ScalarEvolution.cpp revision c72f0c8c57a79fe9d32d9147ec3b8717ade6faa1
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. 1212 for (unsigned i = 0, e = NumOperands; i != e; ++i) { 1213 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1214 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1215 APInt NewScale = 1216 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1217 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1218 // A multiplication of a constant with another add; recurse. 1219 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1220 Interesting |= 1221 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1222 Add->op_begin(), Add->getNumOperands(), 1223 NewScale, SE); 1224 } else { 1225 // A multiplication of a constant with some other value. Update 1226 // the map. 1227 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1228 const SCEV *Key = SE.getMulExpr(MulOps); 1229 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1230 M.insert(std::make_pair(Key, NewScale)); 1231 if (Pair.second) { 1232 NewOps.push_back(Pair.first->first); 1233 } else { 1234 Pair.first->second += NewScale; 1235 // The map already had an entry for this value, which may indicate 1236 // a folding opportunity. 1237 Interesting = true; 1238 } 1239 } 1240 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1241 // Pull a buried constant out to the outside. 1242 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1243 Interesting = true; 1244 AccumulatedConstant += Scale * C->getValue()->getValue(); 1245 } else { 1246 // An ordinary operand. Update the map. 1247 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1248 M.insert(std::make_pair(Ops[i], Scale)); 1249 if (Pair.second) { 1250 NewOps.push_back(Pair.first->first); 1251 } else { 1252 Pair.first->second += Scale; 1253 // The map already had an entry for this value, which may indicate 1254 // a folding opportunity. 1255 Interesting = true; 1256 } 1257 } 1258 } 1259 1260 return Interesting; 1261} 1262 1263namespace { 1264 struct APIntCompare { 1265 bool operator()(const APInt &LHS, const APInt &RHS) const { 1266 return LHS.ult(RHS); 1267 } 1268 }; 1269} 1270 1271/// getAddExpr - Get a canonical add expression, or something simpler if 1272/// possible. 1273const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1274 bool HasNUW, bool HasNSW) { 1275 assert(!Ops.empty() && "Cannot get empty add!"); 1276 if (Ops.size() == 1) return Ops[0]; 1277#ifndef NDEBUG 1278 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1279 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1280 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1281 "SCEVAddExpr operand types don't match!"); 1282#endif 1283 1284 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1285 if (!HasNUW && HasNSW) { 1286 bool All = true; 1287 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1288 if (!isKnownNonNegative(Ops[i])) { 1289 All = false; 1290 break; 1291 } 1292 if (All) HasNUW = true; 1293 } 1294 1295 // Sort by complexity, this groups all similar expression types together. 1296 GroupByComplexity(Ops, LI); 1297 1298 // If there are any constants, fold them together. 1299 unsigned Idx = 0; 1300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1301 ++Idx; 1302 assert(Idx < Ops.size()); 1303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1304 // We found two constants, fold them together! 1305 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1306 RHSC->getValue()->getValue()); 1307 if (Ops.size() == 2) return Ops[0]; 1308 Ops.erase(Ops.begin()+1); // Erase the folded element 1309 LHSC = cast<SCEVConstant>(Ops[0]); 1310 } 1311 1312 // If we are left with a constant zero being added, strip it off. 1313 if (LHSC->getValue()->isZero()) { 1314 Ops.erase(Ops.begin()); 1315 --Idx; 1316 } 1317 1318 if (Ops.size() == 1) return Ops[0]; 1319 } 1320 1321 // Okay, check to see if the same value occurs in the operand list twice. If 1322 // so, merge them together into an multiply expression. Since we sorted the 1323 // list, these values are required to be adjacent. 1324 const Type *Ty = Ops[0]->getType(); 1325 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1326 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1327 // Found a match, merge the two values into a multiply, and add any 1328 // remaining values to the result. 1329 const SCEV *Two = getConstant(Ty, 2); 1330 const SCEV *Mul = getMulExpr(Ops[i], Two); 1331 if (Ops.size() == 2) 1332 return Mul; 1333 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1334 Ops.push_back(Mul); 1335 return getAddExpr(Ops, HasNUW, HasNSW); 1336 } 1337 1338 // Check for truncates. If all the operands are truncated from the same 1339 // type, see if factoring out the truncate would permit the result to be 1340 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1341 // if the contents of the resulting outer trunc fold to something simple. 1342 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1343 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1344 const Type *DstType = Trunc->getType(); 1345 const Type *SrcType = Trunc->getOperand()->getType(); 1346 SmallVector<const SCEV *, 8> LargeOps; 1347 bool Ok = true; 1348 // Check all the operands to see if they can be represented in the 1349 // source type of the truncate. 1350 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1351 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1352 if (T->getOperand()->getType() != SrcType) { 1353 Ok = false; 1354 break; 1355 } 1356 LargeOps.push_back(T->getOperand()); 1357 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1358 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1359 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1360 SmallVector<const SCEV *, 8> LargeMulOps; 1361 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1362 if (const SCEVTruncateExpr *T = 1363 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1364 if (T->getOperand()->getType() != SrcType) { 1365 Ok = false; 1366 break; 1367 } 1368 LargeMulOps.push_back(T->getOperand()); 1369 } else if (const SCEVConstant *C = 1370 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1371 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1372 } else { 1373 Ok = false; 1374 break; 1375 } 1376 } 1377 if (Ok) 1378 LargeOps.push_back(getMulExpr(LargeMulOps)); 1379 } else { 1380 Ok = false; 1381 break; 1382 } 1383 } 1384 if (Ok) { 1385 // Evaluate the expression in the larger type. 1386 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1387 // If it folds to something simple, use it. Otherwise, don't. 1388 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1389 return getTruncateExpr(Fold, DstType); 1390 } 1391 } 1392 1393 // Skip past any other cast SCEVs. 1394 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1395 ++Idx; 1396 1397 // If there are add operands they would be next. 1398 if (Idx < Ops.size()) { 1399 bool DeletedAdd = false; 1400 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1401 // If we have an add, expand the add operands onto the end of the operands 1402 // list. 1403 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1404 Ops.erase(Ops.begin()+Idx); 1405 DeletedAdd = true; 1406 } 1407 1408 // If we deleted at least one add, we added operands to the end of the list, 1409 // and they are not necessarily sorted. Recurse to resort and resimplify 1410 // any operands we just acquired. 1411 if (DeletedAdd) 1412 return getAddExpr(Ops); 1413 } 1414 1415 // Skip over the add expression until we get to a multiply. 1416 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1417 ++Idx; 1418 1419 // Check to see if there are any folding opportunities present with 1420 // operands multiplied by constant values. 1421 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1422 uint64_t BitWidth = getTypeSizeInBits(Ty); 1423 DenseMap<const SCEV *, APInt> M; 1424 SmallVector<const SCEV *, 8> NewOps; 1425 APInt AccumulatedConstant(BitWidth, 0); 1426 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1427 Ops.data(), Ops.size(), 1428 APInt(BitWidth, 1), *this)) { 1429 // Some interesting folding opportunity is present, so its worthwhile to 1430 // re-generate the operands list. Group the operands by constant scale, 1431 // to avoid multiplying by the same constant scale multiple times. 1432 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1433 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1434 E = NewOps.end(); I != E; ++I) 1435 MulOpLists[M.find(*I)->second].push_back(*I); 1436 // Re-generate the operands list. 1437 Ops.clear(); 1438 if (AccumulatedConstant != 0) 1439 Ops.push_back(getConstant(AccumulatedConstant)); 1440 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1441 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1442 if (I->first != 0) 1443 Ops.push_back(getMulExpr(getConstant(I->first), 1444 getAddExpr(I->second))); 1445 if (Ops.empty()) 1446 return getConstant(Ty, 0); 1447 if (Ops.size() == 1) 1448 return Ops[0]; 1449 return getAddExpr(Ops); 1450 } 1451 } 1452 1453 // If we are adding something to a multiply expression, make sure the 1454 // something is not already an operand of the multiply. If so, merge it into 1455 // the multiply. 1456 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1457 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1458 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1459 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1460 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1461 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1462 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1463 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1464 if (Mul->getNumOperands() != 2) { 1465 // If the multiply has more than two operands, we must get the 1466 // Y*Z term. 1467 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1468 MulOps.erase(MulOps.begin()+MulOp); 1469 InnerMul = getMulExpr(MulOps); 1470 } 1471 const SCEV *One = getConstant(Ty, 1); 1472 const SCEV *AddOne = getAddExpr(InnerMul, One); 1473 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1474 if (Ops.size() == 2) return OuterMul; 1475 if (AddOp < Idx) { 1476 Ops.erase(Ops.begin()+AddOp); 1477 Ops.erase(Ops.begin()+Idx-1); 1478 } else { 1479 Ops.erase(Ops.begin()+Idx); 1480 Ops.erase(Ops.begin()+AddOp-1); 1481 } 1482 Ops.push_back(OuterMul); 1483 return getAddExpr(Ops); 1484 } 1485 1486 // Check this multiply against other multiplies being added together. 1487 for (unsigned OtherMulIdx = Idx+1; 1488 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1489 ++OtherMulIdx) { 1490 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1491 // If MulOp occurs in OtherMul, we can fold the two multiplies 1492 // together. 1493 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1494 OMulOp != e; ++OMulOp) 1495 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1496 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1497 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1498 if (Mul->getNumOperands() != 2) { 1499 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1500 Mul->op_end()); 1501 MulOps.erase(MulOps.begin()+MulOp); 1502 InnerMul1 = getMulExpr(MulOps); 1503 } 1504 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1505 if (OtherMul->getNumOperands() != 2) { 1506 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1507 OtherMul->op_end()); 1508 MulOps.erase(MulOps.begin()+OMulOp); 1509 InnerMul2 = getMulExpr(MulOps); 1510 } 1511 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1512 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1513 if (Ops.size() == 2) return OuterMul; 1514 Ops.erase(Ops.begin()+Idx); 1515 Ops.erase(Ops.begin()+OtherMulIdx-1); 1516 Ops.push_back(OuterMul); 1517 return getAddExpr(Ops); 1518 } 1519 } 1520 } 1521 } 1522 1523 // If there are any add recurrences in the operands list, see if any other 1524 // added values are loop invariant. If so, we can fold them into the 1525 // recurrence. 1526 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1527 ++Idx; 1528 1529 // Scan over all recurrences, trying to fold loop invariants into them. 1530 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1531 // Scan all of the other operands to this add and add them to the vector if 1532 // they are loop invariant w.r.t. the recurrence. 1533 SmallVector<const SCEV *, 8> LIOps; 1534 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1535 const Loop *AddRecLoop = AddRec->getLoop(); 1536 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1537 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1538 LIOps.push_back(Ops[i]); 1539 Ops.erase(Ops.begin()+i); 1540 --i; --e; 1541 } 1542 1543 // If we found some loop invariants, fold them into the recurrence. 1544 if (!LIOps.empty()) { 1545 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1546 LIOps.push_back(AddRec->getStart()); 1547 1548 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1549 AddRec->op_end()); 1550 AddRecOps[0] = getAddExpr(LIOps); 1551 1552 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition 1553 // is not associative so this isn't necessarily safe. 1554 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop); 1555 1556 // If all of the other operands were loop invariant, we are done. 1557 if (Ops.size() == 1) return NewRec; 1558 1559 // Otherwise, add the folded AddRec by the non-liv parts. 1560 for (unsigned i = 0;; ++i) 1561 if (Ops[i] == AddRec) { 1562 Ops[i] = NewRec; 1563 break; 1564 } 1565 return getAddExpr(Ops); 1566 } 1567 1568 // Okay, if there weren't any loop invariants to be folded, check to see if 1569 // there are multiple AddRec's with the same loop induction variable being 1570 // added together. If so, we can fold them. 1571 for (unsigned OtherIdx = Idx+1; 1572 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1573 if (OtherIdx != Idx) { 1574 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1575 if (AddRecLoop == OtherAddRec->getLoop()) { 1576 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1577 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1578 AddRec->op_end()); 1579 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1580 if (i >= NewOps.size()) { 1581 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1582 OtherAddRec->op_end()); 1583 break; 1584 } 1585 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1586 } 1587 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop); 1588 1589 if (Ops.size() == 2) return NewAddRec; 1590 1591 Ops.erase(Ops.begin()+Idx); 1592 Ops.erase(Ops.begin()+OtherIdx-1); 1593 Ops.push_back(NewAddRec); 1594 return getAddExpr(Ops); 1595 } 1596 } 1597 1598 // Otherwise couldn't fold anything into this recurrence. Move onto the 1599 // next one. 1600 } 1601 1602 // Okay, it looks like we really DO need an add expr. Check to see if we 1603 // already have one, otherwise create a new one. 1604 FoldingSetNodeID ID; 1605 ID.AddInteger(scAddExpr); 1606 ID.AddInteger(Ops.size()); 1607 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1608 ID.AddPointer(Ops[i]); 1609 void *IP = 0; 1610 SCEVAddExpr *S = 1611 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1612 if (!S) { 1613 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1614 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1615 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1616 O, Ops.size()); 1617 UniqueSCEVs.InsertNode(S, IP); 1618 } 1619 if (HasNUW) S->setHasNoUnsignedWrap(true); 1620 if (HasNSW) S->setHasNoSignedWrap(true); 1621 return S; 1622} 1623 1624/// getMulExpr - Get a canonical multiply expression, or something simpler if 1625/// possible. 1626const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1627 bool HasNUW, bool HasNSW) { 1628 assert(!Ops.empty() && "Cannot get empty mul!"); 1629 if (Ops.size() == 1) return Ops[0]; 1630#ifndef NDEBUG 1631 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1632 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1633 getEffectiveSCEVType(Ops[0]->getType()) && 1634 "SCEVMulExpr operand types don't match!"); 1635#endif 1636 1637 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1638 if (!HasNUW && HasNSW) { 1639 bool All = true; 1640 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1641 if (!isKnownNonNegative(Ops[i])) { 1642 All = false; 1643 break; 1644 } 1645 if (All) HasNUW = true; 1646 } 1647 1648 // Sort by complexity, this groups all similar expression types together. 1649 GroupByComplexity(Ops, LI); 1650 1651 // If there are any constants, fold them together. 1652 unsigned Idx = 0; 1653 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1654 1655 // C1*(C2+V) -> C1*C2 + C1*V 1656 if (Ops.size() == 2) 1657 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1658 if (Add->getNumOperands() == 2 && 1659 isa<SCEVConstant>(Add->getOperand(0))) 1660 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1661 getMulExpr(LHSC, Add->getOperand(1))); 1662 1663 ++Idx; 1664 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1665 // We found two constants, fold them together! 1666 ConstantInt *Fold = ConstantInt::get(getContext(), 1667 LHSC->getValue()->getValue() * 1668 RHSC->getValue()->getValue()); 1669 Ops[0] = getConstant(Fold); 1670 Ops.erase(Ops.begin()+1); // Erase the folded element 1671 if (Ops.size() == 1) return Ops[0]; 1672 LHSC = cast<SCEVConstant>(Ops[0]); 1673 } 1674 1675 // If we are left with a constant one being multiplied, strip it off. 1676 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1677 Ops.erase(Ops.begin()); 1678 --Idx; 1679 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1680 // If we have a multiply of zero, it will always be zero. 1681 return Ops[0]; 1682 } else if (Ops[0]->isAllOnesValue()) { 1683 // If we have a mul by -1 of an add, try distributing the -1 among the 1684 // add operands. 1685 if (Ops.size() == 2) 1686 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1687 SmallVector<const SCEV *, 4> NewOps; 1688 bool AnyFolded = false; 1689 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1690 I != E; ++I) { 1691 const SCEV *Mul = getMulExpr(Ops[0], *I); 1692 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1693 NewOps.push_back(Mul); 1694 } 1695 if (AnyFolded) 1696 return getAddExpr(NewOps); 1697 } 1698 } 1699 1700 if (Ops.size() == 1) 1701 return Ops[0]; 1702 } 1703 1704 // Skip over the add expression until we get to a multiply. 1705 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1706 ++Idx; 1707 1708 // If there are mul operands inline them all into this expression. 1709 if (Idx < Ops.size()) { 1710 bool DeletedMul = false; 1711 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1712 // If we have an mul, expand the mul operands onto the end of the operands 1713 // list. 1714 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1715 Ops.erase(Ops.begin()+Idx); 1716 DeletedMul = true; 1717 } 1718 1719 // If we deleted at least one mul, we added operands to the end of the list, 1720 // and they are not necessarily sorted. Recurse to resort and resimplify 1721 // any operands we just acquired. 1722 if (DeletedMul) 1723 return getMulExpr(Ops); 1724 } 1725 1726 // If there are any add recurrences in the operands list, see if any other 1727 // added values are loop invariant. If so, we can fold them into the 1728 // recurrence. 1729 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1730 ++Idx; 1731 1732 // Scan over all recurrences, trying to fold loop invariants into them. 1733 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1734 // Scan all of the other operands to this mul and add them to the vector if 1735 // they are loop invariant w.r.t. the recurrence. 1736 SmallVector<const SCEV *, 8> LIOps; 1737 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1738 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1739 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1740 LIOps.push_back(Ops[i]); 1741 Ops.erase(Ops.begin()+i); 1742 --i; --e; 1743 } 1744 1745 // If we found some loop invariants, fold them into the recurrence. 1746 if (!LIOps.empty()) { 1747 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1748 SmallVector<const SCEV *, 4> NewOps; 1749 NewOps.reserve(AddRec->getNumOperands()); 1750 const SCEV *Scale = getMulExpr(LIOps); 1751 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1752 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1753 1754 // It's tempting to propagate the NSW flag here, but nsw multiplication 1755 // is not associative so this isn't necessarily safe. 1756 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1757 HasNUW && AddRec->hasNoUnsignedWrap(), 1758 /*HasNSW=*/false); 1759 1760 // If all of the other operands were loop invariant, we are done. 1761 if (Ops.size() == 1) return NewRec; 1762 1763 // Otherwise, multiply the folded AddRec by the non-liv parts. 