ScalarEvolution.cpp revision 4db3581a288dcd7e56f0a1ecdc2316cd85e183c7
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 bool HasNUW, bool HasNSW) { 1196 assert(!Ops.empty() && "Cannot get empty add!"); 1197 if (Ops.size() == 1) return Ops[0]; 1198#ifndef NDEBUG 1199 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1200 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1201 getEffectiveSCEVType(Ops[0]->getType()) && 1202 "SCEVAddExpr operand types don't match!"); 1203#endif 1204 1205 // Sort by complexity, this groups all similar expression types together. 1206 GroupByComplexity(Ops, LI); 1207 1208 // If there are any constants, fold them together. 1209 unsigned Idx = 0; 1210 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1211 ++Idx; 1212 assert(Idx < Ops.size()); 1213 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1214 // We found two constants, fold them together! 1215 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1216 RHSC->getValue()->getValue()); 1217 if (Ops.size() == 2) return Ops[0]; 1218 Ops.erase(Ops.begin()+1); // Erase the folded element 1219 LHSC = cast<SCEVConstant>(Ops[0]); 1220 } 1221 1222 // If we are left with a constant zero being added, strip it off. 1223 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1224 Ops.erase(Ops.begin()); 1225 --Idx; 1226 } 1227 } 1228 1229 if (Ops.size() == 1) return Ops[0]; 1230 1231 // Okay, check to see if the same value occurs in the operand list twice. If 1232 // so, merge them together into an multiply expression. Since we sorted the 1233 // list, these values are required to be adjacent. 1234 const Type *Ty = Ops[0]->getType(); 1235 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1236 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1237 // Found a match, merge the two values into a multiply, and add any 1238 // remaining values to the result. 1239 const SCEV *Two = getIntegerSCEV(2, Ty); 1240 const SCEV *Mul = getMulExpr(Ops[i], Two); 1241 if (Ops.size() == 2) 1242 return Mul; 1243 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1244 Ops.push_back(Mul); 1245 return getAddExpr(Ops, HasNUW, HasNSW); 1246 } 1247 1248 // Check for truncates. If all the operands are truncated from the same 1249 // type, see if factoring out the truncate would permit the result to be 1250 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1251 // if the contents of the resulting outer trunc fold to something simple. 1252 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1253 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1254 const Type *DstType = Trunc->getType(); 1255 const Type *SrcType = Trunc->getOperand()->getType(); 1256 SmallVector<const SCEV *, 8> LargeOps; 1257 bool Ok = true; 1258 // Check all the operands to see if they can be represented in the 1259 // source type of the truncate. 1260 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1261 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1262 if (T->getOperand()->getType() != SrcType) { 1263 Ok = false; 1264 break; 1265 } 1266 LargeOps.push_back(T->getOperand()); 1267 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1268 // This could be either sign or zero extension, but sign extension 1269 // is much more likely to be foldable here. 1270 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1271 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1272 SmallVector<const SCEV *, 8> LargeMulOps; 1273 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1274 if (const SCEVTruncateExpr *T = 1275 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1276 if (T->getOperand()->getType() != SrcType) { 1277 Ok = false; 1278 break; 1279 } 1280 LargeMulOps.push_back(T->getOperand()); 1281 } else if (const SCEVConstant *C = 1282 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1283 // This could be either sign or zero extension, but sign extension 1284 // is much more likely to be foldable here. 1285 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1286 } else { 1287 Ok = false; 1288 break; 1289 } 1290 } 1291 if (Ok) 1292 LargeOps.push_back(getMulExpr(LargeMulOps)); 1293 } else { 1294 Ok = false; 1295 break; 1296 } 1297 } 1298 if (Ok) { 1299 // Evaluate the expression in the larger type. 1300 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1301 // If it folds to something simple, use it. Otherwise, don't. 1302 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1303 return getTruncateExpr(Fold, DstType); 1304 } 1305 } 1306 1307 // Skip past any other cast SCEVs. 1308 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1309 ++Idx; 1310 1311 // If there are add operands they would be next. 1312 if (Idx < Ops.size()) { 1313 bool DeletedAdd = false; 1314 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1315 // If we have an add, expand the add operands onto the end of the operands 1316 // list. 1317 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1318 Ops.erase(Ops.begin()+Idx); 1319 DeletedAdd = true; 1320 } 1321 1322 // If we deleted at least one add, we added operands to the end of the list, 1323 // and they are not necessarily sorted. Recurse to resort and resimplify 1324 // any operands we just aquired. 1325 if (DeletedAdd) 1326 return getAddExpr(Ops); 1327 } 1328 1329 // Skip over the add expression until we get to a multiply. 1330 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1331 ++Idx; 1332 1333 // Check to see if there are any folding opportunities present with 1334 // operands multiplied by constant values. 1335 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1336 uint64_t BitWidth = getTypeSizeInBits(Ty); 1337 DenseMap<const SCEV *, APInt> M; 1338 SmallVector<const SCEV *, 8> NewOps; 1339 APInt AccumulatedConstant(BitWidth, 0); 1340 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1341 Ops, APInt(BitWidth, 1), *this)) { 1342 // Some interesting folding opportunity is present, so its worthwhile to 1343 // re-generate the operands list. Group the operands by constant scale, 1344 // to avoid multiplying by the same constant scale multiple times. 1345 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1346 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1347 E = NewOps.end(); I != E; ++I) 1348 MulOpLists[M.find(*I)->second].push_back(*I); 1349 // Re-generate the operands list. 1350 Ops.clear(); 1351 if (AccumulatedConstant != 0) 1352 Ops.push_back(getConstant(AccumulatedConstant)); 1353 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1354 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1355 if (I->first != 0) 1356 Ops.push_back(getMulExpr(getConstant(I->first), 1357 getAddExpr(I->second))); 1358 if (Ops.empty()) 1359 return getIntegerSCEV(0, Ty); 1360 if (Ops.size() == 1) 1361 return Ops[0]; 1362 return getAddExpr(Ops); 1363 } 1364 } 1365 1366 // If we are adding something to a multiply expression, make sure the 1367 // something is not already an operand of the multiply. If so, merge it into 1368 // the multiply. 1369 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1370 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1371 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1372 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1373 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1374 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1375 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1376 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1377 if (Mul->getNumOperands() != 2) { 1378 // If the multiply has more than two operands, we must get the 1379 // Y*Z term. 1380 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1381 MulOps.erase(MulOps.begin()+MulOp); 1382 InnerMul = getMulExpr(MulOps); 1383 } 1384 const SCEV *One = getIntegerSCEV(1, Ty); 1385 const SCEV *AddOne = getAddExpr(InnerMul, One); 1386 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1387 if (Ops.size() == 2) return OuterMul; 1388 if (AddOp < Idx) { 1389 Ops.erase(Ops.begin()+AddOp); 1390 Ops.erase(Ops.begin()+Idx-1); 1391 } else { 1392 Ops.erase(Ops.begin()+Idx); 1393 Ops.erase(Ops.begin()+AddOp-1); 1394 } 1395 Ops.push_back(OuterMul); 1396 return getAddExpr(Ops); 1397 } 1398 1399 // Check this multiply against other multiplies being added together. 1400 for (unsigned OtherMulIdx = Idx+1; 1401 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1402 ++OtherMulIdx) { 1403 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1404 // If MulOp occurs in OtherMul, we can fold the two multiplies 1405 // together. 1406 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1407 OMulOp != e; ++OMulOp) 1408 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1409 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1410 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1411 if (Mul->getNumOperands() != 2) { 1412 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1413 Mul->op_end()); 1414 MulOps.erase(MulOps.begin()+MulOp); 1415 InnerMul1 = getMulExpr(MulOps); 1416 } 1417 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1418 if (OtherMul->getNumOperands() != 2) { 1419 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1420 OtherMul->op_end()); 1421 MulOps.erase(MulOps.begin()+OMulOp); 1422 InnerMul2 = getMulExpr(MulOps); 1423 } 1424 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1425 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1426 if (Ops.size() == 2) return OuterMul; 1427 Ops.erase(Ops.begin()+Idx); 1428 Ops.erase(Ops.begin()+OtherMulIdx-1); 1429 Ops.push_back(OuterMul); 1430 return getAddExpr(Ops); 1431 } 1432 } 1433 } 1434 } 1435 1436 // If there are any add recurrences in the operands list, see if any other 1437 // added values are loop invariant. If so, we can fold them into the 1438 // recurrence. 1439 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1440 ++Idx; 1441 1442 // Scan over all recurrences, trying to fold loop invariants into them. 1443 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1444 // Scan all of the other operands to this add and add them to the vector if 1445 // they are loop invariant w.r.t. the recurrence. 1446 SmallVector<const SCEV *, 8> LIOps; 1447 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1448 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1449 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1450 LIOps.push_back(Ops[i]); 1451 Ops.erase(Ops.begin()+i); 1452 --i; --e; 1453 } 1454 1455 // If we found some loop invariants, fold them into the recurrence. 1456 if (!LIOps.empty()) { 1457 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1458 LIOps.push_back(AddRec->getStart()); 1459 1460 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1461 AddRec->op_end()); 1462 AddRecOps[0] = getAddExpr(LIOps); 1463 1464 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1465 // If all of the other operands were loop invariant, we are done. 1466 if (Ops.size() == 1) return NewRec; 1467 1468 // Otherwise, add the folded AddRec by the non-liv parts. 1469 for (unsigned i = 0;; ++i) 1470 if (Ops[i] == AddRec) { 1471 Ops[i] = NewRec; 1472 break; 1473 } 1474 return getAddExpr(Ops); 1475 } 1476 1477 // Okay, if there weren't any loop invariants to be folded, check to see if 1478 // there are multiple AddRec's with the same loop induction variable being 1479 // added together. If so, we can fold them. 1480 for (unsigned OtherIdx = Idx+1; 1481 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1482 if (OtherIdx != Idx) { 1483 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1484 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1485 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1486 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1487 AddRec->op_end()); 1488 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1489 if (i >= NewOps.size()) { 1490 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1491 OtherAddRec->op_end()); 1492 break; 1493 } 1494 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1495 } 1496 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1497 1498 if (Ops.size() == 2) return NewAddRec; 1499 1500 Ops.erase(Ops.begin()+Idx); 1501 Ops.erase(Ops.begin()+OtherIdx-1); 1502 Ops.push_back(NewAddRec); 1503 return getAddExpr(Ops); 1504 } 1505 } 1506 1507 // Otherwise couldn't fold anything into this recurrence. Move onto the 1508 // next one. 1509 } 1510 1511 // Okay, it looks like we really DO need an add expr. Check to see if we 1512 // already have one, otherwise create a new one. 1513 FoldingSetNodeID ID; 1514 ID.AddInteger(scAddExpr); 1515 ID.AddInteger(Ops.size()); 1516 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1517 ID.AddPointer(Ops[i]); 1518 void *IP = 0; 1519 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1520 SCEVAddExpr *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1521 new (S) SCEVAddExpr(ID, Ops); 1522 UniqueSCEVs.InsertNode(S, IP); 1523 if (HasNUW) S->setHasNoUnsignedWrap(true); 1524 if (HasNSW) S->setHasNoSignedWrap(true); 1525 return S; 1526} 1527 1528 1529/// getMulExpr - Get a canonical multiply expression, or something simpler if 1530/// possible. 1531const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1532 bool HasNUW, bool HasNSW) { 1533 assert(!Ops.empty() && "Cannot get empty mul!"); 1534#ifndef NDEBUG 1535 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1536 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1537 getEffectiveSCEVType(Ops[0]->getType()) && 1538 "SCEVMulExpr operand types don't match!"); 1539#endif 1540 1541 // Sort by complexity, this groups all similar expression types together. 1542 GroupByComplexity(Ops, LI); 1543 1544 // If there are any constants, fold them together. 1545 unsigned Idx = 0; 1546 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1547 1548 // C1*(C2+V) -> C1*C2 + C1*V 1549 if (Ops.size() == 2) 1550 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1551 if (Add->getNumOperands() == 2 && 1552 isa<SCEVConstant>(Add->getOperand(0))) 1553 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1554 getMulExpr(LHSC, Add->getOperand(1))); 1555 1556 1557 ++Idx; 1558 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1559 // We found two constants, fold them together! 1560 ConstantInt *Fold = ConstantInt::get(getContext(), 1561 LHSC->getValue()->getValue() * 1562 RHSC->getValue()->getValue()); 1563 Ops[0] = getConstant(Fold); 1564 Ops.erase(Ops.begin()+1); // Erase the folded element 1565 if (Ops.size() == 1) return Ops[0]; 1566 LHSC = cast<SCEVConstant>(Ops[0]); 1567 } 1568 1569 // If we are left with a constant one being multiplied, strip it off. 1570 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1571 Ops.erase(Ops.begin()); 1572 --Idx; 1573 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1574 // If we have a multiply of zero, it will always be zero. 1575 return Ops[0]; 1576 } 1577 } 1578 1579 // Skip over the add expression until we get to a multiply. 1580 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1581 ++Idx; 1582 1583 if (Ops.size() == 1) 1584 return Ops[0]; 1585 1586 // If there are mul operands inline them all into this expression. 1587 if (Idx < Ops.size()) { 1588 bool DeletedMul = false; 1589 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1590 // If we have an mul, expand the mul operands onto the end of the operands 1591 // list. 1592 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1593 Ops.erase(Ops.begin()+Idx); 1594 DeletedMul = true; 1595 } 1596 1597 // If we deleted at least one mul, we added operands to the end of the list, 1598 // and they are not necessarily sorted. Recurse to resort and resimplify 1599 // any operands we just aquired. 1600 if (DeletedMul) 1601 return getMulExpr(Ops); 1602 } 1603 1604 // If there are any add recurrences in the operands list, see if any other 1605 // added values are loop invariant. If so, we can fold them into the 1606 // recurrence. 1607 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1608 ++Idx; 1609 1610 // Scan over all recurrences, trying to fold loop invariants into them. 1611 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1612 // Scan all of the other operands to this mul and add them to the vector if 1613 // they are loop invariant w.r.t. the recurrence. 1614 SmallVector<const SCEV *, 8> LIOps; 1615 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1616 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1617 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1618 LIOps.push_back(Ops[i]); 1619 Ops.erase(Ops.begin()+i); 1620 --i; --e; 1621 } 1622 1623 // If we found some loop invariants, fold them into the recurrence. 1624 if (!LIOps.empty()) { 1625 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1626 SmallVector<const SCEV *, 4> NewOps; 1627 NewOps.reserve(AddRec->getNumOperands()); 1628 if (LIOps.size() == 1) { 1629 const SCEV *Scale = LIOps[0]; 1630 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1631 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1632 } else { 1633 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1634 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1635 MulOps.push_back(AddRec->getOperand(i)); 1636 NewOps.push_back(getMulExpr(MulOps)); 1637 } 1638 } 1639 1640 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1641 1642 // If all of the other operands were loop invariant, we are done. 1643 if (Ops.size() == 1) return NewRec; 1644 1645 // Otherwise, multiply the folded AddRec by the non-liv parts. 1646 for (unsigned i = 0;; ++i) 1647 if (Ops[i] == AddRec) { 1648 Ops[i] = NewRec; 1649 break; 1650 } 1651 return getMulExpr(Ops); 1652 } 1653 1654 // Okay, if there weren't any loop invariants to be folded, check to see if 1655 // there are multiple AddRec's with the same loop induction variable being 1656 // multiplied together. If so, we can fold them. 1657 for (unsigned OtherIdx = Idx+1; 1658 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1659 if (OtherIdx != Idx) { 1660 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1661 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1662 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1663 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1664 const SCEV *NewStart = getMulExpr(F->getStart(), 1665 G->getStart()); 1666 const SCEV *B = F->getStepRecurrence(*this); 1667 const SCEV *D = G->getStepRecurrence(*this); 1668 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1669 getMulExpr(G, B), 1670 getMulExpr(B, D)); 1671 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1672 F->getLoop()); 1673 if (Ops.size() == 2) return NewAddRec; 1674 1675 Ops.erase(Ops.begin()+Idx); 1676 Ops.erase(Ops.begin()+OtherIdx-1); 1677 Ops.push_back(NewAddRec); 1678 return getMulExpr(Ops); 1679 } 1680 } 1681 1682 // Otherwise couldn't fold anything into this recurrence. Move onto the 1683 // next one. 1684 } 1685 1686 // Okay, it looks like we really DO need an mul expr. Check to see if we 1687 // already have one, otherwise create a new one. 1688 FoldingSetNodeID ID; 1689 ID.AddInteger(scMulExpr); 1690 ID.AddInteger(Ops.size()); 1691 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1692 ID.AddPointer(Ops[i]); 1693 void *IP = 0; 1694 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1695 SCEVMulExpr *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1696 new (S) SCEVMulExpr(ID, Ops); 1697 UniqueSCEVs.InsertNode(S, IP); 1698 if (HasNUW) S->setHasNoUnsignedWrap(true); 1699 if (HasNSW) S->setHasNoSignedWrap(true); 1700 return S; 1701} 1702 1703/// getUDivExpr - Get a canonical unsigned division expression, or something 1704/// simpler if possible. 