ScalarEvolution.cpp revision 2166f6229042a4d3d65847ebe0d453cd664682ef
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/ConstantRange.h" 78#include "llvm/Support/ErrorHandling.h" 79#include "llvm/Support/GetElementPtrTypeIterator.h" 80#include "llvm/Support/InstIterator.h" 81#include "llvm/Support/MathExtras.h" 82#include "llvm/Support/raw_ostream.h" 83#include "llvm/ADT/Statistic.h" 84#include "llvm/ADT/STLExtras.h" 85#include "llvm/ADT/SmallPtrSet.h" 86#include <algorithm> 87using namespace llvm; 88 89STATISTIC(NumArrayLenItCounts, 90 "Number of trip counts computed with array length"); 91STATISTIC(NumTripCountsComputed, 92 "Number of loops with predictable loop counts"); 93STATISTIC(NumTripCountsNotComputed, 94 "Number of loops without predictable loop counts"); 95STATISTIC(NumBruteForceTripCountsComputed, 96 "Number of loops with trip counts computed by force"); 97 98static cl::opt<unsigned> 99MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 100 cl::desc("Maximum number of iterations SCEV will " 101 "symbolically execute a constant " 102 "derived loop"), 103 cl::init(100)); 104 105static RegisterPass<ScalarEvolution> 106R("scalar-evolution", "Scalar Evolution Analysis", false, true); 107char ScalarEvolution::ID = 0; 108 109//===----------------------------------------------------------------------===// 110// SCEV class definitions 111//===----------------------------------------------------------------------===// 112 113//===----------------------------------------------------------------------===// 114// Implementation of the SCEV class. 115// 116 117SCEV::~SCEV() {} 118 119void SCEV::dump() const { 120 print(errs()); 121 errs() << '\n'; 122} 123 124bool SCEV::isZero() const { 125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 126 return SC->getValue()->isZero(); 127 return false; 128} 129 130bool SCEV::isOne() const { 131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 132 return SC->getValue()->isOne(); 133 return false; 134} 135 136bool SCEV::isAllOnesValue() const { 137 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 138 return SC->getValue()->isAllOnesValue(); 139 return false; 140} 141 142SCEVCouldNotCompute::SCEVCouldNotCompute() : 143 SCEV(FoldingSetNodeID(), scCouldNotCompute) {} 144 145bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 146 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 147 return false; 148} 149 150const Type *SCEVCouldNotCompute::getType() const { 151 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 152 return 0; 153} 154 155bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 156 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 157 return false; 158} 159 160bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 161 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 162 return false; 163} 164 165void SCEVCouldNotCompute::print(raw_ostream &OS) const { 166 OS << "***COULDNOTCOMPUTE***"; 167} 168 169bool SCEVCouldNotCompute::classof(const SCEV *S) { 170 return S->getSCEVType() == scCouldNotCompute; 171} 172 173const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 174 FoldingSetNodeID ID; 175 ID.AddInteger(scConstant); 176 ID.AddPointer(V); 177 void *IP = 0; 178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 179 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 180 new (S) SCEVConstant(ID, V); 181 UniqueSCEVs.InsertNode(S, IP); 182 return S; 183} 184 185const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 186 return getConstant(ConstantInt::get(getContext(), Val)); 187} 188 189const SCEV * 190ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 191 return getConstant( 192 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(raw_ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 202 unsigned SCEVTy, const SCEV *op, const Type *ty) 203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 204 205bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 206 return Op->dominates(BB, DT); 207} 208 209bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->properlyDominates(BB, DT); 211} 212 213SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 214 const SCEV *op, const Type *ty) 215 : SCEVCastExpr(ID, scTruncate, op, ty) { 216 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 217 (Ty->isInteger() || isa<PointerType>(Ty)) && 218 "Cannot truncate non-integer value!"); 219} 220 221void SCEVTruncateExpr::print(raw_ostream &OS) const { 222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 223} 224 225SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 226 const SCEV *op, const Type *ty) 227 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 228 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 229 (Ty->isInteger() || isa<PointerType>(Ty)) && 230 "Cannot zero extend non-integer value!"); 231} 232 233void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 235} 236 237SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 238 const SCEV *op, const Type *ty) 239 : SCEVCastExpr(ID, scSignExtend, op, ty) { 240 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) && 241 (Ty->isInteger() || isa<PointerType>(Ty)) && 242 "Cannot sign extend non-integer value!"); 243} 244 245void SCEVSignExtendExpr::print(raw_ostream &OS) const { 246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 247} 248 249void SCEVCommutativeExpr::print(raw_ostream &OS) const { 250 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 251 const char *OpStr = getOperationStr(); 252 OS << "(" << *Operands[0]; 253 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 254 OS << OpStr << *Operands[i]; 255 OS << ")"; 256} 257 258bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 259 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 260 if (!getOperand(i)->dominates(BB, DT)) 261 return false; 262 } 263 return true; 264} 265 266bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 267 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 268 if (!getOperand(i)->properlyDominates(BB, DT)) 269 return false; 270 } 271 return true; 272} 273 274bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 275 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 276} 277 278bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 279 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 280} 281 282void SCEVUDivExpr::print(raw_ostream &OS) const { 283 OS << "(" << *LHS << " /u " << *RHS << ")"; 284} 285 286const Type *SCEVUDivExpr::getType() const { 287 // In most cases the types of LHS and RHS will be the same, but in some 288 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 289 // depend on the type for correctness, but handling types carefully can 290 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 291 // a pointer type than the RHS, so use the RHS' type here. 292 return RHS->getType(); 293} 294 295bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 296 // Add recurrences are never invariant in the function-body (null loop). 297 if (!QueryLoop) 298 return false; 299 300 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 301 if (QueryLoop->contains(L->getHeader())) 302 return false; 303 304 // This recurrence is variant w.r.t. QueryLoop if any of its operands 305 // are variant. 306 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 307 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 308 return false; 309 310 // Otherwise it's loop-invariant. 311 return true; 312} 313 314void SCEVAddRecExpr::print(raw_ostream &OS) const { 315 OS << "{" << *Operands[0]; 316 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 317 OS << ",+," << *Operands[i]; 318 OS << "}<" << L->getHeader()->getName() + ">"; 319} 320 321void SCEVFieldOffsetExpr::print(raw_ostream &OS) const { 322 // LLVM struct fields don't have names, so just print the field number. 323 OS << "offsetof(" << *STy << ", " << FieldNo << ")"; 324} 325 326void SCEVAllocSizeExpr::print(raw_ostream &OS) const { 327 OS << "sizeof(" << *AllocTy << ")"; 328} 329 330bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 331 // All non-instruction values are loop invariant. All instructions are loop 332 // invariant if they are not contained in the specified loop. 333 // Instructions are never considered invariant in the function body 334 // (null loop) because they are defined within the "loop". 335 if (Instruction *I = dyn_cast<Instruction>(V)) 336 return L && !L->contains(I->getParent()); 337 return true; 338} 339 340bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 341 if (Instruction *I = dyn_cast<Instruction>(getValue())) 342 return DT->dominates(I->getParent(), BB); 343 return true; 344} 345 346bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 347 if (Instruction *I = dyn_cast<Instruction>(getValue())) 348 return DT->properlyDominates(I->getParent(), BB); 349 return true; 350} 351 352const Type *SCEVUnknown::getType() const { 353 return V->getType(); 354} 355 356void SCEVUnknown::print(raw_ostream &OS) const { 357 WriteAsOperand(OS, V, false); 358} 359 360//===----------------------------------------------------------------------===// 361// SCEV Utilities 362//===----------------------------------------------------------------------===// 363 364static bool CompareTypes(const Type *A, const Type *B) { 365 if (A->getTypeID() != B->getTypeID()) 366 return A->getTypeID() < B->getTypeID(); 367 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 368 const IntegerType *BI = cast<IntegerType>(B); 369 return AI->getBitWidth() < BI->getBitWidth(); 370 } 371 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 372 const PointerType *BI = cast<PointerType>(B); 373 return CompareTypes(AI->getElementType(), BI->getElementType()); 374 } 375 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 376 const ArrayType *BI = cast<ArrayType>(B); 377 if (AI->getNumElements() != BI->getNumElements()) 378 return AI->getNumElements() < BI->getNumElements(); 379 return CompareTypes(AI->getElementType(), BI->getElementType()); 380 } 381 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 382 const VectorType *BI = cast<VectorType>(B); 383 if (AI->getNumElements() != BI->getNumElements()) 384 return AI->getNumElements() < BI->getNumElements(); 385 return CompareTypes(AI->getElementType(), BI->getElementType()); 386 } 387 if (const StructType *AI = dyn_cast<StructType>(A)) { 388 const StructType *BI = cast<StructType>(B); 389 if (AI->getNumElements() != BI->getNumElements()) 390 return AI->getNumElements() < BI->getNumElements(); 391 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 392 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 393 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 394 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 395 } 396 return false; 397} 398 399namespace { 400 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 401 /// than the complexity of the RHS. This comparator is used to canonicalize 402 /// expressions. 403 class SCEVComplexityCompare { 404 LoopInfo *LI; 405 public: 406 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 407 408 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 409 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 410 if (LHS == RHS) 411 return false; 412 413 // Primarily, sort the SCEVs by their getSCEVType(). 414 if (LHS->getSCEVType() != RHS->getSCEVType()) 415 return LHS->getSCEVType() < RHS->getSCEVType(); 416 417 // Aside from the getSCEVType() ordering, the particular ordering 418 // isn't very important except that it's beneficial to be consistent, 419 // so that (a + b) and (b + a) don't end up as different expressions. 420 421 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 422 // not as complete as it could be. 423 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 424 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 425 426 // Order pointer values after integer values. This helps SCEVExpander 427 // form GEPs. 428 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType())) 429 return false; 430 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType())) 431 return true; 432 433 // Compare getValueID values. 434 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 435 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 436 437 // Sort arguments by their position. 438 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 439 const Argument *RA = cast<Argument>(RU->getValue()); 440 return LA->getArgNo() < RA->getArgNo(); 441 } 442 443 // For instructions, compare their loop depth, and their opcode. 444 // This is pretty loose. 445 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 446 Instruction *RV = cast<Instruction>(RU->getValue()); 447 448 // Compare loop depths. 449 if (LI->getLoopDepth(LV->getParent()) != 450 LI->getLoopDepth(RV->getParent())) 451 return LI->getLoopDepth(LV->getParent()) < 452 LI->getLoopDepth(RV->getParent()); 453 454 // Compare opcodes. 455 if (LV->getOpcode() != RV->getOpcode()) 456 return LV->getOpcode() < RV->getOpcode(); 457 458 // Compare the number of operands. 459 if (LV->getNumOperands() != RV->getNumOperands()) 460 return LV->getNumOperands() < RV->getNumOperands(); 461 } 462 463 return false; 464 } 465 466 // Compare constant values. 467 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 468 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 469 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 470 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 471 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 472 } 473 474 // Compare addrec loop depths. 475 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 476 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 477 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 478 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 479 } 480 481 // Lexicographically compare n-ary expressions. 482 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 483 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 484 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 485 if (i >= RC->getNumOperands()) 486 return false; 487 if (operator()(LC->getOperand(i), RC->getOperand(i))) 488 return true; 489 if (operator()(RC->getOperand(i), LC->getOperand(i))) 490 return false; 491 } 492 return LC->getNumOperands() < RC->getNumOperands(); 493 } 494 495 // Lexicographically compare udiv expressions. 496 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 497 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 498 if (operator()(LC->getLHS(), RC->getLHS())) 499 return true; 500 if (operator()(RC->getLHS(), LC->getLHS())) 501 return false; 502 if (operator()(LC->getRHS(), RC->getRHS())) 503 return true; 504 if (operator()(RC->getRHS(), LC->getRHS())) 505 return false; 506 return false; 507 } 508 509 // Compare cast expressions by operand. 510 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 511 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 512 return operator()(LC->getOperand(), RC->getOperand()); 513 } 514 515 // Compare offsetof expressions. 516 if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) { 517 const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS); 518 if (CompareTypes(LA->getStructType(), RA->getStructType()) || 519 CompareTypes(RA->getStructType(), LA->getStructType())) 520 return CompareTypes(LA->getStructType(), RA->getStructType()); 521 return LA->getFieldNo() < RA->getFieldNo(); 522 } 523 524 // Compare sizeof expressions by the allocation type. 525 if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) { 526 const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS); 527 return CompareTypes(LA->getAllocType(), RA->getAllocType()); 528 } 529 530 llvm_unreachable("Unknown SCEV kind!"); 531 return false; 532 } 533 }; 534} 535 536/// GroupByComplexity - Given a list of SCEV objects, order them by their 537/// complexity, and group objects of the same complexity together by value. 538/// When this routine is finished, we know that any duplicates in the vector are 539/// consecutive and that complexity is monotonically increasing. 540/// 541/// Note that we go take special precautions to ensure that we get determinstic 542/// results from this routine. In other words, we don't want the results of 543/// this to depend on where the addresses of various SCEV objects happened to 544/// land in memory. 545/// 546static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 547 LoopInfo *LI) { 548 if (Ops.size() < 2) return; // Noop 549 if (Ops.size() == 2) { 550 // This is the common case, which also happens to be trivially simple. 551 // Special case it. 552 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 553 std::swap(Ops[0], Ops[1]); 554 return; 555 } 556 557 // Do the rough sort by complexity. 558 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 559 560 // Now that we are sorted by complexity, group elements of the same 561 // complexity. Note that this is, at worst, N^2, but the vector is likely to 562 // be extremely short in practice. Note that we take this approach because we 563 // do not want to depend on the addresses of the objects we are grouping. 564 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 565 const SCEV *S = Ops[i]; 566 unsigned Complexity = S->getSCEVType(); 567 568 // If there are any objects of the same complexity and same value as this 569 // one, group them. 570 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 571 if (Ops[j] == S) { // Found a duplicate. 572 // Move it to immediately after i'th element. 573 std::swap(Ops[i+1], Ops[j]); 574 ++i; // no need to rescan it. 575 if (i == e-2) return; // Done! 576 } 577 } 578 } 579} 580 581 582 583//===----------------------------------------------------------------------===// 584// Simple SCEV method implementations 585//===----------------------------------------------------------------------===// 586 587/// BinomialCoefficient - Compute BC(It, K). The result has width W. 588/// Assume, K > 0. 589static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 590 ScalarEvolution &SE, 591 const Type* ResultTy) { 592 // Handle the simplest case efficiently. 593 if (K == 1) 594 return SE.getTruncateOrZeroExtend(It, ResultTy); 595 596 // We are using the following formula for BC(It, K): 597 // 598 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 599 // 600 // Suppose, W is the bitwidth of the return value. We must be prepared for 601 // overflow. Hence, we must assure that the result of our computation is 602 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 603 // safe in modular arithmetic. 604 // 605 // However, this code doesn't use exactly that formula; the formula it uses 606 // is something like the following, where T is the number of factors of 2 in 607 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 608 // exponentiation: 609 // 610 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 611 // 612 // This formula is trivially equivalent to the previous formula. However, 613 // this formula can be implemented much more efficiently. The trick is that 614 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 615 // arithmetic. To do exact division in modular arithmetic, all we have 616 // to do is multiply by the inverse. Therefore, this step can be done at 617 // width W. 618 // 619 // The next issue is how to safely do the division by 2^T. The way this 620 // is done is by doing the multiplication step at a width of at least W + T 621 // bits. This way, the bottom W+T bits of the product are accurate. Then, 622 // when we perform the division by 2^T (which is equivalent to a right shift 623 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 624 // truncated out after the division by 2^T. 625 // 626 // In comparison to just directly using the first formula, this technique 627 // is much more efficient; using the first formula requires W * K bits, 628 // but this formula less than W + K bits. Also, the first formula requires 629 // a division step, whereas this formula only requires multiplies and shifts. 630 // 631 // It doesn't matter whether the subtraction step is done in the calculation 632 // width or the input iteration count's width; if the subtraction overflows, 633 // the result must be zero anyway. We prefer here to do it in the width of 634 // the induction variable because it helps a lot for certain cases; CodeGen 635 // isn't smart enough to ignore the overflow, which leads to much less 636 // efficient code if the width of the subtraction is wider than the native 637 // register width. 638 // 639 // (It's possible to not widen at all by pulling out factors of 2 before 640 // the multiplication; for example, K=2 can be calculated as 641 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 642 // extra arithmetic, so it's not an obvious win, and it gets 643 // much more complicated for K > 3.) 644 645 // Protection from insane SCEVs; this bound is conservative, 646 // but it probably doesn't matter. 647 if (K > 1000) 648 return SE.getCouldNotCompute(); 649 650 unsigned W = SE.getTypeSizeInBits(ResultTy); 651 652 // Calculate K! / 2^T and T; we divide out the factors of two before 653 // multiplying for calculating K! / 2^T to avoid overflow. 654 // Other overflow doesn't matter because we only care about the bottom 655 // W bits of the result. 656 APInt OddFactorial(W, 1); 657 unsigned T = 1; 658 for (unsigned i = 3; i <= K; ++i) { 659 APInt Mult(W, i); 660 unsigned TwoFactors = Mult.countTrailingZeros(); 661 T += TwoFactors; 662 Mult = Mult.lshr(TwoFactors); 663 OddFactorial *= Mult; 664 } 665 666 // We need at least W + T bits for the multiplication step 667 unsigned CalculationBits = W + T; 668 669 // Calcuate 2^T, at width T+W. 670 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 671 672 // Calculate the multiplicative inverse of K! / 2^T; 673 // this multiplication factor will perform the exact division by 674 // K! / 2^T. 675 APInt Mod = APInt::getSignedMinValue(W+1); 676 APInt MultiplyFactor = OddFactorial.zext(W+1); 677 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 678 MultiplyFactor = MultiplyFactor.trunc(W); 679 680 // Calculate the product, at width T+W 681 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 682 CalculationBits); 683 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 684 for (unsigned i = 1; i != K; ++i) { 685 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 686 Dividend = SE.getMulExpr(Dividend, 687 SE.getTruncateOrZeroExtend(S, CalculationTy)); 688 } 689 690 // Divide by 2^T 691 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 692 693 // Truncate the result, and divide by K! / 2^T. 694 695 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 696 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 697} 698 699/// evaluateAtIteration - Return the value of this chain of recurrences at 700/// the specified iteration number. We can evaluate this recurrence by 701/// multiplying each element in the chain by the binomial coefficient 702/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 703/// 704/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 705/// 706/// where BC(It, k) stands for binomial coefficient. 707/// 708const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 709 ScalarEvolution &SE) const { 710 const SCEV *Result = getStart(); 711 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 712 // The computation is correct in the face of overflow provided that the 713 // multiplication is performed _after_ the evaluation of the binomial 714 // coefficient. 715 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 716 if (isa<SCEVCouldNotCompute>(Coeff)) 717 return Coeff; 718 719 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 720 } 721 return Result; 722} 723 724//===----------------------------------------------------------------------===// 725// SCEV Expression folder implementations 726//===----------------------------------------------------------------------===// 727 728const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 729 const Type *Ty) { 730 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 731 "This is not a truncating conversion!"); 732 assert(isSCEVable(Ty) && 733 "This is not a conversion to a SCEVable type!"); 734 Ty = getEffectiveSCEVType(Ty); 735 736 FoldingSetNodeID ID; 737 ID.AddInteger(scTruncate); 738 ID.AddPointer(Op); 739 ID.AddPointer(Ty); 740 void *IP = 0; 741 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 742 743 // Fold if the operand is constant. 