ScalarEvolution.cpp revision 204642
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(FoldingSetNodeID(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>(); 181 new (S) SCEVConstant(ID, V); 182 UniqueSCEVs.InsertNode(S, IP); 183 return S; 184} 185 186const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 187 return getConstant(ConstantInt::get(getContext(), Val)); 188} 189 190const SCEV * 191ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 192 return getConstant( 193 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned)); 194} 195 196const Type *SCEVConstant::getType() const { return V->getType(); } 197 198void SCEVConstant::print(raw_ostream &OS) const { 199 WriteAsOperand(OS, V, false); 200} 201 202SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID, 203 unsigned SCEVTy, const SCEV *op, const Type *ty) 204 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 205 206bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 207 return Op->dominates(BB, DT); 208} 209 210bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 211 return Op->properlyDominates(BB, DT); 212} 213 214SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID, 215 const SCEV *op, const Type *ty) 216 : SCEVCastExpr(ID, scTruncate, op, ty) { 217 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 218 (Ty->isIntegerTy() || Ty->isPointerTy()) && 219 "Cannot truncate non-integer value!"); 220} 221 222void SCEVTruncateExpr::print(raw_ostream &OS) const { 223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 224} 225 226SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID, 227 const SCEV *op, const Type *ty) 228 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 229 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 230 (Ty->isIntegerTy() || Ty->isPointerTy()) && 231 "Cannot zero extend non-integer value!"); 232} 233 234void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 236} 237 238SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID, 239 const SCEV *op, const Type *ty) 240 : SCEVCastExpr(ID, scSignExtend, op, ty) { 241 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 242 (Ty->isIntegerTy() || Ty->isPointerTy()) && 243 "Cannot sign extend non-integer value!"); 244} 245 246void SCEVSignExtendExpr::print(raw_ostream &OS) const { 247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 248} 249 250void SCEVCommutativeExpr::print(raw_ostream &OS) const { 251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!"); 252 const char *OpStr = getOperationStr(); 253 OS << "(" << *Operands[0]; 254 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 255 OS << OpStr << *Operands[i]; 256 OS << ")"; 257} 258 259bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 261 if (!getOperand(i)->dominates(BB, DT)) 262 return false; 263 } 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { 269 if (!getOperand(i)->properlyDominates(BB, DT)) 270 return false; 271 } 272 return true; 273} 274 275bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 276 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 277} 278 279bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 280 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 281} 282 283void SCEVUDivExpr::print(raw_ostream &OS) const { 284 OS << "(" << *LHS << " /u " << *RHS << ")"; 285} 286 287const Type *SCEVUDivExpr::getType() const { 288 // In most cases the types of LHS and RHS will be the same, but in some 289 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 290 // depend on the type for correctness, but handling types carefully can 291 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 292 // a pointer type than the RHS, so use the RHS' type here. 293 return RHS->getType(); 294} 295 296bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 297 // Add recurrences are never invariant in the function-body (null loop). 298 if (!QueryLoop) 299 return false; 300 301 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 302 if (QueryLoop->contains(L)) 303 return false; 304 305 // This recurrence is variant w.r.t. QueryLoop if any of its operands 306 // are variant. 307 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 308 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 309 return false; 310 311 // Otherwise it's loop-invariant. 312 return true; 313} 314 315bool 316SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 317 return DT->dominates(L->getHeader(), BB) && 318 SCEVNAryExpr::dominates(BB, DT); 319} 320 321bool 322SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 323 // This uses a "dominates" query instead of "properly dominates" query because 324 // the instruction which produces the addrec's value is a PHI, and a PHI 325 // effectively properly dominates its entire containing block. 326 return DT->dominates(L->getHeader(), BB) && 327 SCEVNAryExpr::properlyDominates(BB, DT); 328} 329 330void SCEVAddRecExpr::print(raw_ostream &OS) const { 331 OS << "{" << *Operands[0]; 332 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 333 OS << ",+," << *Operands[i]; 334 OS << "}<"; 335 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 336 OS << ">"; 337} 338 339bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 340 // All non-instruction values are loop invariant. All instructions are loop 341 // invariant if they are not contained in the specified loop. 342 // Instructions are never considered invariant in the function body 343 // (null loop) because they are defined within the "loop". 344 if (Instruction *I = dyn_cast<Instruction>(V)) 345 return L && !L->contains(I); 346 return true; 347} 348 349bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 350 if (Instruction *I = dyn_cast<Instruction>(getValue())) 351 return DT->dominates(I->getParent(), BB); 352 return true; 353} 354 355bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 356 if (Instruction *I = dyn_cast<Instruction>(getValue())) 357 return DT->properlyDominates(I->getParent(), BB); 358 return true; 359} 360 361const Type *SCEVUnknown::getType() const { 362 return V->getType(); 363} 364 365bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 366 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 367 if (VCE->getOpcode() == Instruction::PtrToInt) 368 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 369 if (CE->getOpcode() == Instruction::GetElementPtr && 370 CE->getOperand(0)->isNullValue() && 371 CE->getNumOperands() == 2) 372 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 373 if (CI->isOne()) { 374 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 375 ->getElementType(); 376 return true; 377 } 378 379 return false; 380} 381 382bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 383 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 384 if (VCE->getOpcode() == Instruction::PtrToInt) 385 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 386 if (CE->getOpcode() == Instruction::GetElementPtr && 387 CE->getOperand(0)->isNullValue()) { 388 const Type *Ty = 389 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 390 if (const StructType *STy = dyn_cast<StructType>(Ty)) 391 if (!STy->isPacked() && 392 CE->getNumOperands() == 3 && 393 CE->getOperand(1)->isNullValue()) { 394 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 395 if (CI->isOne() && 396 STy->getNumElements() == 2 && 397 STy->getElementType(0)->isIntegerTy(1)) { 398 AllocTy = STy->getElementType(1); 399 return true; 400 } 401 } 402 } 403 404 return false; 405} 406 407bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 408 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) 409 if (VCE->getOpcode() == Instruction::PtrToInt) 410 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 411 if (CE->getOpcode() == Instruction::GetElementPtr && 412 CE->getNumOperands() == 3 && 413 CE->getOperand(0)->isNullValue() && 414 CE->getOperand(1)->isNullValue()) { 415 const Type *Ty = 416 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 417 // Ignore vector types here so that ScalarEvolutionExpander doesn't 418 // emit getelementptrs that index into vectors. 419 if (Ty->isStructTy() || Ty->isArrayTy()) { 420 CTy = Ty; 421 FieldNo = CE->getOperand(2); 422 return true; 423 } 424 } 425 426 return false; 427} 428 429void SCEVUnknown::print(raw_ostream &OS) const { 430 const Type *AllocTy; 431 if (isSizeOf(AllocTy)) { 432 OS << "sizeof(" << *AllocTy << ")"; 433 return; 434 } 435 if (isAlignOf(AllocTy)) { 436 OS << "alignof(" << *AllocTy << ")"; 437 return; 438 } 439 440 const Type *CTy; 441 Constant *FieldNo; 442 if (isOffsetOf(CTy, FieldNo)) { 443 OS << "offsetof(" << *CTy << ", "; 444 WriteAsOperand(OS, FieldNo, false); 445 OS << ")"; 446 return; 447 } 448 449 // Otherwise just print it normally. 450 WriteAsOperand(OS, V, false); 451} 452 453//===----------------------------------------------------------------------===// 454// SCEV Utilities 455//===----------------------------------------------------------------------===// 456 457static bool CompareTypes(const Type *A, const Type *B) { 458 if (A->getTypeID() != B->getTypeID()) 459 return A->getTypeID() < B->getTypeID(); 460 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { 461 const IntegerType *BI = cast<IntegerType>(B); 462 return AI->getBitWidth() < BI->getBitWidth(); 463 } 464 if (const PointerType *AI = dyn_cast<PointerType>(A)) { 465 const PointerType *BI = cast<PointerType>(B); 466 return CompareTypes(AI->getElementType(), BI->getElementType()); 467 } 468 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { 469 const ArrayType *BI = cast<ArrayType>(B); 470 if (AI->getNumElements() != BI->getNumElements()) 471 return AI->getNumElements() < BI->getNumElements(); 472 return CompareTypes(AI->getElementType(), BI->getElementType()); 473 } 474 if (const VectorType *AI = dyn_cast<VectorType>(A)) { 475 const VectorType *BI = cast<VectorType>(B); 476 if (AI->getNumElements() != BI->getNumElements()) 477 return AI->getNumElements() < BI->getNumElements(); 478 return CompareTypes(AI->getElementType(), BI->getElementType()); 479 } 480 if (const StructType *AI = dyn_cast<StructType>(A)) { 481 const StructType *BI = cast<StructType>(B); 482 if (AI->getNumElements() != BI->getNumElements()) 483 return AI->getNumElements() < BI->getNumElements(); 484 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) 485 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || 486 CompareTypes(BI->getElementType(i), AI->getElementType(i))) 487 return CompareTypes(AI->getElementType(i), BI->getElementType(i)); 488 } 489 return false; 490} 491 492namespace { 493 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 494 /// than the complexity of the RHS. This comparator is used to canonicalize 495 /// expressions. 496 class SCEVComplexityCompare { 497 LoopInfo *LI; 498 public: 499 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} 500 501 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 502 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 503 if (LHS == RHS) 504 return false; 505 506 // Primarily, sort the SCEVs by their getSCEVType(). 507 if (LHS->getSCEVType() != RHS->getSCEVType()) 508 return LHS->getSCEVType() < RHS->getSCEVType(); 509 510 // Aside from the getSCEVType() ordering, the particular ordering 511 // isn't very important except that it's beneficial to be consistent, 512 // so that (a + b) and (b + a) don't end up as different expressions. 513 514 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 515 // not as complete as it could be. 516 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { 517 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 518 519 // Order pointer values after integer values. This helps SCEVExpander 520 // form GEPs. 521 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy()) 522 return false; 523 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy()) 524 return true; 525 526 // Compare getValueID values. 527 if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) 528 return LU->getValue()->getValueID() < RU->getValue()->getValueID(); 529 530 // Sort arguments by their position. 531 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { 532 const Argument *RA = cast<Argument>(RU->getValue()); 533 return LA->getArgNo() < RA->getArgNo(); 534 } 535 536 // For instructions, compare their loop depth, and their opcode. 537 // This is pretty loose. 538 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { 539 Instruction *RV = cast<Instruction>(RU->getValue()); 540 541 // Compare loop depths. 542 if (LI->getLoopDepth(LV->getParent()) != 543 LI->getLoopDepth(RV->getParent())) 544 return LI->getLoopDepth(LV->getParent()) < 545 LI->getLoopDepth(RV->getParent()); 546 547 // Compare opcodes. 548 if (LV->getOpcode() != RV->getOpcode()) 549 return LV->getOpcode() < RV->getOpcode(); 550 551 // Compare the number of operands. 552 if (LV->getNumOperands() != RV->getNumOperands()) 553 return LV->getNumOperands() < RV->getNumOperands(); 554 } 555 556 return false; 557 } 558 559 // Compare constant values. 560 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { 561 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 562 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) 563 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); 564 return LC->getValue()->getValue().ult(RC->getValue()->getValue()); 565 } 566 567 // Compare addrec loop depths. 568 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { 569 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 570 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) 571 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); 572 } 573 574 // Lexicographically compare n-ary expressions. 575 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { 576 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 577 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { 578 if (i >= RC->getNumOperands()) 579 return false; 580 if (operator()(LC->getOperand(i), RC->getOperand(i))) 581 return true; 582 if (operator()(RC->getOperand(i), LC->getOperand(i))) 583 return false; 584 } 585 return LC->getNumOperands() < RC->getNumOperands(); 586 } 587 588 // Lexicographically compare udiv expressions. 589 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { 590 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 591 if (operator()(LC->getLHS(), RC->getLHS())) 592 return true; 593 if (operator()(RC->getLHS(), LC->getLHS())) 594 return false; 595 if (operator()(LC->getRHS(), RC->getRHS())) 596 return true; 597 if (operator()(RC->getRHS(), LC->getRHS())) 598 return false; 599 return false; 600 } 601 602 // Compare cast expressions by operand. 603 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { 604 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 605 return operator()(LC->getOperand(), RC->getOperand()); 606 } 607 608 llvm_unreachable("Unknown SCEV kind!"); 609 return false; 610 } 611 }; 612} 613 614/// GroupByComplexity - Given a list of SCEV objects, order them by their 615/// complexity, and group objects of the same complexity together by value. 616/// When this routine is finished, we know that any duplicates in the vector are 617/// consecutive and that complexity is monotonically increasing. 618/// 619/// Note that we go take special precautions to ensure that we get deterministic 620/// results from this routine. In other words, we don't want the results of 621/// this to depend on where the addresses of various SCEV objects happened to 622/// land in memory. 623/// 624static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 625 LoopInfo *LI) { 626 if (Ops.size() < 2) return; // Noop 627 if (Ops.size() == 2) { 628 // This is the common case, which also happens to be trivially simple. 629 // Special case it. 630 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 631 std::swap(Ops[0], Ops[1]); 632 return; 633 } 634 635 // Do the rough sort by complexity. 636 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 637 638 // Now that we are sorted by complexity, group elements of the same 639 // complexity. Note that this is, at worst, N^2, but the vector is likely to 640 // be extremely short in practice. Note that we take this approach because we 641 // do not want to depend on the addresses of the objects we are grouping. 642 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 643 const SCEV *S = Ops[i]; 644 unsigned Complexity = S->getSCEVType(); 645 646 // If there are any objects of the same complexity and same value as this 647 // one, group them. 648 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 649 if (Ops[j] == S) { // Found a duplicate. 650 // Move it to immediately after i'th element. 651 std::swap(Ops[i+1], Ops[j]); 652 ++i; // no need to rescan it. 653 if (i == e-2) return; // Done! 654 } 655 } 656 } 657} 658 659 660 661//===----------------------------------------------------------------------===// 662// Simple SCEV method implementations 663//===----------------------------------------------------------------------===// 664 665/// BinomialCoefficient - Compute BC(It, K). The result has width W. 666/// Assume, K > 0. 667static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 668 ScalarEvolution &SE, 669 const Type* ResultTy) { 670 // Handle the simplest case efficiently. 671 if (K == 1) 672 return SE.getTruncateOrZeroExtend(It, ResultTy); 673 674 // We are using the following formula for BC(It, K): 675 // 676 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 677 // 678 // Suppose, W is the bitwidth of the return value. We must be prepared for 679 // overflow. Hence, we must assure that the result of our computation is 680 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 681 // safe in modular arithmetic. 682 // 683 // However, this code doesn't use exactly that formula; the formula it uses 684 // is something like the following, where T is the number of factors of 2 in 685 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 686 // exponentiation: 687 // 688 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 689 // 690 // This formula is trivially equivalent to the previous formula. However, 691 // this formula can be implemented much more efficiently. The trick is that 692 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 693 // arithmetic. To do exact division in modular arithmetic, all we have 694 // to do is multiply by the inverse. Therefore, this step can be done at 695 // width W. 696 // 697 // The next issue is how to safely do the division by 2^T. The way this 698 // is done is by doing the multiplication step at a width of at least W + T 699 // bits. This way, the bottom W+T bits of the product are accurate. Then, 700 // when we perform the division by 2^T (which is equivalent to a right shift 701 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 702 // truncated out after the division by 2^T. 703 // 704 // In comparison to just directly using the first formula, this technique 705 // is much more efficient; using the first formula requires W * K bits, 706 // but this formula less than W + K bits. Also, the first formula requires 707 // a division step, whereas this formula only requires multiplies and shifts. 708 // 709 // It doesn't matter whether the subtraction step is done in the calculation 710 // width or the input iteration count's width; if the subtraction overflows, 711 // the result must be zero anyway. We prefer here to do it in the width of 712 // the induction variable because it helps a lot for certain cases; CodeGen 713 // isn't smart enough to ignore the overflow, which leads to much less 714 // efficient code if the width of the subtraction is wider than the native 715 // register width. 716 // 717 // (It's possible to not widen at all by pulling out factors of 2 before 718 // the multiplication; for example, K=2 can be calculated as 719 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 720 // extra arithmetic, so it's not an obvious win, and it gets 721 // much more complicated for K > 3.) 722 723 // Protection from insane SCEVs; this bound is conservative, 724 // but it probably doesn't matter. 725 if (K > 1000) 726 return SE.getCouldNotCompute(); 727 728 unsigned W = SE.getTypeSizeInBits(ResultTy); 729 730 // Calculate K! / 2^T and T; we divide out the factors of two before 731 // multiplying for calculating K! / 2^T to avoid overflow. 732 // Other overflow doesn't matter because we only care about the bottom 733 // W bits of the result. 734 APInt OddFactorial(W, 1); 735 unsigned T = 1; 736 for (unsigned i = 3; i <= K; ++i) { 737 APInt Mult(W, i); 738 unsigned TwoFactors = Mult.countTrailingZeros(); 739 T += TwoFactors; 740 Mult = Mult.lshr(TwoFactors); 741 OddFactorial *= Mult; 742 } 743 744 // We need at least W + T bits for the multiplication step 745 unsigned CalculationBits = W + T; 746 747 // Calculate 2^T, at width T+W. 748 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 749 750 // Calculate the multiplicative inverse of K! / 2^T; 751 // this multiplication factor will perform the exact division by 752 // K! / 2^T. 753 APInt Mod = APInt::getSignedMinValue(W+1); 754 APInt MultiplyFactor = OddFactorial.zext(W+1); 755 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 756 MultiplyFactor = MultiplyFactor.trunc(W); 757 758 // Calculate the product, at width T+W 759 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 760 CalculationBits); 761 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 762 for (unsigned i = 1; i != K; ++i) { 763 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType())); 764 Dividend = SE.getMulExpr(Dividend, 765 SE.getTruncateOrZeroExtend(S, CalculationTy)); 766 } 767 768 // Divide by 2^T 769 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 770 771 // Truncate the result, and divide by K! / 2^T. 772 773 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 774 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 775} 776 777/// evaluateAtIteration - Return the value of this chain of recurrences at 778/// the specified iteration number. We can evaluate this recurrence by 779/// multiplying each element in the chain by the binomial coefficient 780/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 781/// 782/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 783/// 784/// where BC(It, k) stands for binomial coefficient. 785/// 786const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 787 ScalarEvolution &SE) const { 788 const SCEV *Result = getStart(); 789 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 790 // The computation is correct in the face of overflow provided that the 791 // multiplication is performed _after_ the evaluation of the binomial 792 // coefficient. 793 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 794 if (isa<SCEVCouldNotCompute>(Coeff)) 795 return Coeff; 796 797 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 798 } 799 return Result; 800} 801 802//===----------------------------------------------------------------------===// 803// SCEV Expression folder implementations 804//===----------------------------------------------------------------------===// 805 806const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 807 const Type *Ty) { 808 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 809 "This is not a truncating conversion!"); 810 assert(isSCEVable(Ty) && 811 "This is not a conversion to a SCEVable type!"); 812 Ty = getEffectiveSCEVType(Ty); 813 814 FoldingSetNodeID ID; 815 ID.AddInteger(scTruncate); 816 ID.AddPointer(Op); 817 ID.AddPointer(Ty); 818 void *IP = 0; 819 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 820 821 // Fold if the operand is constant. 822 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 823 return getConstant( 824 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); 825 826 // trunc(trunc(x)) --> trunc(x) 827 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 828 return getTruncateExpr(ST->getOperand(), Ty); 829 830 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 831 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 832 return getTruncateOrSignExtend(SS->getOperand(), Ty); 833 834 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 835 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 836 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 837 838 // If the input value is a chrec scev, truncate the chrec's operands. 