1764 for (unsigned i = 0;; ++i) 1765 if (Ops[i] == AddRec) { 1766 Ops[i] = NewRec; 1767 break; 1768 } 1769 return getMulExpr(Ops); 1770 } 1771 1772 // Okay, if there weren't any loop invariants to be folded, check to see if 1773 // there are multiple AddRec's with the same loop induction variable being 1774 // multiplied together. If so, we can fold them. 1775 for (unsigned OtherIdx = Idx+1; 1776 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1777 if (OtherIdx != Idx) { 1778 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1779 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1780 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1781 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1782 const SCEV *NewStart = getMulExpr(F->getStart(), 1783 G->getStart()); 1784 const SCEV *B = F->getStepRecurrence(*this); 1785 const SCEV *D = G->getStepRecurrence(*this); 1786 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1787 getMulExpr(G, B), 1788 getMulExpr(B, D)); 1789 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1790 F->getLoop()); 1791 if (Ops.size() == 2) return NewAddRec; 1792 1793 Ops.erase(Ops.begin()+Idx); 1794 Ops.erase(Ops.begin()+OtherIdx-1); 1795 Ops.push_back(NewAddRec); 1796 return getMulExpr(Ops); 1797 } 1798 } 1799 1800 // Otherwise couldn't fold anything into this recurrence. Move onto the 1801 // next one. 1802 } 1803 1804 // Okay, it looks like we really DO need an mul expr. Check to see if we 1805 // already have one, otherwise create a new one. 1806 FoldingSetNodeID ID; 1807 ID.AddInteger(scMulExpr); 1808 ID.AddInteger(Ops.size()); 1809 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1810 ID.AddPointer(Ops[i]); 1811 void *IP = 0; 1812 SCEVMulExpr *S = 1813 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1814 if (!S) { 1815 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1816 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1817 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1818 O, Ops.size()); 1819 UniqueSCEVs.InsertNode(S, IP); 1820 } 1821 if (HasNUW) S->setHasNoUnsignedWrap(true); 1822 if (HasNSW) S->setHasNoSignedWrap(true); 1823 return S; 1824} 1825 1826/// getUDivExpr - Get a canonical unsigned division expression, or something 1827/// simpler if possible. 1828const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1829 const SCEV *RHS) { 1830 assert(getEffectiveSCEVType(LHS->getType()) == 1831 getEffectiveSCEVType(RHS->getType()) && 1832 "SCEVUDivExpr operand types don't match!"); 1833 1834 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1835 if (RHSC->getValue()->equalsInt(1)) 1836 return LHS; // X udiv 1 --> x 1837 // If the denominator is zero, the result of the udiv is undefined. Don't 1838 // try to analyze it, because the resolution chosen here may differ from 1839 // the resolution chosen in other parts of the compiler. 1840 if (!RHSC->getValue()->isZero()) { 1841 // Determine if the division can be folded into the operands of 1842 // its operands. 1843 // TODO: Generalize this to non-constants by using known-bits information. 1844 const Type *Ty = LHS->getType(); 1845 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1846 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1847 // For non-power-of-two values, effectively round the value up to the 1848 // nearest power of two. 1849 if (!RHSC->getValue()->getValue().isPowerOf2()) 1850 ++MaxShiftAmt; 1851 const IntegerType *ExtTy = 1852 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1853 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1854 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1855 if (const SCEVConstant *Step = 1856 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1857 if (!Step->getValue()->getValue() 1858 .urem(RHSC->getValue()->getValue()) && 1859 getZeroExtendExpr(AR, ExtTy) == 1860 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1861 getZeroExtendExpr(Step, ExtTy), 1862 AR->getLoop())) { 1863 SmallVector<const SCEV *, 4> Operands; 1864 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1865 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1866 return getAddRecExpr(Operands, AR->getLoop()); 1867 } 1868 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1869 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1870 SmallVector<const SCEV *, 4> Operands; 1871 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1872 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1873 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1874 // Find an operand that's safely divisible. 1875 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1876 const SCEV *Op = M->getOperand(i); 1877 const SCEV *Div = getUDivExpr(Op, RHSC); 1878 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1879 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1880 M->op_end()); 1881 Operands[i] = Div; 1882 return getMulExpr(Operands); 1883 } 1884 } 1885 } 1886 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1887 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1888 SmallVector<const SCEV *, 4> Operands; 1889 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1890 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1891 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1892 Operands.clear(); 1893 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1894 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1895 if (isa<SCEVUDivExpr>(Op) || 1896 getMulExpr(Op, RHS) != A->getOperand(i)) 1897 break; 1898 Operands.push_back(Op); 1899 } 1900 if (Operands.size() == A->getNumOperands()) 1901 return getAddExpr(Operands); 1902 } 1903 } 1904 1905 // Fold if both operands are constant. 1906 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1907 Constant *LHSCV = LHSC->getValue(); 1908 Constant *RHSCV = RHSC->getValue(); 1909 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1910 RHSCV))); 1911 } 1912 } 1913 } 1914 1915 FoldingSetNodeID ID; 1916 ID.AddInteger(scUDivExpr); 1917 ID.AddPointer(LHS); 1918 ID.AddPointer(RHS); 1919 void *IP = 0; 1920 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1921 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1922 LHS, RHS); 1923 UniqueSCEVs.InsertNode(S, IP); 1924 return S; 1925} 1926 1927 1928/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1929/// Simplify the expression as much as possible. 1930const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1931 const SCEV *Step, const Loop *L, 1932 bool HasNUW, bool HasNSW) { 1933 SmallVector<const SCEV *, 4> Operands; 1934 Operands.push_back(Start); 1935 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1936 if (StepChrec->getLoop() == L) { 1937 Operands.insert(Operands.end(), StepChrec->op_begin(), 1938 StepChrec->op_end()); 1939 return getAddRecExpr(Operands, L); 1940 } 1941 1942 Operands.push_back(Step); 1943 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1944} 1945 1946/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1947/// Simplify the expression as much as possible. 1948const SCEV * 1949ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1950 const Loop *L, 1951 bool HasNUW, bool HasNSW) { 1952 if (Operands.size() == 1) return Operands[0]; 1953#ifndef NDEBUG 1954 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1955 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1956 getEffectiveSCEVType(Operands[0]->getType()) && 1957 "SCEVAddRecExpr operand types don't match!"); 1958#endif 1959 1960 if (Operands.back()->isZero()) { 1961 Operands.pop_back(); 1962 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1963 } 1964 1965 // It's tempting to want to call getMaxBackedgeTakenCount count here and 1966 // use that information to infer NUW and NSW flags. However, computing a 1967 // BE count requires calling getAddRecExpr, so we may not yet have a 1968 // meaningful BE count at this point (and if we don't, we'd be stuck 1969 // with a SCEVCouldNotCompute as the cached BE count). 1970 1971 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1972 if (!HasNUW && HasNSW) { 1973 bool All = true; 1974 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1975 if (!isKnownNonNegative(Operands[i])) { 1976 All = false; 1977 break; 1978 } 1979 if (All) HasNUW = true; 1980 } 1981 1982 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1983 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1984 const Loop *NestedLoop = NestedAR->getLoop(); 1985 if (L->contains(NestedLoop->getHeader()) ? 1986 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1987 (!NestedLoop->contains(L->getHeader()) && 1988 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1989 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1990 NestedAR->op_end()); 1991 Operands[0] = NestedAR->getStart(); 1992 // AddRecs require their operands be loop-invariant with respect to their 1993 // loops. Don't perform this transformation if it would break this 1994 // requirement. 1995 bool AllInvariant = true; 1996 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1997 if (!Operands[i]->isLoopInvariant(L)) { 1998 AllInvariant = false; 1999 break; 2000 } 2001 if (AllInvariant) { 2002 NestedOperands[0] = getAddRecExpr(Operands, L); 2003 AllInvariant = true; 2004 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2005 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2006 AllInvariant = false; 2007 break; 2008 } 2009 if (AllInvariant) 2010 // Ok, both add recurrences are valid after the transformation. 2011 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2012 } 2013 // Reset Operands to its original state. 2014 Operands[0] = NestedAR; 2015 } 2016 } 2017 2018 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2019 // already have one, otherwise create a new one. 2020 FoldingSetNodeID ID; 2021 ID.AddInteger(scAddRecExpr); 2022 ID.AddInteger(Operands.size()); 2023 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2024 ID.AddPointer(Operands[i]); 2025 ID.AddPointer(L); 2026 void *IP = 0; 2027 SCEVAddRecExpr *S = 2028 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2029 if (!S) { 2030 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2031 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2032 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2033 O, Operands.size(), L); 2034 UniqueSCEVs.InsertNode(S, IP); 2035 } 2036 if (HasNUW) S->setHasNoUnsignedWrap(true); 2037 if (HasNSW) S->setHasNoSignedWrap(true); 2038 return S; 2039} 2040 2041const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2042 const SCEV *RHS) { 2043 SmallVector<const SCEV *, 2> Ops; 2044 Ops.push_back(LHS); 2045 Ops.push_back(RHS); 2046 return getSMaxExpr(Ops); 2047} 2048 2049const SCEV * 2050ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2051 assert(!Ops.empty() && "Cannot get empty smax!"); 2052 if (Ops.size() == 1) return Ops[0]; 2053#ifndef NDEBUG 2054 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2055 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2056 getEffectiveSCEVType(Ops[0]->getType()) && 2057 "SCEVSMaxExpr operand types don't match!"); 2058#endif 2059 2060 // Sort by complexity, this groups all similar expression types together. 2061 GroupByComplexity(Ops, LI); 2062 2063 // If there are any constants, fold them together. 2064 unsigned Idx = 0; 2065 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2066 ++Idx; 2067 assert(Idx < Ops.size()); 2068 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2069 // We found two constants, fold them together! 2070 ConstantInt *Fold = ConstantInt::get(getContext(), 2071 APIntOps::smax(LHSC->getValue()->getValue(), 2072 RHSC->getValue()->getValue())); 2073 Ops[0] = getConstant(Fold); 2074 Ops.erase(Ops.begin()+1); // Erase the folded element 2075 if (Ops.size() == 1) return Ops[0]; 2076 LHSC = cast<SCEVConstant>(Ops[0]); 2077 } 2078 2079 // If we are left with a constant minimum-int, strip it off. 2080 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2081 Ops.erase(Ops.begin()); 2082 --Idx; 2083 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2084 // If we have an smax with a constant maximum-int, it will always be 2085 // maximum-int. 2086 return Ops[0]; 2087 } 2088 2089 if (Ops.size() == 1) return Ops[0]; 2090 } 2091 2092 // Find the first SMax 2093 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2094 ++Idx; 2095 2096 // Check to see if one of the operands is an SMax. If so, expand its operands 2097 // onto our operand list, and recurse to simplify. 2098 if (Idx < Ops.size()) { 2099 bool DeletedSMax = false; 2100 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2101 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 2102 Ops.erase(Ops.begin()+Idx); 2103 DeletedSMax = true; 2104 } 2105 2106 if (DeletedSMax) 2107 return getSMaxExpr(Ops); 2108 } 2109 2110 // Okay, check to see if the same value occurs in the operand list twice. If 2111 // so, delete one. Since we sorted the list, these values are required to 2112 // be adjacent. 2113 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2114 // X smax Y smax Y --> X smax Y 2115 // X smax Y --> X, if X is always greater than Y 2116 if (Ops[i] == Ops[i+1] || 2117 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2118 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2119 --i; --e; 2120 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2121 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2122 --i; --e; 2123 } 2124 2125 if (Ops.size() == 1) return Ops[0]; 2126 2127 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2128 2129 // Okay, it looks like we really DO need an smax expr. Check to see if we 2130 // already have one, otherwise create a new one. 2131 FoldingSetNodeID ID; 2132 ID.AddInteger(scSMaxExpr); 2133 ID.AddInteger(Ops.size()); 2134 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2135 ID.AddPointer(Ops[i]); 2136 void *IP = 0; 2137 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2138 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2139 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2140 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2141 O, Ops.size()); 2142 UniqueSCEVs.InsertNode(S, IP); 2143 return S; 2144} 2145 2146const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2147 const SCEV *RHS) { 2148 SmallVector<const SCEV *, 2> Ops; 2149 Ops.push_back(LHS); 2150 Ops.push_back(RHS); 2151 return getUMaxExpr(Ops); 2152} 2153 2154const SCEV * 2155ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2156 assert(!Ops.empty() && "Cannot get empty umax!"); 2157 if (Ops.size() == 1) return Ops[0]; 2158#ifndef NDEBUG 2159 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2160 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2161 getEffectiveSCEVType(Ops[0]->getType()) && 2162 "SCEVUMaxExpr operand types don't match!"); 2163#endif 2164 2165 // Sort by complexity, this groups all similar expression types together. 2166 GroupByComplexity(Ops, LI); 2167 2168 // If there are any constants, fold them together. 2169 unsigned Idx = 0; 2170 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2171 ++Idx; 2172 assert(Idx < Ops.size()); 2173 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2174 // We found two constants, fold them together! 2175 ConstantInt *Fold = ConstantInt::get(getContext(), 2176 APIntOps::umax(LHSC->getValue()->getValue(), 2177 RHSC->getValue()->getValue())); 2178 Ops[0] = getConstant(Fold); 2179 Ops.erase(Ops.begin()+1); // Erase the folded element 2180 if (Ops.size() == 1) return Ops[0]; 2181 LHSC = cast<SCEVConstant>(Ops[0]); 2182 } 2183 2184 // If we are left with a constant minimum-int, strip it off. 2185 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2186 Ops.erase(Ops.begin()); 2187 --Idx; 2188 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2189 // If we have an umax with a constant maximum-int, it will always be 2190 // maximum-int. 2191 return Ops[0]; 2192 } 2193 2194 if (Ops.size() == 1) return Ops[0]; 2195 } 2196 2197 // Find the first UMax 2198 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2199 ++Idx; 2200 2201 // Check to see if one of the operands is a UMax. If so, expand its operands 2202 // onto our operand list, and recurse to simplify. 2203 if (Idx < Ops.size()) { 2204 bool DeletedUMax = false; 2205 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2206 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2207 Ops.erase(Ops.begin()+Idx); 2208 DeletedUMax = true; 2209 } 2210 2211 if (DeletedUMax) 2212 return getUMaxExpr(Ops); 2213 } 2214 2215 // Okay, check to see if the same value occurs in the operand list twice. If 2216 // so, delete one. Since we sorted the list, these values are required to 2217 // be adjacent. 2218 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2219 // X umax Y umax Y --> X umax Y 2220 // X umax Y --> X, if X is always greater than Y 2221 if (Ops[i] == Ops[i+1] || 2222 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2223 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2224 --i; --e; 2225 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2226 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2227 --i; --e; 2228 } 2229 2230 if (Ops.size() == 1) return Ops[0]; 2231 2232 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2233 2234 // Okay, it looks like we really DO need a umax expr. Check to see if we 2235 // already have one, otherwise create a new one. 2236 FoldingSetNodeID ID; 2237 ID.AddInteger(scUMaxExpr); 2238 ID.AddInteger(Ops.size()); 2239 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2240 ID.AddPointer(Ops[i]); 2241 void *IP = 0; 2242 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2243 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2244 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2245 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2246 O, Ops.size()); 2247 UniqueSCEVs.InsertNode(S, IP); 2248 return S; 2249} 2250 2251const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2252 const SCEV *RHS) { 2253 // ~smax(~x, ~y) == smin(x, y). 2254 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2255} 2256 2257const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2258 const SCEV *RHS) { 2259 // ~umax(~x, ~y) == umin(x, y) 2260 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2261} 2262 2263const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2264 // If we have TargetData, we can bypass creating a target-independent 2265 // constant expression and then folding it back into a ConstantInt. 2266 // This is just a compile-time optimization. 2267 if (TD) 2268 return getConstant(TD->getIntPtrType(getContext()), 2269 TD->getTypeAllocSize(AllocTy)); 2270 2271 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2272 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2273 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2274 C = Folded; 2275 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2276 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2277} 2278 2279const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2280 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2281 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2282 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2283 C = Folded; 2284 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2285 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2286} 2287 2288const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2289 unsigned FieldNo) { 2290 // If we have TargetData, we can bypass creating a target-independent 2291 // constant expression and then folding it back into a ConstantInt. 2292 // This is just a compile-time optimization. 2293 if (TD) 2294 return getConstant(TD->getIntPtrType(getContext()), 2295 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2296 2297 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2298 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2299 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2300 C = Folded; 2301 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2302 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2303} 2304 2305const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2306 Constant *FieldNo) { 2307 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2308 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2309 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2310 C = Folded; 2311 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2312 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2313} 2314 2315const SCEV *ScalarEvolution::getUnknown(Value *V) { 2316 // Don't attempt to do anything other than create a SCEVUnknown object 2317 // here. createSCEV only calls getUnknown after checking for all other 2318 // interesting possibilities, and any other code that calls getUnknown 2319 // is doing so in order to hide a value from SCEV canonicalization. 2320 2321 FoldingSetNodeID ID; 2322 ID.AddInteger(scUnknown); 2323 ID.AddPointer(V); 2324 void *IP = 0; 2325 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2326 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V); 2327 UniqueSCEVs.InsertNode(S, IP); 2328 return S; 2329} 2330 2331//===----------------------------------------------------------------------===// 2332// Basic SCEV Analysis and PHI Idiom Recognition Code 2333// 2334 2335/// isSCEVable - Test if values of the given type are analyzable within 2336/// the SCEV framework. This primarily includes integer types, and it 2337/// can optionally include pointer types if the ScalarEvolution class 2338/// has access to target-specific information. 2339bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2340 // Integers and pointers are always SCEVable. 2341 return Ty->isIntegerTy() || Ty->isPointerTy(); 2342} 2343 2344/// getTypeSizeInBits - Return the size in bits of the specified type, 2345/// for which isSCEVable must return true. 2346uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2347 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2348 2349 // If we have a TargetData, use it! 2350 if (TD) 2351 return TD->getTypeSizeInBits(Ty); 2352 2353 // Integer types have fixed sizes. 2354 if (Ty->isIntegerTy()) 2355 return Ty->getPrimitiveSizeInBits(); 2356 2357 // The only other support type is pointer. Without TargetData, conservatively 2358 // assume pointers are 64-bit. 2359 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2360 return 64; 2361} 2362 2363/// getEffectiveSCEVType - Return a type with the same bitwidth as 2364/// the given type and which represents how SCEV will treat the given 2365/// type, for which isSCEVable must return true. For pointer types, 2366/// this is the pointer-sized integer type. 2367const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2368 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2369 2370 if (Ty->isIntegerTy()) 2371 return Ty; 2372 2373 // The only other support type is pointer. 