ScalarEvolution.cpp revision 605c14fb115e89a2bad97761ae57b55e8c28ffff
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/Debug.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106static RegisterPass<ScalarEvolution> 107R("scalar-evolution", "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(dbgs()); 122 dbgs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), 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 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 192 return getConstant(ConstantInt::get(ITy, 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 FoldingSetNodeIDRef 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 FoldingSetNodeIDRef ID, 214 const SCEV *op, const Type *ty) 215 : SCEVCastExpr(ID, scTruncate, op, ty) { 216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 217 (Ty->isIntegerTy() || Ty->isPointerTy()) && 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 FoldingSetNodeIDRef ID, 226 const SCEV *op, const Type *ty) 227 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 229 (Ty->isIntegerTy() || Ty->isPointerTy()) && 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 FoldingSetNodeIDRef ID, 238 const SCEV *op, const Type *ty) 239 : SCEVCastExpr(ID, scSignExtend, op, ty) { 240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 241 (Ty->isIntegerTy() || Ty->isPointerTy()) && 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 const char *OpStr = getOperationStr(); 251 OS << "("; 252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 253 OS << **I; 254 if (next(I) != E) 255 OS << OpStr; 256 } 257 OS << ")"; 258} 259 260bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 262 if (!getOperand(i)->dominates(BB, DT)) 263 return false; 264 } 265 return true; 266} 267 268bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 269 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 270 if (!getOperand(i)->properlyDominates(BB, DT)) 271 return false; 272 } 273 return true; 274} 275 276bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 277 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 278} 279 280bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 281 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 282} 283 284void SCEVUDivExpr::print(raw_ostream &OS) const { 285 OS << "(" << *LHS << " /u " << *RHS << ")"; 286} 287 288const Type *SCEVUDivExpr::getType() const { 289 // In most cases the types of LHS and RHS will be the same, but in some 290 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 291 // depend on the type for correctness, but handling types carefully can 292 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 293 // a pointer type than the RHS, so use the RHS' type here. 294 return RHS->getType(); 295} 296 297bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 298 // Add recurrences are never invariant in the function-body (null loop). 299 if (!QueryLoop) 300 return false; 301 302 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 303 if (QueryLoop->contains(L)) 304 return false; 305 306 // This recurrence is variant w.r.t. QueryLoop if any of its operands 307 // are variant. 308 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 309 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 310 return false; 311 312 // Otherwise it's loop-invariant. 313 return true; 314} 315 316bool 317SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 318 return DT->dominates(L->getHeader(), BB) && 319 SCEVNAryExpr::dominates(BB, DT); 320} 321 322bool 323SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 324 // This uses a "dominates" query instead of "properly dominates" query because 325 // the instruction which produces the addrec's value is a PHI, and a PHI 326 // effectively properly dominates its entire containing block. 327 return DT->dominates(L->getHeader(), BB) && 328 SCEVNAryExpr::properlyDominates(BB, DT); 329} 330 331void SCEVAddRecExpr::print(raw_ostream &OS) const { 332 OS << "{" << *Operands[0]; 333 for (unsigned i = 1, e = NumOperands; i != e; ++i) 334 OS << ",+," << *Operands[i]; 335 OS << "}<"; 336 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 337 OS << ">"; 338} 339 340bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 341 // All non-instruction values are loop invariant. All instructions are loop 342 // invariant if they are not contained in the specified loop. 343 // Instructions are never considered invariant in the function body 344 // (null loop) because they are defined within the "loop". 345 if (Instruction *I = dyn_cast<Instruction>(V)) 346 return L && !L->contains(I); 347 return true; 348} 349 350bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 351 if (Instruction *I = dyn_cast<Instruction>(getValue())) 352 return DT->dominates(I->getParent(), BB); 353 return true; 354} 355 356bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 357 if (Instruction *I = dyn_cast<Instruction>(getValue())) 358 return DT->properlyDominates(I->getParent(), BB); 359 return true; 360} 361 362const Type *SCEVUnknown::getType() const { 363 return V->getType(); 364} 365 366bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 367 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 368 if (VCE->getOpcode() == Instruction::PtrToInt) 369 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 370 if (CE->getOpcode() == Instruction::GetElementPtr && 371 CE->getOperand(0)->isNullValue() && 372 CE->getNumOperands() == 2) 373 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 374 if (CI->isOne()) { 375 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 376 ->getElementType(); 377 return true; 378 } 379 380 return false; 381} 382 383bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 384 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 385 if (VCE->getOpcode() == Instruction::PtrToInt) 386 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 387 if (CE->getOpcode() == Instruction::GetElementPtr && 388 CE->getOperand(0)->isNullValue()) { 389 const Type *Ty = 390 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 391 if (const StructType *STy = dyn_cast<StructType>(Ty)) 392 if (!STy->isPacked() && 393 CE->getNumOperands() == 3 && 394 CE->getOperand(1)->isNullValue()) { 395 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 396 if (CI->isOne() && 397 STy->getNumElements() == 2 && 398 STy->getElementType(0)->isIntegerTy(1)) { 399 AllocTy = STy->getElementType(1); 400 return true; 401 } 402 } 403 } 404 405 return false; 406} 407 408bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 409 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 410 if (VCE->getOpcode() == Instruction::PtrToInt) 411 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 412 if (CE->getOpcode() == Instruction::GetElementPtr && 413 CE->getNumOperands() == 3 && 414 CE->getOperand(0)->isNullValue() && 415 CE->getOperand(1)->isNullValue()) { 416 const Type *Ty = 417 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 418 // Ignore vector types here so that ScalarEvolutionExpander doesn't 419 // emit getelementptrs that index into vectors. 420 if (Ty->isStructTy() || Ty->isArrayTy()) { 421 CTy = Ty; 422 FieldNo = CE->getOperand(2); 423 return true; 424 } 425 } 426 427 return false; 428} 429 430void SCEVUnknown::print(raw_ostream &OS) const { 431 const Type *AllocTy; 432 if (isSizeOf(AllocTy)) { 433 OS << "sizeof(" << *AllocTy << ")"; 434 return; 435 } 436 if (isAlignOf(AllocTy)) { 437 OS << "alignof(" << *AllocTy << ")"; 438 return; 439 } 440 441 const Type *CTy; 442 Constant *FieldNo; 443 if (isOffsetOf(CTy, FieldNo)) { 444 OS << "offsetof(" << *CTy << ", "; 445 WriteAsOperand(OS, FieldNo, false); 446 OS << ")"; 447 return; 448 } 449 450 // Otherwise just print it normally. 451 WriteAsOperand(OS, V, false); 452} 453 454//===----------------------------------------------------------------------===// 455// SCEV Utilities 456//===----------------------------------------------------------------------===// 457 458static bool CompareTypes(const Type *A, const Type *B) { 459 if (A->getTypeID() != B->getTypeID()) 460 return A->getTypeID() < B->getTypeID(); 461 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 462 const IntegerType *BI = cast<IntegerType>(B); 463 return AI->getBitWidth() < BI->getBitWidth(); 464 } 465 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 466 const PointerType *BI = cast<PointerType>(B); 467 return CompareTypes(AI->getElementType(), BI->getElementType()); 468 } 469 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 470 const ArrayType *BI = cast<ArrayType>(B); 471 if (AI->getNumElements() != BI->getNumElements()) 472 return AI->getNumElements() < BI->getNumElements(); 473 return CompareTypes(AI->getElementType(), BI->getElementType()); 474 } 475 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 476 const VectorType *BI = cast<VectorType>(B); 477 if (AI->getNumElements() != BI->getNumElements()) 478 return AI->getNumElements() < BI->getNumElements(); 479 return CompareTypes(AI->getElementType(), BI->getElementType()); 480 } 481 if (const StructType *AI = dyn_cast<StructType>(A)) { 482 const StructType *BI = cast<StructType>(B); 483 if (AI->getNumElements() != BI->getNumElements()) 484 return AI->getNumElements() < BI->getNumElements(); 485 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 486 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 487 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 488 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 489 } 490 return false; 491} 492 493namespace { 494 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 495 /// than the complexity of the RHS. This comparator is used to canonicalize 496 /// expressions. 497 class SCEVComplexityCompare { 498 LoopInfo *LI; 499 public: 500 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 501 502 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 503 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 504 if (LHS == RHS) 505 return false; 506 507 // Primarily, sort the SCEVs by their getSCEVType(). 508 if (LHS->getSCEVType() != RHS->getSCEVType()) 509 return LHS->getSCEVType() < RHS->getSCEVType(); 510 511 // Aside from the getSCEVType() ordering, the particular ordering 512 // isn't very important except that it's beneficial to be consistent, 513 // so that (a + b) and (b + a) don't end up as different expressions. 514 515 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 516 // not as complete as it could be. 517 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 518 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 519 520 // Order pointer values after integer values. This helps SCEVExpander 521 // form GEPs. 522 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy()) 523 return false; 524 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy()) 525 return true; 526 527 // Compare getValueID values. 528 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 529 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 530 531 // Sort arguments by their position. 532 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 533 const Argument *RA = cast<Argument>(RU->getValue()); 534 return LA->getArgNo() < RA->getArgNo(); 535 } 536 537 // For instructions, compare their loop depth, and their opcode. 538 // This is pretty loose. 539 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 540 Instruction *RV = cast<Instruction>(RU->getValue()); 541 542 // Compare loop depths. 543 if (LI->getLoopDepth(LV->getParent()) != 544 LI->getLoopDepth(RV->getParent())) 545 return LI->getLoopDepth(LV->getParent()) < 546 LI->getLoopDepth(RV->getParent()); 547 548 // Compare opcodes. 549 if (LV->getOpcode() != RV->getOpcode()) 550 return LV->getOpcode() < RV->getOpcode(); 551 552 // Compare the number of operands. 553 if (LV->getNumOperands() != RV->getNumOperands()) 554 return LV->getNumOperands() < RV->getNumOperands(); 555 } 556 557 return false; 558 } 559 560 // Compare constant values. 561 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 562 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 563 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 564 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 565 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 566 } 567 568 // Compare addrec loop depths. 569 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 570 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 571 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 572 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 573 } 574 575 // Lexicographically compare n-ary expressions. 576 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 578 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 579 if (i >= RC->getNumOperands()) 580 return false; 581 if (operator()(LC->getOperand(i), RC->getOperand(i))) 582 return true; 583 if (operator()(RC->getOperand(i), LC->getOperand(i))) 584 return false; 585 } 586 return LC->getNumOperands() < RC->getNumOperands(); 587 } 588 589 // Lexicographically compare udiv expressions. 590 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 591 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 592 if (operator()(LC->getLHS(), RC->getLHS())) 593 return true; 594 if (operator()(RC->getLHS(), LC->getLHS())) 595 return false; 596 if (operator()(LC->getRHS(), RC->getRHS())) 597 return true; 598 if (operator()(RC->getRHS(), LC->getRHS())) 599 return false; 600 return false; 601 } 602 603 // Compare cast expressions by operand. 604 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 605 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 606 return operator()(LC->getOperand(), RC->getOperand()); 607 } 608 609 llvm_unreachable("Unknown SCEV kind!"); 610 return false; 611 } 612 }; 613} 614 615/// GroupByComplexity - Given a list of SCEV objects, order them by their 616/// complexity, and group objects of the same complexity together by value. 617/// When this routine is finished, we know that any duplicates in the vector are 618/// consecutive and that complexity is monotonically increasing. 619/// 620/// Note that we go take special precautions to ensure that we get deterministic 621/// results from this routine. In other words, we don't want the results of 622/// this to depend on where the addresses of various SCEV objects happened to 623/// land in memory. 624/// 625static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 626 LoopInfo *LI) { 627 if (Ops.size() < 2) return; // Noop 628 if (Ops.size() == 2) { 629 // This is the common case, which also happens to be trivially simple. 630 // Special case it. 631 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 632 std::swap(Ops[0], Ops[1]); 633 return; 634 } 635 636 // Do the rough sort by complexity. 637 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 638 639 // Now that we are sorted by complexity, group elements of the same 640 // complexity. Note that this is, at worst, N^2, but the vector is likely to 641 // be extremely short in practice. Note that we take this approach because we 642 // do not want to depend on the addresses of the objects we are grouping. 643 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 644 const SCEV *S = Ops[i]; 645 unsigned Complexity = S->getSCEVType(); 646 647 // If there are any objects of the same complexity and same value as this 648 // one, group them. 649 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 650 if (Ops[j] == S) { // Found a duplicate. 651 // Move it to immediately after i'th element. 652 std::swap(Ops[i+1], Ops[j]); 653 ++i; // no need to rescan it. 654 if (i == e-2) return; // Done! 655 } 656 } 657 } 658} 659 660 661 662//===----------------------------------------------------------------------===// 663// Simple SCEV method implementations 664//===----------------------------------------------------------------------===// 665 666/// BinomialCoefficient - Compute BC(It, K). The result has width W. 667/// Assume, K > 0. 668static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 669 ScalarEvolution &SE, 670 const Type* ResultTy) { 671 // Handle the simplest case efficiently. 672 if (K == 1) 673 return SE.getTruncateOrZeroExtend(It, ResultTy); 674 675 // We are using the following formula for BC(It, K): 676 // 677 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 678 // 679 // Suppose, W is the bitwidth of the return value. We must be prepared for 680 // overflow. Hence, we must assure that the result of our computation is 681 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 682 // safe in modular arithmetic. 683 // 684 // However, this code doesn't use exactly that formula; the formula it uses 685 // is something like the following, where T is the number of factors of 2 in 686 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 687 // exponentiation: 688 // 689 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 690 // 691 // This formula is trivially equivalent to the previous formula. However, 692 // this formula can be implemented much more efficiently. The trick is that 693 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 694 // arithmetic. To do exact division in modular arithmetic, all we have 695 // to do is multiply by the inverse. Therefore, this step can be done at 696 // width W. 697 // 698 // The next issue is how to safely do the division by 2^T. The way this 699 // is done is by doing the multiplication step at a width of at least W + T 700 // bits. This way, the bottom W+T bits of the product are accurate. Then, 701 // when we perform the division by 2^T (which is equivalent to a right shift 702 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 703 // truncated out after the division by 2^T. 704 // 705 // In comparison to just directly using the first formula, this technique 706 // is much more efficient; using the first formula requires W * K bits, 707 // but this formula less than W + K bits. Also, the first formula requires 708 // a division step, whereas this formula only requires multiplies and shifts. 709 // 710 // It doesn't matter whether the subtraction step is done in the calculation 711 // width or the input iteration count's width; if the subtraction overflows, 712 // the result must be zero anyway. We prefer here to do it in the width of 713 // the induction variable because it helps a lot for certain cases; CodeGen 714 // isn't smart enough to ignore the overflow, which leads to much less 715 // efficient code if the width of the subtraction is wider than the native 716 // register width. 717 // 718 // (It's possible to not widen at all by pulling out factors of 2 before 719 // the multiplication; for example, K=2 can be calculated as 720 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 721 // extra arithmetic, so it's not an obvious win, and it gets 722 // much more complicated for K > 3.) 723 724 // Protection from insane SCEVs; this bound is conservative, 725 // but it probably doesn't matter. 726 if (K > 1000) 727 return SE.getCouldNotCompute(); 728 729 unsigned W = SE.getTypeSizeInBits(ResultTy); 730 731 // Calculate K! / 2^T and T; we divide out the factors of two before 732 // multiplying for calculating K! / 2^T to avoid overflow. 733 // Other overflow doesn't matter because we only care about the bottom 734 // W bits of the result. 735 APInt OddFactorial(W, 1); 736 unsigned T = 1; 737 for (unsigned i = 3; i <= K; ++i) { 738 APInt Mult(W, i); 739 unsigned TwoFactors = Mult.countTrailingZeros(); 740 T += TwoFactors; 741 Mult = Mult.lshr(TwoFactors); 742 OddFactorial *= Mult; 743 } 744 745 // We need at least W + T bits for the multiplication step 746 unsigned CalculationBits = W + T; 747 748 // Calculate 2^T, at width T+W. 749 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 750 751 // Calculate the multiplicative inverse of K! / 2^T; 752 // this multiplication factor will perform the exact division by 753 // K! / 2^T. 754 APInt Mod = APInt::getSignedMinValue(W+1); 755 APInt MultiplyFactor = OddFactorial.zext(W+1); 756 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 757 MultiplyFactor = MultiplyFactor.trunc(W); 758 759 // Calculate the product, at width T+W 760 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 761 CalculationBits); 762 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 763 for (unsigned i = 1; i != K; ++i) { 764 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 765 Dividend = SE.getMulExpr(Dividend, 766 SE.getTruncateOrZeroExtend(S, CalculationTy)); 767 } 768 769 // Divide by 2^T 770 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 771 772 // Truncate the result, and divide by K! / 2^T. 773 774 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 775 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 776} 777 778/// evaluateAtIteration - Return the value of this chain of recurrences at 779/// the specified iteration number. We can evaluate this recurrence by 780/// multiplying each element in the chain by the binomial coefficient 781/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 782/// 783/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 784/// 785/// where BC(It, k) stands for binomial coefficient. 786/// 787const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 788 ScalarEvolution &SE) const { 789 const SCEV *Result = getStart(); 790 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 791 // The computation is correct in the face of overflow provided that the 792 // multiplication is performed _after_ the evaluation of the binomial 793 // coefficient. 794 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 795 if (isa<SCEVCouldNotCompute>(Coeff)) 796 return Coeff; 797 798 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 799 } 800 return Result; 801} 802 803//===----------------------------------------------------------------------===// 804// SCEV Expression folder implementations 805//===----------------------------------------------------------------------===// 806 807const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 808 const Type *Ty) { 809 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 810 "This is not a truncating conversion!"); 811 assert(isSCEVable(Ty) && 812 "This is not a conversion to a SCEVable type!"); 813 Ty = getEffectiveSCEVType(Ty); 814 815 FoldingSetNodeID ID; 816 ID.AddInteger(scTruncate); 817 ID.AddPointer(Op); 818 ID.AddPointer(Ty); 819 void *IP = 0; 820 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 821 822 // Fold if the operand is constant. 823 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 824 return getConstant( 825 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 826 827 // trunc(trunc(x)) --> trunc(x) 828 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 829 return getTruncateExpr(ST->getOperand(), Ty); 830 831 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 832 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 833 return getTruncateOrSignExtend(SS->getOperand(), Ty); 834 835 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 836 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 837 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 838 839 // If the input value is a chrec scev, truncate the chrec's operands. 840 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 841 SmallVector<const SCEV *, 4> Operands; 842 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 843 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 844 return getAddRecExpr(Operands, AddRec->getLoop()); 845 } 846 847 // The cast wasn't folded; create an explicit cast node. 848 // Recompute the insert position, as it may have been invalidated. 849 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 850 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 851 Op, Ty); 852 UniqueSCEVs.InsertNode(S, IP); 853 return S; 854} 855 856const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 857 const Type *Ty) { 858 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 859 "This is not an extending conversion!"); 860 assert(isSCEVable(Ty) && 861 "This is not a conversion to a SCEVable type!"); 862 Ty = getEffectiveSCEVType(Ty); 863 864 // Fold if the operand is constant. 865 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 866 const Type *IntTy = getEffectiveSCEVType(Ty); 867 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 868 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 869 return getConstant(cast<ConstantInt>(C)); 870 } 871 872 // zext(zext(x)) --> zext(x) 873 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 874 return getZeroExtendExpr(SZ->getOperand(), Ty); 875 876 // Before doing any expensive analysis, check to see if we've already 877 // computed a SCEV for this Op and Ty. 878 FoldingSetNodeID ID; 879 ID.AddInteger(scZeroExtend); 880 ID.AddPointer(Op); 881 ID.AddPointer(Ty); 882 void *IP = 0; 883 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 884 885 // If the input value is a chrec scev, and we can prove that the value 886 // did not overflow the old, smaller, value, we can zero extend all of the 887 // operands (often constants). This allows analysis of something like 888 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 889 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 890 if (AR->isAffine()) { 891 const SCEV *Start = AR->getStart(); 892 const SCEV *Step = AR->getStepRecurrence(*this); 893 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 894 const Loop *L = AR->getLoop(); 895 896 // If we have special knowledge that this addrec won't overflow, 897 // we don't need to do any further analysis. 898 if (AR->hasNoUnsignedWrap()) 899 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 900 getZeroExtendExpr(Step, Ty), 901 L); 902 903 // Check whether the backedge-taken count is SCEVCouldNotCompute. 904 // Note that this serves two purposes: It filters out loops that are 905 // simply not analyzable, and it covers the case where this code is 906 // being called from within backedge-taken count analysis, such that 907 // attempting to ask for the backedge-taken count would likely result 908 // in infinite recursion. In the later case, the analysis code will 909 // cope with a conservative value, and it will take care to purge 910 // that value once it has finished. 911 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 912 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 913 // Manually compute the final value for AR, checking for 914 // overflow. 