1705const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1706 const SCEV *RHS) { 1707 assert(getEffectiveSCEVType(LHS->getType()) == 1708 getEffectiveSCEVType(RHS->getType()) && 1709 "SCEVUDivExpr operand types don't match!"); 1710 1711 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1712 if (RHSC->getValue()->equalsInt(1)) 1713 return LHS; // X udiv 1 --> x 1714 if (RHSC->isZero()) 1715 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1716 1717 // Determine if the division can be folded into the operands of 1718 // its operands. 1719 // TODO: Generalize this to non-constants by using known-bits information. 1720 const Type *Ty = LHS->getType(); 1721 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1722 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1723 // For non-power-of-two values, effectively round the value up to the 1724 // nearest power of two. 1725 if (!RHSC->getValue()->getValue().isPowerOf2()) 1726 ++MaxShiftAmt; 1727 const IntegerType *ExtTy = 1728 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1729 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1730 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1731 if (const SCEVConstant *Step = 1732 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1733 if (!Step->getValue()->getValue() 1734 .urem(RHSC->getValue()->getValue()) && 1735 getZeroExtendExpr(AR, ExtTy) == 1736 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1737 getZeroExtendExpr(Step, ExtTy), 1738 AR->getLoop())) { 1739 SmallVector<const SCEV *, 4> Operands; 1740 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1741 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1742 return getAddRecExpr(Operands, AR->getLoop()); 1743 } 1744 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1745 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1746 SmallVector<const SCEV *, 4> Operands; 1747 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1748 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1749 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1750 // Find an operand that's safely divisible. 1751 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1752 const SCEV *Op = M->getOperand(i); 1753 const SCEV *Div = getUDivExpr(Op, RHSC); 1754 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1755 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1756 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1757 MOperands.end()); 1758 Operands[i] = Div; 1759 return getMulExpr(Operands); 1760 } 1761 } 1762 } 1763 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1764 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1765 SmallVector<const SCEV *, 4> Operands; 1766 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1767 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1768 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1769 Operands.clear(); 1770 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1771 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1772 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1773 break; 1774 Operands.push_back(Op); 1775 } 1776 if (Operands.size() == A->getNumOperands()) 1777 return getAddExpr(Operands); 1778 } 1779 } 1780 1781 // Fold if both operands are constant. 1782 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1783 Constant *LHSCV = LHSC->getValue(); 1784 Constant *RHSCV = RHSC->getValue(); 1785 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1786 RHSCV))); 1787 } 1788 } 1789 1790 FoldingSetNodeID ID; 1791 ID.AddInteger(scUDivExpr); 1792 ID.AddPointer(LHS); 1793 ID.AddPointer(RHS); 1794 void *IP = 0; 1795 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1796 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1797 new (S) SCEVUDivExpr(ID, LHS, RHS); 1798 UniqueSCEVs.InsertNode(S, IP); 1799 return S; 1800} 1801 1802 1803/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1804/// Simplify the expression as much as possible. 1805const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1806 const SCEV *Step, const Loop *L, 1807 bool HasNUW, bool HasNSW) { 1808 SmallVector<const SCEV *, 4> Operands; 1809 Operands.push_back(Start); 1810 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1811 if (StepChrec->getLoop() == L) { 1812 Operands.insert(Operands.end(), StepChrec->op_begin(), 1813 StepChrec->op_end()); 1814 return getAddRecExpr(Operands, L); 1815 } 1816 1817 Operands.push_back(Step); 1818 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1819} 1820 1821/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1822/// Simplify the expression as much as possible. 1823const SCEV * 1824ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1825 const Loop *L, 1826 bool HasNUW, bool HasNSW) { 1827 if (Operands.size() == 1) return Operands[0]; 1828#ifndef NDEBUG 1829 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1830 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1831 getEffectiveSCEVType(Operands[0]->getType()) && 1832 "SCEVAddRecExpr operand types don't match!"); 1833#endif 1834 1835 if (Operands.back()->isZero()) { 1836 Operands.pop_back(); 1837 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1838 } 1839 1840 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1841 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1842 const Loop* NestedLoop = NestedAR->getLoop(); 1843 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1844 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1845 NestedAR->op_end()); 1846 Operands[0] = NestedAR->getStart(); 1847 // AddRecs require their operands be loop-invariant with respect to their 1848 // loops. Don't perform this transformation if it would break this 1849 // requirement. 1850 bool AllInvariant = true; 1851 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1852 if (!Operands[i]->isLoopInvariant(L)) { 1853 AllInvariant = false; 1854 break; 1855 } 1856 if (AllInvariant) { 1857 NestedOperands[0] = getAddRecExpr(Operands, L); 1858 AllInvariant = true; 1859 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1860 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1861 AllInvariant = false; 1862 break; 1863 } 1864 if (AllInvariant) 1865 // Ok, both add recurrences are valid after the transformation. 1866 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 1867 } 1868 // Reset Operands to its original state. 1869 Operands[0] = NestedAR; 1870 } 1871 } 1872 1873 FoldingSetNodeID ID; 1874 ID.AddInteger(scAddRecExpr); 1875 ID.AddInteger(Operands.size()); 1876 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1877 ID.AddPointer(Operands[i]); 1878 ID.AddPointer(L); 1879 void *IP = 0; 1880 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1881 SCEVAddRecExpr *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1882 new (S) SCEVAddRecExpr(ID, Operands, L); 1883 UniqueSCEVs.InsertNode(S, IP); 1884 if (HasNUW) S->setHasNoUnsignedWrap(true); 1885 if (HasNSW) S->setHasNoSignedWrap(true); 1886 return S; 1887} 1888 1889const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1890 const SCEV *RHS) { 1891 SmallVector<const SCEV *, 2> Ops; 1892 Ops.push_back(LHS); 1893 Ops.push_back(RHS); 1894 return getSMaxExpr(Ops); 1895} 1896 1897const SCEV * 1898ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1899 assert(!Ops.empty() && "Cannot get empty smax!"); 1900 if (Ops.size() == 1) return Ops[0]; 1901#ifndef NDEBUG 1902 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1903 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1904 getEffectiveSCEVType(Ops[0]->getType()) && 1905 "SCEVSMaxExpr operand types don't match!"); 1906#endif 1907 1908 // Sort by complexity, this groups all similar expression types together. 1909 GroupByComplexity(Ops, LI); 1910 1911 // If there are any constants, fold them together. 1912 unsigned Idx = 0; 1913 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1914 ++Idx; 1915 assert(Idx < Ops.size()); 1916 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1917 // We found two constants, fold them together! 1918 ConstantInt *Fold = ConstantInt::get(getContext(), 1919 APIntOps::smax(LHSC->getValue()->getValue(), 1920 RHSC->getValue()->getValue())); 1921 Ops[0] = getConstant(Fold); 1922 Ops.erase(Ops.begin()+1); // Erase the folded element 1923 if (Ops.size() == 1) return Ops[0]; 1924 LHSC = cast<SCEVConstant>(Ops[0]); 1925 } 1926 1927 // If we are left with a constant minimum-int, strip it off. 1928 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1929 Ops.erase(Ops.begin()); 1930 --Idx; 1931 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1932 // If we have an smax with a constant maximum-int, it will always be 1933 // maximum-int. 1934 return Ops[0]; 1935 } 1936 } 1937 1938 if (Ops.size() == 1) return Ops[0]; 1939 1940 // Find the first SMax 1941 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1942 ++Idx; 1943 1944 // Check to see if one of the operands is an SMax. If so, expand its operands 1945 // onto our operand list, and recurse to simplify. 1946 if (Idx < Ops.size()) { 1947 bool DeletedSMax = false; 1948 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1949 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1950 Ops.erase(Ops.begin()+Idx); 1951 DeletedSMax = true; 1952 } 1953 1954 if (DeletedSMax) 1955 return getSMaxExpr(Ops); 1956 } 1957 1958 // Okay, check to see if the same value occurs in the operand list twice. If 1959 // so, delete one. Since we sorted the list, these values are required to 1960 // be adjacent. 1961 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1962 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1963 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1964 --i; --e; 1965 } 1966 1967 if (Ops.size() == 1) return Ops[0]; 1968 1969 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1970 1971 // Okay, it looks like we really DO need an smax expr. Check to see if we 1972 // already have one, otherwise create a new one. 1973 FoldingSetNodeID ID; 1974 ID.AddInteger(scSMaxExpr); 1975 ID.AddInteger(Ops.size()); 1976 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1977 ID.AddPointer(Ops[i]); 1978 void *IP = 0; 1979 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1980 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1981 new (S) SCEVSMaxExpr(ID, Ops); 1982 UniqueSCEVs.InsertNode(S, IP); 1983 return S; 1984} 1985 1986const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1987 const SCEV *RHS) { 1988 SmallVector<const SCEV *, 2> Ops; 1989 Ops.push_back(LHS); 1990 Ops.push_back(RHS); 1991 return getUMaxExpr(Ops); 1992} 1993 1994const SCEV * 1995ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1996 assert(!Ops.empty() && "Cannot get empty umax!"); 1997 if (Ops.size() == 1) return Ops[0]; 1998#ifndef NDEBUG 1999 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2000 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2001 getEffectiveSCEVType(Ops[0]->getType()) && 2002 "SCEVUMaxExpr operand types don't match!"); 2003#endif 2004 2005 // Sort by complexity, this groups all similar expression types together. 2006 GroupByComplexity(Ops, LI); 2007 2008 // If there are any constants, fold them together. 2009 unsigned Idx = 0; 2010 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2011 ++Idx; 2012 assert(Idx < Ops.size()); 2013 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2014 // We found two constants, fold them together! 2015 ConstantInt *Fold = ConstantInt::get(getContext(), 2016 APIntOps::umax(LHSC->getValue()->getValue(), 2017 RHSC->getValue()->getValue())); 2018 Ops[0] = getConstant(Fold); 2019 Ops.erase(Ops.begin()+1); // Erase the folded element 2020 if (Ops.size() == 1) return Ops[0]; 2021 LHSC = cast<SCEVConstant>(Ops[0]); 2022 } 2023 2024 // If we are left with a constant minimum-int, strip it off. 2025 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2026 Ops.erase(Ops.begin()); 2027 --Idx; 2028 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2029 // If we have an umax with a constant maximum-int, it will always be 2030 // maximum-int. 2031 return Ops[0]; 2032 } 2033 } 2034 2035 if (Ops.size() == 1) return Ops[0]; 2036 2037 // Find the first UMax 2038 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2039 ++Idx; 2040 2041 // Check to see if one of the operands is a UMax. If so, expand its operands 2042 // onto our operand list, and recurse to simplify. 2043 if (Idx < Ops.size()) { 2044 bool DeletedUMax = false; 2045 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2046 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2047 Ops.erase(Ops.begin()+Idx); 2048 DeletedUMax = true; 2049 } 2050 2051 if (DeletedUMax) 2052 return getUMaxExpr(Ops); 2053 } 2054 2055 // Okay, check to see if the same value occurs in the operand list twice. If 2056 // so, delete one. Since we sorted the list, these values are required to 2057 // be adjacent. 2058 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2059 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2060 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2061 --i; --e; 2062 } 2063 2064 if (Ops.size() == 1) return Ops[0]; 2065 2066 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2067 2068 // Okay, it looks like we really DO need a umax expr. Check to see if we 2069 // already have one, otherwise create a new one. 2070 FoldingSetNodeID ID; 2071 ID.AddInteger(scUMaxExpr); 2072 ID.AddInteger(Ops.size()); 2073 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2074 ID.AddPointer(Ops[i]); 2075 void *IP = 0; 2076 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2077 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2078 new (S) SCEVUMaxExpr(ID, Ops); 2079 UniqueSCEVs.InsertNode(S, IP); 2080 return S; 2081} 2082 2083const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2084 const SCEV *RHS) { 2085 // ~smax(~x, ~y) == smin(x, y). 2086 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2087} 2088 2089const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2090 const SCEV *RHS) { 2091 // ~umax(~x, ~y) == umin(x, y) 2092 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2093} 2094 2095const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy, 2096 unsigned FieldNo) { 2097 // If we have TargetData we can determine the constant offset. 2098 if (TD) { 2099 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2100 const StructLayout &SL = *TD->getStructLayout(STy); 2101 uint64_t Offset = SL.getElementOffset(FieldNo); 2102 return getIntegerSCEV(Offset, IntPtrTy); 2103 } 2104 2105 // Field 0 is always at offset 0. 2106 if (FieldNo == 0) { 2107 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2108 return getIntegerSCEV(0, Ty); 2109 } 2110 2111 // Okay, it looks like we really DO need an offsetof expr. Check to see if we 2112 // already have one, otherwise create a new one. 2113 FoldingSetNodeID ID; 2114 ID.AddInteger(scFieldOffset); 2115 ID.AddPointer(STy); 2116 ID.AddInteger(FieldNo); 2117 void *IP = 0; 2118 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2119 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>(); 2120 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2121 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo); 2122 UniqueSCEVs.InsertNode(S, IP); 2123 return S; 2124} 2125 2126const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) { 2127 // If we have TargetData we can determine the constant size. 2128 if (TD && AllocTy->isSized()) { 2129 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2130 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy); 2131 } 2132 2133 // Expand an array size into the element size times the number 2134 // of elements. 2135 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) { 2136 const SCEV *E = getAllocSizeExpr(ATy->getElementType()); 2137 return getMulExpr( 2138 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2139 ATy->getNumElements()))); 2140 } 2141 2142 // Expand a vector size into the element size times the number 2143 // of elements. 2144 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) { 2145 const SCEV *E = getAllocSizeExpr(VTy->getElementType()); 2146 return getMulExpr( 2147 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2148 VTy->getNumElements()))); 2149 } 2150 2151 // Okay, it looks like we really DO need a sizeof expr. Check to see if we 2152 // already have one, otherwise create a new one. 2153 FoldingSetNodeID ID; 2154 ID.AddInteger(scAllocSize); 2155 ID.AddPointer(AllocTy); 2156 void *IP = 0; 2157 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2158 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>(); 2159 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2160 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy); 2161 UniqueSCEVs.InsertNode(S, IP); 2162 return S; 2163} 2164 2165const SCEV *ScalarEvolution::getUnknown(Value *V) { 2166 // Don't attempt to do anything other than create a SCEVUnknown object 2167 // here. createSCEV only calls getUnknown after checking for all other 2168 // interesting possibilities, and any other code that calls getUnknown 2169 // is doing so in order to hide a value from SCEV canonicalization. 2170 2171 FoldingSetNodeID ID; 2172 ID.AddInteger(scUnknown); 2173 ID.AddPointer(V); 2174 void *IP = 0; 2175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2176 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2177 new (S) SCEVUnknown(ID, V); 2178 UniqueSCEVs.InsertNode(S, IP); 2179 return S; 2180} 2181 2182//===----------------------------------------------------------------------===// 2183// Basic SCEV Analysis and PHI Idiom Recognition Code 2184// 2185 2186/// isSCEVable - Test if values of the given type are analyzable within 2187/// the SCEV framework. This primarily includes integer types, and it 2188/// can optionally include pointer types if the ScalarEvolution class 2189/// has access to target-specific information. 2190bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2191 // Integers and pointers are always SCEVable. 2192 return Ty->isInteger() || isa<PointerType>(Ty); 2193} 2194 2195/// getTypeSizeInBits - Return the size in bits of the specified type, 2196/// for which isSCEVable must return true. 2197uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2198 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2199 2200 // If we have a TargetData, use it! 2201 if (TD) 2202 return TD->getTypeSizeInBits(Ty); 2203 2204 // Integer types have fixed sizes. 2205 if (Ty->isInteger()) 2206 return Ty->getPrimitiveSizeInBits(); 2207 2208 // The only other support type is pointer. Without TargetData, conservatively 2209 // assume pointers are 64-bit. 2210 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!"); 2211 return 64; 2212} 2213 2214/// getEffectiveSCEVType - Return a type with the same bitwidth as 2215/// the given type and which represents how SCEV will treat the given 2216/// type, for which isSCEVable must return true. For pointer types, 2217/// this is the pointer-sized integer type. 2218const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2219 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2220 2221 if (Ty->isInteger()) 2222 return Ty; 2223 2224 // The only other support type is pointer. 