2374 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2375 if (TD) return TD->getIntPtrType(getContext()); 2376 2377 // Without TargetData, conservatively assume pointers are 64-bit. 2378 return Type::getInt64Ty(getContext()); 2379} 2380 2381const SCEV *ScalarEvolution::getCouldNotCompute() { 2382 return &CouldNotCompute; 2383} 2384 2385/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2386/// expression and create a new one. 2387const SCEV *ScalarEvolution::getSCEV(Value *V) { 2388 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2389 2390 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2391 if (I != Scalars.end()) return I->second; 2392 const SCEV *S = createSCEV(V); 2393 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2394 return S; 2395} 2396 2397/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2398/// 2399const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2400 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2401 return getConstant( 2402 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2403 2404 const Type *Ty = V->getType(); 2405 Ty = getEffectiveSCEVType(Ty); 2406 return getMulExpr(V, 2407 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2408} 2409 2410/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2411const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2412 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2413 return getConstant( 2414 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2415 2416 const Type *Ty = V->getType(); 2417 Ty = getEffectiveSCEVType(Ty); 2418 const SCEV *AllOnes = 2419 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2420 return getMinusSCEV(AllOnes, V); 2421} 2422 2423/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2424/// 2425const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2426 const SCEV *RHS) { 2427 // X - Y --> X + -Y 2428 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2429} 2430 2431/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2432/// input value to the specified type. If the type must be extended, it is zero 2433/// extended. 2434const SCEV * 2435ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2436 const Type *Ty) { 2437 const Type *SrcTy = V->getType(); 2438 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2439 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2440 "Cannot truncate or zero extend with non-integer arguments!"); 2441 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2442 return V; // No conversion 2443 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2444 return getTruncateExpr(V, Ty); 2445 return getZeroExtendExpr(V, Ty); 2446} 2447 2448/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2449/// input value to the specified type. If the type must be extended, it is sign 2450/// extended. 2451const SCEV * 2452ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2453 const Type *Ty) { 2454 const Type *SrcTy = V->getType(); 2455 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2456 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2457 "Cannot truncate or zero extend with non-integer arguments!"); 2458 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2459 return V; // No conversion 2460 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2461 return getTruncateExpr(V, Ty); 2462 return getSignExtendExpr(V, Ty); 2463} 2464 2465/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2466/// input value to the specified type. If the type must be extended, it is zero 2467/// extended. The conversion must not be narrowing. 2468const SCEV * 2469ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2470 const Type *SrcTy = V->getType(); 2471 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2472 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2473 "Cannot noop or zero extend with non-integer arguments!"); 2474 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2475 "getNoopOrZeroExtend cannot truncate!"); 2476 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2477 return V; // No conversion 2478 return getZeroExtendExpr(V, Ty); 2479} 2480 2481/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2482/// input value to the specified type. If the type must be extended, it is sign 2483/// extended. The conversion must not be narrowing. 2484const SCEV * 2485ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2486 const Type *SrcTy = V->getType(); 2487 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2488 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2489 "Cannot noop or sign extend with non-integer arguments!"); 2490 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2491 "getNoopOrSignExtend cannot truncate!"); 2492 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2493 return V; // No conversion 2494 return getSignExtendExpr(V, Ty); 2495} 2496 2497/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2498/// the input value to the specified type. If the type must be extended, 2499/// it is extended with unspecified bits. The conversion must not be 2500/// narrowing. 2501const SCEV * 2502ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2503 const Type *SrcTy = V->getType(); 2504 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2505 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2506 "Cannot noop or any extend with non-integer arguments!"); 2507 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2508 "getNoopOrAnyExtend cannot truncate!"); 2509 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2510 return V; // No conversion 2511 return getAnyExtendExpr(V, Ty); 2512} 2513 2514/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2515/// input value to the specified type. The conversion must not be widening. 2516const SCEV * 2517ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2518 const Type *SrcTy = V->getType(); 2519 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2520 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2521 "Cannot truncate or noop with non-integer arguments!"); 2522 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2523 "getTruncateOrNoop cannot extend!"); 2524 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2525 return V; // No conversion 2526 return getTruncateExpr(V, Ty); 2527} 2528 2529/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2530/// the types using zero-extension, and then perform a umax operation 2531/// with them. 2532const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2533 const SCEV *RHS) { 2534 const SCEV *PromotedLHS = LHS; 2535 const SCEV *PromotedRHS = RHS; 2536 2537 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2538 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2539 else 2540 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2541 2542 return getUMaxExpr(PromotedLHS, PromotedRHS); 2543} 2544 2545/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2546/// the types using zero-extension, and then perform a umin operation 2547/// with them. 2548const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2549 const SCEV *RHS) { 2550 const SCEV *PromotedLHS = LHS; 2551 const SCEV *PromotedRHS = RHS; 2552 2553 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2554 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2555 else 2556 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2557 2558 return getUMinExpr(PromotedLHS, PromotedRHS); 2559} 2560 2561/// PushDefUseChildren - Push users of the given Instruction 2562/// onto the given Worklist. 2563static void 2564PushDefUseChildren(Instruction *I, 2565 SmallVectorImpl<Instruction *> &Worklist) { 2566 // Push the def-use children onto the Worklist stack. 2567 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2568 UI != UE; ++UI) 2569 Worklist.push_back(cast<Instruction>(UI)); 2570} 2571 2572/// ForgetSymbolicValue - This looks up computed SCEV values for all 2573/// instructions that depend on the given instruction and removes them from 2574/// the Scalars map if they reference SymName. This is used during PHI 2575/// resolution. 2576void 2577ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2578 SmallVector<Instruction *, 16> Worklist; 2579 PushDefUseChildren(PN, Worklist); 2580 2581 SmallPtrSet<Instruction *, 8> Visited; 2582 Visited.insert(PN); 2583 while (!Worklist.empty()) { 2584 Instruction *I = Worklist.pop_back_val(); 2585 if (!Visited.insert(I)) continue; 2586 2587 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2588 Scalars.find(static_cast<Value *>(I)); 2589 if (It != Scalars.end()) { 2590 // Short-circuit the def-use traversal if the symbolic name 2591 // ceases to appear in expressions. 2592 if (It->second != SymName && !It->second->hasOperand(SymName)) 2593 continue; 2594 2595 // SCEVUnknown for a PHI either means that it has an unrecognized 2596 // structure, it's a PHI that's in the progress of being computed 2597 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2598 // additional loop trip count information isn't going to change anything. 2599 // In the second case, createNodeForPHI will perform the necessary 2600 // updates on its own when it gets to that point. In the third, we do 2601 // want to forget the SCEVUnknown. 2602 if (!isa<PHINode>(I) || 2603 !isa<SCEVUnknown>(It->second) || 2604 (I != PN && It->second == SymName)) { 2605 ValuesAtScopes.erase(It->second); 2606 Scalars.erase(It); 2607 } 2608 } 2609 2610 PushDefUseChildren(I, Worklist); 2611 } 2612} 2613 2614/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2615/// a loop header, making it a potential recurrence, or it doesn't. 2616/// 2617const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2618 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2619 if (L->getHeader() == PN->getParent()) { 2620 // The loop may have multiple entrances or multiple exits; we can analyze 2621 // this phi as an addrec if it has a unique entry value and a unique 2622 // backedge value. 2623 Value *BEValueV = 0, *StartValueV = 0; 2624 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2625 Value *V = PN->getIncomingValue(i); 2626 if (L->contains(PN->getIncomingBlock(i))) { 2627 if (!BEValueV) { 2628 BEValueV = V; 2629 } else if (BEValueV != V) { 2630 BEValueV = 0; 2631 break; 2632 } 2633 } else if (!StartValueV) { 2634 StartValueV = V; 2635 } else if (StartValueV != V) { 2636 StartValueV = 0; 2637 break; 2638 } 2639 } 2640 if (BEValueV && StartValueV) { 2641 // While we are analyzing this PHI node, handle its value symbolically. 2642 const SCEV *SymbolicName = getUnknown(PN); 2643 assert(Scalars.find(PN) == Scalars.end() && 2644 "PHI node already processed?"); 2645 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2646 2647 // Using this symbolic name for the PHI, analyze the value coming around 2648 // the back-edge. 2649 const SCEV *BEValue = getSCEV(BEValueV); 2650 2651 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2652 // has a special value for the first iteration of the loop. 2653 2654 // If the value coming around the backedge is an add with the symbolic 2655 // value we just inserted, then we found a simple induction variable! 2656 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2657 // If there is a single occurrence of the symbolic value, replace it 2658 // with a recurrence. 2659 unsigned FoundIndex = Add->getNumOperands(); 2660 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2661 if (Add->getOperand(i) == SymbolicName) 2662 if (FoundIndex == e) { 2663 FoundIndex = i; 2664 break; 2665 } 2666 2667 if (FoundIndex != Add->getNumOperands()) { 2668 // Create an add with everything but the specified operand. 2669 SmallVector<const SCEV *, 8> Ops; 2670 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2671 if (i != FoundIndex) 2672 Ops.push_back(Add->getOperand(i)); 2673 const SCEV *Accum = getAddExpr(Ops); 2674 2675 // This is not a valid addrec if the step amount is varying each 2676 // loop iteration, but is not itself an addrec in this loop. 2677 if (Accum->isLoopInvariant(L) || 2678 (isa<SCEVAddRecExpr>(Accum) && 2679 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2680 bool HasNUW = false; 2681 bool HasNSW = false; 2682 2683 // If the increment doesn't overflow, then neither the addrec nor 2684 // the post-increment will overflow. 2685 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2686 if (OBO->hasNoUnsignedWrap()) 2687 HasNUW = true; 2688 if (OBO->hasNoSignedWrap()) 2689 HasNSW = true; 2690 } 2691 2692 const SCEV *StartVal = getSCEV(StartValueV); 2693 const SCEV *PHISCEV = 2694 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2695 2696 // Since the no-wrap flags are on the increment, they apply to the 2697 // post-incremented value as well. 2698 if (Accum->isLoopInvariant(L)) 2699 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2700 Accum, L, HasNUW, HasNSW); 2701 2702 // Okay, for the entire analysis of this edge we assumed the PHI 2703 // to be symbolic. We now need to go back and purge all of the 2704 // entries for the scalars that use the symbolic expression. 2705 ForgetSymbolicName(PN, SymbolicName); 2706 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2707 return PHISCEV; 2708 } 2709 } 2710 } else if (const SCEVAddRecExpr *AddRec = 2711 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2712 // Otherwise, this could be a loop like this: 2713 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2714 // In this case, j = {1,+,1} and BEValue is j. 2715 // Because the other in-value of i (0) fits the evolution of BEValue 2716 // i really is an addrec evolution. 2717 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2718 const SCEV *StartVal = getSCEV(StartValueV); 2719 2720 // If StartVal = j.start - j.stride, we can use StartVal as the 2721 // initial step of the addrec evolution. 2722 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2723 AddRec->getOperand(1))) { 2724 const SCEV *PHISCEV = 2725 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2726 2727 // Okay, for the entire analysis of this edge we assumed the PHI 2728 // to be symbolic. We now need to go back and purge all of the 2729 // entries for the scalars that use the symbolic expression. 2730 ForgetSymbolicName(PN, SymbolicName); 2731 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2732 return PHISCEV; 2733 } 2734 } 2735 } 2736 } 2737 } 2738 2739 // If the PHI has a single incoming value, follow that value, unless the 2740 // PHI's incoming blocks are in a different loop, in which case doing so 2741 // risks breaking LCSSA form. Instcombine would normally zap these, but 2742 // it doesn't have DominatorTree information, so it may miss cases. 2743 if (Value *V = PN->hasConstantValue(DT)) { 2744 bool AllSameLoop = true; 2745 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2746 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2747 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2748 AllSameLoop = false; 2749 break; 2750 } 2751 if (AllSameLoop) 2752 return getSCEV(V); 2753 } 2754 2755 // If it's not a loop phi, we can't handle it yet. 2756 return getUnknown(PN); 2757} 2758 2759/// createNodeForGEP - Expand GEP instructions into add and multiply 2760/// operations. This allows them to be analyzed by regular SCEV code. 2761/// 2762const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2763 2764 bool InBounds = GEP->isInBounds(); 2765 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2766 Value *Base = GEP->getOperand(0); 2767 // Don't attempt to analyze GEPs over unsized objects. 2768 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2769 return getUnknown(GEP); 2770 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2771 gep_type_iterator GTI = gep_type_begin(GEP); 2772 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2773 E = GEP->op_end(); 2774 I != E; ++I) { 2775 Value *Index = *I; 2776 // Compute the (potentially symbolic) offset in bytes for this index. 2777 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2778 // For a struct, add the member offset. 2779 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2780 TotalOffset = getAddExpr(TotalOffset, 2781 getOffsetOfExpr(STy, FieldNo), 2782 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2783 } else { 2784 // For an array, add the element offset, explicitly scaled. 2785 const SCEV *LocalOffset = getSCEV(Index); 2786 // Getelementptr indices are signed. 2787 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2788 // Lower "inbounds" GEPs to NSW arithmetic. 2789 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2790 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2791 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2792 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2793 } 2794 } 2795 return getAddExpr(getSCEV(Base), TotalOffset, 2796 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2797} 2798 2799/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2800/// guaranteed to end in (at every loop iteration). It is, at the same time, 2801/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2802/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2803uint32_t 2804ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2805 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2806 return C->getValue()->getValue().countTrailingZeros(); 2807 2808 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2809 return std::min(GetMinTrailingZeros(T->getOperand()), 2810 (uint32_t)getTypeSizeInBits(T->getType())); 2811 2812 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2813 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2814 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2815 getTypeSizeInBits(E->getType()) : OpRes; 2816 } 2817 2818 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2819 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2820 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2821 getTypeSizeInBits(E->getType()) : OpRes; 2822 } 2823 2824 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2825 // The result is the min of all operands results. 2826 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2827 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2828 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2829 return MinOpRes; 2830 } 2831 2832 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2833 // The result is the sum of all operands results. 2834 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2835 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2836 for (unsigned i = 1, e = M->getNumOperands(); 2837 SumOpRes != BitWidth && i != e; ++i) 2838 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2839 BitWidth); 2840 return SumOpRes; 2841 } 2842 2843 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2844 // The result is the min of all operands results. 2845 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2846 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2847 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2848 return MinOpRes; 2849 } 2850 2851 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2852 // The result is the min of all operands results. 2853 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2854 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2855 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2856 return MinOpRes; 2857 } 2858 2859 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2860 // The result is the min of all operands results. 2861 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2862 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2863 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2864 return MinOpRes; 2865 } 2866 2867 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2868 // For a SCEVUnknown, ask ValueTracking. 