839 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 840 SmallVector<const SCEV *, 4> Operands; 841 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 842 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 843 return getAddRecExpr(Operands, AddRec->getLoop()); 844 } 845 846 // The cast wasn't folded; create an explicit cast node. 847 // Recompute the insert position, as it may have been invalidated. 848 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 849 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>(); 850 new (S) SCEVTruncateExpr(ID, Op, Ty); 851 UniqueSCEVs.InsertNode(S, IP); 852 return S; 853} 854 855const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 856 const Type *Ty) { 857 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 858 "This is not an extending conversion!"); 859 assert(isSCEVable(Ty) && 860 "This is not a conversion to a SCEVable type!"); 861 Ty = getEffectiveSCEVType(Ty); 862 863 // Fold if the operand is constant. 864 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 865 const Type *IntTy = getEffectiveSCEVType(Ty); 866 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); 867 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 868 return getConstant(cast<ConstantInt>(C)); 869 } 870 871 // zext(zext(x)) --> zext(x) 872 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 873 return getZeroExtendExpr(SZ->getOperand(), Ty); 874 875 // Before doing any expensive analysis, check to see if we've already 876 // computed a SCEV for this Op and Ty. 877 FoldingSetNodeID ID; 878 ID.AddInteger(scZeroExtend); 879 ID.AddPointer(Op); 880 ID.AddPointer(Ty); 881 void *IP = 0; 882 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 883 884 // If the input value is a chrec scev, and we can prove that the value 885 // did not overflow the old, smaller, value, we can zero extend all of the 886 // operands (often constants). This allows analysis of something like 887 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 888 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 889 if (AR->isAffine()) { 890 const SCEV *Start = AR->getStart(); 891 const SCEV *Step = AR->getStepRecurrence(*this); 892 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 893 const Loop *L = AR->getLoop(); 894 895 // If we have special knowledge that this addrec won't overflow, 896 // we don't need to do any further analysis. 897 if (AR->hasNoUnsignedWrap()) 898 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 899 getZeroExtendExpr(Step, Ty), 900 L); 901 902 // Check whether the backedge-taken count is SCEVCouldNotCompute. 903 // Note that this serves two purposes: It filters out loops that are 904 // simply not analyzable, and it covers the case where this code is 905 // being called from within backedge-taken count analysis, such that 906 // attempting to ask for the backedge-taken count would likely result 907 // in infinite recursion. In the later case, the analysis code will 908 // cope with a conservative value, and it will take care to purge 909 // that value once it has finished. 910 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 911 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 912 // Manually compute the final value for AR, checking for 913 // overflow. 914 915 // Check whether the backedge-taken count can be losslessly casted to 916 // the addrec's type. The count is always unsigned. 917 const SCEV *CastedMaxBECount = 918 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 919 const SCEV *RecastedMaxBECount = 920 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 921 if (MaxBECount == RecastedMaxBECount) { 922 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 923 // Check whether Start+Step*MaxBECount has no unsigned overflow. 924 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 925 const SCEV *Add = getAddExpr(Start, ZMul); 926 const SCEV *OperandExtendedAdd = 927 getAddExpr(getZeroExtendExpr(Start, WideTy), 928 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 929 getZeroExtendExpr(Step, WideTy))); 930 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 931 // Return the expression with the addrec on the outside. 932 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 933 getZeroExtendExpr(Step, Ty), 934 L); 935 936 // Similar to above, only this time treat the step value as signed. 937 // This covers loops that count down. 938 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 939 Add = getAddExpr(Start, SMul); 940 OperandExtendedAdd = 941 getAddExpr(getZeroExtendExpr(Start, WideTy), 942 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 943 getSignExtendExpr(Step, WideTy))); 944 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 945 // Return the expression with the addrec on the outside. 946 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 947 getSignExtendExpr(Step, Ty), 948 L); 949 } 950 951 // If the backedge is guarded by a comparison with the pre-inc value 952 // the addrec is safe. Also, if the entry is guarded by a comparison 953 // with the start value and the backedge is guarded by a comparison 954 // with the post-inc value, the addrec is safe. 955 if (isKnownPositive(Step)) { 956 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 957 getUnsignedRange(Step).getUnsignedMax()); 958 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 959 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 960 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 961 AR->getPostIncExpr(*this), N))) 962 // Return the expression with the addrec on the outside. 963 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 964 getZeroExtendExpr(Step, Ty), 965 L); 966 } else if (isKnownNegative(Step)) { 967 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 968 getSignedRange(Step).getSignedMin()); 969 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) && 970 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) || 971 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 972 AR->getPostIncExpr(*this), N))) 973 // Return the expression with the addrec on the outside. 974 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 975 getSignExtendExpr(Step, Ty), 976 L); 977 } 978 } 979 } 980 981 // The cast wasn't folded; create an explicit cast node. 982 // Recompute the insert position, as it may have been invalidated. 983 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 984 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>(); 985 new (S) SCEVZeroExtendExpr(ID, Op, Ty); 986 UniqueSCEVs.InsertNode(S, IP); 987 return S; 988} 989 990const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 991 const Type *Ty) { 992 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 993 "This is not an extending conversion!"); 994 assert(isSCEVable(Ty) && 995 "This is not a conversion to a SCEVable type!"); 996 Ty = getEffectiveSCEVType(Ty); 997 998 // Fold if the operand is constant. 999 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { 1000 const Type *IntTy = getEffectiveSCEVType(Ty); 1001 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); 1002 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); 1003 return getConstant(cast<ConstantInt>(C)); 1004 } 1005 1006 // sext(sext(x)) --> sext(x) 1007 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1008 return getSignExtendExpr(SS->getOperand(), Ty); 1009 1010 // Before doing any expensive analysis, check to see if we've already 1011 // computed a SCEV for this Op and Ty. 1012 FoldingSetNodeID ID; 1013 ID.AddInteger(scSignExtend); 1014 ID.AddPointer(Op); 1015 ID.AddPointer(Ty); 1016 void *IP = 0; 1017 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1018 1019 // If the input value is a chrec scev, and we can prove that the value 1020 // did not overflow the old, smaller, value, we can sign extend all of the 1021 // operands (often constants). This allows analysis of something like 1022 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1023 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1024 if (AR->isAffine()) { 1025 const SCEV *Start = AR->getStart(); 1026 const SCEV *Step = AR->getStepRecurrence(*this); 1027 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1028 const Loop *L = AR->getLoop(); 1029 1030 // If we have special knowledge that this addrec won't overflow, 1031 // we don't need to do any further analysis. 1032 if (AR->hasNoSignedWrap()) 1033 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1034 getSignExtendExpr(Step, Ty), 1035 L); 1036 1037 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1038 // Note that this serves two purposes: It filters out loops that are 1039 // simply not analyzable, and it covers the case where this code is 1040 // being called from within backedge-taken count analysis, such that 1041 // attempting to ask for the backedge-taken count would likely result 1042 // in infinite recursion. In the later case, the analysis code will 1043 // cope with a conservative value, and it will take care to purge 1044 // that value once it has finished. 1045 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1046 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1047 // Manually compute the final value for AR, checking for 1048 // overflow. 1049 1050 // Check whether the backedge-taken count can be losslessly casted to 1051 // the addrec's type. The count is always unsigned. 1052 const SCEV *CastedMaxBECount = 1053 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1054 const SCEV *RecastedMaxBECount = 1055 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1056 if (MaxBECount == RecastedMaxBECount) { 1057 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1058 // Check whether Start+Step*MaxBECount has no signed overflow. 1059 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1060 const SCEV *Add = getAddExpr(Start, SMul); 1061 const SCEV *OperandExtendedAdd = 1062 getAddExpr(getSignExtendExpr(Start, WideTy), 1063 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1064 getSignExtendExpr(Step, WideTy))); 1065 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1066 // Return the expression with the addrec on the outside. 1067 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1068 getSignExtendExpr(Step, Ty), 1069 L); 1070 1071 // Similar to above, only this time treat the step value as unsigned. 1072 // This covers loops that count up with an unsigned step. 1073 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1074 Add = getAddExpr(Start, UMul); 1075 OperandExtendedAdd = 1076 getAddExpr(getSignExtendExpr(Start, WideTy), 1077 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1078 getZeroExtendExpr(Step, WideTy))); 1079 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1080 // Return the expression with the addrec on the outside. 1081 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1082 getZeroExtendExpr(Step, Ty), 1083 L); 1084 } 1085 1086 // If the backedge is guarded by a comparison with the pre-inc value 1087 // the addrec is safe. Also, if the entry is guarded by a comparison 1088 // with the start value and the backedge is guarded by a comparison 1089 // with the post-inc value, the addrec is safe. 1090 if (isKnownPositive(Step)) { 1091 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1092 getSignedRange(Step).getSignedMax()); 1093 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1094 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1095 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1096 AR->getPostIncExpr(*this), N))) 1097 // Return the expression with the addrec on the outside. 1098 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1099 getSignExtendExpr(Step, Ty), 1100 L); 1101 } else if (isKnownNegative(Step)) { 1102 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1103 getSignedRange(Step).getSignedMin()); 1104 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1105 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1106 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1107 AR->getPostIncExpr(*this), N))) 1108 // Return the expression with the addrec on the outside. 1109 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1110 getSignExtendExpr(Step, Ty), 1111 L); 1112 } 1113 } 1114 } 1115 1116 // The cast wasn't folded; create an explicit cast node. 1117 // Recompute the insert position, as it may have been invalidated. 1118 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1119 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>(); 1120 new (S) SCEVSignExtendExpr(ID, Op, Ty); 1121 UniqueSCEVs.InsertNode(S, IP); 1122 return S; 1123} 1124 1125/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1126/// unspecified bits out to the given type. 1127/// 1128const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1129 const Type *Ty) { 1130 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1131 "This is not an extending conversion!"); 1132 assert(isSCEVable(Ty) && 1133 "This is not a conversion to a SCEVable type!"); 1134 Ty = getEffectiveSCEVType(Ty); 1135 1136 // Sign-extend negative constants. 1137 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1138 if (SC->getValue()->getValue().isNegative()) 1139 return getSignExtendExpr(Op, Ty); 1140 1141 // Peel off a truncate cast. 1142 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1143 const SCEV *NewOp = T->getOperand(); 1144 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1145 return getAnyExtendExpr(NewOp, Ty); 1146 return getTruncateOrNoop(NewOp, Ty); 1147 } 1148 1149 // Next try a zext cast. If the cast is folded, use it. 1150 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1151 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1152 return ZExt; 1153 1154 // Next try a sext cast. If the cast is folded, use it. 1155 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1156 if (!isa<SCEVSignExtendExpr>(SExt)) 1157 return SExt; 1158 1159 // Force the cast to be folded into the operands of an addrec. 1160 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1161 SmallVector<const SCEV *, 4> Ops; 1162 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1163 I != E; ++I) 1164 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1165 return getAddRecExpr(Ops, AR->getLoop()); 1166 } 1167 1168 // If the expression is obviously signed, use the sext cast value. 1169 if (isa<SCEVSMaxExpr>(Op)) 1170 return SExt; 1171 1172 // Absent any other information, use the zext cast value. 1173 return ZExt; 1174} 1175 1176/// CollectAddOperandsWithScales - Process the given Ops list, which is 1177/// a list of operands to be added under the given scale, update the given 1178/// map. This is a helper function for getAddRecExpr. As an example of 1179/// what it does, given a sequence of operands that would form an add 1180/// expression like this: 1181/// 1182/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1183/// 1184/// where A and B are constants, update the map with these values: 1185/// 1186/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1187/// 1188/// and add 13 + A*B*29 to AccumulatedConstant. 1189/// This will allow getAddRecExpr to produce this: 1190/// 1191/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1192/// 1193/// This form often exposes folding opportunities that are hidden in 1194/// the original operand list. 1195/// 1196/// Return true iff it appears that any interesting folding opportunities 1197/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1198/// the common case where no interesting opportunities are present, and 1199/// is also used as a check to avoid infinite recursion. 1200/// 1201static bool 1202CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1203 SmallVector<const SCEV *, 8> &NewOps, 1204 APInt &AccumulatedConstant, 1205 const SmallVectorImpl<const SCEV *> &Ops, 1206 const APInt &Scale, 1207 ScalarEvolution &SE) { 1208 bool Interesting = false; 1209 1210 // Iterate over the add operands. 1211 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1212 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1213 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1214 APInt NewScale = 1215 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1216 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1217 // A multiplication of a constant with another add; recurse. 1218 Interesting |= 1219 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1220 cast<SCEVAddExpr>(Mul->getOperand(1)) 1221 ->getOperands(), 1222 NewScale, SE); 1223 } else { 1224 // A multiplication of a constant with some other value. Update 1225 // the map. 1226 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1227 const SCEV *Key = SE.getMulExpr(MulOps); 1228 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1229 M.insert(std::make_pair(Key, NewScale)); 1230 if (Pair.second) { 1231 NewOps.push_back(Pair.first->first); 1232 } else { 1233 Pair.first->second += NewScale; 1234 // The map already had an entry for this value, which may indicate 1235 // a folding opportunity. 1236 Interesting = true; 1237 } 1238 } 1239 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1240 // Pull a buried constant out to the outside. 1241 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero()) 1242 Interesting = true; 1243 AccumulatedConstant += Scale * C->getValue()->getValue(); 1244 } else { 1245 // An ordinary operand. Update the map. 1246 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1247 M.insert(std::make_pair(Ops[i], Scale)); 1248 if (Pair.second) { 1249 NewOps.push_back(Pair.first->first); 1250 } else { 1251 Pair.first->second += Scale; 1252 // The map already had an entry for this value, which may indicate 1253 // a folding opportunity. 1254 Interesting = true; 1255 } 1256 } 1257 } 1258 1259 return Interesting; 1260} 1261 1262namespace { 1263 struct APIntCompare { 1264 bool operator()(const APInt &LHS, const APInt &RHS) const { 1265 return LHS.ult(RHS); 1266 } 1267 }; 1268} 1269 1270/// getAddExpr - Get a canonical add expression, or something simpler if 1271/// possible. 1272const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1273 bool HasNUW, bool HasNSW) { 1274 assert(!Ops.empty() && "Cannot get empty add!"); 1275 if (Ops.size() == 1) return Ops[0]; 1276#ifndef NDEBUG 1277 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1278 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1279 getEffectiveSCEVType(Ops[0]->getType()) && 1280 "SCEVAddExpr operand types don't match!"); 1281#endif 1282 1283 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1284 if (!HasNUW && HasNSW) { 1285 bool All = true; 1286 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1287 if (!isKnownNonNegative(Ops[i])) { 1288 All = false; 1289 break; 1290 } 1291 if (All) HasNUW = true; 1292 } 1293 1294 // Sort by complexity, this groups all similar expression types together. 1295 GroupByComplexity(Ops, LI); 1296 1297 // If there are any constants, fold them together. 1298 unsigned Idx = 0; 1299 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1300 ++Idx; 1301 assert(Idx < Ops.size()); 1302 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1303 // We found two constants, fold them together! 1304 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1305 RHSC->getValue()->getValue()); 1306 if (Ops.size() == 2) return Ops[0]; 1307 Ops.erase(Ops.begin()+1); // Erase the folded element 1308 LHSC = cast<SCEVConstant>(Ops[0]); 1309 } 1310 1311 // If we are left with a constant zero being added, strip it off. 1312 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1313 Ops.erase(Ops.begin()); 1314 --Idx; 1315 } 1316 } 1317 1318 if (Ops.size() == 1) return Ops[0]; 1319 1320 // Okay, check to see if the same value occurs in the operand list twice. If 1321 // so, merge them together into an multiply expression. Since we sorted the 1322 // list, these values are required to be adjacent. 1323 const Type *Ty = Ops[0]->getType(); 1324 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1325 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1326 // Found a match, merge the two values into a multiply, and add any 1327 // remaining values to the result. 1328 const SCEV *Two = getIntegerSCEV(2, Ty); 1329 const SCEV *Mul = getMulExpr(Ops[i], Two); 1330 if (Ops.size() == 2) 1331 return Mul; 1332 Ops.erase(Ops.begin()+i, Ops.begin()+i+2); 1333 Ops.push_back(Mul); 1334 return getAddExpr(Ops, HasNUW, HasNSW); 1335 } 1336 1337 // Check for truncates. If all the operands are truncated from the same 1338 // type, see if factoring out the truncate would permit the result to be 1339 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1340 // if the contents of the resulting outer trunc fold to something simple. 1341 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1342 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1343 const Type *DstType = Trunc->getType(); 1344 const Type *SrcType = Trunc->getOperand()->getType(); 1345 SmallVector<const SCEV *, 8> LargeOps; 1346 bool Ok = true; 1347 // Check all the operands to see if they can be represented in the 1348 // source type of the truncate. 1349 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1350 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1351 if (T->getOperand()->getType() != SrcType) { 1352 Ok = false; 1353 break; 1354 } 1355 LargeOps.push_back(T->getOperand()); 1356 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1357 // This could be either sign or zero extension, but sign extension 1358 // is much more likely to be foldable here. 1359 LargeOps.push_back(getSignExtendExpr(C, SrcType)); 1360 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1361 SmallVector<const SCEV *, 8> LargeMulOps; 1362 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1363 if (const SCEVTruncateExpr *T = 1364 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1365 if (T->getOperand()->getType() != SrcType) { 1366 Ok = false; 1367 break; 1368 } 1369 LargeMulOps.push_back(T->getOperand()); 1370 } else if (const SCEVConstant *C = 1371 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1372 // This could be either sign or zero extension, but sign extension 1373 // is much more likely to be foldable here. 1374 LargeMulOps.push_back(getSignExtendExpr(C, SrcType)); 1375 } else { 1376 Ok = false; 1377 break; 1378 } 1379 } 1380 if (Ok) 1381 LargeOps.push_back(getMulExpr(LargeMulOps)); 1382 } else { 1383 Ok = false; 1384 break; 1385 } 1386 } 1387 if (Ok) { 1388 // Evaluate the expression in the larger type. 1389 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1390 // If it folds to something simple, use it. Otherwise, don't. 1391 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1392 return getTruncateExpr(Fold, DstType); 1393 } 1394 } 1395 1396 // Skip past any other cast SCEVs. 1397 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1398 ++Idx; 1399 1400 // If there are add operands they would be next. 1401 if (Idx < Ops.size()) { 1402 bool DeletedAdd = false; 1403 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1404 // If we have an add, expand the add operands onto the end of the operands 1405 // list. 1406 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); 1407 Ops.erase(Ops.begin()+Idx); 1408 DeletedAdd = true; 1409 } 1410 1411 // If we deleted at least one add, we added operands to the end of the list, 1412 // and they are not necessarily sorted. Recurse to resort and resimplify 1413 // any operands we just acquired. 1414 if (DeletedAdd) 1415 return getAddExpr(Ops); 1416 } 1417 1418 // Skip over the add expression until we get to a multiply. 1419 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1420 ++Idx; 1421 1422 // Check to see if there are any folding opportunities present with 1423 // operands multiplied by constant values. 1424 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1425 uint64_t BitWidth = getTypeSizeInBits(Ty); 1426 DenseMap<const SCEV *, APInt> M; 1427 SmallVector<const SCEV *, 8> NewOps; 1428 APInt AccumulatedConstant(BitWidth, 0); 1429 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1430 Ops, 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 S = SCEVAllocator.Allocate<SCEVAddExpr>(); 1615 new (S) SCEVAddExpr(ID, Ops); 1616 UniqueSCEVs.InsertNode(S, IP); 1617 } 1618 if (HasNUW) S->setHasNoUnsignedWrap(true); 1619 if (HasNSW) S->setHasNoSignedWrap(true); 1620 return S; 1621} 1622 1623/// getMulExpr - Get a canonical multiply expression, or something simpler if 1624/// possible. 