ScalarEvolution.cpp revision 205407
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 return getConstant( 192 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(raw_ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201SCEVCastExpr::SCEVCastExpr(const 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 assert(NumOperands > 1 && "This plus expr shouldn't exist!"); 251 const char *OpStr = getOperationStr(); 252 OS << "(" << *Operands[0]; 253 for (unsigned i = 1, e = NumOperands; i != e; ++i) 254 OS << OpStr << *Operands[i]; 255 OS << ")"; 256} 257 258bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 259 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 260 if (!getOperand(i)->dominates(BB, DT)) 261 return false; 262 } 263 return true; 264} 265 266bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 267 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 268 if (!getOperand(i)->properlyDominates(BB, DT)) 269 return false; 270 } 271 return true; 272} 273 274bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 275 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 276} 277 278bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 279 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 280} 281 282void SCEVUDivExpr::print(raw_ostream &OS) const { 283 OS << "(" << *LHS << " /u " << *RHS << ")"; 284} 285 286const Type *SCEVUDivExpr::getType() const { 287 // In most cases the types of LHS and RHS will be the same, but in some 288 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 289 // depend on the type for correctness, but handling types carefully can 290 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 291 // a pointer type than the RHS, so use the RHS' type here. 292 return RHS->getType(); 293} 294 295bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 296 // Add recurrences are never invariant in the function-body (null loop). 297 if (!QueryLoop) 298 return false; 299 300 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 301 if (QueryLoop->contains(L)) 302 return false; 303 304 // This recurrence is variant w.r.t. QueryLoop if any of its operands 305 // are variant. 306 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 307 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 308 return false; 309 310 // Otherwise it's loop-invariant. 311 return true; 312} 313 314bool 315SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 316 return DT->dominates(L->getHeader(), BB) && 317 SCEVNAryExpr::dominates(BB, DT); 318} 319 320bool 321SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 322 // This uses a "dominates" query instead of "properly dominates" query because 323 // the instruction which produces the addrec's value is a PHI, and a PHI 324 // effectively properly dominates its entire containing block. 325 return DT->dominates(L->getHeader(), BB) && 326 SCEVNAryExpr::properlyDominates(BB, DT); 327} 328 329void SCEVAddRecExpr::print(raw_ostream &OS) const { 330 OS << "{" << *Operands[0]; 331 for (unsigned i = 1, e = NumOperands; i != e; ++i) 332 OS << ",+," << *Operands[i]; 333 OS << "}<"; 334 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 335 OS << ">"; 336} 337 338bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 339 // All non-instruction values are loop invariant. All instructions are loop 340 // invariant if they are not contained in the specified loop. 341 // Instructions are never considered invariant in the function body 342 // (null loop) because they are defined within the "loop". 343 if (Instruction *I = dyn_cast<Instruction>(V)) 344 return L && !L->contains(I); 345 return true; 346} 347 348bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 349 if (Instruction *I = dyn_cast<Instruction>(getValue())) 350 return DT->dominates(I->getParent(), BB); 351 return true; 352} 353 354bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 355 if (Instruction *I = dyn_cast<Instruction>(getValue())) 356 return DT->properlyDominates(I->getParent(), BB); 357 return true; 358} 359 360const Type *SCEVUnknown::getType() const { 361 return V->getType(); 362} 363 364bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 365 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 366 if (VCE->getOpcode() == Instruction::PtrToInt) 367 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 368 if (CE->getOpcode() == Instruction::GetElementPtr && 369 CE->getOperand(0)->isNullValue() && 370 CE->getNumOperands() == 2) 371 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 372 if (CI->isOne()) { 373 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 374 ->getElementType(); 375 return true; 376 } 377 378 return false; 379} 380 381bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 382 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 383 if (VCE->getOpcode() == Instruction::PtrToInt) 384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 385 if (CE->getOpcode() == Instruction::GetElementPtr && 386 CE->getOperand(0)->isNullValue()) { 387 const Type *Ty = 388 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 389 if (const StructType *STy = dyn_cast<StructType>(Ty)) 390 if (!STy->isPacked() && 391 CE->getNumOperands() == 3 && 392 CE->getOperand(1)->isNullValue()) { 393 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 394 if (CI->isOne() && 395 STy->getNumElements() == 2 && 396 STy->getElementType(0)->isIntegerTy(1)) { 397 AllocTy = STy->getElementType(1); 398 return true; 399 } 400 } 401 } 402 403 return false; 404} 405 406bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 408 if (VCE->getOpcode() == Instruction::PtrToInt) 409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 410 if (CE->getOpcode() == Instruction::GetElementPtr && 411 CE->getNumOperands() == 3 && 412 CE->getOperand(0)->isNullValue() && 413 CE->getOperand(1)->isNullValue()) { 414 const Type *Ty = 415 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 416 // Ignore vector types here so that ScalarEvolutionExpander doesn't 417 // emit getelementptrs that index into vectors. 418 if (Ty->isStructTy() || Ty->isArrayTy()) { 419 CTy = Ty; 420 FieldNo = CE->getOperand(2); 421 return true; 422 } 423 } 424 425 return false; 426} 427 428void SCEVUnknown::print(raw_ostream &OS) const { 429 const Type *AllocTy; 430 if (isSizeOf(AllocTy)) { 431 OS << "sizeof(" << *AllocTy << ")"; 432 return; 433 } 434 if (isAlignOf(AllocTy)) { 435 OS << "alignof(" << *AllocTy << ")"; 436 return; 437 } 438 439 const Type *CTy; 440 Constant *FieldNo; 441 if (isOffsetOf(CTy, FieldNo)) { 442 OS << "offsetof(" << *CTy << ", "; 443 WriteAsOperand(OS, FieldNo, false); 444 OS << ")"; 445 return; 446 } 447 448 // Otherwise just print it normally. 449 WriteAsOperand(OS, V, false); 450} 451 452//===----------------------------------------------------------------------===// 453// SCEV Utilities 454//===----------------------------------------------------------------------===// 455 456static bool CompareTypes(const Type *A, const Type *B) { 457 if (A->getTypeID() != B->getTypeID()) 458 return A->getTypeID() < B->getTypeID(); 459 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 460 const IntegerType *BI = cast<IntegerType>(B); 461 return AI->getBitWidth() < BI->getBitWidth(); 462 } 463 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 464 const PointerType *BI = cast<PointerType>(B); 465 return CompareTypes(AI->getElementType(), BI->getElementType()); 466 } 467 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 468 const ArrayType *BI = cast<ArrayType>(B); 469 if (AI->getNumElements() != BI->getNumElements()) 470 return AI->getNumElements() < BI->getNumElements(); 471 return CompareTypes(AI->getElementType(), BI->getElementType()); 472 } 473 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 474 const VectorType *BI = cast<VectorType>(B); 475 if (AI->getNumElements() != BI->getNumElements()) 476 return AI->getNumElements() < BI->getNumElements(); 477 return CompareTypes(AI->getElementType(), BI->getElementType()); 478 } 479 if (const StructType *AI = dyn_cast<StructType>(A)) { 480 const StructType *BI = cast<StructType>(B); 481 if (AI->getNumElements() != BI->getNumElements()) 482 return AI->getNumElements() < BI->getNumElements(); 483 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 484 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 485 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 486 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 487 } 488 return false; 489} 490 491namespace { 492 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 493 /// than the complexity of the RHS. This comparator is used to canonicalize 494 /// expressions. 495 class SCEVComplexityCompare { 496 LoopInfo *LI; 497 public: 498 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 499 500 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 501 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 502 if (LHS == RHS) 503 return false; 504 505 // Primarily, sort the SCEVs by their getSCEVType(). 506 if (LHS->getSCEVType() != RHS->getSCEVType()) 507 return LHS->getSCEVType() < RHS->getSCEVType(); 508 509 // Aside from the getSCEVType() ordering, the particular ordering 510 // isn't very important except that it's beneficial to be consistent, 511 // so that (a + b) and (b + a) don't end up as different expressions. 512 513 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 514 // not as complete as it could be. 515 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 516 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 517 518 // Order pointer values after integer values. This helps SCEVExpander 519 // form GEPs. 520 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy()) 521 return false; 522 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy()) 523 return true; 524 525 // Compare getValueID values. 526 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 527 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 528 529 // Sort arguments by their position. 530 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 531 const Argument *RA = cast<Argument>(RU->getValue()); 532 return LA->getArgNo() < RA->getArgNo(); 533 } 534 535 // For instructions, compare their loop depth, and their opcode. 536 // This is pretty loose. 537 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 538 Instruction *RV = cast<Instruction>(RU->getValue()); 539 540 // Compare loop depths. 541 if (LI->getLoopDepth(LV->getParent()) != 542 LI->getLoopDepth(RV->getParent())) 543 return LI->getLoopDepth(LV->getParent()) < 544 LI->getLoopDepth(RV->getParent()); 545 546 // Compare opcodes. 547 if (LV->getOpcode() != RV->getOpcode()) 548 return LV->getOpcode() < RV->getOpcode(); 549 550 // Compare the number of operands. 551 if (LV->getNumOperands() != RV->getNumOperands()) 552 return LV->getNumOperands() < RV->getNumOperands(); 553 } 554 555 return false; 556 } 557 558 // Compare constant values. 559 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 560 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 561 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 562 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 563 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 564 } 565 566 // Compare addrec loop depths. 567 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 568 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 569 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 570 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 571 } 572 573 // Lexicographically compare n-ary expressions. 574 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 575 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 576 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 577 if (i >= RC->getNumOperands()) 578 return false; 579 if (operator()(LC->getOperand(i), RC->getOperand(i))) 580 return true; 581 if (operator()(RC->getOperand(i), LC->getOperand(i))) 582 return false; 583 } 584 return LC->getNumOperands() < RC->getNumOperands(); 585 } 586 587 // Lexicographically compare udiv expressions. 588 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 589 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 590 if (operator()(LC->getLHS(), RC->getLHS())) 591 return true; 592 if (operator()(RC->getLHS(), LC->getLHS())) 593 return false; 594 if (operator()(LC->getRHS(), RC->getRHS())) 595 return true; 596 if (operator()(RC->getRHS(), LC->getRHS())) 597 return false; 598 return false; 599 } 600 601 // Compare cast expressions by operand. 602 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 603 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 604 return operator()(LC->getOperand(), RC->getOperand()); 605 } 606 607 llvm_unreachable("Unknown SCEV kind!"); 608 return false; 609 } 610 }; 611} 612 613/// GroupByComplexity - Given a list of SCEV objects, order them by their 614/// complexity, and group objects of the same complexity together by value. 615/// When this routine is finished, we know that any duplicates in the vector are 616/// consecutive and that complexity is monotonically increasing. 617/// 618/// Note that we go take special precautions to ensure that we get deterministic 619/// results from this routine. In other words, we don't want the results of 620/// this to depend on where the addresses of various SCEV objects happened to 621/// land in memory. 622/// 623static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 624 LoopInfo *LI) { 625 if (Ops.size() < 2) return; // Noop 626 if (Ops.size() == 2) { 627 // This is the common case, which also happens to be trivially simple. 628 // Special case it. 629 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 630 std::swap(Ops[0], Ops[1]); 631 return; 632 } 633 634 // Do the rough sort by complexity. 635 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 636 637 // Now that we are sorted by complexity, group elements of the same 638 // complexity. Note that this is, at worst, N^2, but the vector is likely to 639 // be extremely short in practice. Note that we take this approach because we 640 // do not want to depend on the addresses of the objects we are grouping. 641 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 642 const SCEV *S = Ops[i]; 643 unsigned Complexity = S->getSCEVType(); 644 645 // If there are any objects of the same complexity and same value as this 646 // one, group them. 647 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 648 if (Ops[j] == S) { // Found a duplicate. 649 // Move it to immediately after i'th element. 650 std::swap(Ops[i+1], Ops[j]); 651 ++i; // no need to rescan it. 652 if (i == e-2) return; // Done! 653 } 654 } 655 } 656} 657 658 659 660//===----------------------------------------------------------------------===// 661// Simple SCEV method implementations 662//===----------------------------------------------------------------------===// 663 664/// BinomialCoefficient - Compute BC(It, K). The result has width W. 665/// Assume, K > 0. 666static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 667 ScalarEvolution &SE, 668 const Type* ResultTy) { 669 // Handle the simplest case efficiently. 670 if (K == 1) 671 return SE.getTruncateOrZeroExtend(It, ResultTy); 672 673 // We are using the following formula for BC(It, K): 674 // 675 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 676 // 677 // Suppose, W is the bitwidth of the return value. We must be prepared for 678 // overflow. Hence, we must assure that the result of our computation is 679 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 680 // safe in modular arithmetic. 681 // 682 // However, this code doesn't use exactly that formula; the formula it uses 683 // is something like the following, where T is the number of factors of 2 in 684 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 685 // exponentiation: 686 // 687 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 688 // 689 // This formula is trivially equivalent to the previous formula. However, 690 // this formula can be implemented much more efficiently. The trick is that 691 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 692 // arithmetic. To do exact division in modular arithmetic, all we have 693 // to do is multiply by the inverse. Therefore, this step can be done at 694 // width W. 695 // 696 // The next issue is how to safely do the division by 2^T. The way this 697 // is done is by doing the multiplication step at a width of at least W + T 698 // bits. This way, the bottom W+T bits of the product are accurate. Then, 699 // when we perform the division by 2^T (which is equivalent to a right shift 700 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 701 // truncated out after the division by 2^T. 702 // 703 // In comparison to just directly using the first formula, this technique 704 // is much more efficient; using the first formula requires W * K bits, 705 // but this formula less than W + K bits. Also, the first formula requires 706 // a division step, whereas this formula only requires multiplies and shifts. 707 // 708 // It doesn't matter whether the subtraction step is done in the calculation 709 // width or the input iteration count's width; if the subtraction overflows, 710 // the result must be zero anyway. We prefer here to do it in the width of 711 // the induction variable because it helps a lot for certain cases; CodeGen 712 // isn't smart enough to ignore the overflow, which leads to much less 713 // efficient code if the width of the subtraction is wider than the native 714 // register width. 715 // 716 // (It's possible to not widen at all by pulling out factors of 2 before 717 // the multiplication; for example, K=2 can be calculated as 718 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 719 // extra arithmetic, so it's not an obvious win, and it gets 720 // much more complicated for K > 3.) 721 722 // Protection from insane SCEVs; this bound is conservative, 723 // but it probably doesn't matter. 724 if (K > 1000) 725 return SE.getCouldNotCompute(); 726 727 unsigned W = SE.getTypeSizeInBits(ResultTy); 728 729 // Calculate K! / 2^T and T; we divide out the factors of two before 730 // multiplying for calculating K! / 2^T to avoid overflow. 731 // Other overflow doesn't matter because we only care about the bottom 732 // W bits of the result. 733 APInt OddFactorial(W, 1); 734 unsigned T = 1; 735 for (unsigned i = 3; i <= K; ++i) { 736 APInt Mult(W, i); 737 unsigned TwoFactors = Mult.countTrailingZeros(); 738 T += TwoFactors; 739 Mult = Mult.lshr(TwoFactors); 740 OddFactorial *= Mult; 741 } 742 743 // We need at least W + T bits for the multiplication step 744 unsigned CalculationBits = W + T; 745 746 // Calculate 2^T, at width T+W. 747 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 748 749 // Calculate the multiplicative inverse of K! / 2^T; 750 // this multiplication factor will perform the exact division by 751 // K! / 2^T. 752 APInt Mod = APInt::getSignedMinValue(W+1); 753 APInt MultiplyFactor = OddFactorial.zext(W+1); 754 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 755 MultiplyFactor = MultiplyFactor.trunc(W); 756 757 // Calculate the product, at width T+W 758 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 759 CalculationBits); 760 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 761 for (unsigned i = 1; i != K; ++i) { 762 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 763 Dividend = SE.getMulExpr(Dividend, 764 SE.getTruncateOrZeroExtend(S, CalculationTy)); 765 } 766 767 // Divide by 2^T 768 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 769 770 // Truncate the result, and divide by K! / 2^T. 771 772 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 773 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 774} 775 776/// evaluateAtIteration - Return the value of this chain of recurrences at 777/// the specified iteration number. We can evaluate this recurrence by 778/// multiplying each element in the chain by the binomial coefficient 779/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 780/// 781/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 782/// 783/// where BC(It, k) stands for binomial coefficient. 784/// 785const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 786 ScalarEvolution &SE) const { 787 const SCEV *Result = getStart(); 788 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 789 // The computation is correct in the face of overflow provided that the 790 // multiplication is performed _after_ the evaluation of the binomial 791 // coefficient. 792 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 793 if (isa<SCEVCouldNotCompute>(Coeff)) 794 return Coeff; 795 796 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 797 } 798 return Result; 799} 800 801//===----------------------------------------------------------------------===// 802// SCEV Expression folder implementations 803//===----------------------------------------------------------------------===// 804 805const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 806 const Type *Ty) { 807 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 808 "This is not a truncating conversion!"); 809 assert(isSCEVable(Ty) && 810 "This is not a conversion to a SCEVable type!"); 811 Ty = getEffectiveSCEVType(Ty); 812 813 FoldingSetNodeID ID; 814 ID.AddInteger(scTruncate); 815 ID.AddPointer(Op); 816 ID.AddPointer(Ty); 817 void *IP = 0; 818 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 819 820 // Fold if the operand is constant. 821 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 822 return getConstant( 823 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 824 825 // trunc(trunc(x)) --> trunc(x) 826 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 827 return getTruncateExpr(ST->getOperand(), Ty); 828 829 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 830 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 831 return getTruncateOrSignExtend(SS->getOperand(), Ty); 832 833 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 834 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 835 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 836 837 // If the input value is a chrec scev, truncate the chrec's operands. 838 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 839 SmallVector<const SCEV *, 4> Operands; 840 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 841 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 842 return getAddRecExpr(Operands, AddRec->getLoop()); 843 } 844 845 // The cast wasn't folded; create an explicit cast node. 846 // Recompute the insert position, as it may have been invalidated. 847 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 848 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 849 Op, Ty); 850 UniqueSCEVs.InsertNode(S, IP); 851 return S; 852} 853 854const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 855 const Type *Ty) { 856 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 857 "This is not an extending conversion!"); 858 assert(isSCEVable(Ty) && 859 "This is not a conversion to a SCEVable type!"); 860 Ty = getEffectiveSCEVType(Ty); 861 862 // Fold if the operand is constant. 863 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 864 const Type *IntTy = getEffectiveSCEVType(Ty); 865 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 866 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 867 return getConstant(cast<ConstantInt>(C)); 868 } 869 870 // zext(zext(x)) --> zext(x) 871 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 872 return getZeroExtendExpr(SZ->getOperand(), Ty); 873 874 // Before doing any expensive analysis, check to see if we've already 875 // computed a SCEV for this Op and Ty. 876 FoldingSetNodeID ID; 877 ID.AddInteger(scZeroExtend); 878 ID.AddPointer(Op); 879 ID.AddPointer(Ty); 880 void *IP = 0; 881 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 882 883 // If the input value is a chrec scev, and we can prove that the value 884 // did not overflow the old, smaller, value, we can zero extend all of the 885 // operands (often constants). This allows analysis of something like 886 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 887 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 888 if (AR->isAffine()) { 889 const SCEV *Start = AR->getStart(); 890 const SCEV *Step = AR->getStepRecurrence(*this); 891 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 892 const Loop *L = AR->getLoop(); 893 894 // If we have special knowledge that this addrec won't overflow, 895 // we don't need to do any further analysis. 896 if (AR->hasNoUnsignedWrap()) 897 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 898 getZeroExtendExpr(Step, Ty), 899 L); 900 901 // Check whether the backedge-taken count is SCEVCouldNotCompute. 