2869 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2870 APInt Mask = APInt::getAllOnesValue(BitWidth); 2871 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2872 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2873 return Zeros.countTrailingOnes(); 2874 } 2875 2876 // SCEVUDivExpr 2877 return 0; 2878} 2879 2880/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2881/// 2882ConstantRange 2883ScalarEvolution::getUnsignedRange(const SCEV *S) { 2884 2885 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2886 return ConstantRange(C->getValue()->getValue()); 2887 2888 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2889 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2890 2891 // If the value has known zeros, the maximum unsigned value will have those 2892 // known zeros as well. 2893 uint32_t TZ = GetMinTrailingZeros(S); 2894 if (TZ != 0) 2895 ConservativeResult = 2896 ConstantRange(APInt::getMinValue(BitWidth), 2897 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2898 2899 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2900 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2901 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2902 X = X.add(getUnsignedRange(Add->getOperand(i))); 2903 return ConservativeResult.intersectWith(X); 2904 } 2905 2906 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2907 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2908 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2909 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2910 return ConservativeResult.intersectWith(X); 2911 } 2912 2913 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2914 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2915 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2916 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2917 return ConservativeResult.intersectWith(X); 2918 } 2919 2920 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2921 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2922 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2923 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2924 return ConservativeResult.intersectWith(X); 2925 } 2926 2927 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2928 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2929 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2930 return ConservativeResult.intersectWith(X.udiv(Y)); 2931 } 2932 2933 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2934 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2935 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2936 } 2937 2938 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2939 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2940 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2941 } 2942 2943 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2944 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2945 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2946 } 2947 2948 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2949 // If there's no unsigned wrap, the value will never be less than its 2950 // initial value. 2951 if (AddRec->hasNoUnsignedWrap()) 2952 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2953 if (!C->getValue()->isZero()) 2954 ConservativeResult = 2955 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)); 2956 2957 // TODO: non-affine addrec 2958 if (AddRec->isAffine()) { 2959 const Type *Ty = AddRec->getType(); 2960 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2961 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2962 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2963 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2964 2965 const SCEV *Start = AddRec->getStart(); 2966 const SCEV *Step = AddRec->getStepRecurrence(*this); 2967 2968 ConstantRange StartRange = getUnsignedRange(Start); 2969 ConstantRange StepRange = getSignedRange(Step); 2970 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 2971 ConstantRange EndRange = 2972 StartRange.add(MaxBECountRange.multiply(StepRange)); 2973 2974 // Check for overflow. This must be done with ConstantRange arithmetic 2975 // because we could be called from within the ScalarEvolution overflow 2976 // checking code. 2977 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 2978 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 2979 ConstantRange ExtMaxBECountRange = 2980 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 2981 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 2982 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 2983 ExtEndRange) 2984 return ConservativeResult; 2985 2986 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2987 EndRange.getUnsignedMin()); 2988 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2989 EndRange.getUnsignedMax()); 2990 if (Min.isMinValue() && Max.isMaxValue()) 2991 return ConservativeResult; 2992 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2993 } 2994 } 2995 2996 return ConservativeResult; 2997 } 2998 2999 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3000 // For a SCEVUnknown, ask ValueTracking. 3001 APInt Mask = APInt::getAllOnesValue(BitWidth); 3002 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3003 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3004 if (Ones == ~Zeros + 1) 3005 return ConservativeResult; 3006 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3007 } 3008 3009 return ConservativeResult; 3010} 3011 3012/// getSignedRange - Determine the signed range for a particular SCEV. 3013/// 3014ConstantRange 3015ScalarEvolution::getSignedRange(const SCEV *S) { 3016 3017 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3018 return ConstantRange(C->getValue()->getValue()); 3019 3020 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3021 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3022 3023 // If the value has known zeros, the maximum signed value will have those 3024 // known zeros as well. 3025 uint32_t TZ = GetMinTrailingZeros(S); 3026 if (TZ != 0) 3027 ConservativeResult = 3028 ConstantRange(APInt::getSignedMinValue(BitWidth), 3029 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3030 3031 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3032 ConstantRange X = getSignedRange(Add->getOperand(0)); 3033 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3034 X = X.add(getSignedRange(Add->getOperand(i))); 3035 return ConservativeResult.intersectWith(X); 3036 } 3037 3038 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3039 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3040 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3041 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3042 return ConservativeResult.intersectWith(X); 3043 } 3044 3045 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3046 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3047 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3048 X = X.smax(getSignedRange(SMax->getOperand(i))); 3049 return ConservativeResult.intersectWith(X); 3050 } 3051 3052 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3053 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3054 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3055 X = X.umax(getSignedRange(UMax->getOperand(i))); 3056 return ConservativeResult.intersectWith(X); 3057 } 3058 3059 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3060 ConstantRange X = getSignedRange(UDiv->getLHS()); 3061 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3062 return ConservativeResult.intersectWith(X.udiv(Y)); 3063 } 3064 3065 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3066 ConstantRange X = getSignedRange(ZExt->getOperand()); 3067 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3068 } 3069 3070 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3071 ConstantRange X = getSignedRange(SExt->getOperand()); 3072 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3073 } 3074 3075 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3076 ConstantRange X = getSignedRange(Trunc->getOperand()); 3077 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3078 } 3079 3080 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3081 // If there's no signed wrap, and all the operands have the same sign or 3082 // zero, the value won't ever change sign. 3083 if (AddRec->hasNoSignedWrap()) { 3084 bool AllNonNeg = true; 3085 bool AllNonPos = true; 3086 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3087 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3088 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3089 } 3090 if (AllNonNeg) 3091 ConservativeResult = ConservativeResult.intersectWith( 3092 ConstantRange(APInt(BitWidth, 0), 3093 APInt::getSignedMinValue(BitWidth))); 3094 else if (AllNonPos) 3095 ConservativeResult = ConservativeResult.intersectWith( 3096 ConstantRange(APInt::getSignedMinValue(BitWidth), 3097 APInt(BitWidth, 1))); 3098 } 3099 3100 // TODO: non-affine addrec 3101 if (AddRec->isAffine()) { 3102 const Type *Ty = AddRec->getType(); 3103 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3104 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3105 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3106 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3107 3108 const SCEV *Start = AddRec->getStart(); 3109 const SCEV *Step = AddRec->getStepRecurrence(*this); 3110 3111 ConstantRange StartRange = getSignedRange(Start); 3112 ConstantRange StepRange = getSignedRange(Step); 3113 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3114 ConstantRange EndRange = 3115 StartRange.add(MaxBECountRange.multiply(StepRange)); 3116 3117 // Check for overflow. This must be done with ConstantRange arithmetic 3118 // because we could be called from within the ScalarEvolution overflow 3119 // checking code. 3120 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3121 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3122 ConstantRange ExtMaxBECountRange = 3123 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3124 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3125 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3126 ExtEndRange) 3127 return ConservativeResult; 3128 3129 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3130 EndRange.getSignedMin()); 3131 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3132 EndRange.getSignedMax()); 3133 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3134 return ConservativeResult; 3135 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3136 } 3137 } 3138 3139 return ConservativeResult; 3140 } 3141 3142 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3143 // For a SCEVUnknown, ask ValueTracking. 3144 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3145 return ConservativeResult; 3146 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3147 if (NS == 1) 3148 return ConservativeResult; 3149 return ConservativeResult.intersectWith( 3150 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3151 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3152 } 3153 3154 return ConservativeResult; 3155} 3156 3157/// createSCEV - We know that there is no SCEV for the specified value. 3158/// Analyze the expression. 3159/// 3160const SCEV *ScalarEvolution::createSCEV(Value *V) { 3161 if (!isSCEVable(V->getType())) 3162 return getUnknown(V); 3163 3164 unsigned Opcode = Instruction::UserOp1; 3165 if (Instruction *I = dyn_cast<Instruction>(V)) { 3166 Opcode = I->getOpcode(); 3167 3168 // Don't attempt to analyze instructions in blocks that aren't 3169 // reachable. Such instructions don't matter, and they aren't required 3170 // to obey basic rules for definitions dominating uses which this 3171 // analysis depends on. 3172 if (!DT->isReachableFromEntry(I->getParent())) 3173 return getUnknown(V); 3174 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3175 Opcode = CE->getOpcode(); 3176 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3177 return getConstant(CI); 3178 else if (isa<ConstantPointerNull>(V)) 3179 return getConstant(V->getType(), 0); 3180 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3181 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3182 else 3183 return getUnknown(V); 3184 3185 Operator *U = cast<Operator>(V); 3186 switch (Opcode) { 3187 case Instruction::Add: 3188 // Don't transfer the NSW and NUW bits from the Add instruction to the 3189 // Add expression, because the Instruction may be guarded by control 3190 // flow and the no-overflow bits may not be valid for the expression in 3191 // any context. 3192 return getAddExpr(getSCEV(U->getOperand(0)), 3193 getSCEV(U->getOperand(1))); 3194 case Instruction::Mul: 3195 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3196 // Mul expression, as with Add. 3197 return getMulExpr(getSCEV(U->getOperand(0)), 3198 getSCEV(U->getOperand(1))); 3199 case Instruction::UDiv: 3200 return getUDivExpr(getSCEV(U->getOperand(0)), 3201 getSCEV(U->getOperand(1))); 3202 case Instruction::Sub: 3203 return getMinusSCEV(getSCEV(U->getOperand(0)), 3204 getSCEV(U->getOperand(1))); 3205 case Instruction::And: 3206 // For an expression like x&255 that merely masks off the high bits, 3207 // use zext(trunc(x)) as the SCEV expression. 3208 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3209 if (CI->isNullValue()) 3210 return getSCEV(U->getOperand(1)); 3211 if (CI->isAllOnesValue()) 3212 return getSCEV(U->getOperand(0)); 3213 const APInt &A = CI->getValue(); 3214 3215 // Instcombine's ShrinkDemandedConstant may strip bits out of 3216 // constants, obscuring what would otherwise be a low-bits mask. 3217 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3218 // knew about to reconstruct a low-bits mask value. 3219 unsigned LZ = A.countLeadingZeros(); 3220 unsigned BitWidth = A.getBitWidth(); 3221 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3222 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3223 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3224 3225 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3226 3227 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3228 return 3229 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3230 IntegerType::get(getContext(), BitWidth - LZ)), 3231 U->getType()); 3232 } 3233 break; 3234 3235 case Instruction::Or: 3236 // If the RHS of the Or is a constant, we may have something like: 3237 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3238 // optimizations will transparently handle this case. 3239 // 3240 // In order for this transformation to be safe, the LHS must be of the 3241 // form X*(2^n) and the Or constant must be less than 2^n. 3242 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3243 const SCEV *LHS = getSCEV(U->getOperand(0)); 3244 const APInt &CIVal = CI->getValue(); 3245 if (GetMinTrailingZeros(LHS) >= 3246 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3247 // Build a plain add SCEV. 3248 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3249 // If the LHS of the add was an addrec and it has no-wrap flags, 3250 // transfer the no-wrap flags, since an or won't introduce a wrap. 3251 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3252 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3253 if (OldAR->hasNoUnsignedWrap()) 3254 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3255 if (OldAR->hasNoSignedWrap()) 3256 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3257 } 3258 return S; 3259 } 3260 } 3261 break; 3262 case Instruction::Xor: 3263 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3264 // If the RHS of the xor is a signbit, then this is just an add. 3265 // Instcombine turns add of signbit into xor as a strength reduction step. 3266 if (CI->getValue().isSignBit()) 3267 return getAddExpr(getSCEV(U->getOperand(0)), 3268 getSCEV(U->getOperand(1))); 3269 3270 // If the RHS of xor is -1, then this is a not operation. 3271 if (CI->isAllOnesValue()) 3272 return getNotSCEV(getSCEV(U->getOperand(0))); 3273 3274 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3275 // This is a variant of the check for xor with -1, and it handles 3276 // the case where instcombine has trimmed non-demanded bits out 3277 // of an xor with -1. 3278 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3279 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3280 if (BO->getOpcode() == Instruction::And && 3281 LCI->getValue() == CI->getValue()) 3282 if (const SCEVZeroExtendExpr *Z = 3283 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3284 const Type *UTy = U->getType(); 3285 const SCEV *Z0 = Z->getOperand(); 3286 const Type *Z0Ty = Z0->getType(); 3287 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3288 3289 // If C is a low-bits mask, the zero extend is serving to 3290 // mask off the high bits. Complement the operand and 3291 // re-apply the zext. 3292 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3293 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3294 3295 // If C is a single bit, it may be in the sign-bit position 3296 // before the zero-extend. In this case, represent the xor 3297 // using an add, which is equivalent, and re-apply the zext. 3298 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3299 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3300 Trunc.isSignBit()) 3301 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3302 UTy); 3303 } 3304 } 3305 break; 3306 3307 case Instruction::Shl: 3308 // Turn shift left of a constant amount into a multiply. 3309 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3310 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3311 3312 // If the shift count is not less than the bitwidth, the result of 3313 // the shift is undefined. Don't try to analyze it, because the 3314 // resolution chosen here may differ from the resolution chosen in 3315 // other parts of the compiler. 3316 if (SA->getValue().uge(BitWidth)) 3317 break; 3318 3319 Constant *X = ConstantInt::get(getContext(), 3320 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3321 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3322 } 3323 break; 3324 3325 case Instruction::LShr: 3326 // Turn logical shift right of a constant into a unsigned divide. 3327 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3328 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3329 3330 // If the shift count is not less than the bitwidth, the result of 3331 // the shift is undefined. Don't try to analyze it, because the 3332 // resolution chosen here may differ from the resolution chosen in 3333 // other parts of the compiler. 3334 if (SA->getValue().uge(BitWidth)) 3335 break; 3336 3337 Constant *X = ConstantInt::get(getContext(), 3338 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3339 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3340 } 3341 break; 3342 3343 case Instruction::AShr: 3344 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3345 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3346 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3347 if (L->getOpcode() == Instruction::Shl && 3348 L->getOperand(1) == U->getOperand(1)) { 3349 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3350 3351 // If the shift count is not less than the bitwidth, the result of 3352 // the shift is undefined. Don't try to analyze it, because the 3353 // resolution chosen here may differ from the resolution chosen in 3354 // other parts of the compiler. 3355 if (CI->getValue().uge(BitWidth)) 3356 break; 3357 3358 uint64_t Amt = BitWidth - CI->getZExtValue(); 3359 if (Amt == BitWidth) 3360 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3361 return 3362 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3363 IntegerType::get(getContext(), 3364 Amt)), 3365 U->getType()); 3366 } 3367 break; 3368 3369 case Instruction::Trunc: 3370 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3371 3372 case Instruction::ZExt: 3373 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3374 3375 case Instruction::SExt: 3376 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3377 3378 case Instruction::BitCast: 3379 // BitCasts are no-op casts so we just eliminate the cast. 3380 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3381 return getSCEV(U->getOperand(0)); 3382 break; 3383 3384 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3385 // lead to pointer expressions which cannot safely be expanded to GEPs, 3386 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3387 // simplifying integer expressions. 3388 3389 case Instruction::GetElementPtr: 3390 return createNodeForGEP(cast<GEPOperator>(U)); 3391 3392 case Instruction::PHI: 3393 return createNodeForPHI(cast<PHINode>(U)); 3394 3395 case Instruction::Select: 3396 // This could be a smax or umax that was lowered earlier. 3397 // Try to recover it. 3398 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3399 Value *LHS = ICI->getOperand(0); 3400 Value *RHS = ICI->getOperand(1); 3401 switch (ICI->getPredicate()) { 3402 case ICmpInst::ICMP_SLT: 3403 case ICmpInst::ICMP_SLE: 3404 std::swap(LHS, RHS); 3405 // fall through 3406 case ICmpInst::ICMP_SGT: 3407 case ICmpInst::ICMP_SGE: 3408 // a >s b ? a+x : b+x -> smax(a, b)+x 3409 // a >s b ? b+x : a+x -> smin(a, b)+x 3410 if (LHS->getType() == U->getType()) { 3411 const SCEV *LS = getSCEV(LHS); 3412 const SCEV *RS = getSCEV(RHS); 3413 const SCEV *LA = getSCEV(U->getOperand(1)); 3414 const SCEV *RA = getSCEV(U->getOperand(2)); 3415 const SCEV *LDiff = getMinusSCEV(LA, LS); 3416 const SCEV *RDiff = getMinusSCEV(RA, RS); 3417 if (LDiff == RDiff) 3418 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3419 LDiff = getMinusSCEV(LA, RS); 3420 RDiff = getMinusSCEV(RA, LS); 3421 if (LDiff == RDiff) 3422 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3423 } 3424 break; 3425 case ICmpInst::ICMP_ULT: 3426 case ICmpInst::ICMP_ULE: 3427 std::swap(LHS, RHS); 3428 // fall through 3429 case ICmpInst::ICMP_UGT: 3430 case ICmpInst::ICMP_UGE: 3431 // a >u b ? a+x : b+x -> umax(a, b)+x 3432 // a >u b ? b+x : a+x -> umin(a, b)+x 3433 if (LHS->getType() == U->getType()) { 3434 const SCEV *LS = getSCEV(LHS); 3435 const SCEV *RS = getSCEV(RHS); 3436 const SCEV *LA = getSCEV(U->getOperand(1)); 3437 const SCEV *RA = getSCEV(U->getOperand(2)); 3438 const SCEV *LDiff = getMinusSCEV(LA, LS); 3439 const SCEV *RDiff = getMinusSCEV(RA, RS); 3440 if (LDiff == RDiff) 3441 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3442 LDiff = getMinusSCEV(LA, RS); 3443 RDiff = getMinusSCEV(RA, LS); 3444 if (LDiff == RDiff) 3445 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3446 } 3447 break; 3448 case ICmpInst::ICMP_NE: 3449 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3450 if (LHS->getType() == U->getType() && 3451 isa<ConstantInt>(RHS) && 3452 cast<ConstantInt>(RHS)->isZero()) { 3453 const SCEV *One = getConstant(LHS->getType(), 1); 3454 const SCEV *LS = getSCEV(LHS); 3455 const SCEV *LA = getSCEV(U->getOperand(1)); 3456 const SCEV *RA = getSCEV(U->getOperand(2)); 3457 const SCEV *LDiff = getMinusSCEV(LA, LS); 3458 const SCEV *RDiff = getMinusSCEV(RA, One); 3459 if (LDiff == RDiff) 3460 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3461 } 3462 break; 3463 case ICmpInst::ICMP_EQ: 3464 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3465 if (LHS->getType() == U->getType() && 3466 isa<ConstantInt>(RHS) && 3467 cast<ConstantInt>(RHS)->isZero()) { 3468 const SCEV *One = getConstant(LHS->getType(), 1); 3469 const SCEV *LS = getSCEV(LHS); 3470 const SCEV *LA = getSCEV(U->getOperand(1)); 3471 const SCEV *RA = getSCEV(U->getOperand(2)); 3472 const SCEV *LDiff = getMinusSCEV(LA, One); 3473 const SCEV *RDiff = getMinusSCEV(RA, LS); 3474 if (LDiff == RDiff) 3475 return getAddExpr(getUMaxExpr(LS, One), LDiff); 3476 } 3477 break; 3478 default: 3479 break; 3480 } 3481 } 3482 3483 default: // We cannot analyze this expression. 