1625const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1626 bool HasNUW, bool HasNSW) { 1627 assert(!Ops.empty() && "Cannot get empty mul!"); 1628 if (Ops.size() == 1) return Ops[0]; 1629#ifndef NDEBUG 1630 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1631 assert(getEffectiveSCEVType(Ops[i]->getType()) == 1632 getEffectiveSCEVType(Ops[0]->getType()) && 1633 "SCEVMulExpr operand types don't match!"); 1634#endif 1635 1636 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1637 if (!HasNUW && HasNSW) { 1638 bool All = true; 1639 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1640 if (!isKnownNonNegative(Ops[i])) { 1641 All = false; 1642 break; 1643 } 1644 if (All) HasNUW = true; 1645 } 1646 1647 // Sort by complexity, this groups all similar expression types together. 1648 GroupByComplexity(Ops, LI); 1649 1650 // If there are any constants, fold them together. 1651 unsigned Idx = 0; 1652 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1653 1654 // C1*(C2+V) -> C1*C2 + C1*V 1655 if (Ops.size() == 2) 1656 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1657 if (Add->getNumOperands() == 2 && 1658 isa<SCEVConstant>(Add->getOperand(0))) 1659 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1660 getMulExpr(LHSC, Add->getOperand(1))); 1661 1662 ++Idx; 1663 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1664 // We found two constants, fold them together! 1665 ConstantInt *Fold = ConstantInt::get(getContext(), 1666 LHSC->getValue()->getValue() * 1667 RHSC->getValue()->getValue()); 1668 Ops[0] = getConstant(Fold); 1669 Ops.erase(Ops.begin()+1); // Erase the folded element 1670 if (Ops.size() == 1) return Ops[0]; 1671 LHSC = cast<SCEVConstant>(Ops[0]); 1672 } 1673 1674 // If we are left with a constant one being multiplied, strip it off. 1675 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1676 Ops.erase(Ops.begin()); 1677 --Idx; 1678 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1679 // If we have a multiply of zero, it will always be zero. 1680 return Ops[0]; 1681 } else if (Ops[0]->isAllOnesValue()) { 1682 // If we have a mul by -1 of an add, try distributing the -1 among the 1683 // add operands. 1684 if (Ops.size() == 2) 1685 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1686 SmallVector<const SCEV *, 4> NewOps; 1687 bool AnyFolded = false; 1688 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1689 I != E; ++I) { 1690 const SCEV *Mul = getMulExpr(Ops[0], *I); 1691 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1692 NewOps.push_back(Mul); 1693 } 1694 if (AnyFolded) 1695 return getAddExpr(NewOps); 1696 } 1697 } 1698 } 1699 1700 // Skip over the add expression until we get to a multiply. 1701 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1702 ++Idx; 1703 1704 if (Ops.size() == 1) 1705 return Ops[0]; 1706 1707 // If there are mul operands inline them all into this expression. 1708 if (Idx < Ops.size()) { 1709 bool DeletedMul = false; 1710 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1711 // If we have an mul, expand the mul operands onto the end of the operands 1712 // list. 1713 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); 1714 Ops.erase(Ops.begin()+Idx); 1715 DeletedMul = true; 1716 } 1717 1718 // If we deleted at least one mul, we added operands to the end of the list, 1719 // and they are not necessarily sorted. Recurse to resort and resimplify 1720 // any operands we just acquired. 1721 if (DeletedMul) 1722 return getMulExpr(Ops); 1723 } 1724 1725 // If there are any add recurrences in the operands list, see if any other 1726 // added values are loop invariant. If so, we can fold them into the 1727 // recurrence. 1728 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1729 ++Idx; 1730 1731 // Scan over all recurrences, trying to fold loop invariants into them. 1732 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1733 // Scan all of the other operands to this mul and add them to the vector if 1734 // they are loop invariant w.r.t. the recurrence. 1735 SmallVector<const SCEV *, 8> LIOps; 1736 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1737 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1738 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1739 LIOps.push_back(Ops[i]); 1740 Ops.erase(Ops.begin()+i); 1741 --i; --e; 1742 } 1743 1744 // If we found some loop invariants, fold them into the recurrence. 1745 if (!LIOps.empty()) { 1746 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1747 SmallVector<const SCEV *, 4> NewOps; 1748 NewOps.reserve(AddRec->getNumOperands()); 1749 if (LIOps.size() == 1) { 1750 const SCEV *Scale = LIOps[0]; 1751 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1752 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1753 } else { 1754 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 1755 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); 1756 MulOps.push_back(AddRec->getOperand(i)); 1757 NewOps.push_back(getMulExpr(MulOps)); 1758 } 1759 } 1760 1761 // It's tempting to propagate the NSW flag here, but nsw multiplication 1762 // is not associative so this isn't necessarily safe. 1763 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1764 HasNUW && AddRec->hasNoUnsignedWrap(), 1765 /*HasNSW=*/false); 1766 1767 // If all of the other operands were loop invariant, we are done. 1768 if (Ops.size() == 1) return NewRec; 1769 1770 // Otherwise, multiply the folded AddRec by the non-liv parts. 1771 for (unsigned i = 0;; ++i) 1772 if (Ops[i] == AddRec) { 1773 Ops[i] = NewRec; 1774 break; 1775 } 1776 return getMulExpr(Ops); 1777 } 1778 1779 // Okay, if there weren't any loop invariants to be folded, check to see if 1780 // there are multiple AddRec's with the same loop induction variable being 1781 // multiplied together. If so, we can fold them. 1782 for (unsigned OtherIdx = Idx+1; 1783 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1784 if (OtherIdx != Idx) { 1785 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1786 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1787 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1788 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1789 const SCEV *NewStart = getMulExpr(F->getStart(), 1790 G->getStart()); 1791 const SCEV *B = F->getStepRecurrence(*this); 1792 const SCEV *D = G->getStepRecurrence(*this); 1793 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1794 getMulExpr(G, B), 1795 getMulExpr(B, D)); 1796 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1797 F->getLoop()); 1798 if (Ops.size() == 2) return NewAddRec; 1799 1800 Ops.erase(Ops.begin()+Idx); 1801 Ops.erase(Ops.begin()+OtherIdx-1); 1802 Ops.push_back(NewAddRec); 1803 return getMulExpr(Ops); 1804 } 1805 } 1806 1807 // Otherwise couldn't fold anything into this recurrence. Move onto the 1808 // next one. 1809 } 1810 1811 // Okay, it looks like we really DO need an mul expr. Check to see if we 1812 // already have one, otherwise create a new one. 1813 FoldingSetNodeID ID; 1814 ID.AddInteger(scMulExpr); 1815 ID.AddInteger(Ops.size()); 1816 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1817 ID.AddPointer(Ops[i]); 1818 void *IP = 0; 1819 SCEVMulExpr *S = 1820 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1821 if (!S) { 1822 S = SCEVAllocator.Allocate<SCEVMulExpr>(); 1823 new (S) SCEVMulExpr(ID, Ops); 1824 UniqueSCEVs.InsertNode(S, IP); 1825 } 1826 if (HasNUW) S->setHasNoUnsignedWrap(true); 1827 if (HasNSW) S->setHasNoSignedWrap(true); 1828 return S; 1829} 1830 1831/// getUDivExpr - Get a canonical unsigned division expression, or something 1832/// simpler if possible. 1833const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1834 const SCEV *RHS) { 1835 assert(getEffectiveSCEVType(LHS->getType()) == 1836 getEffectiveSCEVType(RHS->getType()) && 1837 "SCEVUDivExpr operand types don't match!"); 1838 1839 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1840 if (RHSC->getValue()->equalsInt(1)) 1841 return LHS; // X udiv 1 --> x 1842 if (RHSC->isZero()) 1843 return getIntegerSCEV(0, LHS->getType()); // value is undefined 1844 1845 // Determine if the division can be folded into the operands of 1846 // its operands. 1847 // TODO: Generalize this to non-constants by using known-bits information. 1848 const Type *Ty = LHS->getType(); 1849 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1850 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; 1851 // For non-power-of-two values, effectively round the value up to the 1852 // nearest power of two. 1853 if (!RHSC->getValue()->getValue().isPowerOf2()) 1854 ++MaxShiftAmt; 1855 const IntegerType *ExtTy = 1856 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1857 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1858 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1859 if (const SCEVConstant *Step = 1860 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1861 if (!Step->getValue()->getValue() 1862 .urem(RHSC->getValue()->getValue()) && 1863 getZeroExtendExpr(AR, ExtTy) == 1864 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1865 getZeroExtendExpr(Step, ExtTy), 1866 AR->getLoop())) { 1867 SmallVector<const SCEV *, 4> Operands; 1868 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1869 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1870 return getAddRecExpr(Operands, AR->getLoop()); 1871 } 1872 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1873 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1874 SmallVector<const SCEV *, 4> Operands; 1875 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1876 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1877 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1878 // Find an operand that's safely divisible. 1879 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1880 const SCEV *Op = M->getOperand(i); 1881 const SCEV *Div = getUDivExpr(Op, RHSC); 1882 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1883 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands(); 1884 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(), 1885 MOperands.end()); 1886 Operands[i] = Div; 1887 return getMulExpr(Operands); 1888 } 1889 } 1890 } 1891 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1892 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1893 SmallVector<const SCEV *, 4> Operands; 1894 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1895 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1896 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1897 Operands.clear(); 1898 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1899 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1900 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i)) 1901 break; 1902 Operands.push_back(Op); 1903 } 1904 if (Operands.size() == A->getNumOperands()) 1905 return getAddExpr(Operands); 1906 } 1907 } 1908 1909 // Fold if both operands are constant. 1910 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1911 Constant *LHSCV = LHSC->getValue(); 1912 Constant *RHSCV = RHSC->getValue(); 1913 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1914 RHSCV))); 1915 } 1916 } 1917 1918 FoldingSetNodeID ID; 1919 ID.AddInteger(scUDivExpr); 1920 ID.AddPointer(LHS); 1921 ID.AddPointer(RHS); 1922 void *IP = 0; 1923 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1924 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>(); 1925 new (S) SCEVUDivExpr(ID, LHS, RHS); 1926 UniqueSCEVs.InsertNode(S, IP); 1927 return S; 1928} 1929 1930 1931/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1932/// Simplify the expression as much as possible. 1933const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1934 const SCEV *Step, const Loop *L, 1935 bool HasNUW, bool HasNSW) { 1936 SmallVector<const SCEV *, 4> Operands; 1937 Operands.push_back(Start); 1938 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1939 if (StepChrec->getLoop() == L) { 1940 Operands.insert(Operands.end(), StepChrec->op_begin(), 1941 StepChrec->op_end()); 1942 return getAddRecExpr(Operands, L); 1943 } 1944 1945 Operands.push_back(Step); 1946 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1947} 1948 1949/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1950/// Simplify the expression as much as possible. 1951const SCEV * 1952ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1953 const Loop *L, 1954 bool HasNUW, bool HasNSW) { 1955 if (Operands.size() == 1) return Operands[0]; 1956#ifndef NDEBUG 1957 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 1958 assert(getEffectiveSCEVType(Operands[i]->getType()) == 1959 getEffectiveSCEVType(Operands[0]->getType()) && 1960 "SCEVAddRecExpr operand types don't match!"); 1961#endif 1962 1963 if (Operands.back()->isZero()) { 1964 Operands.pop_back(); 1965 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 1966 } 1967 1968 // It's tempting to want to call getMaxBackedgeTakenCount count here and 1969 // use that information to infer NUW and NSW flags. However, computing a 1970 // BE count requires calling getAddRecExpr, so we may not yet have a 1971 // meaningful BE count at this point (and if we don't, we'd be stuck 1972 // with a SCEVCouldNotCompute as the cached BE count). 1973 1974 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1975 if (!HasNUW && HasNSW) { 1976 bool All = true; 1977 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 1978 if (!isKnownNonNegative(Operands[i])) { 1979 All = false; 1980 break; 1981 } 1982 if (All) HasNUW = true; 1983 } 1984 1985 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 1986 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 1987 const Loop *NestedLoop = NestedAR->getLoop(); 1988 if (L->contains(NestedLoop->getHeader()) ? 1989 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 1990 (!NestedLoop->contains(L->getHeader()) && 1991 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 1992 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 1993 NestedAR->op_end()); 1994 Operands[0] = NestedAR->getStart(); 1995 // AddRecs require their operands be loop-invariant with respect to their 1996 // loops. Don't perform this transformation if it would break this 1997 // requirement. 1998 bool AllInvariant = true; 1999 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2000 if (!Operands[i]->isLoopInvariant(L)) { 2001 AllInvariant = false; 2002 break; 2003 } 2004 if (AllInvariant) { 2005 NestedOperands[0] = getAddRecExpr(Operands, L); 2006 AllInvariant = true; 2007 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2008 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2009 AllInvariant = false; 2010 break; 2011 } 2012 if (AllInvariant) 2013 // Ok, both add recurrences are valid after the transformation. 2014 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2015 } 2016 // Reset Operands to its original state. 2017 Operands[0] = NestedAR; 2018 } 2019 } 2020 2021 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2022 // already have one, otherwise create a new one. 2023 FoldingSetNodeID ID; 2024 ID.AddInteger(scAddRecExpr); 2025 ID.AddInteger(Operands.size()); 2026 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2027 ID.AddPointer(Operands[i]); 2028 ID.AddPointer(L); 2029 void *IP = 0; 2030 SCEVAddRecExpr *S = 2031 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2032 if (!S) { 2033 S = SCEVAllocator.Allocate<SCEVAddRecExpr>(); 2034 new (S) SCEVAddRecExpr(ID, Operands, L); 2035 UniqueSCEVs.InsertNode(S, IP); 2036 } 2037 if (HasNUW) S->setHasNoUnsignedWrap(true); 2038 if (HasNSW) S->setHasNoSignedWrap(true); 2039 return S; 2040} 2041 2042const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2043 const SCEV *RHS) { 2044 SmallVector<const SCEV *, 2> Ops; 2045 Ops.push_back(LHS); 2046 Ops.push_back(RHS); 2047 return getSMaxExpr(Ops); 2048} 2049 2050const SCEV * 2051ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2052 assert(!Ops.empty() && "Cannot get empty smax!"); 2053 if (Ops.size() == 1) return Ops[0]; 2054#ifndef NDEBUG 2055 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2056 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2057 getEffectiveSCEVType(Ops[0]->getType()) && 2058 "SCEVSMaxExpr operand types don't match!"); 2059#endif 2060 2061 // Sort by complexity, this groups all similar expression types together. 2062 GroupByComplexity(Ops, LI); 2063 2064 // If there are any constants, fold them together. 2065 unsigned Idx = 0; 2066 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2067 ++Idx; 2068 assert(Idx < Ops.size()); 2069 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2070 // We found two constants, fold them together! 2071 ConstantInt *Fold = ConstantInt::get(getContext(), 2072 APIntOps::smax(LHSC->getValue()->getValue(), 2073 RHSC->getValue()->getValue())); 2074 Ops[0] = getConstant(Fold); 2075 Ops.erase(Ops.begin()+1); // Erase the folded element 2076 if (Ops.size() == 1) return Ops[0]; 2077 LHSC = cast<SCEVConstant>(Ops[0]); 2078 } 2079 2080 // If we are left with a constant minimum-int, strip it off. 2081 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2082 Ops.erase(Ops.begin()); 2083 --Idx; 2084 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2085 // If we have an smax with a constant maximum-int, it will always be 2086 // maximum-int. 2087 return Ops[0]; 2088 } 2089 } 2090 2091 if (Ops.size() == 1) return Ops[0]; 2092 2093 // Find the first SMax 2094 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2095 ++Idx; 2096 2097 // Check to see if one of the operands is an SMax. If so, expand its operands 2098 // onto our operand list, and recurse to simplify. 2099 if (Idx < Ops.size()) { 2100 bool DeletedSMax = false; 2101 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2102 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); 2103 Ops.erase(Ops.begin()+Idx); 2104 DeletedSMax = true; 2105 } 2106 2107 if (DeletedSMax) 2108 return getSMaxExpr(Ops); 2109 } 2110 2111 // Okay, check to see if the same value occurs in the operand list twice. If 2112 // so, delete one. Since we sorted the list, these values are required to 2113 // be adjacent. 2114 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2115 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y 2116 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2117 --i; --e; 2118 } 2119 2120 if (Ops.size() == 1) return Ops[0]; 2121 2122 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2123 2124 // Okay, it looks like we really DO need an smax expr. Check to see if we 2125 // already have one, otherwise create a new one. 2126 FoldingSetNodeID ID; 2127 ID.AddInteger(scSMaxExpr); 2128 ID.AddInteger(Ops.size()); 2129 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2130 ID.AddPointer(Ops[i]); 2131 void *IP = 0; 2132 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2133 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>(); 2134 new (S) SCEVSMaxExpr(ID, Ops); 2135 UniqueSCEVs.InsertNode(S, IP); 2136 return S; 2137} 2138 2139const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2140 const SCEV *RHS) { 2141 SmallVector<const SCEV *, 2> Ops; 2142 Ops.push_back(LHS); 2143 Ops.push_back(RHS); 2144 return getUMaxExpr(Ops); 2145} 2146 2147const SCEV * 2148ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2149 assert(!Ops.empty() && "Cannot get empty umax!"); 2150 if (Ops.size() == 1) return Ops[0]; 2151#ifndef NDEBUG 2152 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2153 assert(getEffectiveSCEVType(Ops[i]->getType()) == 2154 getEffectiveSCEVType(Ops[0]->getType()) && 2155 "SCEVUMaxExpr operand types don't match!"); 2156#endif 2157 2158 // Sort by complexity, this groups all similar expression types together. 2159 GroupByComplexity(Ops, LI); 2160 2161 // If there are any constants, fold them together. 2162 unsigned Idx = 0; 2163 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2164 ++Idx; 2165 assert(Idx < Ops.size()); 2166 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2167 // We found two constants, fold them together! 2168 ConstantInt *Fold = ConstantInt::get(getContext(), 2169 APIntOps::umax(LHSC->getValue()->getValue(), 2170 RHSC->getValue()->getValue())); 2171 Ops[0] = getConstant(Fold); 2172 Ops.erase(Ops.begin()+1); // Erase the folded element 2173 if (Ops.size() == 1) return Ops[0]; 2174 LHSC = cast<SCEVConstant>(Ops[0]); 2175 } 2176 2177 // If we are left with a constant minimum-int, strip it off. 2178 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2179 Ops.erase(Ops.begin()); 2180 --Idx; 2181 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2182 // If we have an umax with a constant maximum-int, it will always be 2183 // maximum-int. 2184 return Ops[0]; 2185 } 2186 } 2187 2188 if (Ops.size() == 1) return Ops[0]; 2189 2190 // Find the first UMax 2191 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2192 ++Idx; 2193 2194 // Check to see if one of the operands is a UMax. If so, expand its operands 2195 // onto our operand list, and recurse to simplify. 2196 if (Idx < Ops.size()) { 2197 bool DeletedUMax = false; 2198 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2199 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); 2200 Ops.erase(Ops.begin()+Idx); 2201 DeletedUMax = true; 2202 } 2203 2204 if (DeletedUMax) 2205 return getUMaxExpr(Ops); 2206 } 2207 2208 // Okay, check to see if the same value occurs in the operand list twice. If 2209 // so, delete one. Since we sorted the list, these values are required to 2210 // be adjacent. 2211 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2212 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y 2213 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2214 --i; --e; 2215 } 2216 2217 if (Ops.size() == 1) return Ops[0]; 2218 2219 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2220 2221 // Okay, it looks like we really DO need a umax expr. Check to see if we 2222 // already have one, otherwise create a new one. 2223 FoldingSetNodeID ID; 2224 ID.AddInteger(scUMaxExpr); 2225 ID.AddInteger(Ops.size()); 2226 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2227 ID.AddPointer(Ops[i]); 2228 void *IP = 0; 2229 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2230 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>(); 2231 new (S) SCEVUMaxExpr(ID, Ops); 2232 UniqueSCEVs.InsertNode(S, IP); 2233 return S; 2234} 2235 2236const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2237 const SCEV *RHS) { 2238 // ~smax(~x, ~y) == smin(x, y). 2239 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2240} 2241 2242const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2243 const SCEV *RHS) { 2244 // ~umax(~x, ~y) == umin(x, y) 2245 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2246} 2247 2248const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2249 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2250 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2251 C = ConstantFoldConstantExpression(CE, TD); 2252 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2253 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2254} 2255 2256const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2257 Constant *C = ConstantExpr::getAlignOf(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::getOffsetOfExpr(const StructType *STy, 2265 unsigned FieldNo) { 2266 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2267 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2268 C = ConstantFoldConstantExpression(CE, TD); 2269 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2270 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2271} 2272 2273const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2274 Constant *FieldNo) { 2275 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2276 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2277 C = ConstantFoldConstantExpression(CE, TD); 2278 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2279 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2280} 2281 2282const SCEV *ScalarEvolution::getUnknown(Value *V) { 2283 // Don't attempt to do anything other than create a SCEVUnknown object 2284 // here. createSCEV only calls getUnknown after checking for all other 2285 // interesting possibilities, and any other code that calls getUnknown 2286 // is doing so in order to hide a value from SCEV canonicalization. 