902 // Note that this serves two purposes: It filters out loops that are 903 // simply not analyzable, and it covers the case where this code is 904 // being called from within backedge-taken count analysis, such that 905 // attempting to ask for the backedge-taken count would likely result 906 // in infinite recursion. In the later case, the analysis code will 907 // cope with a conservative value, and it will take care to purge 908 // that value once it has finished. 909 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 910 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 911 // Manually compute the final value for AR, checking for 912 // overflow. 913 914 // Check whether the backedge-taken count can be losslessly casted to 915 // the addrec's type. The count is always unsigned. 916 const SCEV *CastedMaxBECount = 917 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 918 const SCEV *RecastedMaxBECount = 919 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 920 if (MaxBECount == RecastedMaxBECount) { 921 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 922 // Check whether Start+Step*MaxBECount has no unsigned overflow. 923 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 924 const SCEV *Add = getAddExpr(Start, ZMul); 925 const SCEV *OperandExtendedAdd = 926 getAddExpr(getZeroExtendExpr(Start, WideTy), 927 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 928 getZeroExtendExpr(Step, WideTy))); 929 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 930 // Return the expression with the addrec on the outside. 931 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 932 getZeroExtendExpr(Step, Ty), 933 L); 934 935 // Similar to above, only this time treat the step value as signed. 936 // This covers loops that count down. 937 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 938 Add = getAddExpr(Start, SMul); 939 OperandExtendedAdd = 940 getAddExpr(getZeroExtendExpr(Start, WideTy), 941 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 942 getSignExtendExpr(Step, WideTy))); 943 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 944 // Return the expression with the addrec on the outside. 945 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 946 getSignExtendExpr(Step, Ty), 947 L); 948 } 949 950 // If the backedge is guarded by a comparison with the pre-inc value 951 // the addrec is safe. Also, if the entry is guarded by a comparison 952 // with the start value and the backedge is guarded by a comparison 953 // with the post-inc value, the addrec is safe. 954 if (isKnownPositive(Step)) { 955 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 956 getUnsignedRange(Step).getUnsignedMax()); 957 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 958 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 959 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 960 AR->getPostIncExpr(*this), N))) 961 // Return the expression with the addrec on the outside. 962 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 963 getZeroExtendExpr(Step, Ty), 964 L); 965 } else if (isKnownNegative(Step)) { 966 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 967 getSignedRange(Step).getSignedMin()); 968 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 969 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 970 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 971 AR->getPostIncExpr(*this), N))) 972 // Return the expression with the addrec on the outside. 973 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 974 getSignExtendExpr(Step, Ty), 975 L); 976 } 977 } 978 } 979 980 // The cast wasn't folded; create an explicit cast node. 981 // Recompute the insert position, as it may have been invalidated. 982 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 983 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 984 Op, Ty); 985 UniqueSCEVs.InsertNode(S, IP); 986 return S; 987} 988 989const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 990 const Type *Ty) { 991 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 992 "This is not an extending conversion!"); 993 assert(isSCEVable(Ty) && 994 "This is not a conversion to a SCEVable type!"); 995 Ty = getEffectiveSCEVType(Ty); 996 997 // Fold if the operand is constant. 998 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 999 const Type *IntTy = getEffectiveSCEVType(Ty); 1000 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 1001 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 1002 return getConstant(cast<ConstantInt>(C)); 1003 } 1004 1005 // sext(sext(x)) --> sext(x) 1006 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1007 return getSignExtendExpr(SS->getOperand(), Ty); 1008 1009 // Before doing any expensive analysis, check to see if we've already 1010 // computed a SCEV for this Op and Ty. 1011 FoldingSetNodeID ID; 1012 ID.AddInteger(scSignExtend); 1013 ID.AddPointer(Op); 1014 ID.AddPointer(Ty); 1015 void *IP = 0; 1016 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1017 1018 // If the input value is a chrec scev, and we can prove that the value 1019 // did not overflow the old, smaller, value, we can sign extend all of the 1020 // operands (often constants). This allows analysis of something like 1021 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1022 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1023 if (AR->isAffine()) { 1024 const SCEV *Start = AR->getStart(); 1025 const SCEV *Step = AR->getStepRecurrence(*this); 1026 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1027 const Loop *L = AR->getLoop(); 1028 1029 // If we have special knowledge that this addrec won't overflow, 1030 // we don't need to do any further analysis. 1031 if (AR->hasNoSignedWrap()) 1032 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1033 getSignExtendExpr(Step, Ty), 1034 L); 1035 1036 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1037 // Note that this serves two purposes: It filters out loops that are 1038 // simply not analyzable, and it covers the case where this code is 1039 // being called from within backedge-taken count analysis, such that 1040 // attempting to ask for the backedge-taken count would likely result 1041 // in infinite recursion. In the later case, the analysis code will 1042 // cope with a conservative value, and it will take care to purge 1043 // that value once it has finished. 1044 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1045 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1046 // Manually compute the final value for AR, checking for 1047 // overflow. 1048 1049 // Check whether the backedge-taken count can be losslessly casted to 1050 // the addrec's type. The count is always unsigned. 1051 const SCEV *CastedMaxBECount = 1052 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1053 const SCEV *RecastedMaxBECount = 1054 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1055 if (MaxBECount == RecastedMaxBECount) { 1056 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1057 // Check whether Start+Step*MaxBECount has no signed overflow. 1058 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1059 const SCEV *Add = getAddExpr(Start, SMul); 1060 const SCEV *OperandExtendedAdd = 1061 getAddExpr(getSignExtendExpr(Start, WideTy), 1062 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1063 getSignExtendExpr(Step, WideTy))); 1064 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1065 // Return the expression with the addrec on the outside. 1066 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1067 getSignExtendExpr(Step, Ty), 1068 L); 1069 1070 // Similar to above, only this time treat the step value as unsigned. 1071 // This covers loops that count up with an unsigned step. 1072 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1073 Add = getAddExpr(Start, UMul); 1074 OperandExtendedAdd = 1075 getAddExpr(getSignExtendExpr(Start, WideTy), 1076 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1077 getZeroExtendExpr(Step, WideTy))); 1078 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1079 // Return the expression with the addrec on the outside. 1080 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1081 getZeroExtendExpr(Step, Ty), 1082 L); 1083 } 1084 1085 // If the backedge is guarded by a comparison with the pre-inc value 1086 // the addrec is safe. Also, if the entry is guarded by a comparison 1087 // with the start value and the backedge is guarded by a comparison 1088 // with the post-inc value, the addrec is safe. 1089 if (isKnownPositive(Step)) { 1090 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1091 getSignedRange(Step).getSignedMax()); 1092 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1093 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1094 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1095 AR->getPostIncExpr(*this), N))) 1096 // Return the expression with the addrec on the outside. 1097 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1098 getSignExtendExpr(Step, Ty), 1099 L); 1100 } else if (isKnownNegative(Step)) { 1101 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1102 getSignedRange(Step).getSignedMin()); 1103 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1104 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1105 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1106 AR->getPostIncExpr(*this), N))) 1107 // Return the expression with the addrec on the outside. 1108 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1109 getSignExtendExpr(Step, Ty), 1110 L); 1111 } 1112 } 1113 } 1114 1115 // The cast wasn't folded; create an explicit cast node. 1116 // Recompute the insert position, as it may have been invalidated. 1117 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1118 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1119 Op, Ty); 1120 UniqueSCEVs.InsertNode(S, IP); 1121 return S; 1122} 1123 1124/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1125/// unspecified bits out to the given type. 1126/// 1127const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1128 const Type *Ty) { 1129 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1130 "This is not an extending conversion!"); 1131 assert(isSCEVable(Ty) && 1132 "This is not a conversion to a SCEVable type!"); 1133 Ty = getEffectiveSCEVType(Ty); 1134 1135 // Sign-extend negative constants. 1136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1137 if (SC->getValue()->getValue().isNegative()) 1138 return getSignExtendExpr(Op, Ty); 1139 1140 // Peel off a truncate cast. 1141 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1142 const SCEV *NewOp = T->getOperand(); 1143 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1144 return getAnyExtendExpr(NewOp, Ty); 1145 return getTruncateOrNoop(NewOp, Ty); 1146 } 1147 1148 // Next try a zext cast. If the cast is folded, use it. 1149 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1150 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1151 return ZExt; 1152 1153 // Next try a sext cast. If the cast is folded, use it. 1154 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1155 if (!isa<SCEVSignExtendExpr>(SExt)) 1156 return SExt; 1157 1158 // Force the cast to be folded into the operands of an addrec. 1159 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1160 SmallVector<const SCEV *, 4> Ops; 1161 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1162 I != E; ++I) 1163 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1164 return getAddRecExpr(Ops, AR->getLoop()); 1165 } 1166 1167 // If the expression is obviously signed, use the sext cast value. 1168 if (isa<SCEVSMaxExpr>(Op)) 1169 return SExt; 1170 1171 // Absent any other information, use the zext cast value. 1172 return ZExt; 1173} 1174 1175/// CollectAddOperandsWithScales - Process the given Ops list, which is 1176/// a list of operands to be added under the given scale, update the given 1177/// map. This is a helper function for getAddRecExpr. As an example of 1178/// what it does, given a sequence of operands that would form an add 1179/// expression like this: 1180/// 1181/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1182/// 1183/// where A and B are constants, update the map with these values: 1184/// 1185/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1186/// 1187/// and add 13 + A*B*29 to AccumulatedConstant. 1188/// This will allow getAddRecExpr to produce this: 1189/// 1190/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1191/// 1192/// This form often exposes folding opportunities that are hidden in 1193/// the original operand list. 1194/// 1195/// Return true iff it appears that any interesting folding opportunities 1196/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1197/// the common case where no interesting opportunities are present, and 1198/// is also used as a check to avoid infinite recursion. 1199/// 1200static bool 1201CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1202 SmallVector<const SCEV *, 8> &NewOps, 1203 APInt &AccumulatedConstant, 1204 const SCEV *const *Ops, size_t NumOperands, 1205 const APInt &Scale, 1206 ScalarEvolution &SE) { 1207 bool Interesting = false; 1208 1209 // Iterate over the add operands. 1210 for (unsigned i = 0, e = NumOperands; i != e; ++i) { 1211 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1212 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1213 APInt NewScale = 1214 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1215 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1216 // A multiplication of a constant with another add; recurse. 1217 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1218 Interesting |= 1219 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1220 Add->op_begin(), Add->getNumOperands(), 1221 NewScale, SE); 1222 } else { 1223 // A multiplication of a constant with some other value. Update 1224 // the map. 1225 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1226 const SCEV *Key = SE.getMulExpr(MulOps); 1227 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1228 M.insert(std::make_pair(Key, NewScale)); 1229 if (Pair.second) { 1230 NewOps.push_back(Pair.first->first); 1231 } else { 1232 Pair.first->second += NewScale; 1233 // The map already had an entry for this value, which may indicate 1234 // a folding opportunity. 1235 Interesting = true; 1236 } 1237 } 1238 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1239 // Pull a buried constant out to the outside. 1240 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1241 Interesting = true; 1242 AccumulatedConstant += Scale * C->getValue()->getValue(); 1243 } else { 1244 // An ordinary operand. Update the map. 1245 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1246 M.insert(std::make_pair(Ops[i], Scale)); 1247 if (Pair.second) { 1248 NewOps.push_back(Pair.first->first); 1249 } else { 1250 Pair.first->second += Scale; 1251 // The map already had an entry for this value, which may indicate 1252 // a folding opportunity. 1253 Interesting = true; 1254 } 1255 } 1256 } 1257 1258 return Interesting; 1259} 1260 1261namespace { 1262 struct APIntCompare { 1263 bool operator()(const APInt &LHS, const APInt &RHS) const { 1264 return LHS.ult(RHS); 1265 } 1266 }; 1267} 1268 1269/// getAddExpr - Get a canonical add expression, or something simpler if 1270/// possible. 1271const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1272 bool HasNUW, bool HasNSW) { 1273 assert(!Ops.empty() && "Cannot get empty add!"); 1274 if (Ops.size() == 1) return Ops[0]; 1275#ifndef NDEBUG 1276 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1277 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1278 getEffectiveSCEVType(Ops[0]->getType()) && 1279 "SCEVAddExpr operand types don't match!"); 1280#endif 1281 1282 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1283 if (!HasNUW && HasNSW) { 1284 bool All = true; 1285 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1286 if (!isKnownNonNegative(Ops[i])) { 1287 All = false; 1288 break; 1289 } 1290 if (All) HasNUW = true; 1291 } 1292 1293 // Sort by complexity, this groups all similar expression types together. 1294 GroupByComplexity(Ops, LI); 1295 1296 // If there are any constants, fold them together. 1297 unsigned Idx = 0; 1298 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1299 ++Idx; 1300 assert(Idx < Ops.size()); 1301 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1302 // We found two constants, fold them together! 1303 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1304 RHSC->getValue()->getValue()); 1305 if (Ops.size() == 2) return Ops[0]; 1306 Ops.erase(Ops.begin()+1); // Erase the folded element 1307 LHSC = cast<SCEVConstant>(Ops[0]); 1308 } 1309 1310 // If we are left with a constant zero being added, strip it off. 1311 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1312 Ops.erase(Ops.begin()); 1313 --Idx; 1314 } 1315 } 1316 1317 if (Ops.size() == 1) return Ops[0]; 1318 1319 // Okay, check to see if the same value occurs in the operand list twice. If 1320 // so, merge them together into an multiply expression. Since we sorted the 1321 // list, these values are required to be adjacent. 1322 const Type *Ty = Ops[0]->getType(); 1323 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1324 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1325 // Found a match, merge the two values into a multiply, and add any 1326 // remaining values to the result. 1327 const SCEV *Two = getIntegerSCEV(2, Ty); 1328 const SCEV *Mul = getMulExpr(Ops[i], Two); 1329 if (Ops.size() == 2) 1330 return Mul; 1331 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1332 Ops.push_back(Mul); 1333 return getAddExpr(Ops, HasNUW, HasNSW); 1334 } 1335 1336 // Check for truncates. If all the operands are truncated from the same 1337 // type, see if factoring out the truncate would permit the result to be 1338 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1339 // if the contents of the resulting outer trunc fold to something simple. 1340 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1341 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1342 const Type *DstType = Trunc->getType(); 1343 const Type *SrcType = Trunc->getOperand()->getType(); 1344 SmallVector<const SCEV *, 8> LargeOps; 1345 bool Ok = true; 1346 // Check all the operands to see if they can be represented in the 1347 // source type of the truncate. 1348 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1349 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1350 if (T->getOperand()->getType() != SrcType) { 1351 Ok = false; 1352 break; 1353 } 1354 LargeOps.push_back(T->getOperand()); 1355 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1356 // This could be either sign or zero extension, but sign extension 1357 // is much more likely to be foldable here. 1358 LargeOps.push_back(getSignExtendExpr(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 // This could be either sign or zero extension, but sign extension 1372 // is much more likely to be foldable here. 1373 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1374 } else { 1375 Ok = false; 1376 break; 1377 } 1378 } 1379 if (Ok) 1380 LargeOps.push_back(getMulExpr(LargeMulOps)); 1381 } else { 1382 Ok = false; 1383 break; 1384 } 1385 } 1386 if (Ok) { 1387 // Evaluate the expression in the larger type. 1388 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1389 // If it folds to something simple, use it. Otherwise, don't. 1390 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1391 return getTruncateExpr(Fold, DstType); 1392 } 1393 } 1394 1395 // Skip past any other cast SCEVs. 1396 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1397 ++Idx; 1398 1399 // If there are add operands they would be next. 1400 if (Idx < Ops.size()) { 1401 bool DeletedAdd = false; 1402 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1403 // If we have an add, expand the add operands onto the end of the operands 1404 // list. 1405 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1406 Ops.erase(Ops.begin()+Idx); 1407 DeletedAdd = true; 1408 } 1409 1410 // If we deleted at least one add, we added operands to the end of the list, 1411 // and they are not necessarily sorted. Recurse to resort and resimplify 1412 // any operands we just acquired. 1413 if (DeletedAdd) 1414 return getAddExpr(Ops); 1415 } 1416 1417 // Skip over the add expression until we get to a multiply. 1418 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1419 ++Idx; 1420 1421 // Check to see if there are any folding opportunities present with 1422 // operands multiplied by constant values. 1423 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1424 uint64_t BitWidth = getTypeSizeInBits(Ty); 1425 DenseMap<const SCEV *, APInt> M; 1426 SmallVector<const SCEV *, 8> NewOps; 1427 APInt AccumulatedConstant(BitWidth, 0); 1428 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1429 Ops.data(), Ops.size(), 1430 APInt(BitWidth, 1), *this)) { 1431 // Some interesting folding opportunity is present, so its worthwhile to 1432 // re-generate the operands list. Group the operands by constant scale, 1433 // to avoid multiplying by the same constant scale multiple times. 1434 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1435 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), 1436 E = NewOps.end(); I != E; ++I) 1437 MulOpLists[M.find(*I)->second].push_back(*I); 1438 // Re-generate the operands list. 1439 Ops.clear(); 1440 if (AccumulatedConstant != 0) 1441 Ops.push_back(getConstant(AccumulatedConstant)); 1442 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1443 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1444 if (I->first != 0) 1445 Ops.push_back(getMulExpr(getConstant(I->first), 1446 getAddExpr(I->second))); 1447 if (Ops.empty()) 1448 return getIntegerSCEV(0, Ty); 1449 if (Ops.size() == 1) 1450 return Ops[0]; 1451 return getAddExpr(Ops); 1452 } 1453 } 1454 1455 // If we are adding something to a multiply expression, make sure the 1456 // something is not already an operand of the multiply. If so, merge it into 1457 // the multiply. 1458 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1459 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1460 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1461 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1462 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1463 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { 1464 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1465 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1466 if (Mul->getNumOperands() != 2) { 1467 // If the multiply has more than two operands, we must get the 1468 // Y*Z term. 1469 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); 1470 MulOps.erase(MulOps.begin()+MulOp); 1471 InnerMul = getMulExpr(MulOps); 1472 } 1473 const SCEV *One = getIntegerSCEV(1, Ty); 1474 const SCEV *AddOne = getAddExpr(InnerMul, One); 1475 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); 1476 if (Ops.size() == 2) return OuterMul; 1477 if (AddOp < Idx) { 1478 Ops.erase(Ops.begin()+AddOp); 1479 Ops.erase(Ops.begin()+Idx-1); 1480 } else { 1481 Ops.erase(Ops.begin()+Idx); 1482 Ops.erase(Ops.begin()+AddOp-1); 1483 } 1484 Ops.push_back(OuterMul); 1485 return getAddExpr(Ops); 1486 } 1487 1488 // Check this multiply against other multiplies being added together. 1489 for (unsigned OtherMulIdx = Idx+1; 1490 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1491 ++OtherMulIdx) { 1492 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1493 // If MulOp occurs in OtherMul, we can fold the two multiplies 1494 // together. 1495 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1496 OMulOp != e; ++OMulOp) 1497 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1498 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1499 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1500 if (Mul->getNumOperands() != 2) { 1501 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1502 Mul->op_end()); 1503 MulOps.erase(MulOps.begin()+MulOp); 1504 InnerMul1 = getMulExpr(MulOps); 1505 } 1506 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1507 if (OtherMul->getNumOperands() != 2) { 1508 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1509 OtherMul->op_end()); 1510 MulOps.erase(MulOps.begin()+OMulOp); 1511 InnerMul2 = getMulExpr(MulOps); 1512 } 1513 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1514 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1515 if (Ops.size() == 2) return OuterMul; 1516 Ops.erase(Ops.begin()+Idx); 1517 Ops.erase(Ops.begin()+OtherMulIdx-1); 1518 Ops.push_back(OuterMul); 1519 return getAddExpr(Ops); 1520 } 1521 } 1522 } 1523 } 1524 1525 // If there are any add recurrences in the operands list, see if any other 1526 // added values are loop invariant. If so, we can fold them into the 1527 // recurrence. 1528 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1529 ++Idx; 1530 1531 // Scan over all recurrences, trying to fold loop invariants into them. 1532 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1533 // Scan all of the other operands to this add and add them to the vector if 1534 // they are loop invariant w.r.t. the recurrence. 