts, and to eliminate casts. 4528bool 4529ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4530 ICmpInst::Predicate Pred, 4531 const SCEV *LHS, const SCEV *RHS) { 4532 // Interpret a null as meaning no loop, where there is obviously no guard 4533 // (interprocedural conditions notwithstanding). 4534 if (!L) return false; 4535 4536 BasicBlock *Predecessor = getLoopPredecessor(L); 4537 BasicBlock *PredecessorDest = L->getHeader(); 4538 4539 // Starting at the loop predecessor, climb up the predecessor chain, as long 4540 // as there are predecessors that can be found that have unique successors 4541 // leading to the original header. 4542 for (; Predecessor; 4543 PredecessorDest = Predecessor, 4544 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4545 4546 BranchInst *LoopEntryPredicate = 4547 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4548 if (!LoopEntryPredicate || 4549 LoopEntryPredicate->isUnconditional()) 4550 continue; 4551 4552 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4553 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4554 return true; 4555 } 4556 4557 return false; 4558} 4559 4560/// isImpliedCond - Test whether the condition described by Pred, LHS, 4561/// and RHS is true whenever the given Cond value evaluates to true. 4562bool ScalarEvolution::isImpliedCond(Value *CondValue, 4563 ICmpInst::Predicate Pred, 4564 const SCEV *LHS, const SCEV *RHS, 4565 bool Inverse) { 4566 // Recursivly handle And and Or conditions. 4567 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4568 if (BO->getOpcode() == Instruction::And) { 4569 if (!Inverse) 4570 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4571 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4572 } else if (BO->getOpcode() == Instruction::Or) { 4573 if (Inverse) 4574 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4575 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4576 } 4577 } 4578 4579 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4580 if (!ICI) return false; 4581 4582 // Bail if the ICmp's operands' types are wider than the needed type 4583 // before attempting to call getSCEV on them. This avoids infinite 4584 // recursion, since the analysis of widening casts can require loop 4585 // exit condition information for overflow checking, which would 4586 // lead back here. 4587 if (getTypeSizeInBits(LHS->getType()) < 4588 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4589 return false; 4590 4591 // Now that we found a conditional branch that dominates the loop, check to 4592 // see if it is the comparison we are looking for. 4593 ICmpInst::Predicate FoundPred; 4594 if (Inverse) 4595 FoundPred = ICI->getInversePredicate(); 4596 else 4597 FoundPred = ICI->getPredicate(); 4598 4599 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4600 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4601 4602 // Balance the types. The case where FoundLHS' type is wider than 4603 // LHS' type is checked for above. 4604 if (getTypeSizeInBits(LHS->getType()) > 4605 getTypeSizeInBits(FoundLHS->getType())) { 4606 if (CmpInst::isSigned(Pred)) { 4607 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4608 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4609 } else { 4610 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4611 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4612 } 4613 } 4614 4615 // Canonicalize the query to match the way instcombine will have 4616 // canonicalized the comparison. 4617 // First, put a constant operand on the right. 4618 if (isa<SCEVConstant>(LHS)) { 4619 std::swap(LHS, RHS); 4620 Pred = ICmpInst::getSwappedPredicate(Pred); 4621 } 4622 // Then, canonicalize comparisons with boundary cases. 