2287 2288 FoldingSetNodeID ID; 2289 ID.AddInteger(scUnknown); 2290 ID.AddPointer(V); 2291 void *IP = 0; 2292 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2293 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>(); 2294 new (S) SCEVUnknown(ID, V); 2295 UniqueSCEVs.InsertNode(S, IP); 2296 return S; 2297} 2298 2299//===----------------------------------------------------------------------===// 2300// Basic SCEV Analysis and PHI Idiom Recognition Code 2301// 2302 2303/// isSCEVable - Test if values of the given type are analyzable within 2304/// the SCEV framework. This primarily includes integer types, and it 2305/// can optionally include pointer types if the ScalarEvolution class 2306/// has access to target-specific information. 2307bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2308 // Integers and pointers are always SCEVable. 2309 return Ty->isIntegerTy() || Ty->isPointerTy(); 2310} 2311 2312/// getTypeSizeInBits - Return the size in bits of the specified type, 2313/// for which isSCEVable must return true. 2314uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2315 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2316 2317 // If we have a TargetData, use it! 2318 if (TD) 2319 return TD->getTypeSizeInBits(Ty); 2320 2321 // Integer types have fixed sizes. 2322 if (Ty->isIntegerTy()) 2323 return Ty->getPrimitiveSizeInBits(); 2324 2325 // The only other support type is pointer. Without TargetData, conservatively 2326 // assume pointers are 64-bit. 2327 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2328 return 64; 2329} 2330 2331/// getEffectiveSCEVType - Return a type with the same bitwidth as 2332/// the given type and which represents how SCEV will treat the given 2333/// type, for which isSCEVable must return true. For pointer types, 2334/// this is the pointer-sized integer type. 2335const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2336 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2337 2338 if (Ty->isIntegerTy()) 2339 return Ty; 2340 2341 // The only other support type is pointer. 2342 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2343 if (TD) return TD->getIntPtrType(getContext()); 2344 2345 // Without TargetData, conservatively assume pointers are 64-bit. 2346 return Type::getInt64Ty(getContext()); 2347} 2348 2349const SCEV *ScalarEvolution::getCouldNotCompute() { 2350 return &CouldNotCompute; 2351} 2352 2353/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2354/// expression and create a new one. 2355const SCEV *ScalarEvolution::getSCEV(Value *V) { 2356 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2357 2358 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); 2359 if (I != Scalars.end()) return I->second; 2360 const SCEV *S = createSCEV(V); 2361 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2362 return S; 2363} 2364 2365/// getIntegerSCEV - Given a SCEVable type, create a constant for the 2366/// specified signed integer value and return a SCEV for the constant. 2367const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) { 2368 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 2369 return getConstant(ConstantInt::get(ITy, Val)); 2370} 2371 2372/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2373/// 2374const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2375 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2376 return getConstant( 2377 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2378 2379 const Type *Ty = V->getType(); 2380 Ty = getEffectiveSCEVType(Ty); 2381 return getMulExpr(V, 2382 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2383} 2384 2385/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2386const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2387 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2388 return getConstant( 2389 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2390 2391 const Type *Ty = V->getType(); 2392 Ty = getEffectiveSCEVType(Ty); 2393 const SCEV *AllOnes = 2394 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2395 return getMinusSCEV(AllOnes, V); 2396} 2397 2398/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2399/// 2400const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2401 const SCEV *RHS) { 2402 // X - Y --> X + -Y 2403 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2404} 2405 2406/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2407/// input value to the specified type. If the type must be extended, it is zero 2408/// extended. 2409const SCEV * 2410ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2411 const Type *Ty) { 2412 const Type *SrcTy = V->getType(); 2413 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2414 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2415 "Cannot truncate or zero extend with non-integer arguments!"); 2416 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2417 return V; // No conversion 2418 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2419 return getTruncateExpr(V, Ty); 2420 return getZeroExtendExpr(V, Ty); 2421} 2422 2423/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2424/// input value to the specified type. If the type must be extended, it is sign 2425/// extended. 2426const SCEV * 2427ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2428 const Type *Ty) { 2429 const Type *SrcTy = V->getType(); 2430 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2431 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2432 "Cannot truncate or zero extend with non-integer arguments!"); 2433 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2434 return V; // No conversion 2435 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2436 return getTruncateExpr(V, Ty); 2437 return getSignExtendExpr(V, Ty); 2438} 2439 2440/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2441/// input value to the specified type. If the type must be extended, it is zero 2442/// extended. The conversion must not be narrowing. 2443const SCEV * 2444ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2445 const Type *SrcTy = V->getType(); 2446 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2447 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2448 "Cannot noop or zero extend with non-integer arguments!"); 2449 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2450 "getNoopOrZeroExtend cannot truncate!"); 2451 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2452 return V; // No conversion 2453 return getZeroExtendExpr(V, Ty); 2454} 2455 2456/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2457/// input value to the specified type. If the type must be extended, it is sign 2458/// extended. The conversion must not be narrowing. 2459const SCEV * 2460ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2461 const Type *SrcTy = V->getType(); 2462 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2463 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2464 "Cannot noop or sign extend with non-integer arguments!"); 2465 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2466 "getNoopOrSignExtend cannot truncate!"); 2467 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2468 return V; // No conversion 2469 return getSignExtendExpr(V, Ty); 2470} 2471 2472/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2473/// the input value to the specified type. If the type must be extended, 2474/// it is extended with unspecified bits. The conversion must not be 2475/// narrowing. 2476const SCEV * 2477ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2478 const Type *SrcTy = V->getType(); 2479 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2480 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2481 "Cannot noop or any extend with non-integer arguments!"); 2482 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2483 "getNoopOrAnyExtend cannot truncate!"); 2484 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2485 return V; // No conversion 2486 return getAnyExtendExpr(V, Ty); 2487} 2488 2489/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2490/// input value to the specified type. The conversion must not be widening. 2491const SCEV * 2492ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2493 const Type *SrcTy = V->getType(); 2494 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2495 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2496 "Cannot truncate or noop with non-integer arguments!"); 2497 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2498 "getTruncateOrNoop cannot extend!"); 2499 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2500 return V; // No conversion 2501 return getTruncateExpr(V, Ty); 2502} 2503 2504/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2505/// the types using zero-extension, and then perform a umax operation 2506/// with them. 2507const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2508 const SCEV *RHS) { 2509 const SCEV *PromotedLHS = LHS; 2510 const SCEV *PromotedRHS = RHS; 2511 2512 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2513 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2514 else 2515 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2516 2517 return getUMaxExpr(PromotedLHS, PromotedRHS); 2518} 2519 2520/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2521/// the types using zero-extension, and then perform a umin operation 2522/// with them. 2523const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2524 const SCEV *RHS) { 2525 const SCEV *PromotedLHS = LHS; 2526 const SCEV *PromotedRHS = RHS; 2527 2528 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2529 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2530 else 2531 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2532 2533 return getUMinExpr(PromotedLHS, PromotedRHS); 2534} 2535 2536/// PushDefUseChildren - Push users of the given Instruction 2537/// onto the given Worklist. 2538static void 2539PushDefUseChildren(Instruction *I, 2540 SmallVectorImpl<Instruction *> &Worklist) { 2541 // Push the def-use children onto the Worklist stack. 2542 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2543 UI != UE; ++UI) 2544 Worklist.push_back(cast<Instruction>(UI)); 2545} 2546 2547/// ForgetSymbolicValue - This looks up computed SCEV values for all 2548/// instructions that depend on the given instruction and removes them from 2549/// the Scalars map if they reference SymName. This is used during PHI 2550/// resolution. 2551void 2552ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2553 SmallVector<Instruction *, 16> Worklist; 2554 PushDefUseChildren(PN, Worklist); 2555 2556 SmallPtrSet<Instruction *, 8> Visited; 2557 Visited.insert(PN); 2558 while (!Worklist.empty()) { 2559 Instruction *I = Worklist.pop_back_val(); 2560 if (!Visited.insert(I)) continue; 2561 2562 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2563 Scalars.find(static_cast<Value *>(I)); 2564 if (It != Scalars.end()) { 2565 // Short-circuit the def-use traversal if the symbolic name 2566 // ceases to appear in expressions. 2567 if (It->second != SymName && !It->second->hasOperand(SymName)) 2568 continue; 2569 2570 // SCEVUnknown for a PHI either means that it has an unrecognized 2571 // structure, it's a PHI that's in the progress of being computed 2572 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2573 // additional loop trip count information isn't going to change anything. 2574 // In the second case, createNodeForPHI will perform the necessary 2575 // updates on its own when it gets to that point. In the third, we do 2576 // want to forget the SCEVUnknown. 2577 if (!isa<PHINode>(I) || 2578 !isa<SCEVUnknown>(It->second) || 2579 (I != PN && It->second == SymName)) { 2580 ValuesAtScopes.erase(It->second); 2581 Scalars.erase(It); 2582 } 2583 } 2584 2585 PushDefUseChildren(I, Worklist); 2586 } 2587} 2588 2589/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2590/// a loop header, making it a potential recurrence, or it doesn't. 2591/// 2592const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2593 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized. 2594 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2595 if (L->getHeader() == PN->getParent()) { 2596 // If it lives in the loop header, it has two incoming values, one 2597 // from outside the loop, and one from inside. 2598 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0)); 2599 unsigned BackEdge = IncomingEdge^1; 2600 2601 // While we are analyzing this PHI node, handle its value symbolically. 2602 const SCEV *SymbolicName = getUnknown(PN); 2603 assert(Scalars.find(PN) == Scalars.end() && 2604 "PHI node already processed?"); 2605 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2606 2607 // Using this symbolic name for the PHI, analyze the value coming around 2608 // the back-edge. 2609 Value *BEValueV = PN->getIncomingValue(BackEdge); 2610 const SCEV *BEValue = getSCEV(BEValueV); 2611 2612 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2613 // has a special value for the first iteration of the loop. 2614 2615 // If the value coming around the backedge is an add with the symbolic 2616 // value we just inserted, then we found a simple induction variable! 2617 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2618 // If there is a single occurrence of the symbolic value, replace it 2619 // with a recurrence. 2620 unsigned FoundIndex = Add->getNumOperands(); 2621 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2622 if (Add->getOperand(i) == SymbolicName) 2623 if (FoundIndex == e) { 2624 FoundIndex = i; 2625 break; 2626 } 2627 2628 if (FoundIndex != Add->getNumOperands()) { 2629 // Create an add with everything but the specified operand. 2630 SmallVector<const SCEV *, 8> Ops; 2631 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2632 if (i != FoundIndex) 2633 Ops.push_back(Add->getOperand(i)); 2634 const SCEV *Accum = getAddExpr(Ops); 2635 2636 // This is not a valid addrec if the step amount is varying each 2637 // loop iteration, but is not itself an addrec in this loop. 2638 if (Accum->isLoopInvariant(L) || 2639 (isa<SCEVAddRecExpr>(Accum) && 2640 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2641 bool HasNUW = false; 2642 bool HasNSW = false; 2643 2644 // If the increment doesn't overflow, then neither the addrec nor 2645 // the post-increment will overflow. 2646 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2647 if (OBO->hasNoUnsignedWrap()) 2648 HasNUW = true; 2649 if (OBO->hasNoSignedWrap()) 2650 HasNSW = true; 2651 } 2652 2653 const SCEV *StartVal = 2654 getSCEV(PN->getIncomingValue(IncomingEdge)); 2655 const SCEV *PHISCEV = 2656 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2657 2658 // Since the no-wrap flags are on the increment, they apply to the 2659 // post-incremented value as well. 2660 if (Accum->isLoopInvariant(L)) 2661 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2662 Accum, L, HasNUW, HasNSW); 2663 2664 // Okay, for the entire analysis of this edge we assumed the PHI 2665 // to be symbolic. We now need to go back and purge all of the 2666 // entries for the scalars that use the symbolic expression. 2667 ForgetSymbolicName(PN, SymbolicName); 2668 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2669 return PHISCEV; 2670 } 2671 } 2672 } else if (const SCEVAddRecExpr *AddRec = 2673 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2674 // Otherwise, this could be a loop like this: 2675 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2676 // In this case, j = {1,+,1} and BEValue is j. 2677 // Because the other in-value of i (0) fits the evolution of BEValue 2678 // i really is an addrec evolution. 2679 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2680 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge)); 2681 2682 // If StartVal = j.start - j.stride, we can use StartVal as the 2683 // initial step of the addrec evolution. 2684 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2685 AddRec->getOperand(1))) { 2686 const SCEV *PHISCEV = 2687 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2688 2689 // Okay, for the entire analysis of this edge we assumed the PHI 2690 // to be symbolic. We now need to go back and purge all of the 2691 // entries for the scalars that use the symbolic expression. 2692 ForgetSymbolicName(PN, SymbolicName); 2693 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2694 return PHISCEV; 2695 } 2696 } 2697 } 2698 2699 return SymbolicName; 2700 } 2701 2702 // If the PHI has a single incoming value, follow that value, unless the 2703 // PHI's incoming blocks are in a different loop, in which case doing so 2704 // risks breaking LCSSA form. Instcombine would normally zap these, but 2705 // it doesn't have DominatorTree information, so it may miss cases. 2706 if (Value *V = PN->hasConstantValue(DT)) { 2707 bool AllSameLoop = true; 2708 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2709 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2710 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2711 AllSameLoop = false; 2712 break; 2713 } 2714 if (AllSameLoop) 2715 return getSCEV(V); 2716 } 2717 2718 // If it's not a loop phi, we can't handle it yet. 2719 return getUnknown(PN); 2720} 2721 2722/// createNodeForGEP - Expand GEP instructions into add and multiply 2723/// operations. This allows them to be analyzed by regular SCEV code. 2724/// 2725const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2726 2727 bool InBounds = GEP->isInBounds(); 2728 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2729 Value *Base = GEP->getOperand(0); 2730 // Don't attempt to analyze GEPs over unsized objects. 2731 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2732 return getUnknown(GEP); 2733 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy); 2734 gep_type_iterator GTI = gep_type_begin(GEP); 2735 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), 2736 E = GEP->op_end(); 2737 I != E; ++I) { 2738 Value *Index = *I; 2739 // Compute the (potentially symbolic) offset in bytes for this index. 2740 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2741 // For a struct, add the member offset. 2742 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2743 TotalOffset = getAddExpr(TotalOffset, 2744 getOffsetOfExpr(STy, FieldNo), 2745 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2746 } else { 2747 // For an array, add the element offset, explicitly scaled. 2748 const SCEV *LocalOffset = getSCEV(Index); 2749 // Getelementptr indices are signed. 2750 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); 2751 // Lower "inbounds" GEPs to NSW arithmetic. 2752 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), 2753 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2754 TotalOffset = getAddExpr(TotalOffset, LocalOffset, 2755 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2756 } 2757 } 2758 return getAddExpr(getSCEV(Base), TotalOffset, 2759 /*HasNUW=*/false, /*HasNSW=*/InBounds); 2760} 2761 2762/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2763/// guaranteed to end in (at every loop iteration). It is, at the same time, 2764/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2765/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2766uint32_t 2767ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2768 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2769 return C->getValue()->getValue().countTrailingZeros(); 2770 2771 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2772 return std::min(GetMinTrailingZeros(T->getOperand()), 2773 (uint32_t)getTypeSizeInBits(T->getType())); 2774 2775 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2776 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2777 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2778 getTypeSizeInBits(E->getType()) : OpRes; 2779 } 2780 2781 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2782 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2783 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2784 getTypeSizeInBits(E->getType()) : OpRes; 2785 } 2786 2787 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2788 // The result is the min of all operands results. 2789 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2790 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2791 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2792 return MinOpRes; 2793 } 2794 2795 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2796 // The result is the sum of all operands results. 2797 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2798 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2799 for (unsigned i = 1, e = M->getNumOperands(); 2800 SumOpRes != BitWidth && i != e; ++i) 2801 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2802 BitWidth); 2803 return SumOpRes; 2804 } 2805 2806 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2807 // The result is the min of all operands results. 2808 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2809 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2810 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2811 return MinOpRes; 2812 } 2813 2814 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2815 // The result is the min of all operands results. 2816 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2817 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2818 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2819 return MinOpRes; 2820 } 2821 2822 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2823 // The result is the min of all operands results. 2824 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2825 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2826 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2827 return MinOpRes; 2828 } 2829 2830 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2831 // For a SCEVUnknown, ask ValueTracking. 2832 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2833 APInt Mask = APInt::getAllOnesValue(BitWidth); 2834 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2835 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2836 return Zeros.countTrailingOnes(); 2837 } 2838 2839 // SCEVUDivExpr 2840 return 0; 2841} 2842 2843/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2844/// 2845ConstantRange 2846ScalarEvolution::getUnsignedRange(const SCEV *S) { 2847 2848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2849 return ConstantRange(C->getValue()->getValue()); 2850 2851 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2852 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2853 2854 // If the value has known zeros, the maximum unsigned value will have those 2855 // known zeros as well. 2856 uint32_t TZ = GetMinTrailingZeros(S); 2857 if (TZ != 0) 2858 ConservativeResult = 2859 ConstantRange(APInt::getMinValue(BitWidth), 2860 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2861 2862 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2863 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2864 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2865 X = X.add(getUnsignedRange(Add->getOperand(i))); 2866 return ConservativeResult.intersectWith(X); 2867 } 2868 2869 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2870 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2871 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2872 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2873 return ConservativeResult.intersectWith(X); 2874 } 2875 2876 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2877 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2878 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2879 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2880 return ConservativeResult.intersectWith(X); 2881 } 2882 2883 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2884 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2885 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 2886 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 2887 return ConservativeResult.intersectWith(X); 2888 } 2889 2890 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 2891 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 2892 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 2893 return ConservativeResult.intersectWith(X.udiv(Y)); 2894 } 2895 2896 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 2897 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 2898 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 2899 } 2900 2901 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 2902 ConstantRange X = getUnsignedRange(SExt->getOperand()); 2903 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 2904 } 2905 2906 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 2907 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 2908 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 2909 } 2910 2911 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 2912 // If there's no unsigned wrap, the value will never be less than its 2913 // initial value. 