1535 SmallVector<const SCEV *, 8> LIOps; 1536 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1537 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1538 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1539 LIOps.push_back(Ops[i]); 1540 Ops.erase(Ops.begin()+i); 1541 --i; --e; 1542 } 1543 1544 // If we found some loop invariants, fold them into the recurrence. 1545 if (!LIOps.empty()) { 1546 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1547 LIOps.push_back(AddRec->getStart()); 1548 1549 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1550 AddRec->op_end()); 1551 AddRecOps[0] = getAddExpr(LIOps); 1552 1553 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition 1554 // is not associative so this isn't necessarily safe. 1555 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop()); 1556 1557 // If all of the other operands were loop invariant, we are done. 1558 if (Ops.size() == 1) return NewRec; 1559 1560 // Otherwise, add the folded AddRec by the non-liv parts. 1561 for (unsigned i = 0;; ++i) 1562 if (Ops[i] == AddRec) { 1563 Ops[i] = NewRec; 1564 break; 1565 } 1566 return getAddExpr(Ops); 1567 } 1568 1569 // Okay, if there weren't any loop invariants to be folded, check to see if 1570 // there are multiple AddRec's with the same loop induction variable being 1571 // added together. If so, we can fold them. 1572 for (unsigned OtherIdx = Idx+1; 1573 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1574 if (OtherIdx != Idx) { 1575 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1576 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1577 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1578 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1579 AddRec->op_end()); 1580 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1581 if (i >= NewOps.size()) { 1582 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, 1583 OtherAddRec->op_end()); 1584 break; 1585 } 1586 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1587 } 1588 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop()); 1589 1590 if (Ops.size() == 2) return NewAddRec; 1591 1592 Ops.erase(Ops.begin()+Idx); 1593 Ops.erase(Ops.begin()+OtherIdx-1); 1594 Ops.push_back(NewAddRec); 1595 return getAddExpr(Ops); 1596 } 1597 } 1598 1599 // Otherwise couldn't fold anything into this recurrence. Move onto the 1600 // next one. 1601 } 1602 1603 // Okay, it looks like we really DO need an add expr. Check to see if we 1604 // already have one, otherwise create a new one. 1605 FoldingSetNodeID ID; 1606 ID.AddInteger(scAddExpr); 1607 ID.AddInteger(Ops.size()); 1608 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1609 ID.AddPointer(Ops[i]); 1610 void *IP = 0; 1611 SCEVAddExpr *S = 1612 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1613 if (!S) { 1614 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1615 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1616 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1617 O, Ops.size()); 1618 UniqueSCEVs.InsertNode(S, IP); 1619 } 1620 if (HasNUW) S->setHasNoUnsignedWrap(true); 1621 if (HasNSW) S->setHasNoSignedWrap(true); 1622 return S; 1623} 1624 1625/// getMulExpr - Get a canonical multiply expression, or something simpler if 1626/// possible. 1627const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1628 bool HasNUW, bool HasNSW) { 1629 assert(!Ops.empty() && "Cannot get empty mul!"); 1630 if (Ops.size() == 1) return Ops[0]; 1631#ifndef NDEBUG 1632 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1633 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1634 getEffectiveSCEVType(Ops[0]->getType()) && 1635 "SCEVMulExpr operand types don't match!"); 1636#endif 1637 1638 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1639 if (!HasNUW && HasNSW) { 1640 bool All = true; 1641 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1642 if (!isKnownNonNegative(Ops[i])) { 1643 All = false; 1644 break; 1645 } 1646 if (All) HasNUW = true; 1647 } 1648 1649 // Sort by complexity, this groups all similar expression types together. 1650 GroupByComplexity(Ops, LI); 1651 1652 // If there are any constants, fold them together. 1653 unsigned Idx = 0; 1654 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1655 1656 // C1*(C2+V) -> C1*C2 + C1*V 1657 if (Ops.size() == 2) 1658 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1659 if (Add->getNumOperands() == 2 && 1660 isa<SCEVConstant>(Add->getOperand(0))) 1661 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1662 getMulExpr(LHSC, Add->getOperand(1))); 1663 1664 ++Idx; 1665 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1666 // We found two constants, fold them together! 1667 ConstantInt *Fold = ConstantInt::get(getContext(), 1668 LHSC->getValue()->getValue() * 1669 RHSC->getValue()->getValue()); 1670 Ops[0] = getConstant(Fold); 1671 Ops.erase(Ops.begin()+1); // Erase the folded element 1672 if (Ops.size() == 1) return Ops[0]; 1673 LHSC = cast<SCEVConstant>(Ops[0]); 1674 } 1675 1676 // If we are left with a constant one being multiplied, strip it off. 1677 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1678 Ops.erase(Ops.begin()); 1679 --Idx; 1680 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1681 // If we have a multiply of zero, it will always be zero. 1682 return Ops[0]; 1683 } else if (Ops[0]->isAllOnesValue()) { 1684 // If we have a mul by -1 of an add, try distributing the -1 among the 1685 // add operands. 1686 if (Ops.size() == 2) 1687 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1688 SmallVector<const SCEV *, 4> NewOps; 1689 bool AnyFolded = false; 1690 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1691 I != E; ++I) { 1692 const SCEV *Mul = getMulExpr(Ops[0], *I); 1693 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1694 NewOps.push_back(Mul); 1695 } 1696 if (AnyFolded) 1697 return getAddExpr(NewOps); 1698 } 1699 } 1700 } 1701 1702 // Skip over the add expression until we get to a multiply. 1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1704 ++Idx; 1705 1706 if (Ops.size() == 1) 1707 return Ops[0]; 1708 1709 // If there are mul operands inline them all into this expression. 1710 if (Idx < Ops.size()) { 1711 bool DeletedMul = false; 1712 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1713 // If we have an mul, expand the mul operands onto the end of the operands 1714 // list. 1715 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1716 Ops.erase(Ops.begin()+Idx); 1717 DeletedMul = true; 1718 } 1719 1720 // If we deleted at least one mul, we added operands to the end of the list, 1721 // and they are not necessarily sorted. Recurse to resort and resimplify 1722 // any operands we just acquired. 1723 if (DeletedMul) 1724 return getMulExpr(Ops); 1725 } 1726 1727 // If there are any add recurrences in the operands list, see if any other 1728 // added values are loop invariant. If so, we can fold them into the 1729 // recurrence. 1730 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1731 ++Idx; 1732 1733 // Scan over all recurrences, trying to fold loop invariants into them. 1734 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1735 // Scan all of the other operands to this mul and add them to the vector if 1736 // they are loop invariant w.r.t. the recurrence. 1737 SmallVector<const SCEV *, 8> LIOps; 1738 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1739 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1740 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1741 LIOps.push_back(Ops[i]); 1742 Ops.erase(Ops.begin()+i); 1743 --i; --e; 1744 } 1745 1746 // If we found some loop invariants, fold them into the recurrence. 1747 if (!LIOps.empty()) { 1748 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1749 SmallVector<const SCEV *, 4> NewOps; 1750 NewOps.reserve(AddRec->getNumOperands()); 1751 if (LIOps.size() == 1) { 1752 const SCEV *Scale = LIOps[0]; 1753 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1754 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1755 } else { 1756 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1757 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1758 MulOps.push_back(AddRec->getOperand(i)); 1759 NewOps.push_back(getMulExpr(MulOps)); 1760 } 1761 } 1762 1763 // It's tempting to propagate the NSW flag here, but nsw multiplication 1764 // is not associative so this isn't necessarily safe. 1765 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1766 HasNUW && AddRec->hasNoUnsignedWrap(), 1767 /*HasNSW=*/false); 1768 1769 // If all of the other operands were loop invariant, we are done. 1770 if (Ops.size() == 1) return NewRec; 1771 1772 // Otherwise, multiply the folded AddRec by the non-liv parts. 1773 for (unsigned i = 0;; ++i) 1774 if (Ops[i] == AddRec) { 1775 Ops[i] = NewRec; 1776 break; 1777 } 1778 return getMulExpr(Ops); 1779 } 1780 1781 // Okay, if there weren't any loop invariants to be folded, check to see if 1782 // there are multiple AddRec's with the same loop induction variable being 1783 // multiplied together. If so, we can fold them. 1784 for (unsigned OtherIdx = Idx+1; 1785 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1786 if (OtherIdx != Idx) { 1787 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1788 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1789 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1790 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1791 const SCEV *NewStart = getMulExpr(F->getStart(), 1792 G->getStart()); 1793 const SCEV *B = F->getStepRecurrence(*this); 1794 const SCEV *D = G->getStepRecurrence(*this); 1795 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1796 getMulExpr(G, B), 1797 getMulExpr(B, D)); 1798 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1799 F->getLoop()); 1800 if (Ops.size() == 2) return NewAddRec; 1801 1802 Ops.erase(Ops.begin()+Idx); 1803 Ops.erase(Ops.begin()+OtherIdx-1); 1804 Ops.push_back(NewAddRec); 1805 return getMulExpr(Ops); 1806 } 1807 } 1808 1809 // Otherwise couldn't fold anything into this recurrence. Move onto the 1810 // next one. 1811 } 1812 1813 // Okay, it looks like we really DO need an mul expr. Check to see if we 1814 // already have one, otherwise create a new one. 1815 FoldingSetNodeID ID; 1816 ID.AddInteger(scMulExpr); 1817 ID.AddInteger(Ops.size()); 1818 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1819 ID.AddPointer(Ops[i]); 1820 void *IP = 0; 1821 SCEVMulExpr *S = 1822 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1823 if (!S) { 1824 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1825 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1826 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1827 O, Ops.size()); 1828 UniqueSCEVs.InsertNode(S, IP); 1829 } 1830 if (HasNUW) S->setHasNoUnsignedWrap(true); 1831 if (HasNSW) S->setHasNoSignedWrap(true); 1832 return S; 1833} 1834 1835/// getUDivExpr - Get a canonical unsigned division expression, or something 1836/// simpler if possible. 1837const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1838 const SCEV *RHS) { 1839 assert(getEffectiveSCEVType(LHS->getType()) == 1840 getEffectiveSCEVType(RHS->getType()) && 1841 "SCEVUDivExpr operand types don't match!"); 1842 1843 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1844 if (RHSC->getValue()->equalsInt(1)) 1845 return LHS; // X udiv 1 --> x 1846 if (RHSC->isZero()) 1847 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1848 1849 // Determine if the division can be folded into the operands of 1850 // its operands. 1851 // TODO: Generalize this to non-constants by using known-bits information. 1852 const Type *Ty = LHS->getType(); 1853 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1854 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1855 // For non-power-of-two values, effectively round the value up to the 1856 // nearest power of two. 1857 if (!RHSC->getValue()->getValue().isPowerOf2()) 1858 ++MaxShiftAmt; 1859 const IntegerType *ExtTy = 1860 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1861 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1862 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1863 if (const SCEVConstant *Step = 1864 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1865 if (!Step->getValue()->getValue() 1866 .urem(RHSC->getValue()->getValue()) && 1867 getZeroExtendExpr(AR, ExtTy) == 1868 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1869 getZeroExtendExpr(Step, ExtTy), 1870 AR->getLoop())) { 1871 SmallVector<const SCEV *, 4> Operands; 1872 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1873 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1874 return getAddRecExpr(Operands, AR->getLoop()); 1875 } 1876 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1877 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1878 SmallVector<const SCEV *, 4> Operands; 1879 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1880 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1881 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1882 // Find an operand that's safely divisible. 1883 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1884 const SCEV *Op = M->getOperand(i); 1885 const SCEV *Div = getUDivExpr(Op, RHSC); 1886 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1887 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), M->op_end()); 1888 Operands[i] = Div; 1889 return getMulExpr(Operands); 1890 } 1891 } 1892 } 1893 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1894 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1895 SmallVector<const SCEV *, 4> Operands; 1896 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1897 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1898 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1899 Operands.clear(); 1900 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1901 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1902 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1903 break; 1904 Operands.push_back(Op); 1905 } 1906 if (Operands.size() == A->getNumOperands()) 1907 return getAddExpr(Operands); 1908 } 1909 } 1910 1911 // Fold if both operands are constant. 1912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1913 Constant *LHSCV = LHSC->getValue(); 1914 Constant *RHSCV = RHSC->getValue(); 1915 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1916 RHSCV))); 1917 } 1918 } 1919 1920 FoldingSetNodeID ID; 1921 ID.AddInteger(scUDivExpr); 1922 ID.AddPointer(LHS); 1923 ID.AddPointer(RHS); 1924 void *IP = 0; 1925 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1926 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1927 LHS, RHS); 1928 UniqueSCEVs.InsertNode(S, IP); 1929 return S; 1930} 1931 1932 1933/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1934/// Simplify the expression as much as possible. 1935const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1936 const SCEV *Step, const Loop *L, 1937 bool HasNUW, bool HasNSW) { 1938 SmallVector<const SCEV *, 4> Operands; 1939 Operands.push_back(Start); 1940 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1941 if (StepChrec->getLoop() == L) { 1942 Operands.insert(Operands.end(), StepChrec->op_begin(), 1943 StepChrec->op_end()); 1944 return getAddRecExpr(Operands, L); 1945 } 1946 1947 Operands.push_back(Step); 1948 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1949} 1950 1951/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1952/// Simplify the expression as much as possible. 1953const SCEV * 1954ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1955 const Loop *L, 1956 bool HasNUW, bool HasNSW) { 1957 if (Operands.size() == 1) return Operands[0]; 1958#ifndef NDEBUG 1959 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1960 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1961 getEffectiveSCEVType(Operands[0]->getType()) && 1962 "SCEVAddRecExpr operand types don't match!"); 1963#endif 1964 1965 if (Operands.back()->isZero()) { 1966 Operands.pop_back(); 1967 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1968 } 1969 1970 // It's tempting to want to call getMaxBackedgeTakenCount count here and 1971 // use that information to infer NUW and NSW flags. However, computing a 1972 // BE count requires calling getAddRecExpr, so we may not yet have a 1973 // meaningful BE count at this point (and if we don't, we'd be stuck 1974 // with a SCEVCouldNotCompute as the cached BE count). 1975 1976 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1977 if (!HasNUW && HasNSW) { 1978 bool All = true; 1979 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1980 if (!isKnownNonNegative(Operands[i])) { 1981 All = false; 1982 break; 1983 } 1984 if (All) HasNUW = true; 1985 } 1986 1987 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1988 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1989 const Loop *NestedLoop = NestedAR->getLoop(); 1990 if (L->contains(NestedLoop->getHeader()) ? 1991 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1992 (!NestedLoop->contains(L->getHeader()) && 1993 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1994 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1995 NestedAR->op_end()); 1996 Operands[0] = NestedAR->getStart(); 1997 // AddRecs require their operands be loop-invariant with respect to their 1998 // loops. Don't perform this transformation if it would break this 1999 // requirement. 2000 bool AllInvariant = true; 2001 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2002 if (!Operands[i]->isLoopInvariant(L)) { 2003 AllInvariant = false; 2004 break; 2005 } 2006 if (AllInvariant) { 2007 NestedOperands[0] = getAddRecExpr(Operands, L); 2008 AllInvariant = true; 2009 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2010 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2011 AllInvariant = false; 2012 break; 2013 } 2014 if (AllInvariant) 2015 // Ok, both add recurrences are valid after the transformation. 2016 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2017 } 2018 // Reset Operands to its original state. 2019 Operands[0] = NestedAR; 2020 } 2021 } 2022 2023 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2024 // already have one, otherwise create a new one. 2025 FoldingSetNodeID ID; 2026 ID.AddInteger(scAddRecExpr); 2027 ID.AddInteger(Operands.size()); 2028 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2029 ID.AddPointer(Operands[i]); 2030 ID.AddPointer(L); 2031 void *IP = 0; 2032 SCEVAddRecExpr *S = 2033 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2034 if (!S) { 2035 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2036 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2037 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2038 O, Operands.size(), L); 2039 UniqueSCEVs.InsertNode(S, IP); 2040 } 2041 if (HasNUW) S->setHasNoUnsignedWrap(true); 2042 if (HasNSW) S->setHasNoSignedWrap(true); 2043 return S; 2044} 2045 2046const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2047 const SCEV *RHS) { 2048 SmallVector<const SCEV *, 2> Ops; 2049 Ops.push_back(LHS); 2050 Ops.push_back(RHS); 2051 return getSMaxExpr(Ops); 2052} 2053 2054const SCEV * 2055ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2056 assert(!Ops.empty() && "Cannot get empty smax!"); 2057 if (Ops.size() == 1) return Ops[0]; 2058#ifndef NDEBUG 2059 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2060 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2061 getEffectiveSCEVType(Ops[0]->getType()) && 2062 "SCEVSMaxExpr operand types don't match!"); 2063#endif 2064 2065 // Sort by complexity, this groups all similar expression types together. 2066 GroupByComplexity(Ops, LI); 2067 2068 // If there are any constants, fold them together. 2069 unsigned Idx = 0; 2070 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2071 ++Idx; 2072 assert(Idx < Ops.size()); 2073 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2074 // We found two constants, fold them together! 2075 ConstantInt *Fold = ConstantInt::get(getContext(), 2076 APIntOps::smax(LHSC->getValue()->getValue(), 2077 RHSC->getValue()->getValue())); 2078 Ops[0] = getConstant(Fold); 2079 Ops.erase(Ops.begin()+1); // Erase the folded element 2080 if (Ops.size() == 1) return Ops[0]; 2081 LHSC = cast<SCEVConstant>(Ops[0]); 2082 } 2083 2084 // If we are left with a constant minimum-int, strip it off. 2085 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2086 Ops.erase(Ops.begin()); 2087 --Idx; 2088 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2089 // If we have an smax with a constant maximum-int, it will always be 2090 // maximum-int. 2091 return Ops[0]; 2092 } 2093 } 2094 2095 if (Ops.size() == 1) return Ops[0]; 2096 2097 // Find the first SMax 2098 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2099 ++Idx; 2100 2101 // Check to see if one of the operands is an SMax. If so, expand its operands 2102 // onto our operand list, and recurse to simplify. 2103 if (Idx < Ops.size()) { 2104 bool DeletedSMax = false; 2105 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2106 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 2107 Ops.erase(Ops.begin()+Idx); 2108 DeletedSMax = true; 2109 } 2110 2111 if (DeletedSMax) 2112 return getSMaxExpr(Ops); 2113 } 2114 2115 // Okay, check to see if the same value occurs in the operand list twice. If 2116 // so, delete one. Since we sorted the list, these values are required to 2117 // be adjacent. 2118 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2119 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 2120 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2121 --i; --e; 2122 } 2123 2124 if (Ops.size() == 1) return Ops[0]; 2125 2126 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2127 2128 // Okay, it looks like we really DO need an smax expr. Check to see if we 2129 // already have one, otherwise create a new one. 2130 FoldingSetNodeID ID; 2131 ID.AddInteger(scSMaxExpr); 2132 ID.AddInteger(Ops.size()); 2133 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2134 ID.AddPointer(Ops[i]); 2135 void *IP = 0; 2136 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2137 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2138 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2139 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2140 O, Ops.size()); 2141 UniqueSCEVs.InsertNode(S, IP); 2142 return S; 2143} 2144 2145const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2146 const SCEV *RHS) { 2147 SmallVector<const SCEV *, 2> Ops; 2148 Ops.push_back(LHS); 2149 Ops.push_back(RHS); 2150 return getUMaxExpr(Ops); 2151} 2152 2153const SCEV * 2154ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2155 assert(!Ops.empty() && "Cannot get empty umax!"); 2156 if (Ops.size() == 1) return Ops[0]; 2157#ifndef NDEBUG 2158 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2159 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2160 getEffectiveSCEVType(Ops[0]->getType()) && 2161 "SCEVUMaxExpr operand types don't match!"); 2162#endif 2163 2164 // Sort by complexity, this groups all similar expression types together. 2165 GroupByComplexity(Ops, LI); 2166 2167 // If there are any constants, fold them together. 2168 unsigned Idx = 0; 2169 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2170 ++Idx; 2171 assert(Idx < Ops.size()); 2172 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2173 // We found two constants, fold them together! 2174 ConstantInt *Fold = ConstantInt::get(getContext(), 2175 APIntOps::umax(LHSC->getValue()->getValue(), 2176 RHSC->getValue()->getValue())); 2177 Ops[0] = getConstant(Fold); 2178 Ops.erase(Ops.begin()+1); // Erase the folded element 2179 if (Ops.size() == 1) return Ops[0]; 2180 LHSC = cast<SCEVConstant>(Ops[0]); 2181 } 2182 2183 // If we are left with a constant minimum-int, strip it off. 2184 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2185 Ops.erase(Ops.begin()); 2186 --Idx; 2187 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2188 // If we have an umax with a constant maximum-int, it will always be 2189 // maximum-int. 2190 return Ops[0]; 2191 } 2192 } 2193 2194 if (Ops.size() == 1) return Ops[0]; 2195 2196 // Find the first UMax 2197 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2198 ++Idx; 2199 2200 // Check to see if one of the operands is a UMax. If so, expand its operands 2201 // onto our operand list, and recurse to simplify. 2202 if (Idx < Ops.size()) { 2203 bool DeletedUMax = false; 2204 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2205 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2206 Ops.erase(Ops.begin()+Idx); 2207 DeletedUMax = true; 2208 } 2209 2210 if (DeletedUMax) 2211 return getUMaxExpr(Ops); 2212 } 2213 2214 // Okay, check to see if the same value occurs in the operand list twice. If 2215 // so, delete one. Since we sorted the list, these values are required to 2216 // be adjacent. 