915 916 // Check whether the backedge-taken count can be losslessly casted to 917 // the addrec's type. The count is always unsigned. 918 const SCEV *CastedMaxBECount = 919 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 920 const SCEV *RecastedMaxBECount = 921 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 922 if (MaxBECount == RecastedMaxBECount) { 923 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 924 // Check whether Start+Step*MaxBECount has no unsigned overflow. 925 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 926 const SCEV *Add = getAddExpr(Start, ZMul); 927 const SCEV *OperandExtendedAdd = 928 getAddExpr(getZeroExtendExpr(Start, WideTy), 929 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 930 getZeroExtendExpr(Step, WideTy))); 931 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 932 // Return the expression with the addrec on the outside. 933 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 934 getZeroExtendExpr(Step, Ty), 935 L); 936 937 // Similar to above, only this time treat the step value as signed. 938 // This covers loops that count down. 939 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 940 Add = getAddExpr(Start, SMul); 941 OperandExtendedAdd = 942 getAddExpr(getZeroExtendExpr(Start, WideTy), 943 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 944 getSignExtendExpr(Step, WideTy))); 945 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 946 // Return the expression with the addrec on the outside. 947 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 948 getSignExtendExpr(Step, Ty), 949 L); 950 } 951 952 // If the backedge is guarded by a comparison with the pre-inc value 953 // the addrec is safe. Also, if the entry is guarded by a comparison 954 // with the start value and the backedge is guarded by a comparison 955 // with the post-inc value, the addrec is safe. 956 if (isKnownPositive(Step)) { 957 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 958 getUnsignedRange(Step).getUnsignedMax()); 959 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 960 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 961 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 962 AR->getPostIncExpr(*this), N))) 963 // Return the expression with the addrec on the outside. 964 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 965 getZeroExtendExpr(Step, Ty), 966 L); 967 } else if (isKnownNegative(Step)) { 968 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 969 getSignedRange(Step).getSignedMin()); 970 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 971 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 972 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 973 AR->getPostIncExpr(*this), N))) 974 // Return the expression with the addrec on the outside. 975 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 976 getSignExtendExpr(Step, Ty), 977 L); 978 } 979 } 980 } 981 982 // The cast wasn't folded; create an explicit cast node. 983 // Recompute the insert position, as it may have been invalidated. 984 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 985 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 986 Op, Ty); 987 UniqueSCEVs.InsertNode(S, IP); 988 return S; 989} 990 991const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 992 const Type *Ty) { 993 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 994 "This is not an extending conversion!"); 995 assert(isSCEVable(Ty) && 996 "This is not a conversion to a SCEVable type!"); 997 Ty = getEffectiveSCEVType(Ty); 998 999 // Fold if the operand is constant. 1000 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 1001 const Type *IntTy = getEffectiveSCEVType(Ty); 1002 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 1003 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 1004 return getConstant(cast<ConstantInt>(C)); 1005 } 1006 1007 // sext(sext(x)) --> sext(x) 1008 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1009 return getSignExtendExpr(SS->getOperand(), Ty); 1010 1011 // Before doing any expensive analysis, check to see if we've already 1012 // computed a SCEV for this Op and Ty. 1013 FoldingSetNodeID ID; 1014 ID.AddInteger(scSignExtend); 1015 ID.AddPointer(Op); 1016 ID.AddPointer(Ty); 1017 void *IP = 0; 1018 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1019 1020 // If the input value is a chrec scev, and we can prove that the value 1021 // did not overflow the old, smaller, value, we can sign extend all of the 1022 // operands (often constants). This allows analysis of something like 1023 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1024 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1025 if (AR->isAffine()) { 1026 const SCEV *Start = AR->getStart(); 1027 const SCEV *Step = AR->getStepRecurrence(*this); 1028 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1029 const Loop *L = AR->getLoop(); 1030 1031 // If we have special knowledge that this addrec won't overflow, 1032 // we don't need to do any further analysis. 1033 if (AR->hasNoSignedWrap()) 1034 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1035 getSignExtendExpr(Step, Ty), 1036 L); 1037 1038 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1039 // Note that this serves two purposes: It filters out loops that are 1040 // simply not analyzable, and it covers the case where this code is 1041 // being called from within backedge-taken count analysis, such that 1042 // attempting to ask for the backedge-taken count would likely result 1043 // in infinite recursion. In the later case, the analysis code will 1044 // cope with a conservative value, and it will take care to purge 1045 // that value once it has finished. 1046 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1047 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1048 // Manually compute the final value for AR, checking for 1049 // overflow. 1050 1051 // Check whether the backedge-taken count can be losslessly casted to 1052 // the addrec's type. The count is always unsigned. 1053 const SCEV *CastedMaxBECount = 1054 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1055 const SCEV *RecastedMaxBECount = 1056 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1057 if (MaxBECount == RecastedMaxBECount) { 1058 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1059 // Check whether Start+Step*MaxBECount has no signed overflow. 1060 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1061 const SCEV *Add = getAddExpr(Start, SMul); 1062 const SCEV *OperandExtendedAdd = 1063 getAddExpr(getSignExtendExpr(Start, WideTy), 1064 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1065 getSignExtendExpr(Step, WideTy))); 1066 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1067 // Return the expression with the addrec on the outside. 1068 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1069 getSignExtendExpr(Step, Ty), 1070 L); 1071 1072 // Similar to above, only this time treat the step value as unsigned. 1073 // This covers loops that count up with an unsigned step. 1074 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1075 Add = getAddExpr(Start, UMul); 1076 OperandExtendedAdd = 1077 getAddExpr(getSignExtendExpr(Start, WideTy), 1078 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1079 getZeroExtendExpr(Step, WideTy))); 1080 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1081 // Return the expression with the addrec on the outside. 1082 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1083 getZeroExtendExpr(Step, Ty), 1084 L); 1085 } 1086 1087 // If the backedge is guarded by a comparison with the pre-inc value 1088 // the addrec is safe. Also, if the entry is guarded by a comparison 1089 // with the start value and the backedge is guarded by a comparison 1090 // with the post-inc value, the addrec is safe. 1091 if (isKnownPositive(Step)) { 1092 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1093 getSignedRange(Step).getSignedMax()); 1094 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1095 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1096 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1097 AR->getPostIncExpr(*this), N))) 1098 // Return the expression with the addrec on the outside. 1099 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1100 getSignExtendExpr(Step, Ty), 1101 L); 1102 } else if (isKnownNegative(Step)) { 1103 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1104 getSignedRange(Step).getSignedMin()); 1105 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1106 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1107 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1108 AR->getPostIncExpr(*this), N))) 1109 // Return the expression with the addrec on the outside. 1110 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1111 getSignExtendExpr(Step, Ty), 1112 L); 1113 } 1114 } 1115 } 1116 1117 // The cast wasn't folded; create an explicit cast node. 1118 // Recompute the insert position, as it may have been invalidated. 1119 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1120 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1121 Op, Ty); 1122 UniqueSCEVs.InsertNode(S, IP); 1123 return S; 1124} 1125 1126/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1127/// unspecified bits out to the given type. 1128/// 1129const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1130 const Type *Ty) { 1131 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1132 "This is not an extending conversion!"); 1133 assert(isSCEVable(Ty) && 1134 "This is not a conversion to a SCEVable type!"); 1135 Ty = getEffectiveSCEVType(Ty); 1136 1137 // Sign-extend negative constants. 1138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1139 if (SC->getValue()->getValue().isNegative()) 1140 return getSignExtendExpr(Op, Ty); 1141 1142 // Peel off a truncate cast. 1143 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1144 const SCEV *NewOp = T->getOperand(); 1145 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1146 return getAnyExtendExpr(NewOp, Ty); 1147 return getTruncateOrNoop(NewOp, Ty); 1148 } 1149 1150 // Next try a zext cast. If the cast is folded, use it. 1151 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1152 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1153 return ZExt; 1154 1155 // Next try a sext cast. If the cast is folded, use it. 1156 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1157 if (!isa<SCEVSignExtendExpr>(SExt)) 1158 return SExt; 1159 1160 // Force the cast to be folded into the operands of an addrec. 1161 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1162 SmallVector<const SCEV *, 4> Ops; 1163 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1164 I != E; ++I) 1165 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1166 return getAddRecExpr(Ops, AR->getLoop()); 1167 } 1168 1169 // If the expression is obviously signed, use the sext cast value. 1170 if (isa<SCEVSMaxExpr>(Op)) 1171 return SExt; 1172 1173 // Absent any other information, use the zext cast value. 1174 return ZExt; 1175} 1176 1177/// CollectAddOperandsWithScales - Process the given Ops list, which is 1178/// a list of operands to be added under the given scale, update the given 1179/// map. This is a helper function for getAddRecExpr. As an example of 1180/// what it does, given a sequence of operands that would form an add 1181/// expression like this: 1182/// 1183/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1184/// 1185/// where A and B are constants, update the map with these values: 1186/// 1187/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1188/// 1189/// and add 13 + A*B*29 to AccumulatedConstant. 1190/// This will allow getAddRecExpr to produce this: 1191/// 1192/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1193/// 1194/// This form often exposes folding opportunities that are hidden in 1195/// the original operand list. 1196/// 1197/// Return true iff it appears that any interesting folding opportunities 1198/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1199/// the common case where no interesting opportunities are present, and 1200/// is also used as a check to avoid infinite recursion. 1201/// 1202static bool 1203CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1204 SmallVector<const SCEV *, 8> &NewOps, 1205 APInt &AccumulatedConstant, 1206 const SCEV *const *Ops, size_t NumOperands, 1207 const APInt &Scale, 1208 ScalarEvolution &SE) { 1209 bool Interesting = false; 1210 1211 // Iterate over the add operands. They are sorted, with constants first. 1212 unsigned i = 0; 1213 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1214 ++i; 1215 // Pull a buried constant out to the outside. 1216 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1217 Interesting = true; 1218 AccumulatedConstant += Scale * C->getValue()->getValue(); 1219 } 1220 1221 // Next comes everything else. We're especially interested in multiplies 1222 // here, but they're in the middle, so just visit the rest with one loop. 1223 for (; i != NumOperands; ++i) { 1224 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1225 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1226 APInt NewScale = 1227 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1228 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1229 // A multiplication of a constant with another add; recurse. 1230 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1231 Interesting |= 1232 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1233 Add->op_begin(), Add->getNumOperands(), 1234 NewScale, SE); 1235 } else { 1236 // A multiplication of a constant with some other value. Update 1237 // the map. 1238 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1239 const SCEV *Key = SE.getMulExpr(MulOps); 1240 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1241 M.insert(std::make_pair(Key, NewScale)); 1242 if (Pair.second) { 1243 NewOps.push_back(Pair.first->first); 1244 } else { 1245 Pair.first->second += NewScale; 1246 // The map already had an entry for this value, which may indicate 1247 // a folding opportunity. 1248 Interesting = true; 1249 } 1250 } 1251 } else { 1252 // An ordinary operand. Update the map. 1253 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1254 M.insert(std::make_pair(Ops[i], Scale)); 1255 if (Pair.second) { 1256 NewOps.push_back(Pair.first->first); 1257 } else { 1258 Pair.first->second += Scale; 1259 // The map already had an entry for this value, which may indicate 1260 // a folding opportunity. 1261 Interesting = true; 1262 } 1263 } 1264 } 1265 1266 return Interesting; 1267} 1268 1269namespace { 1270 struct APIntCompare { 1271 bool operator()(const APInt &LHS, const APInt &RHS) const { 1272 return LHS.ult(RHS); 1273 } 1274 }; 1275} 1276 1277/// getAddExpr - Get a canonical add expression, or something simpler if 1278/// possible. 1279const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1280 bool HasNUW, bool HasNSW) { 1281 assert(!Ops.empty() && "Cannot get empty add!"); 1282 if (Ops.size() == 1) return Ops[0]; 1283#ifndef NDEBUG 1284 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1285 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1286 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1287 "SCEVAddExpr operand types don't match!"); 1288#endif 1289 1290 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1291 if (!HasNUW && HasNSW) { 1292 bool All = true; 1293 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1294 if (!isKnownNonNegative(Ops[i])) { 1295 All = false; 1296 break; 1297 } 1298 if (All) HasNUW = true; 1299 } 1300 1301 // Sort by complexity, this groups all similar expression types together. 1302 GroupByComplexity(Ops, LI); 1303 1304 // If there are any constants, fold them together. 1305 unsigned Idx = 0; 1306 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1307 ++Idx; 1308 assert(Idx < Ops.size()); 1309 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1310 // We found two constants, fold them together! 1311 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1312 RHSC->getValue()->getValue()); 1313 if (Ops.size() == 2) return Ops[0]; 1314 Ops.erase(Ops.begin()+1); // Erase the folded element 1315 LHSC = cast<SCEVConstant>(Ops[0]); 1316 } 1317 1318 // If we are left with a constant zero being added, strip it off. 1319 if (LHSC->getValue()->isZero()) { 1320 Ops.erase(Ops.begin()); 1321 --Idx; 1322 } 1323 1324 if (Ops.size() == 1) return Ops[0]; 1325 } 1326 1327 // Okay, check to see if the same value occurs in the operand list twice. If 1328 // so, merge them together into an multiply expression. Since we sorted the 1329 // list, these values are required to be adjacent. 1330 const Type *Ty = Ops[0]->getType(); 1331 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1332 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1333 // Found a match, merge the two values into a multiply, and add any 1334 // remaining values to the result. 1335 const SCEV *Two = getConstant(Ty, 2); 1336 const SCEV *Mul = getMulExpr(Ops[i], Two); 1337 if (Ops.size() == 2) 1338 return Mul; 1339 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1340 Ops.push_back(Mul); 1341 return getAddExpr(Ops, HasNUW, HasNSW); 1342 } 1343 1344 // Check for truncates. If all the operands are truncated from the same 1345 // type, see if factoring out the truncate would permit the result to be 1346 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1347 // if the contents of the resulting outer trunc fold to something simple. 1348 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1349 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1350 const Type *DstType = Trunc->getType(); 1351 const Type *SrcType = Trunc->getOperand()->getType(); 1352 SmallVector<const SCEV *, 8> LargeOps; 1353 bool Ok = true; 1354 // Check all the operands to see if they can be represented in the 1355 // source type of the truncate. 1356 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1357 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1358 if (T->getOperand()->getType() != SrcType) { 1359 Ok = false; 1360 break; 1361 } 1362 LargeOps.push_back(T->getOperand()); 1363 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1364 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1365 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1366 SmallVector<const SCEV *, 8> LargeMulOps; 1367 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1368 if (const SCEVTruncateExpr *T = 1369 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1370 if (T->getOperand()->getType() != SrcType) { 1371 Ok = false; 1372 break; 1373 } 1374 LargeMulOps.push_back(T->getOperand()); 1375 } else if (const SCEVConstant *C = 1376 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1377 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1378 } else { 1379 Ok = false; 1380 break; 1381 } 1382 } 1383 if (Ok) 1384 LargeOps.push_back(getMulExpr(LargeMulOps)); 1385 } else { 1386 Ok = false; 1387 break; 1388 } 1389 } 1390 if (Ok) { 1391 // Evaluate the expression in the larger type. 1392 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1393 // If it folds to something simple, use it. Otherwise, don't. 1394 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1395 return getTruncateExpr(Fold, DstType); 1396 } 1397 } 1398 1399 // Skip past any other cast SCEVs. 1400 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1401 ++Idx; 1402 1403 // If there are add operands they would be next. 1404 if (Idx < Ops.size()) { 1405 bool DeletedAdd = false; 1406 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1407 // If we have an add, expand the add operands onto the end of the operands 1408 // list. 1409 Ops.erase(Ops.begin()+Idx); 1410 Ops.append(Add->op_begin(), Add->op_end()); 1411 DeletedAdd = true; 1412 } 1413 1414 // If we deleted at least one add, we added operands to the end of the list, 1415 // and they are not necessarily sorted. Recurse to resort and resimplify 1416 // any operands we just acquired. 1417 if (DeletedAdd) 1418 return getAddExpr(Ops); 1419 } 1420 1421 // Skip over the add expression until we get to a multiply. 1422 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1423 ++Idx; 1424 1425 // Check to see if there are any folding opportunities present with 1426 // operands multiplied by constant values. 1427 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1428 uint64_t BitWidth = getTypeSizeInBits(Ty); 1429 DenseMap<const SCEV *, APInt> M; 1430 SmallVector<const SCEV *, 8> NewOps; 1431 APInt AccumulatedConstant(BitWidth, 0); 1432 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1433 Ops.data(), Ops.size(), 1434 APInt(BitWidth, 1), *this)) { 1435 // Some interesting folding opportunity is present, so its worthwhile to 1436 // re-generate the operands list. Group the operands by constant scale, 1437 // to avoid multiplying by the same constant scale multiple times. 1438 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1439 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1440 E = NewOps.end(); I != E; ++I) 1441 MulOpLists[M.find(*I)->second].push_back(*I); 1442 // Re-generate the operands list. 1443 Ops.clear(); 1444 if (AccumulatedConstant != 0) 1445 Ops.push_back(getConstant(AccumulatedConstant)); 1446 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1447 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1448 if (I->first != 0) 1449 Ops.push_back(getMulExpr(getConstant(I->first), 1450 getAddExpr(I->second))); 1451 if (Ops.empty()) 1452 return getConstant(Ty, 0); 1453 if (Ops.size() == 1) 1454 return Ops[0]; 1455 return getAddExpr(Ops); 1456 } 1457 } 1458 1459 // If we are adding something to a multiply expression, make sure the 1460 // something is not already an operand of the multiply. If so, merge it into 1461 // the multiply. 1462 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1463 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1464 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1465 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1466 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1467 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1468 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1469 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1470 if (Mul->getNumOperands() != 2) { 1471 // If the multiply has more than two operands, we must get the 1472 // Y*Z term. 1473 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1474 MulOps.erase(MulOps.begin()+MulOp); 1475 InnerMul = getMulExpr(MulOps); 1476 } 1477 const SCEV *One = getConstant(Ty, 1); 1478 const SCEV *AddOne = getAddExpr(InnerMul, One); 1479 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1480 if (Ops.size() == 2) return OuterMul; 1481 if (AddOp < Idx) { 1482 Ops.erase(Ops.begin()+AddOp); 1483 Ops.erase(Ops.begin()+Idx-1); 1484 } else { 1485 Ops.erase(Ops.begin()+Idx); 1486 Ops.erase(Ops.begin()+AddOp-1); 1487 } 1488 Ops.push_back(OuterMul); 1489 return getAddExpr(Ops); 1490 } 1491 1492 // Check this multiply against other multiplies being added together. 1493 for (unsigned OtherMulIdx = Idx+1; 1494 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1495 ++OtherMulIdx) { 1496 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1497 // If MulOp occurs in OtherMul, we can fold the two multiplies 1498 // together. 1499 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1500 OMulOp != e; ++OMulOp) 1501 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1502 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1503 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1504 if (Mul->getNumOperands() != 2) { 1505 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1506 Mul->op_end()); 1507 MulOps.erase(MulOps.begin()+MulOp); 1508 InnerMul1 = getMulExpr(MulOps); 1509 } 1510 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1511 if (OtherMul->getNumOperands() != 2) { 1512 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1513 OtherMul->op_end()); 1514 MulOps.erase(MulOps.begin()+OMulOp); 1515 InnerMul2 = getMulExpr(MulOps); 1516 } 1517 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1518 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1519 if (Ops.size() == 2) return OuterMul; 1520 Ops.erase(Ops.begin()+Idx); 1521 Ops.erase(Ops.begin()+OtherMulIdx-1); 1522 Ops.push_back(OuterMul); 1523 return getAddExpr(Ops); 1524 } 1525 } 1526 } 1527 } 1528 1529 // If there are any add recurrences in the operands list, see if any other 1530 // added values are loop invariant. If so, we can fold them into the 1531 // recurrence. 1532 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1533 ++Idx; 1534 1535 // Scan over all recurrences, trying to fold loop invariants into them. 1536 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1537 // Scan all of the other operands to this add and add them to the vector if 1538 // they are loop invariant w.r.t. the recurrence. 1539 SmallVector<const SCEV *, 8> LIOps; 1540 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1541 const Loop *AddRecLoop = AddRec->getLoop(); 1542 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1543 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1544 LIOps.push_back(Ops[i]); 1545 Ops.erase(Ops.begin()+i); 1546 --i; --e; 1547 } 1548 1549 // If we found some loop invariants, fold them into the recurrence. 1550 if (!LIOps.empty()) { 1551 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1552 LIOps.push_back(AddRec->getStart()); 1553 1554 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1555 AddRec->op_end()); 1556 AddRecOps[0] = getAddExpr(LIOps); 1557 1558 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition 1559 // is not associative so this isn't necessarily safe. 1560 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop); 1561 1562 // If all of the other operands were loop invariant, we are done. 1563 if (Ops.size() == 1) return NewRec; 1564 1565 // Otherwise, add the folded AddRec by the non-liv parts. 