744 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 745 return getConstant( 746 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 747 748 // trunc(trunc(x)) --> trunc(x) 749 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 750 return getTruncateExpr(ST->getOperand(), Ty); 751 752 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 753 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 754 return getTruncateOrSignExtend(SS->getOperand(), Ty); 755 756 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 757 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 758 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 759 760 // If the input value is a chrec scev, truncate the chrec's operands. 761 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 762 SmallVector<const SCEV *, 4> Operands; 763 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 764 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 765 return getAddRecExpr(Operands, AddRec->getLoop()); 766 } 767 768 // The cast wasn't folded; create an explicit cast node. 769 // Recompute the insert position, as it may have been invalidated. 770 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 771 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 772 new (S) SCEVTruncateExpr(ID, Op, Ty); 773 UniqueSCEVs.InsertNode(S, IP); 774 return S; 775} 776 777const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 778 const Type *Ty) { 779 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 780 "This is not an extending conversion!"); 781 assert(isSCEVable(Ty) && 782 "This is not a conversion to a SCEVable type!"); 783 Ty = getEffectiveSCEVType(Ty); 784 785 // Fold if the operand is constant. 786 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 787 const Type *IntTy = getEffectiveSCEVType(Ty); 788 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 789 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 790 return getConstant(cast<ConstantInt>(C)); 791 } 792 793 // zext(zext(x)) --> zext(x) 794 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 795 return getZeroExtendExpr(SZ->getOperand(), Ty); 796 797 // Before doing any expensive analysis, check to see if we've already 798 // computed a SCEV for this Op and Ty. 799 FoldingSetNodeID ID; 800 ID.AddInteger(scZeroExtend); 801 ID.AddPointer(Op); 802 ID.AddPointer(Ty); 803 void *IP = 0; 804 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 805 806 // If the input value is a chrec scev, and we can prove that the value 807 // did not overflow the old, smaller, value, we can zero extend all of the 808 // operands (often constants). This allows analysis of something like 809 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 810 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 811 if (AR->isAffine()) { 812 const SCEV *Start = AR->getStart(); 813 const SCEV *Step = AR->getStepRecurrence(*this); 814 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 815 const Loop *L = AR->getLoop(); 816 817 // If we have special knowledge that this addrec won't overflow, 818 // we don't need to do any further analysis. 819 if (AR->hasNoUnsignedWrap()) 820 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 821 getZeroExtendExpr(Step, Ty), 822 L); 823 824 // Check whether the backedge-taken count is SCEVCouldNotCompute. 825 // Note that this serves two purposes: It filters out loops that are 826 // simply not analyzable, and it covers the case where this code is 827 // being called from within backedge-taken count analysis, such that 828 // attempting to ask for the backedge-taken count would likely result 829 // in infinite recursion. In the later case, the analysis code will 830 // cope with a conservative value, and it will take care to purge 831 // that value once it has finished. 832 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 833 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 834 // Manually compute the final value for AR, checking for 835 // overflow. 836 837 // Check whether the backedge-taken count can be losslessly casted to 838 // the addrec's type. The count is always unsigned. 839 const SCEV *CastedMaxBECount = 840 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 841 const SCEV *RecastedMaxBECount = 842 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 843 if (MaxBECount == RecastedMaxBECount) { 844 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 845 // Check whether Start+Step*MaxBECount has no unsigned overflow. 846 const SCEV *ZMul = 847 getMulExpr(CastedMaxBECount, 848 getTruncateOrZeroExtend(Step, Start->getType())); 849 const SCEV *Add = getAddExpr(Start, ZMul); 850 const SCEV *OperandExtendedAdd = 851 getAddExpr(getZeroExtendExpr(Start, WideTy), 852 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 853 getZeroExtendExpr(Step, WideTy))); 854 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 855 // Return the expression with the addrec on the outside. 856 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 857 getZeroExtendExpr(Step, Ty), 858 L); 859 860 // Similar to above, only this time treat the step value as signed. 861 // This covers loops that count down. 862 const SCEV *SMul = 863 getMulExpr(CastedMaxBECount, 864 getTruncateOrSignExtend(Step, Start->getType())); 865 Add = getAddExpr(Start, SMul); 866 OperandExtendedAdd = 867 getAddExpr(getZeroExtendExpr(Start, WideTy), 868 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 869 getSignExtendExpr(Step, WideTy))); 870 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 871 // Return the expression with the addrec on the outside. 872 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 873 getSignExtendExpr(Step, Ty), 874 L); 875 } 876 877 // If the backedge is guarded by a comparison with the pre-inc value 878 // the addrec is safe. Also, if the entry is guarded by a comparison 879 // with the start value and the backedge is guarded by a comparison 880 // with the post-inc value, the addrec is safe. 881 if (isKnownPositive(Step)) { 882 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 883 getUnsignedRange(Step).getUnsignedMax()); 884 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 885 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 886 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 887 AR->getPostIncExpr(*this), N))) 888 // Return the expression with the addrec on the outside. 889 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 890 getZeroExtendExpr(Step, Ty), 891 L); 892 } else if (isKnownNegative(Step)) { 893 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 894 getSignedRange(Step).getSignedMin()); 895 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 896 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 897 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 898 AR->getPostIncExpr(*this), N))) 899 // Return the expression with the addrec on the outside. 900 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 901 getSignExtendExpr(Step, Ty), 902 L); 903 } 904 } 905 } 906 907 // The cast wasn't folded; create an explicit cast node. 908 // Recompute the insert position, as it may have been invalidated. 909 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 910 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 911 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 912 UniqueSCEVs.InsertNode(S, IP); 913 return S; 914} 915 916const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 917 const Type *Ty) { 918 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 919 "This is not an extending conversion!"); 920 assert(isSCEVable(Ty) && 921 "This is not a conversion to a SCEVable type!"); 922 Ty = getEffectiveSCEVType(Ty); 923 924 // Fold if the operand is constant. 925 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 926 const Type *IntTy = getEffectiveSCEVType(Ty); 927 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 928 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 929 return getConstant(cast<ConstantInt>(C)); 930 } 931 932 // sext(sext(x)) --> sext(x) 933 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 934 return getSignExtendExpr(SS->getOperand(), Ty); 935 936 // Before doing any expensive analysis, check to see if we've already 937 // computed a SCEV for this Op and Ty. 938 FoldingSetNodeID ID; 939 ID.AddInteger(scSignExtend); 940 ID.AddPointer(Op); 941 ID.AddPointer(Ty); 942 void *IP = 0; 943 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 944 945 // If the input value is a chrec scev, and we can prove that the value 946 // did not overflow the old, smaller, value, we can sign extend all of the 947 // operands (often constants). This allows analysis of something like 948 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 949 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 950 if (AR->isAffine()) { 951 const SCEV *Start = AR->getStart(); 952 const SCEV *Step = AR->getStepRecurrence(*this); 953 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 954 const Loop *L = AR->getLoop(); 955 956 // If we have special knowledge that this addrec won't overflow, 957 // we don't need to do any further analysis. 958 if (AR->hasNoSignedWrap()) 959 return getAddRecExpr(getSignExtendExpr(Start, Ty), 960 getSignExtendExpr(Step, Ty), 961 L); 962 963 // Check whether the backedge-taken count is SCEVCouldNotCompute. 964 // Note that this serves two purposes: It filters out loops that are 965 // simply not analyzable, and it covers the case where this code is 966 // being called from within backedge-taken count analysis, such that 967 // attempting to ask for the backedge-taken count would likely result 968 // in infinite recursion. In the later case, the analysis code will 969 // cope with a conservative value, and it will take care to purge 970 // that value once it has finished. 971 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 972 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 973 // Manually compute the final value for AR, checking for 974 // overflow. 975 976 // Check whether the backedge-taken count can be losslessly casted to 977 // the addrec's type. The count is always unsigned. 978 const SCEV *CastedMaxBECount = 979 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 980 const SCEV *RecastedMaxBECount = 981 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 982 if (MaxBECount == RecastedMaxBECount) { 983 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 984 // Check whether Start+Step*MaxBECount has no signed overflow. 985 const SCEV *SMul = 986 getMulExpr(CastedMaxBECount, 987 getTruncateOrSignExtend(Step, Start->getType())); 988 const SCEV *Add = getAddExpr(Start, SMul); 989 const SCEV *OperandExtendedAdd = 990 getAddExpr(getSignExtendExpr(Start, WideTy), 991 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 992 getSignExtendExpr(Step, WideTy))); 993 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 994 // Return the expression with the addrec on the outside. 995 return getAddRecExpr(getSignExtendExpr(Start, Ty), 996 getSignExtendExpr(Step, Ty), 997 L); 998 999 // Similar to above, only this time treat the step value as unsigned. 1000 // This covers loops that count up with an unsigned step. 1001 const SCEV *UMul = 1002 getMulExpr(CastedMaxBECount, 1003 getTruncateOrZeroExtend(Step, Start->getType())); 1004 Add = getAddExpr(Start, UMul); 1005 OperandExtendedAdd = 1006 getAddExpr(getSignExtendExpr(Start, WideTy), 1007 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1008 getZeroExtendExpr(Step, WideTy))); 1009 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1010 // Return the expression with the addrec on the outside. 1011 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1012 getZeroExtendExpr(Step, Ty), 1013 L); 1014 } 1015 1016 // If the backedge is guarded by a comparison with the pre-inc value 1017 // the addrec is safe. Also, if the entry is guarded by a comparison 1018 // with the start value and the backedge is guarded by a comparison 1019 // with the post-inc value, the addrec is safe. 1020 if (isKnownPositive(Step)) { 1021 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1022 getSignedRange(Step).getSignedMax()); 1023 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1024 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1025 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1026 AR->getPostIncExpr(*this), N))) 1027 // Return the expression with the addrec on the outside. 1028 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1029 getSignExtendExpr(Step, Ty), 1030 L); 1031 } else if (isKnownNegative(Step)) { 1032 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1033 getSignedRange(Step).getSignedMin()); 1034 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1035 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1036 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1037 AR->getPostIncExpr(*this), N))) 1038 // Return the expression with the addrec on the outside. 1039 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1040 getSignExtendExpr(Step, Ty), 1041 L); 1042 } 1043 } 1044 } 1045 1046 // The cast wasn't folded; create an explicit cast node. 1047 // Recompute the insert position, as it may have been invalidated. 1048 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1049 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1050 new (S) SCEVSignExtendExpr(ID, Op, Ty); 1051 UniqueSCEVs.InsertNode(S, IP); 1052 return S; 1053} 1054 1055/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1056/// unspecified bits out to the given type. 1057/// 1058const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1059 const Type *Ty) { 1060 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1061 "This is not an extending conversion!"); 1062 assert(isSCEVable(Ty) && 1063 "This is not a conversion to a SCEVable type!"); 1064 Ty = getEffectiveSCEVType(Ty); 1065 1066 // Sign-extend negative constants. 1067 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1068 if (SC->getValue()->getValue().isNegative()) 1069 return getSignExtendExpr(Op, Ty); 1070 1071 // Peel off a truncate cast. 1072 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1073 const SCEV *NewOp = T->getOperand(); 1074 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1075 return getAnyExtendExpr(NewOp, Ty); 1076 return getTruncateOrNoop(NewOp, Ty); 1077 } 1078 1079 // Next try a zext cast. If the cast is folded, use it. 1080 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1081 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1082 return ZExt; 1083 1084 // Next try a sext cast. If the cast is folded, use it. 1085 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1086 if (!isa<SCEVSignExtendExpr>(SExt)) 1087 return SExt; 1088 1089 // If the expression is obviously signed, use the sext cast value. 1090 if (isa<SCEVSMaxExpr>(Op)) 1091 return SExt; 1092 1093 // Absent any other information, use the zext cast value. 1094 return ZExt; 1095} 1096 1097/// CollectAddOperandsWithScales - Process the given Ops list, which is 1098/// a list of operands to be added under the given scale, update the given 1099/// map. This is a helper function for getAddRecExpr. As an example of 1100/// what it does, given a sequence of operands that would form an add 1101/// expression like this: 1102/// 1103/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1104/// 1105/// where A and B are constants, update the map with these values: 1106/// 1107/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1108/// 1109/// and add 13 + A*B*29 to AccumulatedConstant. 1110/// This will allow getAddRecExpr to produce this: 1111/// 1112/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1113/// 1114/// This form often exposes folding opportunities that are hidden in 1115/// the original operand list. 1116/// 1117/// Return true iff it appears that any interesting folding opportunities 1118/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1119/// the common case where no interesting opportunities are present, and 1120/// is also used as a check to avoid infinite recursion. 1121/// 1122static bool 1123CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1124 SmallVector<const SCEV *, 8> &NewOps, 1125 APInt &AccumulatedConstant, 1126 const SmallVectorImpl<const SCEV *> &Ops, 1127 const APInt &Scale, 1128 ScalarEvolution &SE) { 1129 bool Interesting = false; 1130 1131 // Iterate over the add operands. 1132 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1133 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1134 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1135 APInt NewScale = 1136 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1137 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1138 // A multiplication of a constant with another add; recurse. 1139 Interesting |= 1140 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1141 cast<SCEVAddExpr>(Mul->getOperand(1)) 1142 ->getOperands(), 1143 NewScale, SE); 1144 } else { 1145 // A multiplication of a constant with some other value. Update 1146 // the map. 1147 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1148 const SCEV *Key = SE.getMulExpr(MulOps); 1149 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1150 M.insert(std::make_pair(Key, NewScale)); 1151 if (Pair.second) { 1152 NewOps.push_back(Pair.first->first); 1153 } else { 1154 Pair.first->second += NewScale; 1155 // The map already had an entry for this value, which may indicate 1156 // a folding opportunity. 1157 Interesting = true; 1158 } 1159 } 1160 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1161 // Pull a buried constant out to the outside. 1162 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1163 Interesting = true; 1164 AccumulatedConstant += Scale * C->getValue()->getValue(); 1165 } else { 1166 // An ordinary operand. Update the map. 1167 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1168 M.insert(std::make_pair(Ops[i], Scale)); 1169 if (Pair.second) { 1170 NewOps.push_back(Pair.first->first); 1171 } else { 1172 Pair.first->second += Scale; 1173 // The map already had an entry for this value, which may indicate 1174 // a folding opportunity. 1175 Interesting = true; 1176 } 1177 } 1178 } 1179 1180 return Interesting; 1181} 1182 1183namespace { 1184 struct APIntCompare { 1185 bool operator()(const APInt &LHS, const APInt &RHS) const { 1186 return LHS.ult(RHS); 1187 } 1188 }; 1189} 1190 1191/// getAddExpr - Get a canonical add expression, or something simpler if 1192/// possible. 1193const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1194 bool HasNUW, bool HasNSW) { 1195 assert(!Ops.empty() && "Cannot get empty add!"); 1196 if (Ops.size() == 1) return Ops[0]; 1197#ifndef NDEBUG 1198 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1199 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1200 getEffectiveSCEVType(Ops[0]->getType()) && 1201 "SCEVAddExpr operand types don't match!"); 1202#endif 1203 1204 // Sort by complexity, this groups all similar expression types together. 1205 GroupByComplexity(Ops, LI); 1206 1207 // If there are any constants, fold them together. 1208 unsigned Idx = 0; 1209 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1210 ++Idx; 1211 assert(Idx < Ops.size()); 1212 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1213 // We found two constants, fold them together! 1214 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1215 RHSC->getValue()->getValue()); 1216 if (Ops.size() == 2) return Ops[0]; 1217 Ops.erase(Ops.begin()+1); // Erase the folded element 1218 LHSC = cast<SCEVConstant>(Ops[0]); 1219 } 1220 1221 // If we are left with a constant zero being added, strip it off. 1222 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1223 Ops.erase(Ops.begin()); 1224 --Idx; 1225 } 1226 } 1227 1228 if (Ops.size() == 1) return Ops[0]; 1229 1230 // Okay, check to see if the same value occurs in the operand list twice. If 1231 // so, merge them together into an multiply expression. Since we sorted the 1232 // list, these values are required to be adjacent. 1233 const Type *Ty = Ops[0]->getType(); 1234 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1235 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1236 // Found a match, merge the two values into a multiply, and add any 1237 // remaining values to the result. 1238 const SCEV *Two = getIntegerSCEV(2, Ty); 1239 const SCEV *Mul = getMulExpr(Ops[i], Two); 1240 if (Ops.size() == 2) 1241 return Mul; 1242 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1243 Ops.push_back(Mul); 1244 return getAddExpr(Ops, HasNUW, HasNSW); 1245 } 1246 1247 // Check for truncates. If all the operands are truncated from the same 1248 // type, see if factoring out the truncate would permit the result to be 1249 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1250 // if the contents of the resulting outer trunc fold to something simple. 1251 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1252 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1253 const Type *DstType = Trunc->getType(); 1254 const Type *SrcType = Trunc->getOperand()->getType(); 1255 SmallVector<const SCEV *, 8> LargeOps; 1256 bool Ok = true; 1257 // Check all the operands to see if they can be represented in the 1258 // source type of the truncate. 1259 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1260 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1261 if (T->getOperand()->getType() != SrcType) { 1262 Ok = false; 1263 break; 1264 } 1265 LargeOps.push_back(T->getOperand()); 1266 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1267 // This could be either sign or zero extension, but sign extension 1268 // is much more likely to be foldable here. 1269 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1270 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1271 SmallVector<const SCEV *, 8> LargeMulOps; 1272 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1273 if (const SCEVTruncateExpr *T = 1274 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1275 if (T->getOperand()->getType() != SrcType) { 1276 Ok = false; 1277 break; 1278 } 1279 LargeMulOps.push_back(T->getOperand()); 1280 } else if (const SCEVConstant *C = 1281 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1282 // This could be either sign or zero extension, but sign extension 1283 // is much more likely to be foldable here. 1284 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1285 } else { 1286 Ok = false; 1287 break; 1288 } 1289 } 1290 if (Ok) 1291 LargeOps.push_back(getMulExpr(LargeMulOps)); 1292 } else { 1293 Ok = false; 1294 break; 1295 } 1296 } 1297 if (Ok) { 1298 // Evaluate the expression in the larger type. 1299 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1300 // If it folds to something simple, use it. Otherwise, don't. 1301 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1302 return getTruncateExpr(Fold, DstType); 1303 } 1304 } 1305 1306 // Skip past any other cast SCEVs. 1307 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1308 ++Idx; 1309 1310 // If there are add operands they would be next. 1311 if (Idx < Ops.size()) { 1312 bool DeletedAdd = false; 1313 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1314 // If we have an add, expand the add operands onto the end of the operands 1315 // list. 1316 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1317 Ops.erase(Ops.begin()+Idx); 1318 DeletedAdd = true; 1319 } 1320 1321 // If we deleted at least one add, we added operands to the end of the list, 1322 // and they are not necessarily sorted. Recurse to resort and resimplify 1323 // any operands we just aquired. 1324 if (DeletedAdd) 1325 return getAddExpr(Ops); 1326 } 1327 1328 // Skip over the add expression until we get to a multiply. 1329 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1330 ++Idx; 1331 1332 // Check to see if there are any folding opportunities present with 1333 // operands multiplied by constant values. 1334 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1335 uint64_t BitWidth = getTypeSizeInBits(Ty); 1336 DenseMap<const SCEV *, APInt> M; 1337 SmallVector<const SCEV *, 8> NewOps; 1338 APInt AccumulatedConstant(BitWidth, 0); 1339 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1340 Ops, APInt(BitWidth, 1), *this)) { 1341 // Some interesting folding opportunity is present, so its worthwhile to 1342 // re-generate the operands list. Group the operands by constant scale, 1343 // to avoid multiplying by the same constant scale multiple times. 