2217 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2218 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2219 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2220 --i; --e; 2221 } 2222 2223 if (Ops.size() == 1) return Ops[0]; 2224 2225 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2226 2227 // Okay, it looks like we really DO need a umax expr. Check to see if we 2228 // already have one, otherwise create a new one. 2229 FoldingSetNodeID ID; 2230 ID.AddInteger(scUMaxExpr); 2231 ID.AddInteger(Ops.size()); 2232 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2233 ID.AddPointer(Ops[i]); 2234 void *IP = 0; 2235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2236 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2237 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2238 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2239 O, Ops.size()); 2240 UniqueSCEVs.InsertNode(S, IP); 2241 return S; 2242} 2243 2244const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2245 const SCEV *RHS) { 2246 // ~smax(~x, ~y) == smin(x, y). 2247 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2248} 2249 2250const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2251 const SCEV *RHS) { 2252 // ~umax(~x, ~y) == umin(x, y) 2253 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2254} 2255 2256const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2257 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2258 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2259 C = ConstantFoldConstantExpression(CE, TD); 2260 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2261 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2262} 2263 2264const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2265 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2266 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2267 C = ConstantFoldConstantExpression(CE, TD); 2268 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2269 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2270} 2271 2272const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2273 unsigned FieldNo) { 2274 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2275 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2276 C = ConstantFoldConstantExpression(CE, TD); 2277 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2278 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2279} 2280 2281const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2282 Constant *FieldNo) { 2283 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2284 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2285 C = ConstantFoldConstantExpression(CE, TD); 2286 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2287 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2288} 2289 2290const SCEV *ScalarEvolution::getUnknown(Value *V) { 2291 // Don't attempt to do anything other than create a SCEVUnknown object 2292 // here. createSCEV only calls getUnknown after checking for all other 2293 // interesting possibilities, and any other code that calls getUnknown 2294 // is doing so in order to hide a value from SCEV canonicalization. 2295 2296 FoldingSetNodeID ID; 2297 ID.AddInteger(scUnknown); 2298 ID.AddPointer(V); 2299 void *IP = 0; 2300 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2301 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V); 2302 UniqueSCEVs.InsertNode(S, IP); 2303 return S; 2304} 2305 2306//===----------------------------------------------------------------------===// 2307// Basic SCEV Analysis and PHI Idiom Recognition Code 2308// 2309 2310/// isSCEVable - Test if values of the given type are analyzable within 2311/// the SCEV framework. This primarily includes integer types, and it 2312/// can optionally include pointer types if the ScalarEvolution class 2313/// has access to target-specific information. 2314bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2315 // Integers and pointers are always SCEVable. 2316 return Ty->isIntegerTy() || Ty->isPointerTy(); 2317} 2318 2319/// getTypeSizeInBits - Return the size in bits of the specified type, 2320/// for which isSCEVable must return true. 2321uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2322 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2323 2324 // If we have a TargetData, use it! 2325 if (TD) 2326 return TD->getTypeSizeInBits(Ty); 2327 2328 // Integer types have fixed sizes. 2329 if (Ty->isIntegerTy()) 2330 return Ty->getPrimitiveSizeInBits(); 2331 2332 // The only other support type is pointer. Without TargetData, conservatively 2333 // assume pointers are 64-bit. 2334 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2335 return 64; 2336} 2337 2338/// getEffectiveSCEVType - Return a type with the same bitwidth as 2339/// the given type and which represents how SCEV will treat the given 2340/// type, for which isSCEVable must return true. For pointer types, 2341/// this is the pointer-sized integer type. 2342const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2343 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2344 2345 if (Ty->isIntegerTy()) 2346 return Ty; 2347 2348 // The only other support type is pointer. 2349 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2350 if (TD) return TD->getIntPtrType(getContext()); 2351 2352 // Without TargetData, conservatively assume pointers are 64-bit. 2353 return Type::getInt64Ty(getContext()); 2354} 2355 2356const SCEV *ScalarEvolution::getCouldNotCompute() { 2357 return &CouldNotCompute; 2358} 2359 2360/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2361/// expression and create a new one. 2362const SCEV *ScalarEvolution::getSCEV(Value *V) { 2363 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2364 2365 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2366 if (I != Scalars.end()) return I->second; 2367 const SCEV *S = createSCEV(V); 2368 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2369 return S; 2370} 2371 2372/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2373/// specified signed integer value and return a SCEV for the constant. 2374const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) { 2375 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2376 return getConstant(ConstantInt::get(ITy, Val)); 2377} 2378 2379/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2380/// 2381const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2382 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2383 return getConstant( 2384 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2385 2386 const Type *Ty = V->getType(); 2387 Ty = getEffectiveSCEVType(Ty); 2388 return getMulExpr(V, 2389 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2390} 2391 2392/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2393const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2394 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2395 return getConstant( 2396 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2397 2398 const Type *Ty = V->getType(); 2399 Ty = getEffectiveSCEVType(Ty); 2400 const SCEV *AllOnes = 2401 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2402 return getMinusSCEV(AllOnes, V); 2403} 2404 2405/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2406/// 2407const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2408 const SCEV *RHS) { 2409 // X - Y --> X + -Y 2410 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2411} 2412 2413/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2414/// input value to the specified type. If the type must be extended, it is zero 2415/// extended. 2416const SCEV * 2417ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2418 const Type *Ty) { 2419 const Type *SrcTy = V->getType(); 2420 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2421 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2422 "Cannot truncate or zero extend with non-integer arguments!"); 2423 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2424 return V; // No conversion 2425 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2426 return getTruncateExpr(V, Ty); 2427 return getZeroExtendExpr(V, Ty); 2428} 2429 2430/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2431/// input value to the specified type. If the type must be extended, it is sign 2432/// extended. 2433const SCEV * 2434ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2435 const Type *Ty) { 2436 const Type *SrcTy = V->getType(); 2437 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2438 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2439 "Cannot truncate or zero extend with non-integer arguments!"); 2440 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2441 return V; // No conversion 2442 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2443 return getTruncateExpr(V, Ty); 2444 return getSignExtendExpr(V, Ty); 2445} 2446 2447/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2448/// input value to the specified type. If the type must be extended, it is zero 2449/// extended. The conversion must not be narrowing. 2450const SCEV * 2451ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2452 const Type *SrcTy = V->getType(); 2453 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2454 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2455 "Cannot noop or zero extend with non-integer arguments!"); 2456 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2457 "getNoopOrZeroExtend cannot truncate!"); 2458 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2459 return V; // No conversion 2460 return getZeroExtendExpr(V, Ty); 2461} 2462 2463/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2464/// input value to the specified type. If the type must be extended, it is sign 2465/// extended. The conversion must not be narrowing. 2466const SCEV * 2467ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2468 const Type *SrcTy = V->getType(); 2469 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2470 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2471 "Cannot noop or sign extend with non-integer arguments!"); 2472 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2473 "getNoopOrSignExtend cannot truncate!"); 2474 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2475 return V; // No conversion 2476 return getSignExtendExpr(V, Ty); 2477} 2478 2479/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2480/// the input value to the specified type. If the type must be extended, 2481/// it is extended with unspecified bits. The conversion must not be 2482/// narrowing. 2483const SCEV * 2484ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2485 const Type *SrcTy = V->getType(); 2486 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2487 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2488 "Cannot noop or any extend with non-integer arguments!"); 2489 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2490 "getNoopOrAnyExtend cannot truncate!"); 2491 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2492 return V; // No conversion 2493 return getAnyExtendExpr(V, Ty); 2494} 2495 2496/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2497/// input value to the specified type. The conversion must not be widening. 2498const SCEV * 2499ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2500 const Type *SrcTy = V->getType(); 2501 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2502 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2503 "Cannot truncate or noop with non-integer arguments!"); 2504 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2505 "getTruncateOrNoop cannot extend!"); 2506 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2507 return V; // No conversion 2508 return getTruncateExpr(V, Ty); 2509} 2510 2511/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2512/// the types using zero-extension, and then perform a umax operation 2513/// with them. 2514const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2515 const SCEV *RHS) { 2516 const SCEV *PromotedLHS = LHS; 2517 const SCEV *PromotedRHS = RHS; 2518 2519 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2520 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2521 else 2522 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2523 2524 return getUMaxExpr(PromotedLHS, PromotedRHS); 2525} 2526 2527/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2528/// the types using zero-extension, and then perform a umin operation 2529/// with them. 2530const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2531 const SCEV *RHS) { 2532 const SCEV *PromotedLHS = LHS; 2533 const SCEV *PromotedRHS = RHS; 2534 2535 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2536 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2537 else 2538 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2539 2540 return getUMinExpr(PromotedLHS, PromotedRHS); 2541} 2542 2543/// PushDefUseChildren - Push users of the given Instruction 2544/// onto the given Worklist. 2545static void 2546PushDefUseChildren(Instruction *I, 2547 SmallVectorImpl<Instruction *> &Worklist) { 2548 // Push the def-use children onto the Worklist stack. 2549 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2550 UI != UE; ++UI) 2551 Worklist.push_back(cast<Instruction>(UI)); 2552} 2553 2554/// ForgetSymbolicValue - This looks up computed SCEV values for all 2555/// instructions that depend on the given instruction and removes them from 2556/// the Scalars map if they reference SymName. This is used during PHI 2557/// resolution. 2558void 2559ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2560 SmallVector<Instruction *, 16> Worklist; 2561 PushDefUseChildren(PN, Worklist); 2562 2563 SmallPtrSet<Instruction *, 8> Visited; 2564 Visited.insert(PN); 2565 while (!Worklist.empty()) { 2566 Instruction *I = Worklist.pop_back_val(); 2567 if (!Visited.insert(I)) continue; 2568 2569 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2570 Scalars.find(static_cast<Value *>(I)); 2571 if (It != Scalars.end()) { 2572 // Short-circuit the def-use traversal if the symbolic name 2573 // ceases to appear in expressions. 2574 if (It->second != SymName && !It->second->hasOperand(SymName)) 2575 continue; 2576 2577 // SCEVUnknown for a PHI either means that it has an unrecognized 2578 // structure, it's a PHI that's in the progress of being computed 2579 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2580 // additional loop trip count information isn't going to change anything. 2581 // In the second case, createNodeForPHI will perform the necessary 2582 // updates on its own when it gets to that point. In the third, we do 2583 // want to forget the SCEVUnknown. 2584 if (!isa<PHINode>(I) || 2585 !isa<SCEVUnknown>(It->second) || 2586 (I != PN && It->second == SymName)) { 2587 ValuesAtScopes.erase(It->second); 2588 Scalars.erase(It); 2589 } 2590 } 2591 2592 PushDefUseChildren(I, Worklist); 2593 } 2594} 2595 2596/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2597/// a loop header, making it a potential recurrence, or it doesn't. 2598/// 2599const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2600 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2601 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2602 if (L->getHeader() == PN->getParent()) { 2603 // If it lives in the loop header, it has two incoming values, one 2604 // from outside the loop, and one from inside. 2605 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2606 unsigned BackEdge = IncomingEdge^1; 2607 2608 // While we are analyzing this PHI node, handle its value symbolically. 2609 const SCEV *SymbolicName = getUnknown(PN); 2610 assert(Scalars.find(PN) == Scalars.end() && 2611 "PHI node already processed?"); 2612 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2613 2614 // Using this symbolic name for the PHI, analyze the value coming around 2615 // the back-edge. 2616 Value *BEValueV = PN->getIncomingValue(BackEdge); 2617 const SCEV *BEValue = getSCEV(BEValueV); 2618 2619 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2620 // has a special value for the first iteration of the loop. 2621 2622 // If the value coming around the backedge is an add with the symbolic 2623 // value we just inserted, then we found a simple induction variable! 2624 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2625 // If there is a single occurrence of the symbolic value, replace it 2626 // with a recurrence. 2627 unsigned FoundIndex = Add->getNumOperands(); 2628 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2629 if (Add->getOperand(i) == SymbolicName) 2630 if (FoundIndex == e) { 2631 FoundIndex = i; 2632 break; 2633 } 2634 2635 if (FoundIndex != Add->getNumOperands()) { 2636 // Create an add with everything but the specified operand. 2637 SmallVector<const SCEV *, 8> Ops; 2638 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2639 if (i != FoundIndex) 2640 Ops.push_back(Add->getOperand(i)); 2641 const SCEV *Accum = getAddExpr(Ops); 2642 2643 // This is not a valid addrec if the step amount is varying each 2644 // loop iteration, but is not itself an addrec in this loop. 2645 if (Accum->isLoopInvariant(L) || 2646 (isa<SCEVAddRecExpr>(Accum) && 2647 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2648 bool HasNUW = false; 2649 bool HasNSW = false; 2650 2651 // If the increment doesn't overflow, then neither the addrec nor 2652 // the post-increment will overflow. 2653 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2654 if (OBO->hasNoUnsignedWrap()) 2655 HasNUW = true; 2656 if (OBO->hasNoSignedWrap()) 2657 HasNSW = true; 2658 } 2659 2660 const SCEV *StartVal = 2661 getSCEV(PN->getIncomingValue(IncomingEdge)); 2662 const SCEV *PHISCEV = 2663 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2664 2665 // Since the no-wrap flags are on the increment, they apply to the 2666 // post-incremented value as well. 2667 if (Accum->isLoopInvariant(L)) 2668 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2669 Accum, L, HasNUW, HasNSW); 2670 2671 // Okay, for the entire analysis of this edge we assumed the PHI 2672 // to be symbolic. We now need to go back and purge all of the 2673 // entries for the scalars that use the symbolic expression. 2674 ForgetSymbolicName(PN, SymbolicName); 2675 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2676 return PHISCEV; 2677 } 2678 } 2679 } else if (const SCEVAddRecExpr *AddRec = 2680 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2681 // Otherwise, this could be a loop like this: 2682 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2683 // In this case, j = {1,+,1} and BEValue is j. 2684 // Because the other in-value of i (0) fits the evolution of BEValue 2685 // i really is an addrec evolution. 2686 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2687 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2688 2689 // If StartVal = j.start - j.stride, we can use StartVal as the 2690 // initial step of the addrec evolution. 2691 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2692 AddRec->getOperand(1))) { 2693 const SCEV *PHISCEV = 2694 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2695 2696 // Okay, for the entire analysis of this edge we assumed the PHI 2697 // to be symbolic. We now need to go back and purge all of the 2698 // entries for the scalars that use the symbolic expression. 2699 ForgetSymbolicName(PN, SymbolicName); 2700 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2701 return PHISCEV; 2702 } 2703 } 2704 } 2705 2706 return SymbolicName; 2707 } 2708 2709 // If the PHI has a single incoming value, follow that value, unless the 2710 // PHI's incoming blocks are in a different loop, in which case doing so 2711 // risks breaking LCSSA form. Instcombine would normally zap these, but 2712 // it doesn't have DominatorTree information, so it may miss cases. 2713 if (Value *V = PN->hasConstantValue(DT)) { 2714 bool AllSameLoop = true; 2715 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2716 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2717 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2718 AllSameLoop = false; 2719 break; 2720 } 2721 if (AllSameLoop) 2722 return getSCEV(V); 2723 } 2724 2725 // If it's not a loop phi, we can't handle it yet. 2726 return getUnknown(PN); 2727} 2728 2729/// createNodeForGEP - Expand GEP instructions into add and multiply 2730/// operations. This allows them to be analyzed by regular SCEV code. 2731/// 2732const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2733 2734 bool InBounds = GEP->isInBounds(); 2735 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2736 Value *Base = GEP->getOperand(0); 2737 // Don't attempt to analyze GEPs over unsized objects. 2738 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2739 return getUnknown(GEP); 2740 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2741 gep_type_iterator GTI = gep_type_begin(GEP); 2742 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2743 E = GEP->op_end(); 2744 I != E; ++I) { 2745 Value *Index = *I; 2746 // Compute the (potentially symbolic) offset in bytes for this index. 2747 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2748 // For a struct, add the member offset. 2749 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2750 TotalOffset = getAddExpr(TotalOffset, 2751 getOffsetOfExpr(STy, FieldNo), 2752 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2753 } else { 2754 // For an array, add the element offset, explicitly scaled. 2755 const SCEV *LocalOffset = getSCEV(Index); 2756 // Getelementptr indices are signed. 2757 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2758 // Lower "inbounds" GEPs to NSW arithmetic. 2759 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2760 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2761 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2762 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2763 } 2764 } 2765 return getAddExpr(getSCEV(Base), TotalOffset, 2766 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2767} 2768 2769/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2770/// guaranteed to end in (at every loop iteration). It is, at the same time, 2771/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2772/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2773uint32_t 2774ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2775 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2776 return C->getValue()->getValue().countTrailingZeros(); 2777 2778 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2779 return std::min(GetMinTrailingZeros(T->getOperand()), 2780 (uint32_t)getTypeSizeInBits(T->getType())); 2781 2782 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2783 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2784 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2785 getTypeSizeInBits(E->getType()) : OpRes; 2786 } 2787 2788 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2789 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2790 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2791 getTypeSizeInBits(E->getType()) : OpRes; 2792 } 2793 2794 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2795 // The result is the min of all operands results. 2796 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2797 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2798 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2799 return MinOpRes; 2800 } 2801 2802 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2803 // The result is the sum of all operands results. 2804 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2805 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2806 for (unsigned i = 1, e = M->getNumOperands(); 2807 SumOpRes != BitWidth && i != e; ++i) 2808 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2809 BitWidth); 2810 return SumOpRes; 2811 } 2812 2813 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2814 // The result is the min of all operands results. 2815 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2816 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2817 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2818 return MinOpRes; 2819 } 2820 2821 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2822 // The result is the min of all operands results. 2823 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2824 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2825 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2826 return MinOpRes; 2827 } 2828 2829 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2830 // The result is the min of all operands results. 2831 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2832 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2833 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2834 return MinOpRes; 2835 } 2836 2837 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2838 // For a SCEVUnknown, ask ValueTracking. 