1566 for (unsigned i = 0;; ++i) 1567 if (Ops[i] == AddRec) { 1568 Ops[i] = NewRec; 1569 break; 1570 } 1571 return getAddExpr(Ops); 1572 } 1573 1574 // Okay, if there weren't any loop invariants to be folded, check to see if 1575 // there are multiple AddRec's with the same loop induction variable being 1576 // added together. If so, we can fold them. 1577 for (unsigned OtherIdx = Idx+1; 1578 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1579 if (OtherIdx != Idx) { 1580 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1581 if (AddRecLoop == OtherAddRec->getLoop()) { 1582 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1583 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1584 AddRec->op_end()); 1585 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1586 if (i >= NewOps.size()) { 1587 NewOps.append(OtherAddRec->op_begin()+i, 1588 OtherAddRec->op_end()); 1589 break; 1590 } 1591 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1592 } 1593 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop); 1594 1595 if (Ops.size() == 2) return NewAddRec; 1596 1597 Ops.erase(Ops.begin()+Idx); 1598 Ops.erase(Ops.begin()+OtherIdx-1); 1599 Ops.push_back(NewAddRec); 1600 return getAddExpr(Ops); 1601 } 1602 } 1603 1604 // Otherwise couldn't fold anything into this recurrence. Move onto the 1605 // next one. 1606 } 1607 1608 // Okay, it looks like we really DO need an add expr. Check to see if we 1609 // already have one, otherwise create a new one. 1610 FoldingSetNodeID ID; 1611 ID.AddInteger(scAddExpr); 1612 ID.AddInteger(Ops.size()); 1613 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1614 ID.AddPointer(Ops[i]); 1615 void *IP = 0; 1616 SCEVAddExpr *S = 1617 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1618 if (!S) { 1619 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1620 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1621 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1622 O, Ops.size()); 1623 UniqueSCEVs.InsertNode(S, IP); 1624 } 1625 if (HasNUW) S->setHasNoUnsignedWrap(true); 1626 if (HasNSW) S->setHasNoSignedWrap(true); 1627 return S; 1628} 1629 1630/// getMulExpr - Get a canonical multiply expression, or something simpler if 1631/// possible. 1632const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1633 bool HasNUW, bool HasNSW) { 1634 assert(!Ops.empty() && "Cannot get empty mul!"); 1635 if (Ops.size() == 1) return Ops[0]; 1636#ifndef NDEBUG 1637 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1638 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1639 getEffectiveSCEVType(Ops[0]->getType()) && 1640 "SCEVMulExpr operand types don't match!"); 1641#endif 1642 1643 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1644 if (!HasNUW && HasNSW) { 1645 bool All = true; 1646 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1647 if (!isKnownNonNegative(Ops[i])) { 1648 All = false; 1649 break; 1650 } 1651 if (All) HasNUW = true; 1652 } 1653 1654 // Sort by complexity, this groups all similar expression types together. 1655 GroupByComplexity(Ops, LI); 1656 1657 // If there are any constants, fold them together. 1658 unsigned Idx = 0; 1659 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1660 1661 // C1*(C2+V) -> C1*C2 + C1*V 1662 if (Ops.size() == 2) 1663 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1664 if (Add->getNumOperands() == 2 && 1665 isa<SCEVConstant>(Add->getOperand(0))) 1666 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1667 getMulExpr(LHSC, Add->getOperand(1))); 1668 1669 ++Idx; 1670 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1671 // We found two constants, fold them together! 1672 ConstantInt *Fold = ConstantInt::get(getContext(), 1673 LHSC->getValue()->getValue() * 1674 RHSC->getValue()->getValue()); 1675 Ops[0] = getConstant(Fold); 1676 Ops.erase(Ops.begin()+1); // Erase the folded element 1677 if (Ops.size() == 1) return Ops[0]; 1678 LHSC = cast<SCEVConstant>(Ops[0]); 1679 } 1680 1681 // If we are left with a constant one being multiplied, strip it off. 1682 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1683 Ops.erase(Ops.begin()); 1684 --Idx; 1685 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1686 // If we have a multiply of zero, it will always be zero. 1687 return Ops[0]; 1688 } else if (Ops[0]->isAllOnesValue()) { 1689 // If we have a mul by -1 of an add, try distributing the -1 among the 1690 // add operands. 1691 if (Ops.size() == 2) 1692 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1693 SmallVector<const SCEV *, 4> NewOps; 1694 bool AnyFolded = false; 1695 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1696 I != E; ++I) { 1697 const SCEV *Mul = getMulExpr(Ops[0], *I); 1698 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1699 NewOps.push_back(Mul); 1700 } 1701 if (AnyFolded) 1702 return getAddExpr(NewOps); 1703 } 1704 } 1705 1706 if (Ops.size() == 1) 1707 return Ops[0]; 1708 } 1709 1710 // Skip over the add expression until we get to a multiply. 1711 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1712 ++Idx; 1713 1714 // If there are mul operands inline them all into this expression. 1715 if (Idx < Ops.size()) { 1716 bool DeletedMul = false; 1717 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1718 // If we have an mul, expand the mul operands onto the end of the operands 1719 // list. 1720 Ops.erase(Ops.begin()+Idx); 1721 Ops.append(Mul->op_begin(), Mul->op_end()); 1722 DeletedMul = true; 1723 } 1724 1725 // If we deleted at least one mul, we added operands to the end of the list, 1726 // and they are not necessarily sorted. Recurse to resort and resimplify 1727 // any operands we just acquired. 1728 if (DeletedMul) 1729 return getMulExpr(Ops); 1730 } 1731 1732 // If there are any add recurrences in the operands list, see if any other 1733 // added values are loop invariant. If so, we can fold them into the 1734 // recurrence. 1735 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1736 ++Idx; 1737 1738 // Scan over all recurrences, trying to fold loop invariants into them. 1739 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1740 // Scan all of the other operands to this mul and add them to the vector if 1741 // they are loop invariant w.r.t. the recurrence. 1742 SmallVector<const SCEV *, 8> LIOps; 1743 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1744 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1745 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1746 LIOps.push_back(Ops[i]); 1747 Ops.erase(Ops.begin()+i); 1748 --i; --e; 1749 } 1750 1751 // If we found some loop invariants, fold them into the recurrence. 1752 if (!LIOps.empty()) { 1753 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1754 SmallVector<const SCEV *, 4> NewOps; 1755 NewOps.reserve(AddRec->getNumOperands()); 1756 const SCEV *Scale = getMulExpr(LIOps); 1757 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1758 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1759 1760 // It's tempting to propagate the NSW flag here, but nsw multiplication 1761 // is not associative so this isn't necessarily safe. 1762 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1763 HasNUW && AddRec->hasNoUnsignedWrap(), 1764 /*HasNSW=*/false); 1765 1766 // If all of the other operands were loop invariant, we are done. 1767 if (Ops.size() == 1) return NewRec; 1768 1769 // Otherwise, multiply the folded AddRec by the non-liv parts. 1770 for (unsigned i = 0;; ++i) 1771 if (Ops[i] == AddRec) { 1772 Ops[i] = NewRec; 1773 break; 1774 } 1775 return getMulExpr(Ops); 1776 } 1777 1778 // Okay, if there weren't any loop invariants to be folded, check to see if 1779 // there are multiple AddRec's with the same loop induction variable being 1780 // multiplied together. If so, we can fold them. 1781 for (unsigned OtherIdx = Idx+1; 1782 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1783 if (OtherIdx != Idx) { 1784 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1785 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1786 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1787 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1788 const SCEV *NewStart = getMulExpr(F->getStart(), 1789 G->getStart()); 1790 const SCEV *B = F->getStepRecurrence(*this); 1791 const SCEV *D = G->getStepRecurrence(*this); 1792 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1793 getMulExpr(G, B), 1794 getMulExpr(B, D)); 1795 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1796 F->getLoop()); 1797 if (Ops.size() == 2) return NewAddRec; 1798 1799 Ops.erase(Ops.begin()+Idx); 1800 Ops.erase(Ops.begin()+OtherIdx-1); 1801 Ops.push_back(NewAddRec); 1802 return getMulExpr(Ops); 1803 } 1804 } 1805 1806 // Otherwise couldn't fold anything into this recurrence. Move onto the 1807 // next one. 1808 } 1809 1810 // Okay, it looks like we really DO need an mul expr. Check to see if we 1811 // already have one, otherwise create a new one. 1812 FoldingSetNodeID ID; 1813 ID.AddInteger(scMulExpr); 1814 ID.AddInteger(Ops.size()); 1815 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1816 ID.AddPointer(Ops[i]); 1817 void *IP = 0; 1818 SCEVMulExpr *S = 1819 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1820 if (!S) { 1821 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1822 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1823 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1824 O, Ops.size()); 1825 UniqueSCEVs.InsertNode(S, IP); 1826 } 1827 if (HasNUW) S->setHasNoUnsignedWrap(true); 1828 if (HasNSW) S->setHasNoSignedWrap(true); 1829 return S; 1830} 1831 1832/// getUDivExpr - Get a canonical unsigned division expression, or something 1833/// simpler if possible. 1834const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1835 const SCEV *RHS) { 1836 assert(getEffectiveSCEVType(LHS->getType()) == 1837 getEffectiveSCEVType(RHS->getType()) && 1838 "SCEVUDivExpr operand types don't match!"); 1839 1840 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1841 if (RHSC->getValue()->equalsInt(1)) 1842 return LHS; // X udiv 1 --> x 1843 // If the denominator is zero, the result of the udiv is undefined. Don't 1844 // try to analyze it, because the resolution chosen here may differ from 1845 // the resolution chosen in other parts of the compiler. 1846 if (!RHSC->getValue()->isZero()) { 1847 // Determine if the division can be folded into the operands of 1848 // its operands. 1849 // TODO: Generalize this to non-constants by using known-bits information. 1850 const Type *Ty = LHS->getType(); 1851 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1852 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1853 // For non-power-of-two values, effectively round the value up to the 1854 // nearest power of two. 1855 if (!RHSC->getValue()->getValue().isPowerOf2()) 1856 ++MaxShiftAmt; 1857 const IntegerType *ExtTy = 1858 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1859 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1860 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1861 if (const SCEVConstant *Step = 1862 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1863 if (!Step->getValue()->getValue() 1864 .urem(RHSC->getValue()->getValue()) && 1865 getZeroExtendExpr(AR, ExtTy) == 1866 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1867 getZeroExtendExpr(Step, ExtTy), 1868 AR->getLoop())) { 1869 SmallVector<const SCEV *, 4> Operands; 1870 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1871 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1872 return getAddRecExpr(Operands, AR->getLoop()); 1873 } 1874 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1875 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1876 SmallVector<const SCEV *, 4> Operands; 1877 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1878 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1879 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1880 // Find an operand that's safely divisible. 1881 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1882 const SCEV *Op = M->getOperand(i); 1883 const SCEV *Div = getUDivExpr(Op, RHSC); 1884 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1885 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1886 M->op_end()); 1887 Operands[i] = Div; 1888 return getMulExpr(Operands); 1889 } 1890 } 1891 } 1892 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1893 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1894 SmallVector<const SCEV *, 4> Operands; 1895 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1896 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1897 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1898 Operands.clear(); 1899 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1900 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1901 if (isa<SCEVUDivExpr>(Op) || 1902 getMulExpr(Op, RHS) != A->getOperand(i)) 1903 break; 1904 Operands.push_back(Op); 1905 } 1906 if (Operands.size() == A->getNumOperands()) 1907 return getAddExpr(Operands); 1908 } 1909 } 1910 1911 // Fold if both operands are constant. 1912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1913 Constant *LHSCV = LHSC->getValue(); 1914 Constant *RHSCV = RHSC->getValue(); 1915 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1916 RHSCV))); 1917 } 1918 } 1919 } 1920 1921 FoldingSetNodeID ID; 1922 ID.AddInteger(scUDivExpr); 1923 ID.AddPointer(LHS); 1924 ID.AddPointer(RHS); 1925 void *IP = 0; 1926 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1927 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1928 LHS, RHS); 1929 UniqueSCEVs.InsertNode(S, IP); 1930 return S; 1931} 1932 1933 1934/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1935/// Simplify the expression as much as possible. 1936const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1937 const SCEV *Step, const Loop *L, 1938 bool HasNUW, bool HasNSW) { 1939 SmallVector<const SCEV *, 4> Operands; 1940 Operands.push_back(Start); 1941 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1942 if (StepChrec->getLoop() == L) { 1943 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 1944 return getAddRecExpr(Operands, L); 1945 } 1946 1947 Operands.push_back(Step); 1948 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1949} 1950 1951/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1952/// Simplify the expression as much as possible. 1953const SCEV * 1954ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1955 const Loop *L, 1956 bool HasNUW, bool HasNSW) { 1957 if (Operands.size() == 1) return Operands[0]; 1958#ifndef NDEBUG 1959 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1960 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1961 getEffectiveSCEVType(Operands[0]->getType()) && 1962 "SCEVAddRecExpr operand types don't match!"); 1963#endif 1964 1965 if (Operands.back()->isZero()) { 1966 Operands.pop_back(); 1967 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1968 } 1969 1970 // It's tempting to want to call getMaxBackedgeTakenCount count here and 1971 // use that information to infer NUW and NSW flags. However, computing a 1972 // BE count requires calling getAddRecExpr, so we may not yet have a 1973 // meaningful BE count at this point (and if we don't, we'd be stuck 1974 // with a SCEVCouldNotCompute as the cached BE count). 1975 1976 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1977 if (!HasNUW && HasNSW) { 1978 bool All = true; 1979 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1980 if (!isKnownNonNegative(Operands[i])) { 1981 All = false; 1982 break; 1983 } 1984 if (All) HasNUW = true; 1985 } 1986 1987 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1988 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1989 const Loop *NestedLoop = NestedAR->getLoop(); 1990 if (L->contains(NestedLoop->getHeader()) ? 1991 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1992 (!NestedLoop->contains(L->getHeader()) && 1993 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1994 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1995 NestedAR->op_end()); 1996 Operands[0] = NestedAR->getStart(); 1997 // AddRecs require their operands be loop-invariant with respect to their 1998 // loops. Don't perform this transformation if it would break this 1999 // requirement. 2000 bool AllInvariant = true; 2001 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2002 if (!Operands[i]->isLoopInvariant(L)) { 2003 AllInvariant = false; 2004 break; 2005 } 2006 if (AllInvariant) { 2007 NestedOperands[0] = getAddRecExpr(Operands, L); 2008 AllInvariant = true; 2009 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2010 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2011 AllInvariant = false; 2012 break; 2013 } 2014 if (AllInvariant) 2015 // Ok, both add recurrences are valid after the transformation. 2016 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2017 } 2018 // Reset Operands to its original state. 2019 Operands[0] = NestedAR; 2020 } 2021 } 2022 2023 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2024 // already have one, otherwise create a new one. 2025 FoldingSetNodeID ID; 2026 ID.AddInteger(scAddRecExpr); 2027 ID.AddInteger(Operands.size()); 2028 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2029 ID.AddPointer(Operands[i]); 2030 ID.AddPointer(L); 2031 void *IP = 0; 2032 SCEVAddRecExpr *S = 2033 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2034 if (!S) { 2035 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2036 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2037 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2038 O, Operands.size(), L); 2039 UniqueSCEVs.InsertNode(S, IP); 2040 } 2041 if (HasNUW) S->setHasNoUnsignedWrap(true); 2042 if (HasNSW) S->setHasNoSignedWrap(true); 2043 return S; 2044} 2045 2046const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2047 const SCEV *RHS) { 2048 SmallVector<const SCEV *, 2> Ops; 2049 Ops.push_back(LHS); 2050 Ops.push_back(RHS); 2051 return getSMaxExpr(Ops); 2052} 2053 2054const SCEV * 2055ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2056 assert(!Ops.empty() && "Cannot get empty smax!"); 2057 if (Ops.size() == 1) return Ops[0]; 2058#ifndef NDEBUG 2059 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2060 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2061 getEffectiveSCEVType(Ops[0]->getType()) && 2062 "SCEVSMaxExpr operand types don't match!"); 2063#endif 2064 2065 // Sort by complexity, this groups all similar expression types together. 2066 GroupByComplexity(Ops, LI); 2067 2068 // If there are any constants, fold them together. 2069 unsigned Idx = 0; 2070 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2071 ++Idx; 2072 assert(Idx < Ops.size()); 2073 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2074 // We found two constants, fold them together! 2075 ConstantInt *Fold = ConstantInt::get(getContext(), 2076 APIntOps::smax(LHSC->getValue()->getValue(), 2077 RHSC->getValue()->getValue())); 2078 Ops[0] = getConstant(Fold); 2079 Ops.erase(Ops.begin()+1); // Erase the folded element 2080 if (Ops.size() == 1) return Ops[0]; 2081 LHSC = cast<SCEVConstant>(Ops[0]); 2082 } 2083 2084 // If we are left with a constant minimum-int, strip it off. 2085 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2086 Ops.erase(Ops.begin()); 2087 --Idx; 2088 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2089 // If we have an smax with a constant maximum-int, it will always be 2090 // maximum-int. 2091 return Ops[0]; 2092 } 2093 2094 if (Ops.size() == 1) return Ops[0]; 2095 } 2096 2097 // Find the first SMax 2098 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2099 ++Idx; 2100 2101 // Check to see if one of the operands is an SMax. If so, expand its operands 2102 // onto our operand list, and recurse to simplify. 2103 if (Idx < Ops.size()) { 2104 bool DeletedSMax = false; 2105 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2106 Ops.erase(Ops.begin()+Idx); 2107 Ops.append(SMax->op_begin(), SMax->op_end()); 2108 DeletedSMax = true; 2109 } 2110 2111 if (DeletedSMax) 2112 return getSMaxExpr(Ops); 2113 } 2114 2115 // Okay, check to see if the same value occurs in the operand list twice. If 2116 // so, delete one. Since we sorted the list, these values are required to 2117 // be adjacent. 2118 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2119 // X smax Y smax Y --> X smax Y 2120 // X smax Y --> X, if X is always greater than Y 2121 if (Ops[i] == Ops[i+1] || 2122 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2123 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2124 --i; --e; 2125 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2126 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2127 --i; --e; 2128 } 2129 2130 if (Ops.size() == 1) return Ops[0]; 2131 2132 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2133 2134 // Okay, it looks like we really DO need an smax expr. Check to see if we 2135 // already have one, otherwise create a new one. 2136 FoldingSetNodeID ID; 2137 ID.AddInteger(scSMaxExpr); 2138 ID.AddInteger(Ops.size()); 2139 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2140 ID.AddPointer(Ops[i]); 2141 void *IP = 0; 2142 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2143 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2144 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2145 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2146 O, Ops.size()); 2147 UniqueSCEVs.InsertNode(S, IP); 2148 return S; 2149} 2150 2151const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2152 const SCEV *RHS) { 2153 SmallVector<const SCEV *, 2> Ops; 2154 Ops.push_back(LHS); 2155 Ops.push_back(RHS); 2156 return getUMaxExpr(Ops); 2157} 2158 2159const SCEV * 2160ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2161 assert(!Ops.empty() && "Cannot get empty umax!"); 2162 if (Ops.size() == 1) return Ops[0]; 2163#ifndef NDEBUG 2164 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2165 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2166 getEffectiveSCEVType(Ops[0]->getType()) && 2167 "SCEVUMaxExpr operand types don't match!"); 2168#endif 2169 2170 // Sort by complexity, this groups all similar expression types together. 2171 GroupByComplexity(Ops, LI); 2172 2173 // If there are any constants, fold them together. 2174 unsigned Idx = 0; 2175 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2176 ++Idx; 2177 assert(Idx < Ops.size()); 2178 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2179 // We found two constants, fold them together! 2180 ConstantInt *Fold = ConstantInt::get(getContext(), 2181 APIntOps::umax(LHSC->getValue()->getValue(), 2182 RHSC->getValue()->getValue())); 2183 Ops[0] = getConstant(Fold); 2184 Ops.erase(Ops.begin()+1); // Erase the folded element 2185 if (Ops.size() == 1) return Ops[0]; 2186 LHSC = cast<SCEVConstant>(Ops[0]); 2187 } 2188 2189 // If we are left with a constant minimum-int, strip it off. 2190 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2191 Ops.erase(Ops.begin()); 2192 --Idx; 2193 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2194 // If we have an umax with a constant maximum-int, it will always be 2195 // maximum-int. 2196 return Ops[0]; 2197 } 2198 2199 if (Ops.size() == 1) return Ops[0]; 2200 } 2201 2202 // Find the first UMax 2203 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2204 ++Idx; 2205 2206 // Check to see if one of the operands is a UMax. If so, expand its operands 2207 // onto our operand list, and recurse to simplify. 2208 if (Idx < Ops.size()) { 2209 bool DeletedUMax = false; 2210 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2211 Ops.erase(Ops.begin()+Idx); 2212 Ops.append(UMax->op_begin(), UMax->op_end()); 2213 DeletedUMax = true; 2214 } 2215 2216 if (DeletedUMax) 2217 return getUMaxExpr(Ops); 2218 } 2219 2220 // Okay, check to see if the same value occurs in the operand list twice. If 2221 // so, delete one. Since we sorted the list, these values are required to 2222 // be adjacent. 2223 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2224 // X umax Y umax Y --> X umax Y 2225 // X umax Y --> X, if X is always greater than Y 2226 if (Ops[i] == Ops[i+1] || 2227 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2228 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2229 --i; --e; 2230 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2231 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2232 --i; --e; 2233 } 2234 2235 if (Ops.size() == 1) return Ops[0]; 2236 2237 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2238 2239 // Okay, it looks like we really DO need a umax expr. Check to see if we 2240 // already have one, otherwise create a new one. 2241 FoldingSetNodeID ID; 2242 ID.AddInteger(scUMaxExpr); 2243 ID.AddInteger(Ops.size()); 2244 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2245 ID.AddPointer(Ops[i]); 2246 void *IP = 0; 2247 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2248 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2249 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2250 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2251 O, Ops.size()); 2252 UniqueSCEVs.InsertNode(S, IP); 2253 return S; 2254} 2255 2256const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2257 const SCEV *RHS) { 2258 // ~smax(~x, ~y) == smin(x, y). 2259 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2260} 2261 2262const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2263 const SCEV *RHS) { 2264 // ~umax(~x, ~y) == umin(x, y) 2265 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2266} 2267 2268const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2269 // If we have TargetData, we can bypass creating a target-independent 2270 // constant expression and then folding it back into a ConstantInt. 2271 // This is just a compile-time optimization. 2272 if (TD) 2273 return getConstant(TD->getIntPtrType(getContext()), 2274 TD->getTypeAllocSize(AllocTy)); 2275 2276 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2277 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2278 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2279 C = Folded; 2280 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2281 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2282} 2283 2284const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2285 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2286 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2287 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2288 C = Folded; 2289 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2290 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2291} 2292 2293const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2294 unsigned FieldNo) { 2295 // If we have TargetData, we can bypass creating a target-independent 2296 // constant expression and then folding it back into a ConstantInt. 