4623 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4624 const APInt &RA = RC->getValue()->getValue(); 4625 switch (Pred) { 4626 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4627 case ICmpInst::ICMP_EQ: 4628 case ICmpInst::ICMP_NE: 4629 break; 4630 case ICmpInst::ICMP_UGE: 4631 if ((RA - 1).isMinValue()) { 4632 Pred = ICmpInst::ICMP_NE; 4633 RHS = getConstant(RA - 1); 4634 break; 4635 } 4636 if (RA.isMaxValue()) { 4637 Pred = ICmpInst::ICMP_EQ; 4638 break; 4639 } 4640 if (RA.isMinValue()) return true; 4641 break; 4642 case ICmpInst::ICMP_ULE: 4643 if ((RA + 1).isMaxValue()) { 4644 Pred = ICmpInst::ICMP_NE; 4645 RHS = getConstant(RA + 1); 4646 break; 4647 } 4648 if (RA.isMinValue()) { 4649 Pred = ICmpInst::ICMP_EQ; 4650 break; 4651 } 4652 if (RA.isMaxValue()) return true; 4653 break; 4654 case ICmpInst::ICMP_SGE: 4655 if ((RA - 1).isMinSignedValue()) { 4656 Pred = ICmpInst::ICMP_NE; 4657 RHS = getConstant(RA - 1); 4658 break; 4659 } 4660 if (RA.isMaxSignedValue()) { 4661 Pred = ICmpInst::ICMP_EQ; 4662 break; 4663 } 4664 if (RA.isMinSignedValue()) return true; 4665 break; 4666 case ICmpInst::ICMP_SLE: 4667 if ((RA + 1).isMaxSignedValue()) { 4668 Pred = ICmpInst::ICMP_NE; 4669 RHS = getConstant(RA + 1); 4670 break; 4671 } 4672 if (RA.isMinSignedValue()) { 4673 Pred = ICmpInst::ICMP_EQ; 4674 break; 4675 } 4676 if (RA.isMaxSignedValue()) return true; 4677 break; 4678 case ICmpInst::ICMP_UGT: 4679 if (RA.isMinValue()) { 4680 Pred = ICmpInst::ICMP_NE; 4681 break; 4682 } 4683 if ((RA + 1).isMaxValue()) { 4684 Pred = ICmpInst::ICMP_EQ; 4685 RHS = getConstant(RA + 1); 4686 break; 4687 } 4688 if (RA.isMaxValue()) return false; 4689 break; 4690 case ICmpInst::ICMP_ULT: 4691 if (RA.isMaxValue()) { 4692 Pred = ICmpInst::ICMP_NE; 4693 break; 4694 } 4695 if ((RA - 1).isMinValue()) { 4696 Pred = ICmpInst::ICMP_EQ; 4697 RHS = getConstant(RA - 1); 4698 break; 4699 } 4700 if (RA.isMinValue()) return false; 4701 break; 4702 case ICmpInst::ICMP_SGT: 4703 if (RA.isMinSignedValue()) { 4704 Pred = ICmpInst::ICMP_NE; 4705 break; 4706 } 4707 if ((RA + 1).isMaxSignedValue()) { 4708 Pred = ICmpInst::ICMP_EQ; 4709 RHS = getConstant(RA + 1); 4710 break; 4711 } 4712 if (RA.isMaxSignedValue()) return false; 4713 break; 4714 case ICmpInst::ICMP_SLT: 4715 if (RA.isMaxSignedValue()) { 4716 Pred = ICmpInst::ICMP_NE; 4717 break; 4718 } 4719 if ((RA - 1).isMinSignedValue()) { 4720 Pred = ICmpInst::ICMP_EQ; 4721 RHS = getConstant(RA - 1); 4722 break; 4723 } 4724 if (RA.isMinSignedValue()) return false; 4725 break; 4726 } 4727 } 4728 4729 // Check to see if we can make the LHS or RHS match. 4730 if (LHS == FoundRHS || RHS == FoundLHS) { 4731 if (isa<SCEVConstant>(RHS)) { 4732 std::swap(FoundLHS, FoundRHS); 4733 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4734 } else { 4735 std::swap(LHS, RHS); 4736 Pred = ICmpInst::getSwappedPredicate(Pred); 4737 } 4738 } 4739 4740 // Check whether the found predicate is the same as the desired predicate. 4741 if (FoundPred == Pred) 4742 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4743 4744 // Check whether swapping the found predicate makes it the same as the 4745 // desired predicate. 4746 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4747 if (isa<SCEVConstant>(RHS)) 4748 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4749 else 4750 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4751 RHS, LHS, FoundLHS, FoundRHS); 4752 } 4753 4754 // Check whether the actual condition is beyond sufficient. 4755 if (FoundPred == ICmpInst::ICMP_EQ) 4756 if (ICmpInst::isTrueWhenEqual(Pred)) 4757 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4758 return true; 4759 if (Pred == ICmpInst::ICMP_NE) 4760 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4761 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4762 return true; 4763 4764 // Otherwise assume the worst. 4765 return false; 4766} 4767 4768/// isImpliedCondOperands - Test whether the condition described by Pred, 4769/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4770/// and FoundRHS is true. 4771bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4772 const SCEV *LHS, const SCEV *RHS, 4773 const SCEV *FoundLHS, 4774 const SCEV *FoundRHS) { 4775 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4776 FoundLHS, FoundRHS) || 4777 // ~x < ~y --> x > y 4778 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4779 getNotSCEV(FoundRHS), 4780 getNotSCEV(FoundLHS)); 4781} 4782 4783/// isImpliedCondOperandsHelper - Test whether the condition described by 4784/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4785/// FoundLHS, and FoundRHS is true. 4786bool 4787ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4788 const SCEV *LHS, const SCEV *RHS, 4789 const SCEV *FoundLHS, 4790 const SCEV *FoundRHS) { 4791 switch (Pred) { 