2839 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2840 APInt Mask = APInt::getAllOnesValue(BitWidth); 2841 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2842 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2843 return Zeros.countTrailingOnes(); 2844 } 2845 2846 // SCEVUDivExpr 2847 return 0; 2848} 2849 2850/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2851/// 2852ConstantRange 2853ScalarEvolution::getUnsignedRange(const SCEV *S) { 2854 2855 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2856 return ConstantRange(C->getValue()->getValue()); 2857 2858 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2859 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2860 2861 // If the value has known zeros, the maximum unsigned value will have those 2862 // known zeros as well. 2863 uint32_t TZ = GetMinTrailingZeros(S); 2864 if (TZ != 0) 2865 ConservativeResult = 2866 ConstantRange(APInt::getMinValue(BitWidth), 2867 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2868 2869 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2870 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2871 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2872 X = X.add(getUnsignedRange(Add->getOperand(i))); 2873 return ConservativeResult.intersectWith(X); 2874 } 2875 2876 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2877 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2878 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2879 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2880 return ConservativeResult.intersectWith(X); 2881 } 2882 2883 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2884 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2885 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2886 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2887 return ConservativeResult.intersectWith(X); 2888 } 2889 2890 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2891 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2892 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2893 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2894 return ConservativeResult.intersectWith(X); 2895 } 2896 2897 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2898 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2899 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2900 return ConservativeResult.intersectWith(X.udiv(Y)); 2901 } 2902 2903 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2904 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2905 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2906 } 2907 2908 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2909 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2910 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2911 } 2912 2913 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2914 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2915 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2916 } 2917 2918 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2919 // If there's no unsigned wrap, the value will never be less than its 2920 // initial value. 2921 if (AddRec->hasNoUnsignedWrap()) 2922 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2923 ConservativeResult = 2924 ConstantRange(C->getValue()->getValue(), 2925 APInt(getTypeSizeInBits(C->getType()), 0)); 2926 2927 // TODO: non-affine addrec 2928 if (AddRec->isAffine()) { 2929 const Type *Ty = AddRec->getType(); 2930 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2931 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2932 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2933 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2934 2935 const SCEV *Start = AddRec->getStart(); 2936 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2937 2938 // Check for overflow. 2939 if (!AddRec->hasNoUnsignedWrap()) 2940 return ConservativeResult; 2941 2942 ConstantRange StartRange = getUnsignedRange(Start); 2943 ConstantRange EndRange = getUnsignedRange(End); 2944 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2945 EndRange.getUnsignedMin()); 2946 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2947 EndRange.getUnsignedMax()); 2948 if (Min.isMinValue() && Max.isMaxValue()) 2949 return ConservativeResult; 2950 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2951 } 2952 } 2953 2954 return ConservativeResult; 2955 } 2956 2957 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2958 // For a SCEVUnknown, ask ValueTracking. 2959 APInt Mask = APInt::getAllOnesValue(BitWidth); 2960 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2961 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2962 if (Ones == ~Zeros + 1) 2963 return ConservativeResult; 2964 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 2965 } 2966 2967 return ConservativeResult; 2968} 2969 2970/// getSignedRange - Determine the signed range for a particular SCEV. 2971/// 2972ConstantRange 2973ScalarEvolution::getSignedRange(const SCEV *S) { 2974 2975 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2976 return ConstantRange(C->getValue()->getValue()); 2977 2978 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2979 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2980 2981 // If the value has known zeros, the maximum signed value will have those 2982 // known zeros as well. 2983 uint32_t TZ = GetMinTrailingZeros(S); 2984 if (TZ != 0) 2985 ConservativeResult = 2986 ConstantRange(APInt::getSignedMinValue(BitWidth), 2987 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 2988 2989 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2990 ConstantRange X = getSignedRange(Add->getOperand(0)); 2991 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2992 X = X.add(getSignedRange(Add->getOperand(i))); 2993 return ConservativeResult.intersectWith(X); 2994 } 2995 2996 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2997 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2998 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2999 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3000 return ConservativeResult.intersectWith(X); 3001 } 3002 3003 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3004 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3005 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3006 X = X.smax(getSignedRange(SMax->getOperand(i))); 3007 return ConservativeResult.intersectWith(X); 3008 } 3009 3010 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3011 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3012 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3013 X = X.umax(getSignedRange(UMax->getOperand(i))); 3014 return ConservativeResult.intersectWith(X); 3015 } 3016 3017 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3018 ConstantRange X = getSignedRange(UDiv->getLHS()); 3019 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3020 return ConservativeResult.intersectWith(X.udiv(Y)); 3021 } 3022 3023 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3024 ConstantRange X = getSignedRange(ZExt->getOperand()); 3025 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3026 } 3027 3028 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3029 ConstantRange X = getSignedRange(SExt->getOperand()); 3030 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3031 } 3032 3033 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3034 ConstantRange X = getSignedRange(Trunc->getOperand()); 3035 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3036 } 3037 3038 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3039 // If there's no signed wrap, and all the operands have the same sign or 3040 // zero, the value won't ever change sign. 3041 if (AddRec->hasNoSignedWrap()) { 3042 bool AllNonNeg = true; 3043 bool AllNonPos = true; 3044 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3045 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3046 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3047 } 3048 if (AllNonNeg) 3049 ConservativeResult = ConservativeResult.intersectWith( 3050 ConstantRange(APInt(BitWidth, 0), 3051 APInt::getSignedMinValue(BitWidth))); 3052 else if (AllNonPos) 3053 ConservativeResult = ConservativeResult.intersectWith( 3054 ConstantRange(APInt::getSignedMinValue(BitWidth), 3055 APInt(BitWidth, 1))); 3056 } 3057 3058 // TODO: non-affine addrec 3059 if (AddRec->isAffine()) { 3060 const Type *Ty = AddRec->getType(); 3061 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3062 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3063 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3064 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3065 3066 const SCEV *Start = AddRec->getStart(); 3067 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 3068 3069 // Check for overflow. 3070 if (!AddRec->hasNoSignedWrap()) 3071 return ConservativeResult; 3072 3073 ConstantRange StartRange = getSignedRange(Start); 3074 ConstantRange EndRange = getSignedRange(End); 3075 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3076 EndRange.getSignedMin()); 3077 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3078 EndRange.getSignedMax()); 3079 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3080 return ConservativeResult; 3081 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3082 } 3083 } 3084 3085 return ConservativeResult; 3086 } 3087 3088 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3089 // For a SCEVUnknown, ask ValueTracking. 3090 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3091 return ConservativeResult; 3092 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3093 if (NS == 1) 3094 return ConservativeResult; 3095 return ConservativeResult.intersectWith( 3096 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3097 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3098 } 3099 3100 return ConservativeResult; 3101} 3102 3103/// createSCEV - We know that there is no SCEV for the specified value. 3104/// Analyze the expression. 3105/// 3106const SCEV *ScalarEvolution::createSCEV(Value *V) { 3107 if (!isSCEVable(V->getType())) 3108 return getUnknown(V); 3109 3110 unsigned Opcode = Instruction::UserOp1; 3111 if (Instruction *I = dyn_cast<Instruction>(V)) { 3112 Opcode = I->getOpcode(); 3113 3114 // Don't attempt to analyze instructions in blocks that aren't 3115 // reachable. Such instructions don't matter, and they aren't required 3116 // to obey basic rules for definitions dominating uses which this 3117 // analysis depends on. 3118 if (!DT->isReachableFromEntry(I->getParent())) 3119 return getUnknown(V); 3120 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3121 Opcode = CE->getOpcode(); 3122 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3123 return getConstant(CI); 3124 else if (isa<ConstantPointerNull>(V)) 3125 return getIntegerSCEV(0, V->getType()); 3126 else if (isa<UndefValue>(V)) 3127 return getIntegerSCEV(0, V->getType()); 3128 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3129 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3130 else 3131 return getUnknown(V); 3132 3133 Operator *U = cast<Operator>(V); 3134 switch (Opcode) { 3135 case Instruction::Add: 3136 // Don't transfer the NSW and NUW bits from the Add instruction to the 3137 // Add expression, because the Instruction may be guarded by control 3138 // flow and the no-overflow bits may not be valid for the expression in 3139 // any context. 3140 return getAddExpr(getSCEV(U->getOperand(0)), 3141 getSCEV(U->getOperand(1))); 3142 case Instruction::Mul: 3143 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3144 // Mul expression, as with Add. 3145 return getMulExpr(getSCEV(U->getOperand(0)), 3146 getSCEV(U->getOperand(1))); 3147 case Instruction::UDiv: 3148 return getUDivExpr(getSCEV(U->getOperand(0)), 3149 getSCEV(U->getOperand(1))); 3150 case Instruction::Sub: 3151 return getMinusSCEV(getSCEV(U->getOperand(0)), 3152 getSCEV(U->getOperand(1))); 3153 case Instruction::And: 3154 // For an expression like x&255 that merely masks off the high bits, 3155 // use zext(trunc(x)) as the SCEV expression. 3156 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3157 if (CI->isNullValue()) 3158 return getSCEV(U->getOperand(1)); 3159 if (CI->isAllOnesValue()) 3160 return getSCEV(U->getOperand(0)); 3161 const APInt &A = CI->getValue(); 3162 3163 // Instcombine's ShrinkDemandedConstant may strip bits out of 3164 // constants, obscuring what would otherwise be a low-bits mask. 3165 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3166 // knew about to reconstruct a low-bits mask value. 3167 unsigned LZ = A.countLeadingZeros(); 3168 unsigned BitWidth = A.getBitWidth(); 3169 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3170 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3171 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3172 3173 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3174 3175 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3176 return 3177 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3178 IntegerType::get(getContext(), BitWidth - LZ)), 3179 U->getType()); 3180 } 3181 break; 3182 3183 case Instruction::Or: 3184 // If the RHS of the Or is a constant, we may have something like: 3185 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3186 // optimizations will transparently handle this case. 3187 // 3188 // In order for this transformation to be safe, the LHS must be of the 3189 // form X*(2^n) and the Or constant must be less than 2^n. 3190 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3191 const SCEV *LHS = getSCEV(U->getOperand(0)); 3192 const APInt &CIVal = CI->getValue(); 3193 if (GetMinTrailingZeros(LHS) >= 3194 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3195 // Build a plain add SCEV. 3196 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3197 // If the LHS of the add was an addrec and it has no-wrap flags, 3198 // transfer the no-wrap flags, since an or won't introduce a wrap. 3199 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3200 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3201 if (OldAR->hasNoUnsignedWrap()) 3202 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3203 if (OldAR->hasNoSignedWrap()) 3204 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3205 } 3206 return S; 3207 } 3208 } 3209 break; 3210 case Instruction::Xor: 3211 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3212 // If the RHS of the xor is a signbit, then this is just an add. 3213 // Instcombine turns add of signbit into xor as a strength reduction step. 3214 if (CI->getValue().isSignBit()) 3215 return getAddExpr(getSCEV(U->getOperand(0)), 3216 getSCEV(U->getOperand(1))); 3217 3218 // If the RHS of xor is -1, then this is a not operation. 3219 if (CI->isAllOnesValue()) 3220 return getNotSCEV(getSCEV(U->getOperand(0))); 3221 3222 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3223 // This is a variant of the check for xor with -1, and it handles 3224 // the case where instcombine has trimmed non-demanded bits out 3225 // of an xor with -1. 3226 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3227 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3228 if (BO->getOpcode() == Instruction::And && 3229 LCI->getValue() == CI->getValue()) 3230 if (const SCEVZeroExtendExpr *Z = 3231 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3232 const Type *UTy = U->getType(); 3233 const SCEV *Z0 = Z->getOperand(); 3234 const Type *Z0Ty = Z0->getType(); 3235 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3236 3237 // If C is a low-bits mask, the zero extend is serving to 3238 // mask off the high bits. Complement the operand and 3239 // re-apply the zext. 3240 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3241 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3242 3243 // If C is a single bit, it may be in the sign-bit position 3244 // before the zero-extend. In this case, represent the xor 3245 // using an add, which is equivalent, and re-apply the zext. 3246 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3247 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3248 Trunc.isSignBit()) 3249 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3250 UTy); 3251 } 3252 } 3253 break; 3254 3255 case Instruction::Shl: 3256 // Turn shift left of a constant amount into a multiply. 3257 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3258 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3259 Constant *X = ConstantInt::get(getContext(), 3260 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3261 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3262 } 3263 break; 3264 3265 case Instruction::LShr: 3266 // Turn logical shift right of a constant into a unsigned divide. 3267 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3268 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3269 Constant *X = ConstantInt::get(getContext(), 3270 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3271 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3272 } 3273 break; 3274 3275 case Instruction::AShr: 3276 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3277 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3278 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3279 if (L->getOpcode() == Instruction::Shl && 3280 L->getOperand(1) == U->getOperand(1)) { 3281 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3282 uint64_t Amt = BitWidth - CI->getZExtValue(); 3283 if (Amt == BitWidth) 3284 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3285 if (Amt > BitWidth) 3286 return getIntegerSCEV(0, U->getType()); // value is undefined 3287 return 3288 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3289 IntegerType::get(getContext(), Amt)), 3290 U->getType()); 3291 } 3292 break; 3293 3294 case Instruction::Trunc: 3295 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3296 3297 case Instruction::ZExt: 3298 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3299 3300 case Instruction::SExt: 3301 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3302 3303 case Instruction::BitCast: 3304 // BitCasts are no-op casts so we just eliminate the cast. 3305 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3306 return getSCEV(U->getOperand(0)); 3307 break; 3308 3309 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3310 // lead to pointer expressions which cannot safely be expanded to GEPs, 3311 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3312 // simplifying integer expressions. 3313 3314 case Instruction::GetElementPtr: 3315 return createNodeForGEP(cast<GEPOperator>(U)); 3316 3317 case Instruction::PHI: 3318 return createNodeForPHI(cast<PHINode>(U)); 3319 3320 case Instruction::Select: 3321 // This could be a smax or umax that was lowered earlier. 3322 // Try to recover it. 3323 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3324 Value *LHS = ICI->getOperand(0); 3325 Value *RHS = ICI->getOperand(1); 3326 switch (ICI->getPredicate()) { 3327 case ICmpInst::ICMP_SLT: 3328 case ICmpInst::ICMP_SLE: 3329 std::swap(LHS, RHS); 3330 // fall through 3331 case ICmpInst::ICMP_SGT: 3332 case ICmpInst::ICMP_SGE: 3333 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3334 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3335 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3336 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3337 break; 3338 case ICmpInst::ICMP_ULT: 3339 case ICmpInst::ICMP_ULE: 3340 std::swap(LHS, RHS); 3341 // fall through 3342 case ICmpInst::ICMP_UGT: 3343 case ICmpInst::ICMP_UGE: 3344 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3345 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3346 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3347 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3348 break; 3349 case ICmpInst::ICMP_NE: 3350 // n != 0 ? n : 1 -> umax(n, 1) 3351 if (LHS == U->getOperand(1) && 3352 isa<ConstantInt>(U->getOperand(2)) && 3353 cast<ConstantInt>(U->getOperand(2))->isOne() && 3354 isa<ConstantInt>(RHS) && 3355 cast<ConstantInt>(RHS)->isZero()) 3356 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3357 break; 3358 case ICmpInst::ICMP_EQ: 3359 // n == 0 ? 1 : n -> umax(n, 1) 3360 if (LHS == U->getOperand(2) && 3361 isa<ConstantInt>(U->getOperand(1)) && 3362 cast<ConstantInt>(U->getOperand(1))->isOne() && 3363 isa<ConstantInt>(RHS) && 3364 cast<ConstantInt>(RHS)->isZero()) 3365 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3366 break; 3367 default: 3368 break; 3369 } 3370 } 3371 3372 default: // We cannot analyze this expression. 3373 break; 3374 } 3375 3376 return getUnknown(V); 3377} 3378 3379 3380 3381//===----------------------------------------------------------------------===// 3382// Iteration Count Computation Code 3383// 3384 3385/// getBackedgeTakenCount - If the specified loop has a predictable 3386/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3387/// object. The backedge-taken count is the number of times the loop header 3388/// will be branched to from within the loop. This is one less than the 3389/// trip count of the loop, since it doesn't count the first iteration, 3390/// when the header is branched to from outside the loop. 3391/// 3392/// Note that it is not valid to call this method on a loop without a 3393/// loop-invariant backedge-taken count (see 3394/// hasLoopInvariantBackedgeTakenCount). 3395/// 3396const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3397 return getBackedgeTakenInfo(L).Exact; 3398} 3399 3400/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3401/// return the least SCEV value that is known never to be less than the 3402/// actual backedge taken count. 3403const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3404 return getBackedgeTakenInfo(L).Max; 3405} 3406 3407/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3408/// onto the given Worklist. 3409static void 3410PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3411 BasicBlock *Header = L->getHeader(); 3412 3413 // Push all Loop-header PHIs onto the Worklist stack. 3414 for (BasicBlock::iterator I = Header->begin(); 3415 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3416 Worklist.push_back(PN); 3417} 3418 3419const ScalarEvolution::BackedgeTakenInfo & 3420ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3421 // Initially insert a CouldNotCompute for this loop. If the insertion 3422 // succeeds, proceed to actually compute a backedge-taken count and 3423 // update the value. The temporary CouldNotCompute value tells SCEV 3424 // code elsewhere that it shouldn't attempt to request a new 3425 // backedge-taken count, which could result in infinite recursion. 3426 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3427 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3428 if (Pair.second) { 3429 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3430 if (BECount.Exact != getCouldNotCompute()) { 3431 assert(BECount.Exact->isLoopInvariant(L) && 3432 BECount.Max->isLoopInvariant(L) && 3433 "Computed backedge-taken count isn't loop invariant for loop!"); 3434 ++NumTripCountsComputed; 3435 3436 // Update the value in the map. 3437 Pair.first->second = BECount; 3438 } else { 3439 if (BECount.Max != getCouldNotCompute()) 3440 // Update the value in the map. 3441 Pair.first->second = BECount; 3442 if (isa<PHINode>(L->getHeader()->begin())) 3443 // Only count loops that have phi nodes as not being computable. 3444 ++NumTripCountsNotComputed; 3445 } 3446 3447 // Now that we know more about the trip count for this loop, forget any 3448 // existing SCEV values for PHI nodes in this loop since they are only 3449 // conservative estimates made without the benefit of trip count 3450 // information. This is similar to the code in forgetLoop, except that 3451 // it handles SCEVUnknown PHI nodes specially. 3452 if (BECount.hasAnyInfo()) { 3453 SmallVector<Instruction *, 16> Worklist; 3454 PushLoopPHIs(L, Worklist); 3455 3456 SmallPtrSet<Instruction *, 8> Visited; 3457 while (!Worklist.empty()) { 3458 Instruction *I = Worklist.pop_back_val(); 3459 if (!Visited.insert(I)) continue; 3460 3461 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3462 Scalars.find(static_cast<Value *>(I)); 3463 if (It != Scalars.end()) { 3464 // SCEVUnknown for a PHI either means that it has an unrecognized 3465 // structure, or it's a PHI that's in the progress of being computed 3466 // by createNodeForPHI. In the former case, additional loop trip 3467 // count information isn't going to change anything. In the later 3468 // case, createNodeForPHI will perform the necessary updates on its 3469 // own when it gets to that point. 3470 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3471 ValuesAtScopes.erase(It->second); 3472 Scalars.erase(It); 3473 } 3474 if (PHINode *PN = dyn_cast<PHINode>(I)) 3475 ConstantEvolutionLoopExitValue.erase(PN); 3476 } 3477 3478 PushDefUseChildren(I, Worklist); 3479 } 3480 } 3481 } 3482 return Pair.first->second; 3483} 3484 3485/// forgetLoop - This method should be called by the client when it has 3486/// changed a loop in a way that may effect ScalarEvolution's ability to 3487/// compute a trip count, or if the loop is deleted. 