3484 break; 3485 } 3486 3487 return getUnknown(V); 3488} 3489 3490 3491 3492//===----------------------------------------------------------------------===// 3493// Iteration Count Computation Code 3494// 3495 3496/// getBackedgeTakenCount - If the specified loop has a predictable 3497/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3498/// object. The backedge-taken count is the number of times the loop header 3499/// will be branched to from within the loop. This is one less than the 3500/// trip count of the loop, since it doesn't count the first iteration, 3501/// when the header is branched to from outside the loop. 3502/// 3503/// Note that it is not valid to call this method on a loop without a 3504/// loop-invariant backedge-taken count (see 3505/// hasLoopInvariantBackedgeTakenCount). 3506/// 3507const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3508 return getBackedgeTakenInfo(L).Exact; 3509} 3510 3511/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3512/// return the least SCEV value that is known never to be less than the 3513/// actual backedge taken count. 3514const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3515 return getBackedgeTakenInfo(L).Max; 3516} 3517 3518/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3519/// onto the given Worklist. 3520static void 3521PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3522 BasicBlock *Header = L->getHeader(); 3523 3524 // Push all Loop-header PHIs onto the Worklist stack. 3525 for (BasicBlock::iterator I = Header->begin(); 3526 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3527 Worklist.push_back(PN); 3528} 3529 3530const ScalarEvolution::BackedgeTakenInfo & 3531ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3532 // Initially insert a CouldNotCompute for this loop. If the insertion 3533 // succeeds, proceed to actually compute a backedge-taken count and 3534 // update the value. The temporary CouldNotCompute value tells SCEV 3535 // code elsewhere that it shouldn't attempt to request a new 3536 // backedge-taken count, which could result in infinite recursion. 3537 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3538 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3539 if (Pair.second) { 3540 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3541 if (BECount.Exact != getCouldNotCompute()) { 3542 assert(BECount.Exact->isLoopInvariant(L) && 3543 BECount.Max->isLoopInvariant(L) && 3544 "Computed backedge-taken count isn't loop invariant for loop!"); 3545 ++NumTripCountsComputed; 3546 3547 // Update the value in the map. 3548 Pair.first->second = BECount; 3549 } else { 3550 if (BECount.Max != getCouldNotCompute()) 3551 // Update the value in the map. 3552 Pair.first->second = BECount; 3553 if (isa<PHINode>(L->getHeader()->begin())) 3554 // Only count loops that have phi nodes as not being computable. 3555 ++NumTripCountsNotComputed; 3556 } 3557 3558 // Now that we know more about the trip count for this loop, forget any 3559 // existing SCEV values for PHI nodes in this loop since they are only 3560 // conservative estimates made without the benefit of trip count 3561 // information. This is similar to the code in forgetLoop, except that 3562 // it handles SCEVUnknown PHI nodes specially. 3563 if (BECount.hasAnyInfo()) { 3564 SmallVector<Instruction *, 16> Worklist; 3565 PushLoopPHIs(L, Worklist); 3566 3567 SmallPtrSet<Instruction *, 8> Visited; 3568 while (!Worklist.empty()) { 3569 Instruction *I = Worklist.pop_back_val(); 3570 if (!Visited.insert(I)) continue; 3571 3572 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3573 Scalars.find(static_cast<Value *>(I)); 3574 if (It != Scalars.end()) { 3575 // SCEVUnknown for a PHI either means that it has an unrecognized 3576 // structure, or it's a PHI that's in the progress of being computed 3577 // by createNodeForPHI. In the former case, additional loop trip 3578 // count information isn't going to change anything. In the later 3579 // case, createNodeForPHI will perform the necessary updates on its 3580 // own when it gets to that point. 3581 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3582 ValuesAtScopes.erase(It->second); 3583 Scalars.erase(It); 3584 } 3585 if (PHINode *PN = dyn_cast<PHINode>(I)) 3586 ConstantEvolutionLoopExitValue.erase(PN); 3587 } 3588 3589 PushDefUseChildren(I, Worklist); 3590 } 3591 } 3592 } 3593 return Pair.first->second; 3594} 3595 3596/// forgetLoop - This method should be called by the client when it has 3597/// changed a loop in a way that may effect ScalarEvolution's ability to 3598/// compute a trip count, or if the loop is deleted. 3599void ScalarEvolution::forgetLoop(const Loop *L) { 3600 // Drop any stored trip count value. 3601 BackedgeTakenCounts.erase(L); 3602 3603 // Drop information about expressions based on loop-header PHIs. 3604 SmallVector<Instruction *, 16> Worklist; 3605 PushLoopPHIs(L, Worklist); 3606 3607 SmallPtrSet<Instruction *, 8> Visited; 3608 while (!Worklist.empty()) { 3609 Instruction *I = Worklist.pop_back_val(); 3610 if (!Visited.insert(I)) continue; 3611 3612 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3613 Scalars.find(static_cast<Value *>(I)); 3614 if (It != Scalars.end()) { 3615 ValuesAtScopes.erase(It->second); 3616 Scalars.erase(It); 3617 if (PHINode *PN = dyn_cast<PHINode>(I)) 3618 ConstantEvolutionLoopExitValue.erase(PN); 3619 } 3620 3621 PushDefUseChildren(I, Worklist); 3622 } 3623} 3624 3625/// forgetValue - This method should be called by the client when it has 3626/// changed a value in a way that may effect its value, or which may 3627/// disconnect it from a def-use chain linking it to a loop. 3628void ScalarEvolution::forgetValue(Value *V) { 3629 Instruction *I = dyn_cast<Instruction>(V); 3630 if (!I) return; 3631 3632 // Drop information about expressions based on loop-header PHIs. 3633 SmallVector<Instruction *, 16> Worklist; 3634 Worklist.push_back(I); 3635 3636 SmallPtrSet<Instruction *, 8> Visited; 3637 while (!Worklist.empty()) { 3638 I = Worklist.pop_back_val(); 3639 if (!Visited.insert(I)) continue; 3640 3641 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3642 Scalars.find(static_cast<Value *>(I)); 3643 if (It != Scalars.end()) { 3644 ValuesAtScopes.erase(It->second); 3645 Scalars.erase(It); 3646 if (PHINode *PN = dyn_cast<PHINode>(I)) 3647 ConstantEvolutionLoopExitValue.erase(PN); 3648 } 3649 3650 PushDefUseChildren(I, Worklist); 3651 } 3652} 3653 3654/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3655/// of the specified loop will execute. 3656ScalarEvolution::BackedgeTakenInfo 3657ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3658 SmallVector<BasicBlock *, 8> ExitingBlocks; 3659 L->getExitingBlocks(ExitingBlocks); 3660 3661 // Examine all exits and pick the most conservative values. 3662 const SCEV *BECount = getCouldNotCompute(); 3663 const SCEV *MaxBECount = getCouldNotCompute(); 3664 bool CouldNotComputeBECount = false; 3665 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3666 BackedgeTakenInfo NewBTI = 3667 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3668 3669 if (NewBTI.Exact == getCouldNotCompute()) { 3670 // We couldn't compute an exact value for this exit, so 3671 // we won't be able to compute an exact value for the loop. 3672 CouldNotComputeBECount = true; 3673 BECount = getCouldNotCompute(); 3674 } else if (!CouldNotComputeBECount) { 3675 if (BECount == getCouldNotCompute()) 3676 BECount = NewBTI.Exact; 3677 else 3678 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3679 } 3680 if (MaxBECount == getCouldNotCompute()) 3681 MaxBECount = NewBTI.Max; 3682 else if (NewBTI.Max != getCouldNotCompute()) 3683 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3684 } 3685 3686 return BackedgeTakenInfo(BECount, MaxBECount); 3687} 3688 3689/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3690/// of the specified loop will execute if it exits via the specified block. 3691ScalarEvolution::BackedgeTakenInfo 3692ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3693 BasicBlock *ExitingBlock) { 3694 3695 // Okay, we've chosen an exiting block. See what condition causes us to 3696 // exit at this block. 3697 // 3698 // FIXME: we should be able to handle switch instructions (with a single exit) 3699 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3700 if (ExitBr == 0) return getCouldNotCompute(); 3701 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3702 3703 // At this point, we know we have a conditional branch that determines whether 3704 // the loop is exited. However, we don't know if the branch is executed each 3705 // time through the loop. If not, then the execution count of the branch will 3706 // not be equal to the trip count of the loop. 3707 // 3708 // Currently we check for this by checking to see if the Exit branch goes to 3709 // the loop header. If so, we know it will always execute the same number of 3710 // times as the loop. We also handle the case where the exit block *is* the 3711 // loop header. This is common for un-rotated loops. 3712 // 3713 // If both of those tests fail, walk up the unique predecessor chain to the 3714 // header, stopping if there is an edge that doesn't exit the loop. If the 3715 // header is reached, the execution count of the branch will be equal to the 3716 // trip count of the loop. 3717 // 3718 // More extensive analysis could be done to handle more cases here. 3719 // 3720 if (ExitBr->getSuccessor(0) != L->getHeader() && 3721 ExitBr->getSuccessor(1) != L->getHeader() && 3722 ExitBr->getParent() != L->getHeader()) { 3723 // The simple checks failed, try climbing the unique predecessor chain 3724 // up to the header. 3725 bool Ok = false; 3726 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3727 BasicBlock *Pred = BB->getUniquePredecessor(); 3728 if (!Pred) 3729 return getCouldNotCompute(); 3730 TerminatorInst *PredTerm = Pred->getTerminator(); 3731 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3732 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3733 if (PredSucc == BB) 3734 continue; 3735 // If the predecessor has a successor that isn't BB and isn't 3736 // outside the loop, assume the worst. 3737 if (L->contains(PredSucc)) 3738 return getCouldNotCompute(); 3739 } 3740 if (Pred == L->getHeader()) { 3741 Ok = true; 3742 break; 3743 } 3744 BB = Pred; 3745 } 3746 if (!Ok) 3747 return getCouldNotCompute(); 3748 } 3749 3750 // Proceed to the next level to examine the exit condition expression. 3751 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3752 ExitBr->getSuccessor(0), 3753 ExitBr->getSuccessor(1)); 3754} 3755 3756/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3757/// backedge of the specified loop will execute if its exit condition 3758/// were a conditional branch of ExitCond, TBB, and FBB. 3759ScalarEvolution::BackedgeTakenInfo 3760ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3761 Value *ExitCond, 3762 BasicBlock *TBB, 3763 BasicBlock *FBB) { 3764 // Check if the controlling expression for this loop is an And or Or. 3765 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3766 if (BO->getOpcode() == Instruction::And) { 3767 // Recurse on the operands of the and. 3768 BackedgeTakenInfo BTI0 = 3769 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3770 BackedgeTakenInfo BTI1 = 3771 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3772 const SCEV *BECount = getCouldNotCompute(); 3773 const SCEV *MaxBECount = getCouldNotCompute(); 3774 if (L->contains(TBB)) { 3775 // Both conditions must be true for the loop to continue executing. 3776 // Choose the less conservative count. 3777 if (BTI0.Exact == getCouldNotCompute() || 3778 BTI1.Exact == getCouldNotCompute()) 3779 BECount = getCouldNotCompute(); 3780 else 3781 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3782 if (BTI0.Max == getCouldNotCompute()) 3783 MaxBECount = BTI1.Max; 3784 else if (BTI1.Max == getCouldNotCompute()) 3785 MaxBECount = BTI0.Max; 3786 else 3787 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3788 } else { 3789 // Both conditions must be true for the loop to exit. 3790 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3791 if (BTI0.Exact != getCouldNotCompute() && 3792 BTI1.Exact != getCouldNotCompute()) 3793 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3794 if (BTI0.Max != getCouldNotCompute() && 3795 BTI1.Max != getCouldNotCompute()) 3796 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3797 } 3798 3799 return BackedgeTakenInfo(BECount, MaxBECount); 3800 } 3801 if (BO->getOpcode() == Instruction::Or) { 3802 // Recurse on the operands of the or. 3803 BackedgeTakenInfo BTI0 = 3804 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3805 BackedgeTakenInfo BTI1 = 3806 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3807 const SCEV *BECount = getCouldNotCompute(); 3808 const SCEV *MaxBECount = getCouldNotCompute(); 3809 if (L->contains(FBB)) { 3810 // Both conditions must be false for the loop to continue executing. 3811 // Choose the less conservative count. 3812 if (BTI0.Exact == getCouldNotCompute() || 3813 BTI1.Exact == getCouldNotCompute()) 3814 BECount = getCouldNotCompute(); 3815 else 3816 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3817 if (BTI0.Max == getCouldNotCompute()) 3818 MaxBECount = BTI1.Max; 3819 else if (BTI1.Max == getCouldNotCompute()) 3820 MaxBECount = BTI0.Max; 3821 else 3822 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3823 } else { 3824 // Both conditions must be false for the loop to exit. 3825 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3826 if (BTI0.Exact != getCouldNotCompute() && 3827 BTI1.Exact != getCouldNotCompute()) 3828 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3829 if (BTI0.Max != getCouldNotCompute() && 3830 BTI1.Max != getCouldNotCompute()) 3831 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3832 } 3833 3834 return BackedgeTakenInfo(BECount, MaxBECount); 3835 } 3836 } 3837 3838 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3839 // Proceed to the next level to examine the icmp. 3840 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3841 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3842 3843 // Check for a constant condition. These are normally stripped out by 3844 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3845 // preserve the CFG and is temporarily leaving constant conditions 3846 // in place. 3847 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3848 if (L->contains(FBB) == !CI->getZExtValue()) 3849 // The backedge is always taken. 3850 return getCouldNotCompute(); 3851 else 3852 // The backedge is never taken. 3853 return getConstant(CI->getType(), 0); 3854 } 3855 3856 // If it's not an integer or pointer comparison then compute it the hard way. 3857 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3858} 3859 3860/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3861/// backedge of the specified loop will execute if its exit condition 3862/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3863ScalarEvolution::BackedgeTakenInfo 3864ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3865 ICmpInst *ExitCond, 3866 BasicBlock *TBB, 3867 BasicBlock *FBB) { 3868 3869 // If the condition was exit on true, convert the condition to exit on false 3870 ICmpInst::Predicate Cond; 3871 if (!L->contains(FBB)) 3872 Cond = ExitCond->getPredicate(); 3873 else 3874 Cond = ExitCond->getInversePredicate(); 3875 3876 // Handle common loops like: for (X = "string"; *X; ++X) 3877 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3878 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3879 BackedgeTakenInfo ItCnt = 3880 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3881 if (ItCnt.hasAnyInfo()) 3882 return ItCnt; 3883 } 3884 3885 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3886 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3887 3888 // Try to evaluate any dependencies out of the loop. 3889 LHS = getSCEVAtScope(LHS, L); 3890 RHS = getSCEVAtScope(RHS, L); 3891 3892 // At this point, we would like to compute how many iterations of the 3893 // loop the predicate will return true for these inputs. 3894 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3895 // If there is a loop-invariant, force it into the RHS. 3896 std::swap(LHS, RHS); 3897 Cond = ICmpInst::getSwappedPredicate(Cond); 3898 } 3899 3900 // Simplify the operands before analyzing them. 3901 (void)SimplifyICmpOperands(Cond, LHS, RHS); 3902 3903 // If we have a comparison of a chrec against a constant, try to use value 3904 // ranges to answer this query. 3905 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3906 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3907 if (AddRec->getLoop() == L) { 3908 // Form the constant range. 3909 ConstantRange CompRange( 3910 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3911 3912 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3913 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3914 } 3915 3916 switch (Cond) { 3917 case ICmpInst::ICMP_NE: { // while (X != Y) 3918 // Convert to: while (X-Y != 0) 3919 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3920 if (BTI.hasAnyInfo()) return BTI; 3921 break; 3922 } 3923 case ICmpInst::ICMP_EQ: { // while (X == Y) 3924 // Convert to: while (X-Y == 0) 3925 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3926 if (BTI.hasAnyInfo()) return BTI; 3927 break; 3928 } 3929 case ICmpInst::ICMP_SLT: { 3930 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3931 if (BTI.hasAnyInfo()) return BTI; 3932 break; 3933 } 3934 case ICmpInst::ICMP_SGT: { 3935 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3936 getNotSCEV(RHS), L, true); 3937 if (BTI.hasAnyInfo()) return BTI; 3938 break; 3939 } 3940 case ICmpInst::ICMP_ULT: { 3941 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3942 if (BTI.hasAnyInfo()) return BTI; 3943 break; 3944 } 3945 case ICmpInst::ICMP_UGT: { 3946 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3947 getNotSCEV(RHS), L, false); 3948 if (BTI.hasAnyInfo()) return BTI; 3949 break; 3950 } 3951 default: 3952#if 0 3953 dbgs() << "ComputeBackedgeTakenCount "; 3954 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3955 dbgs() << "[unsigned] "; 3956 dbgs() << *LHS << " " 3957 << Instruction::getOpcodeName(Instruction::ICmp) 3958 << " " << *RHS << "\n"; 3959#endif 3960 break; 3961 } 3962 return 3963 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3964} 3965 3966static ConstantInt * 3967EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3968 ScalarEvolution &SE) { 3969 const SCEV *InVal = SE.getConstant(C); 3970 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3971 assert(isa<SCEVConstant>(Val) && 3972 "Evaluation of SCEV at constant didn't fold correctly?"); 3973 return cast<SCEVConstant>(Val)->getValue(); 3974} 3975 3976/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3977/// and a GEP expression (missing the pointer index) indexing into it, return 3978/// the addressed element of the initializer or null if the index expression is 3979/// invalid. 3980static Constant * 3981GetAddressedElementFromGlobal(GlobalVariable *GV, 3982 const std::vector<ConstantInt*> &Indices) { 3983 Constant *Init = GV->getInitializer(); 3984 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3985 uint64_t Idx = Indices[i]->getZExtValue(); 3986 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3987 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3988 Init = cast<Constant>(CS->getOperand(Idx)); 3989 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3990 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3991 Init = cast<Constant>(CA->getOperand(Idx)); 3992 } else if (isa<ConstantAggregateZero>(Init)) { 3993 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3994 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3995 Init = Constant::getNullValue(STy->getElementType(Idx)); 3996 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3997 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3998 Init = Constant::getNullValue(ATy->getElementType()); 3999 } else { 4000 llvm_unreachable("Unknown constant aggregate type!"); 4001 } 4002 return 0; 4003 } else { 4004 return 0; // Unknown initializer type 4005 } 4006 } 4007 return Init; 4008} 4009 4010/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4011/// 'icmp op load X, cst', try to see if we can compute the backedge 4012/// execution count. 4013ScalarEvolution::BackedgeTakenInfo 4014ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4015 LoadInst *LI, 4016 Constant *RHS, 4017 const Loop *L, 4018 ICmpInst::Predicate predicate) { 4019 if (LI->isVolatile()) return getCouldNotCompute(); 4020 4021 // Check to see if the loaded pointer is a getelementptr of a global. 