ScalarEvolution.cpp revision 7e1fee7ece962e03471d0c7a253c3d23b3cf50ae
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 106INITIALIZE_PASS(ScalarEvolution, "scalar-evolution", 107 "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(dbgs()); 122 dbgs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 181 UniqueSCEVs.InsertNode(S, IP); 182 return S; 183} 184 185const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 186 return getConstant(ConstantInt::get(getContext(), Val)); 187} 188 189const SCEV * 190ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 192 return getConstant(ConstantInt::get(ITy, V, isSigned)); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(raw_ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 202 unsigned SCEVTy, const SCEV *op, const Type *ty) 203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 204 205bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 206 return Op->dominates(BB, DT); 207} 208 209bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->properlyDominates(BB, DT); 211} 212 213SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 214 const SCEV *op, const Type *ty) 215 : SCEVCastExpr(ID, scTruncate, op, ty) { 216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 217 (Ty->isIntegerTy() || Ty->isPointerTy()) && 218 "Cannot truncate non-integer value!"); 219} 220 221void SCEVTruncateExpr::print(raw_ostream &OS) const { 222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 223} 224 225SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 226 const SCEV *op, const Type *ty) 227 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 229 (Ty->isIntegerTy() || Ty->isPointerTy()) && 230 "Cannot zero extend non-integer value!"); 231} 232 233void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 235} 236 237SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 238 const SCEV *op, const Type *ty) 239 : SCEVCastExpr(ID, scSignExtend, op, ty) { 240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 241 (Ty->isIntegerTy() || Ty->isPointerTy()) && 242 "Cannot sign extend non-integer value!"); 243} 244 245void SCEVSignExtendExpr::print(raw_ostream &OS) const { 246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 247} 248 249void SCEVCommutativeExpr::print(raw_ostream &OS) const { 250 const char *OpStr = getOperationStr(); 251 OS << "("; 252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 253 OS << **I; 254 if (llvm::next(I) != E) 255 OS << OpStr; 256 } 257 OS << ")"; 258} 259 260bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 261 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 262 if (!(*I)->dominates(BB, DT)) 263 return false; 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 269 if (!(*I)->properlyDominates(BB, DT)) 270 return false; 271 return true; 272} 273 274bool SCEVNAryExpr::isLoopInvariant(const Loop *L) const { 275 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 276 if (!(*I)->isLoopInvariant(L)) 277 return false; 278 return true; 279} 280 281// hasComputableLoopEvolution - N-ary expressions have computable loop 282// evolutions iff they have at least one operand that varies with the loop, 283// but that all varying operands are computable. 284bool SCEVNAryExpr::hasComputableLoopEvolution(const Loop *L) const { 285 bool HasVarying = false; 286 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 287 const SCEV *S = *I; 288 if (!S->isLoopInvariant(L)) { 289 if (S->hasComputableLoopEvolution(L)) 290 HasVarying = true; 291 else 292 return false; 293 } 294 } 295 return HasVarying; 296} 297 298bool SCEVNAryExpr::hasOperand(const SCEV *O) const { 299 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 300 const SCEV *S = *I; 301 if (O == S || S->hasOperand(O)) 302 return true; 303 } 304 return false; 305} 306 307bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 308 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 309} 310 311bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 312 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 313} 314 315void SCEVUDivExpr::print(raw_ostream &OS) const { 316 OS << "(" << *LHS << " /u " << *RHS << ")"; 317} 318 319const Type *SCEVUDivExpr::getType() const { 320 // In most cases the types of LHS and RHS will be the same, but in some 321 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 322 // depend on the type for correctness, but handling types carefully can 323 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 324 // a pointer type than the RHS, so use the RHS' type here. 325 return RHS->getType(); 326} 327 328bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 329 // Add recurrences are never invariant in the function-body (null loop). 330 if (!QueryLoop) 331 return false; 332 333 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 334 if (QueryLoop->contains(L)) 335 return false; 336 337 // This recurrence is invariant w.r.t. QueryLoop if L contains QueryLoop. 338 if (L->contains(QueryLoop)) 339 return true; 340 341 // This recurrence is variant w.r.t. QueryLoop if any of its operands 342 // are variant. 343 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 344 if (!(*I)->isLoopInvariant(QueryLoop)) 345 return false; 346 347 // Otherwise it's loop-invariant. 348 return true; 349} 350 351bool 352SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 353 return DT->dominates(L->getHeader(), BB) && 354 SCEVNAryExpr::dominates(BB, DT); 355} 356 357bool 358SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 359 // This uses a "dominates" query instead of "properly dominates" query because 360 // the instruction which produces the addrec's value is a PHI, and a PHI 361 // effectively properly dominates its entire containing block. 362 return DT->dominates(L->getHeader(), BB) && 363 SCEVNAryExpr::properlyDominates(BB, DT); 364} 365 366void SCEVAddRecExpr::print(raw_ostream &OS) const { 367 OS << "{" << *Operands[0]; 368 for (unsigned i = 1, e = NumOperands; i != e; ++i) 369 OS << ",+," << *Operands[i]; 370 OS << "}<"; 371 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 372 OS << ">"; 373} 374 375void SCEVUnknown::deleted() { 376 // Clear this SCEVUnknown from ValuesAtScopes. 377 SE->ValuesAtScopes.erase(this); 378 379 // Remove this SCEVUnknown from the uniquing map. 380 SE->UniqueSCEVs.RemoveNode(this); 381 382 // Release the value. 383 setValPtr(0); 384} 385 386void SCEVUnknown::allUsesReplacedWith(Value *New) { 387 // Clear this SCEVUnknown from ValuesAtScopes. 388 SE->ValuesAtScopes.erase(this); 389 390 // Remove this SCEVUnknown from the uniquing map. 391 SE->UniqueSCEVs.RemoveNode(this); 392 393 // Update this SCEVUnknown to point to the new value. This is needed 394 // because there may still be outstanding SCEVs which still point to 395 // this SCEVUnknown. 396 setValPtr(New); 397} 398 399bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 400 // All non-instruction values are loop invariant. All instructions are loop 401 // invariant if they are not contained in the specified loop. 402 // Instructions are never considered invariant in the function body 403 // (null loop) because they are defined within the "loop". 