1344 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1345 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1346 E = NewOps.end(); I != E; ++I) 1347 MulOpLists[M.find(*I)->second].push_back(*I); 1348 // Re-generate the operands list. 1349 Ops.clear(); 1350 if (AccumulatedConstant != 0) 1351 Ops.push_back(getConstant(AccumulatedConstant)); 1352 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1353 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1354 if (I->first != 0) 1355 Ops.push_back(getMulExpr(getConstant(I->first), 1356 getAddExpr(I->second))); 1357 if (Ops.empty()) 1358 return getIntegerSCEV(0, Ty); 1359 if (Ops.size() == 1) 1360 return Ops[0]; 1361 return getAddExpr(Ops); 1362 } 1363 } 1364 1365 // If we are adding something to a multiply expression, make sure the 1366 // something is not already an operand of the multiply. If so, merge it into 1367 // the multiply. 1368 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1369 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1370 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1371 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1372 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1373 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1374 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1375 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1376 if (Mul->getNumOperands() != 2) { 1377 // If the multiply has more than two operands, we must get the 1378 // Y*Z term. 1379 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1380 MulOps.erase(MulOps.begin()+MulOp); 1381 InnerMul = getMulExpr(MulOps); 1382 } 1383 const SCEV *One = getIntegerSCEV(1, Ty); 1384 const SCEV *AddOne = getAddExpr(InnerMul, One); 1385 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1386 if (Ops.size() == 2) return OuterMul; 1387 if (AddOp < Idx) { 1388 Ops.erase(Ops.begin()+AddOp); 1389 Ops.erase(Ops.begin()+Idx-1); 1390 } else { 1391 Ops.erase(Ops.begin()+Idx); 1392 Ops.erase(Ops.begin()+AddOp-1); 1393 } 1394 Ops.push_back(OuterMul); 1395 return getAddExpr(Ops); 1396 } 1397 1398 // Check this multiply against other multiplies being added together. 1399 for (unsigned OtherMulIdx = Idx+1; 1400 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1401 ++OtherMulIdx) { 1402 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1403 // If MulOp occurs in OtherMul, we can fold the two multiplies 1404 // together. 1405 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1406 OMulOp != e; ++OMulOp) 1407 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1408 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1409 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1410 if (Mul->getNumOperands() != 2) { 1411 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1412 Mul->op_end()); 1413 MulOps.erase(MulOps.begin()+MulOp); 1414 InnerMul1 = getMulExpr(MulOps); 1415 } 1416 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1417 if (OtherMul->getNumOperands() != 2) { 1418 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1419 OtherMul->op_end()); 1420 MulOps.erase(MulOps.begin()+OMulOp); 1421 InnerMul2 = getMulExpr(MulOps); 1422 } 1423 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1424 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1425 if (Ops.size() == 2) return OuterMul; 1426 Ops.erase(Ops.begin()+Idx); 1427 Ops.erase(Ops.begin()+OtherMulIdx-1); 1428 Ops.push_back(OuterMul); 1429 return getAddExpr(Ops); 1430 } 1431 } 1432 } 1433 } 1434 1435 // If there are any add recurrences in the operands list, see if any other 1436 // added values are loop invariant. If so, we can fold them into the 1437 // recurrence. 1438 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1439 ++Idx; 1440 1441 // Scan over all recurrences, trying to fold loop invariants into them. 1442 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1443 // Scan all of the other operands to this add and add them to the vector if 1444 // they are loop invariant w.r.t. the recurrence. 1445 SmallVector<const SCEV *, 8> LIOps; 1446 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1447 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1448 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1449 LIOps.push_back(Ops[i]); 1450 Ops.erase(Ops.begin()+i); 1451 --i; --e; 1452 } 1453 1454 // If we found some loop invariants, fold them into the recurrence. 1455 if (!LIOps.empty()) { 1456 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1457 LIOps.push_back(AddRec->getStart()); 1458 1459 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1460 AddRec->op_end()); 1461 AddRecOps[0] = getAddExpr(LIOps); 1462 1463 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1464 // If all of the other operands were loop invariant, we are done. 1465 if (Ops.size() == 1) return NewRec; 1466 1467 // Otherwise, add the folded AddRec by the non-liv parts. 1468 for (unsigned i = 0;; ++i) 1469 if (Ops[i] == AddRec) { 1470 Ops[i] = NewRec; 1471 break; 1472 } 1473 return getAddExpr(Ops); 1474 } 1475 1476 // Okay, if there weren't any loop invariants to be folded, check to see if 1477 // there are multiple AddRec's with the same loop induction variable being 1478 // added together. If so, we can fold them. 1479 for (unsigned OtherIdx = Idx+1; 1480 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1481 if (OtherIdx != Idx) { 1482 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1483 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1484 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1485 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1486 AddRec->op_end()); 1487 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1488 if (i >= NewOps.size()) { 1489 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1490 OtherAddRec->op_end()); 1491 break; 1492 } 1493 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1494 } 1495 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1496 1497 if (Ops.size() == 2) return NewAddRec; 1498 1499 Ops.erase(Ops.begin()+Idx); 1500 Ops.erase(Ops.begin()+OtherIdx-1); 1501 Ops.push_back(NewAddRec); 1502 return getAddExpr(Ops); 1503 } 1504 } 1505 1506 // Otherwise couldn't fold anything into this recurrence. Move onto the 1507 // next one. 1508 } 1509 1510 // Okay, it looks like we really DO need an add expr. Check to see if we 1511 // already have one, otherwise create a new one. 1512 FoldingSetNodeID ID; 1513 ID.AddInteger(scAddExpr); 1514 ID.AddInteger(Ops.size()); 1515 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1516 ID.AddPointer(Ops[i]); 1517 void *IP = 0; 1518 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1519 SCEVAddExpr *S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1520 new (S) SCEVAddExpr(ID, Ops); 1521 UniqueSCEVs.InsertNode(S, IP); 1522 if (HasNUW) S->setHasNoUnsignedWrap(true); 1523 if (HasNSW) S->setHasNoSignedWrap(true); 1524 return S; 1525} 1526 1527 1528/// getMulExpr - Get a canonical multiply expression, or something simpler if 1529/// possible. 1530const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1531 bool HasNUW, bool HasNSW) { 1532 assert(!Ops.empty() && "Cannot get empty mul!"); 1533#ifndef NDEBUG 1534 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1535 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1536 getEffectiveSCEVType(Ops[0]->getType()) && 1537 "SCEVMulExpr operand types don't match!"); 1538#endif 1539 1540 // Sort by complexity, this groups all similar expression types together. 1541 GroupByComplexity(Ops, LI); 1542 1543 // If there are any constants, fold them together. 1544 unsigned Idx = 0; 1545 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1546 1547 // C1*(C2+V) -> C1*C2 + C1*V 1548 if (Ops.size() == 2) 1549 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1550 if (Add->getNumOperands() == 2 && 1551 isa<SCEVConstant>(Add->getOperand(0))) 1552 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1553 getMulExpr(LHSC, Add->getOperand(1))); 1554 1555 1556 ++Idx; 1557 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1558 // We found two constants, fold them together! 1559 ConstantInt *Fold = ConstantInt::get(getContext(), 1560 LHSC->getValue()->getValue() * 1561 RHSC->getValue()->getValue()); 1562 Ops[0] = getConstant(Fold); 1563 Ops.erase(Ops.begin()+1); // Erase the folded element 1564 if (Ops.size() == 1) return Ops[0]; 1565 LHSC = cast<SCEVConstant>(Ops[0]); 1566 } 1567 1568 // If we are left with a constant one being multiplied, strip it off. 1569 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1570 Ops.erase(Ops.begin()); 1571 --Idx; 1572 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1573 // If we have a multiply of zero, it will always be zero. 1574 return Ops[0]; 1575 } 1576 } 1577 1578 // Skip over the add expression until we get to a multiply. 1579 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1580 ++Idx; 1581 1582 if (Ops.size() == 1) 1583 return Ops[0]; 1584 1585 // If there are mul operands inline them all into this expression. 1586 if (Idx < Ops.size()) { 1587 bool DeletedMul = false; 1588 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1589 // If we have an mul, expand the mul operands onto the end of the operands 1590 // list. 1591 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1592 Ops.erase(Ops.begin()+Idx); 1593 DeletedMul = true; 1594 } 1595 1596 // If we deleted at least one mul, we added operands to the end of the list, 1597 // and they are not necessarily sorted. Recurse to resort and resimplify 1598 // any operands we just aquired. 1599 if (DeletedMul) 1600 return getMulExpr(Ops); 1601 } 1602 1603 // If there are any add recurrences in the operands list, see if any other 1604 // added values are loop invariant. If so, we can fold them into the 1605 // recurrence. 1606 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1607 ++Idx; 1608 1609 // Scan over all recurrences, trying to fold loop invariants into them. 1610 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1611 // Scan all of the other operands to this mul and add them to the vector if 1612 // they are loop invariant w.r.t. the recurrence. 1613 SmallVector<const SCEV *, 8> LIOps; 1614 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1615 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1616 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1617 LIOps.push_back(Ops[i]); 1618 Ops.erase(Ops.begin()+i); 1619 --i; --e; 1620 } 1621 1622 // If we found some loop invariants, fold them into the recurrence. 1623 if (!LIOps.empty()) { 1624 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1625 SmallVector<const SCEV *, 4> NewOps; 1626 NewOps.reserve(AddRec->getNumOperands()); 1627 if (LIOps.size() == 1) { 1628 const SCEV *Scale = LIOps[0]; 1629 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1630 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1631 } else { 1632 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1633 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1634 MulOps.push_back(AddRec->getOperand(i)); 1635 NewOps.push_back(getMulExpr(MulOps)); 1636 } 1637 } 1638 1639 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1640 1641 // If all of the other operands were loop invariant, we are done. 1642 if (Ops.size() == 1) return NewRec; 1643 1644 // Otherwise, multiply the folded AddRec by the non-liv parts. 1645 for (unsigned i = 0;; ++i) 1646 if (Ops[i] == AddRec) { 1647 Ops[i] = NewRec; 1648 break; 1649 } 1650 return getMulExpr(Ops); 1651 } 1652 1653 // Okay, if there weren't any loop invariants to be folded, check to see if 1654 // there are multiple AddRec's with the same loop induction variable being 1655 // multiplied together. If so, we can fold them. 1656 for (unsigned OtherIdx = Idx+1; 1657 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1658 if (OtherIdx != Idx) { 1659 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1660 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1661 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1662 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1663 const SCEV *NewStart = getMulExpr(F->getStart(), 1664 G->getStart()); 1665 const SCEV *B = F->getStepRecurrence(*this); 1666 const SCEV *D = G->getStepRecurrence(*this); 1667 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1668 getMulExpr(G, B), 1669 getMulExpr(B, D)); 1670 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1671 F->getLoop()); 1672 if (Ops.size() == 2) return NewAddRec; 1673 1674 Ops.erase(Ops.begin()+Idx); 1675 Ops.erase(Ops.begin()+OtherIdx-1); 1676 Ops.push_back(NewAddRec); 1677 return getMulExpr(Ops); 1678 } 1679 } 1680 1681 // Otherwise couldn't fold anything into this recurrence. Move onto the 1682 // next one. 1683 } 1684 1685 // Okay, it looks like we really DO need an mul expr. Check to see if we 1686 // already have one, otherwise create a new one. 1687 FoldingSetNodeID ID; 1688 ID.AddInteger(scMulExpr); 1689 ID.AddInteger(Ops.size()); 1690 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1691 ID.AddPointer(Ops[i]); 1692 void *IP = 0; 1693 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1694 SCEVMulExpr *S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1695 new (S) SCEVMulExpr(ID, Ops); 1696 UniqueSCEVs.InsertNode(S, IP); 1697 if (HasNUW) S->setHasNoUnsignedWrap(true); 1698 if (HasNSW) S->setHasNoSignedWrap(true); 1699 return S; 1700} 1701 1702/// getUDivExpr - Get a canonical unsigned division expression, or something 1703/// simpler if possible. 1704const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1705 const SCEV *RHS) { 1706 assert(getEffectiveSCEVType(LHS->getType()) == 1707 getEffectiveSCEVType(RHS->getType()) && 1708 "SCEVUDivExpr operand types don't match!"); 1709 1710 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1711 if (RHSC->getValue()->equalsInt(1)) 1712 return LHS; // X udiv 1 --> x 1713 if (RHSC->isZero()) 1714 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1715 1716 // Determine if the division can be folded into the operands of 1717 // its operands. 1718 // TODO: Generalize this to non-constants by using known-bits information. 1719 const Type *Ty = LHS->getType(); 1720 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1721 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1722 // For non-power-of-two values, effectively round the value up to the 1723 // nearest power of two. 1724 if (!RHSC->getValue()->getValue().isPowerOf2()) 1725 ++MaxShiftAmt; 1726 const IntegerType *ExtTy = 1727 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1728 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1729 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1730 if (const SCEVConstant *Step = 1731 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1732 if (!Step->getValue()->getValue() 1733 .urem(RHSC->getValue()->getValue()) && 1734 getZeroExtendExpr(AR, ExtTy) == 1735 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1736 getZeroExtendExpr(Step, ExtTy), 1737 AR->getLoop())) { 1738 SmallVector<const SCEV *, 4> Operands; 1739 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1740 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1741 return getAddRecExpr(Operands, AR->getLoop()); 1742 } 1743 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1744 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1745 SmallVector<const SCEV *, 4> Operands; 1746 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1747 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1748 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1749 // Find an operand that's safely divisible. 1750 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1751 const SCEV *Op = M->getOperand(i); 1752 const SCEV *Div = getUDivExpr(Op, RHSC); 1753 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1754 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1755 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1756 MOperands.end()); 1757 Operands[i] = Div; 1758 return getMulExpr(Operands); 1759 } 1760 } 1761 } 1762 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1763 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1764 SmallVector<const SCEV *, 4> Operands; 1765 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1766 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1767 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1768 Operands.clear(); 1769 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1770 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1771 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1772 break; 1773 Operands.push_back(Op); 1774 } 1775 if (Operands.size() == A->getNumOperands()) 1776 return getAddExpr(Operands); 1777 } 1778 } 1779 1780 // Fold if both operands are constant. 1781 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1782 Constant *LHSCV = LHSC->getValue(); 1783 Constant *RHSCV = RHSC->getValue(); 1784 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1785 RHSCV))); 1786 } 1787 } 1788 1789 FoldingSetNodeID ID; 1790 ID.AddInteger(scUDivExpr); 1791 ID.AddPointer(LHS); 1792 ID.AddPointer(RHS); 1793 void *IP = 0; 1794 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1795 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1796 new (S) SCEVUDivExpr(ID, LHS, RHS); 1797 UniqueSCEVs.InsertNode(S, IP); 1798 return S; 1799} 1800 1801 1802/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1803/// Simplify the expression as much as possible. 1804const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1805 const SCEV *Step, const Loop *L, 1806 bool HasNUW, bool HasNSW) { 1807 SmallVector<const SCEV *, 4> Operands; 1808 Operands.push_back(Start); 1809 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1810 if (StepChrec->getLoop() == L) { 1811 Operands.insert(Operands.end(), StepChrec->op_begin(), 1812 StepChrec->op_end()); 1813 return getAddRecExpr(Operands, L); 1814 } 1815 1816 Operands.push_back(Step); 1817 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1818} 1819 1820/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1821/// Simplify the expression as much as possible. 1822const SCEV * 1823ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1824 const Loop *L, 1825 bool HasNUW, bool HasNSW) { 1826 if (Operands.size() == 1) return Operands[0]; 1827#ifndef NDEBUG 1828 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1829 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1830 getEffectiveSCEVType(Operands[0]->getType()) && 1831 "SCEVAddRecExpr operand types don't match!"); 1832#endif 1833 1834 if (Operands.back()->isZero()) { 1835 Operands.pop_back(); 1836 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1837 } 1838 1839 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1840 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1841 const Loop* NestedLoop = NestedAR->getLoop(); 1842 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) { 1843 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1844 NestedAR->op_end()); 1845 Operands[0] = NestedAR->getStart(); 1846 // AddRecs require their operands be loop-invariant with respect to their 1847 // loops. Don't perform this transformation if it would break this 1848 // requirement. 1849 bool AllInvariant = true; 1850 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1851 if (!Operands[i]->isLoopInvariant(L)) { 1852 AllInvariant = false; 1853 break; 1854 } 1855 if (AllInvariant) { 1856 NestedOperands[0] = getAddRecExpr(Operands, L); 1857 AllInvariant = true; 1858 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 1859 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 1860 AllInvariant = false; 1861 break; 1862 } 1863 if (AllInvariant) 1864 // Ok, both add recurrences are valid after the transformation. 1865 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 1866 } 1867 // Reset Operands to its original state. 1868 Operands[0] = NestedAR; 1869 } 1870 } 1871 1872 FoldingSetNodeID ID; 1873 ID.AddInteger(scAddRecExpr); 1874 ID.AddInteger(Operands.size()); 1875 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1876 ID.AddPointer(Operands[i]); 1877 ID.AddPointer(L); 1878 void *IP = 0; 1879 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1880 SCEVAddRecExpr *S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 1881 new (S) SCEVAddRecExpr(ID, Operands, L); 1882 UniqueSCEVs.InsertNode(S, IP); 1883 if (HasNUW) S->setHasNoUnsignedWrap(true); 1884 if (HasNSW) S->setHasNoSignedWrap(true); 1885 return S; 1886} 1887 1888const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 1889 const SCEV *RHS) { 1890 SmallVector<const SCEV *, 2> Ops; 1891 Ops.push_back(LHS); 1892 Ops.push_back(RHS); 1893 return getSMaxExpr(Ops); 1894} 1895 1896const SCEV * 1897ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1898 assert(!Ops.empty() && "Cannot get empty smax!"); 1899 if (Ops.size() == 1) return Ops[0]; 1900#ifndef NDEBUG 1901 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1902 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1903 getEffectiveSCEVType(Ops[0]->getType()) && 1904 "SCEVSMaxExpr operand types don't match!"); 1905#endif 1906 1907 // Sort by complexity, this groups all similar expression types together. 1908 GroupByComplexity(Ops, LI); 1909 1910 // If there are any constants, fold them together. 1911 unsigned Idx = 0; 1912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1913 ++Idx; 1914 assert(Idx < Ops.size()); 1915 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1916 // We found two constants, fold them together! 1917 ConstantInt *Fold = ConstantInt::get(getContext(), 1918 APIntOps::smax(LHSC->getValue()->getValue(), 1919 RHSC->getValue()->getValue())); 1920 Ops[0] = getConstant(Fold); 1921 Ops.erase(Ops.begin()+1); // Erase the folded element 1922 if (Ops.size() == 1) return Ops[0]; 1923 LHSC = cast<SCEVConstant>(Ops[0]); 1924 } 1925 1926 // If we are left with a constant minimum-int, strip it off. 1927 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 1928 Ops.erase(Ops.begin()); 1929 --Idx; 1930 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 1931 // If we have an smax with a constant maximum-int, it will always be 1932 // maximum-int. 1933 return Ops[0]; 1934 } 1935 } 1936 1937 if (Ops.size() == 1) return Ops[0]; 1938 1939 // Find the first SMax 1940 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 1941 ++Idx; 1942 1943 // Check to see if one of the operands is an SMax. If so, expand its operands 1944 // onto our operand list, and recurse to simplify. 1945 if (Idx < Ops.size()) { 1946 bool DeletedSMax = false; 1947 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 1948 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 1949 Ops.erase(Ops.begin()+Idx); 1950 DeletedSMax = true; 1951 } 1952 1953 if (DeletedSMax) 1954 return getSMaxExpr(Ops); 1955 } 1956 1957 // Okay, check to see if the same value occurs in the operand list twice. If 1958 // so, delete one. Since we sorted the list, these values are required to 1959 // be adjacent. 1960 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1961 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 1962 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 1963 --i; --e; 1964 } 1965 1966 if (Ops.size() == 1) return Ops[0]; 1967 1968 assert(!Ops.empty() && "Reduced smax down to nothing!"); 1969 1970 // Okay, it looks like we really DO need an smax expr. Check to see if we 1971 // already have one, otherwise create a new one. 1972 FoldingSetNodeID ID; 1973 ID.AddInteger(scSMaxExpr); 1974 ID.AddInteger(Ops.size()); 1975 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1976 ID.AddPointer(Ops[i]); 1977 void *IP = 0; 1978 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1979 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 1980 new (S) SCEVSMaxExpr(ID, Ops); 1981 UniqueSCEVs.InsertNode(S, IP); 1982 return S; 1983} 1984 1985const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 1986 const SCEV *RHS) { 1987 SmallVector<const SCEV *, 2> Ops; 1988 Ops.push_back(LHS); 1989 Ops.push_back(RHS); 1990 return getUMaxExpr(Ops); 1991} 1992 1993const SCEV * 1994ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 1995 assert(!Ops.empty() && "Cannot get empty umax!"); 1996 if (Ops.size() == 1) return Ops[0]; 1997#ifndef NDEBUG 1998 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1999 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2000 getEffectiveSCEVType(Ops[0]->getType()) && 2001 "SCEVUMaxExpr operand types don't match!"); 2002#endif 2003 2004 // Sort by complexity, this groups all similar expression types together. 2005 GroupByComplexity(Ops, LI); 2006 2007 // If there are any constants, fold them together. 2008 unsigned Idx = 0; 2009 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2010 ++Idx; 2011 assert(Idx < Ops.size()); 2012 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2013 // We found two constants, fold them together! 