2914 if (AddRec->hasNoUnsignedWrap()) 2915 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 2916 ConservativeResult = 2917 ConstantRange(C->getValue()->getValue(), 2918 APInt(getTypeSizeInBits(C->getType()), 0)); 2919 2920 // TODO: non-affine addrec 2921 if (AddRec->isAffine()) { 2922 const Type *Ty = AddRec->getType(); 2923 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 2924 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 2925 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 2926 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 2927 2928 const SCEV *Start = AddRec->getStart(); 2929 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 2930 2931 // Check for overflow. 2932 if (!AddRec->hasNoUnsignedWrap()) 2933 return ConservativeResult; 2934 2935 ConstantRange StartRange = getUnsignedRange(Start); 2936 ConstantRange EndRange = getUnsignedRange(End); 2937 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 2938 EndRange.getUnsignedMin()); 2939 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 2940 EndRange.getUnsignedMax()); 2941 if (Min.isMinValue() && Max.isMaxValue()) 2942 return ConservativeResult; 2943 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 2944 } 2945 } 2946 2947 return ConservativeResult; 2948 } 2949 2950 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2951 // For a SCEVUnknown, ask ValueTracking. 2952 APInt Mask = APInt::getAllOnesValue(BitWidth); 2953 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2954 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 2955 if (Ones == ~Zeros + 1) 2956 return ConservativeResult; 2957 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 2958 } 2959 2960 return ConservativeResult; 2961} 2962 2963/// getSignedRange - Determine the signed range for a particular SCEV. 2964/// 2965ConstantRange 2966ScalarEvolution::getSignedRange(const SCEV *S) { 2967 2968 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2969 return ConstantRange(C->getValue()->getValue()); 2970 2971 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2972 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2973 2974 // If the value has known zeros, the maximum signed value will have those 2975 // known zeros as well. 2976 uint32_t TZ = GetMinTrailingZeros(S); 2977 if (TZ != 0) 2978 ConservativeResult = 2979 ConstantRange(APInt::getSignedMinValue(BitWidth), 2980 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 2981 2982 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2983 ConstantRange X = getSignedRange(Add->getOperand(0)); 2984 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2985 X = X.add(getSignedRange(Add->getOperand(i))); 2986 return ConservativeResult.intersectWith(X); 2987 } 2988 2989 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2990 ConstantRange X = getSignedRange(Mul->getOperand(0)); 2991 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2992 X = X.multiply(getSignedRange(Mul->getOperand(i))); 2993 return ConservativeResult.intersectWith(X); 2994 } 2995 2996 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2997 ConstantRange X = getSignedRange(SMax->getOperand(0)); 2998 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2999 X = X.smax(getSignedRange(SMax->getOperand(i))); 3000 return ConservativeResult.intersectWith(X); 3001 } 3002 3003 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3004 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3005 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3006 X = X.umax(getSignedRange(UMax->getOperand(i))); 3007 return ConservativeResult.intersectWith(X); 3008 } 3009 3010 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3011 ConstantRange X = getSignedRange(UDiv->getLHS()); 3012 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3013 return ConservativeResult.intersectWith(X.udiv(Y)); 3014 } 3015 3016 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3017 ConstantRange X = getSignedRange(ZExt->getOperand()); 3018 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3019 } 3020 3021 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3022 ConstantRange X = getSignedRange(SExt->getOperand()); 3023 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3024 } 3025 3026 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3027 ConstantRange X = getSignedRange(Trunc->getOperand()); 3028 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3029 } 3030 3031 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3032 // If there's no signed wrap, and all the operands have the same sign or 3033 // zero, the value won't ever change sign. 3034 if (AddRec->hasNoSignedWrap()) { 3035 bool AllNonNeg = true; 3036 bool AllNonPos = true; 3037 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3038 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3039 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3040 } 3041 if (AllNonNeg) 3042 ConservativeResult = ConservativeResult.intersectWith( 3043 ConstantRange(APInt(BitWidth, 0), 3044 APInt::getSignedMinValue(BitWidth))); 3045 else if (AllNonPos) 3046 ConservativeResult = ConservativeResult.intersectWith( 3047 ConstantRange(APInt::getSignedMinValue(BitWidth), 3048 APInt(BitWidth, 1))); 3049 } 3050 3051 // TODO: non-affine addrec 3052 if (AddRec->isAffine()) { 3053 const Type *Ty = AddRec->getType(); 3054 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3055 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3056 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3057 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3058 3059 const SCEV *Start = AddRec->getStart(); 3060 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); 3061 3062 // Check for overflow. 3063 if (!AddRec->hasNoSignedWrap()) 3064 return ConservativeResult; 3065 3066 ConstantRange StartRange = getSignedRange(Start); 3067 ConstantRange EndRange = getSignedRange(End); 3068 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3069 EndRange.getSignedMin()); 3070 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3071 EndRange.getSignedMax()); 3072 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3073 return ConservativeResult; 3074 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3075 } 3076 } 3077 3078 return ConservativeResult; 3079 } 3080 3081 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3082 // For a SCEVUnknown, ask ValueTracking. 3083 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3084 return ConservativeResult; 3085 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3086 if (NS == 1) 3087 return ConservativeResult; 3088 return ConservativeResult.intersectWith( 3089 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3090 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3091 } 3092 3093 return ConservativeResult; 3094} 3095 3096/// createSCEV - We know that there is no SCEV for the specified value. 3097/// Analyze the expression. 3098/// 3099const SCEV *ScalarEvolution::createSCEV(Value *V) { 3100 if (!isSCEVable(V->getType())) 3101 return getUnknown(V); 3102 3103 unsigned Opcode = Instruction::UserOp1; 3104 if (Instruction *I = dyn_cast<Instruction>(V)) 3105 Opcode = I->getOpcode(); 3106 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3107 Opcode = CE->getOpcode(); 3108 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3109 return getConstant(CI); 3110 else if (isa<ConstantPointerNull>(V)) 3111 return getIntegerSCEV(0, V->getType()); 3112 else if (isa<UndefValue>(V)) 3113 return getIntegerSCEV(0, V->getType()); 3114 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3115 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3116 else 3117 return getUnknown(V); 3118 3119 Operator *U = cast<Operator>(V); 3120 switch (Opcode) { 3121 case Instruction::Add: 3122 // Don't transfer the NSW and NUW bits from the Add instruction to the 3123 // Add expression, because the Instruction may be guarded by control 3124 // flow and the no-overflow bits may not be valid for the expression in 3125 // any context. 3126 return getAddExpr(getSCEV(U->getOperand(0)), 3127 getSCEV(U->getOperand(1))); 3128 case Instruction::Mul: 3129 // Don't transfer the NSW and NUW bits from the Mul instruction to the 3130 // Mul expression, as with Add. 3131 return getMulExpr(getSCEV(U->getOperand(0)), 3132 getSCEV(U->getOperand(1))); 3133 case Instruction::UDiv: 3134 return getUDivExpr(getSCEV(U->getOperand(0)), 3135 getSCEV(U->getOperand(1))); 3136 case Instruction::Sub: 3137 return getMinusSCEV(getSCEV(U->getOperand(0)), 3138 getSCEV(U->getOperand(1))); 3139 case Instruction::And: 3140 // For an expression like x&255 that merely masks off the high bits, 3141 // use zext(trunc(x)) as the SCEV expression. 3142 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3143 if (CI->isNullValue()) 3144 return getSCEV(U->getOperand(1)); 3145 if (CI->isAllOnesValue()) 3146 return getSCEV(U->getOperand(0)); 3147 const APInt &A = CI->getValue(); 3148 3149 // Instcombine's ShrinkDemandedConstant may strip bits out of 3150 // constants, obscuring what would otherwise be a low-bits mask. 3151 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3152 // knew about to reconstruct a low-bits mask value. 3153 unsigned LZ = A.countLeadingZeros(); 3154 unsigned BitWidth = A.getBitWidth(); 3155 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3156 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3157 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3158 3159 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3160 3161 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3162 return 3163 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3164 IntegerType::get(getContext(), BitWidth - LZ)), 3165 U->getType()); 3166 } 3167 break; 3168 3169 case Instruction::Or: 3170 // If the RHS of the Or is a constant, we may have something like: 3171 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3172 // optimizations will transparently handle this case. 3173 // 3174 // In order for this transformation to be safe, the LHS must be of the 3175 // form X*(2^n) and the Or constant must be less than 2^n. 3176 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3177 const SCEV *LHS = getSCEV(U->getOperand(0)); 3178 const APInt &CIVal = CI->getValue(); 3179 if (GetMinTrailingZeros(LHS) >= 3180 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3181 // Build a plain add SCEV. 3182 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3183 // If the LHS of the add was an addrec and it has no-wrap flags, 3184 // transfer the no-wrap flags, since an or won't introduce a wrap. 3185 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3186 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3187 if (OldAR->hasNoUnsignedWrap()) 3188 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3189 if (OldAR->hasNoSignedWrap()) 3190 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3191 } 3192 return S; 3193 } 3194 } 3195 break; 3196 case Instruction::Xor: 3197 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3198 // If the RHS of the xor is a signbit, then this is just an add. 3199 // Instcombine turns add of signbit into xor as a strength reduction step. 3200 if (CI->getValue().isSignBit()) 3201 return getAddExpr(getSCEV(U->getOperand(0)), 3202 getSCEV(U->getOperand(1))); 3203 3204 // If the RHS of xor is -1, then this is a not operation. 3205 if (CI->isAllOnesValue()) 3206 return getNotSCEV(getSCEV(U->getOperand(0))); 3207 3208 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3209 // This is a variant of the check for xor with -1, and it handles 3210 // the case where instcombine has trimmed non-demanded bits out 3211 // of an xor with -1. 3212 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3213 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3214 if (BO->getOpcode() == Instruction::And && 3215 LCI->getValue() == CI->getValue()) 3216 if (const SCEVZeroExtendExpr *Z = 3217 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3218 const Type *UTy = U->getType(); 3219 const SCEV *Z0 = Z->getOperand(); 3220 const Type *Z0Ty = Z0->getType(); 3221 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3222 3223 // If C is a low-bits mask, the zero extend is serving to 3224 // mask off the high bits. Complement the operand and 3225 // re-apply the zext. 3226 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3227 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3228 3229 // If C is a single bit, it may be in the sign-bit position 3230 // before the zero-extend. In this case, represent the xor 3231 // using an add, which is equivalent, and re-apply the zext. 3232 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3233 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3234 Trunc.isSignBit()) 3235 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3236 UTy); 3237 } 3238 } 3239 break; 3240 3241 case Instruction::Shl: 3242 // Turn shift left of a constant amount into a multiply. 3243 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3244 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3245 Constant *X = ConstantInt::get(getContext(), 3246 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3247 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3248 } 3249 break; 3250 3251 case Instruction::LShr: 3252 // Turn logical shift right of a constant into a unsigned divide. 3253 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3254 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3255 Constant *X = ConstantInt::get(getContext(), 3256 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth))); 3257 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3258 } 3259 break; 3260 3261 case Instruction::AShr: 3262 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3263 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3264 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0))) 3265 if (L->getOpcode() == Instruction::Shl && 3266 L->getOperand(1) == U->getOperand(1)) { 3267 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3268 uint64_t Amt = BitWidth - CI->getZExtValue(); 3269 if (Amt == BitWidth) 3270 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3271 if (Amt > BitWidth) 3272 return getIntegerSCEV(0, U->getType()); // value is undefined 3273 return 3274 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3275 IntegerType::get(getContext(), Amt)), 3276 U->getType()); 3277 } 3278 break; 3279 3280 case Instruction::Trunc: 3281 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3282 3283 case Instruction::ZExt: 3284 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3285 3286 case Instruction::SExt: 3287 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3288 3289 case Instruction::BitCast: 3290 // BitCasts are no-op casts so we just eliminate the cast. 3291 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3292 return getSCEV(U->getOperand(0)); 3293 break; 3294 3295 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3296 // lead to pointer expressions which cannot safely be expanded to GEPs, 3297 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3298 // simplifying integer expressions. 3299 3300 case Instruction::GetElementPtr: 3301 return createNodeForGEP(cast<GEPOperator>(U)); 3302 3303 case Instruction::PHI: 3304 return createNodeForPHI(cast<PHINode>(U)); 3305 3306 case Instruction::Select: 3307 // This could be a smax or umax that was lowered earlier. 3308 // Try to recover it. 3309 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3310 Value *LHS = ICI->getOperand(0); 3311 Value *RHS = ICI->getOperand(1); 3312 switch (ICI->getPredicate()) { 3313 case ICmpInst::ICMP_SLT: 3314 case ICmpInst::ICMP_SLE: 3315 std::swap(LHS, RHS); 3316 // fall through 3317 case ICmpInst::ICMP_SGT: 3318 case ICmpInst::ICMP_SGE: 3319 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3320 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3321 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3322 return getSMinExpr(getSCEV(LHS), getSCEV(RHS)); 3323 break; 3324 case ICmpInst::ICMP_ULT: 3325 case ICmpInst::ICMP_ULE: 3326 std::swap(LHS, RHS); 3327 // fall through 3328 case ICmpInst::ICMP_UGT: 3329 case ICmpInst::ICMP_UGE: 3330 if (LHS == U->getOperand(1) && RHS == U->getOperand(2)) 3331 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS)); 3332 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1)) 3333 return getUMinExpr(getSCEV(LHS), getSCEV(RHS)); 3334 break; 3335 case ICmpInst::ICMP_NE: 3336 // n != 0 ? n : 1 -> umax(n, 1) 3337 if (LHS == U->getOperand(1) && 3338 isa<ConstantInt>(U->getOperand(2)) && 3339 cast<ConstantInt>(U->getOperand(2))->isOne() && 3340 isa<ConstantInt>(RHS) && 3341 cast<ConstantInt>(RHS)->isZero()) 3342 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2))); 3343 break; 3344 case ICmpInst::ICMP_EQ: 3345 // n == 0 ? 1 : n -> umax(n, 1) 3346 if (LHS == U->getOperand(2) && 3347 isa<ConstantInt>(U->getOperand(1)) && 3348 cast<ConstantInt>(U->getOperand(1))->isOne() && 3349 isa<ConstantInt>(RHS) && 3350 cast<ConstantInt>(RHS)->isZero()) 3351 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1))); 3352 break; 3353 default: 3354 break; 3355 } 3356 } 3357 3358 default: // We cannot analyze this expression. 3359 break; 3360 } 3361 3362 return getUnknown(V); 3363} 3364 3365 3366 3367//===----------------------------------------------------------------------===// 3368// Iteration Count Computation Code 3369// 3370 3371/// getBackedgeTakenCount - If the specified loop has a predictable 3372/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3373/// object. The backedge-taken count is the number of times the loop header 3374/// will be branched to from within the loop. This is one less than the 3375/// trip count of the loop, since it doesn't count the first iteration, 3376/// when the header is branched to from outside the loop. 3377/// 3378/// Note that it is not valid to call this method on a loop without a 3379/// loop-invariant backedge-taken count (see 3380/// hasLoopInvariantBackedgeTakenCount). 3381/// 3382const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3383 return getBackedgeTakenInfo(L).Exact; 3384} 3385 3386/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3387/// return the least SCEV value that is known never to be less than the 3388/// actual backedge taken count. 3389const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3390 return getBackedgeTakenInfo(L).Max; 3391} 3392 3393/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3394/// onto the given Worklist. 3395static void 3396PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3397 BasicBlock *Header = L->getHeader(); 3398 3399 // Push all Loop-header PHIs onto the Worklist stack. 3400 for (BasicBlock::iterator I = Header->begin(); 3401 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3402 Worklist.push_back(PN); 3403} 3404 3405const ScalarEvolution::BackedgeTakenInfo & 3406ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3407 // Initially insert a CouldNotCompute for this loop. If the insertion 3408 // succeeds, proceed to actually compute a backedge-taken count and 3409 // update the value. The temporary CouldNotCompute value tells SCEV 3410 // code elsewhere that it shouldn't attempt to request a new 3411 // backedge-taken count, which could result in infinite recursion. 3412 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3413 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3414 if (Pair.second) { 3415 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3416 if (BECount.Exact != getCouldNotCompute()) { 3417 assert(BECount.Exact->isLoopInvariant(L) && 3418 BECount.Max->isLoopInvariant(L) && 3419 "Computed backedge-taken count isn't loop invariant for loop!"); 3420 ++NumTripCountsComputed; 3421 3422 // Update the value in the map. 3423 Pair.first->second = BECount; 3424 } else { 3425 if (BECount.Max != getCouldNotCompute()) 3426 // Update the value in the map. 3427 Pair.first->second = BECount; 3428 if (isa<PHINode>(L->getHeader()->begin())) 3429 // Only count loops that have phi nodes as not being computable. 3430 ++NumTripCountsNotComputed; 3431 } 3432 3433 // Now that we know more about the trip count for this loop, forget any 3434 // existing SCEV values for PHI nodes in this loop since they are only 3435 // conservative estimates made without the benefit of trip count 3436 // information. This is similar to the code in forgetLoop, except that 3437 // it handles SCEVUnknown PHI nodes specially. 3438 if (BECount.hasAnyInfo()) { 3439 SmallVector<Instruction *, 16> Worklist; 3440 PushLoopPHIs(L, Worklist); 3441 3442 SmallPtrSet<Instruction *, 8> Visited; 3443 while (!Worklist.empty()) { 3444 Instruction *I = Worklist.pop_back_val(); 3445 if (!Visited.insert(I)) continue; 3446 3447 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3448 Scalars.find(static_cast<Value *>(I)); 3449 if (It != Scalars.end()) { 3450 // SCEVUnknown for a PHI either means that it has an unrecognized 3451 // structure, or it's a PHI that's in the progress of being computed 3452 // by createNodeForPHI. In the former case, additional loop trip 3453 // count information isn't going to change anything. In the later 3454 // case, createNodeForPHI will perform the necessary updates on its 3455 // own when it gets to that point. 3456 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3457 ValuesAtScopes.erase(It->second); 3458 Scalars.erase(It); 3459 } 3460 if (PHINode *PN = dyn_cast<PHINode>(I)) 3461 ConstantEvolutionLoopExitValue.erase(PN); 3462 } 3463 3464 PushDefUseChildren(I, Worklist); 3465 } 3466 } 3467 } 3468 return Pair.first->second; 3469} 3470 3471/// forgetLoop - This method should be called by the client when it has 3472/// changed a loop in a way that may effect ScalarEvolution's ability to 3473/// compute a trip count, or if the loop is deleted. 3474void ScalarEvolution::forgetLoop(const Loop *L) { 3475 // Drop any stored trip count value. 3476 BackedgeTakenCounts.erase(L); 3477 3478 // Drop information about expressions based on loop-header PHIs. 3479 SmallVector<Instruction *, 16> Worklist; 3480 PushLoopPHIs(L, Worklist); 3481 3482 SmallPtrSet<Instruction *, 8> Visited; 3483 while (!Worklist.empty()) { 3484 Instruction *I = Worklist.pop_back_val(); 3485 if (!Visited.insert(I)) continue; 3486 3487 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3488 Scalars.find(static_cast<Value *>(I)); 3489 if (It != Scalars.end()) { 3490 ValuesAtScopes.erase(It->second); 3491 Scalars.erase(It); 3492 if (PHINode *PN = dyn_cast<PHINode>(I)) 3493 ConstantEvolutionLoopExitValue.erase(PN); 3494 } 3495 3496 PushDefUseChildren(I, Worklist); 3497 } 3498} 3499 3500/// forgetValue - This method should be called by the client when it has 3501/// changed a value in a way that may effect its value, or which may 3502/// disconnect it from a def-use chain linking it to a loop. 3503void ScalarEvolution::forgetValue(Value *V) { 3504 Instruction *I = dyn_cast<Instruction>(V); 3505 if (!I) return; 3506 3507 // Drop information about expressions based on loop-header PHIs. 3508 SmallVector<Instruction *, 16> Worklist; 3509 Worklist.push_back(I); 3510 3511 SmallPtrSet<Instruction *, 8> Visited; 3512 while (!Worklist.empty()) { 3513 I = Worklist.pop_back_val(); 3514 if (!Visited.insert(I)) continue; 3515 3516 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3517 Scalars.find(static_cast<Value *>(I)); 3518 if (It != Scalars.end()) { 3519 ValuesAtScopes.erase(It->second); 3520 Scalars.erase(It); 3521 if (PHINode *PN = dyn_cast<PHINode>(I)) 3522 ConstantEvolutionLoopExitValue.erase(PN); 3523 } 3524 3525 PushDefUseChildren(I, Worklist); 3526 } 3527} 3528 3529/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3530/// of the specified loop will execute. 