404 if (Instruction *I = dyn_cast<Instruction>(getValue())) 405 return L && !L->contains(I); 406 return true; 407} 408 409bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 410 if (Instruction *I = dyn_cast<Instruction>(getValue())) 411 return DT->dominates(I->getParent(), BB); 412 return true; 413} 414 415bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 416 if (Instruction *I = dyn_cast<Instruction>(getValue())) 417 return DT->properlyDominates(I->getParent(), BB); 418 return true; 419} 420 421const Type *SCEVUnknown::getType() const { 422 return getValue()->getType(); 423} 424 425bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 426 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 427 if (VCE->getOpcode() == Instruction::PtrToInt) 428 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 429 if (CE->getOpcode() == Instruction::GetElementPtr && 430 CE->getOperand(0)->isNullValue() && 431 CE->getNumOperands() == 2) 432 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 433 if (CI->isOne()) { 434 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 435 ->getElementType(); 436 return true; 437 } 438 439 return false; 440} 441 442bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 443 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 444 if (VCE->getOpcode() == Instruction::PtrToInt) 445 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 446 if (CE->getOpcode() == Instruction::GetElementPtr && 447 CE->getOperand(0)->isNullValue()) { 448 const Type *Ty = 449 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 450 if (const StructType *STy = dyn_cast<StructType>(Ty)) 451 if (!STy->isPacked() && 452 CE->getNumOperands() == 3 && 453 CE->getOperand(1)->isNullValue()) { 454 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 455 if (CI->isOne() && 456 STy->getNumElements() == 2 && 457 STy->getElementType(0)->isIntegerTy(1)) { 458 AllocTy = STy->getElementType(1); 459 return true; 460 } 461 } 462 } 463 464 return false; 465} 466 467bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 468 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 469 if (VCE->getOpcode() == Instruction::PtrToInt) 470 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 471 if (CE->getOpcode() == Instruction::GetElementPtr && 472 CE->getNumOperands() == 3 && 473 CE->getOperand(0)->isNullValue() && 474 CE->getOperand(1)->isNullValue()) { 475 const Type *Ty = 476 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 477 // Ignore vector types here so that ScalarEvolutionExpander doesn't 478 // emit getelementptrs that index into vectors. 479 if (Ty->isStructTy() || Ty->isArrayTy()) { 480 CTy = Ty; 481 FieldNo = CE->getOperand(2); 482 return true; 483 } 484 } 485 486 return false; 487} 488 489void SCEVUnknown::print(raw_ostream &OS) const { 490 const Type *AllocTy; 491 if (isSizeOf(AllocTy)) { 492 OS << "sizeof(" << *AllocTy << ")"; 493 return; 494 } 495 if (isAlignOf(AllocTy)) { 496 OS << "alignof(" << *AllocTy << ")"; 497 return; 498 } 499 500 const Type *CTy; 501 Constant *FieldNo; 502 if (isOffsetOf(CTy, FieldNo)) { 503 OS << "offsetof(" << *CTy << ", "; 504 WriteAsOperand(OS, FieldNo, false); 505 OS << ")"; 506 return; 507 } 508 509 // Otherwise just print it normally. 510 WriteAsOperand(OS, getValue(), false); 511} 512 513//===----------------------------------------------------------------------===// 514// SCEV Utilities 515//===----------------------------------------------------------------------===// 516 517namespace { 518 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 519 /// than the complexity of the RHS. This comparator is used to canonicalize 520 /// expressions. 521 class SCEVComplexityCompare { 522 const LoopInfo *const LI; 523 public: 524 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 525 526 // Return true or false if LHS is less than, or at least RHS, respectively. 527 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 528 return compare(LHS, RHS) < 0; 529 } 530 531 // Return negative, zero, or positive, if LHS is less than, equal to, or 532 // greater than RHS, respectively. A three-way result allows recursive 533 // comparisons to be more efficient. 534 int compare(const SCEV *LHS, const SCEV *RHS) const { 535 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 536 if (LHS == RHS) 537 return 0; 538 539 // Primarily, sort the SCEVs by their getSCEVType(). 540 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 541 if (LType != RType) 542 return (int)LType - (int)RType; 543 544 // Aside from the getSCEVType() ordering, the particular ordering 545 // isn't very important except that it's beneficial to be consistent, 546 // so that (a + b) and (b + a) don't end up as different expressions. 547 switch (LType) { 548 case scUnknown: { 549 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 550 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 551 552 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 553 // not as complete as it could be. 554 const Value *LV = LU->getValue(), *RV = RU->getValue(); 555 556 // Order pointer values after integer values. This helps SCEVExpander 557 // form GEPs. 558 bool LIsPointer = LV->getType()->isPointerTy(), 559 RIsPointer = RV->getType()->isPointerTy(); 560 if (LIsPointer != RIsPointer) 561 return (int)LIsPointer - (int)RIsPointer; 562 563 // Compare getValueID values. 564 unsigned LID = LV->getValueID(), 565 RID = RV->getValueID(); 566 if (LID != RID) 567 return (int)LID - (int)RID; 568 569 // Sort arguments by their position. 570 if (const Argument *LA = dyn_cast<Argument>(LV)) { 571 const Argument *RA = cast<Argument>(RV); 572 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 573 return (int)LArgNo - (int)RArgNo; 574 } 575 576 // For instructions, compare their loop depth, and their operand 577 // count. This is pretty loose. 578 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 579 const Instruction *RInst = cast<Instruction>(RV); 580 581 // Compare loop depths. 582 const BasicBlock *LParent = LInst->getParent(), 583 *RParent = RInst->getParent(); 584 if (LParent != RParent) { 585 unsigned LDepth = LI->getLoopDepth(LParent), 586 RDepth = LI->getLoopDepth(RParent); 587 if (LDepth != RDepth) 588 return (int)LDepth - (int)RDepth; 589 } 590 591 // Compare the number of operands. 592 unsigned LNumOps = LInst->getNumOperands(), 593 RNumOps = RInst->getNumOperands(); 594 return (int)LNumOps - (int)RNumOps; 595 } 596 597 return 0; 598 } 599 600 case scConstant: { 601 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 602 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 603 604 // Compare constant values. 605 const APInt &LA = LC->getValue()->getValue(); 606 const APInt &RA = RC->getValue()->getValue(); 607 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 608 if (LBitWidth != RBitWidth) 609 return (int)LBitWidth - (int)RBitWidth; 610 return LA.ult(RA) ? -1 : 1; 611 } 612 613 case scAddRecExpr: { 614 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 615 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 616 617 // Compare addrec loop depths. 618 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 619 if (LLoop != RLoop) { 620 unsigned LDepth = LLoop->getLoopDepth(), 621 RDepth = RLoop->getLoopDepth(); 622 if (LDepth != RDepth) 623 return (int)LDepth - (int)RDepth; 624 } 625 626 // Addrec complexity grows with operand count. 627 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 628 if (LNumOps != RNumOps) 629 return (int)LNumOps - (int)RNumOps; 630 631 // Lexicographically compare. 632 for (unsigned i = 0; i != LNumOps; ++i) { 633 long X = compare(LA->getOperand(i), RA->getOperand(i)); 634 if (X != 0) 635 return X; 636 } 637 638 return 0; 639 } 640 641 case scAddExpr: 642 case scMulExpr: 643 case scSMaxExpr: 644 case scUMaxExpr: { 645 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 646 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 647 648 // Lexicographically compare n-ary expressions. 649 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 650 for (unsigned i = 0; i != LNumOps; ++i) { 651 if (i >= RNumOps) 652 return 1; 653 long X = compare(LC->getOperand(i), RC->getOperand(i)); 654 if (X != 0) 655 return X; 656 } 657 return (int)LNumOps - (int)RNumOps; 658 } 659 660 case scUDivExpr: { 661 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 662 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 663 664 // Lexicographically compare udiv expressions. 665 long X = compare(LC->getLHS(), RC->getLHS()); 666 if (X != 0) 667 return X; 668 return compare(LC->getRHS(), RC->getRHS()); 669 } 670 671 case scTruncate: 672 case scZeroExtend: 673 case scSignExtend: { 674 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 675 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 676 677 // Compare cast expressions by operand. 678 return compare(LC->getOperand(), RC->getOperand()); 679 } 680 681 default: 682 break; 683 } 684 685 llvm_unreachable("Unknown SCEV kind!"); 686 return 0; 687 } 688 }; 689} 690 691/// GroupByComplexity - Given a list of SCEV objects, order them by their 692/// complexity, and group objects of the same complexity together by value. 693/// When this routine is finished, we know that any duplicates in the vector are 694/// consecutive and that complexity is monotonically increasing. 695/// 696/// Note that we go take special precautions to ensure that we get deterministic 697/// results from this routine. In other words, we don't want the results of 698/// this to depend on where the addresses of various SCEV objects happened to 699/// land in memory. 