2014 ConstantInt *Fold = ConstantInt::get(getContext(), 2015 APIntOps::umax(LHSC->getValue()->getValue(), 2016 RHSC->getValue()->getValue())); 2017 Ops[0] = getConstant(Fold); 2018 Ops.erase(Ops.begin()+1); // Erase the folded element 2019 if (Ops.size() == 1) return Ops[0]; 2020 LHSC = cast<SCEVConstant>(Ops[0]); 2021 } 2022 2023 // If we are left with a constant minimum-int, strip it off. 2024 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2025 Ops.erase(Ops.begin()); 2026 --Idx; 2027 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2028 // If we have an umax with a constant maximum-int, it will always be 2029 // maximum-int. 2030 return Ops[0]; 2031 } 2032 } 2033 2034 if (Ops.size() == 1) return Ops[0]; 2035 2036 // Find the first UMax 2037 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2038 ++Idx; 2039 2040 // Check to see if one of the operands is a UMax. If so, expand its operands 2041 // onto our operand list, and recurse to simplify. 2042 if (Idx < Ops.size()) { 2043 bool DeletedUMax = false; 2044 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2045 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2046 Ops.erase(Ops.begin()+Idx); 2047 DeletedUMax = true; 2048 } 2049 2050 if (DeletedUMax) 2051 return getUMaxExpr(Ops); 2052 } 2053 2054 // Okay, check to see if the same value occurs in the operand list twice. If 2055 // so, delete one. Since we sorted the list, these values are required to 2056 // be adjacent. 2057 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2058 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2059 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2060 --i; --e; 2061 } 2062 2063 if (Ops.size() == 1) return Ops[0]; 2064 2065 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2066 2067 // Okay, it looks like we really DO need a umax expr. Check to see if we 2068 // already have one, otherwise create a new one. 2069 FoldingSetNodeID ID; 2070 ID.AddInteger(scUMaxExpr); 2071 ID.AddInteger(Ops.size()); 2072 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2073 ID.AddPointer(Ops[i]); 2074 void *IP = 0; 2075 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2076 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2077 new (S) SCEVUMaxExpr(ID, Ops); 2078 UniqueSCEVs.InsertNode(S, IP); 2079 return S; 2080} 2081 2082const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2083 const SCEV *RHS) { 2084 // ~smax(~x, ~y) == smin(x, y). 2085 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2086} 2087 2088const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2089 const SCEV *RHS) { 2090 // ~umax(~x, ~y) == umin(x, y) 2091 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2092} 2093 2094const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy, 2095 unsigned FieldNo) { 2096 // If we have TargetData we can determine the constant offset. 2097 if (TD) { 2098 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2099 const StructLayout &SL = *TD->getStructLayout(STy); 2100 uint64_t Offset = SL.getElementOffset(FieldNo); 2101 return getIntegerSCEV(Offset, IntPtrTy); 2102 } 2103 2104 // Field 0 is always at offset 0. 2105 if (FieldNo == 0) { 2106 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2107 return getIntegerSCEV(0, Ty); 2108 } 2109 2110 // Okay, it looks like we really DO need an offsetof expr. Check to see if we 2111 // already have one, otherwise create a new one. 2112 FoldingSetNodeID ID; 2113 ID.AddInteger(scFieldOffset); 2114 ID.AddPointer(STy); 2115 ID.AddInteger(FieldNo); 2116 void *IP = 0; 2117 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2118 SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>(); 2119 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2120 new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo); 2121 UniqueSCEVs.InsertNode(S, IP); 2122 return S; 2123} 2124 2125const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) { 2126 // If we have TargetData we can determine the constant size. 2127 if (TD && AllocTy->isSized()) { 2128 const Type *IntPtrTy = TD->getIntPtrType(getContext()); 2129 return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy); 2130 } 2131 2132 // Expand an array size into the element size times the number 2133 // of elements. 2134 if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) { 2135 const SCEV *E = getAllocSizeExpr(ATy->getElementType()); 2136 return getMulExpr( 2137 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2138 ATy->getNumElements()))); 2139 } 2140 2141 // Expand a vector size into the element size times the number 2142 // of elements. 2143 if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) { 2144 const SCEV *E = getAllocSizeExpr(VTy->getElementType()); 2145 return getMulExpr( 2146 E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()), 2147 VTy->getNumElements()))); 2148 } 2149 2150 // Okay, it looks like we really DO need a sizeof expr. Check to see if we 2151 // already have one, otherwise create a new one. 2152 FoldingSetNodeID ID; 2153 ID.AddInteger(scAllocSize); 2154 ID.AddPointer(AllocTy); 2155 void *IP = 0; 2156 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2157 SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>(); 2158 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2159 new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy); 2160 UniqueSCEVs.InsertNode(S, IP); 2161 return S; 2162} 2163 2164const SCEV *ScalarEvolution::getUnknown(Value *V) { 2165 // Don't attempt to do anything other than create a SCEVUnknown object 2166 // here. createSCEV only calls getUnknown after checking for all other 2167 // interesting possibilities, and any other code that calls getUnknown 2168 // is doing so in order to hide a value from SCEV canonicalization. 2169 2170 FoldingSetNodeID ID; 2171 ID.AddInteger(scUnknown); 2172 ID.AddPointer(V); 2173 void *IP = 0; 2174 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2175 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2176 new (S) SCEVUnknown(ID, V); 2177 UniqueSCEVs.InsertNode(S, IP); 2178 return S; 2179} 2180 2181//===----------------------------------------------------------------------===// 2182// Basic SCEV Analysis and PHI Idiom Recognition Code 2183// 2184 2185/// isSCEVable - Test if values of the given type are analyzable within 2186/// the SCEV framework. This primarily includes integer types, and it 2187/// can optionally include pointer types if the ScalarEvolution class 2188/// has access to target-specific information. 2189bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2190 // Integers and pointers are always SCEVable. 2191 return Ty->isInteger() || isa<PointerType>(Ty); 2192} 2193 2194/// getTypeSizeInBits - Return the size in bits of the specified type, 2195/// for which isSCEVable must return true. 2196uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2197 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2198 2199 // If we have a TargetData, use it! 2200 if (TD) 2201 return TD->getTypeSizeInBits(Ty); 2202 2203 // Integer types have fixed sizes. 2204 if (Ty->isInteger()) 2205 return Ty->getPrimitiveSizeInBits(); 2206 2207 // The only other support type is pointer. Without TargetData, conservatively 2208 // assume pointers are 64-bit. 2209 assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!"); 2210 return 64; 2211} 2212 2213/// getEffectiveSCEVType - Return a type with the same bitwidth as 2214/// the given type and which represents how SCEV will treat the given 2215/// type, for which isSCEVable must return true. For pointer types, 2216/// this is the pointer-sized integer type. 2217const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2218 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2219 2220 if (Ty->isInteger()) 2221 return Ty; 2222 2223 // The only other support type is pointer. 2224 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!"); 2225 if (TD) return TD->getIntPtrType(getContext()); 2226 2227 // Without TargetData, conservatively assume pointers are 64-bit. 2228 return Type::getInt64Ty(getContext()); 2229} 2230 2231const SCEV *ScalarEvolution::getCouldNotCompute() { 2232 return &CouldNotCompute; 2233} 2234 2235/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2236/// expression and create a new one. 2237const SCEV *ScalarEvolution::getSCEV(Value *V) { 2238 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2239 2240 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2241 if (I != Scalars.end()) return I->second; 2242 const SCEV *S = createSCEV(V); 2243 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2244 return S; 2245} 2246 2247/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2248/// specified signed integer value and return a SCEV for the constant. 2249const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) { 2250 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2251 return getConstant(ConstantInt::get(ITy, Val)); 2252} 2253 2254/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2255/// 2256const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2257 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2258 return getConstant( 2259 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2260 2261 const Type *Ty = V->getType(); 2262 Ty = getEffectiveSCEVType(Ty); 2263 return getMulExpr(V, 2264 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2265} 2266 2267/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2268const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2269 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2270 return getConstant( 2271 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2272 2273 const Type *Ty = V->getType(); 2274 Ty = getEffectiveSCEVType(Ty); 2275 const SCEV *AllOnes = 2276 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2277 return getMinusSCEV(AllOnes, V); 2278} 2279 2280/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2281/// 2282const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2283 const SCEV *RHS) { 2284 // X - Y --> X + -Y 2285 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2286} 2287 2288/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2289/// input value to the specified type. If the type must be extended, it is zero 2290/// extended. 2291const SCEV * 2292ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2293 const Type *Ty) { 2294 const Type *SrcTy = V->getType(); 2295 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2296 (Ty->isInteger() || isa<PointerType>(Ty)) && 2297 "Cannot truncate or zero extend with non-integer arguments!"); 2298 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2299 return V; // No conversion 2300 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2301 return getTruncateExpr(V, Ty); 2302 return getZeroExtendExpr(V, Ty); 2303} 2304 2305/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2306/// input value to the specified type. If the type must be extended, it is sign 2307/// extended. 2308const SCEV * 2309ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2310 const Type *Ty) { 2311 const Type *SrcTy = V->getType(); 2312 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2313 (Ty->isInteger() || isa<PointerType>(Ty)) && 2314 "Cannot truncate or zero extend with non-integer arguments!"); 2315 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2316 return V; // No conversion 2317 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2318 return getTruncateExpr(V, Ty); 2319 return getSignExtendExpr(V, Ty); 2320} 2321 2322/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2323/// input value to the specified type. If the type must be extended, it is zero 2324/// extended. The conversion must not be narrowing. 2325const SCEV * 2326ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2327 const Type *SrcTy = V->getType(); 2328 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2329 (Ty->isInteger() || isa<PointerType>(Ty)) && 2330 "Cannot noop or zero extend with non-integer arguments!"); 2331 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2332 "getNoopOrZeroExtend cannot truncate!"); 2333 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2334 return V; // No conversion 2335 return getZeroExtendExpr(V, Ty); 2336} 2337 2338/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2339/// input value to the specified type. If the type must be extended, it is sign 2340/// extended. The conversion must not be narrowing. 2341const SCEV * 2342ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2343 const Type *SrcTy = V->getType(); 2344 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2345 (Ty->isInteger() || isa<PointerType>(Ty)) && 2346 "Cannot noop or sign extend with non-integer arguments!"); 2347 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2348 "getNoopOrSignExtend cannot truncate!"); 2349 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2350 return V; // No conversion 2351 return getSignExtendExpr(V, Ty); 2352} 2353 2354/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2355/// the input value to the specified type. If the type must be extended, 2356/// it is extended with unspecified bits. The conversion must not be 2357/// narrowing. 2358const SCEV * 2359ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2360 const Type *SrcTy = V->getType(); 2361 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2362 (Ty->isInteger() || isa<PointerType>(Ty)) && 2363 "Cannot noop or any extend with non-integer arguments!"); 2364 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2365 "getNoopOrAnyExtend cannot truncate!"); 2366 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2367 return V; // No conversion 2368 return getAnyExtendExpr(V, Ty); 2369} 2370 2371/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2372/// input value to the specified type. The conversion must not be widening. 2373const SCEV * 2374ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2375 const Type *SrcTy = V->getType(); 2376 assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) && 2377 (Ty->isInteger() || isa<PointerType>(Ty)) && 2378 "Cannot truncate or noop with non-integer arguments!"); 2379 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2380 "getTruncateOrNoop cannot extend!"); 2381 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2382 return V; // No conversion 2383 return getTruncateExpr(V, Ty); 2384} 2385 2386/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2387/// the types using zero-extension, and then perform a umax operation 2388/// with them. 2389const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2390 const SCEV *RHS) { 2391 const SCEV *PromotedLHS = LHS; 2392 const SCEV *PromotedRHS = RHS; 2393 2394 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2395 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2396 else 2397 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2398 2399 return getUMaxExpr(PromotedLHS, PromotedRHS); 2400} 2401 2402/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2403/// the types using zero-extension, and then perform a umin operation 2404/// with them. 2405const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2406 const SCEV *RHS) { 2407 const SCEV *PromotedLHS = LHS; 2408 const SCEV *PromotedRHS = RHS; 2409 2410 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2411 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2412 else 2413 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2414 2415 return getUMinExpr(PromotedLHS, PromotedRHS); 2416} 2417 2418/// PushDefUseChildren - Push users of the given Instruction 2419/// onto the given Worklist. 2420static void 2421PushDefUseChildren(Instruction *I, 2422 SmallVectorImpl<Instruction *> &Worklist) { 2423 // Push the def-use children onto the Worklist stack. 2424 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2425 UI != UE; ++UI) 2426 Worklist.push_back(cast<Instruction>(UI)); 2427} 2428 2429/// ForgetSymbolicValue - This looks up computed SCEV values for all 2430/// instructions that depend on the given instruction and removes them from 2431/// the Scalars map if they reference SymName. This is used during PHI 2432/// resolution. 2433void 2434ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) { 2435 SmallVector<Instruction *, 16> Worklist; 2436 PushDefUseChildren(I, Worklist); 2437 2438 SmallPtrSet<Instruction *, 8> Visited; 2439 Visited.insert(I); 2440 while (!Worklist.empty()) { 2441 Instruction *I = Worklist.pop_back_val(); 2442 if (!Visited.insert(I)) continue; 2443 2444 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 2445 Scalars.find(static_cast<Value *>(I)); 2446 if (It != Scalars.end()) { 2447 // Short-circuit the def-use traversal if the symbolic name 2448 // ceases to appear in expressions. 2449 if (!It->second->hasOperand(SymName)) 2450 continue; 2451 2452 // SCEVUnknown for a PHI either means that it has an unrecognized 2453 // structure, or it's a PHI that's in the progress of being computed 2454 // by createNodeForPHI. In the former case, additional loop trip 2455 // count information isn't going to change anything. In the later 2456 // case, createNodeForPHI will perform the necessary updates on its 2457 // own when it gets to that point. 2458 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 2459 ValuesAtScopes.erase(It->second); 2460 Scalars.erase(It); 2461 } 2462 } 2463 2464 PushDefUseChildren(I, Worklist); 2465 } 2466} 2467 2468/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2469/// a loop header, making it a potential recurrence, or it doesn't. 2470/// 2471const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2472 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2473 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2474 if (L->getHeader() == PN->getParent()) { 2475 // If it lives in the loop header, it has two incoming values, one 2476 // from outside the loop, and one from inside. 2477 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2478 unsigned BackEdge = IncomingEdge^1; 2479 2480 // While we are analyzing this PHI node, handle its value symbolically. 2481 const SCEV *SymbolicName = getUnknown(PN); 2482 assert(Scalars.find(PN) == Scalars.end() && 2483 "PHI node already processed?"); 2484 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2485 2486 // Using this symbolic name for the PHI, analyze the value coming around 2487 // the back-edge. 2488 Value *BEValueV = PN->getIncomingValue(BackEdge); 2489 const SCEV *BEValue = getSCEV(BEValueV); 2490 2491 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2492 // has a special value for the first iteration of the loop. 2493 2494 // If the value coming around the backedge is an add with the symbolic 2495 // value we just inserted, then we found a simple induction variable! 2496 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2497 // If there is a single occurrence of the symbolic value, replace it 2498 // with a recurrence. 2499 unsigned FoundIndex = Add->getNumOperands(); 2500 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2501 if (Add->getOperand(i) == SymbolicName) 2502 if (FoundIndex == e) { 2503 FoundIndex = i; 2504 break; 2505 } 2506 2507 if (FoundIndex != Add->getNumOperands()) { 2508 // Create an add with everything but the specified operand. 2509 SmallVector<const SCEV *, 8> Ops; 2510 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2511 if (i != FoundIndex) 2512 Ops.push_back(Add->getOperand(i)); 2513 const SCEV *Accum = getAddExpr(Ops); 2514 2515 // This is not a valid addrec if the step amount is varying each 2516 // loop iteration, but is not itself an addrec in this loop. 2517 if (Accum->isLoopInvariant(L) || 2518 (isa<SCEVAddRecExpr>(Accum) && 2519 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2520 const SCEV *StartVal = 2521 getSCEV(PN->getIncomingValue(IncomingEdge)); 2522 const SCEVAddRecExpr *PHISCEV = 2523 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L)); 2524 2525 // If the increment doesn't overflow, then neither the addrec nor the 2526 // post-increment will overflow. 2527 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) 2528 if (OBO->getOperand(0) == PN && 2529 getSCEV(OBO->getOperand(1)) == 2530 PHISCEV->getStepRecurrence(*this)) { 2531 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this); 2532 if (OBO->hasNoUnsignedWrap()) { 2533 const_cast<SCEVAddRecExpr *>(PHISCEV) 2534 ->setHasNoUnsignedWrap(true); 2535 const_cast<SCEVAddRecExpr *>(PostInc) 2536 ->setHasNoUnsignedWrap(true); 2537 } 2538 if (OBO->hasNoSignedWrap()) { 2539 const_cast<SCEVAddRecExpr *>(PHISCEV) 2540 ->setHasNoSignedWrap(true); 2541 const_cast<SCEVAddRecExpr *>(PostInc) 2542 ->setHasNoSignedWrap(true); 2543 } 2544 } 2545 2546 // Okay, for the entire analysis of this edge we assumed the PHI 2547 // to be symbolic. We now need to go back and purge all of the 2548 // entries for the scalars that use the symbolic expression. 2549 ForgetSymbolicName(PN, SymbolicName); 2550 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2551 return PHISCEV; 2552 } 2553 } 2554 } else if (const SCEVAddRecExpr *AddRec = 2555 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2556 // Otherwise, this could be a loop like this: 2557 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2558 // In this case, j = {1,+,1} and BEValue is j. 2559 // Because the other in-value of i (0) fits the evolution of BEValue 2560 // i really is an addrec evolution. 2561 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2562 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2563 2564 // If StartVal = j.start - j.stride, we can use StartVal as the 2565 // initial step of the addrec evolution. 2566 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2567 AddRec->getOperand(1))) { 2568 const SCEV *PHISCEV = 2569 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2570 2571 // Okay, for the entire analysis of this edge we assumed the PHI 2572 // to be symbolic. We now need to go back and purge all of the 2573 // entries for the scalars that use the symbolic expression. 2574 ForgetSymbolicName(PN, SymbolicName); 2575 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2576 return PHISCEV; 2577 } 2578 } 2579 } 2580 2581 return SymbolicName; 2582 } 2583 2584 // It's tempting to recognize PHIs with a unique incoming value, however 2585 // this leads passes like indvars to break LCSSA form. Fortunately, such 2586 // PHIs are rare, as instcombine zaps them. 2587 2588 // If it's not a loop phi, we can't handle it yet. 2589 return getUnknown(PN); 2590} 2591 2592/// createNodeForGEP - Expand GEP instructions into add and multiply 2593/// operations. This allows them to be analyzed by regular SCEV code. 2594/// 2595const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) { 2596 2597 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2598 Value *Base = GEP->getOperand(0); 2599 // Don't attempt to analyze GEPs over unsized objects. 2600 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2601 return getUnknown(GEP); 2602 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2603 gep_type_iterator GTI = gep_type_begin(GEP); 2604 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2605 E = GEP->op_end(); 2606 I != E; ++I) { 2607 Value *Index = *I; 2608 // Compute the (potentially symbolic) offset in bytes for this index. 2609 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2610 // For a struct, add the member offset. 2611 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2612 TotalOffset = getAddExpr(TotalOffset, 2613 getFieldOffsetExpr(STy, FieldNo)); 2614 } else { 2615 // For an array, add the element offset, explicitly scaled. 2616 const SCEV *LocalOffset = getSCEV(Index); 2617 if (!isa<PointerType>(LocalOffset->getType())) 2618 // Getelementptr indicies are signed. 2619 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2620 LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI)); 2621 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2622 } 2623 } 2624 return getAddExpr(getSCEV(Base), TotalOffset); 2625} 2626 2627/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2628/// guaranteed to end in (at every loop iteration). It is, at the same time, 2629/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2630/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2631uint32_t 2632ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2633 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2634 return C->getValue()->getValue().countTrailingZeros(); 2635 2636 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2637 return std::min(GetMinTrailingZeros(T->getOperand()), 2638 (uint32_t)getTypeSizeInBits(T->getType())); 2639 2640 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2641 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2642 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2643 getTypeSizeInBits(E->getType()) : OpRes; 2644 } 2645 2646 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2647 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2648 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2649 getTypeSizeInBits(E->getType()) : OpRes; 2650 } 2651 2652 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2653 // The result is the min of all operands results. 