2225 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2226 if (TD) return TD->getIntPtrType(getContext()); 2227 2228 // Without TargetData, conservatively assume pointers are 64-bit. 2229 return Type::getInt64Ty(getContext()); 2230} 2231 2232const SCEV *ScalarEvolution::getCouldNotCompute() { 2233 return &CouldNotCompute; 2234} 2235 2236/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2237/// expression and create a new one. 2238const SCEV *ScalarEvolution::getSCEV(Value *V) { 2239 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2240 2241 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2242 if (I != Scalars.end()) return I->second; 2243 const SCEV *S = createSCEV(V); 2244 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2245 return S; 2246} 2247 2248/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2249/// specified signed integer value and return a SCEV for the constant. 2250const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2251 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2252 return getConstant(ConstantInt::get(ITy, Val)); 2253} 2254 2255/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2256/// 2257const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2258 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2259 return getConstant( 2260 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2261 2262 const Type *Ty = V->getType(); 2263 Ty = getEffectiveSCEVType(Ty); 2264 return getMulExpr(V, 2265 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2266} 2267 2268/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2269const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2270 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2271 return getConstant( 2272 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2273 2274 const Type *Ty = V->getType(); 2275 Ty = getEffectiveSCEVType(Ty); 2276 const SCEV *AllOnes = 2277 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2278 return getMinusSCEV(AllOnes, V); 2279} 2280 2281/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2282/// 2283const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2284 const SCEV *RHS) { 2285 // X - Y --> X + -Y 2286 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2287} 2288 2289/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2290/// input value to the specified type. If the type must be extended, it is zero 2291/// extended. 2292const SCEV * 2293ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2294 const Type *Ty) { 2295 const Type *SrcTy = V->getType(); 2296 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2297 (Ty->isInteger() || isa<PointerType>(Ty)) && 2298 "Cannot truncate or zero extend with non-integer arguments!"); 2299 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2300 return V; // No conversion 2301 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2302 return getTruncateExpr(V, Ty); 2303 return getZeroExtendExpr(V, Ty); 2304} 2305 2306/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2307/// input value to the specified type. If the type must be extended, it is sign 2308/// extended. 2309const SCEV * 2310ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2311 const Type *Ty) { 2312 const Type *SrcTy = V->getType(); 2313 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2314 (Ty->isInteger() || isa<PointerType>(Ty)) && 2315 "Cannot truncate or zero extend with non-integer arguments!"); 2316 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2317 return V; // No conversion 2318 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2319 return getTruncateExpr(V, Ty); 2320 return getSignExtendExpr(V, Ty); 2321} 2322 2323/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2324/// input value to the specified type. If the type must be extended, it is zero 2325/// extended. The conversion must not be narrowing. 2326const SCEV * 2327ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2328 const Type *SrcTy = V->getType(); 2329 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2330 (Ty->isInteger() || isa<PointerType>(Ty)) && 2331 "Cannot noop or zero extend with non-integer arguments!"); 2332 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2333 "getNoopOrZeroExtend cannot truncate!"); 2334 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2335 return V; // No conversion 2336 return getZeroExtendExpr(V, Ty); 2337} 2338 2339/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2340/// input value to the specified type. If the type must be extended, it is sign 2341/// extended. The conversion must not be narrowing. 2342const SCEV * 2343ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2344 const Type *SrcTy = V->getType(); 2345 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2346 (Ty->isInteger() || isa<PointerType>(Ty)) && 2347 "Cannot noop or sign extend with non-integer arguments!"); 2348 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2349 "getNoopOrSignExtend cannot truncate!"); 2350 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2351 return V; // No conversion 2352 return getSignExtendExpr(V, Ty); 2353} 2354 2355/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2356/// the input value to the specified type. If the type must be extended, 2357/// it is extended with unspecified bits. The conversion must not be 2358/// narrowing. 2359const SCEV * 2360ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2361 const Type *SrcTy = V->getType(); 2362 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2363 (Ty->isInteger() || isa<PointerType>(Ty)) && 2364 "Cannot noop or any extend with non-integer arguments!"); 2365 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2366 "getNoopOrAnyExtend cannot truncate!"); 2367 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2368 return V; // No conversion 2369 return getAnyExtendExpr(V, Ty); 2370} 2371 2372/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2373/// input value to the specified type. The conversion must not be widening. 2374const SCEV * 2375ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2376 const Type *SrcTy = V->getType(); 2377 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2378 (Ty->isInteger() || isa<PointerType>(Ty)) && 2379 "Cannot truncate or noop with non-integer arguments!"); 2380 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2381 "getTruncateOrNoop cannot extend!"); 2382 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2383 return V; // No conversion 2384 return getTruncateExpr(V, Ty); 2385} 2386 2387/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2388/// the types using zero-extension, and then perform a umax operation 2389/// with them. 2390const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2391 const SCEV *RHS) { 2392 const SCEV *PromotedLHS = LHS; 2393 const SCEV *PromotedRHS = RHS; 2394 2395 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2396 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2397 else 2398 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2399 2400 return getUMaxExpr(PromotedLHS, PromotedRHS); 2401} 2402 2403/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2404/// the types using zero-extension, and then perform a umin operation 2405/// with them. 2406const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2407 const SCEV *RHS) { 2408 const SCEV *PromotedLHS = LHS; 2409 const SCEV *PromotedRHS = RHS; 2410 2411 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2412 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2413 else 2414 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2415 2416 return getUMinExpr(PromotedLHS, PromotedRHS); 2417} 2418 2419/// PushDefUseChildren - Push users of the given Instruction 2420/// onto the given Worklist. 2421static void 2422PushDefUseChildren(Instruction *I, 2423 SmallVectorImpl<Instruction *> &Worklist) { 2424 // Push the def-use children onto the Worklist stack. 2425 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2426 UI != UE; ++UI) 2427 Worklist.push_back(cast<Instruction>(UI)); 2428} 2429 2430/// ForgetSymbolicValue - This looks up computed SCEV values for all 2431/// instructions that depend on the given instruction and removes them from 2432/// the Scalars map if they reference SymName. This is used during PHI 2433/// resolution. 2434void 2435ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2436 SmallVector<Instruction *, 16> Worklist; 2437 PushDefUseChildren(I, Worklist); 2438 2439 SmallPtrSet<Instruction *, 8> Visited; 2440 Visited.insert(I); 2441 while (!Worklist.empty()) { 2442 Instruction *I = Worklist.pop_back_val(); 2443 if (!Visited.insert(I)) continue; 2444 2445 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2446 Scalars.find(static_cast<Value *>(I)); 2447 if (It != Scalars.end()) { 2448 // Short-circuit the def-use traversal if the symbolic name 2449 // ceases to appear in expressions. 2450 if (!It->second->hasOperand(SymName)) 2451 continue; 2452 2453 // SCEVUnknown for a PHI either means that it has an unrecognized 2454 // structure, or it's a PHI that's in the progress of being computed 2455 // by createNodeForPHI. In the former case, additional loop trip 2456 // count information isn't going to change anything. In the later 2457 // case, createNodeForPHI will perform the necessary updates on its 2458 // own when it gets to that point. 2459 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 2460 ValuesAtScopes.erase(It->second); 2461 Scalars.erase(It); 2462 } 2463 } 2464 2465 PushDefUseChildren(I, Worklist); 2466 } 2467} 2468 2469/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2470/// a loop header, making it a potential recurrence, or it doesn't. 2471/// 2472const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2473 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2474 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2475 if (L->getHeader() == PN->getParent()) { 2476 // If it lives in the loop header, it has two incoming values, one 2477 // from outside the loop, and one from inside. 2478 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2479 unsigned BackEdge = IncomingEdge^1; 2480 2481 // While we are analyzing this PHI node, handle its value symbolically. 2482 const SCEV *SymbolicName = getUnknown(PN); 2483 assert(Scalars.find(PN) == Scalars.end() && 2484 "PHI node already processed?"); 2485 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2486 2487 // Using this symbolic name for the PHI, analyze the value coming around 2488 // the back-edge. 2489 Value *BEValueV = PN->getIncomingValue(BackEdge); 2490 const SCEV *BEValue = getSCEV(BEValueV); 2491 2492 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2493 // has a special value for the first iteration of the loop. 2494 2495 // If the value coming around the backedge is an add with the symbolic 2496 // value we just inserted, then we found a simple induction variable! 2497 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2498 // If there is a single occurrence of the symbolic value, replace it 2499 // with a recurrence. 2500 unsigned FoundIndex = Add->getNumOperands(); 2501 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2502 if (Add->getOperand(i) == SymbolicName) 2503 if (FoundIndex == e) { 2504 FoundIndex = i; 2505 break; 2506 } 2507 2508 if (FoundIndex != Add->getNumOperands()) { 2509 // Create an add with everything but the specified operand. 2510 SmallVector<const SCEV *, 8> Ops; 2511 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2512 if (i != FoundIndex) 2513 Ops.push_back(Add->getOperand(i)); 2514 const SCEV *Accum = getAddExpr(Ops); 2515 2516 // This is not a valid addrec if the step amount is varying each 2517 // loop iteration, but is not itself an addrec in this loop. 2518 if (Accum->isLoopInvariant(L) || 2519 (isa<SCEVAddRecExpr>(Accum) && 2520 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2521 const SCEV *StartVal = 2522 getSCEV(PN->getIncomingValue(IncomingEdge)); 2523 const SCEVAddRecExpr *PHISCEV = 2524 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L)); 2525 2526 // If the increment doesn't overflow, then neither the addrec nor the 2527 // post-increment will overflow. 2528 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) 2529 if (OBO->getOperand(0) == PN && 2530 getSCEV(OBO->getOperand(1)) == 2531 PHISCEV->getStepRecurrence(*this)) { 2532 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this); 2533 if (OBO->hasNoUnsignedWrap()) { 2534 const_cast<SCEVAddRecExpr *>(PHISCEV) 2535 ->setHasNoUnsignedWrap(true); 2536 const_cast<SCEVAddRecExpr *>(PostInc) 2537 ->setHasNoUnsignedWrap(true); 2538 } 2539 if (OBO->hasNoSignedWrap()) { 2540 const_cast<SCEVAddRecExpr *>(PHISCEV) 2541 ->setHasNoSignedWrap(true); 2542 const_cast<SCEVAddRecExpr *>(PostInc) 2543 ->setHasNoSignedWrap(true); 2544 } 2545 } 2546 2547 // Okay, for the entire analysis of this edge we assumed the PHI 2548 // to be symbolic. We now need to go back and purge all of the 2549 // entries for the scalars that use the symbolic expression. 2550 ForgetSymbolicName(PN, SymbolicName); 2551 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2552 return PHISCEV; 2553 } 2554 } 2555 } else if (const SCEVAddRecExpr *AddRec = 2556 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2557 // Otherwise, this could be a loop like this: 2558 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2559 // In this case, j = {1,+,1} and BEValue is j. 2560 // Because the other in-value of i (0) fits the evolution of BEValue 2561 // i really is an addrec evolution. 2562 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2563 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2564 2565 // If StartVal = j.start - j.stride, we can use StartVal as the 2566 // initial step of the addrec evolution. 2567 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2568 AddRec->getOperand(1))) { 2569 const SCEV *PHISCEV = 2570 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2571 2572 // Okay, for the entire analysis of this edge we assumed the PHI 2573 // to be symbolic. We now need to go back and purge all of the 2574 // entries for the scalars that use the symbolic expression. 2575 ForgetSymbolicName(PN, SymbolicName); 2576 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2577 return PHISCEV; 2578 } 2579 } 2580 } 2581 2582 return SymbolicName; 2583 } 2584 2585 // It's tempting to recognize PHIs with a unique incoming value, however 2586 // this leads passes like indvars to break LCSSA form. Fortunately, such 2587 // PHIs are rare, as instcombine zaps them. 2588 2589 // If it's not a loop phi, we can't handle it yet. 2590 return getUnknown(PN); 2591} 2592 2593/// createNodeForGEP - Expand GEP instructions into add and multiply 2594/// operations. This allows them to be analyzed by regular SCEV code. 2595/// 2596const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) { 2597 2598 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2599 Value *Base = GEP->getOperand(0); 2600 // Don't attempt to analyze GEPs over unsized objects. 2601 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2602 return getUnknown(GEP); 2603 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2604 gep_type_iterator GTI = gep_type_begin(GEP); 2605 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2606 E = GEP->op_end(); 2607 I != E; ++I) { 2608 Value *Index = *I; 2609 // Compute the (potentially symbolic) offset in bytes for this index. 2610 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2611 // For a struct, add the member offset. 2612 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2613 TotalOffset = getAddExpr(TotalOffset, 2614 getFieldOffsetExpr(STy, FieldNo)); 2615 } else { 2616 // For an array, add the element offset, explicitly scaled. 2617 const SCEV *LocalOffset = getSCEV(Index); 2618 if (!isa<PointerType>(LocalOffset->getType())) 2619 // Getelementptr indicies are signed. 2620 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2621 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI)); 2622 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2623 } 2624 } 2625 return getAddExpr(getSCEV(Base), TotalOffset); 2626} 2627 2628/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2629/// guaranteed to end in (at every loop iteration). It is, at the same time, 2630/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2631/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2632uint32_t 2633ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2634 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2635 return C->getValue()->getValue().countTrailingZeros(); 2636 2637 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2638 return std::min(GetMinTrailingZeros(T->getOperand()), 2639 (uint32_t)getTypeSizeInBits(T->getType())); 2640 2641 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2642 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2643 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2644 getTypeSizeInBits(E->getType()) : OpRes; 2645 } 2646 2647 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2648 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2649 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2650 getTypeSizeInBits(E->getType()) : OpRes; 2651 } 2652 2653 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2654 // The result is the min of all operands results. 2655 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2656 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2658 return MinOpRes; 2659 } 2660 2661 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2662 // The result is the sum of all operands results. 2663 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2664 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2665 for (unsigned i = 1, e = M->getNumOperands(); 2666 SumOpRes != BitWidth && i != e; ++i) 2667 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2668 BitWidth); 2669 return SumOpRes; 2670 } 2671 2672 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2673 // The result is the min of all operands results. 2674 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2675 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2676 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2677 return MinOpRes; 2678 } 2679 2680 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2681 // The result is the min of all operands results. 2682 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2683 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2684 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2685 return MinOpRes; 2686 } 2687 2688 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2689 // The result is the min of all operands results. 