700/// 701static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 702 LoopInfo *LI) { 703 if (Ops.size() < 2) return; // Noop 704 if (Ops.size() == 2) { 705 // This is the common case, which also happens to be trivially simple. 706 // Special case it. 707 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 708 std::swap(Ops[0], Ops[1]); 709 return; 710 } 711 712 // Do the rough sort by complexity. 713 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 714 715 // Now that we are sorted by complexity, group elements of the same 716 // complexity. Note that this is, at worst, N^2, but the vector is likely to 717 // be extremely short in practice. Note that we take this approach because we 718 // do not want to depend on the addresses of the objects we are grouping. 719 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 720 const SCEV *S = Ops[i]; 721 unsigned Complexity = S->getSCEVType(); 722 723 // If there are any objects of the same complexity and same value as this 724 // one, group them. 725 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 726 if (Ops[j] == S) { // Found a duplicate. 727 // Move it to immediately after i'th element. 728 std::swap(Ops[i+1], Ops[j]); 729 ++i; // no need to rescan it. 730 if (i == e-2) return; // Done! 731 } 732 } 733 } 734} 735 736 737 738//===----------------------------------------------------------------------===// 739// Simple SCEV method implementations 740//===----------------------------------------------------------------------===// 741 742/// BinomialCoefficient - Compute BC(It, K). The result has width W. 743/// Assume, K > 0. 744static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 745 ScalarEvolution &SE, 746 const Type* ResultTy) { 747 // Handle the simplest case efficiently. 748 if (K == 1) 749 return SE.getTruncateOrZeroExtend(It, ResultTy); 750 751 // We are using the following formula for BC(It, K): 752 // 753 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 754 // 755 // Suppose, W is the bitwidth of the return value. We must be prepared for 756 // overflow. Hence, we must assure that the result of our computation is 757 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 758 // safe in modular arithmetic. 759 // 760 // However, this code doesn't use exactly that formula; the formula it uses 761 // is something like the following, where T is the number of factors of 2 in 762 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 763 // exponentiation: 764 // 765 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 766 // 767 // This formula is trivially equivalent to the previous formula. However, 768 // this formula can be implemented much more efficiently. The trick is that 769 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 770 // arithmetic. To do exact division in modular arithmetic, all we have 771 // to do is multiply by the inverse. Therefore, this step can be done at 772 // width W. 773 // 774 // The next issue is how to safely do the division by 2^T. The way this 775 // is done is by doing the multiplication step at a width of at least W + T 776 // bits. This way, the bottom W+T bits of the product are accurate. Then, 777 // when we perform the division by 2^T (which is equivalent to a right shift 778 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 779 // truncated out after the division by 2^T. 780 // 781 // In comparison to just directly using the first formula, this technique 782 // is much more efficient; using the first formula requires W * K bits, 783 // but this formula less than W + K bits. Also, the first formula requires 784 // a division step, whereas this formula only requires multiplies and shifts. 785 // 786 // It doesn't matter whether the subtraction step is done in the calculation 787 // width or the input iteration count's width; if the subtraction overflows, 788 // the result must be zero anyway. We prefer here to do it in the width of 789 // the induction variable because it helps a lot for certain cases; CodeGen 790 // isn't smart enough to ignore the overflow, which leads to much less 791 // efficient code if the width of the subtraction is wider than the native 792 // register width. 793 // 794 // (It's possible to not widen at all by pulling out factors of 2 before 795 // the multiplication; for example, K=2 can be calculated as 796 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 797 // extra arithmetic, so it's not an obvious win, and it gets 798 // much more complicated for K > 3.) 799 800 // Protection from insane SCEVs; this bound is conservative, 801 // but it probably doesn't matter. 802 if (K > 1000) 803 return SE.getCouldNotCompute(); 804 805 unsigned W = SE.getTypeSizeInBits(ResultTy); 806 807 // Calculate K! / 2^T and T; we divide out the factors of two before 808 // multiplying for calculating K! / 2^T to avoid overflow. 809 // Other overflow doesn't matter because we only care about the bottom 810 // W bits of the result. 811 APInt OddFactorial(W, 1); 812 unsigned T = 1; 813 for (unsigned i = 3; i <= K; ++i) { 814 APInt Mult(W, i); 815 unsigned TwoFactors = Mult.countTrailingZeros(); 816 T += TwoFactors; 817 Mult = Mult.lshr(TwoFactors); 818 OddFactorial *= Mult; 819 } 820 821 // We need at least W + T bits for the multiplication step 822 unsigned CalculationBits = W + T; 823 824 // Calculate 2^T, at width T+W. 825 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 826 827 // Calculate the multiplicative inverse of K! / 2^T; 828 // this multiplication factor will perform the exact division by 829 // K! / 2^T. 830 APInt Mod = APInt::getSignedMinValue(W+1); 831 APInt MultiplyFactor = OddFactorial.zext(W+1); 832 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 833 MultiplyFactor = MultiplyFactor.trunc(W); 834 835 // Calculate the product, at width T+W 836 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 837 CalculationBits); 838 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 839 for (unsigned i = 1; i != K; ++i) { 840 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 841 Dividend = SE.getMulExpr(Dividend, 842 SE.getTruncateOrZeroExtend(S, CalculationTy)); 843 } 844 845 // Divide by 2^T 846 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 847 848 // Truncate the result, and divide by K! / 2^T. 849 850 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 851 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 852} 853 854/// evaluateAtIteration - Return the value of this chain of recurrences at 855/// the specified iteration number. We can evaluate this recurrence by 856/// multiplying each element in the chain by the binomial coefficient 857/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 858/// 859/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 860/// 861/// where BC(It, k) stands for binomial coefficient. 862/// 863const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 864 ScalarEvolution &SE) const { 865 const SCEV *Result = getStart(); 866 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 867 // The computation is correct in the face of overflow provided that the 868 // multiplication is performed _after_ the evaluation of the binomial 869 // coefficient. 870 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 871 if (isa<SCEVCouldNotCompute>(Coeff)) 872 return Coeff; 873 874 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 875 } 876 return Result; 877} 878 879//===----------------------------------------------------------------------===// 880// SCEV Expression folder implementations 881//===----------------------------------------------------------------------===// 882 883const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 884 const Type *Ty) { 885 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 886 "This is not a truncating conversion!"); 887 assert(isSCEVable(Ty) && 888 "This is not a conversion to a SCEVable type!"); 889 Ty = getEffectiveSCEVType(Ty); 890 891 FoldingSetNodeID ID; 892 ID.AddInteger(scTruncate); 893 ID.AddPointer(Op); 894 ID.AddPointer(Ty); 895 void *IP = 0; 896 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 897 898 // Fold if the operand is constant. 