2654 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2655 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2656 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2657 return MinOpRes; 2658 } 2659 2660 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2661 // The result is the sum of all operands results. 2662 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2663 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2664 for (unsigned i = 1, e = M->getNumOperands(); 2665 SumOpRes != BitWidth && i != e; ++i) 2666 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2667 BitWidth); 2668 return SumOpRes; 2669 } 2670 2671 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2672 // The result is the min of all operands results. 2673 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2674 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2675 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2676 return MinOpRes; 2677 } 2678 2679 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2680 // The result is the min of all operands results. 2681 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2682 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2683 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2684 return MinOpRes; 2685 } 2686 2687 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2688 // The result is the min of all operands results. 2689 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2690 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2691 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2692 return MinOpRes; 2693 } 2694 2695 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2696 // For a SCEVUnknown, ask ValueTracking. 2697 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2698 APInt Mask = APInt::getAllOnesValue(BitWidth); 2699 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2700 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2701 return Zeros.countTrailingOnes(); 2702 } 2703 2704 // SCEVUDivExpr 2705 return 0; 2706} 2707 2708/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2709/// 2710ConstantRange 2711ScalarEvolution::getUnsignedRange(const SCEV *S) { 2712 2713 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2714 return ConstantRange(C->getValue()->getValue()); 2715 2716 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2717 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2718 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2719 X = X.add(getUnsignedRange(Add->getOperand(i))); 2720 return X; 2721 } 2722 2723 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2724 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2725 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2726 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2727 return X; 2728 } 2729 2730 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2731 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2732 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2733 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2734 return X; 2735 } 2736 2737 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2738 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2739 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2740 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2741 return X; 2742 } 2743 2744 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2745 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2746 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2747 return X.udiv(Y); 2748 } 2749 2750 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2751 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2752 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2753 } 2754 2755 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2756 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2757 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2758 } 2759 2760 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2761 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2762 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2763 } 2764 2765 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2766 2767 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2768 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2769 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2770 if (!Trip) return FullSet; 2771 2772 // TODO: non-affine addrec 2773 if (AddRec->isAffine()) { 2774 const Type *Ty = AddRec->getType(); 2775 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2776 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2777 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2778 2779 const SCEV *Start = AddRec->getStart(); 2780 const SCEV *Step = AddRec->getStepRecurrence(*this); 2781 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2782 2783 // Check for overflow. 2784 // TODO: This is very conservative. 2785 if (!(Step->isOne() && 2786 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) && 2787 !(Step->isAllOnesValue() && 2788 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End))) 2789 return FullSet; 2790 2791 ConstantRange StartRange = getUnsignedRange(Start); 2792 ConstantRange EndRange = getUnsignedRange(End); 2793 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2794 EndRange.getUnsignedMin()); 2795 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2796 EndRange.getUnsignedMax()); 2797 if (Min.isMinValue() && Max.isMaxValue()) 2798 return FullSet; 2799 return ConstantRange(Min, Max+1); 2800 } 2801 } 2802 } 2803 2804 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2805 // For a SCEVUnknown, ask ValueTracking. 2806 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2807 APInt Mask = APInt::getAllOnesValue(BitWidth); 2808 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2809 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2810 if (Ones == ~Zeros + 1) 2811 return FullSet; 2812 return ConstantRange(Ones, ~Zeros + 1); 2813 } 2814 2815 return FullSet; 2816} 2817 2818/// getSignedRange - Determine the signed range for a particular SCEV. 2819/// 2820ConstantRange 2821ScalarEvolution::getSignedRange(const SCEV *S) { 2822 2823 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2824 return ConstantRange(C->getValue()->getValue()); 2825 2826 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2827 ConstantRange X = getSignedRange(Add->getOperand(0)); 2828 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2829 X = X.add(getSignedRange(Add->getOperand(i))); 2830 return X; 2831 } 2832 2833 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2834 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2835 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2836 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2837 return X; 2838 } 2839 2840 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2841 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2842 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2843 X = X.smax(getSignedRange(SMax->getOperand(i))); 2844 return X; 2845 } 2846 2847 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2848 ConstantRange X = getSignedRange(UMax->getOperand(0)); 2849 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2850 X = X.umax(getSignedRange(UMax->getOperand(i))); 2851 return X; 2852 } 2853 2854 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2855 ConstantRange X = getSignedRange(UDiv->getLHS()); 2856 ConstantRange Y = getSignedRange(UDiv->getRHS()); 2857 return X.udiv(Y); 2858 } 2859 2860 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2861 ConstantRange X = getSignedRange(ZExt->getOperand()); 2862 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth()); 2863 } 2864 2865 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2866 ConstantRange X = getSignedRange(SExt->getOperand()); 2867 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth()); 2868 } 2869 2870 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2871 ConstantRange X = getSignedRange(Trunc->getOperand()); 2872 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth()); 2873 } 2874 2875 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true); 2876 2877 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2878 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop()); 2879 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T); 2880 if (!Trip) return FullSet; 2881 2882 // TODO: non-affine addrec 2883 if (AddRec->isAffine()) { 2884 const Type *Ty = AddRec->getType(); 2885 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2886 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) { 2887 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2888 2889 const SCEV *Start = AddRec->getStart(); 2890 const SCEV *Step = AddRec->getStepRecurrence(*this); 2891 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2892 2893 // Check for overflow. 2894 // TODO: This is very conservative. 2895 if (!(Step->isOne() && 2896 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) && 2897 !(Step->isAllOnesValue() && 2898 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End))) 2899 return FullSet; 2900 2901 ConstantRange StartRange = getSignedRange(Start); 2902 ConstantRange EndRange = getSignedRange(End); 2903 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 2904 EndRange.getSignedMin()); 2905 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 2906 EndRange.getSignedMax()); 2907 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 2908 return FullSet; 2909 return ConstantRange(Min, Max+1); 2910 } 2911 } 2912 } 2913 2914 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2915 // For a SCEVUnknown, ask ValueTracking. 2916 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2917 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 2918 if (NS == 1) 2919 return FullSet; 2920 return 2921 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 2922 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1); 2923 } 2924 2925 return FullSet; 2926} 2927 2928/// createSCEV - We know that there is no SCEV for the specified value. 2929/// Analyze the expression. 2930/// 2931const SCEV *ScalarEvolution::createSCEV(Value *V) { 2932 if (!isSCEVable(V->getType())) 2933 return getUnknown(V); 2934 2935 unsigned Opcode = Instruction::UserOp1; 2936 if (Instruction *I = dyn_cast<Instruction>(V)) 2937 Opcode = I->getOpcode(); 2938 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 2939 Opcode = CE->getOpcode(); 2940 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 2941 return getConstant(CI); 2942 else if (isa<ConstantPointerNull>(V)) 2943 return getIntegerSCEV(0, V->getType()); 2944 else if (isa<UndefValue>(V)) 2945 return getIntegerSCEV(0, V->getType()); 2946 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 2947 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 2948 else 2949 return getUnknown(V); 2950 2951 Operator *U = cast<Operator>(V); 2952 switch (Opcode) { 2953 case Instruction::Add: 2954 // Don't transfer the NSW and NUW bits from the Add instruction to the 2955 // Add expression, because the Instruction may be guarded by control 2956 // flow and the no-overflow bits may not be valid for the expression in 2957 // any context. 2958 return getAddExpr(getSCEV(U->getOperand(0)), 2959 getSCEV(U->getOperand(1))); 2960 case Instruction::Mul: 2961 // Don't transfer the NSW and NUW bits from the Mul instruction to the 2962 // Mul expression, as with Add. 2963 return getMulExpr(getSCEV(U->getOperand(0)), 2964 getSCEV(U->getOperand(1))); 2965 case Instruction::UDiv: 2966 return getUDivExpr(getSCEV(U->getOperand(0)), 2967 getSCEV(U->getOperand(1))); 2968 case Instruction::Sub: 2969 return getMinusSCEV(getSCEV(U->getOperand(0)), 2970 getSCEV(U->getOperand(1))); 2971 case Instruction::And: 2972 // For an expression like x&255 that merely masks off the high bits, 2973 // use zext(trunc(x)) as the SCEV expression. 2974 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 2975 if (CI->isNullValue()) 2976 return getSCEV(U->getOperand(1)); 2977 if (CI->isAllOnesValue()) 2978 return getSCEV(U->getOperand(0)); 2979 const APInt &A = CI->getValue(); 2980 2981 // Instcombine's ShrinkDemandedConstant may strip bits out of 2982 // constants, obscuring what would otherwise be a low-bits mask. 2983 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 2984 // knew about to reconstruct a low-bits mask value. 2985 unsigned LZ = A.countLeadingZeros(); 2986 unsigned BitWidth = A.getBitWidth(); 2987 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 2988 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 2989 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 2990 2991 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 2992 2993 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 2994 return 2995 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 2996 IntegerType::get(getContext(), BitWidth - LZ)), 2997 U->getType()); 2998 } 2999 break; 3000 3001 case Instruction::Or: 3002 // If the RHS of the Or is a constant, we may have something like: 3003 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3004 // optimizations will transparently handle this case. 3005 // 3006 // In order for this transformation to be safe, the LHS must be of the 3007 // form X*(2^n) and the Or constant must be less than 2^n. 3008 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3009 const SCEV *LHS = getSCEV(U->getOperand(0)); 3010 const APInt &CIVal = CI->getValue(); 3011 if (GetMinTrailingZeros(LHS) >= 3012 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3013 // Build a plain add SCEV. 3014 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3015 // If the LHS of the add was an addrec and it has no-wrap flags, 3016 // transfer the no-wrap flags, since an or won't introduce a wrap. 3017 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3018 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3019 if (OldAR->hasNoUnsignedWrap()) 3020 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3021 if (OldAR->hasNoSignedWrap()) 3022 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3023 } 3024 return S; 3025 } 3026 } 3027 break; 3028 case Instruction::Xor: 3029 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3030 // If the RHS of the xor is a signbit, then this is just an add. 3031 // Instcombine turns add of signbit into xor as a strength reduction step. 3032 if (CI->getValue().isSignBit()) 3033 return getAddExpr(getSCEV(U->getOperand(0)), 3034 getSCEV(U->getOperand(1))); 3035 3036 // If the RHS of xor is -1, then this is a not operation. 3037 if (CI->isAllOnesValue()) 3038 return getNotSCEV(getSCEV(U->getOperand(0))); 3039 3040 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3041 // This is a variant of the check for xor with -1, and it handles 3042 // the case where instcombine has trimmed non-demanded bits out 3043 // of an xor with -1. 3044 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3045 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3046 if (BO->getOpcode() == Instruction::And && 3047 LCI->getValue() == CI->getValue()) 3048 if (const SCEVZeroExtendExpr *Z = 3049 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3050 const Type *UTy = U->getType(); 3051 const SCEV *Z0 = Z->getOperand(); 3052 const Type *Z0Ty = Z0->getType(); 3053 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3054 3055 // If C is a low-bits mask, the zero extend is zerving to 3056 // mask off the high bits. Complement the operand and 3057 // re-apply the zext. 3058 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3059 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3060 3061 // If C is a single bit, it may be in the sign-bit position 3062 // before the zero-extend. In this case, represent the xor 3063 // using an add, which is equivalent, and re-apply the zext. 3064 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3065 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3066 Trunc.isSignBit()) 3067 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3068 UTy); 3069 } 3070 } 3071 break; 3072 3073 case Instruction::Shl: 3074 // Turn shift left of a constant amount into a multiply. 3075 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3076 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3077 Constant *X = ConstantInt::get(getContext(), 3078 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3079 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3080 } 3081 break; 3082 3083 case Instruction::LShr: 3084 // Turn logical shift right of a constant into a unsigned divide. 3085 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3086 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth(); 3087 Constant *X = ConstantInt::get(getContext(), 3088 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3089 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3090 } 3091 break; 3092 3093 case Instruction::AShr: 3094 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3095 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3096 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3097 if (L->getOpcode() == Instruction::Shl && 3098 L->getOperand(1) == U->getOperand(1)) { 3099 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3100 uint64_t Amt = BitWidth - CI->getZExtValue(); 3101 if (Amt == BitWidth) 3102 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3103 if (Amt > BitWidth) 3104 return getIntegerSCEV(0, U->getType()); // value is undefined 3105 return 3106 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3107 IntegerType::get(getContext(), Amt)), 3108 U->getType()); 3109 } 3110 break; 3111 3112 case Instruction::Trunc: 3113 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3114 3115 case Instruction::ZExt: 3116 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3117 3118 case Instruction::SExt: 3119 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3120 3121 case Instruction::BitCast: 3122 // BitCasts are no-op casts so we just eliminate the cast. 3123 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3124 return getSCEV(U->getOperand(0)); 3125 break; 3126 3127 // It's tempting to handle inttoptr and ptrtoint, however this can 3128 // lead to pointer expressions which cannot be expanded to GEPs 3129 // (because they may overflow). For now, the only pointer-typed 3130 // expressions we handle are GEPs and address literals. 3131 3132 case Instruction::GetElementPtr: 3133 return createNodeForGEP(U); 3134 3135 case Instruction::PHI: 3136 return createNodeForPHI(cast<PHINode>(U)); 3137 3138 case Instruction::Select: 3139 // This could be a smax or umax that was lowered earlier. 3140 // Try to recover it. 3141 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3142 Value *LHS = ICI->getOperand(0); 3143 Value *RHS = ICI->getOperand(1); 3144 switch (ICI->getPredicate()) { 3145 case ICmpInst::ICMP_SLT: 3146 case ICmpInst::ICMP_SLE: 3147 std::swap(LHS, RHS); 3148 // fall through 3149 case ICmpInst::ICMP_SGT: 3150 case ICmpInst::ICMP_SGE: 3151 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3152 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3153 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3154 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3155 break; 3156 case ICmpInst::ICMP_ULT: 3157 case ICmpInst::ICMP_ULE: 3158 std::swap(LHS, RHS); 3159 // fall through 3160 case ICmpInst::ICMP_UGT: 3161 case ICmpInst::ICMP_UGE: 3162 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3163 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3164 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3165 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3166 break; 3167 case ICmpInst::ICMP_NE: 3168 // n != 0 ? n : 1 -> umax(n, 1) 3169 if (LHS == U->getOperand(1) && 3170 isa<ConstantInt>(U->getOperand(2)) && 3171 cast<ConstantInt>(U->getOperand(2))->isOne() && 3172 isa<ConstantInt>(RHS) && 3173 cast<ConstantInt>(RHS)->isZero()) 3174 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3175 break; 3176 case ICmpInst::ICMP_EQ: 3177 // n == 0 ? 1 : n -> umax(n, 1) 3178 if (LHS == U->getOperand(2) && 3179 isa<ConstantInt>(U->getOperand(1)) && 3180 cast<ConstantInt>(U->getOperand(1))->isOne() && 3181 isa<ConstantInt>(RHS) && 3182 cast<ConstantInt>(RHS)->isZero()) 3183 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3184 break; 3185 default: 3186 break; 3187 } 3188 } 3189 3190 default: // We cannot analyze this expression. 3191 break; 3192 } 3193 3194 return getUnknown(V); 3195} 3196 3197 3198 3199//===----------------------------------------------------------------------===// 3200// Iteration Count Computation Code 3201// 3202 3203/// getBackedgeTakenCount - If the specified loop has a predictable 3204/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3205/// object. The backedge-taken count is the number of times the loop header 3206/// will be branched to from within the loop. This is one less than the 3207/// trip count of the loop, since it doesn't count the first iteration, 3208/// when the header is branched to from outside the loop. 3209/// 3210/// Note that it is not valid to call this method on a loop without a 3211/// loop-invariant backedge-taken count (see 3212/// hasLoopInvariantBackedgeTakenCount). 3213/// 3214const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3215 return getBackedgeTakenInfo(L).Exact; 3216} 3217 3218/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3219/// return the least SCEV value that is known never to be less than the 3220/// actual backedge taken count. 3221const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3222 return getBackedgeTakenInfo(L).Max; 3223} 3224 3225/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3226/// onto the given Worklist. 3227static void 3228PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3229 BasicBlock *Header = L->getHeader(); 3230 3231 // Push all Loop-header PHIs onto the Worklist stack. 3232 for (BasicBlock::iterator I = Header->begin(); 3233 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3234 Worklist.push_back(PN); 3235} 3236 3237const ScalarEvolution::BackedgeTakenInfo & 3238ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3239 // Initially insert a CouldNotCompute for this loop. If the insertion 3240 // succeeds, procede to actually compute a backedge-taken count and 3241 // update the value. The temporary CouldNotCompute value tells SCEV 3242 // code elsewhere that it shouldn't attempt to request a new 3243 // backedge-taken count, which could result in infinite recursion. 3244 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair = 3245 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3246 if (Pair.second) { 3247 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L); 3248 if (ItCount.Exact != getCouldNotCompute()) { 3249 assert(ItCount.Exact->isLoopInvariant(L) && 3250 ItCount.Max->isLoopInvariant(L) && 3251 "Computed trip count isn't loop invariant for loop!"); 3252 ++NumTripCountsComputed; 3253 3254 // Update the value in the map. 3255 Pair.first->second = ItCount; 3256 } else { 3257 if (ItCount.Max != getCouldNotCompute()) 3258 // Update the value in the map. 3259 Pair.first->second = ItCount; 3260 if (isa<PHINode>(L->getHeader()->begin())) 3261 // Only count loops that have phi nodes as not being computable. 3262 ++NumTripCountsNotComputed; 3263 } 3264 3265 // Now that we know more about the trip count for this loop, forget any 3266 // existing SCEV values for PHI nodes in this loop since they are only 3267 // conservative estimates made without the benefit of trip count 3268 // information. This is similar to the code in forgetLoop, except that 3269 // it handles SCEVUnknown PHI nodes specially. 3270 if (ItCount.hasAnyInfo()) { 3271 SmallVector<Instruction *, 16> Worklist; 3272 PushLoopPHIs(L, Worklist); 3273 3274 SmallPtrSet<Instruction *, 8> Visited; 3275 while (!Worklist.empty()) { 3276 Instruction *I = Worklist.pop_back_val(); 3277 if (!Visited.insert(I)) continue; 3278 3279 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3280 Scalars.find(static_cast<Value *>(I)); 3281 if (It != Scalars.end()) { 3282 // SCEVUnknown for a PHI either means that it has an unrecognized 3283 // structure, or it's a PHI that's in the progress of being computed 3284 // by createNodeForPHI. In the former case, additional loop trip 3285 // count information isn't going to change anything. In the later 3286 // case, createNodeForPHI will perform the necessary updates on its 3287 // own when it gets to that point. 