2297 // This is just a compile-time optimization. 2298 if (TD) 2299 return getConstant(TD->getIntPtrType(getContext()), 2300 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2301 2302 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2303 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2304 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2305 C = Folded; 2306 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2307 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2308} 2309 2310const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2311 Constant *FieldNo) { 2312 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2313 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2314 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2315 C = Folded; 2316 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2317 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2318} 2319 2320const SCEV *ScalarEvolution::getUnknown(Value *V) { 2321 // Don't attempt to do anything other than create a SCEVUnknown object 2322 // here. createSCEV only calls getUnknown after checking for all other 2323 // interesting possibilities, and any other code that calls getUnknown 2324 // is doing so in order to hide a value from SCEV canonicalization. 2325 2326 FoldingSetNodeID ID; 2327 ID.AddInteger(scUnknown); 2328 ID.AddPointer(V); 2329 void *IP = 0; 2330 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2331 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V); 2332 UniqueSCEVs.InsertNode(S, IP); 2333 return S; 2334} 2335 2336//===----------------------------------------------------------------------===// 2337// Basic SCEV Analysis and PHI Idiom Recognition Code 2338// 2339 2340/// isSCEVable - Test if values of the given type are analyzable within 2341/// the SCEV framework. This primarily includes integer types, and it 2342/// can optionally include pointer types if the ScalarEvolution class 2343/// has access to target-specific information. 2344bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2345 // Integers and pointers are always SCEVable. 2346 return Ty->isIntegerTy() || Ty->isPointerTy(); 2347} 2348 2349/// getTypeSizeInBits - Return the size in bits of the specified type, 2350/// for which isSCEVable must return true. 2351uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2352 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2353 2354 // If we have a TargetData, use it! 2355 if (TD) 2356 return TD->getTypeSizeInBits(Ty); 2357 2358 // Integer types have fixed sizes. 2359 if (Ty->isIntegerTy()) 2360 return Ty->getPrimitiveSizeInBits(); 2361 2362 // The only other support type is pointer. Without TargetData, conservatively 2363 // assume pointers are 64-bit. 2364 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2365 return 64; 2366} 2367 2368/// getEffectiveSCEVType - Return a type with the same bitwidth as 2369/// the given type and which represents how SCEV will treat the given 2370/// type, for which isSCEVable must return true. For pointer types, 2371/// this is the pointer-sized integer type. 2372const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2373 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2374 2375 if (Ty->isIntegerTy()) 2376 return Ty; 2377 2378 // The only other support type is pointer. 2379 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2380 if (TD) return TD->getIntPtrType(getContext()); 2381 2382 // Without TargetData, conservatively assume pointers are 64-bit. 2383 return Type::getInt64Ty(getContext()); 2384} 2385 2386const SCEV *ScalarEvolution::getCouldNotCompute() { 2387 return &CouldNotCompute; 2388} 2389 2390/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2391/// expression and create a new one. 2392const SCEV *ScalarEvolution::getSCEV(Value *V) { 2393 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2394 2395 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2396 if (I != Scalars.end()) return I->second; 2397 const SCEV *S = createSCEV(V); 2398 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2399 return S; 2400} 2401 2402/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2403/// 2404const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2405 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2406 return getConstant( 2407 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2408 2409 const Type *Ty = V->getType(); 2410 Ty = getEffectiveSCEVType(Ty); 2411 return getMulExpr(V, 2412 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2413} 2414 2415/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2416const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2417 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2418 return getConstant( 2419 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2420 2421 const Type *Ty = V->getType(); 2422 Ty = getEffectiveSCEVType(Ty); 2423 const SCEV *AllOnes = 2424 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2425 return getMinusSCEV(AllOnes, V); 2426} 2427 2428/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2429/// 2430const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2431 const SCEV *RHS) { 2432 // X - Y --> X + -Y 2433 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2434} 2435 2436/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2437/// input value to the specified type. If the type must be extended, it is zero 2438/// extended. 2439const SCEV * 2440ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2441 const Type *Ty) { 2442 const Type *SrcTy = V->getType(); 2443 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2444 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2445 "Cannot truncate or zero extend with non-integer arguments!"); 2446 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2447 return V; // No conversion 2448 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2449 return getTruncateExpr(V, Ty); 2450 return getZeroExtendExpr(V, Ty); 2451} 2452 2453/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2454/// input value to the specified type. If the type must be extended, it is sign 2455/// extended. 2456const SCEV * 2457ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2458 const Type *Ty) { 2459 const Type *SrcTy = V->getType(); 2460 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2461 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2462 "Cannot truncate or zero extend with non-integer arguments!"); 2463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2464 return V; // No conversion 2465 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2466 return getTruncateExpr(V, Ty); 2467 return getSignExtendExpr(V, Ty); 2468} 2469 2470/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2471/// input value to the specified type. If the type must be extended, it is zero 2472/// extended. The conversion must not be narrowing. 2473const SCEV * 2474ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2475 const Type *SrcTy = V->getType(); 2476 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2477 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2478 "Cannot noop or zero extend with non-integer arguments!"); 2479 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2480 "getNoopOrZeroExtend cannot truncate!"); 2481 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2482 return V; // No conversion 2483 return getZeroExtendExpr(V, Ty); 2484} 2485 2486/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2487/// input value to the specified type. If the type must be extended, it is sign 2488/// extended. The conversion must not be narrowing. 2489const SCEV * 2490ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2491 const Type *SrcTy = V->getType(); 2492 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2493 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2494 "Cannot noop or sign extend with non-integer arguments!"); 2495 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2496 "getNoopOrSignExtend cannot truncate!"); 2497 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2498 return V; // No conversion 2499 return getSignExtendExpr(V, Ty); 2500} 2501 2502/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2503/// the input value to the specified type. If the type must be extended, 2504/// it is extended with unspecified bits. The conversion must not be 2505/// narrowing. 2506const SCEV * 2507ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2508 const Type *SrcTy = V->getType(); 2509 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2510 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2511 "Cannot noop or any extend with non-integer arguments!"); 2512 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2513 "getNoopOrAnyExtend cannot truncate!"); 2514 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2515 return V; // No conversion 2516 return getAnyExtendExpr(V, Ty); 2517} 2518 2519/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2520/// input value to the specified type. The conversion must not be widening. 2521const SCEV * 2522ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2523 const Type *SrcTy = V->getType(); 2524 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2525 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2526 "Cannot truncate or noop with non-integer arguments!"); 2527 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2528 "getTruncateOrNoop cannot extend!"); 2529 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2530 return V; // No conversion 2531 return getTruncateExpr(V, Ty); 2532} 2533 2534/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2535/// the types using zero-extension, and then perform a umax operation 2536/// with them. 2537const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2538 const SCEV *RHS) { 2539 const SCEV *PromotedLHS = LHS; 2540 const SCEV *PromotedRHS = RHS; 2541 2542 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2543 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2544 else 2545 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2546 2547 return getUMaxExpr(PromotedLHS, PromotedRHS); 2548} 2549 2550/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2551/// the types using zero-extension, and then perform a umin operation 2552/// with them. 2553const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2554 const SCEV *RHS) { 2555 const SCEV *PromotedLHS = LHS; 2556 const SCEV *PromotedRHS = RHS; 2557 2558 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2559 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2560 else 2561 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2562 2563 return getUMinExpr(PromotedLHS, PromotedRHS); 2564} 2565 2566/// PushDefUseChildren - Push users of the given Instruction 2567/// onto the given Worklist. 2568static void 2569PushDefUseChildren(Instruction *I, 2570 SmallVectorImpl<Instruction *> &Worklist) { 2571 // Push the def-use children onto the Worklist stack. 2572 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2573 UI != UE; ++UI) 2574 Worklist.push_back(cast<Instruction>(UI)); 2575} 2576 2577/// ForgetSymbolicValue - This looks up computed SCEV values for all 2578/// instructions that depend on the given instruction and removes them from 2579/// the Scalars map if they reference SymName. This is used during PHI 2580/// resolution. 2581void 2582ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2583 SmallVector<Instruction *, 16> Worklist; 2584 PushDefUseChildren(PN, Worklist); 2585 2586 SmallPtrSet<Instruction *, 8> Visited; 2587 Visited.insert(PN); 2588 while (!Worklist.empty()) { 2589 Instruction *I = Worklist.pop_back_val(); 2590 if (!Visited.insert(I)) continue; 2591 2592 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2593 Scalars.find(static_cast<Value *>(I)); 2594 if (It != Scalars.end()) { 2595 // Short-circuit the def-use traversal if the symbolic name 2596 // ceases to appear in expressions. 2597 if (It->second != SymName && !It->second->hasOperand(SymName)) 2598 continue; 2599 2600 // SCEVUnknown for a PHI either means that it has an unrecognized 2601 // structure, it's a PHI that's in the progress of being computed 2602 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2603 // additional loop trip count information isn't going to change anything. 2604 // In the second case, createNodeForPHI will perform the necessary 2605 // updates on its own when it gets to that point. In the third, we do 2606 // want to forget the SCEVUnknown. 2607 if (!isa<PHINode>(I) || 2608 !isa<SCEVUnknown>(It->second) || 2609 (I != PN && It->second == SymName)) { 2610 ValuesAtScopes.erase(It->second); 2611 Scalars.erase(It); 2612 } 2613 } 2614 2615 PushDefUseChildren(I, Worklist); 2616 } 2617} 2618 2619/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2620/// a loop header, making it a potential recurrence, or it doesn't. 2621/// 2622const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2623 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2624 if (L->getHeader() == PN->getParent()) { 2625 // The loop may have multiple entrances or multiple exits; we can analyze 2626 // this phi as an addrec if it has a unique entry value and a unique 2627 // backedge value. 2628 Value *BEValueV = 0, *StartValueV = 0; 2629 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2630 Value *V = PN->getIncomingValue(i); 2631 if (L->contains(PN->getIncomingBlock(i))) { 2632 if (!BEValueV) { 2633 BEValueV = V; 2634 } else if (BEValueV != V) { 2635 BEValueV = 0; 2636 break; 2637 } 2638 } else if (!StartValueV) { 2639 StartValueV = V; 2640 } else if (StartValueV != V) { 2641 StartValueV = 0; 2642 break; 2643 } 2644 } 2645 if (BEValueV && StartValueV) { 2646 // While we are analyzing this PHI node, handle its value symbolically. 2647 const SCEV *SymbolicName = getUnknown(PN); 2648 assert(Scalars.find(PN) == Scalars.end() && 2649 "PHI node already processed?"); 2650 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2651 2652 // Using this symbolic name for the PHI, analyze the value coming around 2653 // the back-edge. 2654 const SCEV *BEValue = getSCEV(BEValueV); 2655 2656 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2657 // has a special value for the first iteration of the loop. 2658 2659 // If the value coming around the backedge is an add with the symbolic 2660 // value we just inserted, then we found a simple induction variable! 2661 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2662 // If there is a single occurrence of the symbolic value, replace it 2663 // with a recurrence. 2664 unsigned FoundIndex = Add->getNumOperands(); 2665 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2666 if (Add->getOperand(i) == SymbolicName) 2667 if (FoundIndex == e) { 2668 FoundIndex = i; 2669 break; 2670 } 2671 2672 if (FoundIndex != Add->getNumOperands()) { 2673 // Create an add with everything but the specified operand. 2674 SmallVector<const SCEV *, 8> Ops; 2675 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2676 if (i != FoundIndex) 2677 Ops.push_back(Add->getOperand(i)); 2678 const SCEV *Accum = getAddExpr(Ops); 2679 2680 // This is not a valid addrec if the step amount is varying each 2681 // loop iteration, but is not itself an addrec in this loop. 2682 if (Accum->isLoopInvariant(L) || 2683 (isa<SCEVAddRecExpr>(Accum) && 2684 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2685 bool HasNUW = false; 2686 bool HasNSW = false; 2687 2688 // If the increment doesn't overflow, then neither the addrec nor 2689 // the post-increment will overflow. 2690 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2691 if (OBO->hasNoUnsignedWrap()) 2692 HasNUW = true; 2693 if (OBO->hasNoSignedWrap()) 2694 HasNSW = true; 2695 } 2696 2697 const SCEV *StartVal = getSCEV(StartValueV); 2698 const SCEV *PHISCEV = 2699 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2700 2701 // Since the no-wrap flags are on the increment, they apply to the 2702 // post-incremented value as well. 2703 if (Accum->isLoopInvariant(L)) 2704 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2705 Accum, L, HasNUW, HasNSW); 2706 2707 // Okay, for the entire analysis of this edge we assumed the PHI 2708 // to be symbolic. We now need to go back and purge all of the 2709 // entries for the scalars that use the symbolic expression. 2710 ForgetSymbolicName(PN, SymbolicName); 2711 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2712 return PHISCEV; 2713 } 2714 } 2715 } else if (const SCEVAddRecExpr *AddRec = 2716 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2717 // Otherwise, this could be a loop like this: 2718 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2719 // In this case, j = {1,+,1} and BEValue is j. 2720 // Because the other in-value of i (0) fits the evolution of BEValue 2721 // i really is an addrec evolution. 2722 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2723 const SCEV *StartVal = getSCEV(StartValueV); 2724 2725 // If StartVal = j.start - j.stride, we can use StartVal as the 2726 // initial step of the addrec evolution. 2727 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2728 AddRec->getOperand(1))) { 2729 const SCEV *PHISCEV = 2730 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2731 2732 // Okay, for the entire analysis of this edge we assumed the PHI 2733 // to be symbolic. We now need to go back and purge all of the 2734 // entries for the scalars that use the symbolic expression. 2735 ForgetSymbolicName(PN, SymbolicName); 2736 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2737 return PHISCEV; 2738 } 2739 } 2740 } 2741 } 2742 } 2743 2744 // If the PHI has a single incoming value, follow that value, unless the 2745 // PHI's incoming blocks are in a different loop, in which case doing so 2746 // risks breaking LCSSA form. Instcombine would normally zap these, but 2747 // it doesn't have DominatorTree information, so it may miss cases. 2748 if (Value *V = PN->hasConstantValue(DT)) { 2749 bool AllSameLoop = true; 2750 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2751 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2752 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2753 AllSameLoop = false; 2754 break; 2755 } 2756 if (AllSameLoop) 2757 return getSCEV(V); 2758 } 2759 2760 // If it's not a loop phi, we can't handle it yet. 2761 return getUnknown(PN); 2762} 2763 2764/// createNodeForGEP - Expand GEP instructions into add and multiply 2765/// operations. This allows them to be analyzed by regular SCEV code. 2766/// 2767const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2768 2769 bool InBounds = GEP->isInBounds(); 2770 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2771 Value *Base = GEP->getOperand(0); 2772 // Don't attempt to analyze GEPs over unsized objects. 2773 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2774 return getUnknown(GEP); 2775 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2776 gep_type_iterator GTI = gep_type_begin(GEP); 2777 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2778 E = GEP->op_end(); 2779 I != E; ++I) { 2780 Value *Index = *I; 2781 // Compute the (potentially symbolic) offset in bytes for this index. 2782 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2783 // For a struct, add the member offset. 2784 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2785 TotalOffset = getAddExpr(TotalOffset, 2786 getOffsetOfExpr(STy, FieldNo), 2787 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2788 } else { 2789 // For an array, add the element offset, explicitly scaled. 2790 const SCEV *LocalOffset = getSCEV(Index); 2791 // Getelementptr indices are signed. 2792 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2793 // Lower "inbounds" GEPs to NSW arithmetic. 2794 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2795 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2796 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2797 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2798 } 2799 } 2800 return getAddExpr(getSCEV(Base), TotalOffset, 2801 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2802} 2803 2804/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2805/// guaranteed to end in (at every loop iteration). It is, at the same time, 2806/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2807/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2808uint32_t 2809ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2810 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2811 return C->getValue()->getValue().countTrailingZeros(); 2812 2813 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2814 return std::min(GetMinTrailingZeros(T->getOperand()), 2815 (uint32_t)getTypeSizeInBits(T->getType())); 2816 2817 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2818 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2819 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2820 getTypeSizeInBits(E->getType()) : OpRes; 2821 } 2822 2823 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2824 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2825 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2826 getTypeSizeInBits(E->getType()) : OpRes; 2827 } 2828 2829 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2830 // The result is the min of all operands results. 2831 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2832 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2833 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2834 return MinOpRes; 2835 } 2836 2837 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2838 // The result is the sum of all operands results. 2839 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2840 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2841 for (unsigned i = 1, e = M->getNumOperands(); 2842 SumOpRes != BitWidth && i != e; ++i) 2843 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2844 BitWidth); 2845 return SumOpRes; 2846 } 2847 2848 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2849 // The result is the min of all operands results. 2850 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2851 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2852 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2853 return MinOpRes; 2854 } 2855 2856 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2857 // The result is the min of all operands results. 2858 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2859 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2860 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2861 return MinOpRes; 2862 } 2863 2864 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2865 // The result is the min of all operands results. 2866 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2867 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2868 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2869 return MinOpRes; 2870 } 2871 2872 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2873 // For a SCEVUnknown, ask ValueTracking. 2874 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2875 APInt Mask = APInt::getAllOnesValue(BitWidth); 2876 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2877 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2878 return Zeros.countTrailingOnes(); 2879 } 2880 2881 // SCEVUDivExpr 2882 return 0; 2883} 2884 2885/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2886/// 2887ConstantRange 2888ScalarEvolution::getUnsignedRange(const SCEV *S) { 2889 2890 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2891 return ConstantRange(C->getValue()->getValue()); 2892 2893 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2894 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2895 2896 // If the value has known zeros, the maximum unsigned value will have those 2897 // known zeros as well. 2898 uint32_t TZ = GetMinTrailingZeros(S); 2899 if (TZ != 0) 2900 ConservativeResult = 2901 ConstantRange(APInt::getMinValue(BitWidth), 2902 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2903 2904 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2905 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2906 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2907 X = X.add(getUnsignedRange(Add->getOperand(i))); 2908 return ConservativeResult.intersectWith(X); 2909 } 2910 2911 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2912 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2913 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2914 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2915 return ConservativeResult.intersectWith(X); 2916 } 2917 2918 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2919 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2920 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2921 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2922 return ConservativeResult.intersectWith(X); 2923 } 2924 2925 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2926 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2927 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2928 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2929 return ConservativeResult.intersectWith(X); 2930 } 2931 2932 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2933 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2934 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2935 return ConservativeResult.intersectWith(X.udiv(Y)); 2936 } 2937 2938 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2939 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2940 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2941 } 2942 2943 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2944 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2945 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2946 } 2947 2948 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2949 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2950 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2951 } 2952 2953 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2954 // If there's no unsigned wrap, the value will never be less than its 2955 // initial value. 