899 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 900 return getConstant( 901 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 902 getEffectiveSCEVType(Ty)))); 903 904 // trunc(trunc(x)) --> trunc(x) 905 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 906 return getTruncateExpr(ST->getOperand(), Ty); 907 908 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 909 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 910 return getTruncateOrSignExtend(SS->getOperand(), Ty); 911 912 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 913 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 914 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 915 916 // If the input value is a chrec scev, truncate the chrec's operands. 917 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 918 SmallVector<const SCEV *, 4> Operands; 919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 920 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 921 return getAddRecExpr(Operands, AddRec->getLoop()); 922 } 923 924 // As a special case, fold trunc(undef) to undef. We don't want to 925 // know too much about SCEVUnknowns, but this special case is handy 926 // and harmless. 927 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 928 if (isa<UndefValue>(U->getValue())) 929 return getSCEV(UndefValue::get(Ty)); 930 931 // The cast wasn't folded; create an explicit cast node. We can reuse 932 // the existing insert position since if we get here, we won't have 933 // made any changes which would invalidate it. 934 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 935 Op, Ty); 936 UniqueSCEVs.InsertNode(S, IP); 937 return S; 938} 939 940const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 941 const Type *Ty) { 942 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 943 "This is not an extending conversion!"); 944 assert(isSCEVable(Ty) && 945 "This is not a conversion to a SCEVable type!"); 946 Ty = getEffectiveSCEVType(Ty); 947 948 // Fold if the operand is constant. 949 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 950 return getConstant( 951 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 952 getEffectiveSCEVType(Ty)))); 953 954 // zext(zext(x)) --> zext(x) 955 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 956 return getZeroExtendExpr(SZ->getOperand(), Ty); 957 958 // Before doing any expensive analysis, check to see if we've already 959 // computed a SCEV for this Op and Ty. 960 FoldingSetNodeID ID; 961 ID.AddInteger(scZeroExtend); 962 ID.AddPointer(Op); 963 ID.AddPointer(Ty); 964 void *IP = 0; 965 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 966 967 // If the input value is a chrec scev, and we can prove that the value 968 // did not overflow the old, smaller, value, we can zero extend all of the 969 // operands (often constants). This allows analysis of something like 970 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 971 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 972 if (AR->isAffine()) { 973 const SCEV *Start = AR->getStart(); 974 const SCEV *Step = AR->getStepRecurrence(*this); 975 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 976 const Loop *L = AR->getLoop(); 977 978 // If we have special knowledge that this addrec won't overflow, 979 // we don't need to do any further analysis. 980 if (AR->hasNoUnsignedWrap()) 981 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 982 getZeroExtendExpr(Step, Ty), 983 L); 984 985 // Check whether the backedge-taken count is SCEVCouldNotCompute. 986 // Note that this serves two purposes: It filters out loops that are 987 // simply not analyzable, and it covers the case where this code is 988 // being called from within backedge-taken count analysis, such that 989 // attempting to ask for the backedge-taken count would likely result 990 // in infinite recursion. In the later case, the analysis code will 991 // cope with a conservative value, and it will take care to purge 992 // that value once it has finished. 993 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 994 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 995 // Manually compute the final value for AR, checking for 996 // overflow. 997 998 // Check whether the backedge-taken count can be losslessly casted to 999 // the addrec's type. The count is always unsigned. 1000 const SCEV *CastedMaxBECount = 1001 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1002 const SCEV *RecastedMaxBECount = 1003 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1004 if (MaxBECount == RecastedMaxBECount) { 1005 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1006 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1007 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1008 const SCEV *Add = getAddExpr(Start, ZMul); 1009 const SCEV *OperandExtendedAdd = 1010 getAddExpr(getZeroExtendExpr(Start, WideTy), 1011 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1012 getZeroExtendExpr(Step, WideTy))); 1013 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1014 // Return the expression with the addrec on the outside. 1015 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1016 getZeroExtendExpr(Step, Ty), 1017 L); 1018 1019 // Similar to above, only this time treat the step value as signed. 1020 // This covers loops that count down. 1021 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1022 Add = getAddExpr(Start, SMul); 1023 OperandExtendedAdd = 1024 getAddExpr(getZeroExtendExpr(Start, WideTy), 1025 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1026 getSignExtendExpr(Step, WideTy))); 1027 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1028 // Return the expression with the addrec on the outside. 1029 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1030 getSignExtendExpr(Step, Ty), 1031 L); 1032 } 1033 1034 // If the backedge is guarded by a comparison with the pre-inc value 1035 // the addrec is safe. Also, if the entry is guarded by a comparison 1036 // with the start value and the backedge is guarded by a comparison 1037 // with the post-inc value, the addrec is safe. 1038 if (isKnownPositive(Step)) { 1039 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1040 getUnsignedRange(Step).getUnsignedMax()); 1041 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1042 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1043 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1044 AR->getPostIncExpr(*this), N))) 1045 // Return the expression with the addrec on the outside. 1046 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1047 getZeroExtendExpr(Step, Ty), 1048 L); 1049 } else if (isKnownNegative(Step)) { 1050 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1051 getSignedRange(Step).getSignedMin()); 1052 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1053 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1054 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1055 AR->getPostIncExpr(*this), N))) 1056 // Return the expression with the addrec on the outside. 1057 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1058 getSignExtendExpr(Step, Ty), 1059 L); 1060 } 1061 } 1062 } 1063 1064 // The cast wasn't folded; create an explicit cast node. 1065 // Recompute the insert position, as it may have been invalidated. 1066 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1067 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1068 Op, Ty); 1069 UniqueSCEVs.InsertNode(S, IP); 1070 return S; 1071} 1072 1073const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1074 const Type *Ty) { 1075 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1076 "This is not an extending conversion!"); 1077 assert(isSCEVable(Ty) && 1078 "This is not a conversion to a SCEVable type!"); 1079 Ty = getEffectiveSCEVType(Ty); 1080 1081 // Fold if the operand is constant. 1082 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1083 return getConstant( 1084 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1085 getEffectiveSCEVType(Ty)))); 1086 1087 // sext(sext(x)) --> sext(x) 1088 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1089 return getSignExtendExpr(SS->getOperand(), Ty); 1090 1091 // Before doing any expensive analysis, check to see if we've already 1092 // computed a SCEV for this Op and Ty. 1093 FoldingSetNodeID ID; 1094 ID.AddInteger(scSignExtend); 1095 ID.AddPointer(Op); 1096 ID.AddPointer(Ty); 1097 void *IP = 0; 1098 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1099 1100 // If the input value is a chrec scev, and we can prove that the value 1101 // did not overflow the old, smaller, value, we can sign extend all of the 1102 // operands (often constants). This allows analysis of something like 1103 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1104 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1105 if (AR->isAffine()) { 1106 const SCEV *Start = AR->getStart(); 1107 const SCEV *Step = AR->getStepRecurrence(*this); 1108 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1109 const Loop *L = AR->getLoop(); 1110 1111 // If we have special knowledge that this addrec won't overflow, 1112 // we don't need to do any further analysis. 