3488void ScalarEvolution::forgetLoop(const Loop *L) { 3489 // Drop any stored trip count value. 3490 BackedgeTakenCounts.erase(L); 3491 3492 // Drop information about expressions based on loop-header PHIs. 3493 SmallVector<Instruction *, 16> Worklist; 3494 PushLoopPHIs(L, Worklist); 3495 3496 SmallPtrSet<Instruction *, 8> Visited; 3497 while (!Worklist.empty()) { 3498 Instruction *I = Worklist.pop_back_val(); 3499 if (!Visited.insert(I)) continue; 3500 3501 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3502 Scalars.find(static_cast<Value *>(I)); 3503 if (It != Scalars.end()) { 3504 ValuesAtScopes.erase(It->second); 3505 Scalars.erase(It); 3506 if (PHINode *PN = dyn_cast<PHINode>(I)) 3507 ConstantEvolutionLoopExitValue.erase(PN); 3508 } 3509 3510 PushDefUseChildren(I, Worklist); 3511 } 3512} 3513 3514/// forgetValue - This method should be called by the client when it has 3515/// changed a value in a way that may effect its value, or which may 3516/// disconnect it from a def-use chain linking it to a loop. 3517void ScalarEvolution::forgetValue(Value *V) { 3518 Instruction *I = dyn_cast<Instruction>(V); 3519 if (!I) return; 3520 3521 // Drop information about expressions based on loop-header PHIs. 3522 SmallVector<Instruction *, 16> Worklist; 3523 Worklist.push_back(I); 3524 3525 SmallPtrSet<Instruction *, 8> Visited; 3526 while (!Worklist.empty()) { 3527 I = Worklist.pop_back_val(); 3528 if (!Visited.insert(I)) continue; 3529 3530 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3531 Scalars.find(static_cast<Value *>(I)); 3532 if (It != Scalars.end()) { 3533 ValuesAtScopes.erase(It->second); 3534 Scalars.erase(It); 3535 if (PHINode *PN = dyn_cast<PHINode>(I)) 3536 ConstantEvolutionLoopExitValue.erase(PN); 3537 } 3538 3539 PushDefUseChildren(I, Worklist); 3540 } 3541} 3542 3543/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3544/// of the specified loop will execute. 3545ScalarEvolution::BackedgeTakenInfo 3546ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3547 SmallVector<BasicBlock *, 8> ExitingBlocks; 3548 L->getExitingBlocks(ExitingBlocks); 3549 3550 // Examine all exits and pick the most conservative values. 3551 const SCEV *BECount = getCouldNotCompute(); 3552 const SCEV *MaxBECount = getCouldNotCompute(); 3553 bool CouldNotComputeBECount = false; 3554 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3555 BackedgeTakenInfo NewBTI = 3556 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3557 3558 if (NewBTI.Exact == getCouldNotCompute()) { 3559 // We couldn't compute an exact value for this exit, so 3560 // we won't be able to compute an exact value for the loop. 3561 CouldNotComputeBECount = true; 3562 BECount = getCouldNotCompute(); 3563 } else if (!CouldNotComputeBECount) { 3564 if (BECount == getCouldNotCompute()) 3565 BECount = NewBTI.Exact; 3566 else 3567 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3568 } 3569 if (MaxBECount == getCouldNotCompute()) 3570 MaxBECount = NewBTI.Max; 3571 else if (NewBTI.Max != getCouldNotCompute()) 3572 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3573 } 3574 3575 return BackedgeTakenInfo(BECount, MaxBECount); 3576} 3577 3578/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3579/// of the specified loop will execute if it exits via the specified block. 3580ScalarEvolution::BackedgeTakenInfo 3581ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3582 BasicBlock *ExitingBlock) { 3583 3584 // Okay, we've chosen an exiting block. See what condition causes us to 3585 // exit at this block. 3586 // 3587 // FIXME: we should be able to handle switch instructions (with a single exit) 3588 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3589 if (ExitBr == 0) return getCouldNotCompute(); 3590 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3591 3592 // At this point, we know we have a conditional branch that determines whether 3593 // the loop is exited. However, we don't know if the branch is executed each 3594 // time through the loop. If not, then the execution count of the branch will 3595 // not be equal to the trip count of the loop. 3596 // 3597 // Currently we check for this by checking to see if the Exit branch goes to 3598 // the loop header. If so, we know it will always execute the same number of 3599 // times as the loop. We also handle the case where the exit block *is* the 3600 // loop header. This is common for un-rotated loops. 3601 // 3602 // If both of those tests fail, walk up the unique predecessor chain to the 3603 // header, stopping if there is an edge that doesn't exit the loop. If the 3604 // header is reached, the execution count of the branch will be equal to the 3605 // trip count of the loop. 3606 // 3607 // More extensive analysis could be done to handle more cases here. 3608 // 3609 if (ExitBr->getSuccessor(0) != L->getHeader() && 3610 ExitBr->getSuccessor(1) != L->getHeader() && 3611 ExitBr->getParent() != L->getHeader()) { 3612 // The simple checks failed, try climbing the unique predecessor chain 3613 // up to the header. 3614 bool Ok = false; 3615 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3616 BasicBlock *Pred = BB->getUniquePredecessor(); 3617 if (!Pred) 3618 return getCouldNotCompute(); 3619 TerminatorInst *PredTerm = Pred->getTerminator(); 3620 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3621 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3622 if (PredSucc == BB) 3623 continue; 3624 // If the predecessor has a successor that isn't BB and isn't 3625 // outside the loop, assume the worst. 3626 if (L->contains(PredSucc)) 3627 return getCouldNotCompute(); 3628 } 3629 if (Pred == L->getHeader()) { 3630 Ok = true; 3631 break; 3632 } 3633 BB = Pred; 3634 } 3635 if (!Ok) 3636 return getCouldNotCompute(); 3637 } 3638 3639 // Proceed to the next level to examine the exit condition expression. 3640 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3641 ExitBr->getSuccessor(0), 3642 ExitBr->getSuccessor(1)); 3643} 3644 3645/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3646/// backedge of the specified loop will execute if its exit condition 3647/// were a conditional branch of ExitCond, TBB, and FBB. 3648ScalarEvolution::BackedgeTakenInfo 3649ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3650 Value *ExitCond, 3651 BasicBlock *TBB, 3652 BasicBlock *FBB) { 3653 // Check if the controlling expression for this loop is an And or Or. 3654 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3655 if (BO->getOpcode() == Instruction::And) { 3656 // Recurse on the operands of the and. 3657 BackedgeTakenInfo BTI0 = 3658 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3659 BackedgeTakenInfo BTI1 = 3660 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3661 const SCEV *BECount = getCouldNotCompute(); 3662 const SCEV *MaxBECount = getCouldNotCompute(); 3663 if (L->contains(TBB)) { 3664 // Both conditions must be true for the loop to continue executing. 3665 // Choose the less conservative count. 3666 if (BTI0.Exact == getCouldNotCompute() || 3667 BTI1.Exact == getCouldNotCompute()) 3668 BECount = getCouldNotCompute(); 3669 else 3670 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3671 if (BTI0.Max == getCouldNotCompute()) 3672 MaxBECount = BTI1.Max; 3673 else if (BTI1.Max == getCouldNotCompute()) 3674 MaxBECount = BTI0.Max; 3675 else 3676 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3677 } else { 3678 // Both conditions must be true for the loop to exit. 3679 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3680 if (BTI0.Exact != getCouldNotCompute() && 3681 BTI1.Exact != getCouldNotCompute()) 3682 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3683 if (BTI0.Max != getCouldNotCompute() && 3684 BTI1.Max != getCouldNotCompute()) 3685 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3686 } 3687 3688 return BackedgeTakenInfo(BECount, MaxBECount); 3689 } 3690 if (BO->getOpcode() == Instruction::Or) { 3691 // Recurse on the operands of the or. 3692 BackedgeTakenInfo BTI0 = 3693 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3694 BackedgeTakenInfo BTI1 = 3695 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3696 const SCEV *BECount = getCouldNotCompute(); 3697 const SCEV *MaxBECount = getCouldNotCompute(); 3698 if (L->contains(FBB)) { 3699 // Both conditions must be false for the loop to continue executing. 3700 // Choose the less conservative count. 3701 if (BTI0.Exact == getCouldNotCompute() || 3702 BTI1.Exact == getCouldNotCompute()) 3703 BECount = getCouldNotCompute(); 3704 else 3705 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3706 if (BTI0.Max == getCouldNotCompute()) 3707 MaxBECount = BTI1.Max; 3708 else if (BTI1.Max == getCouldNotCompute()) 3709 MaxBECount = BTI0.Max; 3710 else 3711 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3712 } else { 3713 // Both conditions must be false for the loop to exit. 3714 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3715 if (BTI0.Exact != getCouldNotCompute() && 3716 BTI1.Exact != getCouldNotCompute()) 3717 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3718 if (BTI0.Max != getCouldNotCompute() && 3719 BTI1.Max != getCouldNotCompute()) 3720 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3721 } 3722 3723 return BackedgeTakenInfo(BECount, MaxBECount); 3724 } 3725 } 3726 3727 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3728 // Proceed to the next level to examine the icmp. 3729 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3730 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3731 3732 // Check for a constant condition. These are normally stripped out by 3733 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3734 // preserve the CFG and is temporarily leaving constant conditions 3735 // in place. 3736 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3737 if (L->contains(FBB) == !CI->getZExtValue()) 3738 // The backedge is always taken. 3739 return getCouldNotCompute(); 3740 else 3741 // The backedge is never taken. 3742 return getIntegerSCEV(0, CI->getType()); 3743 } 3744 3745 // If it's not an integer or pointer comparison then compute it the hard way. 3746 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3747} 3748 3749/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3750/// backedge of the specified loop will execute if its exit condition 3751/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3752ScalarEvolution::BackedgeTakenInfo 3753ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3754 ICmpInst *ExitCond, 3755 BasicBlock *TBB, 3756 BasicBlock *FBB) { 3757 3758 // If the condition was exit on true, convert the condition to exit on false 3759 ICmpInst::Predicate Cond; 3760 if (!L->contains(FBB)) 3761 Cond = ExitCond->getPredicate(); 3762 else 3763 Cond = ExitCond->getInversePredicate(); 3764 3765 // Handle common loops like: for (X = "string"; *X; ++X) 3766 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3767 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3768 BackedgeTakenInfo ItCnt = 3769 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3770 if (ItCnt.hasAnyInfo()) 3771 return ItCnt; 3772 } 3773 3774 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3775 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3776 3777 // Try to evaluate any dependencies out of the loop. 3778 LHS = getSCEVAtScope(LHS, L); 3779 RHS = getSCEVAtScope(RHS, L); 3780 3781 // At this point, we would like to compute how many iterations of the 3782 // loop the predicate will return true for these inputs. 3783 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3784 // If there is a loop-invariant, force it into the RHS. 3785 std::swap(LHS, RHS); 3786 Cond = ICmpInst::getSwappedPredicate(Cond); 3787 } 3788 3789 // If we have a comparison of a chrec against a constant, try to use value 3790 // ranges to answer this query. 3791 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3792 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3793 if (AddRec->getLoop() == L) { 3794 // Form the constant range. 3795 ConstantRange CompRange( 3796 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3797 3798 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3799 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3800 } 3801 3802 switch (Cond) { 3803 case ICmpInst::ICMP_NE: { // while (X != Y) 3804 // Convert to: while (X-Y != 0) 3805 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3806 if (BTI.hasAnyInfo()) return BTI; 3807 break; 3808 } 3809 case ICmpInst::ICMP_EQ: { // while (X == Y) 3810 // Convert to: while (X-Y == 0) 3811 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3812 if (BTI.hasAnyInfo()) return BTI; 3813 break; 3814 } 3815 case ICmpInst::ICMP_SLT: { 3816 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3817 if (BTI.hasAnyInfo()) return BTI; 3818 break; 3819 } 3820 case ICmpInst::ICMP_SGT: { 3821 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3822 getNotSCEV(RHS), L, true); 3823 if (BTI.hasAnyInfo()) return BTI; 3824 break; 3825 } 3826 case ICmpInst::ICMP_ULT: { 3827 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3828 if (BTI.hasAnyInfo()) return BTI; 3829 break; 3830 } 3831 case ICmpInst::ICMP_UGT: { 3832 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3833 getNotSCEV(RHS), L, false); 3834 if (BTI.hasAnyInfo()) return BTI; 3835 break; 3836 } 3837 default: 3838#if 0 3839 dbgs() << "ComputeBackedgeTakenCount "; 3840 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3841 dbgs() << "[unsigned] "; 3842 dbgs() << *LHS << " " 3843 << Instruction::getOpcodeName(Instruction::ICmp) 3844 << " " << *RHS << "\n"; 3845#endif 3846 break; 3847 } 3848 return 3849 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3850} 3851 3852static ConstantInt * 3853EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3854 ScalarEvolution &SE) { 3855 const SCEV *InVal = SE.getConstant(C); 3856 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3857 assert(isa<SCEVConstant>(Val) && 3858 "Evaluation of SCEV at constant didn't fold correctly?"); 3859 return cast<SCEVConstant>(Val)->getValue(); 3860} 3861 3862/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3863/// and a GEP expression (missing the pointer index) indexing into it, return 3864/// the addressed element of the initializer or null if the index expression is 3865/// invalid. 3866static Constant * 3867GetAddressedElementFromGlobal(GlobalVariable *GV, 3868 const std::vector<ConstantInt*> &Indices) { 3869 Constant *Init = GV->getInitializer(); 3870 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3871 uint64_t Idx = Indices[i]->getZExtValue(); 3872 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3873 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3874 Init = cast<Constant>(CS->getOperand(Idx)); 3875 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3876 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3877 Init = cast<Constant>(CA->getOperand(Idx)); 3878 } else if (isa<ConstantAggregateZero>(Init)) { 3879 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3880 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3881 Init = Constant::getNullValue(STy->getElementType(Idx)); 3882 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3883 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3884 Init = Constant::getNullValue(ATy->getElementType()); 3885 } else { 3886 llvm_unreachable("Unknown constant aggregate type!"); 3887 } 3888 return 0; 3889 } else { 3890 return 0; // Unknown initializer type 3891 } 3892 } 3893 return Init; 3894} 3895 3896/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3897/// 'icmp op load X, cst', try to see if we can compute the backedge 3898/// execution count. 3899ScalarEvolution::BackedgeTakenInfo 3900ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3901 LoadInst *LI, 3902 Constant *RHS, 3903 const Loop *L, 3904 ICmpInst::Predicate predicate) { 3905 if (LI->isVolatile()) return getCouldNotCompute(); 3906 3907 // Check to see if the loaded pointer is a getelementptr of a global. 3908 // TODO: Use SCEV instead of manually grubbing with GEPs. 3909 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3910 if (!GEP) return getCouldNotCompute(); 3911 3912 // Make sure that it is really a constant global we are gepping, with an 3913 // initializer, and make sure the first IDX is really 0. 3914 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3915 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3916 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3917 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3918 return getCouldNotCompute(); 3919 3920 // Okay, we allow one non-constant index into the GEP instruction. 3921 Value *VarIdx = 0; 3922 std::vector<ConstantInt*> Indexes; 3923 unsigned VarIdxNum = 0; 3924 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3925 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3926 Indexes.push_back(CI); 3927 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3928 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3929 VarIdx = GEP->getOperand(i); 3930 VarIdxNum = i-2; 3931 Indexes.push_back(0); 3932 } 3933 3934 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3935 // Check to see if X is a loop variant variable value now. 3936 const SCEV *Idx = getSCEV(VarIdx); 3937 Idx = getSCEVAtScope(Idx, L); 3938 3939 // We can only recognize very limited forms of loop index expressions, in 3940 // particular, only affine AddRec's like {C1,+,C2}. 3941 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3942 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3943 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3944 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3945 return getCouldNotCompute(); 3946 3947 unsigned MaxSteps = MaxBruteForceIterations; 3948 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3949 ConstantInt *ItCst = ConstantInt::get( 3950 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3951 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3952 3953 // Form the GEP offset. 3954 Indexes[VarIdxNum] = Val; 3955 3956 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3957 if (Result == 0) break; // Cannot compute! 3958 3959 // Evaluate the condition for this iteration. 3960 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3961 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3962 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3963#if 0 3964 dbgs() << "\n***\n*** Computed loop count " << *ItCst 3965 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3966 << "***\n"; 3967#endif 3968 ++NumArrayLenItCounts; 3969 return getConstant(ItCst); // Found terminating iteration! 3970 } 3971 } 3972 return getCouldNotCompute(); 3973} 3974 3975 3976/// CanConstantFold - Return true if we can constant fold an instruction of the 3977/// specified type, assuming that all operands were constants. 3978static bool CanConstantFold(const Instruction *I) { 3979 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3980 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3981 return true; 3982 3983 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3984 if (const Function *F = CI->getCalledFunction()) 3985 return canConstantFoldCallTo(F); 3986 return false; 3987} 3988 3989/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3990/// in the loop that V is derived from. We allow arbitrary operations along the 3991/// way, but the operands of an operation must either be constants or a value 3992/// derived from a constant PHI. If this expression does not fit with these 3993/// constraints, return null. 3994static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3995 // If this is not an instruction, or if this is an instruction outside of the 3996 // loop, it can't be derived from a loop PHI. 3997 Instruction *I = dyn_cast<Instruction>(V); 3998 if (I == 0 || !L->contains(I)) return 0; 3999 4000 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4001 if (L->getHeader() == I->getParent()) 4002 return PN; 4003 else 4004 // We don't currently keep track of the control flow needed to evaluate 4005 // PHIs, so we cannot handle PHIs inside of loops. 4006 return 0; 4007 } 4008 4009 // If we won't be able to constant fold this expression even if the operands 4010 // are constants, return early. 4011 if (!CanConstantFold(I)) return 0; 4012 4013 // Otherwise, we can evaluate this instruction if all of its operands are 4014 // constant or derived from a PHI node themselves. 4015 PHINode *PHI = 0; 4016 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4017 if (!(isa<Constant>(I->getOperand(Op)) || 4018 isa<GlobalValue>(I->getOperand(Op)))) { 4019 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4020 if (P == 0) return 0; // Not evolving from PHI 4021 if (PHI == 0) 4022 PHI = P; 4023 else if (PHI != P) 4024 return 0; // Evolving from multiple different PHIs. 4025 } 4026 4027 // This is a expression evolving from a constant PHI! 4028 return PHI; 4029} 4030 4031/// EvaluateExpression - Given an expression that passes the 4032/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4033/// in the loop has the value PHIVal. If we can't fold this expression for some 4034/// reason, return null. 4035static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4036 const TargetData *TD) { 4037 if (isa<PHINode>(V)) return PHIVal; 4038 if (Constant *C = dyn_cast<Constant>(V)) return C; 4039 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 4040 Instruction *I = cast<Instruction>(V); 4041 4042 std::vector<Constant*> Operands; 4043 Operands.resize(I->getNumOperands()); 4044 4045 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4046 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4047 if (Operands[i] == 0) return 0; 4048 } 4049 4050 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4051 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4052 Operands[1], TD); 4053 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4054 &Operands[0], Operands.size(), TD); 4055} 4056 4057/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4058/// in the header of its containing loop, we know the loop executes a 4059/// constant number of times, and the PHI node is just a recurrence 4060/// involving constants, fold it. 4061Constant * 4062ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4063 const APInt &BEs, 4064 const Loop *L) { 4065 std::map<PHINode*, Constant*>::iterator I = 4066 ConstantEvolutionLoopExitValue.find(PN); 4067 if (I != ConstantEvolutionLoopExitValue.end()) 4068 return I->second; 4069 4070 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 4071 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4072 4073 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4074 4075 // Since the loop is canonicalized, the PHI node must have two entries. One 4076 // entry must be a constant (coming in from outside of the loop), and the 4077 // second must be derived from the same PHI. 4078 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4079 Constant *StartCST = 4080 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4081 if (StartCST == 0) 4082 return RetVal = 0; // Must be a constant. 4083 4084 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4085 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4086 if (PN2 != PN) 4087 return RetVal = 0; // Not derived from same PHI. 4088 4089 // Execute the loop symbolically to determine the exit value. 4090 if (BEs.getActiveBits() >= 32) 4091 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4092 4093 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4094 unsigned IterationNum = 0; 4095 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4096 if (IterationNum == NumIterations) 4097 return RetVal = PHIVal; // Got exit value! 4098 4099 // Compute the value of the PHI node for the next iteration. 4100 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4101 if (NextPHI == PHIVal) 4102 return RetVal = NextPHI; // Stopped evolving! 4103 if (NextPHI == 0) 4104 return 0; // Couldn't evaluate! 4105 PHIVal = NextPHI; 4106 } 4107} 4108 4109/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4110/// constant number of times (the condition evolves only from constants), 4111/// try to evaluate a few iterations of the loop until we get the exit 4112/// condition gets a value of ExitWhen (true or false). If we cannot 4113/// evaluate the trip count of the loop, return getCouldNotCompute(). 