2956 if (AddRec->hasNoUnsignedWrap()) 2957 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2958 if (!C->getValue()->isZero()) 2959 ConservativeResult = 2960 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)); 2961 2962 // TODO: non-affine addrec 2963 if (AddRec->isAffine()) { 2964 const Type *Ty = AddRec->getType(); 2965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2966 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2967 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2968 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2969 2970 const SCEV *Start = AddRec->getStart(); 2971 const SCEV *Step = AddRec->getStepRecurrence(*this); 2972 2973 ConstantRange StartRange = getUnsignedRange(Start); 2974 ConstantRange StepRange = getSignedRange(Step); 2975 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 2976 ConstantRange EndRange = 2977 StartRange.add(MaxBECountRange.multiply(StepRange)); 2978 2979 // Check for overflow. This must be done with ConstantRange arithmetic 2980 // because we could be called from within the ScalarEvolution overflow 2981 // checking code. 2982 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 2983 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 2984 ConstantRange ExtMaxBECountRange = 2985 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 2986 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 2987 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 2988 ExtEndRange) 2989 return ConservativeResult; 2990 2991 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2992 EndRange.getUnsignedMin()); 2993 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2994 EndRange.getUnsignedMax()); 2995 if (Min.isMinValue() && Max.isMaxValue()) 2996 return ConservativeResult; 2997 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2998 } 2999 } 3000 3001 return ConservativeResult; 3002 } 3003 3004 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3005 // For a SCEVUnknown, ask ValueTracking. 3006 APInt Mask = APInt::getAllOnesValue(BitWidth); 3007 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3008 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3009 if (Ones == ~Zeros + 1) 3010 return ConservativeResult; 3011 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3012 } 3013 3014 return ConservativeResult; 3015} 3016 3017/// getSignedRange - Determine the signed range for a particular SCEV. 3018/// 3019ConstantRange 3020ScalarEvolution::getSignedRange(const SCEV *S) { 3021 3022 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3023 return ConstantRange(C->getValue()->getValue()); 3024 3025 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3026 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3027 3028 // If the value has known zeros, the maximum signed value will have those 3029 // known zeros as well. 3030 uint32_t TZ = GetMinTrailingZeros(S); 3031 if (TZ != 0) 3032 ConservativeResult = 3033 ConstantRange(APInt::getSignedMinValue(BitWidth), 3034 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3035 3036 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3037 ConstantRange X = getSignedRange(Add->getOperand(0)); 3038 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3039 X = X.add(getSignedRange(Add->getOperand(i))); 3040 return ConservativeResult.intersectWith(X); 3041 } 3042 3043 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3044 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3045 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3046 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3047 return ConservativeResult.intersectWith(X); 3048 } 3049 3050 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3051 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3052 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3053 X = X.smax(getSignedRange(SMax->getOperand(i))); 3054 return ConservativeResult.intersectWith(X); 3055 } 3056 3057 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3058 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3059 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3060 X = X.umax(getSignedRange(UMax->getOperand(i))); 3061 return ConservativeResult.intersectWith(X); 3062 } 3063 3064 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3065 ConstantRange X = getSignedRange(UDiv->getLHS()); 3066 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3067 return ConservativeResult.intersectWith(X.udiv(Y)); 3068 } 3069 3070 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3071 ConstantRange X = getSignedRange(ZExt->getOperand()); 3072 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3073 } 3074 3075 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3076 ConstantRange X = getSignedRange(SExt->getOperand()); 3077 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3078 } 3079 3080 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3081 ConstantRange X = getSignedRange(Trunc->getOperand()); 3082 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3083 } 3084 3085 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3086 // If there's no signed wrap, and all the operands have the same sign or 3087 // zero, the value won't ever change sign. 3088 if (AddRec->hasNoSignedWrap()) { 3089 bool AllNonNeg = true; 3090 bool AllNonPos = true; 3091 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3092 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3093 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3094 } 3095 if (AllNonNeg) 3096 ConservativeResult = ConservativeResult.intersectWith( 3097 ConstantRange(APInt(BitWidth, 0), 3098 APInt::getSignedMinValue(BitWidth))); 3099 else if (AllNonPos) 3100 ConservativeResult = ConservativeResult.intersectWith( 3101 ConstantRange(APInt::getSignedMinValue(BitWidth), 3102 APInt(BitWidth, 1))); 3103 } 3104 3105 // TODO: non-affine addrec 3106 if (AddRec->isAffine()) { 3107 const Type *Ty = AddRec->getType(); 3108 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3109 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3110 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3111 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3112 3113 const SCEV *Start = AddRec->getStart(); 3114 const SCEV *Step = AddRec->getStepRecurrence(*this); 3115 3116 ConstantRange StartRange = getSignedRange(Start); 3117 ConstantRange StepRange = getSignedRange(Step); 3118 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3119 ConstantRange EndRange = 3120 StartRange.add(MaxBECountRange.multiply(StepRange)); 3121 3122 // Check for overflow. This must be done with ConstantRange arithmetic 3123 // because we could be called from within the ScalarEvolution overflow 3124 // checking code. 3125 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3126 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3127 ConstantRange ExtMaxBECountRange = 3128 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3129 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3130 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3131 ExtEndRange) 3132 return ConservativeResult; 3133 3134 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3135 EndRange.getSignedMin()); 3136 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3137 EndRange.getSignedMax()); 3138 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3139 return ConservativeResult; 3140 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3141 } 3142 } 3143 3144 return ConservativeResult; 3145 } 3146 3147 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3148 // For a SCEVUnknown, ask ValueTracking. 3149 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3150 return ConservativeResult; 3151 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3152 if (NS == 1) 3153 return ConservativeResult; 3154 return ConservativeResult.intersectWith( 3155 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3156 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3157 } 3158 3159 return ConservativeResult; 3160} 3161 3162/// createSCEV - We know that there is no SCEV for the specified value. 3163/// Analyze the expression. 3164/// 3165const SCEV *ScalarEvolution::createSCEV(Value *V) { 3166 if (!isSCEVable(V->getType())) 3167 return getUnknown(V); 3168 3169 unsigned Opcode = Instruction::UserOp1; 3170 if (Instruction *I = dyn_cast<Instruction>(V)) { 3171 Opcode = I->getOpcode(); 3172 3173 // Don't attempt to analyze instructions in blocks that aren't 3174 // reachable. Such instructions don't matter, and they aren't required 3175 // to obey basic rules for definitions dominating uses which this 3176 // analysis depends on. 3177 if (!DT->isReachableFromEntry(I->getParent())) 3178 return getUnknown(V); 3179 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3180 Opcode = CE->getOpcode(); 3181 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3182 return getConstant(CI); 3183 else if (isa<ConstantPointerNull>(V)) 3184 return getConstant(V->getType(), 0); 3185 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3186 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3187 else 3188 return getUnknown(V); 3189 3190 Operator *U = cast<Operator>(V); 3191 switch (Opcode) { 3192 case Instruction::Add: 3193 // Don't transfer the NSW and NUW bits from the Add instruction to the 3194 // Add expression, because the Instruction may be guarded by control 3195 // flow and the no-overflow bits may not be valid for the expression in 3196 // any context. 3197 return getAddExpr(getSCEV(U->getOperand(0)), 3198 getSCEV(U->getOperand(1))); 3199 case Instruction::Mul: 3200 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3201 // Mul expression, as with Add. 3202 return getMulExpr(getSCEV(U->getOperand(0)), 3203 getSCEV(U->getOperand(1))); 3204 case Instruction::UDiv: 3205 return getUDivExpr(getSCEV(U->getOperand(0)), 3206 getSCEV(U->getOperand(1))); 3207 case Instruction::Sub: 3208 return getMinusSCEV(getSCEV(U->getOperand(0)), 3209 getSCEV(U->getOperand(1))); 3210 case Instruction::And: 3211 // For an expression like x&255 that merely masks off the high bits, 3212 // use zext(trunc(x)) as the SCEV expression. 3213 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3214 if (CI->isNullValue()) 3215 return getSCEV(U->getOperand(1)); 3216 if (CI->isAllOnesValue()) 3217 return getSCEV(U->getOperand(0)); 3218 const APInt &A = CI->getValue(); 3219 3220 // Instcombine's ShrinkDemandedConstant may strip bits out of 3221 // constants, obscuring what would otherwise be a low-bits mask. 3222 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3223 // knew about to reconstruct a low-bits mask value. 3224 unsigned LZ = A.countLeadingZeros(); 3225 unsigned BitWidth = A.getBitWidth(); 3226 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3227 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3228 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3229 3230 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3231 3232 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3233 return 3234 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3235 IntegerType::get(getContext(), BitWidth - LZ)), 3236 U->getType()); 3237 } 3238 break; 3239 3240 case Instruction::Or: 3241 // If the RHS of the Or is a constant, we may have something like: 3242 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3243 // optimizations will transparently handle this case. 3244 // 3245 // In order for this transformation to be safe, the LHS must be of the 3246 // form X*(2^n) and the Or constant must be less than 2^n. 3247 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3248 const SCEV *LHS = getSCEV(U->getOperand(0)); 3249 const APInt &CIVal = CI->getValue(); 3250 if (GetMinTrailingZeros(LHS) >= 3251 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3252 // Build a plain add SCEV. 3253 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3254 // If the LHS of the add was an addrec and it has no-wrap flags, 3255 // transfer the no-wrap flags, since an or won't introduce a wrap. 3256 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3257 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3258 if (OldAR->hasNoUnsignedWrap()) 3259 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3260 if (OldAR->hasNoSignedWrap()) 3261 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3262 } 3263 return S; 3264 } 3265 } 3266 break; 3267 case Instruction::Xor: 3268 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3269 // If the RHS of the xor is a signbit, then this is just an add. 3270 // Instcombine turns add of signbit into xor as a strength reduction step. 3271 if (CI->getValue().isSignBit()) 3272 return getAddExpr(getSCEV(U->getOperand(0)), 3273 getSCEV(U->getOperand(1))); 3274 3275 // If the RHS of xor is -1, then this is a not operation. 3276 if (CI->isAllOnesValue()) 3277 return getNotSCEV(getSCEV(U->getOperand(0))); 3278 3279 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3280 // This is a variant of the check for xor with -1, and it handles 3281 // the case where instcombine has trimmed non-demanded bits out 3282 // of an xor with -1. 3283 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3284 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3285 if (BO->getOpcode() == Instruction::And && 3286 LCI->getValue() == CI->getValue()) 3287 if (const SCEVZeroExtendExpr *Z = 3288 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3289 const Type *UTy = U->getType(); 3290 const SCEV *Z0 = Z->getOperand(); 3291 const Type *Z0Ty = Z0->getType(); 3292 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3293 3294 // If C is a low-bits mask, the zero extend is serving to 3295 // mask off the high bits. Complement the operand and 3296 // re-apply the zext. 3297 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3298 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3299 3300 // If C is a single bit, it may be in the sign-bit position 3301 // before the zero-extend. In this case, represent the xor 3302 // using an add, which is equivalent, and re-apply the zext. 3303 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3304 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3305 Trunc.isSignBit()) 3306 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3307 UTy); 3308 } 3309 } 3310 break; 3311 3312 case Instruction::Shl: 3313 // Turn shift left of a constant amount into a multiply. 3314 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3315 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3316 3317 // If the shift count is not less than the bitwidth, the result of 3318 // the shift is undefined. Don't try to analyze it, because the 3319 // resolution chosen here may differ from the resolution chosen in 3320 // other parts of the compiler. 3321 if (SA->getValue().uge(BitWidth)) 3322 break; 3323 3324 Constant *X = ConstantInt::get(getContext(), 3325 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3326 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3327 } 3328 break; 3329 3330 case Instruction::LShr: 3331 // Turn logical shift right of a constant into a unsigned divide. 3332 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3333 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3334 3335 // If the shift count is not less than the bitwidth, the result of 3336 // the shift is undefined. Don't try to analyze it, because the 3337 // resolution chosen here may differ from the resolution chosen in 3338 // other parts of the compiler. 3339 if (SA->getValue().uge(BitWidth)) 3340 break; 3341 3342 Constant *X = ConstantInt::get(getContext(), 3343 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3344 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3345 } 3346 break; 3347 3348 case Instruction::AShr: 3349 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3350 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3351 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3352 if (L->getOpcode() == Instruction::Shl && 3353 L->getOperand(1) == U->getOperand(1)) { 3354 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3355 3356 // If the shift count is not less than the bitwidth, the result of 3357 // the shift is undefined. Don't try to analyze it, because the 3358 // resolution chosen here may differ from the resolution chosen in 3359 // other parts of the compiler. 3360 if (CI->getValue().uge(BitWidth)) 3361 break; 3362 3363 uint64_t Amt = BitWidth - CI->getZExtValue(); 3364 if (Amt == BitWidth) 3365 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3366 return 3367 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3368 IntegerType::get(getContext(), 3369 Amt)), 3370 U->getType()); 3371 } 3372 break; 3373 3374 case Instruction::Trunc: 3375 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3376 3377 case Instruction::ZExt: 3378 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3379 3380 case Instruction::SExt: 3381 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3382 3383 case Instruction::BitCast: 3384 // BitCasts are no-op casts so we just eliminate the cast. 3385 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3386 return getSCEV(U->getOperand(0)); 3387 break; 3388 3389 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3390 // lead to pointer expressions which cannot safely be expanded to GEPs, 3391 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3392 // simplifying integer expressions. 3393 3394 case Instruction::GetElementPtr: 3395 return createNodeForGEP(cast<GEPOperator>(U)); 3396 3397 case Instruction::PHI: 3398 return createNodeForPHI(cast<PHINode>(U)); 3399 3400 case Instruction::Select: 3401 // This could be a smax or umax that was lowered earlier. 3402 // Try to recover it. 3403 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3404 Value *LHS = ICI->getOperand(0); 3405 Value *RHS = ICI->getOperand(1); 3406 switch (ICI->getPredicate()) { 3407 case ICmpInst::ICMP_SLT: 3408 case ICmpInst::ICMP_SLE: 3409 std::swap(LHS, RHS); 3410 // fall through 3411 case ICmpInst::ICMP_SGT: 3412 case ICmpInst::ICMP_SGE: 3413 // a >s b ? a+x : b+x -> smax(a, b)+x 3414 // a >s b ? b+x : a+x -> smin(a, b)+x 3415 if (LHS->getType() == U->getType()) { 3416 const SCEV *LS = getSCEV(LHS); 3417 const SCEV *RS = getSCEV(RHS); 3418 const SCEV *LA = getSCEV(U->getOperand(1)); 3419 const SCEV *RA = getSCEV(U->getOperand(2)); 3420 const SCEV *LDiff = getMinusSCEV(LA, LS); 3421 const SCEV *RDiff = getMinusSCEV(RA, RS); 3422 if (LDiff == RDiff) 3423 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3424 LDiff = getMinusSCEV(LA, RS); 3425 RDiff = getMinusSCEV(RA, LS); 3426 if (LDiff == RDiff) 3427 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3428 } 3429 break; 3430 case ICmpInst::ICMP_ULT: 3431 case ICmpInst::ICMP_ULE: 3432 std::swap(LHS, RHS); 3433 // fall through 3434 case ICmpInst::ICMP_UGT: 3435 case ICmpInst::ICMP_UGE: 3436 // a >u b ? a+x : b+x -> umax(a, b)+x 3437 // a >u b ? b+x : a+x -> umin(a, b)+x 3438 if (LHS->getType() == U->getType()) { 3439 const SCEV *LS = getSCEV(LHS); 3440 const SCEV *RS = getSCEV(RHS); 3441 const SCEV *LA = getSCEV(U->getOperand(1)); 3442 const SCEV *RA = getSCEV(U->getOperand(2)); 3443 const SCEV *LDiff = getMinusSCEV(LA, LS); 3444 const SCEV *RDiff = getMinusSCEV(RA, RS); 3445 if (LDiff == RDiff) 3446 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3447 LDiff = getMinusSCEV(LA, RS); 3448 RDiff = getMinusSCEV(RA, LS); 3449 if (LDiff == RDiff) 3450 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3451 } 3452 break; 3453 case ICmpInst::ICMP_NE: 3454 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3455 if (LHS->getType() == U->getType() && 3456 isa<ConstantInt>(RHS) && 3457 cast<ConstantInt>(RHS)->isZero()) { 3458 const SCEV *One = getConstant(LHS->getType(), 1); 3459 const SCEV *LS = getSCEV(LHS); 3460 const SCEV *LA = getSCEV(U->getOperand(1)); 3461 const SCEV *RA = getSCEV(U->getOperand(2)); 3462 const SCEV *LDiff = getMinusSCEV(LA, LS); 3463 const SCEV *RDiff = getMinusSCEV(RA, One); 3464 if (LDiff == RDiff) 3465 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3466 } 3467 break; 3468 case ICmpInst::ICMP_EQ: 3469 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3470 if (LHS->getType() == U->getType() && 3471 isa<ConstantInt>(RHS) && 3472 cast<ConstantInt>(RHS)->isZero()) { 3473 const SCEV *One = getConstant(LHS->getType(), 1); 3474 const SCEV *LS = getSCEV(LHS); 3475 const SCEV *LA = getSCEV(U->getOperand(1)); 3476 const SCEV *RA = getSCEV(U->getOperand(2)); 3477 const SCEV *LDiff = getMinusSCEV(LA, One); 3478 const SCEV *RDiff = getMinusSCEV(RA, LS); 3479 if (LDiff == RDiff) 3480 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3481 } 3482 break; 3483 default: 3484 break; 3485 } 3486 } 3487 3488 default: // We cannot analyze this expression. 3489 break; 3490 } 3491 3492 return getUnknown(V); 3493} 3494 3495 3496 3497//===----------------------------------------------------------------------===// 3498// Iteration Count Computation Code 3499// 3500 3501/// getBackedgeTakenCount - If the specified loop has a predictable 3502/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3503/// object. The backedge-taken count is the number of times the loop header 3504/// will be branched to from within the loop. This is one less than the 3505/// trip count of the loop, since it doesn't count the first iteration, 3506/// when the header is branched to from outside the loop. 3507/// 3508/// Note that it is not valid to call this method on a loop without a 3509/// loop-invariant backedge-taken count (see 3510/// hasLoopInvariantBackedgeTakenCount). 3511/// 3512const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3513 return getBackedgeTakenInfo(L).Exact; 3514} 3515 3516/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3517/// return the least SCEV value that is known never to be less than the 3518/// actual backedge taken count. 3519const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3520 return getBackedgeTakenInfo(L).Max; 3521} 3522 3523/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3524/// onto the given Worklist. 3525static void 3526PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3527 BasicBlock *Header = L->getHeader(); 3528 3529 // Push all Loop-header PHIs onto the Worklist stack. 3530 for (BasicBlock::iterator I = Header->begin(); 3531 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3532 Worklist.push_back(PN); 3533} 3534 3535const ScalarEvolution::BackedgeTakenInfo & 3536ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3537 // Initially insert a CouldNotCompute for this loop. If the insertion 3538 // succeeds, proceed to actually compute a backedge-taken count and 3539 // update the value. The temporary CouldNotCompute value tells SCEV 3540 // code elsewhere that it shouldn't attempt to request a new 3541 // backedge-taken count, which could result in infinite recursion. 3542 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3543 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3544 if (Pair.second) { 3545 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3546 if (BECount.Exact != getCouldNotCompute()) { 3547 assert(BECount.Exact->isLoopInvariant(L) && 3548 BECount.Max->isLoopInvariant(L) && 3549 "Computed backedge-taken count isn't loop invariant for loop!"); 3550 ++NumTripCountsComputed; 3551 3552 // Update the value in the map. 3553 Pair.first->second = BECount; 3554 } else { 3555 if (BECount.Max != getCouldNotCompute()) 3556 // Update the value in the map. 3557 Pair.first->second = BECount; 3558 if (isa<PHINode>(L->getHeader()->begin())) 3559 // Only count loops that have phi nodes as not being computable. 3560 ++NumTripCountsNotComputed; 3561 } 3562 3563 // Now that we know more about the trip count for this loop, forget any 3564 // existing SCEV values for PHI nodes in this loop since they are only 3565 // conservative estimates made without the benefit of trip count 3566 // information. This is similar to the code in forgetLoop, except that 3567 // it handles SCEVUnknown PHI nodes specially. 3568 if (BECount.hasAnyInfo()) { 3569 SmallVector<Instruction *, 16> Worklist; 3570 PushLoopPHIs(L, Worklist); 3571 3572 SmallPtrSet<Instruction *, 8> Visited; 3573 while (!Worklist.empty()) { 3574 Instruction *I = Worklist.pop_back_val(); 3575 if (!Visited.insert(I)) continue; 3576 3577 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3578 Scalars.find(static_cast<Value *>(I)); 3579 if (It != Scalars.end()) { 3580 // SCEVUnknown for a PHI either means that it has an unrecognized 3581 // structure, or it's a PHI that's in the progress of being computed 3582 // by createNodeForPHI. In the former case, additional loop trip 3583 // count information isn't going to change anything. In the later 3584 // case, createNodeForPHI will perform the necessary updates on its 3585 // own when it gets to that point. 3586 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3587 ValuesAtScopes.erase(It->second); 3588 Scalars.erase(It); 3589 } 3590 if (PHINode *PN = dyn_cast<PHINode>(I)) 3591 ConstantEvolutionLoopExitValue.erase(PN); 3592 } 3593 3594 PushDefUseChildren(I, Worklist); 3595 } 3596 } 3597 } 3598 return Pair.first->second; 3599} 3600 3601/// forgetLoop - This method should be called by the client when it has 3602/// changed a loop in a way that may effect ScalarEvolution's ability to 3603/// compute a trip count, or if the loop is deleted. 3604void ScalarEvolution::forgetLoop(const Loop *L) { 3605 // Drop any stored trip count value. 3606 BackedgeTakenCounts.erase(L); 3607 3608 // Drop information about expressions based on loop-header PHIs. 3609 SmallVector<Instruction *, 16> Worklist; 3610 PushLoopPHIs(L, Worklist); 3611 3612 SmallPtrSet<Instruction *, 8> Visited; 3613 while (!Worklist.empty()) { 3614 Instruction *I = Worklist.pop_back_val(); 3615 if (!Visited.insert(I)) continue; 3616 3617 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3618 Scalars.find(static_cast<Value *>(I)); 3619 if (It != Scalars.end()) { 3620 ValuesAtScopes.erase(It->second); 3621 Scalars.erase(It); 3622 if (PHINode *PN = dyn_cast<PHINode>(I)) 3623 ConstantEvolutionLoopExitValue.erase(PN); 3624 } 3625 3626 PushDefUseChildren(I, Worklist); 3627 } 3628} 3629 3630/// forgetValue - This method should be called by the client when it has 3631/// changed a value in a way that may effect its value, or which may 3632/// disconnect it from a def-use chain linking it to a loop. 3633void ScalarEvolution::forgetValue(Value *V) { 3634 Instruction *I = dyn_cast<Instruction>(V); 3635 if (!I) return; 3636 3637 // Drop information about expressions based on loop-header PHIs. 3638 SmallVector<Instruction *, 16> Worklist; 3639 Worklist.push_back(I); 3640 3641 SmallPtrSet<Instruction *, 8> Visited; 3642 while (!Worklist.empty()) { 3643 I = Worklist.pop_back_val(); 3644 if (!Visited.insert(I)) continue; 3645 3646 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3647 Scalars.find(static_cast<Value *>(I)); 3648 if (It != Scalars.end()) { 3649 ValuesAtScopes.erase(It->second); 3650 Scalars.erase(It); 3651 if (PHINode *PN = dyn_cast<PHINode>(I)) 3652 ConstantEvolutionLoopExitValue.erase(PN); 3653 } 3654 3655 PushDefUseChildren(I, Worklist); 3656 } 3657} 3658 3659/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3660/// of the specified loop will execute. 