1113 if (AR->hasNoSignedWrap()) 1114 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1115 getSignExtendExpr(Step, Ty), 1116 L); 1117 1118 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1119 // Note that this serves two purposes: It filters out loops that are 1120 // simply not analyzable, and it covers the case where this code is 1121 // being called from within backedge-taken count analysis, such that 1122 // attempting to ask for the backedge-taken count would likely result 1123 // in infinite recursion. In the later case, the analysis code will 1124 // cope with a conservative value, and it will take care to purge 1125 // that value once it has finished. 1126 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1127 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1128 // Manually compute the final value for AR, checking for 1129 // overflow. 1130 1131 // Check whether the backedge-taken count can be losslessly casted to 1132 // the addrec's type. The count is always unsigned. 1133 const SCEV *CastedMaxBECount = 1134 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1135 const SCEV *RecastedMaxBECount = 1136 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1137 if (MaxBECount == RecastedMaxBECount) { 1138 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1139 // Check whether Start+Step*MaxBECount has no signed overflow. 1140 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1141 const SCEV *Add = getAddExpr(Start, SMul); 1142 const SCEV *OperandExtendedAdd = 1143 getAddExpr(getSignExtendExpr(Start, WideTy), 1144 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1145 getSignExtendExpr(Step, WideTy))); 1146 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1147 // Return the expression with the addrec on the outside. 1148 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1149 getSignExtendExpr(Step, Ty), 1150 L); 1151 1152 // Similar to above, only this time treat the step value as unsigned. 1153 // This covers loops that count up with an unsigned step. 1154 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1155 Add = getAddExpr(Start, UMul); 1156 OperandExtendedAdd = 1157 getAddExpr(getSignExtendExpr(Start, WideTy), 1158 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1159 getZeroExtendExpr(Step, WideTy))); 1160 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1161 // Return the expression with the addrec on the outside. 1162 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1163 getZeroExtendExpr(Step, Ty), 1164 L); 1165 } 1166 1167 // If the backedge is guarded by a comparison with the pre-inc value 1168 // the addrec is safe. Also, if the entry is guarded by a comparison 1169 // with the start value and the backedge is guarded by a comparison 1170 // with the post-inc value, the addrec is safe. 1171 if (isKnownPositive(Step)) { 1172 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1173 getSignedRange(Step).getSignedMax()); 1174 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1175 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1176 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1177 AR->getPostIncExpr(*this), N))) 1178 // Return the expression with the addrec on the outside. 1179 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1180 getSignExtendExpr(Step, Ty), 1181 L); 1182 } else if (isKnownNegative(Step)) { 1183 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1184 getSignedRange(Step).getSignedMin()); 1185 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1186 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1187 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1188 AR->getPostIncExpr(*this), N))) 1189 // Return the expression with the addrec on the outside. 1190 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1191 getSignExtendExpr(Step, Ty), 1192 L); 1193 } 1194 } 1195 } 1196 1197 // The cast wasn't folded; create an explicit cast node. 1198 // Recompute the insert position, as it may have been invalidated. 1199 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1200 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1201 Op, Ty); 1202 UniqueSCEVs.InsertNode(S, IP); 1203 return S; 1204} 1205 1206/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1207/// unspecified bits out to the given type. 1208/// 1209const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1210 const Type *Ty) { 1211 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1212 "This is not an extending conversion!"); 1213 assert(isSCEVable(Ty) && 1214 "This is not a conversion to a SCEVable type!"); 1215 Ty = getEffectiveSCEVType(Ty); 1216 1217 // Sign-extend negative constants. 1218 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1219 if (SC->getValue()->getValue().isNegative()) 1220 return getSignExtendExpr(Op, Ty); 1221 1222 // Peel off a truncate cast. 1223 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1224 const SCEV *NewOp = T->getOperand(); 1225 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1226 return getAnyExtendExpr(NewOp, Ty); 1227 return getTruncateOrNoop(NewOp, Ty); 1228 } 1229 1230 // Next try a zext cast. If the cast is folded, use it. 1231 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1232 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1233 return ZExt; 1234 1235 // Next try a sext cast. If the cast is folded, use it. 1236 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1237 if (!isa<SCEVSignExtendExpr>(SExt)) 1238 return SExt; 1239 1240 // Force the cast to be folded into the operands of an addrec. 1241 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1242 SmallVector<const SCEV *, 4> Ops; 1243 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1244 I != E; ++I) 1245 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1246 return getAddRecExpr(Ops, AR->getLoop()); 1247 } 1248 1249 // As a special case, fold anyext(undef) to undef. We don't want to 1250 // know too much about SCEVUnknowns, but this special case is handy 1251 // and harmless. 1252 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1253 if (isa<UndefValue>(U->getValue())) 1254 return getSCEV(UndefValue::get(Ty)); 1255 1256 // If the expression is obviously signed, use the sext cast value. 1257 if (isa<SCEVSMaxExpr>(Op)) 1258 return SExt; 1259 1260 // Absent any other information, use the zext cast value. 1261 return ZExt; 1262} 1263 1264/// CollectAddOperandsWithScales - Process the given Ops list, which is 1265/// a list of operands to be added under the given scale, update the given 1266/// map. This is a helper function for getAddRecExpr. As an example of 1267/// what it does, given a sequence of operands that would form an add 1268/// expression like this: 1269/// 1270/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1271/// 1272/// where A and B are constants, update the map with these values: 1273/// 1274/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1275/// 1276/// and add 13 + A*B*29 to AccumulatedConstant. 1277/// This will allow getAddRecExpr to produce this: 1278/// 1279/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1280/// 1281/// This form often exposes folding opportunities that are hidden in 1282/// the original operand list. 1283/// 1284/// Return true iff it appears that any interesting folding opportunities 1285/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1286/// the common case where no interesting opportunities are present, and 1287/// is also used as a check to avoid infinite recursion. 1288/// 1289static bool 1290CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1291 SmallVector<const SCEV *, 8> &NewOps, 1292 APInt &AccumulatedConstant, 1293 const SCEV *const *Ops, size_t NumOperands, 1294 const APInt &Scale, 1295 ScalarEvolution &SE) { 1296 bool Interesting = false; 1297 1298 // Iterate over the add operands. They are sorted, with constants first. 