3531ScalarEvolution::BackedgeTakenInfo 3532ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3533 SmallVector<BasicBlock *, 8> ExitingBlocks; 3534 L->getExitingBlocks(ExitingBlocks); 3535 3536 // Examine all exits and pick the most conservative values. 3537 const SCEV *BECount = getCouldNotCompute(); 3538 const SCEV *MaxBECount = getCouldNotCompute(); 3539 bool CouldNotComputeBECount = false; 3540 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3541 BackedgeTakenInfo NewBTI = 3542 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3543 3544 if (NewBTI.Exact == getCouldNotCompute()) { 3545 // We couldn't compute an exact value for this exit, so 3546 // we won't be able to compute an exact value for the loop. 3547 CouldNotComputeBECount = true; 3548 BECount = getCouldNotCompute(); 3549 } else if (!CouldNotComputeBECount) { 3550 if (BECount == getCouldNotCompute()) 3551 BECount = NewBTI.Exact; 3552 else 3553 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3554 } 3555 if (MaxBECount == getCouldNotCompute()) 3556 MaxBECount = NewBTI.Max; 3557 else if (NewBTI.Max != getCouldNotCompute()) 3558 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3559 } 3560 3561 return BackedgeTakenInfo(BECount, MaxBECount); 3562} 3563 3564/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3565/// of the specified loop will execute if it exits via the specified block. 3566ScalarEvolution::BackedgeTakenInfo 3567ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3568 BasicBlock *ExitingBlock) { 3569 3570 // Okay, we've chosen an exiting block. See what condition causes us to 3571 // exit at this block. 3572 // 3573 // FIXME: we should be able to handle switch instructions (with a single exit) 3574 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3575 if (ExitBr == 0) return getCouldNotCompute(); 3576 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3577 3578 // At this point, we know we have a conditional branch that determines whether 3579 // the loop is exited. However, we don't know if the branch is executed each 3580 // time through the loop. If not, then the execution count of the branch will 3581 // not be equal to the trip count of the loop. 3582 // 3583 // Currently we check for this by checking to see if the Exit branch goes to 3584 // the loop header. If so, we know it will always execute the same number of 3585 // times as the loop. We also handle the case where the exit block *is* the 3586 // loop header. This is common for un-rotated loops. 3587 // 3588 // If both of those tests fail, walk up the unique predecessor chain to the 3589 // header, stopping if there is an edge that doesn't exit the loop. If the 3590 // header is reached, the execution count of the branch will be equal to the 3591 // trip count of the loop. 3592 // 3593 // More extensive analysis could be done to handle more cases here. 3594 // 3595 if (ExitBr->getSuccessor(0) != L->getHeader() && 3596 ExitBr->getSuccessor(1) != L->getHeader() && 3597 ExitBr->getParent() != L->getHeader()) { 3598 // The simple checks failed, try climbing the unique predecessor chain 3599 // up to the header. 3600 bool Ok = false; 3601 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3602 BasicBlock *Pred = BB->getUniquePredecessor(); 3603 if (!Pred) 3604 return getCouldNotCompute(); 3605 TerminatorInst *PredTerm = Pred->getTerminator(); 3606 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3607 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3608 if (PredSucc == BB) 3609 continue; 3610 // If the predecessor has a successor that isn't BB and isn't 3611 // outside the loop, assume the worst. 3612 if (L->contains(PredSucc)) 3613 return getCouldNotCompute(); 3614 } 3615 if (Pred == L->getHeader()) { 3616 Ok = true; 3617 break; 3618 } 3619 BB = Pred; 3620 } 3621 if (!Ok) 3622 return getCouldNotCompute(); 3623 } 3624 3625 // Proceed to the next level to examine the exit condition expression. 3626 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3627 ExitBr->getSuccessor(0), 3628 ExitBr->getSuccessor(1)); 3629} 3630 3631/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3632/// backedge of the specified loop will execute if its exit condition 3633/// were a conditional branch of ExitCond, TBB, and FBB. 3634ScalarEvolution::BackedgeTakenInfo 3635ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3636 Value *ExitCond, 3637 BasicBlock *TBB, 3638 BasicBlock *FBB) { 3639 // Check if the controlling expression for this loop is an And or Or. 3640 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3641 if (BO->getOpcode() == Instruction::And) { 3642 // Recurse on the operands of the and. 3643 BackedgeTakenInfo BTI0 = 3644 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3645 BackedgeTakenInfo BTI1 = 3646 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3647 const SCEV *BECount = getCouldNotCompute(); 3648 const SCEV *MaxBECount = getCouldNotCompute(); 3649 if (L->contains(TBB)) { 3650 // Both conditions must be true for the loop to continue executing. 3651 // Choose the less conservative count. 3652 if (BTI0.Exact == getCouldNotCompute() || 3653 BTI1.Exact == getCouldNotCompute()) 3654 BECount = getCouldNotCompute(); 3655 else 3656 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3657 if (BTI0.Max == getCouldNotCompute()) 3658 MaxBECount = BTI1.Max; 3659 else if (BTI1.Max == getCouldNotCompute()) 3660 MaxBECount = BTI0.Max; 3661 else 3662 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3663 } else { 3664 // Both conditions must be true for the loop to exit. 3665 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3666 if (BTI0.Exact != getCouldNotCompute() && 3667 BTI1.Exact != getCouldNotCompute()) 3668 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3669 if (BTI0.Max != getCouldNotCompute() && 3670 BTI1.Max != getCouldNotCompute()) 3671 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3672 } 3673 3674 return BackedgeTakenInfo(BECount, MaxBECount); 3675 } 3676 if (BO->getOpcode() == Instruction::Or) { 3677 // Recurse on the operands of the or. 3678 BackedgeTakenInfo BTI0 = 3679 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3680 BackedgeTakenInfo BTI1 = 3681 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3682 const SCEV *BECount = getCouldNotCompute(); 3683 const SCEV *MaxBECount = getCouldNotCompute(); 3684 if (L->contains(FBB)) { 3685 // Both conditions must be false for the loop to continue executing. 3686 // Choose the less conservative count. 3687 if (BTI0.Exact == getCouldNotCompute() || 3688 BTI1.Exact == getCouldNotCompute()) 3689 BECount = getCouldNotCompute(); 3690 else 3691 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3692 if (BTI0.Max == getCouldNotCompute()) 3693 MaxBECount = BTI1.Max; 3694 else if (BTI1.Max == getCouldNotCompute()) 3695 MaxBECount = BTI0.Max; 3696 else 3697 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3698 } else { 3699 // Both conditions must be false for the loop to exit. 3700 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3701 if (BTI0.Exact != getCouldNotCompute() && 3702 BTI1.Exact != getCouldNotCompute()) 3703 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3704 if (BTI0.Max != getCouldNotCompute() && 3705 BTI1.Max != getCouldNotCompute()) 3706 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); 3707 } 3708 3709 return BackedgeTakenInfo(BECount, MaxBECount); 3710 } 3711 } 3712 3713 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3714 // Proceed to the next level to examine the icmp. 3715 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3716 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3717 3718 // Check for a constant condition. These are normally stripped out by 3719 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3720 // preserve the CFG and is temporarily leaving constant conditions 3721 // in place. 3722 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3723 if (L->contains(FBB) == !CI->getZExtValue()) 3724 // The backedge is always taken. 3725 return getCouldNotCompute(); 3726 else 3727 // The backedge is never taken. 3728 return getIntegerSCEV(0, CI->getType()); 3729 } 3730 3731 // If it's not an integer or pointer comparison then compute it the hard way. 3732 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3733} 3734 3735/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 3736/// backedge of the specified loop will execute if its exit condition 3737/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 3738ScalarEvolution::BackedgeTakenInfo 3739ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 3740 ICmpInst *ExitCond, 3741 BasicBlock *TBB, 3742 BasicBlock *FBB) { 3743 3744 // If the condition was exit on true, convert the condition to exit on false 3745 ICmpInst::Predicate Cond; 3746 if (!L->contains(FBB)) 3747 Cond = ExitCond->getPredicate(); 3748 else 3749 Cond = ExitCond->getInversePredicate(); 3750 3751 // Handle common loops like: for (X = "string"; *X; ++X) 3752 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 3753 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 3754 BackedgeTakenInfo ItCnt = 3755 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 3756 if (ItCnt.hasAnyInfo()) 3757 return ItCnt; 3758 } 3759 3760 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 3761 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 3762 3763 // Try to evaluate any dependencies out of the loop. 3764 LHS = getSCEVAtScope(LHS, L); 3765 RHS = getSCEVAtScope(RHS, L); 3766 3767 // At this point, we would like to compute how many iterations of the 3768 // loop the predicate will return true for these inputs. 3769 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 3770 // If there is a loop-invariant, force it into the RHS. 3771 std::swap(LHS, RHS); 3772 Cond = ICmpInst::getSwappedPredicate(Cond); 3773 } 3774 3775 // If we have a comparison of a chrec against a constant, try to use value 3776 // ranges to answer this query. 3777 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 3778 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 3779 if (AddRec->getLoop() == L) { 3780 // Form the constant range. 3781 ConstantRange CompRange( 3782 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 3783 3784 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 3785 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 3786 } 3787 3788 switch (Cond) { 3789 case ICmpInst::ICMP_NE: { // while (X != Y) 3790 // Convert to: while (X-Y != 0) 3791 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 3792 if (BTI.hasAnyInfo()) return BTI; 3793 break; 3794 } 3795 case ICmpInst::ICMP_EQ: { // while (X == Y) 3796 // Convert to: while (X-Y == 0) 3797 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 3798 if (BTI.hasAnyInfo()) return BTI; 3799 break; 3800 } 3801 case ICmpInst::ICMP_SLT: { 3802 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 3803 if (BTI.hasAnyInfo()) return BTI; 3804 break; 3805 } 3806 case ICmpInst::ICMP_SGT: { 3807 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3808 getNotSCEV(RHS), L, true); 3809 if (BTI.hasAnyInfo()) return BTI; 3810 break; 3811 } 3812 case ICmpInst::ICMP_ULT: { 3813 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 3814 if (BTI.hasAnyInfo()) return BTI; 3815 break; 3816 } 3817 case ICmpInst::ICMP_UGT: { 3818 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 3819 getNotSCEV(RHS), L, false); 3820 if (BTI.hasAnyInfo()) return BTI; 3821 break; 3822 } 3823 default: 3824#if 0 3825 dbgs() << "ComputeBackedgeTakenCount "; 3826 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 3827 dbgs() << "[unsigned] "; 3828 dbgs() << *LHS << " " 3829 << Instruction::getOpcodeName(Instruction::ICmp) 3830 << " " << *RHS << "\n"; 3831#endif 3832 break; 3833 } 3834 return 3835 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3836} 3837 3838static ConstantInt * 3839EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 3840 ScalarEvolution &SE) { 3841 const SCEV *InVal = SE.getConstant(C); 3842 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 3843 assert(isa<SCEVConstant>(Val) && 3844 "Evaluation of SCEV at constant didn't fold correctly?"); 3845 return cast<SCEVConstant>(Val)->getValue(); 3846} 3847 3848/// GetAddressedElementFromGlobal - Given a global variable with an initializer 3849/// and a GEP expression (missing the pointer index) indexing into it, return 3850/// the addressed element of the initializer or null if the index expression is 3851/// invalid. 3852static Constant * 3853GetAddressedElementFromGlobal(GlobalVariable *GV, 3854 const std::vector<ConstantInt*> &Indices) { 3855 Constant *Init = GV->getInitializer(); 3856 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 3857 uint64_t Idx = Indices[i]->getZExtValue(); 3858 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 3859 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 3860 Init = cast<Constant>(CS->getOperand(Idx)); 3861 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 3862 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 3863 Init = cast<Constant>(CA->getOperand(Idx)); 3864 } else if (isa<ConstantAggregateZero>(Init)) { 3865 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 3866 assert(Idx < STy->getNumElements() && "Bad struct index!"); 3867 Init = Constant::getNullValue(STy->getElementType(Idx)); 3868 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 3869 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 3870 Init = Constant::getNullValue(ATy->getElementType()); 3871 } else { 3872 llvm_unreachable("Unknown constant aggregate type!"); 3873 } 3874 return 0; 3875 } else { 3876 return 0; // Unknown initializer type 3877 } 3878 } 3879 return Init; 3880} 3881 3882/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 3883/// 'icmp op load X, cst', try to see if we can compute the backedge 3884/// execution count. 3885ScalarEvolution::BackedgeTakenInfo 3886ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 3887 LoadInst *LI, 3888 Constant *RHS, 3889 const Loop *L, 3890 ICmpInst::Predicate predicate) { 3891 if (LI->isVolatile()) return getCouldNotCompute(); 3892 3893 // Check to see if the loaded pointer is a getelementptr of a global. 3894 // TODO: Use SCEV instead of manually grubbing with GEPs. 3895 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 3896 if (!GEP) return getCouldNotCompute(); 3897 3898 // Make sure that it is really a constant global we are gepping, with an 3899 // initializer, and make sure the first IDX is really 0. 3900 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 3901 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 3902 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 3903 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 3904 return getCouldNotCompute(); 3905 3906 // Okay, we allow one non-constant index into the GEP instruction. 3907 Value *VarIdx = 0; 3908 std::vector<ConstantInt*> Indexes; 3909 unsigned VarIdxNum = 0; 3910 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 3911 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 3912 Indexes.push_back(CI); 3913 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 3914 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 3915 VarIdx = GEP->getOperand(i); 3916 VarIdxNum = i-2; 3917 Indexes.push_back(0); 3918 } 3919 3920 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 3921 // Check to see if X is a loop variant variable value now. 3922 const SCEV *Idx = getSCEV(VarIdx); 3923 Idx = getSCEVAtScope(Idx, L); 3924 3925 // We can only recognize very limited forms of loop index expressions, in 3926 // particular, only affine AddRec's like {C1,+,C2}. 3927 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 3928 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 3929 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 3930 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 3931 return getCouldNotCompute(); 3932 3933 unsigned MaxSteps = MaxBruteForceIterations; 3934 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 3935 ConstantInt *ItCst = ConstantInt::get( 3936 cast<IntegerType>(IdxExpr->getType()), IterationNum); 3937 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 3938 3939 // Form the GEP offset. 3940 Indexes[VarIdxNum] = Val; 3941 3942 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 3943 if (Result == 0) break; // Cannot compute! 3944 3945 // Evaluate the condition for this iteration. 3946 Result = ConstantExpr::getICmp(predicate, Result, RHS); 3947 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 3948 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 3949#if 0 3950 dbgs() << "\n***\n*** Computed loop count " << *ItCst 3951 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 3952 << "***\n"; 3953#endif 3954 ++NumArrayLenItCounts; 3955 return getConstant(ItCst); // Found terminating iteration! 3956 } 3957 } 3958 return getCouldNotCompute(); 3959} 3960 3961 3962/// CanConstantFold - Return true if we can constant fold an instruction of the 3963/// specified type, assuming that all operands were constants. 3964static bool CanConstantFold(const Instruction *I) { 3965 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 3966 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 3967 return true; 3968 3969 if (const CallInst *CI = dyn_cast<CallInst>(I)) 3970 if (const Function *F = CI->getCalledFunction()) 3971 return canConstantFoldCallTo(F); 3972 return false; 3973} 3974 3975/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 3976/// in the loop that V is derived from. We allow arbitrary operations along the 3977/// way, but the operands of an operation must either be constants or a value 3978/// derived from a constant PHI. If this expression does not fit with these 3979/// constraints, return null. 3980static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 3981 // If this is not an instruction, or if this is an instruction outside of the 3982 // loop, it can't be derived from a loop PHI. 3983 Instruction *I = dyn_cast<Instruction>(V); 3984 if (I == 0 || !L->contains(I)) return 0; 3985 3986 if (PHINode *PN = dyn_cast<PHINode>(I)) { 3987 if (L->getHeader() == I->getParent()) 3988 return PN; 3989 else 3990 // We don't currently keep track of the control flow needed to evaluate 3991 // PHIs, so we cannot handle PHIs inside of loops. 3992 return 0; 3993 } 3994 3995 // If we won't be able to constant fold this expression even if the operands 3996 // are constants, return early. 3997 if (!CanConstantFold(I)) return 0; 3998 3999 // Otherwise, we can evaluate this instruction if all of its operands are 4000 // constant or derived from a PHI node themselves. 4001 PHINode *PHI = 0; 4002 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4003 if (!(isa<Constant>(I->getOperand(Op)) || 4004 isa<GlobalValue>(I->getOperand(Op)))) { 4005 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4006 if (P == 0) return 0; // Not evolving from PHI 4007 if (PHI == 0) 4008 PHI = P; 4009 else if (PHI != P) 4010 return 0; // Evolving from multiple different PHIs. 4011 } 4012 4013 // This is a expression evolving from a constant PHI! 4014 return PHI; 4015} 4016 4017/// EvaluateExpression - Given an expression that passes the 4018/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4019/// in the loop has the value PHIVal. If we can't fold this expression for some 4020/// reason, return null. 4021static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4022 const TargetData *TD) { 4023 if (isa<PHINode>(V)) return PHIVal; 4024 if (Constant *C = dyn_cast<Constant>(V)) return C; 4025 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; 4026 Instruction *I = cast<Instruction>(V); 4027 4028 std::vector<Constant*> Operands; 4029 Operands.resize(I->getNumOperands()); 4030 4031 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4032 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4033 if (Operands[i] == 0) return 0; 4034 } 4035 4036 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4037 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4038 Operands[1], TD); 4039 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4040 &Operands[0], Operands.size(), TD); 4041} 4042 4043/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4044/// in the header of its containing loop, we know the loop executes a 4045/// constant number of times, and the PHI node is just a recurrence 4046/// involving constants, fold it. 4047Constant * 4048ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4049 const APInt &BEs, 4050 const Loop *L) { 4051 std::map<PHINode*, Constant*>::iterator I = 4052 ConstantEvolutionLoopExitValue.find(PN); 4053 if (I != ConstantEvolutionLoopExitValue.end()) 4054 return I->second; 4055 4056 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations))) 4057 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4058 4059 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4060 4061 // Since the loop is canonicalized, the PHI node must have two entries. One 4062 // entry must be a constant (coming in from outside of the loop), and the 4063 // second must be derived from the same PHI. 4064 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4065 Constant *StartCST = 4066 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4067 if (StartCST == 0) 4068 return RetVal = 0; // Must be a constant. 4069 4070 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4071 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4072 if (PN2 != PN) 4073 return RetVal = 0; // Not derived from same PHI. 4074 4075 // Execute the loop symbolically to determine the exit value. 4076 if (BEs.getActiveBits() >= 32) 4077 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4078 4079 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4080 unsigned IterationNum = 0; 4081 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4082 if (IterationNum == NumIterations) 4083 return RetVal = PHIVal; // Got exit value! 4084 4085 // Compute the value of the PHI node for the next iteration. 4086 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4087 if (NextPHI == PHIVal) 4088 return RetVal = NextPHI; // Stopped evolving! 4089 if (NextPHI == 0) 4090 return 0; // Couldn't evaluate! 4091 PHIVal = NextPHI; 4092 } 4093} 4094 4095/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4096/// constant number of times (the condition evolves only from constants), 4097/// try to evaluate a few iterations of the loop until we get the exit 4098/// condition gets a value of ExitWhen (true or false). If we cannot 4099/// evaluate the trip count of the loop, return getCouldNotCompute(). 4100const SCEV * 4101ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4102 Value *Cond, 4103 bool ExitWhen) { 4104 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4105 if (PN == 0) return getCouldNotCompute(); 4106 4107 // Since the loop is canonicalized, the PHI node must have two entries. One 4108 // entry must be a constant (coming in from outside of the loop), and the 4109 // second must be derived from the same PHI. 4110 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4111 Constant *StartCST = 4112 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4113 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4114 4115 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4116 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); 4117 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. 4118 4119 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4120 // the loop symbolically to determine when the condition gets a value of 4121 // "ExitWhen". 4122 unsigned IterationNum = 0; 4123 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4124 for (Constant *PHIVal = StartCST; 4125 IterationNum != MaxIterations; ++IterationNum) { 4126 ConstantInt *CondVal = 4127 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4128 4129 // Couldn't symbolically evaluate. 4130 if (!CondVal) return getCouldNotCompute(); 4131 4132 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4133 ++NumBruteForceTripCountsComputed; 4134 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4135 } 4136 4137 // Compute the value of the PHI node for the next iteration. 4138 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4139 if (NextPHI == 0 || NextPHI == PHIVal) 4140 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4141 PHIVal = NextPHI; 4142 } 4143 4144 // Too many iterations were needed to evaluate. 