3661ScalarEvolution::BackedgeTakenInfo 3662ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3663 SmallVector<BasicBlock *, 8> ExitingBlocks; 3664 L->getExitingBlocks(ExitingBlocks); 3665 3666 // Examine all exits and pick the most conservative values. 3667 const SCEV *BECount = getCouldNotCompute(); 3668 const SCEV *MaxBECount = getCouldNotCompute(); 3669 bool CouldNotComputeBECount = false; 3670 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3671 BackedgeTakenInfo NewBTI = 3672 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3673 3674 if (NewBTI.Exact == getCouldNotCompute()) { 3675 // We couldn't compute an exact value for this exit, so 3676 // we won't be able to compute an exact value for the loop. 3677 CouldNotComputeBECount = true; 3678 BECount = getCouldNotCompute(); 3679 } else if (!CouldNotComputeBECount) { 3680 if (BECount == getCouldNotCompute()) 3681 BECount = NewBTI.Exact; 3682 else 3683 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3684 } 3685 if (MaxBECount == getCouldNotCompute()) 3686 MaxBECount = NewBTI.Max; 3687 else if (NewBTI.Max != getCouldNotCompute()) 3688 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3689 } 3690 3691 return BackedgeTakenInfo(BECount, MaxBECount); 3692} 3693 3694/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3695/// of the specified loop will execute if it exits via the specified block. 3696ScalarEvolution::BackedgeTakenInfo 3697ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3698 BasicBlock *ExitingBlock) { 3699 3700 // Okay, we've chosen an exiting block. See what condition causes us to 3701 // exit at this block. 3702 // 3703 // FIXME: we should be able to handle switch instructions (with a single exit) 3704 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3705 if (ExitBr == 0) return getCouldNotCompute(); 3706 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3707 3708 // At this point, we know we have a conditional branch that determines whether 3709 // the loop is exited. However, we don't know if the branch is executed each 3710 // time through the loop. If not, then the execution count of the branch will 3711 // not be equal to the trip count of the loop. 3712 // 3713 // Currently we check for this by checking to see if the Exit branch goes to 3714 // the loop header. If so, we know it will always execute the same number of 3715 // times as the loop. We also handle the case where the exit block *is* the 3716 // loop header. This is common for un-rotated loops. 3717 // 3718 // If both of those tests fail, walk up the unique predecessor chain to the 3719 // header, stopping if there is an edge that doesn't exit the loop. If the 3720 // header is reached, the execution count of the branch will be equal to the 3721 // trip count of the loop. 3722 // 3723 // More extensive analysis could be done to handle more cases here. 3724 // 3725 if (ExitBr->getSuccessor(0) != L->getHeader() && 3726 ExitBr->getSuccessor(1) != L->getHeader() && 3727 ExitBr->getParent() != L->getHeader()) { 3728 // The simple checks failed, try climbing the unique predecessor chain 3729 // up to the header. 3730 bool Ok = false; 3731 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3732 BasicBlock *Pred = BB->getUniquePredecessor(); 3733 if (!Pred) 3734 return getCouldNotCompute(); 3735 TerminatorInst *PredTerm = Pred->getTerminator(); 3736 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3737 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3738 if (PredSucc == BB) 3739 continue; 3740 // If the predecessor has a successor that isn't BB and isn't 3741 // outside the loop, assume the worst. 3742 if (L->contains(PredSucc)) 3743 return getCouldNotCompute(); 3744 } 3745 if (Pred == L->getHeader()) { 3746 Ok = true; 3747 break; 3748 } 3749 BB = Pred; 3750 } 3751 if (!Ok) 3752 return getCouldNotCompute(); 3753 } 3754 3755 // Proceed to the next level to examine the exit condition expression. 3756 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3757 ExitBr->getSuccessor(0), 3758 ExitBr->getSuccessor(1)); 3759} 3760 3761/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3762/// backedge of the specified loop will execute if its exit condition 3763/// were a conditional branch of ExitCond, TBB, and FBB. 3764ScalarEvolution::BackedgeTakenInfo 3765ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3766 Value *ExitCond, 3767 BasicBlock *TBB, 3768 BasicBlock *FBB) { 3769 // Check if the controlling expression for this loop is an And or Or. 3770 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3771 if (BO->getOpcode() == Instruction::And) { 3772 // Recurse on the operands of the and. 3773 BackedgeTakenInfo BTI0 = 3774 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3775 BackedgeTakenInfo BTI1 = 3776 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3777 const SCEV *BECount = getCouldNotCompute(); 3778 const SCEV *MaxBECount = getCouldNotCompute(); 3779 if (L->contains(TBB)) { 3780 // Both conditions must be true for the loop to continue executing. 3781 // Choose the less conservative count. 3782 if (BTI0.Exact == getCouldNotCompute() || 3783 BTI1.Exact == getCouldNotCompute()) 3784 BECount = getCouldNotCompute(); 3785 else 3786 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3787 if (BTI0.Max == getCouldNotCompute()) 3788 MaxBECount = BTI1.Max; 3789 else if (BTI1.Max == getCouldNotCompute()) 3790 MaxBECount = BTI0.Max; 3791 else 3792 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3793 } else { 3794 // Both conditions must be true for the loop to exit. 3795 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3796 if (BTI0.Exact != getCouldNotCompute() && 3797 BTI1.Exact != getCouldNotCompute()) 3798 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3799 if (BTI0.Max != getCouldNotCompute() && 3800 BTI1.Max != getCouldNotCompute()) 3801 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3802 } 3803 3804 return BackedgeTakenInfo(BECount, MaxBECount); 3805 } 3806 if (BO->getOpcode() == Instruction::Or) { 3807 // Recurse on the operands of the or. 3808 BackedgeTakenInfo BTI0 = 3809 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3810 BackedgeTakenInfo BTI1 = 3811 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3812 const SCEV *BECount = getCouldNotCompute(); 3813 const SCEV *MaxBECount = getCouldNotCompute(); 3814 if (L->contains(FBB)) { 3815 // Both conditions must be false for the loop to continue executing. 3816 // Choose the less conservative count. 3817 if (BTI0.Exact == getCouldNotCompute() || 3818 BTI1.Exact == getCouldNotCompute()) 3819 BECount = getCouldNotCompute(); 3820 else 3821 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3822 if (BTI0.Max == getCouldNotCompute()) 3823 MaxBECount = BTI1.Max; 3824 else if (BTI1.Max == getCouldNotCompute()) 3825 MaxBECount = BTI0.Max; 3826 else 3827 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3828 } else { 3829 // Both conditions must be false for the loop to exit. 3830 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3831 if (BTI0.Exact != getCouldNotCompute() && 3832 BTI1.Exact != getCouldNotCompute()) 3833 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3834 if (BTI0.Max != getCouldNotCompute() && 3835 BTI1.Max != getCouldNotCompute()) 3836 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3837 } 3838 3839 return BackedgeTakenInfo(BECount, MaxBECount); 3840 } 3841 } 3842 3843 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3844 // Proceed to the next level to examine the icmp. 3845 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3846 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3847 3848 // Check for a constant condition. These are normally stripped out by 3849 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3850 // preserve the CFG and is temporarily leaving constant conditions 3851 // in place. 3852 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3853 if (L->contains(FBB) == !CI->getZExtValue()) 3854 // The backedge is always taken. 3855 return getCouldNotCompute(); 3856 else 3857 // The backedge is never taken. 3858 return getConstant(CI->getType(), 0); 3859 } 3860 3861 // If it's not an integer or pointer comparison then compute it the hard way. 3862 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3863} 3864 3865/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3866/// backedge of the specified loop will execute if its exit condition 3867/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3868ScalarEvolution::BackedgeTakenInfo 3869ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3870 ICmpInst *ExitCond, 3871 BasicBlock *TBB, 3872 BasicBlock *FBB) { 3873 3874 // If the condition was exit on true, convert the condition to exit on false 3875 ICmpInst::Predicate Cond; 3876 if (!L->contains(FBB)) 3877 Cond = ExitCond->getPredicate(); 3878 else 3879 Cond = ExitCond->getInversePredicate(); 3880 3881 // Handle common loops like: for (X = "string"; *X; ++X) 3882 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3883 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3884 BackedgeTakenInfo ItCnt = 3885 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3886 if (ItCnt.hasAnyInfo()) 3887 return ItCnt; 3888 } 3889 3890 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3891 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3892 3893 // Try to evaluate any dependencies out of the loop. 3894 LHS = getSCEVAtScope(LHS, L); 3895 RHS = getSCEVAtScope(RHS, L); 3896 3897 // At this point, we would like to compute how many iterations of the 3898 // loop the predicate will return true for these inputs. 3899 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3900 // If there is a loop-invariant, force it into the RHS. 3901 std::swap(LHS, RHS); 3902 Cond = ICmpInst::getSwappedPredicate(Cond); 3903 } 3904 3905 // Simplify the operands before analyzing them. 3906 (void)SimplifyICmpOperands(Cond, LHS, RHS); 3907 3908 // If we have a comparison of a chrec against a constant, try to use value 3909 // ranges to answer this query. 3910 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3911 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3912 if (AddRec->getLoop() == L) { 3913 // Form the constant range. 3914 ConstantRange CompRange( 3915 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3916 3917 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3918 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3919 } 3920 3921 switch (Cond) { 3922 case ICmpInst::ICMP_NE: { // while (X != Y) 3923 // Convert to: while (X-Y != 0) 3924 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3925 if (BTI.hasAnyInfo()) return BTI; 3926 break; 3927 } 3928 case ICmpInst::ICMP_EQ: { // while (X == Y) 3929 // Convert to: while (X-Y == 0) 3930 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3931 if (BTI.hasAnyInfo()) return BTI; 3932 break; 3933 } 3934 case ICmpInst::ICMP_SLT: { 3935 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3936 if (BTI.hasAnyInfo()) return BTI; 3937 break; 3938 } 3939 case ICmpInst::ICMP_SGT: { 3940 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3941 getNotSCEV(RHS), L, true); 3942 if (BTI.hasAnyInfo()) return BTI; 3943 break; 3944 } 3945 case ICmpInst::ICMP_ULT: { 3946 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3947 if (BTI.hasAnyInfo()) return BTI; 3948 break; 3949 } 3950 case ICmpInst::ICMP_UGT: { 3951 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3952 getNotSCEV(RHS), L, false); 3953 if (BTI.hasAnyInfo()) return BTI; 3954 break; 3955 } 3956 default: 3957#if 0 3958 dbgs() << "ComputeBackedgeTakenCount "; 3959 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3960 dbgs() << "[unsigned] "; 3961 dbgs() << *LHS << " " 3962 << Instruction::getOpcodeName(Instruction::ICmp) 3963 << " " << *RHS << "\n"; 3964#endif 3965 break; 3966 } 3967 return 3968 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3969} 3970 3971static ConstantInt * 3972EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3973 ScalarEvolution &SE) { 3974 const SCEV *InVal = SE.getConstant(C); 3975 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3976 assert(isa<SCEVConstant>(Val) && 3977 "Evaluation of SCEV at constant didn't fold correctly?"); 3978 return cast<SCEVConstant>(Val)->getValue(); 3979} 3980 3981/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3982/// and a GEP expression (missing the pointer index) indexing into it, return 3983/// the addressed element of the initializer or null if the index expression is 3984/// invalid. 3985static Constant * 3986GetAddressedElementFromGlobal(GlobalVariable *GV, 3987 const std::vector<ConstantInt*> &Indices) { 3988 Constant *Init = GV->getInitializer(); 3989 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3990 uint64_t Idx = Indices[i]->getZExtValue(); 3991 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3992 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3993 Init = cast<Constant>(CS->getOperand(Idx)); 3994 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3995 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3996 Init = cast<Constant>(CA->getOperand(Idx)); 3997 } else if (isa<ConstantAggregateZero>(Init)) { 3998 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3999 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4000 Init = Constant::getNullValue(STy->getElementType(Idx)); 4001 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4002 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4003 Init = Constant::getNullValue(ATy->getElementType()); 4004 } else { 4005 llvm_unreachable("Unknown constant aggregate type!"); 4006 } 4007 return 0; 4008 } else { 4009 return 0; // Unknown initializer type 4010 } 4011 } 4012 return Init; 4013} 4014 4015/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4016/// 'icmp op load X, cst', try to see if we can compute the backedge 4017/// execution count. 4018ScalarEvolution::BackedgeTakenInfo 4019ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4020 LoadInst *LI, 4021 Constant *RHS, 4022 const Loop *L, 4023 ICmpInst::Predicate predicate) { 4024 if (LI->isVolatile()) return getCouldNotCompute(); 4025 4026 // Check to see if the loaded pointer is a getelementptr of a global. 4027 // TODO: Use SCEV instead of manually grubbing with GEPs. 4028 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4029 if (!GEP) return getCouldNotCompute(); 4030 4031 // Make sure that it is really a constant global we are gepping, with an 4032 // initializer, and make sure the first IDX is really 0. 4033 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4034 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4035 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4036 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4037 return getCouldNotCompute(); 4038 4039 // Okay, we allow one non-constant index into the GEP instruction. 4040 Value *VarIdx = 0; 4041 std::vector<ConstantInt*> Indexes; 4042 unsigned VarIdxNum = 0; 4043 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4044 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4045 Indexes.push_back(CI); 4046 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4047 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4048 VarIdx = GEP->getOperand(i); 4049 VarIdxNum = i-2; 4050 Indexes.push_back(0); 4051 } 4052 4053 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4054 // Check to see if X is a loop variant variable value now. 4055 const SCEV *Idx = getSCEV(VarIdx); 4056 Idx = getSCEVAtScope(Idx, L); 4057 4058 // We can only recognize very limited forms of loop index expressions, in 4059 // particular, only affine AddRec's like {C1,+,C2}. 4060 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4061 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4062 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4063 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4064 return getCouldNotCompute(); 4065 4066 unsigned MaxSteps = MaxBruteForceIterations; 4067 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4068 ConstantInt *ItCst = ConstantInt::get( 4069 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4070 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4071 4072 // Form the GEP offset. 4073 Indexes[VarIdxNum] = Val; 4074 4075 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4076 if (Result == 0) break; // Cannot compute! 4077 4078 // Evaluate the condition for this iteration. 4079 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4080 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4081 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4082#if 0 4083 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4084 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4085 << "***\n"; 4086#endif 4087 ++NumArrayLenItCounts; 4088 return getConstant(ItCst); // Found terminating iteration! 4089 } 4090 } 4091 return getCouldNotCompute(); 4092} 4093 4094 4095/// CanConstantFold - Return true if we can constant fold an instruction of the 4096/// specified type, assuming that all operands were constants. 4097static bool CanConstantFold(const Instruction *I) { 4098 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4099 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4100 return true; 4101 4102 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4103 if (const Function *F = CI->getCalledFunction()) 4104 return canConstantFoldCallTo(F); 4105 return false; 4106} 4107 4108/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4109/// in the loop that V is derived from. We allow arbitrary operations along the 4110/// way, but the operands of an operation must either be constants or a value 4111/// derived from a constant PHI. If this expression does not fit with these 4112/// constraints, return null. 4113static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4114 // If this is not an instruction, or if this is an instruction outside of the 4115 // loop, it can't be derived from a loop PHI. 4116 Instruction *I = dyn_cast<Instruction>(V); 4117 if (I == 0 || !L->contains(I)) return 0; 4118 4119 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4120 if (L->getHeader() == I->getParent()) 4121 return PN; 4122 else 4123 // We don't currently keep track of the control flow needed to evaluate 4124 // PHIs, so we cannot handle PHIs inside of loops. 4125 return 0; 4126 } 4127 4128 // If we won't be able to constant fold this expression even if the operands 4129 // are constants, return early. 4130 if (!CanConstantFold(I)) return 0; 4131 4132 // Otherwise, we can evaluate this instruction if all of its operands are 4133 // constant or derived from a PHI node themselves. 4134 PHINode *PHI = 0; 4135 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4136 if (!isa<Constant>(I->getOperand(Op))) { 4137 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4138 if (P == 0) return 0; // Not evolving from PHI 4139 if (PHI == 0) 4140 PHI = P; 4141 else if (PHI != P) 4142 return 0; // Evolving from multiple different PHIs. 4143 } 4144 4145 // This is a expression evolving from a constant PHI! 4146 return PHI; 4147} 4148 4149/// EvaluateExpression - Given an expression that passes the 4150/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4151/// in the loop has the value PHIVal. If we can't fold this expression for some 4152/// reason, return null. 4153static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4154 const TargetData *TD) { 4155 if (isa<PHINode>(V)) return PHIVal; 4156 if (Constant *C = dyn_cast<Constant>(V)) return C; 4157 Instruction *I = cast<Instruction>(V); 4158 4159 std::vector<Constant*> Operands(I->getNumOperands()); 4160 4161 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4162 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4163 if (Operands[i] == 0) return 0; 4164 } 4165 4166 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4167 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4168 Operands[1], TD); 4169 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4170 &Operands[0], Operands.size(), TD); 4171} 4172 4173/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4174/// in the header of its containing loop, we know the loop executes a 4175/// constant number of times, and the PHI node is just a recurrence 4176/// involving constants, fold it. 4177Constant * 4178ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4179 const APInt &BEs, 4180 const Loop *L) { 4181 std::map<PHINode*, Constant*>::iterator I = 4182 ConstantEvolutionLoopExitValue.find(PN); 4183 if (I != ConstantEvolutionLoopExitValue.end()) 4184 return I->second; 4185 4186 if (BEs.ugt(MaxBruteForceIterations)) 4187 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4188 4189 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4190 4191 // Since the loop is canonicalized, the PHI node must have two entries. One 4192 // entry must be a constant (coming in from outside of the loop), and the 4193 // second must be derived from the same PHI. 4194 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4195 Constant *StartCST = 4196 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4197 if (StartCST == 0) 4198 return RetVal = 0; // Must be a constant. 4199 4200 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4201 if (getConstantEvolvingPHI(BEValue, L) != PN && 4202 !isa<Constant>(BEValue)) 4203 return RetVal = 0; // Not derived from same PHI. 4204 4205 // Execute the loop symbolically to determine the exit value. 4206 if (BEs.getActiveBits() >= 32) 4207 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4208 4209 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4210 unsigned IterationNum = 0; 4211 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4212 if (IterationNum == NumIterations) 4213 return RetVal = PHIVal; // Got exit value! 4214 4215 // Compute the value of the PHI node for the next iteration. 4216 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4217 if (NextPHI == PHIVal) 4218 return RetVal = NextPHI; // Stopped evolving! 4219 if (NextPHI == 0) 4220 return 0; // Couldn't evaluate! 4221 PHIVal = NextPHI; 4222 } 4223} 4224 4225/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4226/// constant number of times (the condition evolves only from constants), 4227/// try to evaluate a few iterations of the loop until we get the exit 4228/// condition gets a value of ExitWhen (true or false). If we cannot 4229/// evaluate the trip count of the loop, return getCouldNotCompute(). 4230const SCEV * 4231ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4232 Value *Cond, 4233 bool ExitWhen) { 4234 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4235 if (PN == 0) return getCouldNotCompute(); 4236 4237 // If the loop is canonicalized, the PHI will have exactly two entries. 4238 // That's the only form we support here. 4239 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4240 4241 // One entry must be a constant (coming in from outside of the loop), and the 4242 // second must be derived from the same PHI. 4243 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4244 Constant *StartCST = 4245 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4246 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4247 4248 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4249 if (getConstantEvolvingPHI(BEValue, L) != PN && 4250 !isa<Constant>(BEValue)) 4251 return getCouldNotCompute(); // Not derived from same PHI. 4252 4253 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4254 // the loop symbolically to determine when the condition gets a value of 4255 // "ExitWhen". 4256 unsigned IterationNum = 0; 4257 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4258 for (Constant *PHIVal = StartCST; 4259 IterationNum != MaxIterations; ++IterationNum) { 4260 ConstantInt *CondVal = 4261 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4262 4263 // Couldn't symbolically evaluate. 4264 if (!CondVal) return getCouldNotCompute(); 4265 4266 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4267 ++NumBruteForceTripCountsComputed; 4268 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4269 } 4270 4271 // Compute the value of the PHI node for the next iteration. 4272 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4273 if (NextPHI == 0 || NextPHI == PHIVal) 4274 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4275 PHIVal = NextPHI; 4276 } 4277 4278 // Too many iterations were needed to evaluate. 4279 return getCouldNotCompute(); 4280} 4281 4282/// getSCEVAtScope - Return a SCEV expression for the specified value 4283/// at the specified scope in the program. The L value specifies a loop 4284/// nest to evaluate the expression at, where null is the top-level or a 4285/// specified loop is immediately inside of the loop. 4286/// 4287/// This method can be used to compute the exit value for a variable defined 4288/// in a loop by querying what the value will hold in the parent loop. 4289/// 4290/// In the case that a relevant loop exit value cannot be computed, the 4291/// original value V is returned. 4292const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4293 // Check to see if we've folded this expression at this loop before. 4294 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4295 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4296 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4297 if (!Pair.second) 4298 return Pair.first->second ? Pair.first->second : V; 4299 4300 // Otherwise compute it. 4301 const SCEV *C = computeSCEVAtScope(V, L); 4302 ValuesAtScopes[V][L] = C; 4303 return C; 4304} 4305 4306const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4307 if (isa<SCEVConstant>(V)) return V; 4308 4309 // If this instruction is evolved from a constant-evolving PHI, compute the 4310 // exit value from the loop without using SCEVs. 