1299 unsigned i = 0; 1300 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1301 ++i; 1302 // Pull a buried constant out to the outside. 1303 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1304 Interesting = true; 1305 AccumulatedConstant += Scale * C->getValue()->getValue(); 1306 } 1307 1308 // Next comes everything else. We're especially interested in multiplies 1309 // here, but they're in the middle, so just visit the rest with one loop. 1310 for (; i != NumOperands; ++i) { 1311 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1312 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1313 APInt NewScale = 1314 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1315 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1316 // A multiplication of a constant with another add; recurse. 1317 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1318 Interesting |= 1319 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1320 Add->op_begin(), Add->getNumOperands(), 1321 NewScale, SE); 1322 } else { 1323 // A multiplication of a constant with some other value. Update 1324 // the map. 1325 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1326 const SCEV *Key = SE.getMulExpr(MulOps); 1327 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1328 M.insert(std::make_pair(Key, NewScale)); 1329 if (Pair.second) { 1330 NewOps.push_back(Pair.first->first); 1331 } else { 1332 Pair.first->second += NewScale; 1333 // The map already had an entry for this value, which may indicate 1334 // a folding opportunity. 1335 Interesting = true; 1336 } 1337 } 1338 } else { 1339 // An ordinary operand. Update the map. 1340 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1341 M.insert(std::make_pair(Ops[i], Scale)); 1342 if (Pair.second) { 1343 NewOps.push_back(Pair.first->first); 1344 } else { 1345 Pair.first->second += Scale; 1346 // The map already had an entry for this value, which may indicate 1347 // a folding opportunity. 1348 Interesting = true; 1349 } 1350 } 1351 } 1352 1353 return Interesting; 1354} 1355 1356namespace { 1357 struct APIntCompare { 1358 bool operator()(const APInt &LHS, const APInt &RHS) const { 1359 return LHS.ult(RHS); 1360 } 1361 }; 1362} 1363 1364/// getAddExpr - Get a canonical add expression, or something simpler if 1365/// possible. 1366const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1367 bool HasNUW, bool HasNSW) { 1368 assert(!Ops.empty() && "Cannot get empty add!"); 1369 if (Ops.size() == 1) return Ops[0]; 1370#ifndef NDEBUG 1371 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1372 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1373 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1374 "SCEVAddExpr operand types don't match!"); 1375#endif 1376 1377 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1378 if (!HasNUW && HasNSW) { 1379 bool All = true; 1380 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1381 E = Ops.end(); I != E; ++I) 1382 if (!isKnownNonNegative(*I)) { 1383 All = false; 1384 break; 1385 } 1386 if (All) HasNUW = true; 1387 } 1388 1389 // Sort by complexity, this groups all similar expression types together. 1390 GroupByComplexity(Ops, LI); 1391 1392 // If there are any constants, fold them together. 1393 unsigned Idx = 0; 1394 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1395 ++Idx; 1396 assert(Idx < Ops.size()); 1397 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1398 // We found two constants, fold them together! 1399 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1400 RHSC->getValue()->getValue()); 1401 if (Ops.size() == 2) return Ops[0]; 1402 Ops.erase(Ops.begin()+1); // Erase the folded element 1403 LHSC = cast<SCEVConstant>(Ops[0]); 1404 } 1405 1406 // If we are left with a constant zero being added, strip it off. 1407 if (LHSC->getValue()->isZero()) { 1408 Ops.erase(Ops.begin()); 1409 --Idx; 1410 } 1411 1412 if (Ops.size() == 1) return Ops[0]; 1413 } 1414 1415 // Okay, check to see if the same value occurs in the operand list more than 1416 // once. If so, merge them together into an multiply expression. Since we 1417 // sorted the list, these values are required to be adjacent. 1418 const Type *Ty = Ops[0]->getType(); 1419 bool FoundMatch = false; 1420 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1421 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1422 // Scan ahead to count how many equal operands there are. 1423 unsigned Count = 2; 1424 while (i+Count != e && Ops[i+Count] == Ops[i]) 1425 ++Count; 1426 // Merge the values into a multiply. 1427 const SCEV *Scale = getConstant(Ty, Count); 1428 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1429 if (Ops.size() == Count) 1430 return Mul; 1431 Ops[i] = Mul; 1432 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1433 --i; e -= Count - 1; 1434 FoundMatch = true; 1435 } 1436 if (FoundMatch) 1437 return getAddExpr(Ops, HasNUW, HasNSW); 1438 1439 // Check for truncates. If all the operands are truncated from the same 1440 // type, see if factoring out the truncate would permit the result to be 1441 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1442 // if the contents of the resulting outer trunc fold to something simple. 1443 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1444 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1445 const Type *DstType = Trunc->getType(); 1446 const Type *SrcType = Trunc->getOperand()->getType(); 1447 SmallVector<const SCEV *, 8> LargeOps; 1448 bool Ok = true; 1449 // Check all the operands to see if they can be represented in the 1450 // source type of the truncate. 1451 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1452 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1453 if (T->getOperand()->getType() != SrcType) { 1454 Ok = false; 1455 break; 1456 } 1457 LargeOps.push_back(T->getOperand()); 1458 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1459 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1460 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1461 SmallVector<const SCEV *, 8> LargeMulOps; 1462 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1463 if (const SCEVTruncateExpr *T = 1464 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1465 if (T->getOperand()->getType() != SrcType) { 1466 Ok = false; 1467 break; 1468 } 1469 LargeMulOps.push_back(T->getOperand()); 1470 } else if (const SCEVConstant *C = 1471 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1472 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1473 } else { 1474 Ok = false; 1475 break; 1476 } 1477 } 1478 if (Ok) 1479 LargeOps.push_back(getMulExpr(LargeMulOps)); 1480 } else { 1481 Ok = false; 1482 break; 1483 } 1484 } 1485 if (Ok) { 1486 // Evaluate the expression in the larger type. 1487 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1488 // If it folds to something simple, use it. Otherwise, don't. 1489 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1490 return getTruncateExpr(Fold, DstType); 1491 } 1492 } 1493 1494 // Skip past any other cast SCEVs. 1495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1496 ++Idx; 1497 1498 // If there are add operands they would be next. 1499 if (Idx < Ops.size()) { 1500 bool DeletedAdd = false; 1501 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1502 // If we have an add, expand the add operands onto the end of the operands 1503 // list. 1504 Ops.erase(Ops.begin()+Idx); 1505 Ops.append(Add->op_begin(), Add->op_end()); 1506 DeletedAdd = true; 1507 } 1508 1509 // If we deleted at least one add, we added operands to the end of the list, 1510 // and they are not necessarily sorted. Recurse to resort and resimplify 1511 // any operands we just acquired. 1512 if (DeletedAdd) 1513 return getAddExpr(Ops); 1514 } 1515 1516 // Skip over the add expression until we get to a multiply. 1517 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1518 ++Idx; 1519 1520 // Check to see if there are any folding opportunities present with 1521 // operands multiplied by constant values. 