2690 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2691 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2692 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2693 return MinOpRes; 2694 } 2695 2696 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2697 // For a SCEVUnknown, ask ValueTracking. 2698 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2699 APInt Mask = APInt::getAllOnesValue(BitWidth); 2700 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2701 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2702 return Zeros.countTrailingOnes(); 2703 } 2704 2705 // SCEVUDivExpr 2706 return 0; 2707} 2708 2709/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2710/// 2711ConstantRange 2712ScalarEvolution::getUnsignedRange(const SCEV *S) { 2713 2714 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2715 return ConstantRange(C->getValue()->getValue()); 2716 2717 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2718 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2719 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2720 X = X.add(getUnsignedRange(Add->getOperand(i))); 2721 return X; 2722 } 2723 2724 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2725 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2726 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2727 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2728 return X; 2729 } 2730 2731 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2732 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2733 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2734 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2735 return X; 2736 } 2737 2738 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2739 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2740 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2741 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2742 return X; 2743 } 2744 2745 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2746 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2747 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2748 return X.udiv(Y); 2749 } 2750 2751 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2752 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2753 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2754 } 2755 2756 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2757 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2758 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2759 } 2760 2761 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2762 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2763 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2764 } 2765 2766 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2767 2768 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2769 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2770 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2771 if (!Trip) return FullSet; 2772 2773 // TODO: non-affine addrec 2774 if (AddRec->isAffine()) { 2775 const Type *Ty = AddRec->getType(); 2776 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2777 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2778 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2779 2780 const SCEV *Start = AddRec->getStart(); 2781 const SCEV *Step = AddRec->getStepRecurrence(*this); 2782 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2783 2784 // Check for overflow. 2785 // TODO: This is very conservative. 2786 if (!(Step->isOne() && 2787 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) && 2788 !(Step->isAllOnesValue() && 2789 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End))) 2790 return FullSet; 2791 2792 ConstantRange StartRange = getUnsignedRange(Start); 2793 ConstantRange EndRange = getUnsignedRange(End); 2794 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2795 EndRange.getUnsignedMin()); 2796 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2797 EndRange.getUnsignedMax()); 2798 if (Min.isMinValue() && Max.isMaxValue()) 2799 return FullSet; 2800 return ConstantRange(Min, Max+1); 2801 } 2802 } 2803 } 2804 2805 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2806 // For a SCEVUnknown, ask ValueTracking. 2807 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2808 APInt Mask = APInt::getAllOnesValue(BitWidth); 2809 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2810 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2811 if (Ones == ~Zeros + 1) 2812 return FullSet; 2813 return ConstantRange(Ones, ~Zeros + 1); 2814 } 2815 2816 return FullSet; 2817} 2818 2819/// getSignedRange - Determine the signed range for a particular SCEV. 2820/// 2821ConstantRange 2822ScalarEvolution::getSignedRange(const SCEV *S) { 2823 2824 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2825 return ConstantRange(C->getValue()->getValue()); 2826 2827 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2828 ConstantRange X = getSignedRange(Add->getOperand(0)); 2829 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2830 X = X.add(getSignedRange(Add->getOperand(i))); 2831 return X; 2832 } 2833 2834 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2835 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2836 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2837 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2838 return X; 2839 } 2840 2841 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2842 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2843 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2844 X = X.smax(getSignedRange(SMax->getOperand(i))); 2845 return X; 2846 } 2847 2848 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2849 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2850 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2851 X = X.umax(getSignedRange(UMax->getOperand(i))); 2852 return X; 2853 } 2854 2855 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2856 ConstantRange X = getSignedRange(UDiv->getLHS()); 2857 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2858 return X.udiv(Y); 2859 } 2860 2861 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2862 ConstantRange X = getSignedRange(ZExt->getOperand()); 2863 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2864 } 2865 2866 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2867 ConstantRange X = getSignedRange(SExt->getOperand()); 2868 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2869 } 2870 2871 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2872 ConstantRange X = getSignedRange(Trunc->getOperand()); 2873 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2874 } 2875 2876 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2877 2878 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2879 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2880 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2881 if (!Trip) return FullSet; 2882 2883 // TODO: non-affine addrec 2884 if (AddRec->isAffine()) { 2885 const Type *Ty = AddRec->getType(); 2886 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2887 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2888 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2889 2890 const SCEV *Start = AddRec->getStart(); 2891 const SCEV *Step = AddRec->getStepRecurrence(*this); 2892 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2893 2894 // Check for overflow. 2895 // TODO: This is very conservative. 2896 if (!(Step->isOne() && 2897 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2898 !(Step->isAllOnesValue() && 2899 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2900 return FullSet; 2901 2902 ConstantRange StartRange = getSignedRange(Start); 2903 ConstantRange EndRange = getSignedRange(End); 2904 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2905 EndRange.getSignedMin()); 2906 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2907 EndRange.getSignedMax()); 2908 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2909 return FullSet; 2910 return ConstantRange(Min, Max+1); 2911 } 2912 } 2913 } 2914 2915 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2916 // For a SCEVUnknown, ask ValueTracking. 2917 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2918 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2919 if (NS == 1) 2920 return FullSet; 2921 return 2922 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2923 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2924 } 2925 2926 return FullSet; 2927} 2928 2929/// createSCEV - We know that there is no SCEV for the specified value. 2930/// Analyze the expression. 2931/// 2932const SCEV *ScalarEvolution::createSCEV(Value *V) { 2933 if (!isSCEVable(V->getType())) 2934 return getUnknown(V); 2935 2936 unsigned Opcode = Instruction::UserOp1; 2937 if (Instruction *I = dyn_cast<Instruction>(V)) 2938 Opcode = I->getOpcode(); 2939 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2940 Opcode = CE->getOpcode(); 2941 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2942 return getConstant(CI); 2943 else if (isa<ConstantPointerNull>(V)) 2944 return getIntegerSCEV(0, V->getType()); 2945 else if (isa<UndefValue>(V)) 2946 return getIntegerSCEV(0, V->getType()); 2947 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 2948 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 2949 else 2950 return getUnknown(V); 2951 2952 Operator *U = cast<Operator>(V); 2953 switch (Opcode) { 2954 case Instruction::Add: { 2955 AddOperator *A = cast<AddOperator>(U); 2956 return getAddExpr(getSCEV(U->getOperand(0)), 2957 getSCEV(U->getOperand(1)), 2958 A->hasNoUnsignedWrap(), 2959 A->hasNoSignedWrap()); 2960 } 2961 case Instruction::Mul: { 2962 MulOperator *M = cast<MulOperator>(U); 2963 return getMulExpr(getSCEV(U->getOperand(0)), 2964 getSCEV(U->getOperand(1)), 2965 M->hasNoUnsignedWrap(), 2966 M->hasNoSignedWrap()); 2967 } 2968 case Instruction::UDiv: 2969 return getUDivExpr(getSCEV(U->getOperand(0)), 2970 getSCEV(U->getOperand(1))); 2971 case Instruction::Sub: 2972 return getMinusSCEV(getSCEV(U->getOperand(0)), 2973 getSCEV(U->getOperand(1))); 2974 case Instruction::And: 2975 // For an expression like x&255 that merely masks off the high bits, 2976 // use zext(trunc(x)) as the SCEV expression. 2977 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2978 if (CI->isNullValue()) 2979 return getSCEV(U->getOperand(1)); 2980 if (CI->isAllOnesValue()) 2981 return getSCEV(U->getOperand(0)); 2982 const APInt &A = CI->getValue(); 2983 2984 // Instcombine's ShrinkDemandedConstant may strip bits out of 2985 // constants, obscuring what would otherwise be a low-bits mask. 2986 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2987 // knew about to reconstruct a low-bits mask value. 2988 unsigned LZ = A.countLeadingZeros(); 2989 unsigned BitWidth = A.getBitWidth(); 2990 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2991 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2992 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2993 2994 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2995 2996 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2997 return 2998 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2999 IntegerType::get(getContext(), BitWidth - LZ)), 3000 U->getType()); 3001 } 3002 break; 3003 3004 case Instruction::Or: 3005 // If the RHS of the Or is a constant, we may have something like: 3006 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3007 // optimizations will transparently handle this case. 3008 // 3009 // In order for this transformation to be safe, the LHS must be of the 3010 // form X*(2^n) and the Or constant must be less than 2^n. 3011 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3012 const SCEV *LHS = getSCEV(U->getOperand(0)); 3013 const APInt &CIVal = CI->getValue(); 3014 if (GetMinTrailingZeros(LHS) >= 3015 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3016 // Build a plain add SCEV. 3017 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3018 // If the LHS of the add was an addrec and it has no-wrap flags, 3019 // transfer the no-wrap flags, since an or won't introduce a wrap. 3020 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3021 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3022 if (OldAR->hasNoUnsignedWrap()) 3023 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3024 if (OldAR->hasNoSignedWrap()) 3025 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3026 } 3027 return S; 3028 } 3029 } 3030 break; 3031 case Instruction::Xor: 3032 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3033 // If the RHS of the xor is a signbit, then this is just an add. 3034 // Instcombine turns add of signbit into xor as a strength reduction step. 3035 if (CI->getValue().isSignBit()) 3036 return getAddExpr(getSCEV(U->getOperand(0)), 3037 getSCEV(U->getOperand(1))); 3038 3039 // If the RHS of xor is -1, then this is a not operation. 3040 if (CI->isAllOnesValue()) 3041 return getNotSCEV(getSCEV(U->getOperand(0))); 3042 3043 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3044 // This is a variant of the check for xor with -1, and it handles 3045 // the case where instcombine has trimmed non-demanded bits out 3046 // of an xor with -1. 3047 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3048 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3049 if (BO->getOpcode() == Instruction::And && 3050 LCI->getValue() == CI->getValue()) 3051 if (const SCEVZeroExtendExpr *Z = 3052 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3053 const Type *UTy = U->getType(); 3054 const SCEV *Z0 = Z->getOperand(); 3055 const Type *Z0Ty = Z0->getType(); 3056 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3057 3058 // If C is a low-bits mask, the zero extend is zerving to 3059 // mask off the high bits. Complement the operand and 3060 // re-apply the zext. 3061 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3062 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3063 3064 // If C is a single bit, it may be in the sign-bit position 3065 // before the zero-extend. In this case, represent the xor 3066 // using an add, which is equivalent, and re-apply the zext. 3067 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3068 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3069 Trunc.isSignBit()) 3070 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3071 UTy); 3072 } 3073 } 3074 break; 3075 3076 case Instruction::Shl: 3077 // Turn shift left of a constant amount into a multiply. 3078 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3079 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3080 Constant *X = ConstantInt::get(getContext(), 3081 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3082 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3083 } 3084 break; 3085 3086 case Instruction::LShr: 3087 // Turn logical shift right of a constant into a unsigned divide. 3088 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3089 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3090 Constant *X = ConstantInt::get(getContext(), 3091 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3092 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3093 } 3094 break; 3095 3096 case Instruction::AShr: 3097 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3098 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3099 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3100 if (L->getOpcode() == Instruction::Shl && 3101 L->getOperand(1) == U->getOperand(1)) { 3102 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3103 uint64_t Amt = BitWidth - CI->getZExtValue(); 3104 if (Amt == BitWidth) 3105 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3106 if (Amt > BitWidth) 3107 return getIntegerSCEV(0, U->getType()); // value is undefined 3108 return 3109 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3110 IntegerType::get(getContext(), Amt)), 3111 U->getType()); 3112 } 3113 break; 3114 3115 case Instruction::Trunc: 3116 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3117 3118 case Instruction::ZExt: 3119 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3120 3121 case Instruction::SExt: 3122 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3123 3124 case Instruction::BitCast: 3125 // BitCasts are no-op casts so we just eliminate the cast. 3126 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3127 return getSCEV(U->getOperand(0)); 3128 break; 3129 3130 // It's tempting to handle inttoptr and ptrtoint, however this can 3131 // lead to pointer expressions which cannot be expanded to GEPs 3132 // (because they may overflow). For now, the only pointer-typed 3133 // expressions we handle are GEPs and address literals. 3134 3135 case Instruction::GetElementPtr: 3136 return createNodeForGEP(U); 3137 3138 case Instruction::PHI: 3139 return createNodeForPHI(cast<PHINode>(U)); 3140 3141 case Instruction::Select: 3142 // This could be a smax or umax that was lowered earlier. 3143 // Try to recover it. 3144 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3145 Value *LHS = ICI->getOperand(0); 3146 Value *RHS = ICI->getOperand(1); 3147 switch (ICI->getPredicate()) { 3148 case ICmpInst::ICMP_SLT: 3149 case ICmpInst::ICMP_SLE: 3150 std::swap(LHS, RHS); 3151 // fall through 3152 case ICmpInst::ICMP_SGT: 3153 case ICmpInst::ICMP_SGE: 3154 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3155 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3156 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3157 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3158 break; 3159 case ICmpInst::ICMP_ULT: 3160 case ICmpInst::ICMP_ULE: 3161 std::swap(LHS, RHS); 3162 // fall through 3163 case ICmpInst::ICMP_UGT: 3164 case ICmpInst::ICMP_UGE: 3165 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3166 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3167 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3168 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3169 break; 3170 case ICmpInst::ICMP_NE: 3171 // n != 0 ? n : 1 -> umax(n, 1) 3172 if (LHS == U->getOperand(1) && 3173 isa<ConstantInt>(U->getOperand(2)) && 3174 cast<ConstantInt>(U->getOperand(2))->isOne() && 3175 isa<ConstantInt>(RHS) && 3176 cast<ConstantInt>(RHS)->isZero()) 3177 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3178 break; 3179 case ICmpInst::ICMP_EQ: 3180 // n == 0 ? 1 : n -> umax(n, 1) 3181 if (LHS == U->getOperand(2) && 3182 isa<ConstantInt>(U->getOperand(1)) && 3183 cast<ConstantInt>(U->getOperand(1))->isOne() && 3184 isa<ConstantInt>(RHS) && 3185 cast<ConstantInt>(RHS)->isZero()) 3186 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3187 break; 3188 default: 3189 break; 3190 } 3191 } 3192 3193 default: // We cannot analyze this expression. 3194 break; 3195 } 3196 3197 return getUnknown(V); 3198} 3199 3200 3201 3202//===----------------------------------------------------------------------===// 3203// Iteration Count Computation Code 3204// 3205 3206/// getBackedgeTakenCount - If the specified loop has a predictable 3207/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3208/// object. The backedge-taken count is the number of times the loop header 3209/// will be branched to from within the loop. This is one less than the 3210/// trip count of the loop, since it doesn't count the first iteration, 3211/// when the header is branched to from outside the loop. 3212/// 3213/// Note that it is not valid to call this method on a loop without a 3214/// loop-invariant backedge-taken count (see 3215/// hasLoopInvariantBackedgeTakenCount). 