4792 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4793 case ICmpInst::ICMP_EQ: 4794 case ICmpInst::ICMP_NE: 4795 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4796 return true; 4797 break; 4798 case ICmpInst::ICMP_SLT: 4799 case ICmpInst::ICMP_SLE: 4800 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4801 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4802 return true; 4803 break; 4804 case ICmpInst::ICMP_SGT: 4805 case ICmpInst::ICMP_SGE: 4806 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4807 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4808 return true; 4809 break; 4810 case ICmpInst::ICMP_ULT: 4811 case ICmpInst::ICMP_ULE: 4812 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4813 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4814 return true; 4815 break; 4816 case ICmpInst::ICMP_UGT: 4817 case ICmpInst::ICMP_UGE: 4818 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4819 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4820 return true; 4821 break; 4822 } 4823 4824 return false; 4825} 4826 4827/// getBECount - Subtract the end and start values and divide by the step, 4828/// rounding up, to get the number of times the backedge is executed. Return 4829/// CouldNotCompute if an intermediate computation overflows. 4830const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4831 const SCEV *End, 4832 const SCEV *Step, 4833 bool NoWrap) { 4834 const Type *Ty = Start->getType(); 4835 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4836 const SCEV *Diff = getMinusSCEV(End, Start); 4837 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4838 4839 // Add an adjustment to the difference between End and Start so that 4840 // the division will effectively round up. 4841 const SCEV *Add = getAddExpr(Diff, RoundUp); 4842 4843 if (!NoWrap) { 4844 // Check Add for unsigned overflow. 4845 // TODO: More sophisticated things could be done here. 4846 const Type *WideTy = IntegerType::get(getContext(), 4847 getTypeSizeInBits(Ty) + 1); 4848 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 4849 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 4850 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 4851 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4852 return getCouldNotCompute(); 4853 } 4854 4855 return getUDivExpr(Add, Step); 4856} 4857 4858/// HowManyLessThans - Return the number of times a backedge containing the 4859/// specified less-than comparison will execute. If not computable, return 4860/// CouldNotCompute. 4861ScalarEvolution::BackedgeTakenInfo 4862ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4863 const Loop *L, bool isSigned) { 4864 // Only handle: "ADDREC < LoopInvariant". 4865 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4866 4867 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4868 if (!AddRec || AddRec->getLoop() != L) 4869 return getCouldNotCompute(); 4870 4871 // Check to see if we have a flag which makes analysis easy. 4872 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 4873 AddRec->hasNoUnsignedWrap(); 4874 4875 if (AddRec->isAffine()) { 4876 // FORNOW: We only support unit strides. 4877 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4878 const SCEV *Step = AddRec->getStepRecurrence(*this); 4879 4880 // TODO: handle non-constant strides. 4881 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4882 if (!CStep || CStep->isZero()) 4883 return getCouldNotCompute(); 4884 if (CStep->isOne()) { 4885 // With unit stride, the iteration never steps past the limit value. 4886 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4887 if (NoWrap) { 4888 // We know the iteration won't step past the maximum value for its type. 4889 ; 4890 } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4891 // Test whether a positive iteration iteration can step past the limit 4892 // value and past the maximum value for its type in a single step. 4893 if (isSigned) { 4894 APInt Max = APInt::getSignedMaxValue(BitWidth); 4895 if ((Max - CStep->getValue()->getValue()) 4896 .slt(CLimit->getValue()->getValue())) 4897 return getCouldNotCompute(); 4898 } else { 4899 APInt Max = APInt::getMaxValue(BitWidth); 4900 if ((Max - CStep->getValue()->getValue()) 4901 .ult(CLimit->getValue()->getValue())) 4902 return getCouldNotCompute(); 4903 } 4904 } else 4905 // TODO: handle non-constant limit values below. 