1522 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1523 uint64_t BitWidth = getTypeSizeInBits(Ty); 1524 DenseMap<const SCEV *, APInt> M; 1525 SmallVector<const SCEV *, 8> NewOps; 1526 APInt AccumulatedConstant(BitWidth, 0); 1527 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1528 Ops.data(), Ops.size(), 1529 APInt(BitWidth, 1), *this)) { 1530 // Some interesting folding opportunity is present, so its worthwhile to 1531 // re-generate the operands list. Group the operands by constant scale, 1532 // to avoid multiplying by the same constant scale multiple times. 1533 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1534 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1535 E = NewOps.end(); I != E; ++I) 1536 MulOpLists[M.find(*I)->second].push_back(*I); 1537 // Re-generate the operands list. 1538 Ops.clear(); 1539 if (AccumulatedConstant != 0) 1540 Ops.push_back(getConstant(AccumulatedConstant)); 1541 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1542 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1543 if (I->first != 0) 1544 Ops.push_back(getMulExpr(getConstant(I->first), 1545 getAddExpr(I->second))); 1546 if (Ops.empty()) 1547 return getConstant(Ty, 0); 1548 if (Ops.size() == 1) 1549 return Ops[0]; 1550 return getAddExpr(Ops); 1551 } 1552 } 1553 1554 // If we are adding something to a multiply expression, make sure the 1555 // something is not already an operand of the multiply. If so, merge it into 1556 // the multiply. 1557 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1558 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1559 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1560 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1561 if (isa<SCEVConstant>(MulOpSCEV)) 1562 continue; 1563 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1564 if (MulOpSCEV == Ops[AddOp]) { 1565 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1566 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1567 if (Mul->getNumOperands() != 2) { 1568 // If the multiply has more than two operands, we must get the 1569 // Y*Z term. 1570 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1571 Mul->op_begin()+MulOp); 1572 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1573 InnerMul = getMulExpr(MulOps); 1574 } 1575 const SCEV *One = getConstant(Ty, 1); 1576 const SCEV *AddOne = getAddExpr(One, InnerMul); 1577 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1578 if (Ops.size() == 2) return OuterMul; 1579 if (AddOp < Idx) { 1580 Ops.erase(Ops.begin()+AddOp); 1581 Ops.erase(Ops.begin()+Idx-1); 1582 } else { 1583 Ops.erase(Ops.begin()+Idx); 1584 Ops.erase(Ops.begin()+AddOp-1); 1585 } 1586 Ops.push_back(OuterMul); 1587 return getAddExpr(Ops); 1588 } 1589 1590 // Check this multiply against other multiplies being added together. 1591 bool AnyFold = false; 1592 for (unsigned OtherMulIdx = Idx+1; 1593 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1594 ++OtherMulIdx) { 1595 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1596 // If MulOp occurs in OtherMul, we can fold the two multiplies 1597 // together. 1598 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1599 OMulOp != e; ++OMulOp) 1600 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1601 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1602 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1603 if (Mul->getNumOperands() != 2) { 1604 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1605 Mul->op_begin()+MulOp); 1606 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1607 InnerMul1 = getMulExpr(MulOps); 1608 } 1609 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1610 if (OtherMul->getNumOperands() != 2) { 1611 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1612 OtherMul->op_begin()+OMulOp); 1613 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1614 InnerMul2 = getMulExpr(MulOps); 1615 } 1616 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1617 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1618 if (Ops.size() == 2) return OuterMul; 1619 Ops[Idx] = OuterMul; 1620 Ops.erase(Ops.begin()+OtherMulIdx); 1621 OtherMulIdx = Idx; 1622 AnyFold = true; 1623 } 1624 } 1625 if (AnyFold) 1626 return getAddExpr(Ops); 1627 } 1628 } 1629 1630 // If there are any add recurrences in the operands list, see if any other 1631 // added values are loop invariant. If so, we can fold them into the 1632 // recurrence. 1633 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1634 ++Idx; 1635 1636 // Scan over all recurrences, trying to fold loop invariants into them. 1637 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1638 // Scan all of the other operands to this add and add them to the vector if 1639 // they are loop invariant w.r.t. the recurrence. 1640 SmallVector<const SCEV *, 8> LIOps; 1641 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1642 const Loop *AddRecLoop = AddRec->getLoop(); 1643 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1644 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1645 LIOps.push_back(Ops[i]); 1646 Ops.erase(Ops.begin()+i); 1647 --i; --e; 1648 } 1649 1650 // If we found some loop invariants, fold them into the recurrence. 1651 if (!LIOps.empty()) { 1652 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1653 LIOps.push_back(AddRec->getStart()); 1654 1655 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1656 AddRec->op_end()); 1657 AddRecOps[0] = getAddExpr(LIOps); 1658 1659 // Build the new addrec. Propagate the NUW and NSW flags if both the 1660 // outer add and the inner addrec are guaranteed to have no overflow. 1661 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1662 HasNUW && AddRec->hasNoUnsignedWrap(), 1663 HasNSW && AddRec->hasNoSignedWrap()); 1664 1665 // If all of the other operands were loop invariant, we are done. 1666 if (Ops.size() == 1) return NewRec; 1667 1668 // Otherwise, add the folded AddRec by the non-liv parts. 1669 for (unsigned i = 0;; ++i) 1670 if (Ops[i] == AddRec) { 1671 Ops[i] = NewRec; 1672 break; 1673 } 1674 return getAddExpr(Ops); 1675 } 1676 1677 // Okay, if there weren't any loop invariants to be folded, check to see if 1678 // there are multiple AddRec's with the same loop induction variable being 1679 // added together. If so, we can fold them. 1680 for (unsigned OtherIdx = Idx+1; 1681 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1682 ++OtherIdx) 1683 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1684 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1685 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1686 AddRec->op_end()); 1687 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1688 ++OtherIdx) 1689 if (const SCEVAddRecExpr *AR = 1690 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1691 if (AR->getLoop() == AddRecLoop) { 1692 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) { 1693 if (i >= AddRecOps.size()) { 1694 AddRecOps.append(AR->op_begin()+i, AR->op_end()); 1695 break; 1696 } 1697 AddRecOps[i] = getAddExpr(AddRecOps[i], AR->getOperand(i)); 1698 } 1699 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1700 } 1701 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1702 return getAddExpr(Ops); 1703 } 1704 1705 // Otherwise couldn't fold anything into this recurrence. Move onto the 1706 // next one. 1707 } 1708 1709 // Okay, it looks like we really DO need an add expr. Check to see if we 1710 // already have one, otherwise create a new one. 1711 FoldingSetNodeID ID; 1712 ID.AddInteger(scAddExpr); 1713 ID.AddInteger(Ops.size()); 1714 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1715 ID.AddPointer(Ops[i]); 1716 void *IP = 0; 1717 SCEVAddExpr *S = 1718 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1719 if (!S) { 1720 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1721 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1722 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1723 O, Ops.size()); 1724 UniqueSCEVs.InsertNode(S, IP); 1725 } 1726 if (HasNUW) S->setHasNoUnsignedWrap(true); 1727 if (HasNSW) S->setHasNoSignedWrap(true); 1728 return S; 1729} 1730 1731/// getMulExpr - Get a canonical multiply expression, or something simpler if 1732/// possible. 