4145 return getCouldNotCompute(); 4146} 4147 4148/// getSCEVAtScope - Return a SCEV expression for the specified value 4149/// at the specified scope in the program. The L value specifies a loop 4150/// nest to evaluate the expression at, where null is the top-level or a 4151/// specified loop is immediately inside of the loop. 4152/// 4153/// This method can be used to compute the exit value for a variable defined 4154/// in a loop by querying what the value will hold in the parent loop. 4155/// 4156/// In the case that a relevant loop exit value cannot be computed, the 4157/// original value V is returned. 4158const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4159 // Check to see if we've folded this expression at this loop before. 4160 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4161 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4162 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4163 if (!Pair.second) 4164 return Pair.first->second ? Pair.first->second : V; 4165 4166 // Otherwise compute it. 4167 const SCEV *C = computeSCEVAtScope(V, L); 4168 ValuesAtScopes[V][L] = C; 4169 return C; 4170} 4171 4172const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4173 if (isa<SCEVConstant>(V)) return V; 4174 4175 // If this instruction is evolved from a constant-evolving PHI, compute the 4176 // exit value from the loop without using SCEVs. 4177 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4178 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4179 const Loop *LI = (*this->LI)[I->getParent()]; 4180 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4181 if (PHINode *PN = dyn_cast<PHINode>(I)) 4182 if (PN->getParent() == LI->getHeader()) { 4183 // Okay, there is no closed form solution for the PHI node. Check 4184 // to see if the loop that contains it has a known backedge-taken 4185 // count. If so, we may be able to force computation of the exit 4186 // value. 4187 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4188 if (const SCEVConstant *BTCC = 4189 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4190 // Okay, we know how many times the containing loop executes. If 4191 // this is a constant evolving PHI node, get the final value at 4192 // the specified iteration number. 4193 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4194 BTCC->getValue()->getValue(), 4195 LI); 4196 if (RV) return getSCEV(RV); 4197 } 4198 } 4199 4200 // Okay, this is an expression that we cannot symbolically evaluate 4201 // into a SCEV. Check to see if it's possible to symbolically evaluate 4202 // the arguments into constants, and if so, try to constant propagate the 4203 // result. This is particularly useful for computing loop exit values. 4204 if (CanConstantFold(I)) { 4205 std::vector<Constant*> Operands; 4206 Operands.reserve(I->getNumOperands()); 4207 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4208 Value *Op = I->getOperand(i); 4209 if (Constant *C = dyn_cast<Constant>(Op)) { 4210 Operands.push_back(C); 4211 } else { 4212 // If any of the operands is non-constant and if they are 4213 // non-integer and non-pointer, don't even try to analyze them 4214 // with scev techniques. 4215 if (!isSCEVable(Op->getType())) 4216 return V; 4217 4218 const SCEV *OpV = getSCEVAtScope(Op, L); 4219 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { 4220 Constant *C = SC->getValue(); 4221 if (C->getType() != Op->getType()) 4222 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4223 Op->getType(), 4224 false), 4225 C, Op->getType()); 4226 Operands.push_back(C); 4227 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { 4228 if (Constant *C = dyn_cast<Constant>(SU->getValue())) { 4229 if (C->getType() != Op->getType()) 4230 C = 4231 ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4232 Op->getType(), 4233 false), 4234 C, Op->getType()); 4235 Operands.push_back(C); 4236 } else 4237 return V; 4238 } else { 4239 return V; 4240 } 4241 } 4242 } 4243 4244 Constant *C = 0; 4245 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4246 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4247 Operands[0], Operands[1], TD); 4248 else 4249 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4250 &Operands[0], Operands.size(), TD); 4251 if (C) 4252 return getSCEV(C); 4253 } 4254 } 4255 4256 // This is some other type of SCEVUnknown, just return it. 4257 return V; 4258 } 4259 4260 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4261 // Avoid performing the look-up in the common case where the specified 4262 // expression has no loop-variant portions. 4263 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4264 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4265 if (OpAtScope != Comm->getOperand(i)) { 4266 // Okay, at least one of these operands is loop variant but might be 4267 // foldable. Build a new instance of the folded commutative expression. 4268 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4269 Comm->op_begin()+i); 4270 NewOps.push_back(OpAtScope); 4271 4272 for (++i; i != e; ++i) { 4273 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4274 NewOps.push_back(OpAtScope); 4275 } 4276 if (isa<SCEVAddExpr>(Comm)) 4277 return getAddExpr(NewOps); 4278 if (isa<SCEVMulExpr>(Comm)) 4279 return getMulExpr(NewOps); 4280 if (isa<SCEVSMaxExpr>(Comm)) 4281 return getSMaxExpr(NewOps); 4282 if (isa<SCEVUMaxExpr>(Comm)) 4283 return getUMaxExpr(NewOps); 4284 llvm_unreachable("Unknown commutative SCEV type!"); 4285 } 4286 } 4287 // If we got here, all operands are loop invariant. 4288 return Comm; 4289 } 4290 4291 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4292 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4293 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4294 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4295 return Div; // must be loop invariant 4296 return getUDivExpr(LHS, RHS); 4297 } 4298 4299 // If this is a loop recurrence for a loop that does not contain L, then we 4300 // are dealing with the final value computed by the loop. 4301 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4302 if (!L || !AddRec->getLoop()->contains(L)) { 4303 // To evaluate this recurrence, we need to know how many times the AddRec 4304 // loop iterates. Compute this now. 4305 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4306 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4307 4308 // Then, evaluate the AddRec. 4309 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4310 } 4311 return AddRec; 4312 } 4313 4314 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4315 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4316 if (Op == Cast->getOperand()) 4317 return Cast; // must be loop invariant 4318 return getZeroExtendExpr(Op, Cast->getType()); 4319 } 4320 4321 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4322 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4323 if (Op == Cast->getOperand()) 4324 return Cast; // must be loop invariant 4325 return getSignExtendExpr(Op, Cast->getType()); 4326 } 4327 4328 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4329 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4330 if (Op == Cast->getOperand()) 4331 return Cast; // must be loop invariant 4332 return getTruncateExpr(Op, Cast->getType()); 4333 } 4334 4335 llvm_unreachable("Unknown SCEV type!"); 4336 return 0; 4337} 4338 4339/// getSCEVAtScope - This is a convenience function which does 4340/// getSCEVAtScope(getSCEV(V), L). 4341const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4342 return getSCEVAtScope(getSCEV(V), L); 4343} 4344 4345/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4346/// following equation: 4347/// 4348/// A * X = B (mod N) 4349/// 4350/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4351/// A and B isn't important. 4352/// 4353/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4354static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4355 ScalarEvolution &SE) { 4356 uint32_t BW = A.getBitWidth(); 4357 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4358 assert(A != 0 && "A must be non-zero."); 4359 4360 // 1. D = gcd(A, N) 4361 // 4362 // The gcd of A and N may have only one prime factor: 2. The number of 4363 // trailing zeros in A is its multiplicity 4364 uint32_t Mult2 = A.countTrailingZeros(); 4365 // D = 2^Mult2 4366 4367 // 2. Check if B is divisible by D. 4368 // 4369 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4370 // is not less than multiplicity of this prime factor for D. 4371 if (B.countTrailingZeros() < Mult2) 4372 return SE.getCouldNotCompute(); 4373 4374 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4375 // modulo (N / D). 4376 // 4377 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4378 // bit width during computations. 4379 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4380 APInt Mod(BW + 1, 0); 4381 Mod.set(BW - Mult2); // Mod = N / D 4382 APInt I = AD.multiplicativeInverse(Mod); 4383 4384 // 4. Compute the minimum unsigned root of the equation: 4385 // I * (B / D) mod (N / D) 4386 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4387 4388 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4389 // bits. 4390 return SE.getConstant(Result.trunc(BW)); 4391} 4392 4393/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4394/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4395/// might be the same) or two SCEVCouldNotCompute objects. 4396/// 4397static std::pair<const SCEV *,const SCEV *> 4398SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4399 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4400 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4401 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4402 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4403 4404 // We currently can only solve this if the coefficients are constants. 4405 if (!LC || !MC || !NC) { 4406 const SCEV *CNC = SE.getCouldNotCompute(); 4407 return std::make_pair(CNC, CNC); 4408 } 4409 4410 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4411 const APInt &L = LC->getValue()->getValue(); 4412 const APInt &M = MC->getValue()->getValue(); 4413 const APInt &N = NC->getValue()->getValue(); 4414 APInt Two(BitWidth, 2); 4415 APInt Four(BitWidth, 4); 4416 4417 { 4418 using namespace APIntOps; 4419 const APInt& C = L; 4420 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4421 // The B coefficient is M-N/2 4422 APInt B(M); 4423 B -= sdiv(N,Two); 4424 4425 // The A coefficient is N/2 4426 APInt A(N.sdiv(Two)); 4427 4428 // Compute the B^2-4ac term. 4429 APInt SqrtTerm(B); 4430 SqrtTerm *= B; 4431 SqrtTerm -= Four * (A * C); 4432 4433 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4434 // integer value or else APInt::sqrt() will assert. 4435 APInt SqrtVal(SqrtTerm.sqrt()); 4436 4437 // Compute the two solutions for the quadratic formula. 4438 // The divisions must be performed as signed divisions. 4439 APInt NegB(-B); 4440 APInt TwoA( A << 1 ); 4441 if (TwoA.isMinValue()) { 4442 const SCEV *CNC = SE.getCouldNotCompute(); 4443 return std::make_pair(CNC, CNC); 4444 } 4445 4446 LLVMContext &Context = SE.getContext(); 4447 4448 ConstantInt *Solution1 = 4449 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4450 ConstantInt *Solution2 = 4451 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4452 4453 return std::make_pair(SE.getConstant(Solution1), 4454 SE.getConstant(Solution2)); 4455 } // end APIntOps namespace 4456} 4457 4458/// HowFarToZero - Return the number of times a backedge comparing the specified 4459/// value to zero will execute. If not computable, return CouldNotCompute. 4460ScalarEvolution::BackedgeTakenInfo 4461ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4462 // If the value is a constant 4463 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4464 // If the value is already zero, the branch will execute zero times. 4465 if (C->getValue()->isZero()) return C; 4466 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4467 } 4468 4469 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4470 if (!AddRec || AddRec->getLoop() != L) 4471 return getCouldNotCompute(); 4472 4473 if (AddRec->isAffine()) { 4474 // If this is an affine expression, the execution count of this branch is 4475 // the minimum unsigned root of the following equation: 4476 // 4477 // Start + Step*N = 0 (mod 2^BW) 4478 // 4479 // equivalent to: 4480 // 4481 // Step*N = -Start (mod 2^BW) 4482 // 4483 // where BW is the common bit width of Start and Step. 4484 4485 // Get the initial value for the loop. 4486 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4487 L->getParentLoop()); 4488 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4489 L->getParentLoop()); 4490 4491 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4492 // For now we handle only constant steps. 4493 4494 // First, handle unitary steps. 4495 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4496 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4497 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4498 return Start; // N = Start (as unsigned) 4499 4500 // Then, try to solve the above equation provided that Start is constant. 4501 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4502 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4503 -StartC->getValue()->getValue(), 4504 *this); 4505 } 4506 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4507 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4508 // the quadratic equation to solve it. 4509 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4510 *this); 4511 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4512 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4513 if (R1) { 4514#if 0 4515 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4516 << " sol#2: " << *R2 << "\n"; 4517#endif 4518 // Pick the smallest positive root value. 4519 if (ConstantInt *CB = 4520 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4521 R1->getValue(), R2->getValue()))) { 4522 if (CB->getZExtValue() == false) 4523 std::swap(R1, R2); // R1 is the minimum root now. 4524 4525 // We can only use this value if the chrec ends up with an exact zero 4526 // value at this index. When solving for "X*X != 5", for example, we 4527 // should not accept a root of 2. 4528 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4529 if (Val->isZero()) 4530 return R1; // We found a quadratic root! 4531 } 4532 } 4533 } 4534 4535 return getCouldNotCompute(); 4536} 4537 4538/// HowFarToNonZero - Return the number of times a backedge checking the 4539/// specified value for nonzero will execute. If not computable, return 4540/// CouldNotCompute 4541ScalarEvolution::BackedgeTakenInfo 4542ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4543 // Loops that look like: while (X == 0) are very strange indeed. We don't 4544 // handle them yet except for the trivial case. This could be expanded in the 4545 // future as needed. 4546 4547 // If the value is a constant, check to see if it is known to be non-zero 4548 // already. If so, the backedge will execute zero times. 4549 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4550 if (!C->getValue()->isNullValue()) 4551 return getIntegerSCEV(0, C->getType()); 4552 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4553 } 4554 4555 // We could implement others, but I really doubt anyone writes loops like 4556 // this, and if they did, they would already be constant folded. 4557 return getCouldNotCompute(); 4558} 4559 4560/// getLoopPredecessor - If the given loop's header has exactly one unique 4561/// predecessor outside the loop, return it. Otherwise return null. 4562/// 4563BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { 4564 BasicBlock *Header = L->getHeader(); 4565 BasicBlock *Pred = 0; 4566 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); 4567 PI != E; ++PI) 4568 if (!L->contains(*PI)) { 4569 if (Pred && Pred != *PI) return 0; // Multiple predecessors. 4570 Pred = *PI; 4571 } 4572 return Pred; 4573} 4574 4575/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4576/// (which may not be an immediate predecessor) which has exactly one 4577/// successor from which BB is reachable, or null if no such block is 4578/// found. 4579/// 4580BasicBlock * 4581ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4582 // If the block has a unique predecessor, then there is no path from the 4583 // predecessor to the block that does not go through the direct edge 4584 // from the predecessor to the block. 4585 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4586 return Pred; 4587 4588 // A loop's header is defined to be a block that dominates the loop. 4589 // If the header has a unique predecessor outside the loop, it must be 4590 // a block that has exactly one successor that can reach the loop. 4591 if (Loop *L = LI->getLoopFor(BB)) 4592 return getLoopPredecessor(L); 4593 4594 return 0; 4595} 4596 4597/// HasSameValue - SCEV structural equivalence is usually sufficient for 4598/// testing whether two expressions are equal, however for the purposes of 4599/// looking for a condition guarding a loop, it can be useful to be a little 4600/// more general, since a front-end may have replicated the controlling 4601/// expression. 4602/// 4603static bool HasSameValue(const SCEV *A, const SCEV *B) { 4604 // Quick check to see if they are the same SCEV. 4605 if (A == B) return true; 4606 4607 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4608 // two different instructions with the same value. Check for this case. 4609 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4610 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4611 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4612 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4613 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4614 return true; 4615 4616 // Otherwise assume they may have a different value. 4617 return false; 4618} 4619 4620bool ScalarEvolution::isKnownNegative(const SCEV *S) { 4621 return getSignedRange(S).getSignedMax().isNegative(); 4622} 4623 4624bool ScalarEvolution::isKnownPositive(const SCEV *S) { 4625 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 4626} 4627 4628bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 4629 return !getSignedRange(S).getSignedMin().isNegative(); 4630} 4631 4632bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 4633 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 4634} 4635 4636bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 4637 return isKnownNegative(S) || isKnownPositive(S); 4638} 4639 4640bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 4641 const SCEV *LHS, const SCEV *RHS) { 4642 4643 if (HasSameValue(LHS, RHS)) 4644 return ICmpInst::isTrueWhenEqual(Pred); 4645 4646 switch (Pred) { 4647 default: 4648 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4649 break; 4650 case ICmpInst::ICMP_SGT: 4651 Pred = ICmpInst::ICMP_SLT; 4652 std::swap(LHS, RHS); 4653 case ICmpInst::ICMP_SLT: { 4654 ConstantRange LHSRange = getSignedRange(LHS); 4655 ConstantRange RHSRange = getSignedRange(RHS); 4656 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 4657 return true; 4658 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 4659 return false; 4660 break; 4661 } 4662 case ICmpInst::ICMP_SGE: 4663 Pred = ICmpInst::ICMP_SLE; 4664 std::swap(LHS, RHS); 4665 case ICmpInst::ICMP_SLE: { 4666 ConstantRange LHSRange = getSignedRange(LHS); 4667 ConstantRange RHSRange = getSignedRange(RHS); 4668 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 4669 return true; 4670 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 4671 return false; 4672 break; 4673 } 4674 case ICmpInst::ICMP_UGT: 4675 Pred = ICmpInst::ICMP_ULT; 4676 std::swap(LHS, RHS); 4677 case ICmpInst::ICMP_ULT: { 4678 ConstantRange LHSRange = getUnsignedRange(LHS); 4679 ConstantRange RHSRange = getUnsignedRange(RHS); 4680 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 4681 return true; 4682 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 4683 return false; 4684 break; 4685 } 4686 case ICmpInst::ICMP_UGE: 4687 Pred = ICmpInst::ICMP_ULE; 4688 std::swap(LHS, RHS); 4689 case ICmpInst::ICMP_ULE: { 4690 ConstantRange LHSRange = getUnsignedRange(LHS); 4691 ConstantRange RHSRange = getUnsignedRange(RHS); 4692 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 4693 return true; 4694 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 4695 return false; 4696 break; 4697 } 4698 case ICmpInst::ICMP_NE: { 4699 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 4700 return true; 4701 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 4702 return true; 4703 4704 const SCEV *Diff = getMinusSCEV(LHS, RHS); 4705 if (isKnownNonZero(Diff)) 4706 return true; 4707 break; 4708 } 4709 case ICmpInst::ICMP_EQ: 4710 // The check at the top of the function catches the case where 4711 // the values are known to be equal. 4712 break; 4713 } 4714 return false; 4715} 4716 4717/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 4718/// protected by a conditional between LHS and RHS. This is used to 4719/// to eliminate casts. 4720bool 4721ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 4722 ICmpInst::Predicate Pred, 4723 const SCEV *LHS, const SCEV *RHS) { 4724 // Interpret a null as meaning no loop, where there is obviously no guard 4725 // (interprocedural conditions notwithstanding). 4726 if (!L) return true; 4727 4728 BasicBlock *Latch = L->getLoopLatch(); 4729 if (!Latch) 4730 return false; 4731 4732 BranchInst *LoopContinuePredicate = 4733 dyn_cast<BranchInst>(Latch->getTerminator()); 4734 if (!LoopContinuePredicate || 4735 LoopContinuePredicate->isUnconditional()) 4736 return false; 4737 4738 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, 4739 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 4740} 4741 4742/// isLoopGuardedByCond - Test whether entry to the loop is protected 4743/// by a conditional between LHS and RHS. This is used to help avoid max 4744/// expressions in loop trip counts, and to eliminate casts. 4745bool 4746ScalarEvolution::isLoopGuardedByCond(const Loop *L, 4747 ICmpInst::Predicate Pred, 4748 const SCEV *LHS, const SCEV *RHS) { 4749 // Interpret a null as meaning no loop, where there is obviously no guard 4750 // (interprocedural conditions notwithstanding). 4751 if (!L) return false; 4752 4753 BasicBlock *Predecessor = getLoopPredecessor(L); 4754 BasicBlock *PredecessorDest = L->getHeader(); 4755 4756 // Starting at the loop predecessor, climb up the predecessor chain, as long 4757 // as there are predecessors that can be found that have unique successors 4758 // leading to the original header. 4759 for (; Predecessor; 4760 PredecessorDest = Predecessor, 4761 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) { 4762 4763 BranchInst *LoopEntryPredicate = 4764 dyn_cast<BranchInst>(Predecessor->getTerminator()); 4765 if (!LoopEntryPredicate || 4766 LoopEntryPredicate->isUnconditional()) 4767 continue; 4768 4769 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, 4770 LoopEntryPredicate->getSuccessor(0) != PredecessorDest)) 4771 return true; 4772 } 4773 4774 return false; 4775} 4776 4777/// isImpliedCond - Test whether the condition described by Pred, LHS, 4778/// and RHS is true whenever the given Cond value evaluates to true. 4779bool ScalarEvolution::isImpliedCond(Value *CondValue, 4780 ICmpInst::Predicate Pred, 4781 const SCEV *LHS, const SCEV *RHS, 4782 bool Inverse) { 4783 // Recursively handle And and Or conditions. 