4311 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4312 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4313 const Loop *LI = (*this->LI)[I->getParent()]; 4314 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4315 if (PHINode *PN = dyn_cast<PHINode>(I)) 4316 if (PN->getParent() == LI->getHeader()) { 4317 // Okay, there is no closed form solution for the PHI node. Check 4318 // to see if the loop that contains it has a known backedge-taken 4319 // count. If so, we may be able to force computation of the exit 4320 // value. 4321 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4322 if (const SCEVConstant *BTCC = 4323 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4324 // Okay, we know how many times the containing loop executes. If 4325 // this is a constant evolving PHI node, get the final value at 4326 // the specified iteration number. 4327 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4328 BTCC->getValue()->getValue(), 4329 LI); 4330 if (RV) return getSCEV(RV); 4331 } 4332 } 4333 4334 // Okay, this is an expression that we cannot symbolically evaluate 4335 // into a SCEV. Check to see if it's possible to symbolically evaluate 4336 // the arguments into constants, and if so, try to constant propagate the 4337 // result. This is particularly useful for computing loop exit values. 4338 if (CanConstantFold(I)) { 4339 std::vector<Constant*> Operands; 4340 Operands.reserve(I->getNumOperands()); 4341 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4342 Value *Op = I->getOperand(i); 4343 if (Constant *C = dyn_cast<Constant>(Op)) { 4344 Operands.push_back(C); 4345 } else { 4346 // If any of the operands is non-constant and if they are 4347 // non-integer and non-pointer, don't even try to analyze them 4348 // with scev techniques. 4349 if (!isSCEVable(Op->getType())) 4350 return V; 4351 4352 const SCEV *OpV = getSCEVAtScope(Op, L); 4353 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4354 Constant *C = SC->getValue(); 4355 if (C->getType() != Op->getType()) 4356 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4357 Op->getType(), 4358 false), 4359 C, Op->getType()); 4360 Operands.push_back(C); 4361 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4362 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4363 if (C->getType() != Op->getType()) 4364 C = 4365 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4366 Op->getType(), 4367 false), 4368 C, Op->getType()); 4369 Operands.push_back(C); 4370 } else 4371 return V; 4372 } else { 4373 return V; 4374 } 4375 } 4376 } 4377 4378 Constant *C = 0; 4379 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4380 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4381 Operands[0], Operands[1], TD); 4382 else 4383 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4384 &Operands[0], Operands.size(), TD); 4385 if (C) 4386 return getSCEV(C); 4387 } 4388 } 4389 4390 // This is some other type of SCEVUnknown, just return it. 4391 return V; 4392 } 4393 4394 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4395 // Avoid performing the look-up in the common case where the specified 4396 // expression has no loop-variant portions. 4397 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4398 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4399 if (OpAtScope != Comm->getOperand(i)) { 4400 // Okay, at least one of these operands is loop variant but might be 4401 // foldable. Build a new instance of the folded commutative expression. 4402 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4403 Comm->op_begin()+i); 4404 NewOps.push_back(OpAtScope); 4405 4406 for (++i; i != e; ++i) { 4407 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4408 NewOps.push_back(OpAtScope); 4409 } 4410 if (isa<SCEVAddExpr>(Comm)) 4411 return getAddExpr(NewOps); 4412 if (isa<SCEVMulExpr>(Comm)) 4413 return getMulExpr(NewOps); 4414 if (isa<SCEVSMaxExpr>(Comm)) 4415 return getSMaxExpr(NewOps); 4416 if (isa<SCEVUMaxExpr>(Comm)) 4417 return getUMaxExpr(NewOps); 4418 llvm_unreachable("Unknown commutative SCEV type!"); 4419 } 4420 } 4421 // If we got here, all operands are loop invariant. 4422 return Comm; 4423 } 4424 4425 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4426 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4427 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4428 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4429 return Div; // must be loop invariant 4430 return getUDivExpr(LHS, RHS); 4431 } 4432 4433 // If this is a loop recurrence for a loop that does not contain L, then we 4434 // are dealing with the final value computed by the loop. 4435 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4436 if (!L || !AddRec->getLoop()->contains(L)) { 4437 // To evaluate this recurrence, we need to know how many times the AddRec 4438 // loop iterates. Compute this now. 4439 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4440 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4441 4442 // Then, evaluate the AddRec. 4443 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4444 } 4445 return AddRec; 4446 } 4447 4448 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4449 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4450 if (Op == Cast->getOperand()) 4451 return Cast; // must be loop invariant 4452 return getZeroExtendExpr(Op, Cast->getType()); 4453 } 4454 4455 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4456 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4457 if (Op == Cast->getOperand()) 4458 return Cast; // must be loop invariant 4459 return getSignExtendExpr(Op, Cast->getType()); 4460 } 4461 4462 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4463 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4464 if (Op == Cast->getOperand()) 4465 return Cast; // must be loop invariant 4466 return getTruncateExpr(Op, Cast->getType()); 4467 } 4468 4469 llvm_unreachable("Unknown SCEV type!"); 4470 return 0; 4471} 4472 4473/// getSCEVAtScope - This is a convenience function which does 4474/// getSCEVAtScope(getSCEV(V), L). 4475const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4476 return getSCEVAtScope(getSCEV(V), L); 4477} 4478 4479/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4480/// following equation: 4481/// 4482/// A * X = B (mod N) 4483/// 4484/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4485/// A and B isn't important. 4486/// 4487/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4488static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4489 ScalarEvolution &SE) { 4490 uint32_t BW = A.getBitWidth(); 4491 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4492 assert(A != 0 && "A must be non-zero."); 4493 4494 // 1. D = gcd(A, N) 4495 // 4496 // The gcd of A and N may have only one prime factor: 2. The number of 4497 // trailing zeros in A is its multiplicity 4498 uint32_t Mult2 = A.countTrailingZeros(); 4499 // D = 2^Mult2 4500 4501 // 2. Check if B is divisible by D. 4502 // 4503 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4504 // is not less than multiplicity of this prime factor for D. 4505 if (B.countTrailingZeros() < Mult2) 4506 return SE.getCouldNotCompute(); 4507 4508 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4509 // modulo (N / D). 4510 // 4511 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4512 // bit width during computations. 4513 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4514 APInt Mod(BW + 1, 0); 4515 Mod.set(BW - Mult2); // Mod = N / D 4516 APInt I = AD.multiplicativeInverse(Mod); 4517 4518 // 4. Compute the minimum unsigned root of the equation: 4519 // I * (B / D) mod (N / D) 4520 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4521 4522 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4523 // bits. 4524 return SE.getConstant(Result.trunc(BW)); 4525} 4526 4527/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4528/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4529/// might be the same) or two SCEVCouldNotCompute objects. 4530/// 4531static std::pair<const SCEV *,const SCEV *> 4532SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4533 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4534 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4535 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4536 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4537 4538 // We currently can only solve this if the coefficients are constants. 4539 if (!LC || !MC || !NC) { 4540 const SCEV *CNC = SE.getCouldNotCompute(); 4541 return std::make_pair(CNC, CNC); 4542 } 4543 4544 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4545 const APInt &L = LC->getValue()->getValue(); 4546 const APInt &M = MC->getValue()->getValue(); 4547 const APInt &N = NC->getValue()->getValue(); 4548 APInt Two(BitWidth, 2); 4549 APInt Four(BitWidth, 4); 4550 4551 { 4552 using namespace APIntOps; 4553 const APInt& C = L; 4554 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4555 // The B coefficient is M-N/2 4556 APInt B(M); 4557 B -= sdiv(N,Two); 4558 4559 // The A coefficient is N/2 4560 APInt A(N.sdiv(Two)); 4561 4562 // Compute the B^2-4ac term. 4563 APInt SqrtTerm(B); 4564 SqrtTerm *= B; 4565 SqrtTerm -= Four * (A * C); 4566 4567 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4568 // integer value or else APInt::sqrt() will assert. 4569 APInt SqrtVal(SqrtTerm.sqrt()); 4570 4571 // Compute the two solutions for the quadratic formula. 4572 // The divisions must be performed as signed divisions. 4573 APInt NegB(-B); 4574 APInt TwoA( A << 1 ); 4575 if (TwoA.isMinValue()) { 4576 const SCEV *CNC = SE.getCouldNotCompute(); 4577 return std::make_pair(CNC, CNC); 4578 } 4579 4580 LLVMContext &Context = SE.getContext(); 4581 4582 ConstantInt *Solution1 = 4583 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4584 ConstantInt *Solution2 = 4585 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4586 4587 return std::make_pair(SE.getConstant(Solution1), 4588 SE.getConstant(Solution2)); 4589 } // end APIntOps namespace 4590} 4591 4592/// HowFarToZero - Return the number of times a backedge comparing the specified 4593/// value to zero will execute. If not computable, return CouldNotCompute. 4594ScalarEvolution::BackedgeTakenInfo 4595ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4596 // If the value is a constant 4597 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4598 // If the value is already zero, the branch will execute zero times. 4599 if (C->getValue()->isZero()) return C; 4600 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4601 } 4602 4603 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4604 if (!AddRec || AddRec->getLoop() != L) 4605 return getCouldNotCompute(); 4606 4607 if (AddRec->isAffine()) { 4608 // If this is an affine expression, the execution count of this branch is 4609 // the minimum unsigned root of the following equation: 4610 // 4611 // Start + Step*N = 0 (mod 2^BW) 4612 // 4613 // equivalent to: 4614 // 4615 // Step*N = -Start (mod 2^BW) 4616 // 4617 // where BW is the common bit width of Start and Step. 4618 4619 // Get the initial value for the loop. 4620 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4621 L->getParentLoop()); 4622 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4623 L->getParentLoop()); 4624 4625 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4626 // For now we handle only constant steps. 4627 4628 // First, handle unitary steps. 4629 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4630 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4631 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4632 return Start; // N = Start (as unsigned) 4633 4634 // Then, try to solve the above equation provided that Start is constant. 4635 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4636 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4637 -StartC->getValue()->getValue(), 4638 *this); 4639 } 4640 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4641 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4642 // the quadratic equation to solve it. 4643 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4644 *this); 4645 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4646 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4647 if (R1) { 4648#if 0 4649 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4650 << " sol#2: " << *R2 << "\n"; 4651#endif 4652 // Pick the smallest positive root value. 4653 if (ConstantInt *CB = 4654 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4655 R1->getValue(), R2->getValue()))) { 4656 if (CB->getZExtValue() == false) 4657 std::swap(R1, R2); // R1 is the minimum root now. 4658 4659 // We can only use this value if the chrec ends up with an exact zero 4660 // value at this index. When solving for "X*X != 5", for example, we 4661 // should not accept a root of 2. 4662 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4663 if (Val->isZero()) 4664 return R1; // We found a quadratic root! 4665 } 4666 } 4667 } 4668 4669 return getCouldNotCompute(); 4670} 4671 4672/// HowFarToNonZero - Return the number of times a backedge checking the 4673/// specified value for nonzero will execute. If not computable, return 4674/// CouldNotCompute 4675ScalarEvolution::BackedgeTakenInfo 4676ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4677 // Loops that look like: while (X == 0) are very strange indeed. We don't 4678 // handle them yet except for the trivial case. This could be expanded in the 4679 // future as needed. 4680 4681 // If the value is a constant, check to see if it is known to be non-zero 4682 // already. If so, the backedge will execute zero times. 4683 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4684 if (!C->getValue()->isNullValue()) 4685 return getConstant(C->getType(), 0); 4686 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4687 } 4688 4689 // We could implement others, but I really doubt anyone writes loops like 4690 // this, and if they did, they would already be constant folded. 4691 return getCouldNotCompute(); 4692} 4693 4694/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4695/// (which may not be an immediate predecessor) which has exactly one 4696/// successor from which BB is reachable, or null if no such block is 4697/// found. 4698/// 4699std::pair<BasicBlock *, BasicBlock *> 4700ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4701 // If the block has a unique predecessor, then there is no path from the 4702 // predecessor to the block that does not go through the direct edge 4703 // from the predecessor to the block. 4704 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4705 return std::make_pair(Pred, BB); 4706 4707 // A loop's header is defined to be a block that dominates the loop. 4708 // If the header has a unique predecessor outside the loop, it must be 4709 // a block that has exactly one successor that can reach the loop. 4710 if (Loop *L = LI->getLoopFor(BB)) 4711 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4712 4713 return std::pair<BasicBlock *, BasicBlock *>(); 4714} 4715 4716/// HasSameValue - SCEV structural equivalence is usually sufficient for 4717/// testing whether two expressions are equal, however for the purposes of 4718/// looking for a condition guarding a loop, it can be useful to be a little 4719/// more general, since a front-end may have replicated the controlling 4720/// expression. 4721/// 4722static bool HasSameValue(const SCEV *A, const SCEV *B) { 4723 // Quick check to see if they are the same SCEV. 4724 if (A == B) return true; 4725 4726 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4727 // two different instructions with the same value. Check for this case. 4728 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4729 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4730 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4731 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4732 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4733 return true; 4734 4735 // Otherwise assume they may have a different value. 4736 return false; 4737} 4738 4739/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4740/// predicate Pred. Return true iff any changes were made. 4741/// 4742bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4743 const SCEV *&LHS, const SCEV *&RHS) { 4744 bool Changed = false; 4745 4746 // Canonicalize a constant to the right side. 4747 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4748 // Check for both operands constant. 4749 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4750 if (ConstantExpr::getICmp(Pred, 4751 LHSC->getValue(), 4752 RHSC->getValue())->isNullValue()) 4753 goto trivially_false; 4754 else 4755 goto trivially_true; 4756 } 4757 // Otherwise swap the operands to put the constant on the right. 4758 std::swap(LHS, RHS); 4759 Pred = ICmpInst::getSwappedPredicate(Pred); 4760 Changed = true; 4761 } 4762 4763 // If we're comparing an addrec with a value which is loop-invariant in the 4764 // addrec's loop, put the addrec on the left. Also make a dominance check, 4765 // as both operands could be addrecs loop-invariant in each other's loop. 4766 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4767 const Loop *L = AR->getLoop(); 4768 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4769 std::swap(LHS, RHS); 4770 Pred = ICmpInst::getSwappedPredicate(Pred); 4771 Changed = true; 4772 } 4773 } 4774 4775 // If there's a constant operand, canonicalize comparisons with boundary 4776 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4777 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4778 const APInt &RA = RC->getValue()->getValue(); 4779 switch (Pred) { 4780 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4781 case ICmpInst::ICMP_EQ: 4782 case ICmpInst::ICMP_NE: 4783 break; 4784 case ICmpInst::ICMP_UGE: 4785 if ((RA - 1).isMinValue()) { 4786 Pred = ICmpInst::ICMP_NE; 4787 RHS = getConstant(RA - 1); 4788 Changed = true; 4789 break; 4790 } 4791 if (RA.isMaxValue()) { 4792 Pred = ICmpInst::ICMP_EQ; 4793 Changed = true; 4794 break; 4795 } 4796 if (RA.isMinValue()) goto trivially_true; 4797 4798 Pred = ICmpInst::ICMP_UGT; 4799 RHS = getConstant(RA - 1); 4800 Changed = true; 4801 break; 4802 case ICmpInst::ICMP_ULE: 4803 if ((RA + 1).isMaxValue()) { 4804 Pred = ICmpInst::ICMP_NE; 4805 RHS = getConstant(RA + 1); 4806 Changed = true; 4807 break; 4808 } 4809 if (RA.isMinValue()) { 4810 Pred = ICmpInst::ICMP_EQ; 4811 Changed = true; 4812 break; 4813 } 4814 if (RA.isMaxValue()) goto trivially_true; 4815 4816 Pred = ICmpInst::ICMP_ULT; 4817 RHS = getConstant(RA + 1); 4818 Changed = true; 4819 break; 4820 case ICmpInst::ICMP_SGE: 4821 if ((RA - 1).isMinSignedValue()) { 4822 Pred = ICmpInst::ICMP_NE; 4823 RHS = getConstant(RA - 1); 4824 Changed = true; 4825 break; 4826 } 4827 if (RA.isMaxSignedValue()) { 4828 Pred = ICmpInst::ICMP_EQ; 4829 Changed = true; 4830 break; 4831 } 4832 if (RA.isMinSignedValue()) goto trivially_true; 4833 4834 Pred = ICmpInst::ICMP_SGT; 4835 RHS = getConstant(RA - 1); 4836 Changed = true; 4837 break; 4838 case ICmpInst::ICMP_SLE: 4839 if ((RA + 1).isMaxSignedValue()) { 4840 Pred = ICmpInst::ICMP_NE; 4841 RHS = getConstant(RA + 1); 4842 Changed = true; 4843 break; 4844 } 4845 if (RA.isMinSignedValue()) { 4846 Pred = ICmpInst::ICMP_EQ; 4847 Changed = true; 4848 break; 4849 } 4850 if (RA.isMaxSignedValue()) goto trivially_true; 4851 4852 Pred = ICmpInst::ICMP_SLT; 4853 RHS = getConstant(RA + 1); 4854 Changed = true; 4855 break; 4856 case ICmpInst::ICMP_UGT: 4857 if (RA.isMinValue()) { 4858 Pred = ICmpInst::ICMP_NE; 4859 Changed = true; 4860 break; 4861 } 4862 if ((RA + 1).isMaxValue()) { 4863 Pred = ICmpInst::ICMP_EQ; 4864 RHS = getConstant(RA + 1); 4865 Changed = true; 4866 break; 4867 } 4868 if (RA.isMaxValue()) goto trivially_false; 4869 break; 4870 case ICmpInst::ICMP_ULT: 4871 if (RA.isMaxValue()) { 4872 Pred = ICmpInst::ICMP_NE; 4873 Changed = true; 4874 break; 4875 } 4876 if ((RA - 1).isMinValue()) { 4877 Pred = ICmpInst::ICMP_EQ; 4878 RHS = getConstant(RA - 1); 4879 Changed = true; 4880 break; 4881 } 4882 if (RA.isMinValue()) goto trivially_false; 4883 break; 4884 case ICmpInst::ICMP_SGT: 4885 if (RA.isMinSignedValue()) { 4886 Pred = ICmpInst::ICMP_NE; 4887 Changed = true; 4888 break; 4889 } 4890 if ((RA + 1).isMaxSignedValue()) { 4891 Pred = ICmpInst::ICMP_EQ; 4892 RHS = getConstant(RA + 1); 4893 Changed = true; 4894 break; 4895 } 4896 if (RA.isMaxSignedValue()) goto trivially_false; 4897 break; 4898 case ICmpInst::ICMP_SLT: 4899 if (RA.isMaxSignedValue()) { 4900 Pred = ICmpInst::ICMP_NE; 4901 Changed = true; 4902 break; 4903 } 4904 if ((RA - 1).isMinSignedValue()) { 4905 Pred = ICmpInst::ICMP_EQ; 4906 RHS = getConstant(RA - 1); 4907 Changed = true; 4908 break; 4909 } 4910 if (RA.isMinSignedValue()) goto trivially_false; 4911 break; 4912 } 4913 } 4914 4915 // Check for obvious equality. 4916 if (HasSameValue(LHS, RHS)) { 4917 if (ICmpInst::isTrueWhenEqual(Pred)) 4918 goto trivially_true; 4919 if (ICmpInst::isFalseWhenEqual(Pred)) 4920 goto trivially_false; 4921 } 4922 4923 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 4924 // adding or subtracting 1 from one of the operands. 4925 switch (Pred) { 4926 case ICmpInst::ICMP_SLE: 4927 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 4928 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 4929 /*HasNUW=*/false, /*HasNSW=*/true); 4930 Pred = ICmpInst::ICMP_SLT; 4931 Changed = true; 4932 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 4933 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 4934 /*HasNUW=*/false, /*HasNSW=*/true); 4935 Pred = ICmpInst::ICMP_SLT; 4936 Changed = true; 4937 } 4938 break; 4939 case ICmpInst::ICMP_SGE: 4940 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 4941 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 4942 /*HasNUW=*/false, /*HasNSW=*/true); 4943 Pred = ICmpInst::ICMP_SGT; 4944 Changed = true; 4945 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 4946 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 4947 /*HasNUW=*/false, /*HasNSW=*/true); 4948 Pred = ICmpInst::ICMP_SGT; 4949 Changed = true; 4950 } 4951 break; 4952 case ICmpInst::ICMP_ULE: 4953 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 4954 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 4955 /*HasNUW=*/true, /*HasNSW=*/false); 4956 Pred = ICmpInst::ICMP_ULT; 4957 Changed = true; 4958 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 4959 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 4960 /*HasNUW=*/true, /*HasNSW=*/false); 4961 Pred = ICmpInst::ICMP_ULT; 4962 Changed = true; 4963 } 4964 break; 4965 case ICmpInst::ICMP_UGE: 4966 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 4967 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 4968 /*HasNUW=*/true, /*HasNSW=*/false); 4969 Pred = ICmpInst::ICMP_UGT; 4970 Changed = true; 4971 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 4972 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 4973 /*HasNUW=*/true, /*HasNSW=*/false); 4974 Pred = ICmpInst::ICMP_UGT; 4975 Changed = true; 4976 } 4977 break; 4978 default: 4979 break; 4980 } 4981 4982 // TODO: More simplifications are possible here. 4983 4984 return Changed; 4985 4986trivially_true: 4987 // Return 0 == 0. 4988 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 4989 Pred = ICmpInst::ICMP_EQ; 4990 return true; 4991 4992trivially_false: 4993 // Return 0 != 0. 4994 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 4995 Pred = ICmpInst::ICMP_NE; 4996 return true; 4997} 4998 4999bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5000 return getSignedRange(S).getSignedMax().isNegative(); 5001} 5002 5003bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5004 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5005} 5006 5007bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5008 return !getSignedRange(S).getSignedMin().isNegative(); 5009} 5010 5011bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5012 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5013} 5014 5015bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5016 return isKnownNegative(S) || isKnownPositive(S); 5017} 5018 5019bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5020 const SCEV *LHS, const SCEV *RHS) { 5021 // Canonicalize the inputs first. 5022 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5023 5024 // If LHS or RHS is an addrec, check to see if the condition is true in 5025 // every iteration of the loop. 5026 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5027 if (isLoopEntryGuardedByCond( 5028 AR->getLoop(), Pred, AR->getStart(), RHS) && 5029 isLoopBackedgeGuardedByCond( 5030 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5031 return true; 5032 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5033 if (isLoopEntryGuardedByCond( 5034 AR->getLoop(), Pred, LHS, AR->getStart()) && 5035 isLoopBackedgeGuardedByCond( 5036 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5037 return true; 5038 5039 // Otherwise see what can be done with known constant ranges. 5040 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5041} 5042 5043bool 5044ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5045 const SCEV *LHS, const SCEV *RHS) { 5046 if (HasSameValue(LHS, RHS)) 5047 return ICmpInst::isTrueWhenEqual(Pred); 5048 5049 // This code is split out from isKnownPredicate because it is called from 5050 // within isLoopEntryGuardedByCond. 