3216/// 3217const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3218 return getBackedgeTakenInfo(L).Exact; 3219} 3220 3221/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3222/// return the least SCEV value that is known never to be less than the 3223/// actual backedge taken count. 3224const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3225 return getBackedgeTakenInfo(L).Max; 3226} 3227 3228/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3229/// onto the given Worklist. 3230static void 3231PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3232 BasicBlock *Header = L->getHeader(); 3233 3234 // Push all Loop-header PHIs onto the Worklist stack. 3235 for (BasicBlock::iterator I = Header->begin(); 3236 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3237 Worklist.push_back(PN); 3238} 3239 3240const ScalarEvolution::BackedgeTakenInfo & 3241ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3242 // Initially insert a CouldNotCompute for this loop. If the insertion 3243 // succeeds, procede to actually compute a backedge-taken count and 3244 // update the value. The temporary CouldNotCompute value tells SCEV 3245 // code elsewhere that it shouldn't attempt to request a new 3246 // backedge-taken count, which could result in infinite recursion. 3247 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3248 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3249 if (Pair.second) { 3250 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3251 if (ItCount.Exact != getCouldNotCompute()) { 3252 assert(ItCount.Exact->isLoopInvariant(L) && 3253 ItCount.Max->isLoopInvariant(L) && 3254 "Computed trip count isn't loop invariant for loop!"); 3255 ++NumTripCountsComputed; 3256 3257 // Update the value in the map. 3258 Pair.first->second = ItCount; 3259 } else { 3260 if (ItCount.Max != getCouldNotCompute()) 3261 // Update the value in the map. 3262 Pair.first->second = ItCount; 3263 if (isa<PHINode>(L->getHeader()->begin())) 3264 // Only count loops that have phi nodes as not being computable. 3265 ++NumTripCountsNotComputed; 3266 } 3267 3268 // Now that we know more about the trip count for this loop, forget any 3269 // existing SCEV values for PHI nodes in this loop since they are only 3270 // conservative estimates made without the benefit of trip count 3271 // information. This is similar to the code in 3272 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI 3273 // nodes specially. 3274 if (ItCount.hasAnyInfo()) { 3275 SmallVector<Instruction *, 16> Worklist; 3276 PushLoopPHIs(L, Worklist); 3277 3278 SmallPtrSet<Instruction *, 8> Visited; 3279 while (!Worklist.empty()) { 3280 Instruction *I = Worklist.pop_back_val(); 3281 if (!Visited.insert(I)) continue; 3282 3283 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3284 Scalars.find(static_cast<Value *>(I)); 3285 if (It != Scalars.end()) { 3286 // SCEVUnknown for a PHI either means that it has an unrecognized 3287 // structure, or it's a PHI that's in the progress of being computed 3288 // by createNodeForPHI. In the former case, additional loop trip 3289 // count information isn't going to change anything. In the later 3290 // case, createNodeForPHI will perform the necessary updates on its 3291 // own when it gets to that point. 3292 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3293 ValuesAtScopes.erase(It->second); 3294 Scalars.erase(It); 3295 } 3296 if (PHINode *PN = dyn_cast<PHINode>(I)) 3297 ConstantEvolutionLoopExitValue.erase(PN); 3298 } 3299 3300 PushDefUseChildren(I, Worklist); 3301 } 3302 } 3303 } 3304 return Pair.first->second; 3305} 3306 3307/// forgetLoopBackedgeTakenCount - This method should be called by the 3308/// client when it has changed a loop in a way that may effect 3309/// ScalarEvolution's ability to compute a trip count, or if the loop 3310/// is deleted. 3311void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) { 3312 BackedgeTakenCounts.erase(L); 3313 3314 SmallVector<Instruction *, 16> Worklist; 3315 PushLoopPHIs(L, Worklist); 3316 3317 SmallPtrSet<Instruction *, 8> Visited; 3318 while (!Worklist.empty()) { 3319 Instruction *I = Worklist.pop_back_val(); 3320 if (!Visited.insert(I)) continue; 3321 3322 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3323 Scalars.find(static_cast<Value *>(I)); 3324 if (It != Scalars.end()) { 3325 ValuesAtScopes.erase(It->second); 3326 Scalars.erase(It); 3327 if (PHINode *PN = dyn_cast<PHINode>(I)) 3328 ConstantEvolutionLoopExitValue.erase(PN); 3329 } 3330 3331 PushDefUseChildren(I, Worklist); 3332 } 3333} 3334 3335/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3336/// of the specified loop will execute. 3337ScalarEvolution::BackedgeTakenInfo 3338ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3339 SmallVector<BasicBlock*, 8> ExitingBlocks; 3340 L->getExitingBlocks(ExitingBlocks); 3341 3342 // Examine all exits and pick the most conservative values. 3343 const SCEV *BECount = getCouldNotCompute(); 3344 const SCEV *MaxBECount = getCouldNotCompute(); 3345 bool CouldNotComputeBECount = false; 3346 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3347 BackedgeTakenInfo NewBTI = 3348 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3349 3350 if (NewBTI.Exact == getCouldNotCompute()) { 3351 // We couldn't compute an exact value for this exit, so 3352 // we won't be able to compute an exact value for the loop. 3353 CouldNotComputeBECount = true; 3354 BECount = getCouldNotCompute(); 3355 } else if (!CouldNotComputeBECount) { 3356 if (BECount == getCouldNotCompute()) 3357 BECount = NewBTI.Exact; 3358 else 3359 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3360 } 3361 if (MaxBECount == getCouldNotCompute()) 3362 MaxBECount = NewBTI.Max; 3363 else if (NewBTI.Max != getCouldNotCompute()) 3364 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3365 } 3366 3367 return BackedgeTakenInfo(BECount, MaxBECount); 3368} 3369 3370/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3371/// of the specified loop will execute if it exits via the specified block. 3372ScalarEvolution::BackedgeTakenInfo 3373ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3374 BasicBlock *ExitingBlock) { 3375 3376 // Okay, we've chosen an exiting block. See what condition causes us to 3377 // exit at this block. 3378 // 3379 // FIXME: we should be able to handle switch instructions (with a single exit) 3380 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3381 if (ExitBr == 0) return getCouldNotCompute(); 3382 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3383 3384 // At this point, we know we have a conditional branch that determines whether 3385 // the loop is exited. However, we don't know if the branch is executed each 3386 // time through the loop. If not, then the execution count of the branch will 3387 // not be equal to the trip count of the loop. 3388 // 3389 // Currently we check for this by checking to see if the Exit branch goes to 3390 // the loop header. If so, we know it will always execute the same number of 3391 // times as the loop. We also handle the case where the exit block *is* the 3392 // loop header. This is common for un-rotated loops. 3393 // 3394 // If both of those tests fail, walk up the unique predecessor chain to the 3395 // header, stopping if there is an edge that doesn't exit the loop. If the 3396 // header is reached, the execution count of the branch will be equal to the 3397 // trip count of the loop. 3398 // 3399 // More extensive analysis could be done to handle more cases here. 3400 // 3401 if (ExitBr->getSuccessor(0) != L->getHeader() && 3402 ExitBr->getSuccessor(1) != L->getHeader() && 3403 ExitBr->getParent() != L->getHeader()) { 3404 // The simple checks failed, try climbing the unique predecessor chain 3405 // up to the header. 3406 bool Ok = false; 3407 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3408 BasicBlock *Pred = BB->getUniquePredecessor(); 3409 if (!Pred) 3410 return getCouldNotCompute(); 3411 TerminatorInst *PredTerm = Pred->getTerminator(); 3412 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3413 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3414 if (PredSucc == BB) 3415 continue; 3416 // If the predecessor has a successor that isn't BB and isn't 3417 // outside the loop, assume the worst. 3418 if (L->contains(PredSucc)) 3419 return getCouldNotCompute(); 3420 } 3421 if (Pred == L->getHeader()) { 3422 Ok = true; 3423 break; 3424 } 3425 BB = Pred; 3426 } 3427 if (!Ok) 3428 return getCouldNotCompute(); 3429 } 3430 3431 // Procede to the next level to examine the exit condition expression. 3432 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3433 ExitBr->getSuccessor(0), 3434 ExitBr->getSuccessor(1)); 3435} 3436 3437/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3438/// backedge of the specified loop will execute if its exit condition 3439/// were a conditional branch of ExitCond, TBB, and FBB. 3440ScalarEvolution::BackedgeTakenInfo 3441ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3442 Value *ExitCond, 3443 BasicBlock *TBB, 3444 BasicBlock *FBB) { 3445 // Check if the controlling expression for this loop is an And or Or. 3446 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3447 if (BO->getOpcode() == Instruction::And) { 3448 // Recurse on the operands of the and. 3449 BackedgeTakenInfo BTI0 = 3450 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3451 BackedgeTakenInfo BTI1 = 3452 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3453 const SCEV *BECount = getCouldNotCompute(); 3454 const SCEV *MaxBECount = getCouldNotCompute(); 3455 if (L->contains(TBB)) { 3456 // Both conditions must be true for the loop to continue executing. 3457 // Choose the less conservative count. 3458 if (BTI0.Exact == getCouldNotCompute() || 3459 BTI1.Exact == getCouldNotCompute()) 3460 BECount = getCouldNotCompute(); 3461 else 3462 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3463 if (BTI0.Max == getCouldNotCompute()) 3464 MaxBECount = BTI1.Max; 3465 else if (BTI1.Max == getCouldNotCompute()) 3466 MaxBECount = BTI0.Max; 3467 else 3468 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3469 } else { 3470 // Both conditions must be true for the loop to exit. 3471 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3472 if (BTI0.Exact != getCouldNotCompute() && 3473 BTI1.Exact != getCouldNotCompute()) 3474 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3475 if (BTI0.Max != getCouldNotCompute() && 3476 BTI1.Max != getCouldNotCompute()) 3477 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3478 } 3479 3480 return BackedgeTakenInfo(BECount, MaxBECount); 3481 } 3482 if (BO->getOpcode() == Instruction::Or) { 3483 // Recurse on the operands of the or. 3484 BackedgeTakenInfo BTI0 = 3485 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3486 BackedgeTakenInfo BTI1 = 3487 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3488 const SCEV *BECount = getCouldNotCompute(); 3489 const SCEV *MaxBECount = getCouldNotCompute(); 3490 if (L->contains(FBB)) { 3491 // Both conditions must be false for the loop to continue executing. 3492 // Choose the less conservative count. 3493 if (BTI0.Exact == getCouldNotCompute() || 3494 BTI1.Exact == getCouldNotCompute()) 3495 BECount = getCouldNotCompute(); 3496 else 3497 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3498 if (BTI0.Max == getCouldNotCompute()) 3499 MaxBECount = BTI1.Max; 3500 else if (BTI1.Max == getCouldNotCompute()) 3501 MaxBECount = BTI0.Max; 3502 else 3503 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3504 } else { 3505 // Both conditions must be false for the loop to exit. 3506 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3507 if (BTI0.Exact != getCouldNotCompute() && 3508 BTI1.Exact != getCouldNotCompute()) 3509 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3510 if (BTI0.Max != getCouldNotCompute() && 3511 BTI1.Max != getCouldNotCompute()) 3512 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3513 } 3514 3515 return BackedgeTakenInfo(BECount, MaxBECount); 3516 } 3517 } 3518 3519 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3520 // Procede to the next level to examine the icmp. 3521 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3522 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3523 3524 // If it's not an integer or pointer comparison then compute it the hard way. 3525 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3526} 3527 3528/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3529/// backedge of the specified loop will execute if its exit condition 3530/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3531ScalarEvolution::BackedgeTakenInfo 3532ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3533 ICmpInst *ExitCond, 3534 BasicBlock *TBB, 3535 BasicBlock *FBB) { 3536 3537 // If the condition was exit on true, convert the condition to exit on false 3538 ICmpInst::Predicate Cond; 3539 if (!L->contains(FBB)) 3540 Cond = ExitCond->getPredicate(); 3541 else 3542 Cond = ExitCond->getInversePredicate(); 3543 3544 // Handle common loops like: for (X = "string"; *X; ++X) 3545 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3546 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3547 const SCEV *ItCnt = 3548 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3549 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3550 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3551 return BackedgeTakenInfo(ItCnt, 3552 isa<SCEVConstant>(ItCnt) ? ItCnt : 3553 getConstant(APInt::getMaxValue(BitWidth)-1)); 3554 } 3555 } 3556 3557 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3558 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3559 3560 // Try to evaluate any dependencies out of the loop. 3561 LHS = getSCEVAtScope(LHS, L); 3562 RHS = getSCEVAtScope(RHS, L); 3563 3564 // At this point, we would like to compute how many iterations of the 3565 // loop the predicate will return true for these inputs. 3566 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3567 // If there is a loop-invariant, force it into the RHS. 3568 std::swap(LHS, RHS); 3569 Cond = ICmpInst::getSwappedPredicate(Cond); 3570 } 3571 3572 // If we have a comparison of a chrec against a constant, try to use value 3573 // ranges to answer this query. 3574 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3575 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3576 if (AddRec->getLoop() == L) { 3577 // Form the constant range. 3578 ConstantRange CompRange( 3579 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3580 3581 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3582 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3583 } 3584 3585 switch (Cond) { 3586 case ICmpInst::ICMP_NE: { // while (X != Y) 3587 // Convert to: while (X-Y != 0) 3588 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3589 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3590 break; 3591 } 3592 case ICmpInst::ICMP_EQ: { // while (X == Y) 3593 // Convert to: while (X-Y == 0) 3594 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3595 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3596 break; 3597 } 3598 case ICmpInst::ICMP_SLT: { 3599 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3600 if (BTI.hasAnyInfo()) return BTI; 3601 break; 3602 } 3603 case ICmpInst::ICMP_SGT: { 3604 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3605 getNotSCEV(RHS), L, true); 3606 if (BTI.hasAnyInfo()) return BTI; 3607 break; 3608 } 3609 case ICmpInst::ICMP_ULT: { 3610 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3611 if (BTI.hasAnyInfo()) return BTI; 3612 break; 3613 } 3614 case ICmpInst::ICMP_UGT: { 3615 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3616 getNotSCEV(RHS), L, false); 3617 if (BTI.hasAnyInfo()) return BTI; 3618 break; 3619 } 3620 default: 3621#if 0 3622 errs() << "ComputeBackedgeTakenCount "; 3623 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3624 errs() << "[unsigned] "; 3625 errs() << *LHS << " " 3626 << Instruction::getOpcodeName(Instruction::ICmp) 3627 << " " << *RHS << "\n"; 3628#endif 3629 break; 3630 } 3631 return 3632 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3633} 3634 3635static ConstantInt * 3636EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3637 ScalarEvolution &SE) { 3638 const SCEV *InVal = SE.getConstant(C); 3639 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3640 assert(isa<SCEVConstant>(Val) && 3641 "Evaluation of SCEV at constant didn't fold correctly?"); 3642 return cast<SCEVConstant>(Val)->getValue(); 3643} 3644 3645/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3646/// and a GEP expression (missing the pointer index) indexing into it, return 3647/// the addressed element of the initializer or null if the index expression is 3648/// invalid. 3649static Constant * 3650GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV, 3651 const std::vector<ConstantInt*> &Indices) { 3652 Constant *Init = GV->getInitializer(); 3653 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3654 uint64_t Idx = Indices[i]->getZExtValue(); 3655 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3656 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3657 Init = cast<Constant>(CS->getOperand(Idx)); 3658 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3659 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3660 Init = cast<Constant>(CA->getOperand(Idx)); 3661 } else if (isa<ConstantAggregateZero>(Init)) { 3662 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3663 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3664 Init = Constant::getNullValue(STy->getElementType(Idx)); 3665 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3666 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3667 Init = Constant::getNullValue(ATy->getElementType()); 3668 } else { 3669 llvm_unreachable("Unknown constant aggregate type!"); 3670 } 3671 return 0; 3672 } else { 3673 return 0; // Unknown initializer type 3674 } 3675 } 3676 return Init; 3677} 3678 3679/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3680/// 'icmp op load X, cst', try to see if we can compute the backedge 3681/// execution count. 3682const SCEV * 3683ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3684 LoadInst *LI, 3685 Constant *RHS, 3686 const Loop *L, 3687 ICmpInst::Predicate predicate) { 3688 if (LI->isVolatile()) return getCouldNotCompute(); 3689 3690 // Check to see if the loaded pointer is a getelementptr of a global. 3691 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3692 if (!GEP) return getCouldNotCompute(); 3693 3694 // Make sure that it is really a constant global we are gepping, with an 3695 // initializer, and make sure the first IDX is really 0. 