4784 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { 4785 if (BO->getOpcode() == Instruction::And) { 4786 if (!Inverse) 4787 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4788 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4789 } else if (BO->getOpcode() == Instruction::Or) { 4790 if (Inverse) 4791 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || 4792 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); 4793 } 4794 } 4795 4796 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); 4797 if (!ICI) return false; 4798 4799 // Bail if the ICmp's operands' types are wider than the needed type 4800 // before attempting to call getSCEV on them. This avoids infinite 4801 // recursion, since the analysis of widening casts can require loop 4802 // exit condition information for overflow checking, which would 4803 // lead back here. 4804 if (getTypeSizeInBits(LHS->getType()) < 4805 getTypeSizeInBits(ICI->getOperand(0)->getType())) 4806 return false; 4807 4808 // Now that we found a conditional branch that dominates the loop, check to 4809 // see if it is the comparison we are looking for. 4810 ICmpInst::Predicate FoundPred; 4811 if (Inverse) 4812 FoundPred = ICI->getInversePredicate(); 4813 else 4814 FoundPred = ICI->getPredicate(); 4815 4816 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 4817 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 4818 4819 // Balance the types. The case where FoundLHS' type is wider than 4820 // LHS' type is checked for above. 4821 if (getTypeSizeInBits(LHS->getType()) > 4822 getTypeSizeInBits(FoundLHS->getType())) { 4823 if (CmpInst::isSigned(Pred)) { 4824 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 4825 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 4826 } else { 4827 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 4828 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 4829 } 4830 } 4831 4832 // Canonicalize the query to match the way instcombine will have 4833 // canonicalized the comparison. 4834 // First, put a constant operand on the right. 4835 if (isa<SCEVConstant>(LHS)) { 4836 std::swap(LHS, RHS); 4837 Pred = ICmpInst::getSwappedPredicate(Pred); 4838 } 4839 // Then, canonicalize comparisons with boundary cases. 4840 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4841 const APInt &RA = RC->getValue()->getValue(); 4842 switch (Pred) { 4843 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4844 case ICmpInst::ICMP_EQ: 4845 case ICmpInst::ICMP_NE: 4846 break; 4847 case ICmpInst::ICMP_UGE: 4848 if ((RA - 1).isMinValue()) { 4849 Pred = ICmpInst::ICMP_NE; 4850 RHS = getConstant(RA - 1); 4851 break; 4852 } 4853 if (RA.isMaxValue()) { 4854 Pred = ICmpInst::ICMP_EQ; 4855 break; 4856 } 4857 if (RA.isMinValue()) return true; 4858 break; 4859 case ICmpInst::ICMP_ULE: 4860 if ((RA + 1).isMaxValue()) { 4861 Pred = ICmpInst::ICMP_NE; 4862 RHS = getConstant(RA + 1); 4863 break; 4864 } 4865 if (RA.isMinValue()) { 4866 Pred = ICmpInst::ICMP_EQ; 4867 break; 4868 } 4869 if (RA.isMaxValue()) return true; 4870 break; 4871 case ICmpInst::ICMP_SGE: 4872 if ((RA - 1).isMinSignedValue()) { 4873 Pred = ICmpInst::ICMP_NE; 4874 RHS = getConstant(RA - 1); 4875 break; 4876 } 4877 if (RA.isMaxSignedValue()) { 4878 Pred = ICmpInst::ICMP_EQ; 4879 break; 4880 } 4881 if (RA.isMinSignedValue()) return true; 4882 break; 4883 case ICmpInst::ICMP_SLE: 4884 if ((RA + 1).isMaxSignedValue()) { 4885 Pred = ICmpInst::ICMP_NE; 4886 RHS = getConstant(RA + 1); 4887 break; 4888 } 4889 if (RA.isMinSignedValue()) { 4890 Pred = ICmpInst::ICMP_EQ; 4891 break; 4892 } 4893 if (RA.isMaxSignedValue()) return true; 4894 break; 4895 case ICmpInst::ICMP_UGT: 4896 if (RA.isMinValue()) { 4897 Pred = ICmpInst::ICMP_NE; 4898 break; 4899 } 4900 if ((RA + 1).isMaxValue()) { 4901 Pred = ICmpInst::ICMP_EQ; 4902 RHS = getConstant(RA + 1); 4903 break; 4904 } 4905 if (RA.isMaxValue()) return false; 4906 break; 4907 case ICmpInst::ICMP_ULT: 4908 if (RA.isMaxValue()) { 4909 Pred = ICmpInst::ICMP_NE; 4910 break; 4911 } 4912 if ((RA - 1).isMinValue()) { 4913 Pred = ICmpInst::ICMP_EQ; 4914 RHS = getConstant(RA - 1); 4915 break; 4916 } 4917 if (RA.isMinValue()) return false; 4918 break; 4919 case ICmpInst::ICMP_SGT: 4920 if (RA.isMinSignedValue()) { 4921 Pred = ICmpInst::ICMP_NE; 4922 break; 4923 } 4924 if ((RA + 1).isMaxSignedValue()) { 4925 Pred = ICmpInst::ICMP_EQ; 4926 RHS = getConstant(RA + 1); 4927 break; 4928 } 4929 if (RA.isMaxSignedValue()) return false; 4930 break; 4931 case ICmpInst::ICMP_SLT: 4932 if (RA.isMaxSignedValue()) { 4933 Pred = ICmpInst::ICMP_NE; 4934 break; 4935 } 4936 if ((RA - 1).isMinSignedValue()) { 4937 Pred = ICmpInst::ICMP_EQ; 4938 RHS = getConstant(RA - 1); 4939 break; 4940 } 4941 if (RA.isMinSignedValue()) return false; 4942 break; 4943 } 4944 } 4945 4946 // Check to see if we can make the LHS or RHS match. 4947 if (LHS == FoundRHS || RHS == FoundLHS) { 4948 if (isa<SCEVConstant>(RHS)) { 4949 std::swap(FoundLHS, FoundRHS); 4950 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 4951 } else { 4952 std::swap(LHS, RHS); 4953 Pred = ICmpInst::getSwappedPredicate(Pred); 4954 } 4955 } 4956 4957 // Check whether the found predicate is the same as the desired predicate. 4958 if (FoundPred == Pred) 4959 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 4960 4961 // Check whether swapping the found predicate makes it the same as the 4962 // desired predicate. 4963 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 4964 if (isa<SCEVConstant>(RHS)) 4965 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 4966 else 4967 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 4968 RHS, LHS, FoundLHS, FoundRHS); 4969 } 4970 4971 // Check whether the actual condition is beyond sufficient. 4972 if (FoundPred == ICmpInst::ICMP_EQ) 4973 if (ICmpInst::isTrueWhenEqual(Pred)) 4974 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 4975 return true; 4976 if (Pred == ICmpInst::ICMP_NE) 4977 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 4978 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 4979 return true; 4980 4981 // Otherwise assume the worst. 4982 return false; 4983} 4984 4985/// isImpliedCondOperands - Test whether the condition described by Pred, 4986/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 4987/// and FoundRHS is true. 4988bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 4989 const SCEV *LHS, const SCEV *RHS, 4990 const SCEV *FoundLHS, 4991 const SCEV *FoundRHS) { 4992 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 4993 FoundLHS, FoundRHS) || 4994 // ~x < ~y --> x > y 4995 isImpliedCondOperandsHelper(Pred, LHS, RHS, 4996 getNotSCEV(FoundRHS), 4997 getNotSCEV(FoundLHS)); 4998} 4999 5000/// isImpliedCondOperandsHelper - Test whether the condition described by 5001/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5002/// FoundLHS, and FoundRHS is true. 5003bool 5004ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5005 const SCEV *LHS, const SCEV *RHS, 5006 const SCEV *FoundLHS, 5007 const SCEV *FoundRHS) { 5008 switch (Pred) { 5009 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5010 case ICmpInst::ICMP_EQ: 5011 case ICmpInst::ICMP_NE: 5012 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5013 return true; 5014 break; 5015 case ICmpInst::ICMP_SLT: 5016 case ICmpInst::ICMP_SLE: 5017 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5018 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5019 return true; 5020 break; 5021 case ICmpInst::ICMP_SGT: 5022 case ICmpInst::ICMP_SGE: 5023 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5024 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5025 return true; 5026 break; 5027 case ICmpInst::ICMP_ULT: 5028 case ICmpInst::ICMP_ULE: 5029 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5030 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5031 return true; 5032 break; 5033 case ICmpInst::ICMP_UGT: 5034 case ICmpInst::ICMP_UGE: 5035 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5036 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5037 return true; 5038 break; 5039 } 5040 5041 return false; 5042} 5043 5044/// getBECount - Subtract the end and start values and divide by the step, 5045/// rounding up, to get the number of times the backedge is executed. Return 5046/// CouldNotCompute if an intermediate computation overflows. 5047const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5048 const SCEV *End, 5049 const SCEV *Step, 5050 bool NoWrap) { 5051 assert(!isKnownNegative(Step) && 5052 "This code doesn't handle negative strides yet!"); 5053 5054 const Type *Ty = Start->getType(); 5055 const SCEV *NegOne = getIntegerSCEV(-1, Ty); 5056 const SCEV *Diff = getMinusSCEV(End, Start); 5057 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5058 5059 // Add an adjustment to the difference between End and Start so that 5060 // the division will effectively round up. 5061 const SCEV *Add = getAddExpr(Diff, RoundUp); 5062 5063 if (!NoWrap) { 5064 // Check Add for unsigned overflow. 5065 // TODO: More sophisticated things could be done here. 5066 const Type *WideTy = IntegerType::get(getContext(), 5067 getTypeSizeInBits(Ty) + 1); 5068 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5069 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5070 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5071 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5072 return getCouldNotCompute(); 5073 } 5074 5075 return getUDivExpr(Add, Step); 5076} 5077 5078/// HowManyLessThans - Return the number of times a backedge containing the 5079/// specified less-than comparison will execute. If not computable, return 5080/// CouldNotCompute. 5081ScalarEvolution::BackedgeTakenInfo 5082ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5083 const Loop *L, bool isSigned) { 5084 // Only handle: "ADDREC < LoopInvariant". 5085 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5086 5087 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5088 if (!AddRec || AddRec->getLoop() != L) 5089 return getCouldNotCompute(); 5090 5091 // Check to see if we have a flag which makes analysis easy. 5092 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5093 AddRec->hasNoUnsignedWrap(); 5094 5095 if (AddRec->isAffine()) { 5096 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5097 const SCEV *Step = AddRec->getStepRecurrence(*this); 5098 5099 if (Step->isZero()) 5100 return getCouldNotCompute(); 5101 if (Step->isOne()) { 5102 // With unit stride, the iteration never steps past the limit value. 5103 } else if (isKnownPositive(Step)) { 5104 // Test whether a positive iteration can step past the limit 5105 // value and past the maximum value for its type in a single step. 5106 // Note that it's not sufficient to check NoWrap here, because even 5107 // though the value after a wrap is undefined, it's not undefined 5108 // behavior, so if wrap does occur, the loop could either terminate or 5109 // loop infinitely, but in either case, the loop is guaranteed to 5110 // iterate at least until the iteration where the wrapping occurs. 5111 const SCEV *One = getIntegerSCEV(1, Step->getType()); 5112 if (isSigned) { 5113 APInt Max = APInt::getSignedMaxValue(BitWidth); 5114 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5115 .slt(getSignedRange(RHS).getSignedMax())) 5116 return getCouldNotCompute(); 5117 } else { 5118 APInt Max = APInt::getMaxValue(BitWidth); 5119 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5120 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5121 return getCouldNotCompute(); 5122 } 5123 } else 5124 // TODO: Handle negative strides here and below. 5125 return getCouldNotCompute(); 5126 5127 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5128 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5129 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5130 // treat m-n as signed nor unsigned due to overflow possibility. 5131 5132 // First, we get the value of the LHS in the first iteration: n 5133 const SCEV *Start = AddRec->getOperand(0); 5134 5135 // Determine the minimum constant start value. 5136 const SCEV *MinStart = getConstant(isSigned ? 5137 getSignedRange(Start).getSignedMin() : 5138 getUnsignedRange(Start).getUnsignedMin()); 5139 5140 // If we know that the condition is true in order to enter the loop, 5141 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5142 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5143 // the division must round up. 5144 const SCEV *End = RHS; 5145 if (!isLoopGuardedByCond(L, 5146 isSigned ? ICmpInst::ICMP_SLT : 5147 ICmpInst::ICMP_ULT, 5148 getMinusSCEV(Start, Step), RHS)) 5149 End = isSigned ? getSMaxExpr(RHS, Start) 5150 : getUMaxExpr(RHS, Start); 5151 5152 // Determine the maximum constant end value. 5153 const SCEV *MaxEnd = getConstant(isSigned ? 5154 getSignedRange(End).getSignedMax() : 5155 getUnsignedRange(End).getUnsignedMax()); 5156 5157 // If MaxEnd is within a step of the maximum integer value in its type, 5158 // adjust it down to the minimum value which would produce the same effect. 5159 // This allows the subsequent ceiling division of (N+(step-1))/step to 5160 // compute the correct value. 5161 const SCEV *StepMinusOne = getMinusSCEV(Step, 5162 getIntegerSCEV(1, Step->getType())); 5163 MaxEnd = isSigned ? 5164 getSMinExpr(MaxEnd, 5165 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5166 StepMinusOne)) : 5167 getUMinExpr(MaxEnd, 5168 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5169 StepMinusOne)); 5170 5171 // Finally, we subtract these two values and divide, rounding up, to get 5172 // the number of times the backedge is executed. 5173 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5174 5175 // The maximum backedge count is similar, except using the minimum start 5176 // value and the maximum end value. 5177 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5178 5179 return BackedgeTakenInfo(BECount, MaxBECount); 5180 } 5181 5182 return getCouldNotCompute(); 5183} 5184 5185/// getNumIterationsInRange - Return the number of iterations of this loop that 5186/// produce values in the specified constant range. Another way of looking at 5187/// this is that it returns the first iteration number where the value is not in 5188/// the condition, thus computing the exit count. If the iteration count can't 5189/// be computed, an instance of SCEVCouldNotCompute is returned. 5190const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5191 ScalarEvolution &SE) const { 5192 if (Range.isFullSet()) // Infinite loop. 5193 return SE.getCouldNotCompute(); 5194 5195 // If the start is a non-zero constant, shift the range to simplify things. 5196 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5197 if (!SC->getValue()->isZero()) { 5198 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5199 Operands[0] = SE.getIntegerSCEV(0, SC->getType()); 5200 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5201 if (const SCEVAddRecExpr *ShiftedAddRec = 5202 dyn_cast<SCEVAddRecExpr>(Shifted)) 5203 return ShiftedAddRec->getNumIterationsInRange( 5204 Range.subtract(SC->getValue()->getValue()), SE); 5205 // This is strange and shouldn't happen. 5206 return SE.getCouldNotCompute(); 5207 } 5208 5209 // The only time we can solve this is when we have all constant indices. 5210 // Otherwise, we cannot determine the overflow conditions. 5211 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5212 if (!isa<SCEVConstant>(getOperand(i))) 5213 return SE.getCouldNotCompute(); 5214 5215 5216 // Okay at this point we know that all elements of the chrec are constants and 5217 // that the start element is zero. 5218 5219 // First check to see if the range contains zero. If not, the first 5220 // iteration exits. 5221 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5222 if (!Range.contains(APInt(BitWidth, 0))) 5223 return SE.getIntegerSCEV(0, getType()); 5224 5225 if (isAffine()) { 5226 // If this is an affine expression then we have this situation: 5227 // Solve {0,+,A} in Range === Ax in Range 5228 5229 // We know that zero is in the range. If A is positive then we know that 5230 // the upper value of the range must be the first possible exit value. 5231 // If A is negative then the lower of the range is the last possible loop 5232 // value. Also note that we already checked for a full range. 5233 APInt One(BitWidth,1); 5234 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5235 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5236 5237 // The exit value should be (End+A)/A. 5238 APInt ExitVal = (End + A).udiv(A); 5239 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5240 5241 // Evaluate at the exit value. If we really did fall out of the valid 5242 // range, then we computed our trip count, otherwise wrap around or other 5243 // things must have happened. 5244 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5245 if (Range.contains(Val->getValue())) 5246 return SE.getCouldNotCompute(); // Something strange happened 5247 5248 // Ensure that the previous value is in the range. This is a sanity check. 5249 assert(Range.contains( 5250 EvaluateConstantChrecAtConstant(this, 5251 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5252 "Linear scev computation is off in a bad way!"); 5253 return SE.getConstant(ExitValue); 5254 } else if (isQuadratic()) { 5255 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5256 // quadratic equation to solve it. To do this, we must frame our problem in 5257 // terms of figuring out when zero is crossed, instead of when 5258 // Range.getUpper() is crossed. 5259 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5260 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5261 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5262 5263 // Next, solve the constructed addrec 5264 std::pair<const SCEV *,const SCEV *> Roots = 5265 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5266 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5267 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5268 if (R1) { 5269 // Pick the smallest positive root value. 5270 if (ConstantInt *CB = 5271 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5272 R1->getValue(), R2->getValue()))) { 5273 if (CB->getZExtValue() == false) 5274 std::swap(R1, R2); // R1 is the minimum root now. 5275 5276 // Make sure the root is not off by one. The returned iteration should 5277 // not be in the range, but the previous one should be. When solving 5278 // for "X*X < 5", for example, we should not return a root of 2. 5279 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5280 R1->getValue(), 5281 SE); 5282 if (Range.contains(R1Val->getValue())) { 5283 // The next iteration must be out of the range... 5284 ConstantInt *NextVal = 5285 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5286 5287 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5288 if (!Range.contains(R1Val->getValue())) 5289 return SE.getConstant(NextVal); 5290 return SE.getCouldNotCompute(); // Something strange happened 5291 } 5292 5293 // If R1 was not in the range, then it is a good return value. Make 5294 // sure that R1-1 WAS in the range though, just in case. 5295 ConstantInt *NextVal = 5296 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5297 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5298 if (Range.contains(R1Val->getValue())) 5299 return R1; 5300 return SE.getCouldNotCompute(); // Something strange happened 5301 } 5302 } 5303 } 5304 5305 return SE.getCouldNotCompute(); 5306} 5307 5308 5309 5310//===----------------------------------------------------------------------===// 5311// SCEVCallbackVH Class Implementation 5312//===----------------------------------------------------------------------===// 5313 5314void ScalarEvolution::SCEVCallbackVH::deleted() { 5315 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5316 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5317 SE->ConstantEvolutionLoopExitValue.erase(PN); 5318 SE->Scalars.erase(getValPtr()); 5319 // this now dangles! 5320} 5321 5322void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { 5323 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5324 5325 // Forget all the expressions associated with users of the old value, 5326 // so that future queries will recompute the expressions using the new 5327 // value. 5328 SmallVector<User *, 16> Worklist; 5329 SmallPtrSet<User *, 8> Visited; 5330 Value *Old = getValPtr(); 5331 bool DeleteOld = false; 5332 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5333 UI != UE; ++UI) 5334 Worklist.push_back(*UI); 5335 while (!Worklist.empty()) { 5336 User *U = Worklist.pop_back_val(); 5337 // Deleting the Old value will cause this to dangle. Postpone 5338 // that until everything else is done. 5339 if (U == Old) { 5340 DeleteOld = true; 5341 continue; 5342 } 5343 if (!Visited.insert(U)) 5344 continue; 5345 if (PHINode *PN = dyn_cast<PHINode>(U)) 5346 SE->ConstantEvolutionLoopExitValue.erase(PN); 5347 SE->Scalars.erase(U); 5348 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5349 UI != UE; ++UI) 5350 Worklist.push_back(*UI); 5351 } 5352 // Delete the Old value if it (indirectly) references itself. 5353 if (DeleteOld) { 5354 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5355 SE->ConstantEvolutionLoopExitValue.erase(PN); 5356 SE->Scalars.erase(Old); 5357 // this now dangles! 5358 } 5359 // this may dangle! 5360} 5361 5362ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5363 : CallbackVH(V), SE(se) {} 5364 5365//===----------------------------------------------------------------------===// 5366// ScalarEvolution Class Implementation 5367//===----------------------------------------------------------------------===// 5368 5369ScalarEvolution::ScalarEvolution() 5370 : FunctionPass(&ID) { 5371} 5372 5373bool ScalarEvolution::runOnFunction(Function &F) { 5374 this->F = &F; 5375 LI = &getAnalysis<LoopInfo>(); 5376 TD = getAnalysisIfAvailable<TargetData>(); 5377 DT = &getAnalysis<DominatorTree>(); 5378 return false; 5379} 5380 5381void ScalarEvolution::releaseMemory() { 5382 Scalars.clear(); 5383 BackedgeTakenCounts.clear(); 5384 ConstantEvolutionLoopExitValue.clear(); 5385 ValuesAtScopes.clear(); 5386 UniqueSCEVs.clear(); 5387 SCEVAllocator.Reset(); 5388} 5389 5390void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5391 AU.setPreservesAll(); 5392 AU.addRequiredTransitive<LoopInfo>(); 5393 AU.addRequiredTransitive<DominatorTree>(); 5394} 5395 5396bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5397 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5398} 5399 5400static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5401 const Loop *L) { 5402 // Print all inner loops first 5403 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5404 PrintLoopInfo(OS, SE, *I); 5405 5406 OS << "Loop "; 5407 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5408 OS << ": "; 5409 5410 SmallVector<BasicBlock *, 8> ExitBlocks; 5411 L->getExitBlocks(ExitBlocks); 5412 if (ExitBlocks.size() != 1) 5413 OS << "<multiple exits> "; 5414 5415 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5416 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5417 } else { 5418 OS << "Unpredictable backedge-taken count. "; 5419 } 5420 5421 OS << "\n" 5422 "Loop "; 5423 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5424 OS << ": "; 5425 5426 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5427 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5428 } else { 5429 OS << "Unpredictable max backedge-taken count. "; 5430 } 5431 5432 OS << "\n"; 5433} 5434 5435void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5436 // ScalarEvolution's implementation of the print method is to print 5437 // out SCEV values of all instructions that are interesting. Doing 5438 // this potentially causes it to create new SCEV objects though, 5439 // which technically conflicts with the const qualifier. This isn't 5440 // observable from outside the class though, so casting away the 5441 // const isn't dangerous. 5442 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5443 5444 OS << "Classifying expressions for: "; 5445 WriteAsOperand(OS, F, /*PrintType=*/false); 5446 OS << "\n"; 5447 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5448 if (isSCEVable(I->getType())) { 5449 OS << *I << '\n'; 5450 OS << " --> "; 5451 const SCEV *SV = SE.getSCEV(&*I); 5452 SV->print(OS); 5453 5454 const Loop *L = LI->getLoopFor((*I).getParent()); 5455 5456 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5457 if (AtUse != SV) { 5458 OS << " --> "; 5459 AtUse->print(OS); 5460 } 5461 5462 if (L) { 5463 OS << "\t\t" "Exits: "; 5464 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5465 if (!ExitValue->isLoopInvariant(L)) { 5466 OS << "<<Unknown>>"; 5467 } else { 5468 OS << *ExitValue; 5469 } 5470 } 5471 5472 OS << "\n"; 5473 } 5474 5475 OS << "Determining loop execution counts for: "; 5476 WriteAsOperand(OS, F, /*PrintType=*/false); 5477 OS << "\n"; 5478 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5479 PrintLoopInfo(OS, &SE, *I); 5480} 5481 5482