4114const SCEV * 4115ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4116 Value *Cond, 4117 bool ExitWhen) { 4118 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4119 if (PN == 0) return getCouldNotCompute(); 4120 4121 // Since the loop is canonicalized, the PHI node must have two entries. One 4122 // entry must be a constant (coming in from outside of the loop), and the 4123 // second must be derived from the same PHI. 4124 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4125 Constant *StartCST = 4126 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4127 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4128 4129 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4130 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4131 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 4132 4133 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4134 // the loop symbolically to determine when the condition gets a value of 4135 // "ExitWhen". 4136 unsigned IterationNum = 0; 4137 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4138 for (Constant *PHIVal = StartCST; 4139 IterationNum != MaxIterations; ++IterationNum) { 4140 ConstantInt *CondVal = 4141 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4142 4143 // Couldn't symbolically evaluate. 4144 if (!CondVal) return getCouldNotCompute(); 4145 4146 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4147 ++NumBruteForceTripCountsComputed; 4148 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4149 } 4150 4151 // Compute the value of the PHI node for the next iteration. 4152 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4153 if (NextPHI == 0 || NextPHI == PHIVal) 4154 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4155 PHIVal = NextPHI; 4156 } 4157 4158 // Too many iterations were needed to evaluate. 4159 return getCouldNotCompute(); 4160} 4161 4162/// getSCEVAtScope - Return a SCEV expression for the specified value 4163/// at the specified scope in the program. The L value specifies a loop 4164/// nest to evaluate the expression at, where null is the top-level or a 4165/// specified loop is immediately inside of the loop. 4166/// 4167/// This method can be used to compute the exit value for a variable defined 4168/// in a loop by querying what the value will hold in the parent loop. 4169/// 4170/// In the case that a relevant loop exit value cannot be computed, the 4171/// original value V is returned. 4172const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4173 // Check to see if we've folded this expression at this loop before. 4174 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4175 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4176 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4177 if (!Pair.second) 4178 return Pair.first->second ? Pair.first->second : V; 4179 4180 // Otherwise compute it. 4181 const SCEV *C = computeSCEVAtScope(V, L); 4182 ValuesAtScopes[V][L] = C; 4183 return C; 4184} 4185 4186const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4187 if (isa<SCEVConstant>(V)) return V; 4188 4189 // If this instruction is evolved from a constant-evolving PHI, compute the 4190 // exit value from the loop without using SCEVs. 4191 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4192 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4193 const Loop *LI = (*this->LI)[I->getParent()]; 4194 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4195 if (PHINode *PN = dyn_cast<PHINode>(I)) 4196 if (PN->getParent() == LI->getHeader()) { 4197 // Okay, there is no closed form solution for the PHI node. Check 4198 // to see if the loop that contains it has a known backedge-taken 4199 // count. If so, we may be able to force computation of the exit 4200 // value. 4201 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4202 if (const SCEVConstant *BTCC = 4203 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4204 // Okay, we know how many times the containing loop executes. If 4205 // this is a constant evolving PHI node, get the final value at 4206 // the specified iteration number. 4207 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4208 BTCC->getValue()->getValue(), 4209 LI); 4210 if (RV) return getSCEV(RV); 4211 } 4212 } 4213 4214 // Okay, this is an expression that we cannot symbolically evaluate 4215 // into a SCEV. Check to see if it's possible to symbolically evaluate 4216 // the arguments into constants, and if so, try to constant propagate the 4217 // result. This is particularly useful for computing loop exit values. 4218 if (CanConstantFold(I)) { 4219 std::vector<Constant*> Operands; 4220 Operands.reserve(I->getNumOperands()); 4221 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4222 Value *Op = I->getOperand(i); 4223 if (Constant *C = dyn_cast<Constant>(Op)) { 4224 Operands.push_back(C); 4225 } else { 4226 // If any of the operands is non-constant and if they are 4227 // non-integer and non-pointer, don't even try to analyze them 4228 // with scev techniques. 4229 if (!isSCEVable(Op->getType())) 4230 return V; 4231 4232 const SCEV *OpV = getSCEVAtScope(Op, L); 4233 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4234 Constant *C = SC->getValue(); 4235 if (C->getType() != Op->getType()) 4236 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4237 Op->getType(), 4238 false), 4239 C, Op->getType()); 4240 Operands.push_back(C); 4241 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4242 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4243 if (C->getType() != Op->getType()) 4244 C = 4245 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4246 Op->getType(), 4247 false), 4248 C, Op->getType()); 4249 Operands.push_back(C); 4250 } else 4251 return V; 4252 } else { 4253 return V; 4254 } 4255 } 4256 } 4257 4258 Constant *C = 0; 4259 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4260 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4261 Operands[0], Operands[1], TD); 4262 else 4263 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4264 &Operands[0], Operands.size(), TD); 4265 if (C) 4266 return getSCEV(C); 4267 } 4268 } 4269 4270 // This is some other type of SCEVUnknown, just return it. 4271 return V; 4272 } 4273 4274 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4275 // Avoid performing the look-up in the common case where the specified 4276 // expression has no loop-variant portions. 4277 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4278 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4279 if (OpAtScope != Comm->getOperand(i)) { 4280 // Okay, at least one of these operands is loop variant but might be 4281 // foldable. Build a new instance of the folded commutative expression. 4282 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4283 Comm->op_begin()+i); 4284 NewOps.push_back(OpAtScope); 4285 4286 for (++i; i != e; ++i) { 4287 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4288 NewOps.push_back(OpAtScope); 4289 } 4290 if (isa<SCEVAddExpr>(Comm)) 4291 return getAddExpr(NewOps); 4292 if (isa<SCEVMulExpr>(Comm)) 4293 return getMulExpr(NewOps); 4294 if (isa<SCEVSMaxExpr>(Comm)) 4295 return getSMaxExpr(NewOps); 4296 if (isa<SCEVUMaxExpr>(Comm)) 4297 return getUMaxExpr(NewOps); 4298 llvm_unreachable("Unknown commutative SCEV type!"); 4299 } 4300 } 4301 // If we got here, all operands are loop invariant. 4302 return Comm; 4303 } 4304 4305 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4306 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4307 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4308 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4309 return Div; // must be loop invariant 4310 return getUDivExpr(LHS, RHS); 4311 } 4312 4313 // If this is a loop recurrence for a loop that does not contain L, then we 4314 // are dealing with the final value computed by the loop. 4315 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4316 if (!L || !AddRec->getLoop()->contains(L)) { 4317 // To evaluate this recurrence, we need to know how many times the AddRec 4318 // loop iterates. Compute this now. 4319 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4320 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4321 4322 // Then, evaluate the AddRec. 4323 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4324 } 4325 return AddRec; 4326 } 4327 4328 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4329 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4330 if (Op == Cast->getOperand()) 4331 return Cast; // must be loop invariant 4332 return getZeroExtendExpr(Op, Cast->getType()); 4333 } 4334 4335 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4336 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4337 if (Op == Cast->getOperand()) 4338 return Cast; // must be loop invariant 4339 return getSignExtendExpr(Op, Cast->getType()); 4340 } 4341 4342 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4343 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4344 if (Op == Cast->getOperand()) 4345 return Cast; // must be loop invariant 4346 return getTruncateExpr(Op, Cast->getType()); 4347 } 4348 4349 llvm_unreachable("Unknown SCEV type!"); 4350 return 0; 4351} 4352 4353/// getSCEVAtScope - This is a convenience function which does 4354/// getSCEVAtScope(getSCEV(V), L). 4355const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4356 return getSCEVAtScope(getSCEV(V), L); 4357} 4358 4359/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4360/// following equation: 4361/// 4362/// A * X = B (mod N) 4363/// 4364/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4365/// A and B isn't important. 4366/// 4367/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4368static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4369 ScalarEvolution &SE) { 4370 uint32_t BW = A.getBitWidth(); 4371 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4372 assert(A != 0 && "A must be non-zero."); 4373 4374 // 1. D = gcd(A, N) 4375 // 4376 // The gcd of A and N may have only one prime factor: 2. The number of 4377 // trailing zeros in A is its multiplicity 4378 uint32_t Mult2 = A.countTrailingZeros(); 4379 // D = 2^Mult2 4380 4381 // 2. Check if B is divisible by D. 4382 // 4383 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4384 // is not less than multiplicity of this prime factor for D. 4385 if (B.countTrailingZeros() < Mult2) 4386 return SE.getCouldNotCompute(); 4387 4388 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4389 // modulo (N / D). 4390 // 4391 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4392 // bit width during computations. 4393 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4394 APInt Mod(BW + 1, 0); 4395 Mod.set(BW - Mult2); // Mod = N / D 4396 APInt I = AD.multiplicativeInverse(Mod); 4397 4398 // 4. Compute the minimum unsigned root of the equation: 4399 // I * (B / D) mod (N / D) 4400 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4401 4402 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4403 // bits. 4404 return SE.getConstant(Result.trunc(BW)); 4405} 4406 4407/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4408/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4409/// might be the same) or two SCEVCouldNotCompute objects. 4410/// 4411static std::pair<const SCEV *,const SCEV *> 4412SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4413 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4414 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4415 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4416 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4417 4418 // We currently can only solve this if the coefficients are constants. 4419 if (!LC || !MC || !NC) { 4420 const SCEV *CNC = SE.getCouldNotCompute(); 4421 return std::make_pair(CNC, CNC); 4422 } 4423 4424 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4425 const APInt &L = LC->getValue()->getValue(); 4426 const APInt &M = MC->getValue()->getValue(); 4427 const APInt &N = NC->getValue()->getValue(); 4428 APInt Two(BitWidth, 2); 4429 APInt Four(BitWidth, 4); 4430 4431 { 4432 using namespace APIntOps; 4433 const APInt& C = L; 4434 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4435 // The B coefficient is M-N/2 4436 APInt B(M); 4437 B -= sdiv(N,Two); 4438 4439 // The A coefficient is N/2 4440 APInt A(N.sdiv(Two)); 4441 4442 // Compute the B^2-4ac term. 4443 APInt SqrtTerm(B); 4444 SqrtTerm *= B; 4445 SqrtTerm -= Four * (A * C); 4446 4447 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4448 // integer value or else APInt::sqrt() will assert. 4449 APInt SqrtVal(SqrtTerm.sqrt()); 4450 4451 // Compute the two solutions for the quadratic formula. 4452 // The divisions must be performed as signed divisions. 4453 APInt NegB(-B); 4454 APInt TwoA( A << 1 ); 4455 if (TwoA.isMinValue()) { 4456 const SCEV *CNC = SE.getCouldNotCompute(); 4457 return std::make_pair(CNC, CNC); 4458 } 4459 4460 LLVMContext &Context = SE.getContext(); 4461 4462 ConstantInt *Solution1 = 4463 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4464 ConstantInt *Solution2 = 4465 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4466 4467 return std::make_pair(SE.getConstant(Solution1), 4468 SE.getConstant(Solution2)); 4469 } // end APIntOps namespace 4470} 4471 4472/// HowFarToZero - Return the number of times a backedge comparing the specified 4473/// value to zero will execute. If not computable, return CouldNotCompute. 4474ScalarEvolution::BackedgeTakenInfo 4475ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4476 // If the value is a constant 4477 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4478 // If the value is already zero, the branch will execute zero times. 4479 if (C->getValue()->isZero()) return C; 4480 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4481 } 4482 4483 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4484 if (!AddRec || AddRec->getLoop() != L) 4485 return getCouldNotCompute(); 4486 4487 if (AddRec->isAffine()) { 4488 // If this is an affine expression, the execution count of this branch is 4489 // the minimum unsigned root of the following equation: 4490 // 4491 // Start + Step*N = 0 (mod 2^BW) 4492 // 4493 // equivalent to: 4494 // 4495 // Step*N = -Start (mod 2^BW) 4496 // 4497 // where BW is the common bit width of Start and Step. 4498 4499 // Get the initial value for the loop. 4500 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4501 L->getParentLoop()); 4502 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4503 L->getParentLoop()); 4504 4505 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4506 // For now we handle only constant steps. 4507 4508 // First, handle unitary steps. 4509 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4510 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4511 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4512 return Start; // N = Start (as unsigned) 4513 4514 // Then, try to solve the above equation provided that Start is constant. 4515 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4516 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4517 -StartC->getValue()->getValue(), 4518 *this); 4519 } 4520 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4521 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4522 // the quadratic equation to solve it. 4523 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4524 *this); 4525 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4526 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4527 if (R1) { 4528#if 0 4529 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4530 << " sol#2: " << *R2 << "\n"; 4531#endif 4532 // Pick the smallest positive root value. 4533 if (ConstantInt *CB = 4534 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4535 R1->getValue(), R2->getValue()))) { 4536 if (CB->getZExtValue() == false) 4537 std::swap(R1, R2); // R1 is the minimum root now. 4538 4539 // We can only use this value if the chrec ends up with an exact zero 4540 // value at this index. When solving for "X*X != 5", for example, we 4541 // should not accept a root of 2. 4542 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4543 if (Val->isZero()) 4544 return R1; // We found a quadratic root! 4545 } 4546 } 4547 } 4548 4549 return getCouldNotCompute(); 4550} 4551 4552/// HowFarToNonZero - Return the number of times a backedge checking the 4553/// specified value for nonzero will execute. If not computable, return 4554/// CouldNotCompute 4555ScalarEvolution::BackedgeTakenInfo 4556ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4557 // Loops that look like: while (X == 0) are very strange indeed. We don't 4558 // handle them yet except for the trivial case. This could be expanded in the 4559 // future as needed. 4560 4561 // If the value is a constant, check to see if it is known to be non-zero 4562 // already. If so, the backedge will execute zero times. 4563 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4564 if (!C->getValue()->isNullValue()) 4565 return getIntegerSCEV(0, C->getType()); 4566 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4567 } 4568 4569 // We could implement others, but I really doubt anyone writes loops like 4570 // this, and if they did, they would already be constant folded. 4571 return getCouldNotCompute(); 4572} 4573 4574/// getLoopPredecessor - If the given loop's header has exactly one unique 4575/// predecessor outside the loop, return it. Otherwise return null. 4576/// 4577BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4578 BasicBlock *Header = L->getHeader(); 4579 BasicBlock *Pred = 0; 4580 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4581 PI != E; ++PI) 4582 if (!L->contains(*PI)) { 4583 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4584 Pred = *PI; 4585 } 4586 return Pred; 4587} 4588 4589/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4590/// (which may not be an immediate predecessor) which has exactly one 4591/// successor from which BB is reachable, or null if no such block is 4592/// found. 4593/// 4594BasicBlock * 4595ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4596 // If the block has a unique predecessor, then there is no path from the 4597 // predecessor to the block that does not go through the direct edge 4598 // from the predecessor to the block. 4599 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4600 return Pred; 4601 4602 // A loop's header is defined to be a block that dominates the loop. 4603 // If the header has a unique predecessor outside the loop, it must be 4604 // a block that has exactly one successor that can reach the loop. 4605 if (Loop *L = LI->getLoopFor(BB)) 4606 return getLoopPredecessor(L); 4607 4608 return 0; 4609} 4610 4611/// HasSameValue - SCEV structural equivalence is usually sufficient for 4612/// testing whether two expressions are equal, however for the purposes of 4613/// looking for a condition guarding a loop, it can be useful to be a little 4614/// more general, since a front-end may have replicated the controlling 4615/// expression. 4616/// 4617static bool HasSameValue(const SCEV *A, const SCEV *B) { 4618 // Quick check to see if they are the same SCEV. 4619 if (A == B) return true; 4620 4621 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4622 // two different instructions with the same value. Check for this case. 4623 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4624 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4625 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4626 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4627 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4628 return true; 4629 4630 // Otherwise assume they may have a different value. 4631 return false; 4632} 4633 4634bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4635 return getSignedRange(S).getSignedMax().isNegative(); 4636} 4637 4638bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4639 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4640} 4641 4642bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4643 return !getSignedRange(S).getSignedMin().isNegative(); 4644} 4645 4646bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4647 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4648} 4649 4650bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4651 return isKnownNegative(S) || isKnownPositive(S); 4652} 4653 4654bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4655 const SCEV *LHS, const SCEV *RHS) { 4656 4657 if (HasSameValue(LHS, RHS)) 4658 return ICmpInst::isTrueWhenEqual(Pred); 4659 4660 switch (Pred) { 4661 default: 4662 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4663 break; 4664 case ICmpInst::ICMP_SGT: 4665 Pred = ICmpInst::ICMP_SLT; 4666 std::swap(LHS, RHS); 4667 case ICmpInst::ICMP_SLT: { 4668 ConstantRange LHSRange = getSignedRange(LHS); 4669 ConstantRange RHSRange = getSignedRange(RHS); 4670 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4671 return true; 4672 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4673 return false; 4674 break; 4675 } 4676 case ICmpInst::ICMP_SGE: 4677 Pred = ICmpInst::ICMP_SLE; 4678 std::swap(LHS, RHS); 4679 case ICmpInst::ICMP_SLE: { 4680 ConstantRange LHSRange = getSignedRange(LHS); 4681 ConstantRange RHSRange = getSignedRange(RHS); 4682 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4683 return true; 4684 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4685 return false; 4686 break; 4687 } 4688 case ICmpInst::ICMP_UGT: 4689 Pred = ICmpInst::ICMP_ULT; 4690 std::swap(LHS, RHS); 4691 case ICmpInst::ICMP_ULT: { 4692 ConstantRange LHSRange = getUnsignedRange(LHS); 4693 ConstantRange RHSRange = getUnsignedRange(RHS); 4694 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4695 return true; 4696 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4697 return false; 4698 break; 4699 } 4700 case ICmpInst::ICMP_UGE: 4701 Pred = ICmpInst::ICMP_ULE; 4702 std::swap(LHS, RHS); 4703 case ICmpInst::ICMP_ULE: { 4704 ConstantRange LHSRange = getUnsignedRange(LHS); 4705 ConstantRange RHSRange = getUnsignedRange(RHS); 4706 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4707 return true; 4708 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4709 return false; 4710 break; 4711 } 4712 case ICmpInst::ICMP_NE: { 4713 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4714 return true; 4715 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4716 return true; 4717 4718 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4719 if (isKnownNonZero(Diff)) 4720 return true; 4721 break; 4722 } 4723 case ICmpInst::ICMP_EQ: 4724 // The check at the top of the function catches the case where 4725 // the values are known to be equal. 4726 break; 4727 } 4728 return false; 4729} 4730 4731/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4732/// protected by a conditional between LHS and RHS. This is used to 4733/// to eliminate casts. 4734bool 4735ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4736 ICmpInst::Predicate Pred, 4737 const SCEV *LHS, const SCEV *RHS) { 4738 // Interpret a null as meaning no loop, where there is obviously no guard 4739 // (interprocedural conditions notwithstanding). 4740 if (!L) return true; 4741 4742 BasicBlock *Latch = L->getLoopLatch(); 4743 if (!Latch) 4744 return false; 4745 4746 BranchInst *LoopContinuePredicate = 4747 dyn_cast<BranchInst>(Latch->getTerminator()); 4748 if (!LoopContinuePredicate || 4749 LoopContinuePredicate->isUnconditional()) 4750 return false; 4751 4752 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4753 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4754} 4755 4756/// isLoopGuardedByCond - Test whether entry to the loop is protected 4757/// by a conditional between LHS and RHS. This is used to help avoid max 4758/// expressions in loop trip counts, and to eliminate casts. 4759bool 4760ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4761 ICmpInst::Predicate Pred, 4762 const SCEV *LHS, const SCEV *RHS) { 4763 // Interpret a null as meaning no loop, where there is obviously no guard 4764 // (interprocedural conditions notwithstanding). 4765 if (!L) return false; 4766 4767 BasicBlock *Predecessor = getLoopPredecessor(L); 4768 BasicBlock *PredecessorDest = L->getHeader(); 4769 4770 // Starting at the loop predecessor, climb up the predecessor chain, as long 4771 // as there are predecessors that can be found that have unique successors 4772 // leading to the original header. 4773 for (; Predecessor; 4774 PredecessorDest = Predecessor, 4775 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4776 4777 BranchInst *LoopEntryPredicate = 4778 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4779 if (!LoopEntryPredicate || 4780 LoopEntryPredicate->isUnconditional()) 4781 continue; 4782 4783 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4784 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4785 return true; 4786 } 4787 4788 return false; 4789} 4790 4791/// isImpliedCond - Test whether the condition described by Pred, LHS, 4792/// and RHS is true whenever the given Cond value evaluates to true. 4793bool ScalarEvolution::isImpliedCond(Value *CondValue, 4794 ICmpInst::Predicate Pred, 4795 const SCEV *LHS, const SCEV *RHS, 4796 bool Inverse) { 4797 // Recursively handle And and Or conditions. 