4906 return getCouldNotCompute(); 4907 } else 4908 // TODO: handle negative strides below. 4909 return getCouldNotCompute(); 4910 4911 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4912 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4913 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4914 // treat m-n as signed nor unsigned due to overflow possibility. 4915 4916 // First, we get the value of the LHS in the first iteration: n 4917 const SCEV *Start = AddRec->getOperand(0); 4918 4919 // Determine the minimum constant start value. 4920 const SCEV *MinStart = getConstant(isSigned ? 4921 getSignedRange(Start).getSignedMin() : 4922 getUnsignedRange(Start).getUnsignedMin()); 4923 4924 // If we know that the condition is true in order to enter the loop, 4925 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4926 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4927 // the division must round up. 4928 const SCEV *End = RHS; 4929 if (!isLoopGuardedByCond(L, 4930 isSigned ? ICmpInst::ICMP_SLT : 4931 ICmpInst::ICMP_ULT, 4932 getMinusSCEV(Start, Step), RHS)) 4933 End = isSigned ? getSMaxExpr(RHS, Start) 4934 : getUMaxExpr(RHS, Start); 4935 4936 // Determine the maximum constant end value. 4937 const SCEV *MaxEnd = getConstant(isSigned ? 4938 getSignedRange(End).getSignedMax() : 4939 getUnsignedRange(End).getUnsignedMax()); 4940 4941 // Finally, we subtract these two values and divide, rounding up, to get 4942 // the number of times the backedge is executed. 4943 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 4944 4945 // The maximum backedge count is similar, except using the minimum start 4946 // value and the maximum end value. 4947 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 4948 4949 return BackedgeTakenInfo(BECount, MaxBECount); 4950 } 4951 4952 return getCouldNotCompute(); 4953} 4954 4955/// getNumIterationsInRange - Return the number of iterations of this loop that 4956/// produce values in the specified constant range. Another way of looking at 4957/// this is that it returns the first iteration number where the value is not in 4958/// the condition, thus computing the exit count. If the iteration count can't 4959/// be computed, an instance of SCEVCouldNotCompute is returned. 4960const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4961 ScalarEvolution &SE) const { 4962 if (Range.isFullSet()) // Infinite loop. 4963 return SE.getCouldNotCompute(); 4964 4965 // If the start is a non-zero constant, shift the range to simplify things. 4966 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4967 if (!SC->getValue()->isZero()) { 4968 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4969 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4970 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4971 if (const SCEVAddRecExpr *ShiftedAddRec = 4972 dyn_cast<SCEVAddRecExpr>(Shifted)) 4973 return ShiftedAddRec->getNumIterationsInRange( 4974 Range.subtract(SC->getValue()->getValue()), SE); 4975 // This is strange and shouldn't happen. 4976 return SE.getCouldNotCompute(); 4977 } 4978 4979 // The only time we can solve this is when we have all constant indices. 4980 // Otherwise, we cannot determine the overflow conditions. 4981 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4982 if (!isa<SCEVConstant>(getOperand(i))) 4983 return SE.getCouldNotCompute(); 4984 4985 4986 // Okay at this point we know that all elements of the chrec are constants and 4987 // that the start element is zero. 4988 4989 // First check to see if the range contains zero. If not, the first 4990 // iteration exits. 4991 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 4992 if (!Range.contains(APInt(BitWidth, 0))) 4993 return SE.getIntegerSCEV(0, getType()); 4994 4995 if (isAffine()) { 4996 // If this is an affine expression then we have this situation: 4997 // Solve {0,+,A} in Range === Ax in Range 4998 4999 // We know that zero is in the range. If A is positive then we know that 5000 // the upper value of the range must be the first possible exit value. 5001 // If A is negative then the lower of the range is the last possible loop 5002 // value. Also note that we already checked for a full range. 