3288 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3289 ValuesAtScopes.erase(It->second); 3290 Scalars.erase(It); 3291 } 3292 if (PHINode *PN = dyn_cast<PHINode>(I)) 3293 ConstantEvolutionLoopExitValue.erase(PN); 3294 } 3295 3296 PushDefUseChildren(I, Worklist); 3297 } 3298 } 3299 } 3300 return Pair.first->second; 3301} 3302 3303/// forgetLoop - This method should be called by the client when it has 3304/// changed a loop in a way that may effect ScalarEvolution's ability to 3305/// compute a trip count, or if the loop is deleted. 3306void ScalarEvolution::forgetLoop(const Loop *L) { 3307 // Drop any stored trip count value. 3308 BackedgeTakenCounts.erase(L); 3309 3310 // Drop information about expressions based on loop-header PHIs. 3311 SmallVector<Instruction *, 16> Worklist; 3312 PushLoopPHIs(L, Worklist); 3313 3314 SmallPtrSet<Instruction *, 8> Visited; 3315 while (!Worklist.empty()) { 3316 Instruction *I = Worklist.pop_back_val(); 3317 if (!Visited.insert(I)) continue; 3318 3319 std::map<SCEVCallbackVH, const SCEV*>::iterator It = 3320 Scalars.find(static_cast<Value *>(I)); 3321 if (It != Scalars.end()) { 3322 ValuesAtScopes.erase(It->second); 3323 Scalars.erase(It); 3324 if (PHINode *PN = dyn_cast<PHINode>(I)) 3325 ConstantEvolutionLoopExitValue.erase(PN); 3326 } 3327 3328 PushDefUseChildren(I, Worklist); 3329 } 3330} 3331 3332/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3333/// of the specified loop will execute. 3334ScalarEvolution::BackedgeTakenInfo 3335ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3336 SmallVector<BasicBlock*, 8> ExitingBlocks; 3337 L->getExitingBlocks(ExitingBlocks); 3338 3339 // Examine all exits and pick the most conservative values. 3340 const SCEV *BECount = getCouldNotCompute(); 3341 const SCEV *MaxBECount = getCouldNotCompute(); 3342 bool CouldNotComputeBECount = false; 3343 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3344 BackedgeTakenInfo NewBTI = 3345 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3346 3347 if (NewBTI.Exact == getCouldNotCompute()) { 3348 // We couldn't compute an exact value for this exit, so 3349 // we won't be able to compute an exact value for the loop. 3350 CouldNotComputeBECount = true; 3351 BECount = getCouldNotCompute(); 3352 } else if (!CouldNotComputeBECount) { 3353 if (BECount == getCouldNotCompute()) 3354 BECount = NewBTI.Exact; 3355 else 3356 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3357 } 3358 if (MaxBECount == getCouldNotCompute()) 3359 MaxBECount = NewBTI.Max; 3360 else if (NewBTI.Max != getCouldNotCompute()) 3361 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3362 } 3363 3364 return BackedgeTakenInfo(BECount, MaxBECount); 3365} 3366 3367/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3368/// of the specified loop will execute if it exits via the specified block. 3369ScalarEvolution::BackedgeTakenInfo 3370ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3371 BasicBlock *ExitingBlock) { 3372 3373 // Okay, we've chosen an exiting block. See what condition causes us to 3374 // exit at this block. 3375 // 3376 // FIXME: we should be able to handle switch instructions (with a single exit) 3377 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3378 if (ExitBr == 0) return getCouldNotCompute(); 3379 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3380 3381 // At this point, we know we have a conditional branch that determines whether 3382 // the loop is exited. However, we don't know if the branch is executed each 3383 // time through the loop. If not, then the execution count of the branch will 3384 // not be equal to the trip count of the loop. 3385 // 3386 // Currently we check for this by checking to see if the Exit branch goes to 3387 // the loop header. If so, we know it will always execute the same number of 3388 // times as the loop. We also handle the case where the exit block *is* the 3389 // loop header. This is common for un-rotated loops. 3390 // 3391 // If both of those tests fail, walk up the unique predecessor chain to the 3392 // header, stopping if there is an edge that doesn't exit the loop. If the 3393 // header is reached, the execution count of the branch will be equal to the 3394 // trip count of the loop. 3395 // 3396 // More extensive analysis could be done to handle more cases here. 3397 // 3398 if (ExitBr->getSuccessor(0) != L->getHeader() && 3399 ExitBr->getSuccessor(1) != L->getHeader() && 3400 ExitBr->getParent() != L->getHeader()) { 3401 // The simple checks failed, try climbing the unique predecessor chain 3402 // up to the header. 3403 bool Ok = false; 3404 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3405 BasicBlock *Pred = BB->getUniquePredecessor(); 3406 if (!Pred) 3407 return getCouldNotCompute(); 3408 TerminatorInst *PredTerm = Pred->getTerminator(); 3409 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3410 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3411 if (PredSucc == BB) 3412 continue; 3413 // If the predecessor has a successor that isn't BB and isn't 3414 // outside the loop, assume the worst. 3415 if (L->contains(PredSucc)) 3416 return getCouldNotCompute(); 3417 } 3418 if (Pred == L->getHeader()) { 3419 Ok = true; 3420 break; 3421 } 3422 BB = Pred; 3423 } 3424 if (!Ok) 3425 return getCouldNotCompute(); 3426 } 3427 3428 // Procede to the next level to examine the exit condition expression. 3429 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3430 ExitBr->getSuccessor(0), 3431 ExitBr->getSuccessor(1)); 3432} 3433 3434/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3435/// backedge of the specified loop will execute if its exit condition 3436/// were a conditional branch of ExitCond, TBB, and FBB. 3437ScalarEvolution::BackedgeTakenInfo 3438ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3439 Value *ExitCond, 3440 BasicBlock *TBB, 3441 BasicBlock *FBB) { 3442 // Check if the controlling expression for this loop is an And or Or. 3443 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3444 if (BO->getOpcode() == Instruction::And) { 3445 // Recurse on the operands of the and. 3446 BackedgeTakenInfo BTI0 = 3447 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3448 BackedgeTakenInfo BTI1 = 3449 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3450 const SCEV *BECount = getCouldNotCompute(); 3451 const SCEV *MaxBECount = getCouldNotCompute(); 3452 if (L->contains(TBB)) { 3453 // Both conditions must be true for the loop to continue executing. 3454 // Choose the less conservative count. 3455 if (BTI0.Exact == getCouldNotCompute() || 3456 BTI1.Exact == getCouldNotCompute()) 3457 BECount = getCouldNotCompute(); 3458 else 3459 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3460 if (BTI0.Max == getCouldNotCompute()) 3461 MaxBECount = BTI1.Max; 3462 else if (BTI1.Max == getCouldNotCompute()) 3463 MaxBECount = BTI0.Max; 3464 else 3465 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3466 } else { 3467 // Both conditions must be true for the loop to exit. 3468 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3469 if (BTI0.Exact != getCouldNotCompute() && 3470 BTI1.Exact != getCouldNotCompute()) 3471 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3472 if (BTI0.Max != getCouldNotCompute() && 3473 BTI1.Max != getCouldNotCompute()) 3474 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3475 } 3476 3477 return BackedgeTakenInfo(BECount, MaxBECount); 3478 } 3479 if (BO->getOpcode() == Instruction::Or) { 3480 // Recurse on the operands of the or. 3481 BackedgeTakenInfo BTI0 = 3482 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3483 BackedgeTakenInfo BTI1 = 3484 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3485 const SCEV *BECount = getCouldNotCompute(); 3486 const SCEV *MaxBECount = getCouldNotCompute(); 3487 if (L->contains(FBB)) { 3488 // Both conditions must be false for the loop to continue executing. 3489 // Choose the less conservative count. 3490 if (BTI0.Exact == getCouldNotCompute() || 3491 BTI1.Exact == getCouldNotCompute()) 3492 BECount = getCouldNotCompute(); 3493 else 3494 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3495 if (BTI0.Max == getCouldNotCompute()) 3496 MaxBECount = BTI1.Max; 3497 else if (BTI1.Max == getCouldNotCompute()) 3498 MaxBECount = BTI0.Max; 3499 else 3500 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3501 } else { 3502 // Both conditions must be false for the loop to exit. 3503 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3504 if (BTI0.Exact != getCouldNotCompute() && 3505 BTI1.Exact != getCouldNotCompute()) 3506 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3507 if (BTI0.Max != getCouldNotCompute() && 3508 BTI1.Max != getCouldNotCompute()) 3509 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3510 } 3511 3512 return BackedgeTakenInfo(BECount, MaxBECount); 3513 } 3514 } 3515 3516 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3517 // Procede to the next level to examine the icmp. 3518 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3519 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3520 3521 // If it's not an integer or pointer comparison then compute it the hard way. 3522 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3523} 3524 3525/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3526/// backedge of the specified loop will execute if its exit condition 3527/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3528ScalarEvolution::BackedgeTakenInfo 3529ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3530 ICmpInst *ExitCond, 3531 BasicBlock *TBB, 3532 BasicBlock *FBB) { 3533 3534 // If the condition was exit on true, convert the condition to exit on false 3535 ICmpInst::Predicate Cond; 3536 if (!L->contains(FBB)) 3537 Cond = ExitCond->getPredicate(); 3538 else 3539 Cond = ExitCond->getInversePredicate(); 3540 3541 // Handle common loops like: for (X = "string"; *X; ++X) 3542 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3543 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3544 const SCEV *ItCnt = 3545 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3546 if (!isa<SCEVCouldNotCompute>(ItCnt)) { 3547 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType()); 3548 return BackedgeTakenInfo(ItCnt, 3549 isa<SCEVConstant>(ItCnt) ? ItCnt : 3550 getConstant(APInt::getMaxValue(BitWidth)-1)); 3551 } 3552 } 3553 3554 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3555 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3556 3557 // Try to evaluate any dependencies out of the loop. 3558 LHS = getSCEVAtScope(LHS, L); 3559 RHS = getSCEVAtScope(RHS, L); 3560 3561 // At this point, we would like to compute how many iterations of the 3562 // loop the predicate will return true for these inputs. 3563 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3564 // If there is a loop-invariant, force it into the RHS. 3565 std::swap(LHS, RHS); 3566 Cond = ICmpInst::getSwappedPredicate(Cond); 3567 } 3568 3569 // If we have a comparison of a chrec against a constant, try to use value 3570 // ranges to answer this query. 3571 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3572 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3573 if (AddRec->getLoop() == L) { 3574 // Form the constant range. 3575 ConstantRange CompRange( 3576 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3577 3578 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3579 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3580 } 3581 3582 switch (Cond) { 3583 case ICmpInst::ICMP_NE: { // while (X != Y) 3584 // Convert to: while (X-Y != 0) 3585 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3586 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3587 break; 3588 } 3589 case ICmpInst::ICMP_EQ: { // while (X == Y) 3590 // Convert to: while (X-Y == 0) 3591 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3592 if (!isa<SCEVCouldNotCompute>(TC)) return TC; 3593 break; 3594 } 3595 case ICmpInst::ICMP_SLT: { 3596 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3597 if (BTI.hasAnyInfo()) return BTI; 3598 break; 3599 } 3600 case ICmpInst::ICMP_SGT: { 3601 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3602 getNotSCEV(RHS), L, true); 3603 if (BTI.hasAnyInfo()) return BTI; 3604 break; 3605 } 3606 case ICmpInst::ICMP_ULT: { 3607 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3608 if (BTI.hasAnyInfo()) return BTI; 3609 break; 3610 } 3611 case ICmpInst::ICMP_UGT: { 3612 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3613 getNotSCEV(RHS), L, false); 3614 if (BTI.hasAnyInfo()) return BTI; 3615 break; 3616 } 3617 default: 3618#if 0 3619 errs() << "ComputeBackedgeTakenCount "; 3620 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3621 errs() << "[unsigned] "; 3622 errs() << *LHS << " " 3623 << Instruction::getOpcodeName(Instruction::ICmp) 3624 << " " << *RHS << "\n"; 3625#endif 3626 break; 3627 } 3628 return 3629 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3630} 3631 3632static ConstantInt * 3633EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3634 ScalarEvolution &SE) { 3635 const SCEV *InVal = SE.getConstant(C); 3636 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3637 assert(isa<SCEVConstant>(Val) && 3638 "Evaluation of SCEV at constant didn't fold correctly?"); 3639 return cast<SCEVConstant>(Val)->getValue(); 3640} 3641 3642/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3643/// and a GEP expression (missing the pointer index) indexing into it, return 3644/// the addressed element of the initializer or null if the index expression is 3645/// invalid. 3646static Constant * 3647GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV, 3648 const std::vector<ConstantInt*> &Indices) { 3649 Constant *Init = GV->getInitializer(); 3650 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3651 uint64_t Idx = Indices[i]->getZExtValue(); 3652 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3653 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3654 Init = cast<Constant>(CS->getOperand(Idx)); 3655 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3656 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3657 Init = cast<Constant>(CA->getOperand(Idx)); 3658 } else if (isa<ConstantAggregateZero>(Init)) { 3659 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3660 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3661 Init = Constant::getNullValue(STy->getElementType(Idx)); 3662 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3663 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3664 Init = Constant::getNullValue(ATy->getElementType()); 3665 } else { 3666 llvm_unreachable("Unknown constant aggregate type!"); 3667 } 3668 return 0; 3669 } else { 3670 return 0; // Unknown initializer type 3671 } 3672 } 3673 return Init; 3674} 3675 3676/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3677/// 'icmp op load X, cst', try to see if we can compute the backedge 3678/// execution count. 3679const SCEV * 3680ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3681 LoadInst *LI, 3682 Constant *RHS, 3683 const Loop *L, 3684 ICmpInst::Predicate predicate) { 3685 if (LI->isVolatile()) return getCouldNotCompute(); 3686 3687 // Check to see if the loaded pointer is a getelementptr of a global. 3688 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3689 if (!GEP) return getCouldNotCompute(); 3690 3691 // Make sure that it is really a constant global we are gepping, with an 3692 // initializer, and make sure the first IDX is really 0. 3693 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3694 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3695 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3696 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3697 return getCouldNotCompute(); 3698 3699 // Okay, we allow one non-constant index into the GEP instruction. 3700 Value *VarIdx = 0; 3701 std::vector<ConstantInt*> Indexes; 3702 unsigned VarIdxNum = 0; 3703 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3704 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3705 Indexes.push_back(CI); 3706 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3707 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3708 VarIdx = GEP->getOperand(i); 3709 VarIdxNum = i-2; 3710 Indexes.push_back(0); 3711 } 3712 3713 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3714 // Check to see if X is a loop variant variable value now. 3715 const SCEV *Idx = getSCEV(VarIdx); 3716 Idx = getSCEVAtScope(Idx, L); 3717 3718 // We can only recognize very limited forms of loop index expressions, in 3719 // particular, only affine AddRec's like {C1,+,C2}. 3720 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3721 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3722 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3723 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3724 return getCouldNotCompute(); 3725 3726 unsigned MaxSteps = MaxBruteForceIterations; 3727 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3728 ConstantInt *ItCst = ConstantInt::get( 3729 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3730 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3731 3732 // Form the GEP offset. 3733 Indexes[VarIdxNum] = Val; 3734 3735 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes); 3736 if (Result == 0) break; // Cannot compute! 3737 3738 // Evaluate the condition for this iteration. 3739 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3740 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3741 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3742#if 0 3743 errs() << "\n***\n*** Computed loop count " << *ItCst 3744 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3745 << "***\n"; 3746#endif 3747 ++NumArrayLenItCounts; 3748 return getConstant(ItCst); // Found terminating iteration! 3749 } 3750 } 3751 return getCouldNotCompute(); 3752} 3753 3754 3755/// CanConstantFold - Return true if we can constant fold an instruction of the 3756/// specified type, assuming that all operands were constants. 3757static bool CanConstantFold(const Instruction *I) { 3758 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3759 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3760 return true; 3761 3762 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3763 if (const Function *F = CI->getCalledFunction()) 3764 return canConstantFoldCallTo(F); 3765 return false; 3766} 3767 3768/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3769/// in the loop that V is derived from. We allow arbitrary operations along the 3770/// way, but the operands of an operation must either be constants or a value 3771/// derived from a constant PHI. If this expression does not fit with these 3772/// constraints, return null. 3773static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3774 // If this is not an instruction, or if this is an instruction outside of the 3775 // loop, it can't be derived from a loop PHI. 3776 Instruction *I = dyn_cast<Instruction>(V); 3777 if (I == 0 || !L->contains(I->getParent())) return 0; 3778 3779 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3780 if (L->getHeader() == I->getParent()) 3781 return PN; 3782 else 3783 // We don't currently keep track of the control flow needed to evaluate 3784 // PHIs, so we cannot handle PHIs inside of loops. 3785 return 0; 3786 } 3787 3788 // If we won't be able to constant fold this expression even if the operands 3789 // are constants, return early. 3790 if (!CanConstantFold(I)) return 0; 3791 3792 // Otherwise, we can evaluate this instruction if all of its operands are 3793 // constant or derived from a PHI node themselves. 3794 PHINode *PHI = 0; 3795 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 3796 if (!(isa<Constant>(I->getOperand(Op)) || 3797 isa<GlobalValue>(I->getOperand(Op)))) { 3798 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 3799 if (P == 0) return 0; // Not evolving from PHI 3800 if (PHI == 0) 3801 PHI = P; 3802 else if (PHI != P) 3803 return 0; // Evolving from multiple different PHIs. 3804 } 3805 3806 // This is a expression evolving from a constant PHI! 3807 return PHI; 3808} 3809 3810/// EvaluateExpression - Given an expression that passes the 3811/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 3812/// in the loop has the value PHIVal. If we can't fold this expression for some 3813/// reason, return null. 3814static Constant *EvaluateExpression(Value *V, Constant *PHIVal) { 3815 if (isa<PHINode>(V)) return PHIVal; 3816 if (Constant *C = dyn_cast<Constant>(V)) return C; 3817 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 3818 Instruction *I = cast<Instruction>(V); 3819 LLVMContext &Context = I->getParent()->getContext(); 3820 3821 std::vector<Constant*> Operands; 3822 Operands.resize(I->getNumOperands()); 3823 3824 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 3825 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal); 3826 if (Operands[i] == 0) return 0; 3827 } 3828 3829 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 3830 return ConstantFoldCompareInstOperands(CI->getPredicate(), 3831 &Operands[0], Operands.size(), 3832 Context); 3833 else 3834 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 3835 &Operands[0], Operands.size(), 3836 Context); 3837} 3838 3839/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 3840/// in the header of its containing loop, we know the loop executes a 3841/// constant number of times, and the PHI node is just a recurrence 3842/// involving constants, fold it. 3843Constant * 3844ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 3845 const APInt& BEs, 3846 const Loop *L) { 3847 std::map<PHINode*, Constant*>::iterator I = 3848 ConstantEvolutionLoopExitValue.find(PN); 3849 if (I != ConstantEvolutionLoopExitValue.end()) 3850 return I->second; 3851 3852 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 3853 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 3854 3855 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 3856 3857 // Since the loop is canonicalized, the PHI node must have two entries. One 3858 // entry must be a constant (coming in from outside of the loop), and the 3859 // second must be derived from the same PHI. 3860 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3861 Constant *StartCST = 3862 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3863 if (StartCST == 0) 3864 return RetVal = 0; // Must be a constant. 3865 3866 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3867 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3868 if (PN2 != PN) 3869 return RetVal = 0; // Not derived from same PHI. 3870 3871 // Execute the loop symbolically to determine the exit value. 3872 if (BEs.getActiveBits() >= 32) 3873 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 3874 3875 unsigned NumIterations = BEs.getZExtValue(); // must be in range 3876 unsigned IterationNum = 0; 3877 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 3878 if (IterationNum == NumIterations) 3879 return RetVal = PHIVal; // Got exit value! 3880 3881 // Compute the value of the PHI node for the next iteration. 3882 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3883 if (NextPHI == PHIVal) 3884 return RetVal = NextPHI; // Stopped evolving! 3885 if (NextPHI == 0) 3886 return 0; // Couldn't evaluate! 3887 PHIVal = NextPHI; 3888 } 3889} 3890 3891/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 3892/// constant number of times (the condition evolves only from constants), 3893/// try to evaluate a few iterations of the loop until we get the exit 3894/// condition gets a value of ExitWhen (true or false). If we cannot 3895/// evaluate the trip count of the loop, return getCouldNotCompute(). 3896const SCEV * 3897ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 3898 Value *Cond, 3899 bool ExitWhen) { 3900 PHINode *PN = getConstantEvolvingPHI(Cond, L); 3901 if (PN == 0) return getCouldNotCompute(); 3902 3903 // Since the loop is canonicalized, the PHI node must have two entries. One 3904 // entry must be a constant (coming in from outside of the loop), and the 3905 // second must be derived from the same PHI. 3906 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 3907 Constant *StartCST = 3908 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 3909 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 3910 3911 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 3912 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 3913 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 3914 3915 // Okay, we find a PHI node that defines the trip count of this loop. Execute 3916 // the loop symbolically to determine when the condition gets a value of 3917 // "ExitWhen". 