3696 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3697 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3698 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3699 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3700 return getCouldNotCompute(); 3701 3702 // Okay, we allow one non-constant index into the GEP instruction. 3703 Value *VarIdx = 0; 3704 std::vector<ConstantInt*> Indexes; 3705 unsigned VarIdxNum = 0; 3706 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3707 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3708 Indexes.push_back(CI); 3709 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3710 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3711 VarIdx = GEP->getOperand(i); 3712 VarIdxNum = i-2; 3713 Indexes.push_back(0); 3714 } 3715 3716 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3717 // Check to see if X is a loop variant variable value now. 3718 const SCEV *Idx = getSCEV(VarIdx); 3719 Idx = getSCEVAtScope(Idx, L); 3720 3721 // We can only recognize very limited forms of loop index expressions, in 3722 // particular, only affine AddRec's like {C1,+,C2}. 3723 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3724 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3725 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3726 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3727 return getCouldNotCompute(); 3728 3729 unsigned MaxSteps = MaxBruteForceIterations; 3730 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3731 ConstantInt *ItCst = ConstantInt::get( 3732 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3733 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3734 3735 // Form the GEP offset. 3736 Indexes[VarIdxNum] = Val; 3737 3738 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes); 3739 if (Result == 0) break; // Cannot compute! 3740 3741 // Evaluate the condition for this iteration. 3742 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3743 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3744 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3745#if 0 3746 errs() << "\n***\n*** Computed loop count " << *ItCst 3747 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3748 << "***\n"; 3749#endif 3750 ++NumArrayLenItCounts; 3751 return getConstant(ItCst); // Found terminating iteration! 3752 } 3753 } 3754 return getCouldNotCompute(); 3755} 3756 3757 3758/// CanConstantFold - Return true if we can constant fold an instruction of the 3759/// specified type, assuming that all operands were constants. 3760static bool CanConstantFold(const Instruction *I) { 3761 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3762 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3763 return true; 3764 3765 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3766 if (const Function *F = CI->getCalledFunction()) 3767 return canConstantFoldCallTo(F); 3768 return false; 3769} 3770 3771/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3772/// in the loop that V is derived from. We allow arbitrary operations along the 3773/// way, but the operands of an operation must either be constants or a value 3774/// derived from a constant PHI. If this expression does not fit with these 3775/// constraints, return null. 3776static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3777 // If this is not an instruction, or if this is an instruction outside of the 3778 // loop, it can't be derived from a loop PHI. 3779 Instruction *I = dyn_cast<Instruction>(V); 3780 if (I == 0 || !L->contains(I->getParent())) return 0; 3781 3782 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3783 if (L->getHeader() == I->getParent()) 3784 return PN; 3785 else 3786 // We don't currently keep track of the control flow needed to evaluate 3787 // PHIs, so we cannot handle PHIs inside of loops. 3788 return 0; 3789 } 3790 3791 // If we won't be able to constant fold this expression even if the operands 3792 // are constants, return early. 3793 if (!CanConstantFold(I)) return 0; 3794 3795 // Otherwise, we can evaluate this instruction if all of its operands are 3796 // constant or derived from a PHI node themselves. 3797 PHINode *PHI = 0; 3798 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3799 if (!(isa<Constant>(I->getOperand(Op)) || 3800 isa<GlobalValue>(I->getOperand(Op)))) { 3801 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3802 if (P == 0) return 0; // Not evolving from PHI 3803 if (PHI == 0) 3804 PHI = P; 3805 else if (PHI != P) 3806 return 0; // Evolving from multiple different PHIs. 3807 } 3808 3809 // This is a expression evolving from a constant PHI! 3810 return PHI; 3811} 3812 3813/// EvaluateExpression - Given an expression that passes the 3814/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3815/// in the loop has the value PHIVal. If we can't fold this expression for some 3816/// reason, return null. 3817static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3818 if (isa<PHINode>(V)) return PHIVal; 3819 if (Constant *C = dyn_cast<Constant>(V)) return C; 3820 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3821 Instruction *I = cast<Instruction>(V); 3822 LLVMContext &Context = I->getParent()->getContext(); 3823 3824 std::vector<Constant*> Operands; 3825 Operands.resize(I->getNumOperands()); 3826 3827 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3828 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3829 if (Operands[i] == 0) return 0; 3830 } 3831 3832 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3833 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3834 &Operands[0], Operands.size(), 3835 Context); 3836 else 3837 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3838 &Operands[0], Operands.size(), 3839 Context); 3840} 3841 3842/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3843/// in the header of its containing loop, we know the loop executes a 3844/// constant number of times, and the PHI node is just a recurrence 3845/// involving constants, fold it. 3846Constant * 3847ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3848 const APInt& BEs, 3849 const Loop *L) { 3850 std::map<PHINode*, Constant*>::iterator I = 3851 ConstantEvolutionLoopExitValue.find(PN); 3852 if (I != ConstantEvolutionLoopExitValue.end()) 3853 return I->second; 3854 3855 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3856 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3857 3858 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3859 3860 // Since the loop is canonicalized, the PHI node must have two entries. One 3861 // entry must be a constant (coming in from outside of the loop), and the 3862 // second must be derived from the same PHI. 3863 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3864 Constant *StartCST = 3865 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3866 if (StartCST == 0) 3867 return RetVal = 0; // Must be a constant. 3868 3869 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3870 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3871 if (PN2 != PN) 3872 return RetVal = 0; // Not derived from same PHI. 3873 3874 // Execute the loop symbolically to determine the exit value. 3875 if (BEs.getActiveBits() >= 32) 3876 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3877 3878 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3879 unsigned IterationNum = 0; 3880 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3881 if (IterationNum == NumIterations) 3882 return RetVal = PHIVal; // Got exit value! 3883 3884 // Compute the value of the PHI node for the next iteration. 3885 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3886 if (NextPHI == PHIVal) 3887 return RetVal = NextPHI; // Stopped evolving! 3888 if (NextPHI == 0) 3889 return 0; // Couldn't evaluate! 3890 PHIVal = NextPHI; 3891 } 3892} 3893 3894/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 3895/// constant number of times (the condition evolves only from constants), 3896/// try to evaluate a few iterations of the loop until we get the exit 3897/// condition gets a value of ExitWhen (true or false). If we cannot 3898/// evaluate the trip count of the loop, return getCouldNotCompute(). 3899const SCEV * 3900ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3901 Value *Cond, 3902 bool ExitWhen) { 3903 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3904 if (PN == 0) return getCouldNotCompute(); 3905 3906 // Since the loop is canonicalized, the PHI node must have two entries. One 3907 // entry must be a constant (coming in from outside of the loop), and the 3908 // second must be derived from the same PHI. 3909 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3910 Constant *StartCST = 3911 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3912 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3913 3914 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3915 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3916 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3917 3918 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3919 // the loop symbolically to determine when the condition gets a value of 3920 // "ExitWhen". 3921 unsigned IterationNum = 0; 3922 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3923 for (Constant *PHIVal = StartCST; 3924 IterationNum != MaxIterations; ++IterationNum) { 3925 ConstantInt *CondVal = 3926 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3927 3928 // Couldn't symbolically evaluate. 3929 if (!CondVal) return getCouldNotCompute(); 3930 3931 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3932 ++NumBruteForceTripCountsComputed; 3933 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 3934 } 3935 3936 // Compute the value of the PHI node for the next iteration. 3937 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3938 if (NextPHI == 0 || NextPHI == PHIVal) 3939 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3940 PHIVal = NextPHI; 3941 } 3942 3943 // Too many iterations were needed to evaluate. 3944 return getCouldNotCompute(); 3945} 3946 3947/// getSCEVAtScope - Return a SCEV expression for the specified value 3948/// at the specified scope in the program. The L value specifies a loop 3949/// nest to evaluate the expression at, where null is the top-level or a 3950/// specified loop is immediately inside of the loop. 3951/// 3952/// This method can be used to compute the exit value for a variable defined 3953/// in a loop by querying what the value will hold in the parent loop. 3954/// 3955/// In the case that a relevant loop exit value cannot be computed, the 3956/// original value V is returned. 3957const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3958 // Check to see if we've folded this expression at this loop before. 3959 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 3960 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 3961 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 3962 if (!Pair.second) 3963 return Pair.first->second ? Pair.first->second : V; 3964 3965 // Otherwise compute it. 3966 const SCEV *C = computeSCEVAtScope(V, L); 3967 ValuesAtScopes[V][L] = C; 3968 return C; 3969} 3970 3971const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 3972 if (isa<SCEVConstant>(V)) return V; 3973 3974 // If this instruction is evolved from a constant-evolving PHI, compute the 3975 // exit value from the loop without using SCEVs. 3976 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3977 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3978 const Loop *LI = (*this->LI)[I->getParent()]; 3979 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3980 if (PHINode *PN = dyn_cast<PHINode>(I)) 3981 if (PN->getParent() == LI->getHeader()) { 3982 // Okay, there is no closed form solution for the PHI node. Check 3983 // to see if the loop that contains it has a known backedge-taken 3984 // count. If so, we may be able to force computation of the exit 3985 // value. 3986 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3987 if (const SCEVConstant *BTCC = 3988 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3989 // Okay, we know how many times the containing loop executes. If 3990 // this is a constant evolving PHI node, get the final value at 3991 // the specified iteration number. 3992 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3993 BTCC->getValue()->getValue(), 3994 LI); 3995 if (RV) return getSCEV(RV); 3996 } 3997 } 3998 3999 // Okay, this is an expression that we cannot symbolically evaluate 4000 // into a SCEV. Check to see if it's possible to symbolically evaluate 4001 // the arguments into constants, and if so, try to constant propagate the 4002 // result. This is particularly useful for computing loop exit values. 4003 if (CanConstantFold(I)) { 4004 std::vector<Constant*> Operands; 4005 Operands.reserve(I->getNumOperands()); 4006 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4007 Value *Op = I->getOperand(i); 4008 if (Constant *C = dyn_cast<Constant>(Op)) { 4009 Operands.push_back(C); 4010 } else { 4011 // If any of the operands is non-constant and if they are 4012 // non-integer and non-pointer, don't even try to analyze them 4013 // with scev techniques. 4014 if (!isSCEVable(Op->getType())) 4015 return V; 4016 4017 const SCEV* OpV = getSCEVAtScope(Op, L); 4018 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4019 Constant *C = SC->getValue(); 4020 if (C->getType() != Op->getType()) 4021 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4022 Op->getType(), 4023 false), 4024 C, Op->getType()); 4025 Operands.push_back(C); 4026 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4027 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4028 if (C->getType() != Op->getType()) 4029 C = 4030 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4031 Op->getType(), 4032 false), 4033 C, Op->getType()); 4034 Operands.push_back(C); 4035 } else 4036 return V; 4037 } else { 4038 return V; 4039 } 4040 } 4041 } 4042 4043 Constant *C; 4044 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4045 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4046 &Operands[0], Operands.size(), 4047 getContext()); 4048 else 4049 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4050 &Operands[0], Operands.size(), 4051 getContext()); 4052 return getSCEV(C); 4053 } 4054 } 4055 4056 // This is some other type of SCEVUnknown, just return it. 4057 return V; 4058 } 4059 4060 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4061 // Avoid performing the look-up in the common case where the specified 4062 // expression has no loop-variant portions. 4063 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4064 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4065 if (OpAtScope != Comm->getOperand(i)) { 4066 // Okay, at least one of these operands is loop variant but might be 4067 // foldable. Build a new instance of the folded commutative expression. 4068 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4069 Comm->op_begin()+i); 4070 NewOps.push_back(OpAtScope); 4071 4072 for (++i; i != e; ++i) { 4073 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4074 NewOps.push_back(OpAtScope); 4075 } 4076 if (isa<SCEVAddExpr>(Comm)) 4077 return getAddExpr(NewOps); 4078 if (isa<SCEVMulExpr>(Comm)) 4079 return getMulExpr(NewOps); 4080 if (isa<SCEVSMaxExpr>(Comm)) 4081 return getSMaxExpr(NewOps); 4082 if (isa<SCEVUMaxExpr>(Comm)) 4083 return getUMaxExpr(NewOps); 4084 llvm_unreachable("Unknown commutative SCEV type!"); 4085 } 4086 } 4087 // If we got here, all operands are loop invariant. 4088 return Comm; 4089 } 4090 4091 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4092 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4093 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4094 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4095 return Div; // must be loop invariant 4096 return getUDivExpr(LHS, RHS); 4097 } 4098 4099 // If this is a loop recurrence for a loop that does not contain L, then we 4100 // are dealing with the final value computed by the loop. 4101 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4102 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 4103 // To evaluate this recurrence, we need to know how many times the AddRec 4104 // loop iterates. Compute this now. 4105 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4106 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4107 4108 // Then, evaluate the AddRec. 4109 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4110 } 4111 return AddRec; 4112 } 4113 4114 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4115 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4116 if (Op == Cast->getOperand()) 4117 return Cast; // must be loop invariant 4118 return getZeroExtendExpr(Op, Cast->getType()); 4119 } 4120 4121 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4122 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4123 if (Op == Cast->getOperand()) 4124 return Cast; // must be loop invariant 4125 return getSignExtendExpr(Op, Cast->getType()); 4126 } 4127 4128 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4129 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4130 if (Op == Cast->getOperand()) 4131 return Cast; // must be loop invariant 4132 return getTruncateExpr(Op, Cast->getType()); 4133 } 4134 4135 if (isa<SCEVTargetDataConstant>(V)) 4136 return V; 4137 4138 llvm_unreachable("Unknown SCEV type!"); 4139 return 0; 4140} 4141 4142/// getSCEVAtScope - This is a convenience function which does 4143/// getSCEVAtScope(getSCEV(V), L). 4144const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4145 return getSCEVAtScope(getSCEV(V), L); 4146} 4147 4148/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4149/// following equation: 4150/// 4151/// A * X = B (mod N) 4152/// 4153/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4154/// A and B isn't important. 4155/// 4156/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4157static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4158 ScalarEvolution &SE) { 4159 uint32_t BW = A.getBitWidth(); 4160 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4161 assert(A != 0 && "A must be non-zero."); 4162 4163 // 1. D = gcd(A, N) 4164 // 4165 // The gcd of A and N may have only one prime factor: 2. The number of 4166 // trailing zeros in A is its multiplicity 4167 uint32_t Mult2 = A.countTrailingZeros(); 4168 // D = 2^Mult2 4169 4170 // 2. Check if B is divisible by D. 4171 // 4172 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4173 // is not less than multiplicity of this prime factor for D. 4174 if (B.countTrailingZeros() < Mult2) 4175 return SE.getCouldNotCompute(); 4176 4177 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4178 // modulo (N / D). 4179 // 4180 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4181 // bit width during computations. 4182 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4183 APInt Mod(BW + 1, 0); 4184 Mod.set(BW - Mult2); // Mod = N / D 4185 APInt I = AD.multiplicativeInverse(Mod); 4186 4187 // 4. Compute the minimum unsigned root of the equation: 4188 // I * (B / D) mod (N / D) 4189 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4190 4191 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4192 // bits. 4193 return SE.getConstant(Result.trunc(BW)); 4194} 4195 4196/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4197/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4198/// might be the same) or two SCEVCouldNotCompute objects. 