5003 APInt One(BitWidth,1); 5004 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5005 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5006 5007 // The exit value should be (End+A)/A. 5008 APInt ExitVal = (End + A).udiv(A); 5009 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5010 5011 // Evaluate at the exit value. If we really did fall out of the valid 5012 // range, then we computed our trip count, otherwise wrap around or other 5013 // things must have happened. 5014 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5015 if (Range.contains(Val->getValue())) 5016 return SE.getCouldNotCompute(); // Something strange happened 5017 5018 // Ensure that the previous value is in the range. This is a sanity check. 5019 assert(Range.contains( 5020 EvaluateConstantChrecAtConstant(this, 5021 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5022 "Linear scev computation is off in a bad way!"); 5023 return SE.getConstant(ExitValue); 5024 } else if (isQuadratic()) { 5025 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5026 // quadratic equation to solve it. To do this, we must frame our problem in 5027 // terms of figuring out when zero is crossed, instead of when 5028 // Range.getUpper() is crossed. 5029 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5030 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5031 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5032 5033 // Next, solve the constructed addrec 5034 std::pair<const SCEV *,const SCEV *> Roots = 5035 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5036 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5037 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5038 if (R1) { 5039 // Pick the smallest positive root value. 5040 if (ConstantInt *CB = 5041 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5042 R1->getValue(), R2->getValue()))) { 5043 if (CB->getZExtValue() == false) 5044 std::swap(R1, R2); // R1 is the minimum root now. 5045 5046 // Make sure the root is not off by one. The returned iteration should 5047 // not be in the range, but the previous one should be. When solving 5048 // for "X*X < 5", for example, we should not return a root of 2. 5049 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5050 R1->getValue(), 5051 SE); 5052 if (Range.contains(R1Val->getValue())) { 5053 // The next iteration must be out of the range... 5054 ConstantInt *NextVal = 5055 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5056 5057 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5058 if (!Range.contains(R1Val->getValue())) 5059 return SE.getConstant(NextVal); 5060 return SE.getCouldNotCompute(); // Something strange happened 5061 } 5062 5063 // If R1 was not in the range, then it is a good return value. Make 5064 // sure that R1-1 WAS in the range though, just in case. 5065 ConstantInt *NextVal = 5066 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5067 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5068 if (Range.contains(R1Val->getValue())) 5069 return R1; 5070 return SE.getCouldNotCompute(); // Something strange happened 5071 } 5072 } 5073 } 5074 5075 return SE.getCouldNotCompute(); 5076} 5077 5078 5079 5080//===----------------------------------------------------------------------===// 5081// SCEVCallbackVH Class Implementation 5082//===----------------------------------------------------------------------===// 5083 5084void ScalarEvolution::SCEVCallbackVH::deleted() { 5085 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5086 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5087 SE->ConstantEvolutionLoopExitValue.erase(PN); 5088 SE->Scalars.erase(getValPtr()); 5089 // this now dangles! 5090} 5091 5092void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5093 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5094 5095 // Forget all the expressions associated with users of the old value, 5096 // so that future queries will recompute the expressions using the new 5097 // value. 