4022 // TODO: Use SCEV instead of manually grubbing with GEPs. 4023 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4024 if (!GEP) return getCouldNotCompute(); 4025 4026 // Make sure that it is really a constant global we are gepping, with an 4027 // initializer, and make sure the first IDX is really 0. 4028 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4029 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4030 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4031 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4032 return getCouldNotCompute(); 4033 4034 // Okay, we allow one non-constant index into the GEP instruction. 4035 Value *VarIdx = 0; 4036 std::vector<ConstantInt*> Indexes; 4037 unsigned VarIdxNum = 0; 4038 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4039 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4040 Indexes.push_back(CI); 4041 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4042 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4043 VarIdx = GEP->getOperand(i); 4044 VarIdxNum = i-2; 4045 Indexes.push_back(0); 4046 } 4047 4048 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4049 // Check to see if X is a loop variant variable value now. 4050 const SCEV *Idx = getSCEV(VarIdx); 4051 Idx = getSCEVAtScope(Idx, L); 4052 4053 // We can only recognize very limited forms of loop index expressions, in 4054 // particular, only affine AddRec's like {C1,+,C2}. 4055 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4056 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4057 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4058 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4059 return getCouldNotCompute(); 4060 4061 unsigned MaxSteps = MaxBruteForceIterations; 4062 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4063 ConstantInt *ItCst = ConstantInt::get( 4064 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4065 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4066 4067 // Form the GEP offset. 4068 Indexes[VarIdxNum] = Val; 4069 4070 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4071 if (Result == 0) break; // Cannot compute! 4072 4073 // Evaluate the condition for this iteration. 4074 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4075 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4076 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4077#if 0 4078 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4079 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4080 << "***\n"; 4081#endif 4082 ++NumArrayLenItCounts; 4083 return getConstant(ItCst); // Found terminating iteration! 4084 } 4085 } 4086 return getCouldNotCompute(); 4087} 4088 4089 4090/// CanConstantFold - Return true if we can constant fold an instruction of the 4091/// specified type, assuming that all operands were constants. 4092static bool CanConstantFold(const Instruction *I) { 4093 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4094 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4095 return true; 4096 4097 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4098 if (const Function *F = CI->getCalledFunction()) 4099 return canConstantFoldCallTo(F); 4100 return false; 4101} 4102 4103/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4104/// in the loop that V is derived from. We allow arbitrary operations along the 4105/// way, but the operands of an operation must either be constants or a value 4106/// derived from a constant PHI. If this expression does not fit with these 4107/// constraints, return null. 4108static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4109 // If this is not an instruction, or if this is an instruction outside of the 4110 // loop, it can't be derived from a loop PHI. 4111 Instruction *I = dyn_cast<Instruction>(V); 4112 if (I == 0 || !L->contains(I)) return 0; 4113 4114 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4115 if (L->getHeader() == I->getParent()) 4116 return PN; 4117 else 4118 // We don't currently keep track of the control flow needed to evaluate 4119 // PHIs, so we cannot handle PHIs inside of loops. 4120 return 0; 4121 } 4122 4123 // If we won't be able to constant fold this expression even if the operands 4124 // are constants, return early. 4125 if (!CanConstantFold(I)) return 0; 4126 4127 // Otherwise, we can evaluate this instruction if all of its operands are 4128 // constant or derived from a PHI node themselves. 4129 PHINode *PHI = 0; 4130 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4131 if (!(isa<Constant>(I->getOperand(Op)) || 4132 isa<GlobalValue>(I->getOperand(Op)))) { 4133 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4134 if (P == 0) return 0; // Not evolving from PHI 4135 if (PHI == 0) 4136 PHI = P; 4137 else if (PHI != P) 4138 return 0; // Evolving from multiple different PHIs. 4139 } 4140 4141 // This is a expression evolving from a constant PHI! 4142 return PHI; 4143} 4144 4145/// EvaluateExpression - Given an expression that passes the 4146/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4147/// in the loop has the value PHIVal. If we can't fold this expression for some 4148/// reason, return null. 4149static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4150 const TargetData *TD) { 4151 if (isa<PHINode>(V)) return PHIVal; 4152 if (Constant *C = dyn_cast<Constant>(V)) return C; 4153 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 4154 Instruction *I = cast<Instruction>(V); 4155 4156 std::vector<Constant*> Operands; 4157 Operands.resize(I->getNumOperands()); 4158 4159 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4160 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4161 if (Operands[i] == 0) return 0; 4162 } 4163 4164 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4165 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4166 Operands[1], TD); 4167 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4168 &Operands[0], Operands.size(), TD); 4169} 4170 4171/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4172/// in the header of its containing loop, we know the loop executes a 4173/// constant number of times, and the PHI node is just a recurrence 4174/// involving constants, fold it. 4175Constant * 4176ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4177 const APInt &BEs, 4178 const Loop *L) { 4179 std::map<PHINode*, Constant*>::iterator I = 4180 ConstantEvolutionLoopExitValue.find(PN); 4181 if (I != ConstantEvolutionLoopExitValue.end()) 4182 return I->second; 4183 4184 if (BEs.ugt(MaxBruteForceIterations)) 4185 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4186 4187 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4188 4189 // Since the loop is canonicalized, the PHI node must have two entries. One 4190 // entry must be a constant (coming in from outside of the loop), and the 4191 // second must be derived from the same PHI. 4192 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4193 Constant *StartCST = 4194 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4195 if (StartCST == 0) 4196 return RetVal = 0; // Must be a constant. 4197 4198 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4199 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4200 if (PN2 != PN) 4201 return RetVal = 0; // Not derived from same PHI. 4202 4203 // Execute the loop symbolically to determine the exit value. 4204 if (BEs.getActiveBits() >= 32) 4205 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4206 4207 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4208 unsigned IterationNum = 0; 4209 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4210 if (IterationNum == NumIterations) 4211 return RetVal = PHIVal; // Got exit value! 4212 4213 // Compute the value of the PHI node for the next iteration. 4214 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4215 if (NextPHI == PHIVal) 4216 return RetVal = NextPHI; // Stopped evolving! 4217 if (NextPHI == 0) 4218 return 0; // Couldn't evaluate! 4219 PHIVal = NextPHI; 4220 } 4221} 4222 4223/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4224/// constant number of times (the condition evolves only from constants), 4225/// try to evaluate a few iterations of the loop until we get the exit 4226/// condition gets a value of ExitWhen (true or false). If we cannot 4227/// evaluate the trip count of the loop, return getCouldNotCompute(). 4228const SCEV * 4229ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4230 Value *Cond, 4231 bool ExitWhen) { 4232 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4233 if (PN == 0) return getCouldNotCompute(); 4234 4235 // Since the loop is canonicalized, the PHI node must have two entries. One 4236 // entry must be a constant (coming in from outside of the loop), and the 4237 // second must be derived from the same PHI. 4238 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4239 Constant *StartCST = 4240 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4241 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4242 4243 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4244 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4245 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 4246 4247 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4248 // the loop symbolically to determine when the condition gets a value of 4249 // "ExitWhen". 4250 unsigned IterationNum = 0; 4251 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4252 for (Constant *PHIVal = StartCST; 4253 IterationNum != MaxIterations; ++IterationNum) { 4254 ConstantInt *CondVal = 4255 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4256 4257 // Couldn't symbolically evaluate. 4258 if (!CondVal) return getCouldNotCompute(); 4259 4260 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4261 ++NumBruteForceTripCountsComputed; 4262 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4263 } 4264 4265 // Compute the value of the PHI node for the next iteration. 4266 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4267 if (NextPHI == 0 || NextPHI == PHIVal) 4268 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4269 PHIVal = NextPHI; 4270 } 4271 4272 // Too many iterations were needed to evaluate. 4273 return getCouldNotCompute(); 4274} 4275 4276/// getSCEVAtScope - Return a SCEV expression for the specified value 4277/// at the specified scope in the program. The L value specifies a loop 4278/// nest to evaluate the expression at, where null is the top-level or a 4279/// specified loop is immediately inside of the loop. 4280/// 4281/// This method can be used to compute the exit value for a variable defined 4282/// in a loop by querying what the value will hold in the parent loop. 4283/// 4284/// In the case that a relevant loop exit value cannot be computed, the 4285/// original value V is returned. 4286const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4287 // Check to see if we've folded this expression at this loop before. 4288 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4289 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4290 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4291 if (!Pair.second) 4292 return Pair.first->second ? Pair.first->second : V; 4293 4294 // Otherwise compute it. 4295 const SCEV *C = computeSCEVAtScope(V, L); 4296 ValuesAtScopes[V][L] = C; 4297 return C; 4298} 4299 4300const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4301 if (isa<SCEVConstant>(V)) return V; 4302 4303 // If this instruction is evolved from a constant-evolving PHI, compute the 4304 // exit value from the loop without using SCEVs. 4305 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4306 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4307 const Loop *LI = (*this->LI)[I->getParent()]; 4308 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4309 if (PHINode *PN = dyn_cast<PHINode>(I)) 4310 if (PN->getParent() == LI->getHeader()) { 4311 // Okay, there is no closed form solution for the PHI node. Check 4312 // to see if the loop that contains it has a known backedge-taken 4313 // count. If so, we may be able to force computation of the exit 4314 // value. 4315 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4316 if (const SCEVConstant *BTCC = 4317 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4318 // Okay, we know how many times the containing loop executes. If 4319 // this is a constant evolving PHI node, get the final value at 4320 // the specified iteration number. 4321 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4322 BTCC->getValue()->getValue(), 4323 LI); 4324 if (RV) return getSCEV(RV); 4325 } 4326 } 4327 4328 // Okay, this is an expression that we cannot symbolically evaluate 4329 // into a SCEV. Check to see if it's possible to symbolically evaluate 4330 // the arguments into constants, and if so, try to constant propagate the 4331 // result. This is particularly useful for computing loop exit values. 4332 if (CanConstantFold(I)) { 4333 std::vector<Constant*> Operands; 4334 Operands.reserve(I->getNumOperands()); 4335 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4336 Value *Op = I->getOperand(i); 4337 if (Constant *C = dyn_cast<Constant>(Op)) { 4338 Operands.push_back(C); 4339 } else { 4340 // If any of the operands is non-constant and if they are 4341 // non-integer and non-pointer, don't even try to analyze them 4342 // with scev techniques. 4343 if (!isSCEVable(Op->getType())) 4344 return V; 4345 4346 const SCEV *OpV = getSCEVAtScope(Op, L); 4347 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4348 Constant *C = SC->getValue(); 4349 if (C->getType() != Op->getType()) 4350 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4351 Op->getType(), 4352 false), 4353 C, Op->getType()); 4354 Operands.push_back(C); 4355 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4356 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4357 if (C->getType() != Op->getType()) 4358 C = 4359 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4360 Op->getType(), 4361 false), 4362 C, Op->getType()); 4363 Operands.push_back(C); 4364 } else 4365 return V; 4366 } else { 4367 return V; 4368 } 4369 } 4370 } 4371 4372 Constant *C = 0; 4373 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4374 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4375 Operands[0], Operands[1], TD); 4376 else 4377 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4378 &Operands[0], Operands.size(), TD); 4379 if (C) 4380 return getSCEV(C); 4381 } 4382 } 4383 4384 // This is some other type of SCEVUnknown, just return it. 4385 return V; 4386 } 4387 4388 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4389 // Avoid performing the look-up in the common case where the specified 4390 // expression has no loop-variant portions. 4391 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4392 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4393 if (OpAtScope != Comm->getOperand(i)) { 4394 // Okay, at least one of these operands is loop variant but might be 4395 // foldable. Build a new instance of the folded commutative expression. 4396 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4397 Comm->op_begin()+i); 4398 NewOps.push_back(OpAtScope); 4399 4400 for (++i; i != e; ++i) { 4401 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4402 NewOps.push_back(OpAtScope); 4403 } 4404 if (isa<SCEVAddExpr>(Comm)) 4405 return getAddExpr(NewOps); 4406 if (isa<SCEVMulExpr>(Comm)) 4407 return getMulExpr(NewOps); 4408 if (isa<SCEVSMaxExpr>(Comm)) 4409 return getSMaxExpr(NewOps); 4410 if (isa<SCEVUMaxExpr>(Comm)) 4411 return getUMaxExpr(NewOps); 4412 llvm_unreachable("Unknown commutative SCEV type!"); 4413 } 4414 } 4415 // If we got here, all operands are loop invariant. 4416 return Comm; 4417 } 4418 4419 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4420 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4421 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4422 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4423 return Div; // must be loop invariant 4424 return getUDivExpr(LHS, RHS); 4425 } 4426 4427 // If this is a loop recurrence for a loop that does not contain L, then we 4428 // are dealing with the final value computed by the loop. 4429 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4430 if (!L || !AddRec->getLoop()->contains(L)) { 4431 // To evaluate this recurrence, we need to know how many times the AddRec 4432 // loop iterates. Compute this now. 4433 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4434 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4435 4436 // Then, evaluate the AddRec. 4437 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4438 } 4439 return AddRec; 4440 } 4441 4442 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4443 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4444 if (Op == Cast->getOperand()) 4445 return Cast; // must be loop invariant 4446 return getZeroExtendExpr(Op, Cast->getType()); 4447 } 4448 4449 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4450 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4451 if (Op == Cast->getOperand()) 4452 return Cast; // must be loop invariant 4453 return getSignExtendExpr(Op, Cast->getType()); 4454 } 4455 4456 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4457 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4458 if (Op == Cast->getOperand()) 4459 return Cast; // must be loop invariant 4460 return getTruncateExpr(Op, Cast->getType()); 4461 } 4462 4463 llvm_unreachable("Unknown SCEV type!"); 4464 return 0; 4465} 4466 4467/// getSCEVAtScope - This is a convenience function which does 4468/// getSCEVAtScope(getSCEV(V), L). 4469const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4470 return getSCEVAtScope(getSCEV(V), L); 4471} 4472 4473/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4474/// following equation: 4475/// 4476/// A * X = B (mod N) 4477/// 4478/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4479/// A and B isn't important. 4480/// 4481/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4482static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4483 ScalarEvolution &SE) { 4484 uint32_t BW = A.getBitWidth(); 4485 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4486 assert(A != 0 && "A must be non-zero."); 4487 4488 // 1. D = gcd(A, N) 4489 // 4490 // The gcd of A and N may have only one prime factor: 2. The number of 4491 // trailing zeros in A is its multiplicity 4492 uint32_t Mult2 = A.countTrailingZeros(); 4493 // D = 2^Mult2 4494 4495 // 2. Check if B is divisible by D. 4496 // 4497 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4498 // is not less than multiplicity of this prime factor for D. 4499 if (B.countTrailingZeros() < Mult2) 4500 return SE.getCouldNotCompute(); 4501 4502 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4503 // modulo (N / D). 4504 // 4505 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4506 // bit width during computations. 4507 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4508 APInt Mod(BW + 1, 0); 4509 Mod.set(BW - Mult2); // Mod = N / D 4510 APInt I = AD.multiplicativeInverse(Mod); 4511 4512 // 4. Compute the minimum unsigned root of the equation: 4513 // I * (B / D) mod (N / D) 4514 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4515 4516 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4517 // bits. 4518 return SE.getConstant(Result.trunc(BW)); 4519} 4520 4521/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4522/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4523/// might be the same) or two SCEVCouldNotCompute objects. 4524/// 4525static std::pair<const SCEV *,const SCEV *> 4526SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4527 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4528 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4529 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4530 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4531 4532 // We currently can only solve this if the coefficients are constants. 4533 if (!LC || !MC || !NC) { 4534 const SCEV *CNC = SE.getCouldNotCompute(); 4535 return std::make_pair(CNC, CNC); 4536 } 4537 4538 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4539 const APInt &L = LC->getValue()->getValue(); 4540 const APInt &M = MC->getValue()->getValue(); 4541 const APInt &N = NC->getValue()->getValue(); 4542 APInt Two(BitWidth, 2); 4543 APInt Four(BitWidth, 4); 4544 4545 { 4546 using namespace APIntOps; 4547 const APInt& C = L; 4548 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4549 // The B coefficient is M-N/2 4550 APInt B(M); 4551 B -= sdiv(N,Two); 4552 4553 // The A coefficient is N/2 4554 APInt A(N.sdiv(Two)); 4555 4556 // Compute the B^2-4ac term. 4557 APInt SqrtTerm(B); 4558 SqrtTerm *= B; 4559 SqrtTerm -= Four * (A * C); 4560 4561 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4562 // integer value or else APInt::sqrt() will assert. 4563 APInt SqrtVal(SqrtTerm.sqrt()); 4564 4565 // Compute the two solutions for the quadratic formula. 4566 // The divisions must be performed as signed divisions. 4567 APInt NegB(-B); 4568 APInt TwoA( A << 1 ); 4569 if (TwoA.isMinValue()) { 4570 const SCEV *CNC = SE.getCouldNotCompute(); 4571 return std::make_pair(CNC, CNC); 4572 } 4573 4574 LLVMContext &Context = SE.getContext(); 4575 4576 ConstantInt *Solution1 = 4577 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4578 ConstantInt *Solution2 = 4579 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4580 4581 return std::make_pair(SE.getConstant(Solution1), 4582 SE.getConstant(Solution2)); 4583 } // end APIntOps namespace 4584} 4585 4586/// HowFarToZero - Return the number of times a backedge comparing the specified 4587/// value to zero will execute. If not computable, return CouldNotCompute. 