4199/// 4200static std::pair<const SCEV *,const SCEV *> 4201SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4202 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4203 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4204 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4205 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4206 4207 // We currently can only solve this if the coefficients are constants. 4208 if (!LC || !MC || !NC) { 4209 const SCEV *CNC = SE.getCouldNotCompute(); 4210 return std::make_pair(CNC, CNC); 4211 } 4212 4213 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4214 const APInt &L = LC->getValue()->getValue(); 4215 const APInt &M = MC->getValue()->getValue(); 4216 const APInt &N = NC->getValue()->getValue(); 4217 APInt Two(BitWidth, 2); 4218 APInt Four(BitWidth, 4); 4219 4220 { 4221 using namespace APIntOps; 4222 const APInt& C = L; 4223 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4224 // The B coefficient is M-N/2 4225 APInt B(M); 4226 B -= sdiv(N,Two); 4227 4228 // The A coefficient is N/2 4229 APInt A(N.sdiv(Two)); 4230 4231 // Compute the B^2-4ac term. 4232 APInt SqrtTerm(B); 4233 SqrtTerm *= B; 4234 SqrtTerm -= Four * (A * C); 4235 4236 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4237 // integer value or else APInt::sqrt() will assert. 4238 APInt SqrtVal(SqrtTerm.sqrt()); 4239 4240 // Compute the two solutions for the quadratic formula. 4241 // The divisions must be performed as signed divisions. 4242 APInt NegB(-B); 4243 APInt TwoA( A << 1 ); 4244 if (TwoA.isMinValue()) { 4245 const SCEV *CNC = SE.getCouldNotCompute(); 4246 return std::make_pair(CNC, CNC); 4247 } 4248 4249 LLVMContext &Context = SE.getContext(); 4250 4251 ConstantInt *Solution1 = 4252 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4253 ConstantInt *Solution2 = 4254 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4255 4256 return std::make_pair(SE.getConstant(Solution1), 4257 SE.getConstant(Solution2)); 4258 } // end APIntOps namespace 4259} 4260 4261/// HowFarToZero - Return the number of times a backedge comparing the specified 4262/// value to zero will execute. If not computable, return CouldNotCompute. 4263const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4264 // If the value is a constant 4265 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4266 // If the value is already zero, the branch will execute zero times. 4267 if (C->getValue()->isZero()) return C; 4268 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4269 } 4270 4271 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4272 if (!AddRec || AddRec->getLoop() != L) 4273 return getCouldNotCompute(); 4274 4275 if (AddRec->isAffine()) { 4276 // If this is an affine expression, the execution count of this branch is 4277 // the minimum unsigned root of the following equation: 4278 // 4279 // Start + Step*N = 0 (mod 2^BW) 4280 // 4281 // equivalent to: 4282 // 4283 // Step*N = -Start (mod 2^BW) 4284 // 4285 // where BW is the common bit width of Start and Step. 4286 4287 // Get the initial value for the loop. 4288 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4289 L->getParentLoop()); 4290 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4291 L->getParentLoop()); 4292 4293 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4294 // For now we handle only constant steps. 4295 4296 // First, handle unitary steps. 4297 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4298 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4299 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4300 return Start; // N = Start (as unsigned) 4301 4302 // Then, try to solve the above equation provided that Start is constant. 4303 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4304 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4305 -StartC->getValue()->getValue(), 4306 *this); 4307 } 4308 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4309 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4310 // the quadratic equation to solve it. 4311 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4312 *this); 4313 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4314 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4315 if (R1) { 4316#if 0 4317 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4318 << " sol#2: " << *R2 << "\n"; 4319#endif 4320 // Pick the smallest positive root value. 4321 if (ConstantInt *CB = 4322 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4323 R1->getValue(), R2->getValue()))) { 4324 if (CB->getZExtValue() == false) 4325 std::swap(R1, R2); // R1 is the minimum root now. 4326 4327 // We can only use this value if the chrec ends up with an exact zero 4328 // value at this index. When solving for "X*X != 5", for example, we 4329 // should not accept a root of 2. 4330 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4331 if (Val->isZero()) 4332 return R1; // We found a quadratic root! 4333 } 4334 } 4335 } 4336 4337 return getCouldNotCompute(); 4338} 4339 4340/// HowFarToNonZero - Return the number of times a backedge checking the 4341/// specified value for nonzero will execute. If not computable, return 4342/// CouldNotCompute 4343const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4344 // Loops that look like: while (X == 0) are very strange indeed. We don't 4345 // handle them yet except for the trivial case. This could be expanded in the 4346 // future as needed. 4347 4348 // If the value is a constant, check to see if it is known to be non-zero 4349 // already. If so, the backedge will execute zero times. 4350 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4351 if (!C->getValue()->isNullValue()) 4352 return getIntegerSCEV(0, C->getType()); 4353 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4354 } 4355 4356 // We could implement others, but I really doubt anyone writes loops like 4357 // this, and if they did, they would already be constant folded. 4358 return getCouldNotCompute(); 4359} 4360 4361/// getLoopPredecessor - If the given loop's header has exactly one unique 4362/// predecessor outside the loop, return it. Otherwise return null. 4363/// 4364BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4365 BasicBlock *Header = L->getHeader(); 4366 BasicBlock *Pred = 0; 4367 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4368 PI != E; ++PI) 4369 if (!L->contains(*PI)) { 4370 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4371 Pred = *PI; 4372 } 4373 return Pred; 4374} 4375 4376/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4377/// (which may not be an immediate predecessor) which has exactly one 4378/// successor from which BB is reachable, or null if no such block is 4379/// found. 4380/// 4381BasicBlock * 4382ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4383 // If the block has a unique predecessor, then there is no path from the 4384 // predecessor to the block that does not go through the direct edge 4385 // from the predecessor to the block. 4386 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4387 return Pred; 4388 4389 // A loop's header is defined to be a block that dominates the loop. 4390 // If the header has a unique predecessor outside the loop, it must be 4391 // a block that has exactly one successor that can reach the loop. 4392 if (Loop *L = LI->getLoopFor(BB)) 4393 return getLoopPredecessor(L); 4394 4395 return 0; 4396} 4397 4398/// HasSameValue - SCEV structural equivalence is usually sufficient for 4399/// testing whether two expressions are equal, however for the purposes of 4400/// looking for a condition guarding a loop, it can be useful to be a little 4401/// more general, since a front-end may have replicated the controlling 4402/// expression. 4403/// 4404static bool HasSameValue(const SCEV *A, const SCEV *B) { 4405 // Quick check to see if they are the same SCEV. 4406 if (A == B) return true; 4407 4408 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4409 // two different instructions with the same value. Check for this case. 4410 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4411 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4412 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4413 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4414 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4415 return true; 4416 4417 // Otherwise assume they may have a different value. 4418 return false; 4419} 4420 4421bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4422 return getSignedRange(S).getSignedMax().isNegative(); 4423} 4424 4425bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4426 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4427} 4428 4429bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4430 return !getSignedRange(S).getSignedMin().isNegative(); 4431} 4432 4433bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4434 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4435} 4436 4437bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4438 return isKnownNegative(S) || isKnownPositive(S); 4439} 4440 4441bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4442 const SCEV *LHS, const SCEV *RHS) { 4443 4444 if (HasSameValue(LHS, RHS)) 4445 return ICmpInst::isTrueWhenEqual(Pred); 4446 4447 switch (Pred) { 4448 default: 4449 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4450 break; 4451 case ICmpInst::ICMP_SGT: 4452 Pred = ICmpInst::ICMP_SLT; 4453 std::swap(LHS, RHS); 4454 case ICmpInst::ICMP_SLT: { 4455 ConstantRange LHSRange = getSignedRange(LHS); 4456 ConstantRange RHSRange = getSignedRange(RHS); 4457 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4458 return true; 4459 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4460 return false; 4461 break; 4462 } 4463 case ICmpInst::ICMP_SGE: 4464 Pred = ICmpInst::ICMP_SLE; 4465 std::swap(LHS, RHS); 4466 case ICmpInst::ICMP_SLE: { 4467 ConstantRange LHSRange = getSignedRange(LHS); 4468 ConstantRange RHSRange = getSignedRange(RHS); 4469 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4470 return true; 4471 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4472 return false; 4473 break; 4474 } 4475 case ICmpInst::ICMP_UGT: 4476 Pred = ICmpInst::ICMP_ULT; 4477 std::swap(LHS, RHS); 4478 case ICmpInst::ICMP_ULT: { 4479 ConstantRange LHSRange = getUnsignedRange(LHS); 4480 ConstantRange RHSRange = getUnsignedRange(RHS); 4481 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4482 return true; 4483 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4484 return false; 4485 break; 4486 } 4487 case ICmpInst::ICMP_UGE: 4488 Pred = ICmpInst::ICMP_ULE; 4489 std::swap(LHS, RHS); 4490 case ICmpInst::ICMP_ULE: { 4491 ConstantRange LHSRange = getUnsignedRange(LHS); 4492 ConstantRange RHSRange = getUnsignedRange(RHS); 4493 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4494 return true; 4495 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4496 return false; 4497 break; 4498 } 4499 case ICmpInst::ICMP_NE: { 4500 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4501 return true; 4502 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4503 return true; 4504 4505 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4506 if (isKnownNonZero(Diff)) 4507 return true; 4508 break; 4509 } 4510 case ICmpInst::ICMP_EQ: 4511 // The check at the top of the function catches the case where 4512 // the values are known to be equal. 4513 break; 4514 } 4515 return false; 4516} 4517 4518/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4519/// protected by a conditional between LHS and RHS. This is used to 4520/// to eliminate casts. 4521bool 4522ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4523 ICmpInst::Predicate Pred, 4524 const SCEV *LHS, const SCEV *RHS) { 4525 // Interpret a null as meaning no loop, where there is obviously no guard 4526 // (interprocedural conditions notwithstanding). 4527 if (!L) return true; 4528 4529 BasicBlock *Latch = L->getLoopLatch(); 4530 if (!Latch) 4531 return false; 4532 4533 BranchInst *LoopContinuePredicate = 4534 dyn_cast<BranchInst>(Latch->getTerminator()); 4535 if (!LoopContinuePredicate || 4536 LoopContinuePredicate->isUnconditional()) 4537 return false; 4538 4539 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4540 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4541} 4542 4543/// isLoopGuardedByCond - Test whether entry to the loop is protected 4544/// by a conditional between LHS and RHS. This is used to help avoid max 4545/// expressions in loop trip counts, and to eliminate casts. 4546bool 4547ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4548 ICmpInst::Predicate Pred, 4549 const SCEV *LHS, const SCEV *RHS) { 4550 // Interpret a null as meaning no loop, where there is obviously no guard 4551 // (interprocedural conditions notwithstanding). 4552 if (!L) return false; 4553 4554 BasicBlock *Predecessor = getLoopPredecessor(L); 4555 BasicBlock *PredecessorDest = L->getHeader(); 4556 4557 // Starting at the loop predecessor, climb up the predecessor chain, as long 4558 // as there are predecessors that can be found that have unique successors 4559 // leading to the original header. 4560 for (; Predecessor; 4561 PredecessorDest = Predecessor, 4562 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4563 4564 BranchInst *LoopEntryPredicate = 4565 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4566 if (!LoopEntryPredicate || 4567 LoopEntryPredicate->isUnconditional()) 4568 continue; 4569 4570 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4571 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4572 return true; 4573 } 4574 4575 return false; 4576} 4577 4578/// isImpliedCond - Test whether the condition described by Pred, LHS, 4579/// and RHS is true whenever the given Cond value evaluates to true. 4580bool ScalarEvolution::isImpliedCond(Value *CondValue, 4581 ICmpInst::Predicate Pred, 4582 const SCEV *LHS, const SCEV *RHS, 4583 bool Inverse) { 4584 // Recursivly handle And and Or conditions. 4585 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4586 if (BO->getOpcode() == Instruction::And) { 4587 if (!Inverse) 4588 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4589 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4590 } else if (BO->getOpcode() == Instruction::Or) { 4591 if (Inverse) 4592 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4593 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4594 } 4595 } 4596 4597 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4598 if (!ICI) return false; 4599 4600 // Bail if the ICmp's operands' types are wider than the needed type 4601 // before attempting to call getSCEV on them. This avoids infinite 4602 // recursion, since the analysis of widening casts can require loop 4603 // exit condition information for overflow checking, which would 4604 // lead back here. 4605 if (getTypeSizeInBits(LHS->getType()) < 4606 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4607 return false; 4608 4609 // Now that we found a conditional branch that dominates the loop, check to 4610 // see if it is the comparison we are looking for. 4611 ICmpInst::Predicate FoundPred; 4612 if (Inverse) 4613 FoundPred = ICI->getInversePredicate(); 4614 else 4615 FoundPred = ICI->getPredicate(); 4616 4617 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4618 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4619 4620 // Balance the types. The case where FoundLHS' type is wider than 4621 // LHS' type is checked for above. 4622 if (getTypeSizeInBits(LHS->getType()) > 4623 getTypeSizeInBits(FoundLHS->getType())) { 4624 if (CmpInst::isSigned(Pred)) { 4625 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4626 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4627 } else { 4628 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4629 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4630 } 4631 } 4632 4633 // Canonicalize the query to match the way instcombine will have 4634 // canonicalized the comparison. 4635 // First, put a constant operand on the right. 4636 if (isa<SCEVConstant>(LHS)) { 4637 std::swap(LHS, RHS); 4638 Pred = ICmpInst::getSwappedPredicate(Pred); 4639 } 4640 // Then, canonicalize comparisons with boundary cases. 4641 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4642 const APInt &RA = RC->getValue()->getValue(); 4643 switch (Pred) { 4644 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4645 case ICmpInst::ICMP_EQ: 4646 case ICmpInst::ICMP_NE: 4647 break; 4648 case ICmpInst::ICMP_UGE: 4649 if ((RA - 1).isMinValue()) { 4650 Pred = ICmpInst::ICMP_NE; 4651 RHS = getConstant(RA - 1); 4652 break; 4653 } 4654 if (RA.isMaxValue()) { 4655 Pred = ICmpInst::ICMP_EQ; 4656 break; 4657 } 4658 if (RA.isMinValue()) return true; 4659 break; 4660 case ICmpInst::ICMP_ULE: 4661 if ((RA + 1).isMaxValue()) { 4662 Pred = ICmpInst::ICMP_NE; 4663 RHS = getConstant(RA + 1); 4664 break; 4665 } 4666 if (RA.isMinValue()) { 4667 Pred = ICmpInst::ICMP_EQ; 4668 break; 4669 } 4670 if (RA.isMaxValue()) return true; 4671 break; 4672 case ICmpInst::ICMP_SGE: 4673 if ((RA - 1).isMinSignedValue()) { 4674 Pred = ICmpInst::ICMP_NE; 4675 RHS = getConstant(RA - 1); 4676 break; 4677 } 4678 if (RA.isMaxSignedValue()) { 4679 Pred = ICmpInst::ICMP_EQ; 4680 break; 4681 } 4682 if (RA.isMinSignedValue()) return true; 4683 break; 4684 case ICmpInst::ICMP_SLE: 4685 if ((RA + 1).isMaxSignedValue()) { 4686 Pred = ICmpInst::ICMP_NE; 4687 RHS = getConstant(RA + 1); 4688 break; 4689 } 4690 if (RA.isMinSignedValue()) { 4691 Pred = ICmpInst::ICMP_EQ; 4692 break; 4693 } 4694 if (RA.isMaxSignedValue()) return true; 4695 break; 4696 case ICmpInst::ICMP_UGT: 4697 if (RA.isMinValue()) { 4698 Pred = ICmpInst::ICMP_NE; 4699 break; 4700 } 4701 if ((RA + 1).isMaxValue()) { 4702 Pred = ICmpInst::ICMP_EQ; 4703 RHS = getConstant(RA + 1); 4704 break; 4705 } 4706 if (RA.isMaxValue()) return false; 4707 break; 4708 case ICmpInst::ICMP_ULT: 4709 if (RA.isMaxValue()) { 4710 Pred = ICmpInst::ICMP_NE; 4711 break; 4712 } 4713 if ((RA - 1).isMinValue()) { 4714 Pred = ICmpInst::ICMP_EQ; 4715 RHS = getConstant(RA - 1); 4716 break; 4717 } 4718 if (RA.isMinValue()) return false; 4719 break; 4720 case ICmpInst::ICMP_SGT: 4721 if (RA.isMinSignedValue()) { 4722 Pred = ICmpInst::ICMP_NE; 4723 break; 4724 } 4725 if ((RA + 1).isMaxSignedValue()) { 4726 Pred = ICmpInst::ICMP_EQ; 4727 RHS = getConstant(RA + 1); 4728 break; 4729 } 4730 if (RA.isMaxSignedValue()) return false; 4731 break; 4732 case ICmpInst::ICMP_SLT: 4733 if (RA.isMaxSignedValue()) { 4734 Pred = ICmpInst::ICMP_NE; 4735 break; 4736 } 4737 if ((RA - 1).isMinSignedValue()) { 4738 Pred = ICmpInst::ICMP_EQ; 4739 RHS = getConstant(RA - 1); 4740 break; 4741 } 4742 if (RA.isMinSignedValue()) return false; 4743 break; 4744 } 4745 } 4746 4747 // Check to see if we can make the LHS or RHS match. 