5098 SmallVector<User *, 16> Worklist; 5099 SmallPtrSet<User *, 8> Visited; 5100 Value *Old = getValPtr(); 5101 bool DeleteOld = false; 5102 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5103 UI != UE; ++UI) 5104 Worklist.push_back(*UI); 5105 while (!Worklist.empty()) { 5106 User *U = Worklist.pop_back_val(); 5107 // Deleting the Old value will cause this to dangle. Postpone 5108 // that until everything else is done. 5109 if (U == Old) { 5110 DeleteOld = true; 5111 continue; 5112 } 5113 if (!Visited.insert(U)) 5114 continue; 5115 if (PHINode *PN = dyn_cast<PHINode>(U)) 5116 SE->ConstantEvolutionLoopExitValue.erase(PN); 5117 SE->Scalars.erase(U); 5118 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5119 UI != UE; ++UI) 5120 Worklist.push_back(*UI); 5121 } 5122 // Delete the Old value if it (indirectly) references itself. 5123 if (DeleteOld) { 5124 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5125 SE->ConstantEvolutionLoopExitValue.erase(PN); 5126 SE->Scalars.erase(Old); 5127 // this now dangles! 5128 } 5129 // this may dangle! 5130} 5131 5132ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5133 : CallbackVH(V), SE(se) {} 5134 5135//===----------------------------------------------------------------------===// 5136// ScalarEvolution Class Implementation 5137//===----------------------------------------------------------------------===// 5138 5139ScalarEvolution::ScalarEvolution() 5140 : FunctionPass(&ID) { 5141} 5142 5143bool ScalarEvolution::runOnFunction(Function &F) { 5144 this->F = &F; 5145 LI = &getAnalysis<LoopInfo>(); 5146 TD = getAnalysisIfAvailable<TargetData>(); 5147 return false; 5148} 5149 5150void ScalarEvolution::releaseMemory() { 5151 Scalars.clear(); 5152 BackedgeTakenCounts.clear(); 5153 ConstantEvolutionLoopExitValue.clear(); 5154 ValuesAtScopes.clear(); 5155 UniqueSCEVs.clear(); 5156 SCEVAllocator.Reset(); 5157} 5158 5159void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5160 AU.setPreservesAll(); 5161 AU.addRequiredTransitive<LoopInfo>(); 5162} 5163 5164bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5165 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5166} 5167 5168static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5169 const Loop *L) { 5170 // Print all inner loops first 5171 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5172 PrintLoopInfo(OS, SE, *I); 5173 5174 OS << "Loop " << L->getHeader()->getName() << ": "; 5175 5176 SmallVector<BasicBlock*, 8> ExitBlocks; 5177 L->getExitBlocks(ExitBlocks); 5178 if (ExitBlocks.size() != 1) 5179 OS << "<multiple exits> "; 5180 5181 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5182 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5183 } else { 5184 OS << "Unpredictable backedge-taken count. "; 5185 } 5186 5187 OS << "\n"; 5188 OS << "Loop " << L->getHeader()->getName() << ": "; 5189 5190 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5191 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5192 } else { 5193 OS << "Unpredictable max backedge-taken count. "; 5194 } 5195 5196 OS << "\n"; 5197} 5198 5199void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 5200 // ScalarEvolution's implementaiton of the print method is to print 5201 // out SCEV values of all instructions that are interesting. Doing 5202 // this potentially causes it to create new SCEV objects though, 5203 // which technically conflicts with the const qualifier. This isn't 5204 // observable from outside the class though, so casting away the 5205 // const isn't dangerous. 5206 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 5207 5208 OS << "Classifying expressions for: " << F->getName() << "\n"; 5209 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5210 if (isSCEVable(I->getType())) { 5211 OS << *I << '\n'; 5212 OS << " --> "; 5213 const SCEV *SV = SE.getSCEV(&*I); 5214 SV->print(OS); 5215 5216 const Loop *L = LI->getLoopFor((*I).getParent()); 5217 5218 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5219 if (AtUse != SV) { 5220 OS << " --> "; 5221 AtUse->print(OS); 5222 } 5223 5224 if (L) { 5225 OS << "\t\t" "Exits: "; 5226 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5227 if (!ExitValue->isLoopInvariant(L)) { 5228 OS << "<<Unknown>>"; 5229 } else { 5230 OS << *ExitValue; 5231 } 5232 } 5233 5234 OS << "\n"; 5235 } 5236 5237 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 5238 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5239 PrintLoopInfo(OS, &SE, *I); 5240} 5241 5242