4798 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4799 if (BO->getOpcode() == Instruction::And) { 4800 if (!Inverse) 4801 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4802 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4803 } else if (BO->getOpcode() == Instruction::Or) { 4804 if (Inverse) 4805 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4806 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4807 } 4808 } 4809 4810 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4811 if (!ICI) return false; 4812 4813 // Bail if the ICmp's operands' types are wider than the needed type 4814 // before attempting to call getSCEV on them. This avoids infinite 4815 // recursion, since the analysis of widening casts can require loop 4816 // exit condition information for overflow checking, which would 4817 // lead back here. 4818 if (getTypeSizeInBits(LHS->getType()) < 4819 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4820 return false; 4821 4822 // Now that we found a conditional branch that dominates the loop, check to 4823 // see if it is the comparison we are looking for. 4824 ICmpInst::Predicate FoundPred; 4825 if (Inverse) 4826 FoundPred = ICI->getInversePredicate(); 4827 else 4828 FoundPred = ICI->getPredicate(); 4829 4830 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4831 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4832 4833 // Balance the types. The case where FoundLHS' type is wider than 4834 // LHS' type is checked for above. 4835 if (getTypeSizeInBits(LHS->getType()) > 4836 getTypeSizeInBits(FoundLHS->getType())) { 4837 if (CmpInst::isSigned(Pred)) { 4838 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4839 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4840 } else { 4841 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4842 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4843 } 4844 } 4845 4846 // Canonicalize the query to match the way instcombine will have 4847 // canonicalized the comparison. 4848 // First, put a constant operand on the right. 4849 if (isa<SCEVConstant>(LHS)) { 4850 std::swap(LHS, RHS); 4851 Pred = ICmpInst::getSwappedPredicate(Pred); 4852 } 4853 // Then, canonicalize comparisons with boundary cases. 4854 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4855 const APInt &RA = RC->getValue()->getValue(); 4856 switch (Pred) { 4857 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4858 case ICmpInst::ICMP_EQ: 4859 case ICmpInst::ICMP_NE: 4860 break; 4861 case ICmpInst::ICMP_UGE: 4862 if ((RA - 1).isMinValue()) { 4863 Pred = ICmpInst::ICMP_NE; 4864 RHS = getConstant(RA - 1); 4865 break; 4866 } 4867 if (RA.isMaxValue()) { 4868 Pred = ICmpInst::ICMP_EQ; 4869 break; 4870 } 4871 if (RA.isMinValue()) return true; 4872 break; 4873 case ICmpInst::ICMP_ULE: 4874 if ((RA + 1).isMaxValue()) { 4875 Pred = ICmpInst::ICMP_NE; 4876 RHS = getConstant(RA + 1); 4877 break; 4878 } 4879 if (RA.isMinValue()) { 4880 Pred = ICmpInst::ICMP_EQ; 4881 break; 4882 } 4883 if (RA.isMaxValue()) return true; 4884 break; 4885 case ICmpInst::ICMP_SGE: 4886 if ((RA - 1).isMinSignedValue()) { 4887 Pred = ICmpInst::ICMP_NE; 4888 RHS = getConstant(RA - 1); 4889 break; 4890 } 4891 if (RA.isMaxSignedValue()) { 4892 Pred = ICmpInst::ICMP_EQ; 4893 break; 4894 } 4895 if (RA.isMinSignedValue()) return true; 4896 break; 4897 case ICmpInst::ICMP_SLE: 4898 if ((RA + 1).isMaxSignedValue()) { 4899 Pred = ICmpInst::ICMP_NE; 4900 RHS = getConstant(RA + 1); 4901 break; 4902 } 4903 if (RA.isMinSignedValue()) { 4904 Pred = ICmpInst::ICMP_EQ; 4905 break; 4906 } 4907 if (RA.isMaxSignedValue()) return true; 4908 break; 4909 case ICmpInst::ICMP_UGT: 4910 if (RA.isMinValue()) { 4911 Pred = ICmpInst::ICMP_NE; 4912 break; 4913 } 4914 if ((RA + 1).isMaxValue()) { 4915 Pred = ICmpInst::ICMP_EQ; 4916 RHS = getConstant(RA + 1); 4917 break; 4918 } 4919 if (RA.isMaxValue()) return false; 4920 break; 4921 case ICmpInst::ICMP_ULT: 4922 if (RA.isMaxValue()) { 4923 Pred = ICmpInst::ICMP_NE; 4924 break; 4925 } 4926 if ((RA - 1).isMinValue()) { 4927 Pred = ICmpInst::ICMP_EQ; 4928 RHS = getConstant(RA - 1); 4929 break; 4930 } 4931 if (RA.isMinValue()) return false; 4932 break; 4933 case ICmpInst::ICMP_SGT: 4934 if (RA.isMinSignedValue()) { 4935 Pred = ICmpInst::ICMP_NE; 4936 break; 4937 } 4938 if ((RA + 1).isMaxSignedValue()) { 4939 Pred = ICmpInst::ICMP_EQ; 4940 RHS = getConstant(RA + 1); 4941 break; 4942 } 4943 if (RA.isMaxSignedValue()) return false; 4944 break; 4945 case ICmpInst::ICMP_SLT: 4946 if (RA.isMaxSignedValue()) { 4947 Pred = ICmpInst::ICMP_NE; 4948 break; 4949 } 4950 if ((RA - 1).isMinSignedValue()) { 4951 Pred = ICmpInst::ICMP_EQ; 4952 RHS = getConstant(RA - 1); 4953 break; 4954 } 4955 if (RA.isMinSignedValue()) return false; 4956 break; 4957 } 4958 } 4959 4960 // Check to see if we can make the LHS or RHS match. 4961 if (LHS == FoundRHS || RHS == FoundLHS) { 4962 if (isa<SCEVConstant>(RHS)) { 4963 std::swap(FoundLHS, FoundRHS); 4964 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4965 } else { 4966 std::swap(LHS, RHS); 4967 Pred = ICmpInst::getSwappedPredicate(Pred); 4968 } 4969 } 4970 4971 // Check whether the found predicate is the same as the desired predicate. 4972 if (FoundPred == Pred) 4973 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4974 4975 // Check whether swapping the found predicate makes it the same as the 4976 // desired predicate. 4977 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4978 if (isa<SCEVConstant>(RHS)) 4979 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4980 else 4981 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4982 RHS, LHS, FoundLHS, FoundRHS); 4983 } 4984 4985 // Check whether the actual condition is beyond sufficient. 4986 if (FoundPred == ICmpInst::ICMP_EQ) 4987 if (ICmpInst::isTrueWhenEqual(Pred)) 4988 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4989 return true; 4990 if (Pred == ICmpInst::ICMP_NE) 4991 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4992 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4993 return true; 4994 4995 // Otherwise assume the worst. 4996 return false; 4997} 4998 4999/// isImpliedCondOperands - Test whether the condition described by Pred, 5000/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5001/// and FoundRHS is true. 5002bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5003 const SCEV *LHS, const SCEV *RHS, 5004 const SCEV *FoundLHS, 5005 const SCEV *FoundRHS) { 5006 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5007 FoundLHS, FoundRHS) || 5008 // ~x < ~y --> x > y 5009 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5010 getNotSCEV(FoundRHS), 5011 getNotSCEV(FoundLHS)); 5012} 5013 5014/// isImpliedCondOperandsHelper - Test whether the condition described by 5015/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5016/// FoundLHS, and FoundRHS is true. 5017bool 5018ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5019 const SCEV *LHS, const SCEV *RHS, 5020 const SCEV *FoundLHS, 5021 const SCEV *FoundRHS) { 5022 switch (Pred) { 5023 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5024 case ICmpInst::ICMP_EQ: 5025 case ICmpInst::ICMP_NE: 5026 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5027 return true; 5028 break; 5029 case ICmpInst::ICMP_SLT: 5030 case ICmpInst::ICMP_SLE: 5031 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5032 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5033 return true; 5034 break; 5035 case ICmpInst::ICMP_SGT: 5036 case ICmpInst::ICMP_SGE: 5037 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5038 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5039 return true; 5040 break; 5041 case ICmpInst::ICMP_ULT: 5042 case ICmpInst::ICMP_ULE: 5043 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5044 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5045 return true; 5046 break; 5047 case ICmpInst::ICMP_UGT: 5048 case ICmpInst::ICMP_UGE: 5049 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5050 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5051 return true; 5052 break; 5053 } 5054 5055 return false; 5056} 5057 5058/// getBECount - Subtract the end and start values and divide by the step, 5059/// rounding up, to get the number of times the backedge is executed. Return 5060/// CouldNotCompute if an intermediate computation overflows. 5061const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5062 const SCEV *End, 5063 const SCEV *Step, 5064 bool NoWrap) { 5065 assert(!isKnownNegative(Step) && 5066 "This code doesn't handle negative strides yet!"); 5067 5068 const Type *Ty = Start->getType(); 5069 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 5070 const SCEV *Diff = getMinusSCEV(End, Start); 5071 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5072 5073 // Add an adjustment to the difference between End and Start so that 5074 // the division will effectively round up. 5075 const SCEV *Add = getAddExpr(Diff, RoundUp); 5076 5077 if (!NoWrap) { 5078 // Check Add for unsigned overflow. 5079 // TODO: More sophisticated things could be done here. 5080 const Type *WideTy = IntegerType::get(getContext(), 5081 getTypeSizeInBits(Ty) + 1); 5082 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5083 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5084 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5085 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5086 return getCouldNotCompute(); 5087 } 5088 5089 return getUDivExpr(Add, Step); 5090} 5091 5092/// HowManyLessThans - Return the number of times a backedge containing the 5093/// specified less-than comparison will execute. If not computable, return 5094/// CouldNotCompute. 5095ScalarEvolution::BackedgeTakenInfo 5096ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5097 const Loop *L, bool isSigned) { 5098 // Only handle: "ADDREC < LoopInvariant". 5099 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5100 5101 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5102 if (!AddRec || AddRec->getLoop() != L) 5103 return getCouldNotCompute(); 5104 5105 // Check to see if we have a flag which makes analysis easy. 5106 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5107 AddRec->hasNoUnsignedWrap(); 5108 5109 if (AddRec->isAffine()) { 5110 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5111 const SCEV *Step = AddRec->getStepRecurrence(*this); 5112 5113 if (Step->isZero()) 5114 return getCouldNotCompute(); 5115 if (Step->isOne()) { 5116 // With unit stride, the iteration never steps past the limit value. 5117 } else if (isKnownPositive(Step)) { 5118 // Test whether a positive iteration can step past the limit 5119 // value and past the maximum value for its type in a single step. 5120 // Note that it's not sufficient to check NoWrap here, because even 5121 // though the value after a wrap is undefined, it's not undefined 5122 // behavior, so if wrap does occur, the loop could either terminate or 5123 // loop infinitely, but in either case, the loop is guaranteed to 5124 // iterate at least until the iteration where the wrapping occurs. 5125 const SCEV *One = getIntegerSCEV(1, Step->getType()); 5126 if (isSigned) { 5127 APInt Max = APInt::getSignedMaxValue(BitWidth); 5128 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5129 .slt(getSignedRange(RHS).getSignedMax())) 5130 return getCouldNotCompute(); 5131 } else { 5132 APInt Max = APInt::getMaxValue(BitWidth); 5133 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5134 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5135 return getCouldNotCompute(); 5136 } 5137 } else 5138 // TODO: Handle negative strides here and below. 5139 return getCouldNotCompute(); 5140 5141 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5142 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5143 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5144 // treat m-n as signed nor unsigned due to overflow possibility. 5145 5146 // First, we get the value of the LHS in the first iteration: n 5147 const SCEV *Start = AddRec->getOperand(0); 5148 5149 // Determine the minimum constant start value. 5150 const SCEV *MinStart = getConstant(isSigned ? 5151 getSignedRange(Start).getSignedMin() : 5152 getUnsignedRange(Start).getUnsignedMin()); 5153 5154 // If we know that the condition is true in order to enter the loop, 5155 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5156 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5157 // the division must round up. 5158 const SCEV *End = RHS; 5159 if (!isLoopGuardedByCond(L, 5160 isSigned ? ICmpInst::ICMP_SLT : 5161 ICmpInst::ICMP_ULT, 5162 getMinusSCEV(Start, Step), RHS)) 5163 End = isSigned ? getSMaxExpr(RHS, Start) 5164 : getUMaxExpr(RHS, Start); 5165 5166 // Determine the maximum constant end value. 5167 const SCEV *MaxEnd = getConstant(isSigned ? 5168 getSignedRange(End).getSignedMax() : 5169 getUnsignedRange(End).getUnsignedMax()); 5170 5171 // If MaxEnd is within a step of the maximum integer value in its type, 5172 // adjust it down to the minimum value which would produce the same effect. 5173 // This allows the subsequent ceiling division of (N+(step-1))/step to 5174 // compute the correct value. 5175 const SCEV *StepMinusOne = getMinusSCEV(Step, 5176 getIntegerSCEV(1, Step->getType())); 5177 MaxEnd = isSigned ? 5178 getSMinExpr(MaxEnd, 5179 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5180 StepMinusOne)) : 5181 getUMinExpr(MaxEnd, 5182 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5183 StepMinusOne)); 5184 5185 // Finally, we subtract these two values and divide, rounding up, to get 5186 // the number of times the backedge is executed. 5187 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5188 5189 // The maximum backedge count is similar, except using the minimum start 5190 // value and the maximum end value. 5191 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5192 5193 return BackedgeTakenInfo(BECount, MaxBECount); 5194 } 5195 5196 return getCouldNotCompute(); 5197} 5198 5199/// getNumIterationsInRange - Return the number of iterations of this loop that 5200/// produce values in the specified constant range. Another way of looking at 5201/// this is that it returns the first iteration number where the value is not in 5202/// the condition, thus computing the exit count. If the iteration count can't 5203/// be computed, an instance of SCEVCouldNotCompute is returned. 5204const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5205 ScalarEvolution &SE) const { 5206 if (Range.isFullSet()) // Infinite loop. 5207 return SE.getCouldNotCompute(); 5208 5209 // If the start is a non-zero constant, shift the range to simplify things. 5210 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5211 if (!SC->getValue()->isZero()) { 5212 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5213 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 5214 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5215 if (const SCEVAddRecExpr *ShiftedAddRec = 5216 dyn_cast<SCEVAddRecExpr>(Shifted)) 5217 return ShiftedAddRec->getNumIterationsInRange( 5218 Range.subtract(SC->getValue()->getValue()), SE); 5219 // This is strange and shouldn't happen. 5220 return SE.getCouldNotCompute(); 5221 } 5222 5223 // The only time we can solve this is when we have all constant indices. 5224 // Otherwise, we cannot determine the overflow conditions. 5225 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5226 if (!isa<SCEVConstant>(getOperand(i))) 5227 return SE.getCouldNotCompute(); 5228 5229 5230 // Okay at this point we know that all elements of the chrec are constants and 5231 // that the start element is zero. 5232 5233 // First check to see if the range contains zero. If not, the first 5234 // iteration exits. 5235 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5236 if (!Range.contains(APInt(BitWidth, 0))) 5237 return SE.getIntegerSCEV(0, getType()); 5238 5239 if (isAffine()) { 5240 // If this is an affine expression then we have this situation: 5241 // Solve {0,+,A} in Range === Ax in Range 5242 5243 // We know that zero is in the range. If A is positive then we know that 5244 // the upper value of the range must be the first possible exit value. 5245 // If A is negative then the lower of the range is the last possible loop 5246 // value. Also note that we already checked for a full range. 5247 APInt One(BitWidth,1); 5248 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5249 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5250 5251 // The exit value should be (End+A)/A. 5252 APInt ExitVal = (End + A).udiv(A); 5253 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5254 5255 // Evaluate at the exit value. If we really did fall out of the valid 5256 // range, then we computed our trip count, otherwise wrap around or other 5257 // things must have happened. 5258 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5259 if (Range.contains(Val->getValue())) 5260 return SE.getCouldNotCompute(); // Something strange happened 5261 5262 // Ensure that the previous value is in the range. This is a sanity check. 5263 assert(Range.contains( 5264 EvaluateConstantChrecAtConstant(this, 5265 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5266 "Linear scev computation is off in a bad way!"); 5267 return SE.getConstant(ExitValue); 5268 } else if (isQuadratic()) { 5269 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5270 // quadratic equation to solve it. To do this, we must frame our problem in 5271 // terms of figuring out when zero is crossed, instead of when 5272 // Range.getUpper() is crossed. 5273 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5274 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5275 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5276 5277 // Next, solve the constructed addrec 5278 std::pair<const SCEV *,const SCEV *> Roots = 5279 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5280 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5281 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5282 if (R1) { 5283 // Pick the smallest positive root value. 5284 if (ConstantInt *CB = 5285 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5286 R1->getValue(), R2->getValue()))) { 5287 if (CB->getZExtValue() == false) 5288 std::swap(R1, R2); // R1 is the minimum root now. 5289 5290 // Make sure the root is not off by one. The returned iteration should 5291 // not be in the range, but the previous one should be. When solving 5292 // for "X*X < 5", for example, we should not return a root of 2. 5293 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5294 R1->getValue(), 5295 SE); 5296 if (Range.contains(R1Val->getValue())) { 5297 // The next iteration must be out of the range... 5298 ConstantInt *NextVal = 5299 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5300 5301 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5302 if (!Range.contains(R1Val->getValue())) 5303 return SE.getConstant(NextVal); 5304 return SE.getCouldNotCompute(); // Something strange happened 5305 } 5306 5307 // If R1 was not in the range, then it is a good return value. Make 5308 // sure that R1-1 WAS in the range though, just in case. 5309 ConstantInt *NextVal = 5310 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5311 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5312 if (Range.contains(R1Val->getValue())) 5313 return R1; 5314 return SE.getCouldNotCompute(); // Something strange happened 5315 } 5316 } 5317 } 5318 5319 return SE.getCouldNotCompute(); 5320} 5321 5322 5323 5324//===----------------------------------------------------------------------===// 5325// SCEVCallbackVH Class Implementation 5326//===----------------------------------------------------------------------===// 5327 5328void ScalarEvolution::SCEVCallbackVH::deleted() { 5329 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5330 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5331 SE->ConstantEvolutionLoopExitValue.erase(PN); 5332 SE->Scalars.erase(getValPtr()); 5333 // this now dangles! 5334} 5335 5336void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5337 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5338 5339 // Forget all the expressions associated with users of the old value, 5340 // so that future queries will recompute the expressions using the new 5341 // value. 5342 SmallVector<User *, 16> Worklist; 5343 SmallPtrSet<User *, 8> Visited; 5344 Value *Old = getValPtr(); 5345 bool DeleteOld = false; 5346 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5347 UI != UE; ++UI) 5348 Worklist.push_back(*UI); 5349 while (!Worklist.empty()) { 5350 User *U = Worklist.pop_back_val(); 5351 // Deleting the Old value will cause this to dangle. Postpone 5352 // that until everything else is done. 5353 if (U == Old) { 5354 DeleteOld = true; 5355 continue; 5356 } 5357 if (!Visited.insert(U)) 5358 continue; 5359 if (PHINode *PN = dyn_cast<PHINode>(U)) 5360 SE->ConstantEvolutionLoopExitValue.erase(PN); 5361 SE->Scalars.erase(U); 5362 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5363 UI != UE; ++UI) 5364 Worklist.push_back(*UI); 5365 } 5366 // Delete the Old value if it (indirectly) references itself. 5367 if (DeleteOld) { 5368 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5369 SE->ConstantEvolutionLoopExitValue.erase(PN); 5370 SE->Scalars.erase(Old); 5371 // this now dangles! 5372 } 5373 // this may dangle! 5374} 5375 5376ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5377 : CallbackVH(V), SE(se) {} 5378 5379//===----------------------------------------------------------------------===// 5380// ScalarEvolution Class Implementation 5381//===----------------------------------------------------------------------===// 5382 5383ScalarEvolution::ScalarEvolution() 5384 : FunctionPass(&ID) { 5385} 5386 5387bool ScalarEvolution::runOnFunction(Function &F) { 5388 this->F = &F; 5389 LI = &getAnalysis<LoopInfo>(); 5390 TD = getAnalysisIfAvailable<TargetData>(); 5391 DT = &getAnalysis<DominatorTree>(); 5392 return false; 5393} 5394 5395void ScalarEvolution::releaseMemory() { 5396 Scalars.clear(); 5397 BackedgeTakenCounts.clear(); 5398 ConstantEvolutionLoopExitValue.clear(); 5399 ValuesAtScopes.clear(); 5400 UniqueSCEVs.clear(); 5401 SCEVAllocator.Reset(); 5402} 5403 5404void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5405 AU.setPreservesAll(); 5406 AU.addRequiredTransitive<LoopInfo>(); 5407 AU.addRequiredTransitive<DominatorTree>(); 5408} 5409 5410bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5411 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5412} 5413 5414static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5415 const Loop *L) { 5416 // Print all inner loops first 5417 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5418 PrintLoopInfo(OS, SE, *I); 5419 5420 OS << "Loop "; 5421 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5422 OS << ": "; 5423 5424 SmallVector<BasicBlock *, 8> ExitBlocks; 5425 L->getExitBlocks(ExitBlocks); 5426 if (ExitBlocks.size() != 1) 5427 OS << "<multiple exits> "; 5428 5429 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5430 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5431 } else { 5432 OS << "Unpredictable backedge-taken count. "; 5433 } 5434 5435 OS << "\n" 5436 "Loop "; 5437 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5438 OS << ": "; 5439 5440 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5441 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5442 } else { 5443 OS << "Unpredictable max backedge-taken count. "; 5444 } 5445 5446 OS << "\n"; 5447} 5448 5449void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5450 // ScalarEvolution's implementation of the print method is to print 5451 // out SCEV values of all instructions that are interesting. Doing 5452 // this potentially causes it to create new SCEV objects though, 5453 // which technically conflicts with the const qualifier. This isn't 5454 // observable from outside the class though, so casting away the 5455 // const isn't dangerous. 5456 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5457 5458 OS << "Classifying expressions for: "; 5459 WriteAsOperand(OS, F, /*PrintType=*/false); 5460 OS << "\n"; 5461 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5462 if (isSCEVable(I->getType())) { 5463 OS << *I << '\n'; 5464 OS << " --> "; 5465 const SCEV *SV = SE.getSCEV(&*I); 5466 SV->print(OS); 5467 5468 const Loop *L = LI->getLoopFor((*I).getParent()); 5469 5470 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5471 if (AtUse != SV) { 5472 OS << " --> "; 5473 AtUse->print(OS); 5474 } 5475 5476 if (L) { 5477 OS << "\t\t" "Exits: "; 5478 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5479 if (!ExitValue->isLoopInvariant(L)) { 5480 OS << "<<Unknown>>"; 5481 } else { 5482 OS << *ExitValue; 5483 } 5484 } 5485 5486 OS << "\n"; 5487 } 5488 5489 OS << "Determining loop execution counts for: "; 5490 WriteAsOperand(OS, F, /*PrintType=*/false); 5491 OS << "\n"; 5492 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5493 PrintLoopInfo(OS, &SE, *I); 5494} 5495 5496