4588ScalarEvolution::BackedgeTakenInfo 4589ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4590 // If the value is a constant 4591 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4592 // If the value is already zero, the branch will execute zero times. 4593 if (C->getValue()->isZero()) return C; 4594 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4595 } 4596 4597 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4598 if (!AddRec || AddRec->getLoop() != L) 4599 return getCouldNotCompute(); 4600 4601 if (AddRec->isAffine()) { 4602 // If this is an affine expression, the execution count of this branch is 4603 // the minimum unsigned root of the following equation: 4604 // 4605 // Start + Step*N = 0 (mod 2^BW) 4606 // 4607 // equivalent to: 4608 // 4609 // Step*N = -Start (mod 2^BW) 4610 // 4611 // where BW is the common bit width of Start and Step. 4612 4613 // Get the initial value for the loop. 4614 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4615 L->getParentLoop()); 4616 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4617 L->getParentLoop()); 4618 4619 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4620 // For now we handle only constant steps. 4621 4622 // First, handle unitary steps. 4623 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4624 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4625 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4626 return Start; // N = Start (as unsigned) 4627 4628 // Then, try to solve the above equation provided that Start is constant. 4629 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4630 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4631 -StartC->getValue()->getValue(), 4632 *this); 4633 } 4634 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4635 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4636 // the quadratic equation to solve it. 4637 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4638 *this); 4639 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4640 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4641 if (R1) { 4642#if 0 4643 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4644 << " sol#2: " << *R2 << "\n"; 4645#endif 4646 // Pick the smallest positive root value. 4647 if (ConstantInt *CB = 4648 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4649 R1->getValue(), R2->getValue()))) { 4650 if (CB->getZExtValue() == false) 4651 std::swap(R1, R2); // R1 is the minimum root now. 4652 4653 // We can only use this value if the chrec ends up with an exact zero 4654 // value at this index. When solving for "X*X != 5", for example, we 4655 // should not accept a root of 2. 4656 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4657 if (Val->isZero()) 4658 return R1; // We found a quadratic root! 4659 } 4660 } 4661 } 4662 4663 return getCouldNotCompute(); 4664} 4665 4666/// HowFarToNonZero - Return the number of times a backedge checking the 4667/// specified value for nonzero will execute. If not computable, return 4668/// CouldNotCompute 4669ScalarEvolution::BackedgeTakenInfo 4670ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4671 // Loops that look like: while (X == 0) are very strange indeed. We don't 4672 // handle them yet except for the trivial case. This could be expanded in the 4673 // future as needed. 4674 4675 // If the value is a constant, check to see if it is known to be non-zero 4676 // already. If so, the backedge will execute zero times. 4677 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4678 if (!C->getValue()->isNullValue()) 4679 return getConstant(C->getType(), 0); 4680 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4681 } 4682 4683 // We could implement others, but I really doubt anyone writes loops like 4684 // this, and if they did, they would already be constant folded. 4685 return getCouldNotCompute(); 4686} 4687 4688/// getLoopPredecessor - If the given loop's header has exactly one unique 4689/// predecessor outside the loop, return it. Otherwise return null. 4690/// This is less strict that the loop "preheader" concept, which requires 4691/// the predecessor to have only one single successor. 4692/// 4693BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4694 BasicBlock *Header = L->getHeader(); 4695 BasicBlock *Pred = 0; 4696 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4697 PI != E; ++PI) 4698 if (!L->contains(*PI)) { 4699 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4700 Pred = *PI; 4701 } 4702 return Pred; 4703} 4704 4705/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4706/// (which may not be an immediate predecessor) which has exactly one 4707/// successor from which BB is reachable, or null if no such block is 4708/// found. 4709/// 4710std::pair<BasicBlock *, BasicBlock *> 4711ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4712 // If the block has a unique predecessor, then there is no path from the 4713 // predecessor to the block that does not go through the direct edge 4714 // from the predecessor to the block. 4715 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4716 return std::make_pair(Pred, BB); 4717 4718 // A loop's header is defined to be a block that dominates the loop. 4719 // If the header has a unique predecessor outside the loop, it must be 4720 // a block that has exactly one successor that can reach the loop. 4721 if (Loop *L = LI->getLoopFor(BB)) 4722 return std::make_pair(getLoopPredecessor(L), L->getHeader()); 4723 4724 return std::pair<BasicBlock *, BasicBlock *>(); 4725} 4726 4727/// HasSameValue - SCEV structural equivalence is usually sufficient for 4728/// testing whether two expressions are equal, however for the purposes of 4729/// looking for a condition guarding a loop, it can be useful to be a little 4730/// more general, since a front-end may have replicated the controlling 4731/// expression. 4732/// 4733static bool HasSameValue(const SCEV *A, const SCEV *B) { 4734 // Quick check to see if they are the same SCEV. 4735 if (A == B) return true; 4736 4737 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4738 // two different instructions with the same value. Check for this case. 4739 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4740 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4741 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4742 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4743 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4744 return true; 4745 4746 // Otherwise assume they may have a different value. 4747 return false; 4748} 4749 4750/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4751/// predicate Pred. Return true iff any changes were made. 4752/// 4753bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4754 const SCEV *&LHS, const SCEV *&RHS) { 4755 bool Changed = false; 4756 4757 // Canonicalize a constant to the right side. 4758 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4759 // Check for both operands constant. 4760 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4761 if (ConstantExpr::getICmp(Pred, 4762 LHSC->getValue(), 4763 RHSC->getValue())->isNullValue()) 4764 goto trivially_false; 4765 else 4766 goto trivially_true; 4767 } 4768 // Otherwise swap the operands to put the constant on the right. 4769 std::swap(LHS, RHS); 4770 Pred = ICmpInst::getSwappedPredicate(Pred); 4771 Changed = true; 4772 } 4773 4774 // If we're comparing an addrec with a value which is loop-invariant in the 4775 // addrec's loop, put the addrec on the left. Also make a dominance check, 4776 // as both operands could be addrecs loop-invariant in each other's loop. 4777 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4778 const Loop *L = AR->getLoop(); 4779 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4780 std::swap(LHS, RHS); 4781 Pred = ICmpInst::getSwappedPredicate(Pred); 4782 Changed = true; 4783 } 4784 } 4785 4786 // If there's a constant operand, canonicalize comparisons with boundary 4787 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4788 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4789 const APInt &RA = RC->getValue()->getValue(); 4790 switch (Pred) { 4791 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4792 case ICmpInst::ICMP_EQ: 4793 case ICmpInst::ICMP_NE: 4794 break; 4795 case ICmpInst::ICMP_UGE: 4796 if ((RA - 1).isMinValue()) { 4797 Pred = ICmpInst::ICMP_NE; 4798 RHS = getConstant(RA - 1); 4799 Changed = true; 4800 break; 4801 } 4802 if (RA.isMaxValue()) { 4803 Pred = ICmpInst::ICMP_EQ; 4804 Changed = true; 4805 break; 4806 } 4807 if (RA.isMinValue()) goto trivially_true; 4808 4809 Pred = ICmpInst::ICMP_UGT; 4810 RHS = getConstant(RA - 1); 4811 Changed = true; 4812 break; 4813 case ICmpInst::ICMP_ULE: 4814 if ((RA + 1).isMaxValue()) { 4815 Pred = ICmpInst::ICMP_NE; 4816 RHS = getConstant(RA + 1); 4817 Changed = true; 4818 break; 4819 } 4820 if (RA.isMinValue()) { 4821 Pred = ICmpInst::ICMP_EQ; 4822 Changed = true; 4823 break; 4824 } 4825 if (RA.isMaxValue()) goto trivially_true; 4826 4827 Pred = ICmpInst::ICMP_ULT; 4828 RHS = getConstant(RA + 1); 4829 Changed = true; 4830 break; 4831 case ICmpInst::ICMP_SGE: 4832 if ((RA - 1).isMinSignedValue()) { 4833 Pred = ICmpInst::ICMP_NE; 4834 RHS = getConstant(RA - 1); 4835 Changed = true; 4836 break; 4837 } 4838 if (RA.isMaxSignedValue()) { 4839 Pred = ICmpInst::ICMP_EQ; 4840 Changed = true; 4841 break; 4842 } 4843 if (RA.isMinSignedValue()) goto trivially_true; 4844 4845 Pred = ICmpInst::ICMP_SGT; 4846 RHS = getConstant(RA - 1); 4847 Changed = true; 4848 break; 4849 case ICmpInst::ICMP_SLE: 4850 if ((RA + 1).isMaxSignedValue()) { 4851 Pred = ICmpInst::ICMP_NE; 4852 RHS = getConstant(RA + 1); 4853 Changed = true; 4854 break; 4855 } 4856 if (RA.isMinSignedValue()) { 4857 Pred = ICmpInst::ICMP_EQ; 4858 Changed = true; 4859 break; 4860 } 4861 if (RA.isMaxSignedValue()) goto trivially_true; 4862 4863 Pred = ICmpInst::ICMP_SLT; 4864 RHS = getConstant(RA + 1); 4865 Changed = true; 4866 break; 4867 case ICmpInst::ICMP_UGT: 4868 if (RA.isMinValue()) { 4869 Pred = ICmpInst::ICMP_NE; 4870 Changed = true; 4871 break; 4872 } 4873 if ((RA + 1).isMaxValue()) { 4874 Pred = ICmpInst::ICMP_EQ; 4875 RHS = getConstant(RA + 1); 4876 Changed = true; 4877 break; 4878 } 4879 if (RA.isMaxValue()) goto trivially_false; 4880 break; 4881 case ICmpInst::ICMP_ULT: 4882 if (RA.isMaxValue()) { 4883 Pred = ICmpInst::ICMP_NE; 4884 Changed = true; 4885 break; 4886 } 4887 if ((RA - 1).isMinValue()) { 4888 Pred = ICmpInst::ICMP_EQ; 4889 RHS = getConstant(RA - 1); 4890 Changed = true; 4891 break; 4892 } 4893 if (RA.isMinValue()) goto trivially_false; 4894 break; 4895 case ICmpInst::ICMP_SGT: 4896 if (RA.isMinSignedValue()) { 4897 Pred = ICmpInst::ICMP_NE; 4898 Changed = true; 4899 break; 4900 } 4901 if ((RA + 1).isMaxSignedValue()) { 4902 Pred = ICmpInst::ICMP_EQ; 4903 RHS = getConstant(RA + 1); 4904 Changed = true; 4905 break; 4906 } 4907 if (RA.isMaxSignedValue()) goto trivially_false; 4908 break; 4909 case ICmpInst::ICMP_SLT: 4910 if (RA.isMaxSignedValue()) { 4911 Pred = ICmpInst::ICMP_NE; 4912 Changed = true; 4913 break; 4914 } 4915 if ((RA - 1).isMinSignedValue()) { 4916 Pred = ICmpInst::ICMP_EQ; 4917 RHS = getConstant(RA - 1); 4918 Changed = true; 4919 break; 4920 } 4921 if (RA.isMinSignedValue()) goto trivially_false; 4922 break; 4923 } 4924 } 4925 4926 // Check for obvious equality. 4927 if (HasSameValue(LHS, RHS)) { 4928 if (ICmpInst::isTrueWhenEqual(Pred)) 4929 goto trivially_true; 4930 if (ICmpInst::isFalseWhenEqual(Pred)) 4931 goto trivially_false; 4932 } 4933 4934 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 4935 // adding or subtracting 1 from one of the operands. 4936 switch (Pred) { 4937 case ICmpInst::ICMP_SLE: 4938 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 4939 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 4940 /*HasNUW=*/false, /*HasNSW=*/true); 4941 Pred = ICmpInst::ICMP_SLT; 4942 Changed = true; 4943 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 4944 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 4945 /*HasNUW=*/false, /*HasNSW=*/true); 4946 Pred = ICmpInst::ICMP_SLT; 4947 Changed = true; 4948 } 4949 break; 4950 case ICmpInst::ICMP_SGE: 4951 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 4952 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 4953 /*HasNUW=*/false, /*HasNSW=*/true); 4954 Pred = ICmpInst::ICMP_SGT; 4955 Changed = true; 4956 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 4957 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 4958 /*HasNUW=*/false, /*HasNSW=*/true); 4959 Pred = ICmpInst::ICMP_SGT; 4960 Changed = true; 4961 } 4962 break; 4963 case ICmpInst::ICMP_ULE: 4964 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 4965 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 4966 /*HasNUW=*/true, /*HasNSW=*/false); 4967 Pred = ICmpInst::ICMP_ULT; 4968 Changed = true; 4969 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 4970 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 4971 /*HasNUW=*/true, /*HasNSW=*/false); 4972 Pred = ICmpInst::ICMP_ULT; 4973 Changed = true; 4974 } 4975 break; 4976 case ICmpInst::ICMP_UGE: 4977 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 4978 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 4979 /*HasNUW=*/true, /*HasNSW=*/false); 4980 Pred = ICmpInst::ICMP_UGT; 4981 Changed = true; 4982 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 4983 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 4984 /*HasNUW=*/true, /*HasNSW=*/false); 4985 Pred = ICmpInst::ICMP_UGT; 4986 Changed = true; 4987 } 4988 break; 4989 default: 4990 break; 4991 } 4992 4993 // TODO: More simplifications are possible here. 4994 4995 return Changed; 4996 4997trivially_true: 4998 // Return 0 == 0. 4999 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5000 Pred = ICmpInst::ICMP_EQ; 5001 return true; 5002 5003trivially_false: 5004 // Return 0 != 0. 5005 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5006 Pred = ICmpInst::ICMP_NE; 5007 return true; 5008} 5009 5010bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5011 return getSignedRange(S).getSignedMax().isNegative(); 5012} 5013 5014bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5015 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5016} 5017 5018bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5019 return !getSignedRange(S).getSignedMin().isNegative(); 5020} 5021 5022bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5023 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5024} 5025 5026bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5027 return isKnownNegative(S) || isKnownPositive(S); 5028} 5029 5030bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5031 const SCEV *LHS, const SCEV *RHS) { 5032 // Canonicalize the inputs first. 5033 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5034 5035 // If LHS or RHS is an addrec, check to see if the condition is true in 5036 // every iteration of the loop. 5037 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5038 if (isLoopEntryGuardedByCond( 5039 AR->getLoop(), Pred, AR->getStart(), RHS) && 5040 isLoopBackedgeGuardedByCond( 5041 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5042 return true; 5043 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5044 if (isLoopEntryGuardedByCond( 5045 AR->getLoop(), Pred, LHS, AR->getStart()) && 5046 isLoopBackedgeGuardedByCond( 5047 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5048 return true; 5049 5050 // Otherwise see what can be done with known constant ranges. 5051 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5052} 5053 5054bool 5055ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5056 const SCEV *LHS, const SCEV *RHS) { 5057 if (HasSameValue(LHS, RHS)) 5058 return ICmpInst::isTrueWhenEqual(Pred); 5059 5060 // This code is split out from isKnownPredicate because it is called from 5061 // within isLoopEntryGuardedByCond. 5062 switch (Pred) { 5063 default: 5064 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5065 break; 5066 case ICmpInst::ICMP_SGT: 5067 Pred = ICmpInst::ICMP_SLT; 5068 std::swap(LHS, RHS); 5069 case ICmpInst::ICMP_SLT: { 5070 ConstantRange LHSRange = getSignedRange(LHS); 5071 ConstantRange RHSRange = getSignedRange(RHS); 5072 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5073 return true; 5074 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5075 return false; 5076 break; 5077 } 5078 case ICmpInst::ICMP_SGE: 5079 Pred = ICmpInst::ICMP_SLE; 5080 std::swap(LHS, RHS); 5081 case ICmpInst::ICMP_SLE: { 5082 ConstantRange LHSRange = getSignedRange(LHS); 5083 ConstantRange RHSRange = getSignedRange(RHS); 5084 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5085 return true; 5086 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5087 return false; 5088 break; 5089 } 5090 case ICmpInst::ICMP_UGT: 5091 Pred = ICmpInst::ICMP_ULT; 5092 std::swap(LHS, RHS); 5093 case ICmpInst::ICMP_ULT: { 5094 ConstantRange LHSRange = getUnsignedRange(LHS); 5095 ConstantRange RHSRange = getUnsignedRange(RHS); 5096 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5097 return true; 5098 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5099 return false; 5100 break; 5101 } 5102 case ICmpInst::ICMP_UGE: 5103 Pred = ICmpInst::ICMP_ULE; 5104 std::swap(LHS, RHS); 5105 case ICmpInst::ICMP_ULE: { 5106 ConstantRange LHSRange = getUnsignedRange(LHS); 5107 ConstantRange RHSRange = getUnsignedRange(RHS); 5108 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5109 return true; 5110 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5111 return false; 5112 break; 5113 } 5114 case ICmpInst::ICMP_NE: { 5115 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5116 return true; 5117 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5118 return true; 5119 5120 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5121 if (isKnownNonZero(Diff)) 5122 return true; 5123 break; 5124 } 5125 case ICmpInst::ICMP_EQ: 5126 // The check at the top of the function catches the case where 5127 // the values are known to be equal. 5128 break; 5129 } 5130 return false; 5131} 5132 5133/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5134/// protected by a conditional between LHS and RHS. This is used to 5135/// to eliminate casts. 5136bool 5137ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5138 ICmpInst::Predicate Pred, 5139 const SCEV *LHS, const SCEV *RHS) { 5140 // Interpret a null as meaning no loop, where there is obviously no guard 5141 // (interprocedural conditions notwithstanding). 5142 if (!L) return true; 5143 5144 BasicBlock *Latch = L->getLoopLatch(); 5145 if (!Latch) 5146 return false; 5147 5148 BranchInst *LoopContinuePredicate = 5149 dyn_cast<BranchInst>(Latch->getTerminator()); 5150 if (!LoopContinuePredicate || 5151 LoopContinuePredicate->isUnconditional()) 5152 return false; 5153 5154 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 5155 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5156} 5157 5158/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5159/// by a conditional between LHS and RHS. This is used to help avoid max 5160/// expressions in loop trip counts, and to eliminate casts. 5161bool 5162ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5163 ICmpInst::Predicate Pred, 5164 const SCEV *LHS, const SCEV *RHS) { 5165 // Interpret a null as meaning no loop, where there is obviously no guard 5166 // (interprocedural conditions notwithstanding). 5167 if (!L) return false; 5168 5169 // Starting at the loop predecessor, climb up the predecessor chain, as long 5170 // as there are predecessors that can be found that have unique successors 5171 // leading to the original header. 5172 for (std::pair<BasicBlock *, BasicBlock *> 5173 Pair(getLoopPredecessor(L), L->getHeader()); 5174 Pair.first; 5175 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5176 5177 BranchInst *LoopEntryPredicate = 5178 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5179 if (!LoopEntryPredicate || 5180 LoopEntryPredicate->isUnconditional()) 5181 continue; 5182 5183 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 5184 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5185 return true; 5186 } 5187 5188 return false; 5189} 5190 5191/// isImpliedCond - Test whether the condition described by Pred, LHS, 5192/// and RHS is true whenever the given Cond value evaluates to true. 5193bool ScalarEvolution::isImpliedCond(Value *CondValue, 5194 ICmpInst::Predicate Pred, 5195 const SCEV *LHS, const SCEV *RHS, 5196 bool Inverse) { 5197 // Recursively handle And and Or conditions. 5198 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 5199 if (BO->getOpcode() == Instruction::And) { 5200 if (!Inverse) 5201 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 5202 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 5203 } else if (BO->getOpcode() == Instruction::Or) { 5204 if (Inverse) 5205 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 5206 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 5207 } 5208 } 5209 5210 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 5211 if (!ICI) return false; 5212 5213 // Bail if the ICmp's operands' types are wider than the needed type 5214 // before attempting to call getSCEV on them. This avoids infinite 5215 // recursion, since the analysis of widening casts can require loop 5216 // exit condition information for overflow checking, which would 5217 // lead back here. 5218 if (getTypeSizeInBits(LHS->getType()) < 5219 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5220 return false; 5221 5222 // Now that we found a conditional branch that dominates the loop, check to 5223 // see if it is the comparison we are looking for. 5224 ICmpInst::Predicate FoundPred; 5225 if (Inverse) 5226 FoundPred = ICI->getInversePredicate(); 5227 else 5228 FoundPred = ICI->getPredicate(); 5229 5230 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5231 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5232 5233 // Balance the types. The case where FoundLHS' type is wider than 5234 // LHS' type is checked for above. 