3918 unsigned IterationNum = 0; 3919 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 3920 for (Constant *PHIVal = StartCST; 3921 IterationNum != MaxIterations; ++IterationNum) { 3922 ConstantInt *CondVal = 3923 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal)); 3924 3925 // Couldn't symbolically evaluate. 3926 if (!CondVal) return getCouldNotCompute(); 3927 3928 if (CondVal->getValue() == uint64_t(ExitWhen)) { 3929 ++NumBruteForceTripCountsComputed; 3930 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 3931 } 3932 3933 // Compute the value of the PHI node for the next iteration. 3934 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal); 3935 if (NextPHI == 0 || NextPHI == PHIVal) 3936 return getCouldNotCompute();// Couldn't evaluate or not making progress... 3937 PHIVal = NextPHI; 3938 } 3939 3940 // Too many iterations were needed to evaluate. 3941 return getCouldNotCompute(); 3942} 3943 3944/// getSCEVAtScope - Return a SCEV expression for the specified value 3945/// at the specified scope in the program. The L value specifies a loop 3946/// nest to evaluate the expression at, where null is the top-level or a 3947/// specified loop is immediately inside of the loop. 3948/// 3949/// This method can be used to compute the exit value for a variable defined 3950/// in a loop by querying what the value will hold in the parent loop. 3951/// 3952/// In the case that a relevant loop exit value cannot be computed, the 3953/// original value V is returned. 3954const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 3955 // Check to see if we've folded this expression at this loop before. 3956 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 3957 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 3958 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 3959 if (!Pair.second) 3960 return Pair.first->second ? Pair.first->second : V; 3961 3962 // Otherwise compute it. 3963 const SCEV *C = computeSCEVAtScope(V, L); 3964 ValuesAtScopes[V][L] = C; 3965 return C; 3966} 3967 3968const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 3969 if (isa<SCEVConstant>(V)) return V; 3970 3971 // If this instruction is evolved from a constant-evolving PHI, compute the 3972 // exit value from the loop without using SCEVs. 3973 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 3974 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 3975 const Loop *LI = (*this->LI)[I->getParent()]; 3976 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 3977 if (PHINode *PN = dyn_cast<PHINode>(I)) 3978 if (PN->getParent() == LI->getHeader()) { 3979 // Okay, there is no closed form solution for the PHI node. Check 3980 // to see if the loop that contains it has a known backedge-taken 3981 // count. If so, we may be able to force computation of the exit 3982 // value. 3983 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 3984 if (const SCEVConstant *BTCC = 3985 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 3986 // Okay, we know how many times the containing loop executes. If 3987 // this is a constant evolving PHI node, get the final value at 3988 // the specified iteration number. 3989 Constant *RV = getConstantEvolutionLoopExitValue(PN, 3990 BTCC->getValue()->getValue(), 3991 LI); 3992 if (RV) return getSCEV(RV); 3993 } 3994 } 3995 3996 // Okay, this is an expression that we cannot symbolically evaluate 3997 // into a SCEV. Check to see if it's possible to symbolically evaluate 3998 // the arguments into constants, and if so, try to constant propagate the 3999 // result. This is particularly useful for computing loop exit values. 4000 if (CanConstantFold(I)) { 4001 std::vector<Constant*> Operands; 4002 Operands.reserve(I->getNumOperands()); 4003 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4004 Value *Op = I->getOperand(i); 4005 if (Constant *C = dyn_cast<Constant>(Op)) { 4006 Operands.push_back(C); 4007 } else { 4008 // If any of the operands is non-constant and if they are 4009 // non-integer and non-pointer, don't even try to analyze them 4010 // with scev techniques. 4011 if (!isSCEVable(Op->getType())) 4012 return V; 4013 4014 const SCEV* OpV = getSCEVAtScope(Op, L); 4015 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4016 Constant *C = SC->getValue(); 4017 if (C->getType() != Op->getType()) 4018 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4019 Op->getType(), 4020 false), 4021 C, Op->getType()); 4022 Operands.push_back(C); 4023 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4024 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4025 if (C->getType() != Op->getType()) 4026 C = 4027 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4028 Op->getType(), 4029 false), 4030 C, Op->getType()); 4031 Operands.push_back(C); 4032 } else 4033 return V; 4034 } else { 4035 return V; 4036 } 4037 } 4038 } 4039 4040 Constant *C; 4041 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4042 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4043 &Operands[0], Operands.size(), 4044 getContext()); 4045 else 4046 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4047 &Operands[0], Operands.size(), 4048 getContext()); 4049 return getSCEV(C); 4050 } 4051 } 4052 4053 // This is some other type of SCEVUnknown, just return it. 4054 return V; 4055 } 4056 4057 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4058 // Avoid performing the look-up in the common case where the specified 4059 // expression has no loop-variant portions. 4060 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4061 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4062 if (OpAtScope != Comm->getOperand(i)) { 4063 // Okay, at least one of these operands is loop variant but might be 4064 // foldable. Build a new instance of the folded commutative expression. 4065 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4066 Comm->op_begin()+i); 4067 NewOps.push_back(OpAtScope); 4068 4069 for (++i; i != e; ++i) { 4070 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4071 NewOps.push_back(OpAtScope); 4072 } 4073 if (isa<SCEVAddExpr>(Comm)) 4074 return getAddExpr(NewOps); 4075 if (isa<SCEVMulExpr>(Comm)) 4076 return getMulExpr(NewOps); 4077 if (isa<SCEVSMaxExpr>(Comm)) 4078 return getSMaxExpr(NewOps); 4079 if (isa<SCEVUMaxExpr>(Comm)) 4080 return getUMaxExpr(NewOps); 4081 llvm_unreachable("Unknown commutative SCEV type!"); 4082 } 4083 } 4084 // If we got here, all operands are loop invariant. 4085 return Comm; 4086 } 4087 4088 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4089 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4090 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4091 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4092 return Div; // must be loop invariant 4093 return getUDivExpr(LHS, RHS); 4094 } 4095 4096 // If this is a loop recurrence for a loop that does not contain L, then we 4097 // are dealing with the final value computed by the loop. 4098 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4099 if (!L || !AddRec->getLoop()->contains(L->getHeader())) { 4100 // To evaluate this recurrence, we need to know how many times the AddRec 4101 // loop iterates. Compute this now. 4102 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4103 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4104 4105 // Then, evaluate the AddRec. 4106 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4107 } 4108 return AddRec; 4109 } 4110 4111 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4112 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4113 if (Op == Cast->getOperand()) 4114 return Cast; // must be loop invariant 4115 return getZeroExtendExpr(Op, Cast->getType()); 4116 } 4117 4118 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4119 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4120 if (Op == Cast->getOperand()) 4121 return Cast; // must be loop invariant 4122 return getSignExtendExpr(Op, Cast->getType()); 4123 } 4124 4125 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4126 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4127 if (Op == Cast->getOperand()) 4128 return Cast; // must be loop invariant 4129 return getTruncateExpr(Op, Cast->getType()); 4130 } 4131 4132 if (isa<SCEVTargetDataConstant>(V)) 4133 return V; 4134 4135 llvm_unreachable("Unknown SCEV type!"); 4136 return 0; 4137} 4138 4139/// getSCEVAtScope - This is a convenience function which does 4140/// getSCEVAtScope(getSCEV(V), L). 4141const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4142 return getSCEVAtScope(getSCEV(V), L); 4143} 4144 4145/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4146/// following equation: 4147/// 4148/// A * X = B (mod N) 4149/// 4150/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4151/// A and B isn't important. 4152/// 4153/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4154static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4155 ScalarEvolution &SE) { 4156 uint32_t BW = A.getBitWidth(); 4157 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4158 assert(A != 0 && "A must be non-zero."); 4159 4160 // 1. D = gcd(A, N) 4161 // 4162 // The gcd of A and N may have only one prime factor: 2. The number of 4163 // trailing zeros in A is its multiplicity 4164 uint32_t Mult2 = A.countTrailingZeros(); 4165 // D = 2^Mult2 4166 4167 // 2. Check if B is divisible by D. 4168 // 4169 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4170 // is not less than multiplicity of this prime factor for D. 4171 if (B.countTrailingZeros() < Mult2) 4172 return SE.getCouldNotCompute(); 4173 4174 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4175 // modulo (N / D). 4176 // 4177 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4178 // bit width during computations. 4179 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4180 APInt Mod(BW + 1, 0); 4181 Mod.set(BW - Mult2); // Mod = N / D 4182 APInt I = AD.multiplicativeInverse(Mod); 4183 4184 // 4. Compute the minimum unsigned root of the equation: 4185 // I * (B / D) mod (N / D) 4186 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4187 4188 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4189 // bits. 4190 return SE.getConstant(Result.trunc(BW)); 4191} 4192 4193/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4194/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4195/// might be the same) or two SCEVCouldNotCompute objects. 4196/// 4197static std::pair<const SCEV *,const SCEV *> 4198SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4199 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4200 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4201 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4202 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4203 4204 // We currently can only solve this if the coefficients are constants. 4205 if (!LC || !MC || !NC) { 4206 const SCEV *CNC = SE.getCouldNotCompute(); 4207 return std::make_pair(CNC, CNC); 4208 } 4209 4210 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4211 const APInt &L = LC->getValue()->getValue(); 4212 const APInt &M = MC->getValue()->getValue(); 4213 const APInt &N = NC->getValue()->getValue(); 4214 APInt Two(BitWidth, 2); 4215 APInt Four(BitWidth, 4); 4216 4217 { 4218 using namespace APIntOps; 4219 const APInt& C = L; 4220 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4221 // The B coefficient is M-N/2 4222 APInt B(M); 4223 B -= sdiv(N,Two); 4224 4225 // The A coefficient is N/2 4226 APInt A(N.sdiv(Two)); 4227 4228 // Compute the B^2-4ac term. 4229 APInt SqrtTerm(B); 4230 SqrtTerm *= B; 4231 SqrtTerm -= Four * (A * C); 4232 4233 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4234 // integer value or else APInt::sqrt() will assert. 4235 APInt SqrtVal(SqrtTerm.sqrt()); 4236 4237 // Compute the two solutions for the quadratic formula. 4238 // The divisions must be performed as signed divisions. 4239 APInt NegB(-B); 4240 APInt TwoA( A << 1 ); 4241 if (TwoA.isMinValue()) { 4242 const SCEV *CNC = SE.getCouldNotCompute(); 4243 return std::make_pair(CNC, CNC); 4244 } 4245 4246 LLVMContext &Context = SE.getContext(); 4247 4248 ConstantInt *Solution1 = 4249 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4250 ConstantInt *Solution2 = 4251 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4252 4253 return std::make_pair(SE.getConstant(Solution1), 4254 SE.getConstant(Solution2)); 4255 } // end APIntOps namespace 4256} 4257 4258/// HowFarToZero - Return the number of times a backedge comparing the specified 4259/// value to zero will execute. If not computable, return CouldNotCompute. 4260const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4261 // If the value is a constant 4262 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4263 // If the value is already zero, the branch will execute zero times. 4264 if (C->getValue()->isZero()) return C; 4265 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4266 } 4267 4268 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4269 if (!AddRec || AddRec->getLoop() != L) 4270 return getCouldNotCompute(); 4271 4272 if (AddRec->isAffine()) { 4273 // If this is an affine expression, the execution count of this branch is 4274 // the minimum unsigned root of the following equation: 4275 // 4276 // Start + Step*N = 0 (mod 2^BW) 4277 // 4278 // equivalent to: 4279 // 4280 // Step*N = -Start (mod 2^BW) 4281 // 4282 // where BW is the common bit width of Start and Step. 4283 4284 // Get the initial value for the loop. 4285 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4286 L->getParentLoop()); 4287 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4288 L->getParentLoop()); 4289 4290 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4291 // For now we handle only constant steps. 4292 4293 // First, handle unitary steps. 4294 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4295 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4296 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4297 return Start; // N = Start (as unsigned) 4298 4299 // Then, try to solve the above equation provided that Start is constant. 4300 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4301 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4302 -StartC->getValue()->getValue(), 4303 *this); 4304 } 4305 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) { 4306 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4307 // the quadratic equation to solve it. 4308 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4309 *this); 4310 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4311 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4312 if (R1) { 4313#if 0 4314 errs() << "HFTZ: " << *V << " - sol#1: " << *R1 4315 << " sol#2: " << *R2 << "\n"; 4316#endif 4317 // Pick the smallest positive root value. 4318 if (ConstantInt *CB = 4319 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4320 R1->getValue(), R2->getValue()))) { 4321 if (CB->getZExtValue() == false) 4322 std::swap(R1, R2); // R1 is the minimum root now. 4323 4324 // We can only use this value if the chrec ends up with an exact zero 4325 // value at this index. When solving for "X*X != 5", for example, we 4326 // should not accept a root of 2. 4327 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4328 if (Val->isZero()) 4329 return R1; // We found a quadratic root! 4330 } 4331 } 4332 } 4333 4334 return getCouldNotCompute(); 4335} 4336 4337/// HowFarToNonZero - Return the number of times a backedge checking the 4338/// specified value for nonzero will execute. If not computable, return 4339/// CouldNotCompute 4340const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4341 // Loops that look like: while (X == 0) are very strange indeed. We don't 4342 // handle them yet except for the trivial case. This could be expanded in the 4343 // future as needed. 4344 4345 // If the value is a constant, check to see if it is known to be non-zero 4346 // already. If so, the backedge will execute zero times. 4347 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4348 if (!C->getValue()->isNullValue()) 4349 return getIntegerSCEV(0, C->getType()); 4350 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4351 } 4352 4353 // We could implement others, but I really doubt anyone writes loops like 4354 // this, and if they did, they would already be constant folded. 4355 return getCouldNotCompute(); 4356} 4357 4358/// getLoopPredecessor - If the given loop's header has exactly one unique 4359/// predecessor outside the loop, return it. Otherwise return null. 4360/// 4361BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4362 BasicBlock *Header = L->getHeader(); 4363 BasicBlock *Pred = 0; 4364 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4365 PI != E; ++PI) 4366 if (!L->contains(*PI)) { 4367 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4368 Pred = *PI; 4369 } 4370 return Pred; 4371} 4372 4373/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4374/// (which may not be an immediate predecessor) which has exactly one 4375/// successor from which BB is reachable, or null if no such block is 4376/// found. 4377/// 4378BasicBlock * 4379ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4380 // If the block has a unique predecessor, then there is no path from the 4381 // predecessor to the block that does not go through the direct edge 4382 // from the predecessor to the block. 4383 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4384 return Pred; 4385 4386 // A loop's header is defined to be a block that dominates the loop. 4387 // If the header has a unique predecessor outside the loop, it must be 4388 // a block that has exactly one successor that can reach the loop. 4389 if (Loop *L = LI->getLoopFor(BB)) 4390 return getLoopPredecessor(L); 4391 4392 return 0; 4393} 4394 4395/// HasSameValue - SCEV structural equivalence is usually sufficient for 4396/// testing whether two expressions are equal, however for the purposes of 4397/// looking for a condition guarding a loop, it can be useful to be a little 4398/// more general, since a front-end may have replicated the controlling 4399/// expression. 4400/// 4401static bool HasSameValue(const SCEV *A, const SCEV *B) { 4402 // Quick check to see if they are the same SCEV. 4403 if (A == B) return true; 4404 4405 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4406 // two different instructions with the same value. Check for this case. 4407 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4408 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4409 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4410 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4411 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4412 return true; 4413 4414 // Otherwise assume they may have a different value. 4415 return false; 4416} 4417 4418bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4419 return getSignedRange(S).getSignedMax().isNegative(); 4420} 4421 4422bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4423 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4424} 4425 4426bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4427 return !getSignedRange(S).getSignedMin().isNegative(); 4428} 4429 4430bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4431 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4432} 4433 4434bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4435 return isKnownNegative(S) || isKnownPositive(S); 4436} 4437 4438bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4439 const SCEV *LHS, const SCEV *RHS) { 4440 4441 if (HasSameValue(LHS, RHS)) 4442 return ICmpInst::isTrueWhenEqual(Pred); 4443 4444 switch (Pred) { 4445 default: 4446 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4447 break; 4448 case ICmpInst::ICMP_SGT: 4449 Pred = ICmpInst::ICMP_SLT; 4450 std::swap(LHS, RHS); 4451 case ICmpInst::ICMP_SLT: { 4452 ConstantRange LHSRange = getSignedRange(LHS); 4453 ConstantRange RHSRange = getSignedRange(RHS); 4454 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4455 return true; 4456 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4457 return false; 4458 break; 4459 } 4460 case ICmpInst::ICMP_SGE: 4461 Pred = ICmpInst::ICMP_SLE; 4462 std::swap(LHS, RHS); 4463 case ICmpInst::ICMP_SLE: { 4464 ConstantRange LHSRange = getSignedRange(LHS); 4465 ConstantRange RHSRange = getSignedRange(RHS); 4466 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4467 return true; 4468 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4469 return false; 4470 break; 4471 } 4472 case ICmpInst::ICMP_UGT: 4473 Pred = ICmpInst::ICMP_ULT; 4474 std::swap(LHS, RHS); 4475 case ICmpInst::ICMP_ULT: { 4476 ConstantRange LHSRange = getUnsignedRange(LHS); 4477 ConstantRange RHSRange = getUnsignedRange(RHS); 4478 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4479 return true; 4480 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4481 return false; 4482 break; 4483 } 4484 case ICmpInst::ICMP_UGE: 4485 Pred = ICmpInst::ICMP_ULE; 4486 std::swap(LHS, RHS); 4487 case ICmpInst::ICMP_ULE: { 4488 ConstantRange LHSRange = getUnsignedRange(LHS); 4489 ConstantRange RHSRange = getUnsignedRange(RHS); 4490 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4491 return true; 4492 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4493 return false; 4494 break; 4495 } 4496 case ICmpInst::ICMP_NE: { 4497 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4498 return true; 4499 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4500 return true; 4501 4502 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4503 if (isKnownNonZero(Diff)) 4504 return true; 4505 break; 4506 } 4507 case ICmpInst::ICMP_EQ: 4508 // The check at the top of the function catches the case where 4509 // the values are known to be equal. 4510 break; 4511 } 4512 return false; 4513} 4514 4515/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4516/// protected by a conditional between LHS and RHS. This is used to 4517/// to eliminate casts. 4518bool 4519ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4520 ICmpInst::Predicate Pred, 4521 const SCEV *LHS, const SCEV *RHS) { 4522 // Interpret a null as meaning no loop, where there is obviously no guard 4523 // (interprocedural conditions notwithstanding). 4524 if (!L) return true; 4525 4526 BasicBlock *Latch = L->getLoopLatch(); 4527 if (!Latch) 4528 return false; 4529 4530 BranchInst *LoopContinuePredicate = 4531 dyn_cast<BranchInst>(Latch->getTerminator()); 4532 if (!LoopContinuePredicate || 4533 LoopContinuePredicate->isUnconditional()) 4534 return false; 4535 4536 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4537 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4538} 4539 4540/// isLoopGuardedByCond - Test whether entry to the loop is protected 4541/// by a conditional between LHS and RHS. This is used to help avoid max 4542/// expressions in loop trip counts, and to eliminate casts. 4543bool 4544ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4545 ICmpInst::Predicate Pred, 4546 const SCEV *LHS, const SCEV *RHS) { 4547 // Interpret a null as meaning no loop, where there is obviously no guard 4548 // (interprocedural conditions notwithstanding). 4549 if (!L) return false; 4550 4551 BasicBlock *Predecessor = getLoopPredecessor(L); 4552 BasicBlock *PredecessorDest = L->getHeader(); 4553 4554 // Starting at the loop predecessor, climb up the predecessor chain, as long 4555 // as there are predecessors that can be found that have unique successors 4556 // leading to the original header. 4557 for (; Predecessor; 4558 PredecessorDest = Predecessor, 4559 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4560 4561 BranchInst *LoopEntryPredicate = 4562 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4563 if (!LoopEntryPredicate || 4564 LoopEntryPredicate->isUnconditional()) 4565 continue; 4566 4567 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4568 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4569 return true; 4570 } 4571 4572 return false; 4573} 4574 4575/// isImpliedCond - Test whether the condition described by Pred, LHS, 4576/// and RHS is true whenever the given Cond value evaluates to true. 4577bool ScalarEvolution::isImpliedCond(Value *CondValue, 4578 ICmpInst::Predicate Pred, 4579 const SCEV *LHS, const SCEV *RHS, 4580 bool Inverse) { 4581 // Recursivly handle And and Or conditions. 