5051 switch (Pred) { 5052 default: 5053 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5054 break; 5055 case ICmpInst::ICMP_SGT: 5056 Pred = ICmpInst::ICMP_SLT; 5057 std::swap(LHS, RHS); 5058 case ICmpInst::ICMP_SLT: { 5059 ConstantRange LHSRange = getSignedRange(LHS); 5060 ConstantRange RHSRange = getSignedRange(RHS); 5061 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5062 return true; 5063 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5064 return false; 5065 break; 5066 } 5067 case ICmpInst::ICMP_SGE: 5068 Pred = ICmpInst::ICMP_SLE; 5069 std::swap(LHS, RHS); 5070 case ICmpInst::ICMP_SLE: { 5071 ConstantRange LHSRange = getSignedRange(LHS); 5072 ConstantRange RHSRange = getSignedRange(RHS); 5073 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5074 return true; 5075 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5076 return false; 5077 break; 5078 } 5079 case ICmpInst::ICMP_UGT: 5080 Pred = ICmpInst::ICMP_ULT; 5081 std::swap(LHS, RHS); 5082 case ICmpInst::ICMP_ULT: { 5083 ConstantRange LHSRange = getUnsignedRange(LHS); 5084 ConstantRange RHSRange = getUnsignedRange(RHS); 5085 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5086 return true; 5087 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5088 return false; 5089 break; 5090 } 5091 case ICmpInst::ICMP_UGE: 5092 Pred = ICmpInst::ICMP_ULE; 5093 std::swap(LHS, RHS); 5094 case ICmpInst::ICMP_ULE: { 5095 ConstantRange LHSRange = getUnsignedRange(LHS); 5096 ConstantRange RHSRange = getUnsignedRange(RHS); 5097 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5098 return true; 5099 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5100 return false; 5101 break; 5102 } 5103 case ICmpInst::ICMP_NE: { 5104 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5105 return true; 5106 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5107 return true; 5108 5109 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5110 if (isKnownNonZero(Diff)) 5111 return true; 5112 break; 5113 } 5114 case ICmpInst::ICMP_EQ: 5115 // The check at the top of the function catches the case where 5116 // the values are known to be equal. 5117 break; 5118 } 5119 return false; 5120} 5121 5122/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5123/// protected by a conditional between LHS and RHS. This is used to 5124/// to eliminate casts. 5125bool 5126ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5127 ICmpInst::Predicate Pred, 5128 const SCEV *LHS, const SCEV *RHS) { 5129 // Interpret a null as meaning no loop, where there is obviously no guard 5130 // (interprocedural conditions notwithstanding). 5131 if (!L) return true; 5132 5133 BasicBlock *Latch = L->getLoopLatch(); 5134 if (!Latch) 5135 return false; 5136 5137 BranchInst *LoopContinuePredicate = 5138 dyn_cast<BranchInst>(Latch->getTerminator()); 5139 if (!LoopContinuePredicate || 5140 LoopContinuePredicate->isUnconditional()) 5141 return false; 5142 5143 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 5144 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5145} 5146 5147/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5148/// by a conditional between LHS and RHS. This is used to help avoid max 5149/// expressions in loop trip counts, and to eliminate casts. 5150bool 5151ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5152 ICmpInst::Predicate Pred, 5153 const SCEV *LHS, const SCEV *RHS) { 5154 // Interpret a null as meaning no loop, where there is obviously no guard 5155 // (interprocedural conditions notwithstanding). 5156 if (!L) return false; 5157 5158 // Starting at the loop predecessor, climb up the predecessor chain, as long 5159 // as there are predecessors that can be found that have unique successors 5160 // leading to the original header. 5161 for (std::pair<BasicBlock *, BasicBlock *> 5162 Pair(L->getLoopPredecessor(), L->getHeader()); 5163 Pair.first; 5164 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5165 5166 BranchInst *LoopEntryPredicate = 5167 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5168 if (!LoopEntryPredicate || 5169 LoopEntryPredicate->isUnconditional()) 5170 continue; 5171 5172 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 5173 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5174 return true; 5175 } 5176 5177 return false; 5178} 5179 5180/// isImpliedCond - Test whether the condition described by Pred, LHS, 5181/// and RHS is true whenever the given Cond value evaluates to true. 5182bool ScalarEvolution::isImpliedCond(Value *CondValue, 5183 ICmpInst::Predicate Pred, 5184 const SCEV *LHS, const SCEV *RHS, 5185 bool Inverse) { 5186 // Recursively handle And and Or conditions. 5187 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 5188 if (BO->getOpcode() == Instruction::And) { 5189 if (!Inverse) 5190 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 5191 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 5192 } else if (BO->getOpcode() == Instruction::Or) { 5193 if (Inverse) 5194 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 5195 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 5196 } 5197 } 5198 5199 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 5200 if (!ICI) return false; 5201 5202 // Bail if the ICmp's operands' types are wider than the needed type 5203 // before attempting to call getSCEV on them. This avoids infinite 5204 // recursion, since the analysis of widening casts can require loop 5205 // exit condition information for overflow checking, which would 5206 // lead back here. 5207 if (getTypeSizeInBits(LHS->getType()) < 5208 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5209 return false; 5210 5211 // Now that we found a conditional branch that dominates the loop, check to 5212 // see if it is the comparison we are looking for. 5213 ICmpInst::Predicate FoundPred; 5214 if (Inverse) 5215 FoundPred = ICI->getInversePredicate(); 5216 else 5217 FoundPred = ICI->getPredicate(); 5218 5219 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5220 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5221 5222 // Balance the types. The case where FoundLHS' type is wider than 5223 // LHS' type is checked for above. 5224 if (getTypeSizeInBits(LHS->getType()) > 5225 getTypeSizeInBits(FoundLHS->getType())) { 5226 if (CmpInst::isSigned(Pred)) { 5227 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5228 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5229 } else { 5230 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5231 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5232 } 5233 } 5234 5235 // Canonicalize the query to match the way instcombine will have 5236 // canonicalized the comparison. 5237 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5238 if (LHS == RHS) 5239 return CmpInst::isTrueWhenEqual(Pred); 5240 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5241 if (FoundLHS == FoundRHS) 5242 return CmpInst::isFalseWhenEqual(Pred); 5243 5244 // Check to see if we can make the LHS or RHS match. 5245 if (LHS == FoundRHS || RHS == FoundLHS) { 5246 if (isa<SCEVConstant>(RHS)) { 5247 std::swap(FoundLHS, FoundRHS); 5248 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5249 } else { 5250 std::swap(LHS, RHS); 5251 Pred = ICmpInst::getSwappedPredicate(Pred); 5252 } 5253 } 5254 5255 // Check whether the found predicate is the same as the desired predicate. 5256 if (FoundPred == Pred) 5257 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5258 5259 // Check whether swapping the found predicate makes it the same as the 5260 // desired predicate. 5261 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5262 if (isa<SCEVConstant>(RHS)) 5263 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5264 else 5265 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5266 RHS, LHS, FoundLHS, FoundRHS); 5267 } 5268 5269 // Check whether the actual condition is beyond sufficient. 5270 if (FoundPred == ICmpInst::ICMP_EQ) 5271 if (ICmpInst::isTrueWhenEqual(Pred)) 5272 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5273 return true; 5274 if (Pred == ICmpInst::ICMP_NE) 5275 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5276 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5277 return true; 5278 5279 // Otherwise assume the worst. 5280 return false; 5281} 5282 5283/// isImpliedCondOperands - Test whether the condition described by Pred, 5284/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5285/// and FoundRHS is true. 5286bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5287 const SCEV *LHS, const SCEV *RHS, 5288 const SCEV *FoundLHS, 5289 const SCEV *FoundRHS) { 5290 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5291 FoundLHS, FoundRHS) || 5292 // ~x < ~y --> x > y 5293 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5294 getNotSCEV(FoundRHS), 5295 getNotSCEV(FoundLHS)); 5296} 5297 5298/// isImpliedCondOperandsHelper - Test whether the condition described by 5299/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5300/// FoundLHS, and FoundRHS is true. 5301bool 5302ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5303 const SCEV *LHS, const SCEV *RHS, 5304 const SCEV *FoundLHS, 5305 const SCEV *FoundRHS) { 5306 switch (Pred) { 5307 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5308 case ICmpInst::ICMP_EQ: 5309 case ICmpInst::ICMP_NE: 5310 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5311 return true; 5312 break; 5313 case ICmpInst::ICMP_SLT: 5314 case ICmpInst::ICMP_SLE: 5315 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5316 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5317 return true; 5318 break; 5319 case ICmpInst::ICMP_SGT: 5320 case ICmpInst::ICMP_SGE: 5321 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5322 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5323 return true; 5324 break; 5325 case ICmpInst::ICMP_ULT: 5326 case ICmpInst::ICMP_ULE: 5327 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5328 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5329 return true; 5330 break; 5331 case ICmpInst::ICMP_UGT: 5332 case ICmpInst::ICMP_UGE: 5333 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5334 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5335 return true; 5336 break; 5337 } 5338 5339 return false; 5340} 5341 5342/// getBECount - Subtract the end and start values and divide by the step, 5343/// rounding up, to get the number of times the backedge is executed. Return 5344/// CouldNotCompute if an intermediate computation overflows. 5345const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5346 const SCEV *End, 5347 const SCEV *Step, 5348 bool NoWrap) { 5349 assert(!isKnownNegative(Step) && 5350 "This code doesn't handle negative strides yet!"); 5351 5352 const Type *Ty = Start->getType(); 5353 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5354 const SCEV *Diff = getMinusSCEV(End, Start); 5355 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5356 5357 // Add an adjustment to the difference between End and Start so that 5358 // the division will effectively round up. 5359 const SCEV *Add = getAddExpr(Diff, RoundUp); 5360 5361 if (!NoWrap) { 5362 // Check Add for unsigned overflow. 5363 // TODO: More sophisticated things could be done here. 5364 const Type *WideTy = IntegerType::get(getContext(), 5365 getTypeSizeInBits(Ty) + 1); 5366 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5367 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5368 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5369 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5370 return getCouldNotCompute(); 5371 } 5372 5373 return getUDivExpr(Add, Step); 5374} 5375 5376/// HowManyLessThans - Return the number of times a backedge containing the 5377/// specified less-than comparison will execute. If not computable, return 5378/// CouldNotCompute. 5379ScalarEvolution::BackedgeTakenInfo 5380ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5381 const Loop *L, bool isSigned) { 5382 // Only handle: "ADDREC < LoopInvariant". 5383 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5384 5385 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5386 if (!AddRec || AddRec->getLoop() != L) 5387 return getCouldNotCompute(); 5388 5389 // Check to see if we have a flag which makes analysis easy. 5390 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5391 AddRec->hasNoUnsignedWrap(); 5392 5393 if (AddRec->isAffine()) { 5394 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5395 const SCEV *Step = AddRec->getStepRecurrence(*this); 5396 5397 if (Step->isZero()) 5398 return getCouldNotCompute(); 5399 if (Step->isOne()) { 5400 // With unit stride, the iteration never steps past the limit value. 5401 } else if (isKnownPositive(Step)) { 5402 // Test whether a positive iteration can step past the limit 5403 // value and past the maximum value for its type in a single step. 5404 // Note that it's not sufficient to check NoWrap here, because even 5405 // though the value after a wrap is undefined, it's not undefined 5406 // behavior, so if wrap does occur, the loop could either terminate or 5407 // loop infinitely, but in either case, the loop is guaranteed to 5408 // iterate at least until the iteration where the wrapping occurs. 5409 const SCEV *One = getConstant(Step->getType(), 1); 5410 if (isSigned) { 5411 APInt Max = APInt::getSignedMaxValue(BitWidth); 5412 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5413 .slt(getSignedRange(RHS).getSignedMax())) 5414 return getCouldNotCompute(); 5415 } else { 5416 APInt Max = APInt::getMaxValue(BitWidth); 5417 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5418 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5419 return getCouldNotCompute(); 5420 } 5421 } else 5422 // TODO: Handle negative strides here and below. 5423 return getCouldNotCompute(); 5424 5425 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5426 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5427 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5428 // treat m-n as signed nor unsigned due to overflow possibility. 5429 5430 // First, we get the value of the LHS in the first iteration: n 5431 const SCEV *Start = AddRec->getOperand(0); 5432 5433 // Determine the minimum constant start value. 5434 const SCEV *MinStart = getConstant(isSigned ? 5435 getSignedRange(Start).getSignedMin() : 5436 getUnsignedRange(Start).getUnsignedMin()); 5437 5438 // If we know that the condition is true in order to enter the loop, 5439 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5440 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5441 // the division must round up. 5442 const SCEV *End = RHS; 5443 if (!isLoopEntryGuardedByCond(L, 5444 isSigned ? ICmpInst::ICMP_SLT : 5445 ICmpInst::ICMP_ULT, 5446 getMinusSCEV(Start, Step), RHS)) 5447 End = isSigned ? getSMaxExpr(RHS, Start) 5448 : getUMaxExpr(RHS, Start); 5449 5450 // Determine the maximum constant end value. 5451 const SCEV *MaxEnd = getConstant(isSigned ? 5452 getSignedRange(End).getSignedMax() : 5453 getUnsignedRange(End).getUnsignedMax()); 5454 5455 // If MaxEnd is within a step of the maximum integer value in its type, 5456 // adjust it down to the minimum value which would produce the same effect. 5457 // This allows the subsequent ceiling division of (N+(step-1))/step to 5458 // compute the correct value. 5459 const SCEV *StepMinusOne = getMinusSCEV(Step, 5460 getConstant(Step->getType(), 1)); 5461 MaxEnd = isSigned ? 5462 getSMinExpr(MaxEnd, 5463 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5464 StepMinusOne)) : 5465 getUMinExpr(MaxEnd, 5466 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5467 StepMinusOne)); 5468 5469 // Finally, we subtract these two values and divide, rounding up, to get 5470 // the number of times the backedge is executed. 5471 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5472 5473 // The maximum backedge count is similar, except using the minimum start 5474 // value and the maximum end value. 5475 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5476 5477 return BackedgeTakenInfo(BECount, MaxBECount); 5478 } 5479 5480 return getCouldNotCompute(); 5481} 5482 5483/// getNumIterationsInRange - Return the number of iterations of this loop that 5484/// produce values in the specified constant range. Another way of looking at 5485/// this is that it returns the first iteration number where the value is not in 5486/// the condition, thus computing the exit count. If the iteration count can't 5487/// be computed, an instance of SCEVCouldNotCompute is returned. 5488const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5489 ScalarEvolution &SE) const { 5490 if (Range.isFullSet()) // Infinite loop. 5491 return SE.getCouldNotCompute(); 5492 5493 // If the start is a non-zero constant, shift the range to simplify things. 5494 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5495 if (!SC->getValue()->isZero()) { 5496 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5497 Operands[0] = SE.getConstant(SC->getType(), 0); 5498 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5499 if (const SCEVAddRecExpr *ShiftedAddRec = 5500 dyn_cast<SCEVAddRecExpr>(Shifted)) 5501 return ShiftedAddRec->getNumIterationsInRange( 5502 Range.subtract(SC->getValue()->getValue()), SE); 5503 // This is strange and shouldn't happen. 5504 return SE.getCouldNotCompute(); 5505 } 5506 5507 // The only time we can solve this is when we have all constant indices. 5508 // Otherwise, we cannot determine the overflow conditions. 5509 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5510 if (!isa<SCEVConstant>(getOperand(i))) 5511 return SE.getCouldNotCompute(); 5512 5513 5514 // Okay at this point we know that all elements of the chrec are constants and 5515 // that the start element is zero. 5516 5517 // First check to see if the range contains zero. If not, the first 5518 // iteration exits. 5519 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5520 if (!Range.contains(APInt(BitWidth, 0))) 5521 return SE.getConstant(getType(), 0); 5522 5523 if (isAffine()) { 5524 // If this is an affine expression then we have this situation: 5525 // Solve {0,+,A} in Range === Ax in Range 5526 5527 // We know that zero is in the range. If A is positive then we know that 5528 // the upper value of the range must be the first possible exit value. 5529 // If A is negative then the lower of the range is the last possible loop 5530 // value. Also note that we already checked for a full range. 5531 APInt One(BitWidth,1); 5532 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5533 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5534 5535 // The exit value should be (End+A)/A. 5536 APInt ExitVal = (End + A).udiv(A); 5537 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5538 5539 // Evaluate at the exit value. If we really did fall out of the valid 5540 // range, then we computed our trip count, otherwise wrap around or other 5541 // things must have happened. 5542 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5543 if (Range.contains(Val->getValue())) 5544 return SE.getCouldNotCompute(); // Something strange happened 5545 5546 // Ensure that the previous value is in the range. This is a sanity check. 5547 assert(Range.contains( 5548 EvaluateConstantChrecAtConstant(this, 5549 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5550 "Linear scev computation is off in a bad way!"); 5551 return SE.getConstant(ExitValue); 5552 } else if (isQuadratic()) { 5553 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5554 // quadratic equation to solve it. To do this, we must frame our problem in 5555 // terms of figuring out when zero is crossed, instead of when 5556 // Range.getUpper() is crossed. 5557 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5558 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5559 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5560 5561 // Next, solve the constructed addrec 5562 std::pair<const SCEV *,const SCEV *> Roots = 5563 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5564 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5565 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5566 if (R1) { 5567 // Pick the smallest positive root value. 5568 if (ConstantInt *CB = 5569 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5570 R1->getValue(), R2->getValue()))) { 5571 if (CB->getZExtValue() == false) 5572 std::swap(R1, R2); // R1 is the minimum root now. 5573 5574 // Make sure the root is not off by one. The returned iteration should 5575 // not be in the range, but the previous one should be. When solving 5576 // for "X*X < 5", for example, we should not return a root of 2. 5577 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5578 R1->getValue(), 5579 SE); 5580 if (Range.contains(R1Val->getValue())) { 5581 // The next iteration must be out of the range... 5582 ConstantInt *NextVal = 5583 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5584 5585 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5586 if (!Range.contains(R1Val->getValue())) 5587 return SE.getConstant(NextVal); 5588 return SE.getCouldNotCompute(); // Something strange happened 5589 } 5590 5591 // If R1 was not in the range, then it is a good return value. Make 5592 // sure that R1-1 WAS in the range though, just in case. 5593 ConstantInt *NextVal = 5594 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5595 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5596 if (Range.contains(R1Val->getValue())) 5597 return R1; 5598 return SE.getCouldNotCompute(); // Something strange happened 5599 } 5600 } 5601 } 5602 5603 return SE.getCouldNotCompute(); 5604} 5605 5606 5607 5608//===----------------------------------------------------------------------===// 5609// SCEVCallbackVH Class Implementation 5610//===----------------------------------------------------------------------===// 5611 5612void ScalarEvolution::SCEVCallbackVH::deleted() { 5613 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5614 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5615 SE->ConstantEvolutionLoopExitValue.erase(PN); 5616 SE->Scalars.erase(getValPtr()); 5617 // this now dangles! 5618} 5619 5620void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5621 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5622 5623 // Forget all the expressions associated with users of the old value, 5624 // so that future queries will recompute the expressions using the new 5625 // value. 5626 SmallVector<User *, 16> Worklist; 5627 SmallPtrSet<User *, 8> Visited; 5628 Value *Old = getValPtr(); 5629 bool DeleteOld = false; 5630 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5631 UI != UE; ++UI) 5632 Worklist.push_back(*UI); 5633 while (!Worklist.empty()) { 5634 User *U = Worklist.pop_back_val(); 5635 // Deleting the Old value will cause this to dangle. Postpone 5636 // that until everything else is done. 5637 if (U == Old) { 5638 DeleteOld = true; 5639 continue; 5640 } 5641 if (!Visited.insert(U)) 5642 continue; 5643 if (PHINode *PN = dyn_cast<PHINode>(U)) 5644 SE->ConstantEvolutionLoopExitValue.erase(PN); 5645 SE->Scalars.erase(U); 5646 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5647 UI != UE; ++UI) 5648 Worklist.push_back(*UI); 5649 } 5650 // Delete the Old value if it (indirectly) references itself. 5651 if (DeleteOld) { 5652 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5653 SE->ConstantEvolutionLoopExitValue.erase(PN); 5654 SE->Scalars.erase(Old); 5655 // this now dangles! 5656 } 5657 // this may dangle! 5658} 5659 5660ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5661 : CallbackVH(V), SE(se) {} 5662 5663//===----------------------------------------------------------------------===// 5664// ScalarEvolution Class Implementation 5665//===----------------------------------------------------------------------===// 5666 5667ScalarEvolution::ScalarEvolution() 5668 : FunctionPass(&ID) { 5669} 5670 5671bool ScalarEvolution::runOnFunction(Function &F) { 5672 this->F = &F; 5673 LI = &getAnalysis<LoopInfo>(); 5674 TD = getAnalysisIfAvailable<TargetData>(); 5675 DT = &getAnalysis<DominatorTree>(); 5676 return false; 5677} 5678 5679void ScalarEvolution::releaseMemory() { 5680 Scalars.clear(); 5681 BackedgeTakenCounts.clear(); 5682 ConstantEvolutionLoopExitValue.clear(); 5683 ValuesAtScopes.clear(); 5684 UniqueSCEVs.clear(); 5685 SCEVAllocator.Reset(); 5686} 5687 5688void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5689 AU.setPreservesAll(); 5690 AU.addRequiredTransitive<LoopInfo>(); 5691 AU.addRequiredTransitive<DominatorTree>(); 5692} 5693 5694bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5695 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5696} 5697 5698static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5699 const Loop *L) { 5700 // Print all inner loops first 5701 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5702 PrintLoopInfo(OS, SE, *I); 5703 5704 OS << "Loop "; 5705 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5706 OS << ": "; 5707 5708 SmallVector<BasicBlock *, 8> ExitBlocks; 5709 L->getExitBlocks(ExitBlocks); 5710 if (ExitBlocks.size() != 1) 5711 OS << "<multiple exits> "; 5712 5713 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5714 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5715 } else { 5716 OS << "Unpredictable backedge-taken count. "; 5717 } 5718 5719 OS << "\n" 5720 "Loop "; 5721 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5722 OS << ": "; 5723 5724 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5725 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5726 } else { 5727 OS << "Unpredictable max backedge-taken count. "; 5728 } 5729 5730 OS << "\n"; 5731} 5732 5733void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5734 // ScalarEvolution's implementation of the print method is to print 5735 // out SCEV values of all instructions that are interesting. Doing 5736 // this potentially causes it to create new SCEV objects though, 5737 // which technically conflicts with the const qualifier. This isn't 5738 // observable from outside the class though, so casting away the 5739 // const isn't dangerous. 5740 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5741 5742 OS << "Classifying expressions for: "; 5743 WriteAsOperand(OS, F, /*PrintType=*/false); 5744 OS << "\n"; 5745 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5746 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5747 OS << *I << '\n'; 5748 OS << " --> "; 5749 const SCEV *SV = SE.getSCEV(&*I); 5750 SV->print(OS); 5751 5752 const Loop *L = LI->getLoopFor((*I).getParent()); 5753 5754 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5755 if (AtUse != SV) { 5756 OS << " --> "; 5757 AtUse->print(OS); 5758 } 5759 5760 if (L) { 5761 OS << "\t\t" "Exits: "; 5762 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5763 if (!ExitValue->isLoopInvariant(L)) { 5764 OS << "<<Unknown>>"; 5765 } else { 5766 OS << *ExitValue; 5767 } 5768 } 5769 5770 OS << "\n"; 5771 } 5772 5773 OS << "Determining loop execution counts for: "; 5774 WriteAsOperand(OS, F, /*PrintType=*/false); 5775 OS << "\n"; 5776 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5777 PrintLoopInfo(OS, &SE, *I); 5778} 5779 5780