5235 if (getTypeSizeInBits(LHS->getType()) > 5236 getTypeSizeInBits(FoundLHS->getType())) { 5237 if (CmpInst::isSigned(Pred)) { 5238 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5239 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5240 } else { 5241 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5242 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5243 } 5244 } 5245 5246 // Canonicalize the query to match the way instcombine will have 5247 // canonicalized the comparison. 5248 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5249 if (LHS == RHS) 5250 return CmpInst::isTrueWhenEqual(Pred); 5251 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5252 if (FoundLHS == FoundRHS) 5253 return CmpInst::isFalseWhenEqual(Pred); 5254 5255 // Check to see if we can make the LHS or RHS match. 5256 if (LHS == FoundRHS || RHS == FoundLHS) { 5257 if (isa<SCEVConstant>(RHS)) { 5258 std::swap(FoundLHS, FoundRHS); 5259 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5260 } else { 5261 std::swap(LHS, RHS); 5262 Pred = ICmpInst::getSwappedPredicate(Pred); 5263 } 5264 } 5265 5266 // Check whether the found predicate is the same as the desired predicate. 5267 if (FoundPred == Pred) 5268 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5269 5270 // Check whether swapping the found predicate makes it the same as the 5271 // desired predicate. 5272 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5273 if (isa<SCEVConstant>(RHS)) 5274 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5275 else 5276 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5277 RHS, LHS, FoundLHS, FoundRHS); 5278 } 5279 5280 // Check whether the actual condition is beyond sufficient. 5281 if (FoundPred == ICmpInst::ICMP_EQ) 5282 if (ICmpInst::isTrueWhenEqual(Pred)) 5283 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5284 return true; 5285 if (Pred == ICmpInst::ICMP_NE) 5286 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5287 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5288 return true; 5289 5290 // Otherwise assume the worst. 5291 return false; 5292} 5293 5294/// isImpliedCondOperands - Test whether the condition described by Pred, 5295/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5296/// and FoundRHS is true. 5297bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5298 const SCEV *LHS, const SCEV *RHS, 5299 const SCEV *FoundLHS, 5300 const SCEV *FoundRHS) { 5301 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5302 FoundLHS, FoundRHS) || 5303 // ~x < ~y --> x > y 5304 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5305 getNotSCEV(FoundRHS), 5306 getNotSCEV(FoundLHS)); 5307} 5308 5309/// isImpliedCondOperandsHelper - Test whether the condition described by 5310/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5311/// FoundLHS, and FoundRHS is true. 5312bool 5313ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5314 const SCEV *LHS, const SCEV *RHS, 5315 const SCEV *FoundLHS, 5316 const SCEV *FoundRHS) { 5317 switch (Pred) { 5318 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5319 case ICmpInst::ICMP_EQ: 5320 case ICmpInst::ICMP_NE: 5321 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5322 return true; 5323 break; 5324 case ICmpInst::ICMP_SLT: 5325 case ICmpInst::ICMP_SLE: 5326 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5327 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5328 return true; 5329 break; 5330 case ICmpInst::ICMP_SGT: 5331 case ICmpInst::ICMP_SGE: 5332 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5333 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5334 return true; 5335 break; 5336 case ICmpInst::ICMP_ULT: 5337 case ICmpInst::ICMP_ULE: 5338 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5339 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5340 return true; 5341 break; 5342 case ICmpInst::ICMP_UGT: 5343 case ICmpInst::ICMP_UGE: 5344 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5345 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5346 return true; 5347 break; 5348 } 5349 5350 return false; 5351} 5352 5353/// getBECount - Subtract the end and start values and divide by the step, 5354/// rounding up, to get the number of times the backedge is executed. Return 5355/// CouldNotCompute if an intermediate computation overflows. 5356const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5357 const SCEV *End, 5358 const SCEV *Step, 5359 bool NoWrap) { 5360 assert(!isKnownNegative(Step) && 5361 "This code doesn't handle negative strides yet!"); 5362 5363 const Type *Ty = Start->getType(); 5364 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5365 const SCEV *Diff = getMinusSCEV(End, Start); 5366 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5367 5368 // Add an adjustment to the difference between End and Start so that 5369 // the division will effectively round up. 5370 const SCEV *Add = getAddExpr(Diff, RoundUp); 5371 5372 if (!NoWrap) { 5373 // Check Add for unsigned overflow. 5374 // TODO: More sophisticated things could be done here. 5375 const Type *WideTy = IntegerType::get(getContext(), 5376 getTypeSizeInBits(Ty) + 1); 5377 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5378 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5379 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5380 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5381 return getCouldNotCompute(); 5382 } 5383 5384 return getUDivExpr(Add, Step); 5385} 5386 5387/// HowManyLessThans - Return the number of times a backedge containing the 5388/// specified less-than comparison will execute. If not computable, return 5389/// CouldNotCompute. 5390ScalarEvolution::BackedgeTakenInfo 5391ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5392 const Loop *L, bool isSigned) { 5393 // Only handle: "ADDREC < LoopInvariant". 5394 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5395 5396 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5397 if (!AddRec || AddRec->getLoop() != L) 5398 return getCouldNotCompute(); 5399 5400 // Check to see if we have a flag which makes analysis easy. 5401 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5402 AddRec->hasNoUnsignedWrap(); 5403 5404 if (AddRec->isAffine()) { 5405 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5406 const SCEV *Step = AddRec->getStepRecurrence(*this); 5407 5408 if (Step->isZero()) 5409 return getCouldNotCompute(); 5410 if (Step->isOne()) { 5411 // With unit stride, the iteration never steps past the limit value. 5412 } else if (isKnownPositive(Step)) { 5413 // Test whether a positive iteration can step past the limit 5414 // value and past the maximum value for its type in a single step. 5415 // Note that it's not sufficient to check NoWrap here, because even 5416 // though the value after a wrap is undefined, it's not undefined 5417 // behavior, so if wrap does occur, the loop could either terminate or 5418 // loop infinitely, but in either case, the loop is guaranteed to 5419 // iterate at least until the iteration where the wrapping occurs. 5420 const SCEV *One = getConstant(Step->getType(), 1); 5421 if (isSigned) { 5422 APInt Max = APInt::getSignedMaxValue(BitWidth); 5423 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5424 .slt(getSignedRange(RHS).getSignedMax())) 5425 return getCouldNotCompute(); 5426 } else { 5427 APInt Max = APInt::getMaxValue(BitWidth); 5428 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5429 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5430 return getCouldNotCompute(); 5431 } 5432 } else 5433 // TODO: Handle negative strides here and below. 5434 return getCouldNotCompute(); 5435 5436 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5437 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5438 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5439 // treat m-n as signed nor unsigned due to overflow possibility. 5440 5441 // First, we get the value of the LHS in the first iteration: n 5442 const SCEV *Start = AddRec->getOperand(0); 5443 5444 // Determine the minimum constant start value. 5445 const SCEV *MinStart = getConstant(isSigned ? 5446 getSignedRange(Start).getSignedMin() : 5447 getUnsignedRange(Start).getUnsignedMin()); 5448 5449 // If we know that the condition is true in order to enter the loop, 5450 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5451 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5452 // the division must round up. 5453 const SCEV *End = RHS; 5454 if (!isLoopEntryGuardedByCond(L, 5455 isSigned ? ICmpInst::ICMP_SLT : 5456 ICmpInst::ICMP_ULT, 5457 getMinusSCEV(Start, Step), RHS)) 5458 End = isSigned ? getSMaxExpr(RHS, Start) 5459 : getUMaxExpr(RHS, Start); 5460 5461 // Determine the maximum constant end value. 5462 const SCEV *MaxEnd = getConstant(isSigned ? 5463 getSignedRange(End).getSignedMax() : 5464 getUnsignedRange(End).getUnsignedMax()); 5465 5466 // If MaxEnd is within a step of the maximum integer value in its type, 5467 // adjust it down to the minimum value which would produce the same effect. 5468 // This allows the subsequent ceiling division of (N+(step-1))/step to 5469 // compute the correct value. 5470 const SCEV *StepMinusOne = getMinusSCEV(Step, 5471 getConstant(Step->getType(), 1)); 5472 MaxEnd = isSigned ? 5473 getSMinExpr(MaxEnd, 5474 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5475 StepMinusOne)) : 5476 getUMinExpr(MaxEnd, 5477 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5478 StepMinusOne)); 5479 5480 // Finally, we subtract these two values and divide, rounding up, to get 5481 // the number of times the backedge is executed. 5482 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5483 5484 // The maximum backedge count is similar, except using the minimum start 5485 // value and the maximum end value. 5486 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5487 5488 return BackedgeTakenInfo(BECount, MaxBECount); 5489 } 5490 5491 return getCouldNotCompute(); 5492} 5493 5494/// getNumIterationsInRange - Return the number of iterations of this loop that 5495/// produce values in the specified constant range. Another way of looking at 5496/// this is that it returns the first iteration number where the value is not in 5497/// the condition, thus computing the exit count. If the iteration count can't 5498/// be computed, an instance of SCEVCouldNotCompute is returned. 5499const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5500 ScalarEvolution &SE) const { 5501 if (Range.isFullSet()) // Infinite loop. 5502 return SE.getCouldNotCompute(); 5503 5504 // If the start is a non-zero constant, shift the range to simplify things. 5505 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5506 if (!SC->getValue()->isZero()) { 5507 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5508 Operands[0] = SE.getConstant(SC->getType(), 0); 5509 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5510 if (const SCEVAddRecExpr *ShiftedAddRec = 5511 dyn_cast<SCEVAddRecExpr>(Shifted)) 5512 return ShiftedAddRec->getNumIterationsInRange( 5513 Range.subtract(SC->getValue()->getValue()), SE); 5514 // This is strange and shouldn't happen. 5515 return SE.getCouldNotCompute(); 5516 } 5517 5518 // The only time we can solve this is when we have all constant indices. 5519 // Otherwise, we cannot determine the overflow conditions. 5520 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5521 if (!isa<SCEVConstant>(getOperand(i))) 5522 return SE.getCouldNotCompute(); 5523 5524 5525 // Okay at this point we know that all elements of the chrec are constants and 5526 // that the start element is zero. 5527 5528 // First check to see if the range contains zero. If not, the first 5529 // iteration exits. 5530 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5531 if (!Range.contains(APInt(BitWidth, 0))) 5532 return SE.getConstant(getType(), 0); 5533 5534 if (isAffine()) { 5535 // If this is an affine expression then we have this situation: 5536 // Solve {0,+,A} in Range === Ax in Range 5537 5538 // We know that zero is in the range. If A is positive then we know that 5539 // the upper value of the range must be the first possible exit value. 5540 // If A is negative then the lower of the range is the last possible loop 5541 // value. Also note that we already checked for a full range. 5542 APInt One(BitWidth,1); 5543 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5544 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5545 5546 // The exit value should be (End+A)/A. 5547 APInt ExitVal = (End + A).udiv(A); 5548 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5549 5550 // Evaluate at the exit value. If we really did fall out of the valid 5551 // range, then we computed our trip count, otherwise wrap around or other 5552 // things must have happened. 5553 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5554 if (Range.contains(Val->getValue())) 5555 return SE.getCouldNotCompute(); // Something strange happened 5556 5557 // Ensure that the previous value is in the range. This is a sanity check. 5558 assert(Range.contains( 5559 EvaluateConstantChrecAtConstant(this, 5560 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5561 "Linear scev computation is off in a bad way!"); 5562 return SE.getConstant(ExitValue); 5563 } else if (isQuadratic()) { 5564 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5565 // quadratic equation to solve it. To do this, we must frame our problem in 5566 // terms of figuring out when zero is crossed, instead of when 5567 // Range.getUpper() is crossed. 5568 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5569 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5570 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5571 5572 // Next, solve the constructed addrec 5573 std::pair<const SCEV *,const SCEV *> Roots = 5574 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5575 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5576 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5577 if (R1) { 5578 // Pick the smallest positive root value. 5579 if (ConstantInt *CB = 5580 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5581 R1->getValue(), R2->getValue()))) { 5582 if (CB->getZExtValue() == false) 5583 std::swap(R1, R2); // R1 is the minimum root now. 5584 5585 // Make sure the root is not off by one. The returned iteration should 5586 // not be in the range, but the previous one should be. When solving 5587 // for "X*X < 5", for example, we should not return a root of 2. 5588 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5589 R1->getValue(), 5590 SE); 5591 if (Range.contains(R1Val->getValue())) { 5592 // The next iteration must be out of the range... 5593 ConstantInt *NextVal = 5594 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5595 5596 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5597 if (!Range.contains(R1Val->getValue())) 5598 return SE.getConstant(NextVal); 5599 return SE.getCouldNotCompute(); // Something strange happened 5600 } 5601 5602 // If R1 was not in the range, then it is a good return value. Make 5603 // sure that R1-1 WAS in the range though, just in case. 5604 ConstantInt *NextVal = 5605 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5606 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5607 if (Range.contains(R1Val->getValue())) 5608 return R1; 5609 return SE.getCouldNotCompute(); // Something strange happened 5610 } 5611 } 5612 } 5613 5614 return SE.getCouldNotCompute(); 5615} 5616 5617 5618 5619//===----------------------------------------------------------------------===// 5620// SCEVCallbackVH Class Implementation 5621//===----------------------------------------------------------------------===// 5622 5623void ScalarEvolution::SCEVCallbackVH::deleted() { 5624 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5625 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5626 SE->ConstantEvolutionLoopExitValue.erase(PN); 5627 SE->Scalars.erase(getValPtr()); 5628 // this now dangles! 5629} 5630 5631void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5632 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5633 5634 // Forget all the expressions associated with users of the old value, 5635 // so that future queries will recompute the expressions using the new 5636 // value. 5637 SmallVector<User *, 16> Worklist; 5638 SmallPtrSet<User *, 8> Visited; 5639 Value *Old = getValPtr(); 5640 bool DeleteOld = false; 5641 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5642 UI != UE; ++UI) 5643 Worklist.push_back(*UI); 5644 while (!Worklist.empty()) { 5645 User *U = Worklist.pop_back_val(); 5646 // Deleting the Old value will cause this to dangle. Postpone 5647 // that until everything else is done. 5648 if (U == Old) { 5649 DeleteOld = true; 5650 continue; 5651 } 5652 if (!Visited.insert(U)) 5653 continue; 5654 if (PHINode *PN = dyn_cast<PHINode>(U)) 5655 SE->ConstantEvolutionLoopExitValue.erase(PN); 5656 SE->Scalars.erase(U); 5657 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5658 UI != UE; ++UI) 5659 Worklist.push_back(*UI); 5660 } 5661 // Delete the Old value if it (indirectly) references itself. 5662 if (DeleteOld) { 5663 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5664 SE->ConstantEvolutionLoopExitValue.erase(PN); 5665 SE->Scalars.erase(Old); 5666 // this now dangles! 5667 } 5668 // this may dangle! 5669} 5670 5671ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5672 : CallbackVH(V), SE(se) {} 5673 5674//===----------------------------------------------------------------------===// 5675// ScalarEvolution Class Implementation 5676//===----------------------------------------------------------------------===// 5677 5678ScalarEvolution::ScalarEvolution() 5679 : FunctionPass(&ID) { 5680} 5681 5682bool ScalarEvolution::runOnFunction(Function &F) { 5683 this->F = &F; 5684 LI = &getAnalysis<LoopInfo>(); 5685 TD = getAnalysisIfAvailable<TargetData>(); 5686 DT = &getAnalysis<DominatorTree>(); 5687 return false; 5688} 5689 5690void ScalarEvolution::releaseMemory() { 5691 Scalars.clear(); 5692 BackedgeTakenCounts.clear(); 5693 ConstantEvolutionLoopExitValue.clear(); 5694 ValuesAtScopes.clear(); 5695 UniqueSCEVs.clear(); 5696 SCEVAllocator.Reset(); 5697} 5698 5699void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5700 AU.setPreservesAll(); 5701 AU.addRequiredTransitive<LoopInfo>(); 5702 AU.addRequiredTransitive<DominatorTree>(); 5703} 5704 5705bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5706 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5707} 5708 5709static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5710 const Loop *L) { 5711 // Print all inner loops first 5712 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5713 PrintLoopInfo(OS, SE, *I); 5714 5715 OS << "Loop "; 5716 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5717 OS << ": "; 5718 5719 SmallVector<BasicBlock *, 8> ExitBlocks; 5720 L->getExitBlocks(ExitBlocks); 5721 if (ExitBlocks.size() != 1) 5722 OS << "<multiple exits> "; 5723 5724 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5725 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5726 } else { 5727 OS << "Unpredictable backedge-taken count. "; 5728 } 5729 5730 OS << "\n" 5731 "Loop "; 5732 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5733 OS << ": "; 5734 5735 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5736 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5737 } else { 5738 OS << "Unpredictable max backedge-taken count. "; 5739 } 5740 5741 OS << "\n"; 5742} 5743 5744void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5745 // ScalarEvolution's implementation of the print method is to print 5746 // out SCEV values of all instructions that are interesting. Doing 5747 // this potentially causes it to create new SCEV objects though, 5748 // which technically conflicts with the const qualifier. This isn't 5749 // observable from outside the class though, so casting away the 5750 // const isn't dangerous. 5751 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5752 5753 OS << "Classifying expressions for: "; 5754 WriteAsOperand(OS, F, /*PrintType=*/false); 5755 OS << "\n"; 5756 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5757 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5758 OS << *I << '\n'; 5759 OS << " --> "; 5760 const SCEV *SV = SE.getSCEV(&*I); 5761 SV->print(OS); 5762 5763 const Loop *L = LI->getLoopFor((*I).getParent()); 5764 5765 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5766 if (AtUse != SV) { 5767 OS << " --> "; 5768 AtUse->print(OS); 5769 } 5770 5771 if (L) { 5772 OS << "\t\t" "Exits: "; 5773 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5774 if (!ExitValue->isLoopInvariant(L)) { 5775 OS << "<<Unknown>>"; 5776 } else { 5777 OS << *ExitValue; 5778 } 5779 } 5780 5781 OS << "\n"; 5782 } 5783 5784 OS << "Determining loop execution counts for: "; 5785 WriteAsOperand(OS, F, /*PrintType=*/false); 5786 OS << "\n"; 5787 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5788 PrintLoopInfo(OS, &SE, *I); 5789} 5790 5791