4582 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4583 if (BO->getOpcode() == Instruction::And) { 4584 if (!Inverse) 4585 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4586 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4587 } else if (BO->getOpcode() == Instruction::Or) { 4588 if (Inverse) 4589 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4590 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4591 } 4592 } 4593 4594 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4595 if (!ICI) return false; 4596 4597 // Bail if the ICmp's operands' types are wider than the needed type 4598 // before attempting to call getSCEV on them. This avoids infinite 4599 // recursion, since the analysis of widening casts can require loop 4600 // exit condition information for overflow checking, which would 4601 // lead back here. 4602 if (getTypeSizeInBits(LHS->getType()) < 4603 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4604 return false; 4605 4606 // Now that we found a conditional branch that dominates the loop, check to 4607 // see if it is the comparison we are looking for. 4608 ICmpInst::Predicate FoundPred; 4609 if (Inverse) 4610 FoundPred = ICI->getInversePredicate(); 4611 else 4612 FoundPred = ICI->getPredicate(); 4613 4614 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4615 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4616 4617 // Balance the types. The case where FoundLHS' type is wider than 4618 // LHS' type is checked for above. 4619 if (getTypeSizeInBits(LHS->getType()) > 4620 getTypeSizeInBits(FoundLHS->getType())) { 4621 if (CmpInst::isSigned(Pred)) { 4622 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4623 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4624 } else { 4625 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4626 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4627 } 4628 } 4629 4630 // Canonicalize the query to match the way instcombine will have 4631 // canonicalized the comparison. 4632 // First, put a constant operand on the right. 4633 if (isa<SCEVConstant>(LHS)) { 4634 std::swap(LHS, RHS); 4635 Pred = ICmpInst::getSwappedPredicate(Pred); 4636 } 4637 // Then, canonicalize comparisons with boundary cases. 4638 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4639 const APInt &RA = RC->getValue()->getValue(); 4640 switch (Pred) { 4641 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4642 case ICmpInst::ICMP_EQ: 4643 case ICmpInst::ICMP_NE: 4644 break; 4645 case ICmpInst::ICMP_UGE: 4646 if ((RA - 1).isMinValue()) { 4647 Pred = ICmpInst::ICMP_NE; 4648 RHS = getConstant(RA - 1); 4649 break; 4650 } 4651 if (RA.isMaxValue()) { 4652 Pred = ICmpInst::ICMP_EQ; 4653 break; 4654 } 4655 if (RA.isMinValue()) return true; 4656 break; 4657 case ICmpInst::ICMP_ULE: 4658 if ((RA + 1).isMaxValue()) { 4659 Pred = ICmpInst::ICMP_NE; 4660 RHS = getConstant(RA + 1); 4661 break; 4662 } 4663 if (RA.isMinValue()) { 4664 Pred = ICmpInst::ICMP_EQ; 4665 break; 4666 } 4667 if (RA.isMaxValue()) return true; 4668 break; 4669 case ICmpInst::ICMP_SGE: 4670 if ((RA - 1).isMinSignedValue()) { 4671 Pred = ICmpInst::ICMP_NE; 4672 RHS = getConstant(RA - 1); 4673 break; 4674 } 4675 if (RA.isMaxSignedValue()) { 4676 Pred = ICmpInst::ICMP_EQ; 4677 break; 4678 } 4679 if (RA.isMinSignedValue()) return true; 4680 break; 4681 case ICmpInst::ICMP_SLE: 4682 if ((RA + 1).isMaxSignedValue()) { 4683 Pred = ICmpInst::ICMP_NE; 4684 RHS = getConstant(RA + 1); 4685 break; 4686 } 4687 if (RA.isMinSignedValue()) { 4688 Pred = ICmpInst::ICMP_EQ; 4689 break; 4690 } 4691 if (RA.isMaxSignedValue()) return true; 4692 break; 4693 case ICmpInst::ICMP_UGT: 4694 if (RA.isMinValue()) { 4695 Pred = ICmpInst::ICMP_NE; 4696 break; 4697 } 4698 if ((RA + 1).isMaxValue()) { 4699 Pred = ICmpInst::ICMP_EQ; 4700 RHS = getConstant(RA + 1); 4701 break; 4702 } 4703 if (RA.isMaxValue()) return false; 4704 break; 4705 case ICmpInst::ICMP_ULT: 4706 if (RA.isMaxValue()) { 4707 Pred = ICmpInst::ICMP_NE; 4708 break; 4709 } 4710 if ((RA - 1).isMinValue()) { 4711 Pred = ICmpInst::ICMP_EQ; 4712 RHS = getConstant(RA - 1); 4713 break; 4714 } 4715 if (RA.isMinValue()) return false; 4716 break; 4717 case ICmpInst::ICMP_SGT: 4718 if (RA.isMinSignedValue()) { 4719 Pred = ICmpInst::ICMP_NE; 4720 break; 4721 } 4722 if ((RA + 1).isMaxSignedValue()) { 4723 Pred = ICmpInst::ICMP_EQ; 4724 RHS = getConstant(RA + 1); 4725 break; 4726 } 4727 if (RA.isMaxSignedValue()) return false; 4728 break; 4729 case ICmpInst::ICMP_SLT: 4730 if (RA.isMaxSignedValue()) { 4731 Pred = ICmpInst::ICMP_NE; 4732 break; 4733 } 4734 if ((RA - 1).isMinSignedValue()) { 4735 Pred = ICmpInst::ICMP_EQ; 4736 RHS = getConstant(RA - 1); 4737 break; 4738 } 4739 if (RA.isMinSignedValue()) return false; 4740 break; 4741 } 4742 } 4743 4744 // Check to see if we can make the LHS or RHS match. 4745 if (LHS == FoundRHS || RHS == FoundLHS) { 4746 if (isa<SCEVConstant>(RHS)) { 4747 std::swap(FoundLHS, FoundRHS); 4748 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4749 } else { 4750 std::swap(LHS, RHS); 4751 Pred = ICmpInst::getSwappedPredicate(Pred); 4752 } 4753 } 4754 4755 // Check whether the found predicate is the same as the desired predicate. 4756 if (FoundPred == Pred) 4757 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4758 4759 // Check whether swapping the found predicate makes it the same as the 4760 // desired predicate. 4761 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4762 if (isa<SCEVConstant>(RHS)) 4763 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4764 else 4765 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4766 RHS, LHS, FoundLHS, FoundRHS); 4767 } 4768 4769 // Check whether the actual condition is beyond sufficient. 4770 if (FoundPred == ICmpInst::ICMP_EQ) 4771 if (ICmpInst::isTrueWhenEqual(Pred)) 4772 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4773 return true; 4774 if (Pred == ICmpInst::ICMP_NE) 4775 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4776 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4777 return true; 4778 4779 // Otherwise assume the worst. 4780 return false; 4781} 4782 4783/// isImpliedCondOperands - Test whether the condition described by Pred, 4784/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS, 4785/// and FoundRHS is true. 4786bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4787 const SCEV *LHS, const SCEV *RHS, 4788 const SCEV *FoundLHS, 4789 const SCEV *FoundRHS) { 4790 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4791 FoundLHS, FoundRHS) || 4792 // ~x < ~y --> x > y 4793 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4794 getNotSCEV(FoundRHS), 4795 getNotSCEV(FoundLHS)); 4796} 4797 4798/// isImpliedCondOperandsHelper - Test whether the condition described by 4799/// Pred, LHS, and RHS is true whenever the condition desribed by Pred, 4800/// FoundLHS, and FoundRHS is true. 4801bool 4802ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 4803 const SCEV *LHS, const SCEV *RHS, 4804 const SCEV *FoundLHS, 4805 const SCEV *FoundRHS) { 4806 switch (Pred) { 4807 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4808 case ICmpInst::ICMP_EQ: 4809 case ICmpInst::ICMP_NE: 4810 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 4811 return true; 4812 break; 4813 case ICmpInst::ICMP_SLT: 4814 case ICmpInst::ICMP_SLE: 4815 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 4816 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 4817 return true; 4818 break; 4819 case ICmpInst::ICMP_SGT: 4820 case ICmpInst::ICMP_SGE: 4821 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 4822 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 4823 return true; 4824 break; 4825 case ICmpInst::ICMP_ULT: 4826 case ICmpInst::ICMP_ULE: 4827 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 4828 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 4829 return true; 4830 break; 4831 case ICmpInst::ICMP_UGT: 4832 case ICmpInst::ICMP_UGE: 4833 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 4834 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 4835 return true; 4836 break; 4837 } 4838 4839 return false; 4840} 4841 4842/// getBECount - Subtract the end and start values and divide by the step, 4843/// rounding up, to get the number of times the backedge is executed. Return 4844/// CouldNotCompute if an intermediate computation overflows. 4845const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 4846 const SCEV *End, 4847 const SCEV *Step, 4848 bool NoWrap) { 4849 const Type *Ty = Start->getType(); 4850 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 4851 const SCEV *Diff = getMinusSCEV(End, Start); 4852 const SCEV *RoundUp = getAddExpr(Step, NegOne); 4853 4854 // Add an adjustment to the difference between End and Start so that 4855 // the division will effectively round up. 4856 const SCEV *Add = getAddExpr(Diff, RoundUp); 4857 4858 if (!NoWrap) { 4859 // Check Add for unsigned overflow. 4860 // TODO: More sophisticated things could be done here. 4861 const Type *WideTy = IntegerType::get(getContext(), 4862 getTypeSizeInBits(Ty) + 1); 4863 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 4864 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 4865 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 4866 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 4867 return getCouldNotCompute(); 4868 } 4869 4870 return getUDivExpr(Add, Step); 4871} 4872 4873/// HowManyLessThans - Return the number of times a backedge containing the 4874/// specified less-than comparison will execute. If not computable, return 4875/// CouldNotCompute. 4876ScalarEvolution::BackedgeTakenInfo 4877ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 4878 const Loop *L, bool isSigned) { 4879 // Only handle: "ADDREC < LoopInvariant". 4880 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 4881 4882 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 4883 if (!AddRec || AddRec->getLoop() != L) 4884 return getCouldNotCompute(); 4885 4886 // Check to see if we have a flag which makes analysis easy. 4887 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 4888 AddRec->hasNoUnsignedWrap(); 4889 4890 if (AddRec->isAffine()) { 4891 // FORNOW: We only support unit strides. 4892 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 4893 const SCEV *Step = AddRec->getStepRecurrence(*this); 4894 4895 // TODO: handle non-constant strides. 4896 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step); 4897 if (!CStep || CStep->isZero()) 4898 return getCouldNotCompute(); 4899 if (CStep->isOne()) { 4900 // With unit stride, the iteration never steps past the limit value. 4901 } else if (CStep->getValue()->getValue().isStrictlyPositive()) { 4902 if (NoWrap) { 4903 // We know the iteration won't step past the maximum value for its type. 4904 ; 4905 } else if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) { 4906 // Test whether a positive iteration iteration can step past the limit 4907 // value and past the maximum value for its type in a single step. 4908 if (isSigned) { 4909 APInt Max = APInt::getSignedMaxValue(BitWidth); 4910 if ((Max - CStep->getValue()->getValue()) 4911 .slt(CLimit->getValue()->getValue())) 4912 return getCouldNotCompute(); 4913 } else { 4914 APInt Max = APInt::getMaxValue(BitWidth); 4915 if ((Max - CStep->getValue()->getValue()) 4916 .ult(CLimit->getValue()->getValue())) 4917 return getCouldNotCompute(); 4918 } 4919 } else 4920 // TODO: handle non-constant limit values below. 4921 return getCouldNotCompute(); 4922 } else 4923 // TODO: handle negative strides below. 4924 return getCouldNotCompute(); 4925 4926 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 4927 // m. So, we count the number of iterations in which {n,+,s} < m is true. 4928 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 4929 // treat m-n as signed nor unsigned due to overflow possibility. 4930 4931 // First, we get the value of the LHS in the first iteration: n 4932 const SCEV *Start = AddRec->getOperand(0); 4933 4934 // Determine the minimum constant start value. 4935 const SCEV *MinStart = getConstant(isSigned ? 4936 getSignedRange(Start).getSignedMin() : 4937 getUnsignedRange(Start).getUnsignedMin()); 4938 4939 // If we know that the condition is true in order to enter the loop, 4940 // then we know that it will run exactly (m-n)/s times. Otherwise, we 4941 // only know that it will execute (max(m,n)-n)/s times. In both cases, 4942 // the division must round up. 4943 const SCEV *End = RHS; 4944 if (!isLoopGuardedByCond(L, 4945 isSigned ? ICmpInst::ICMP_SLT : 4946 ICmpInst::ICMP_ULT, 4947 getMinusSCEV(Start, Step), RHS)) 4948 End = isSigned ? getSMaxExpr(RHS, Start) 4949 : getUMaxExpr(RHS, Start); 4950 4951 // Determine the maximum constant end value. 4952 const SCEV *MaxEnd = getConstant(isSigned ? 4953 getSignedRange(End).getSignedMax() : 4954 getUnsignedRange(End).getUnsignedMax()); 4955 4956 // Finally, we subtract these two values and divide, rounding up, to get 4957 // the number of times the backedge is executed. 4958 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 4959 4960 // The maximum backedge count is similar, except using the minimum start 4961 // value and the maximum end value. 4962 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 4963 4964 return BackedgeTakenInfo(BECount, MaxBECount); 4965 } 4966 4967 return getCouldNotCompute(); 4968} 4969 4970/// getNumIterationsInRange - Return the number of iterations of this loop that 4971/// produce values in the specified constant range. Another way of looking at 4972/// this is that it returns the first iteration number where the value is not in 4973/// the condition, thus computing the exit count. If the iteration count can't 4974/// be computed, an instance of SCEVCouldNotCompute is returned. 4975const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 4976 ScalarEvolution &SE) const { 4977 if (Range.isFullSet()) // Infinite loop. 4978 return SE.getCouldNotCompute(); 4979 4980 // If the start is a non-zero constant, shift the range to simplify things. 4981 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 4982 if (!SC->getValue()->isZero()) { 4983 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 4984 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 4985 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 4986 if (const SCEVAddRecExpr *ShiftedAddRec = 4987 dyn_cast<SCEVAddRecExpr>(Shifted)) 4988 return ShiftedAddRec->getNumIterationsInRange( 4989 Range.subtract(SC->getValue()->getValue()), SE); 4990 // This is strange and shouldn't happen. 4991 return SE.getCouldNotCompute(); 4992 } 4993 4994 // The only time we can solve this is when we have all constant indices. 4995 // Otherwise, we cannot determine the overflow conditions. 4996 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 4997 if (!isa<SCEVConstant>(getOperand(i))) 4998 return SE.getCouldNotCompute(); 4999 5000 5001 // Okay at this point we know that all elements of the chrec are constants and 5002 // that the start element is zero. 5003 5004 // First check to see if the range contains zero. If not, the first 5005 // iteration exits. 5006 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5007 if (!Range.contains(APInt(BitWidth, 0))) 5008 return SE.getIntegerSCEV(0, getType()); 5009 5010 if (isAffine()) { 5011 // If this is an affine expression then we have this situation: 5012 // Solve {0,+,A} in Range === Ax in Range 5013 5014 // We know that zero is in the range. If A is positive then we know that 5015 // the upper value of the range must be the first possible exit value. 5016 // If A is negative then the lower of the range is the last possible loop 5017 // value. Also note that we already checked for a full range. 5018 APInt One(BitWidth,1); 5019 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5020 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5021 5022 // The exit value should be (End+A)/A. 5023 APInt ExitVal = (End + A).udiv(A); 5024 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5025 5026 // Evaluate at the exit value. If we really did fall out of the valid 5027 // range, then we computed our trip count, otherwise wrap around or other 5028 // things must have happened. 5029 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5030 if (Range.contains(Val->getValue())) 5031 return SE.getCouldNotCompute(); // Something strange happened 5032 5033 // Ensure that the previous value is in the range. This is a sanity check. 5034 assert(Range.contains( 5035 EvaluateConstantChrecAtConstant(this, 5036 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5037 "Linear scev computation is off in a bad way!"); 5038 return SE.getConstant(ExitValue); 5039 } else if (isQuadratic()) { 5040 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5041 // quadratic equation to solve it. To do this, we must frame our problem in 5042 // terms of figuring out when zero is crossed, instead of when 5043 // Range.getUpper() is crossed. 5044 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5045 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5046 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5047 5048 // Next, solve the constructed addrec 5049 std::pair<const SCEV *,const SCEV *> Roots = 5050 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5051 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5052 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5053 if (R1) { 5054 // Pick the smallest positive root value. 5055 if (ConstantInt *CB = 5056 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5057 R1->getValue(), R2->getValue()))) { 5058 if (CB->getZExtValue() == false) 5059 std::swap(R1, R2); // R1 is the minimum root now. 5060 5061 // Make sure the root is not off by one. The returned iteration should 5062 // not be in the range, but the previous one should be. When solving 5063 // for "X*X < 5", for example, we should not return a root of 2. 5064 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5065 R1->getValue(), 5066 SE); 5067 if (Range.contains(R1Val->getValue())) { 5068 // The next iteration must be out of the range... 5069 ConstantInt *NextVal = 5070 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5071 5072 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5073 if (!Range.contains(R1Val->getValue())) 5074 return SE.getConstant(NextVal); 5075 return SE.getCouldNotCompute(); // Something strange happened 5076 } 5077 5078 // If R1 was not in the range, then it is a good return value. Make 5079 // sure that R1-1 WAS in the range though, just in case. 5080 ConstantInt *NextVal = 5081 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5082 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5083 if (Range.contains(R1Val->getValue())) 5084 return R1; 5085 return SE.getCouldNotCompute(); // Something strange happened 5086 } 5087 } 5088 } 5089 5090 return SE.getCouldNotCompute(); 5091} 5092 5093 5094 5095//===----------------------------------------------------------------------===// 5096// SCEVCallbackVH Class Implementation 5097//===----------------------------------------------------------------------===// 5098 5099void ScalarEvolution::SCEVCallbackVH::deleted() { 5100 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5101 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5102 SE->ConstantEvolutionLoopExitValue.erase(PN); 5103 SE->Scalars.erase(getValPtr()); 5104 // this now dangles! 5105} 5106 5107void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5108 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5109 5110 // Forget all the expressions associated with users of the old value, 5111 // so that future queries will recompute the expressions using the new 5112 // value. 5113 SmallVector<User *, 16> Worklist; 5114 SmallPtrSet<User *, 8> Visited; 5115 Value *Old = getValPtr(); 5116 bool DeleteOld = false; 5117 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5118 UI != UE; ++UI) 5119 Worklist.push_back(*UI); 5120 while (!Worklist.empty()) { 5121 User *U = Worklist.pop_back_val(); 5122 // Deleting the Old value will cause this to dangle. Postpone 5123 // that until everything else is done. 5124 if (U == Old) { 5125 DeleteOld = true; 5126 continue; 5127 } 5128 if (!Visited.insert(U)) 5129 continue; 5130 if (PHINode *PN = dyn_cast<PHINode>(U)) 5131 SE->ConstantEvolutionLoopExitValue.erase(PN); 5132 SE->Scalars.erase(U); 5133 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5134 UI != UE; ++UI) 5135 Worklist.push_back(*UI); 5136 } 5137 // Delete the Old value if it (indirectly) references itself. 5138 if (DeleteOld) { 5139 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5140 SE->ConstantEvolutionLoopExitValue.erase(PN); 5141 SE->Scalars.erase(Old); 5142 // this now dangles! 5143 } 5144 // this may dangle! 5145} 5146 5147ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5148 : CallbackVH(V), SE(se) {} 5149 5150//===----------------------------------------------------------------------===// 5151// ScalarEvolution Class Implementation 5152//===----------------------------------------------------------------------===// 5153 5154FunctionPass *createScalarEvolutionPass() { return new ScalarEvolution(); } 5155 5156ScalarEvolution::ScalarEvolution() 5157 : FunctionPass(&ID) { 5158} 5159 5160bool ScalarEvolution::runOnFunction(Function &F) { 5161 this->F = &F; 5162 LI = &getAnalysis<LoopInfo>(); 5163 TD = getAnalysisIfAvailable<TargetData>(); 5164 return false; 5165} 5166 5167void ScalarEvolution::releaseMemory() { 5168 Scalars.clear(); 5169 BackedgeTakenCounts.clear(); 5170 ConstantEvolutionLoopExitValue.clear(); 5171 ValuesAtScopes.clear(); 5172 UniqueSCEVs.clear(); 5173 SCEVAllocator.Reset(); 5174} 5175 5176void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5177 AU.setPreservesAll(); 5178 AU.addRequiredTransitive<LoopInfo>(); 5179} 5180 5181bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5182 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5183} 5184 5185static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5186 const Loop *L) { 5187 // Print all inner loops first 5188 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5189 PrintLoopInfo(OS, SE, *I); 5190 5191 OS << "Loop " << L->getHeader()->getName() << ": "; 5192 5193 SmallVector<BasicBlock*, 8> ExitBlocks; 5194 L->getExitBlocks(ExitBlocks); 5195 if (ExitBlocks.size() != 1) 5196 OS << "<multiple exits> "; 5197 5198 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5199 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5200 } else { 5201 OS << "Unpredictable backedge-taken count. "; 5202 } 5203 5204 OS << "\n"; 5205 OS << "Loop " << L->getHeader()->getName() << ": "; 5206 5207 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5208 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5209 } else { 5210 OS << "Unpredictable max backedge-taken count. "; 5211 } 5212 5213 OS << "\n"; 5214} 5215 5216void ScalarEvolution::print(raw_ostream &OS, const Module* ) const { 5217 // ScalarEvolution's implementaiton of the print method is to print 5218 // out SCEV values of all instructions that are interesting. Doing 5219 // this potentially causes it to create new SCEV objects though, 5220 // which technically conflicts with the const qualifier. This isn't 5221 // observable from outside the class though, so casting away the 5222 // const isn't dangerous. 5223 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this); 5224 5225 OS << "Classifying expressions for: " << F->getName() << "\n"; 5226 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5227 if (isSCEVable(I->getType())) { 5228 OS << *I << '\n'; 5229 OS << " --> "; 5230 const SCEV *SV = SE.getSCEV(&*I); 5231 SV->print(OS); 5232 5233 const Loop *L = LI->getLoopFor((*I).getParent()); 5234 5235 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5236 if (AtUse != SV) { 5237 OS << " --> "; 5238 AtUse->print(OS); 5239 } 5240 5241 if (L) { 5242 OS << "\t\t" "Exits: "; 5243 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5244 if (!ExitValue->isLoopInvariant(L)) { 5245 OS << "<<Unknown>>"; 5246 } else { 5247 OS << *ExitValue; 5248 } 5249 } 5250 5251 OS << "\n"; 5252 } 5253 5254 OS << "Determining loop execution counts for: " << F->getName() << "\n"; 5255 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5256 PrintLoopInfo(OS, &SE, *I); 5257} 5258 5259