4748 if (LHS == FoundRHS || RHS == FoundLHS) { 4749 if (isa<SCEVConstant>(RHS)) { 4750 std::swap(FoundLHS, FoundRHS); 4751 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4752 } else { 4753 std::swap(LHS, RHS); 4754 Pred = ICmpInst::getSwappedPredicate(Pred); 4755 } 4756 } 4757 4758 // Check whether the found predicate is the same as the desired predicate. 4759 if (FoundPred == Pred) 4760 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4761 4762 // Check whether swapping the found predicate makes it the same as the 4763 // desired predicate. 4764 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4765 if (isa<SCEVConstant>(RHS)) 4766 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4767 else 4768 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4769 RHS, LHS, FoundLHS, FoundRHS); 4770 } 4771 4772 // Check whether the actual condition is beyond sufficient. 4773 if (FoundPred == ICmpInst::ICMP_EQ) 4774 if (ICmpInst::isTrueWhenEqual(Pred)) 4775 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4776 return true; 4777 if (Pred == ICmpInst::ICMP_NE) 4778 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4779 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4780 return true; 4781 4782 // Otherwise assume the worst. 4783 return false; 4784} 4785 4786/// isImpliedCondOperands - Test whether the condition described by Pred, 4787/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4788/// and FoundRHS is true. 4789bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4790 const SCEV *LHS, const SCEV *RHS, 4791 const SCEV *FoundLHS, 4792 const SCEV *FoundRHS) { 4793 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4794 FoundLHS, FoundRHS) || 4795 // ~x < ~y --> x > y 4796 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4797 getNotSCEV(FoundRHS), 4798 getNotSCEV(FoundLHS)); 4799} 4800 4801/// isImpliedCondOperandsHelper - Test whether the condition described by 4802/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4803/// FoundLHS, and FoundRHS is true. 4804bool 4805ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4806 const SCEV *LHS, const SCEV *RHS, 4807 const SCEV *FoundLHS, 4808 const SCEV *FoundRHS) { 4809 switch (Pred) { 4810 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4811 case ICmpInst::ICMP_EQ: 4812 case ICmpInst::ICMP_NE: 4813 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4814 return true; 4815 break; 4816 case ICmpInst::ICMP_SLT: 4817 case ICmpInst::ICMP_SLE: 4818 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4819 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4820 return true; 4821 break; 4822 case ICmpInst::ICMP_SGT: 4823 case ICmpInst::ICMP_SGE: 4824 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4825 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4826 return true; 4827 break; 4828 case ICmpInst::ICMP_ULT: 4829 case ICmpInst::ICMP_ULE: 4830 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4831 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4832 return true; 4833 break; 4834 case ICmpInst::ICMP_UGT: 4835 case ICmpInst::ICMP_UGE: 4836 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4837 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4838 return true; 4839 break; 4840 } 4841 4842 return false; 4843} 4844 4845/// getBECount - Subtract the end and start values and divide by the step, 4846/// rounding up, to get the number of times the backedge is executed. Return 4847/// CouldNotCompute if an intermediate computation overflows. 4848const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4849 const SCEV *End, 4850 const SCEV *Step, 4851 bool NoWrap) { 4852 const Type *Ty = Start->getType(); 4853 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4854 const SCEV *Diff = getMinusSCEV(End, Start); 4855 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4856 4857 // Add an adjustment to the difference between End and Start so that 4858 // the division will effectively round up. 4859 const SCEV *Add = getAddExpr(Diff, RoundUp); 4860 4861 if (!NoWrap) { 4862 // Check Add for unsigned overflow. 4863 // TODO: More sophisticated things could be done here. 4864 const Type *WideTy = IntegerType::get(getContext(), 4865 getTypeSizeInBits(Ty) + 1); 4866 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 4867 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 4868 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 4869 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4870 return getCouldNotCompute(); 4871 } 4872 4873 return getUDivExpr(Add, Step); 4874} 4875 4876/// HowManyLessThans - Return the number of times a backedge containing the 4877/// specified less-than comparison will execute. If not computable, return 4878/// CouldNotCompute. 4879ScalarEvolution::BackedgeTakenInfo 4880ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4881 const Loop *L, bool isSigned) { 4882 // Only handle: "ADDREC < LoopInvariant". 4883 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4884 4885 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4886 if (!AddRec || AddRec->getLoop() != L) 4887 return getCouldNotCompute(); 4888 4889 // Check to see if we have a flag which makes analysis easy. 4890 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 4891 AddRec->hasNoUnsignedWrap(); 4892 4893 if (AddRec->isAffine()) { 4894 // FORNOW: We only support unit strides. 4895 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4896 const SCEV *Step = AddRec->getStepRecurrence(*this); 4897 4898 // TODO: handle non-constant strides. 4899 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4900 if (!CStep || CStep->isZero()) 4901 return getCouldNotCompute(); 4902 if (CStep->isOne()) { 4903 // With unit stride, the iteration never steps past the limit value. 4904 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4905 if (NoWrap) { 4906 // We know the iteration won't step past the maximum value for its type. 4907 ; 4908 } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4909 // Test whether a positive iteration iteration can step past the limit 4910 // value and past the maximum value for its type in a single step. 4911 if (isSigned) { 4912 APInt Max = APInt::getSignedMaxValue(BitWidth); 4913 if ((Max - CStep->getValue()->getValue()) 4914 .slt(CLimit->getValue()->getValue())) 4915 return getCouldNotCompute(); 4916 } else { 4917 APInt Max = APInt::getMaxValue(BitWidth); 4918 if ((Max - CStep->getValue()->getValue()) 4919 .ult(CLimit->getValue()->getValue())) 4920 return getCouldNotCompute(); 4921 } 4922 } else 4923 // TODO: handle non-constant limit values below. 4924 return getCouldNotCompute(); 4925 } else 4926 // TODO: handle negative strides below. 4927 return getCouldNotCompute(); 4928 4929 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4930 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4931 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4932 // treat m-n as signed nor unsigned due to overflow possibility. 4933 4934 // First, we get the value of the LHS in the first iteration: n 4935 const SCEV *Start = AddRec->getOperand(0); 4936 4937 // Determine the minimum constant start value. 4938 const SCEV *MinStart = getConstant(isSigned ? 4939 getSignedRange(Start).getSignedMin() : 4940 getUnsignedRange(Start).getUnsignedMin()); 4941 4942 // If we know that the condition is true in order to enter the loop, 4943 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4944 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4945 // the division must round up. 4946 const SCEV *End = RHS; 4947 if (!isLoopGuardedByCond(L, 4948 isSigned ? ICmpInst::ICMP_SLT : 4949 ICmpInst::ICMP_ULT, 4950 getMinusSCEV(Start, Step), RHS)) 4951 End = isSigned ? getSMaxExpr(RHS, Start) 4952 : getUMaxExpr(RHS, Start); 4953 4954 // Determine the maximum constant end value. 4955 const SCEV *MaxEnd = getConstant(isSigned ? 4956 getSignedRange(End).getSignedMax() : 4957 getUnsignedRange(End).getUnsignedMax()); 4958 4959 // Finally, we subtract these two values and divide, rounding up, to get 4960 // the number of times the backedge is executed. 4961 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 4962 4963 // The maximum backedge count is similar, except using the minimum start 4964 // value and the maximum end value. 4965 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 4966 4967 return BackedgeTakenInfo(BECount, MaxBECount); 4968 } 4969 4970 return getCouldNotCompute(); 4971} 4972 4973/// getNumIterationsInRange - Return the number of iterations of this loop that 4974/// produce values in the specified constant range. Another way of looking at 4975/// this is that it returns the first iteration number where the value is not in 4976/// the condition, thus computing the exit count. If the iteration count can't 4977/// be computed, an instance of SCEVCouldNotCompute is returned. 4978const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4979 ScalarEvolution &SE) const { 4980 if (Range.isFullSet()) // Infinite loop. 4981 return SE.getCouldNotCompute(); 4982 4983 // If the start is a non-zero constant, shift the range to simplify things. 4984 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4985 if (!SC->getValue()->isZero()) { 4986 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4987 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4988 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4989 if (const SCEVAddRecExpr *ShiftedAddRec = 4990 dyn_cast<SCEVAddRecExpr>(Shifted)) 4991 return ShiftedAddRec->getNumIterationsInRange( 4992 Range.subtract(SC->getValue()->getValue()), SE); 4993 // This is strange and shouldn't happen. 4994 return SE.getCouldNotCompute(); 4995 } 4996 4997 // The only time we can solve this is when we have all constant indices. 4998 // Otherwise, we cannot determine the overflow conditions. 4999 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5000 if (!isa<SCEVConstant>(getOperand(i))) 5001 return SE.getCouldNotCompute(); 5002 5003 5004 // Okay at this point we know that all elements of the chrec are constants and 5005 // that the start element is zero. 5006 5007 // First check to see if the range contains zero. If not, the first 5008 // iteration exits. 5009 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5010 if (!Range.contains(APInt(BitWidth, 0))) 5011 return SE.getIntegerSCEV(0, getType()); 5012 5013 if (isAffine()) { 5014 // If this is an affine expression then we have this situation: 5015 // Solve {0,+,A} in Range === Ax in Range 5016 5017 // We know that zero is in the range. If A is positive then we know that 5018 // the upper value of the range must be the first possible exit value. 5019 // If A is negative then the lower of the range is the last possible loop 5020 // value. Also note that we already checked for a full range. 5021 APInt One(BitWidth,1); 5022 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5023 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5024 5025 // The exit value should be (End+A)/A. 5026 APInt ExitVal = (End + A).udiv(A); 5027 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5028 5029 // Evaluate at the exit value. If we really did fall out of the valid 5030 // range, then we computed our trip count, otherwise wrap around or other 5031 // things must have happened. 5032 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5033 if (Range.contains(Val->getValue())) 5034 return SE.getCouldNotCompute(); // Something strange happened 5035 5036 // Ensure that the previous value is in the range. This is a sanity check. 5037 assert(Range.contains( 5038 EvaluateConstantChrecAtConstant(this, 5039 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5040 "Linear scev computation is off in a bad way!"); 5041 return SE.getConstant(ExitValue); 5042 } else if (isQuadratic()) { 5043 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5044 // quadratic equation to solve it. To do this, we must frame our problem in 5045 // terms of figuring out when zero is crossed, instead of when 5046 // Range.getUpper() is crossed. 5047 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5048 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5049 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5050 5051 // Next, solve the constructed addrec 5052 std::pair<const SCEV *,const SCEV *> Roots = 5053 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5054 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5055 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5056 if (R1) { 5057 // Pick the smallest positive root value. 5058 if (ConstantInt *CB = 5059 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5060 R1->getValue(), R2->getValue()))) { 5061 if (CB->getZExtValue() == false) 5062 std::swap(R1, R2); // R1 is the minimum root now. 5063 5064 // Make sure the root is not off by one. The returned iteration should 5065 // not be in the range, but the previous one should be. When solving 5066 // for "X*X < 5", for example, we should not return a root of 2. 5067 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5068 R1->getValue(), 5069 SE); 5070 if (Range.contains(R1Val->getValue())) { 5071 // The next iteration must be out of the range... 5072 ConstantInt *NextVal = 5073 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5074 5075 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5076 if (!Range.contains(R1Val->getValue())) 5077 return SE.getConstant(NextVal); 5078 return SE.getCouldNotCompute(); // Something strange happened 5079 } 5080 5081 // If R1 was not in the range, then it is a good return value. Make 5082 // sure that R1-1 WAS in the range though, just in case. 5083 ConstantInt *NextVal = 5084 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5085 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5086 if (Range.contains(R1Val->getValue())) 5087 return R1; 5088 return SE.getCouldNotCompute(); // Something strange happened 5089 } 5090 } 5091 } 5092 5093 return SE.getCouldNotCompute(); 5094} 5095 5096 5097 5098//===----------------------------------------------------------------------===// 5099// SCEVCallbackVH Class Implementation 5100//===----------------------------------------------------------------------===// 5101 5102void ScalarEvolution::SCEVCallbackVH::deleted() { 5103 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5104 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5105 SE->ConstantEvolutionLoopExitValue.erase(PN); 5106 SE->Scalars.erase(getValPtr()); 5107 // this now dangles! 5108} 5109 5110void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5111 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5112 5113 // Forget all the expressions associated with users of the old value, 5114 // so that future queries will recompute the expressions using the new 5115 // value. 5116 SmallVector<User *, 16> Worklist; 5117 SmallPtrSet<User *, 8> Visited; 5118 Value *Old = getValPtr(); 5119 bool DeleteOld = false; 5120 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5121 UI != UE; ++UI) 5122 Worklist.push_back(*UI); 5123 while (!Worklist.empty()) { 5124 User *U = Worklist.pop_back_val(); 5125 // Deleting the Old value will cause this to dangle. Postpone 5126 // that until everything else is done. 5127 if (U == Old) { 5128 DeleteOld = true; 5129 continue; 5130 } 5131 if (!Visited.insert(U)) 5132 continue; 5133 if (PHINode *PN = dyn_cast<PHINode>(U)) 5134 SE->ConstantEvolutionLoopExitValue.erase(PN); 5135 SE->Scalars.erase(U); 5136 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5137 UI != UE; ++UI) 5138 Worklist.push_back(*UI); 5139 } 5140 // Delete the Old value if it (indirectly) references itself. 5141 if (DeleteOld) { 5142 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5143 SE->ConstantEvolutionLoopExitValue.erase(PN); 5144 SE->Scalars.erase(Old); 5145 // this now dangles! 5146 } 5147 // this may dangle! 5148} 5149 5150ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5151 : CallbackVH(V), SE(se) {} 5152 5153//===----------------------------------------------------------------------===// 5154// ScalarEvolution Class Implementation 5155//===----------------------------------------------------------------------===// 5156 5157ScalarEvolution::ScalarEvolution() 5158 : FunctionPass(&ID) { 5159} 5160 5161bool ScalarEvolution::runOnFunction(Function &F) { 5162 this->F = &F; 5163 LI = &getAnalysis<LoopInfo>(); 5164 TD = getAnalysisIfAvailable<TargetData>(); 5165 return false; 5166} 5167 5168void ScalarEvolution::releaseMemory() { 5169 Scalars.clear(); 5170 BackedgeTakenCounts.clear(); 5171 ConstantEvolutionLoopExitValue.clear(); 5172 ValuesAtScopes.clear(); 5173 UniqueSCEVs.clear(); 5174 SCEVAllocator.Reset(); 5175} 5176 5177void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5178 AU.setPreservesAll(); 5179 AU.addRequiredTransitive<LoopInfo>(); 5180} 5181 5182bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5183 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5184} 5185 5186static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5187 const Loop *L) { 5188 // Print all inner loops first 5189 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5190 PrintLoopInfo(OS, SE, *I); 5191 5192 OS << "Loop " << L->getHeader()->getName() << ": "; 5193 5194 SmallVector<BasicBlock*, 8> ExitBlocks; 5195 L->getExitBlocks(ExitBlocks); 5196 if (ExitBlocks.size() != 1) 5197 OS << "<multiple exits> "; 5198 5199 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5200 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5201 } else { 5202 OS << "Unpredictable backedge-taken count. "; 5203 } 5204 5205 OS << "\n"; 5206 OS << "Loop " << L->getHeader()->getName() << ": "; 5207 5208 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5209 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5210 } else { 5211 OS << "Unpredictable max backedge-taken count. "; 5212 } 5213 5214 OS << "\n"; 5215} 5216 5217void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 5218 // ScalarEvolution's implementaiton of the print method is to print 5219 // out SCEV values of all instructions that are interesting. Doing 5220 // this potentially causes it to create new SCEV objects though, 5221 // which technically conflicts with the const qualifier. This isn't 5222 // observable from outside the class though, so casting away the 5223 // const isn't dangerous. 5224 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 5225 5226 OS << "Classifying expressions for: " << F->getName() << "\n"; 5227 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5228 if (isSCEVable(I->getType())) { 5229 OS << *I << '\n'; 5230 OS << " --> "; 5231 const SCEV *SV = SE.getSCEV(&*I); 5232 SV->print(OS); 5233 5234 const Loop *L = LI->getLoopFor((*I).getParent()); 5235 5236 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5237 if (AtUse != SV) { 5238 OS << " --> "; 5239 AtUse->print(OS); 5240 } 5241 5242 if (L) { 5243 OS << "\t\t" "Exits: "; 5244 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5245 if (!ExitValue->isLoopInvariant(L)) { 5246 OS << "<<Unknown>>"; 5247 } else { 5248 OS << *ExitValue; 5249 } 5250 } 5251 5252 OS << "\n"; 5253 } 5254 5255 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 5256 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5257 PrintLoopInfo(OS, &SE, *I); 5258} 5259 5260