1733const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1734 bool HasNUW, bool HasNSW) { 1735 assert(!Ops.empty() && "Cannot get empty mul!"); 1736 if (Ops.size() == 1) return Ops[0]; 1737#ifndef NDEBUG 1738 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1739 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1740 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1741 "SCEVMulExpr operand types don't match!"); 1742#endif 1743 1744 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1745 if (!HasNUW && HasNSW) { 1746 bool All = true; 1747 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1748 E = Ops.end(); I != E; ++I) 1749 if (!isKnownNonNegative(*I)) { 1750 All = false; 1751 break; 1752 } 1753 if (All) HasNUW = true; 1754 } 1755 1756 // Sort by complexity, this groups all similar expression types together. 1757 GroupByComplexity(Ops, LI); 1758 1759 // If there are any constants, fold them together. 1760 unsigned Idx = 0; 1761 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1762 1763 // C1*(C2+V) -> C1*C2 + C1*V 1764 if (Ops.size() == 2) 1765 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1766 if (Add->getNumOperands() == 2 && 1767 isa<SCEVConstant>(Add->getOperand(0))) 1768 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1769 getMulExpr(LHSC, Add->getOperand(1))); 1770 1771 ++Idx; 1772 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1773 // We found two constants, fold them together! 1774 ConstantInt *Fold = ConstantInt::get(getContext(), 1775 LHSC->getValue()->getValue() * 1776 RHSC->getValue()->getValue()); 1777 Ops[0] = getConstant(Fold); 1778 Ops.erase(Ops.begin()+1); // Erase the folded element 1779 if (Ops.size() == 1) return Ops[0]; 1780 LHSC = cast<SCEVConstant>(Ops[0]); 1781 } 1782 1783 // If we are left with a constant one being multiplied, strip it off. 1784 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1785 Ops.erase(Ops.begin()); 1786 --Idx; 1787 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1788 // If we have a multiply of zero, it will always be zero. 1789 return Ops[0]; 1790 } else if (Ops[0]->isAllOnesValue()) { 1791 // If we have a mul by -1 of an add, try distributing the -1 among the 1792 // add operands. 1793 if (Ops.size() == 2) 1794 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1795 SmallVector<const SCEV *, 4> NewOps; 1796 bool AnyFolded = false; 1797 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1798 I != E; ++I) { 1799 const SCEV *Mul = getMulExpr(Ops[0], *I); 1800 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1801 NewOps.push_back(Mul); 1802 } 1803 if (AnyFolded) 1804 return getAddExpr(NewOps); 1805 } 1806 } 1807 1808 if (Ops.size() == 1) 1809 return Ops[0]; 1810 } 1811 1812 // Skip over the add expression until we get to a multiply. 1813 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1814 ++Idx; 1815 1816 // If there are mul operands inline them all into this expression. 1817 if (Idx < Ops.size()) { 1818 bool DeletedMul = false; 1819 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1820 // If we have an mul, expand the mul operands onto the end of the operands 1821 // list. 1822 Ops.erase(Ops.begin()+Idx); 1823 Ops.append(Mul->op_begin(), Mul->op_end()); 1824 DeletedMul = true; 1825 } 1826 1827 // If we deleted at least one mul, we added operands to the end of the list, 1828 // and they are not necessarily sorted. Recurse to resort and resimplify 1829 // any operands we just acquired. 1830 if (DeletedMul) 1831 return getMulExpr(Ops); 1832 } 1833 1834 // If there are any add recurrences in the operands list, see if any other 1835 // added values are loop invariant. If so, we can fold them into the 1836 // recurrence. 1837 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1838 ++Idx; 1839 1840 // Scan over all recurrences, trying to fold loop invariants into them. 1841 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1842 // Scan all of the other operands to this mul and add them to the vector if 1843 // they are loop invariant w.r.t. the recurrence. 1844 SmallVector<const SCEV *, 8> LIOps; 1845 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1846 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1847 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1848 LIOps.push_back(Ops[i]); 1849 Ops.erase(Ops.begin()+i); 1850 --i; --e; 1851 } 1852 1853 // If we found some loop invariants, fold them into the recurrence. 1854 if (!LIOps.empty()) { 1855 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1856 SmallVector<const SCEV *, 4> NewOps; 1857 NewOps.reserve(AddRec->getNumOperands()); 1858 const SCEV *Scale = getMulExpr(LIOps); 1859 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1860 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1861 1862 // Build the new addrec. Propagate the NUW and NSW flags if both the 1863 // outer mul and the inner addrec are guaranteed to have no overflow. 1864 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1865 HasNUW && AddRec->hasNoUnsignedWrap(), 1866 HasNSW && AddRec->hasNoSignedWrap()); 1867 1868 // If all of the other operands were loop invariant, we are done. 1869 if (Ops.size() == 1) return NewRec; 1870 1871 // Otherwise, multiply the folded AddRec by the non-liv parts. 1872 for (unsigned i = 0;; ++i) 1873 if (Ops[i] == AddRec) { 1874 Ops[i] = NewRec; 1875 break; 1876 } 1877 return getMulExpr(Ops); 1878 } 1879 1880 // Okay, if there weren't any loop invariants to be folded, check to see if 1881 // there are multiple AddRec's with the same loop induction variable being 1882 // multiplied together. If so, we can fold them. 1883 for (unsigned OtherIdx = Idx+1; 1884 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1885 if (OtherIdx != Idx) { 1886 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1887 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1888 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1889 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1890 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1891 const SCEV *B = F->getStepRecurrence(*this); 1892 const SCEV *D = G->getStepRecurrence(*this); 1893 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1894 getMulExpr(G, B), 1895 getMulExpr(B, D)); 1896 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1897 F->getLoop()); 1898 if (Ops.size() == 2) return NewAddRec; 1899 1900 Ops.erase(Ops.begin()+Idx); 1901 Ops.erase(Ops.begin()+OtherIdx-1); 1902 Ops.push_back(NewAddRec); 1903 return getMulExpr(Ops); 1904 } 1905 } 1906 1907 // Otherwise couldn't fold anything into this recurrence. Move onto the 1908 // next one. 1909 } 1910 1911 // Okay, it looks like we really DO need an mul expr. Check to see if we 1912 // already have one, otherwise create a new one. 1913 FoldingSetNodeID ID; 1914 ID.AddInteger(scMulExpr); 1915 ID.AddInteger(Ops.size()); 1916 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1917 ID.AddPointer(Ops[i]); 1918 void *IP = 0; 1919 SCEVMulExpr *S = 1920 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1921 if (!S) { 1922 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1923 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1924 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1925 O, Ops.size()); 1926 UniqueSCEVs.InsertNode(S, IP); 1927 } 1928 if (HasNUW) S->setHasNoUnsignedWrap(true); 1929 if (HasNSW) S->setHasNoSignedWrap(true); 1930 return S; 1931} 1932 1933/// getUDivExpr - Get a canonical unsigned division expression, or something 1934/// simpler if possible. 1935const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1936 const SCEV *RHS) { 1937 assert(getEffectiveSCEVType(LHS->getType()) == 1938 getEffectiveSCEVType(RHS->getType()) && 1939 "SCEVUDivExpr operand types don't match!"); 1940 1941 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1942 if (RHSC->getValue()->equalsInt(1)) 1943 return LHS; // X udiv 1 --> x 1944 // If the denominator is zero, the result of the udiv is undefined. Don't 1945 // try to analyze it, because the resolution chosen here may differ from 1946 // the resolution chosen in other parts of the compiler. 1947 if (!RHSC->getValue()->isZero()) { 1948 // Determine if the division can be folded into the operands of 1949 // its operands. 1950 // TODO: Generalize this to non-constants by using known-bits information. 1951 const Type *Ty = LHS->getType(); 1952 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1953 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1954 // For non-power-of-two values, effectively round the value up to the 1955 // nearest power of two. 1956 if (!RHSC->getValue()->getValue().isPowerOf2()) 1957 ++MaxShiftAmt; 1958 const IntegerType *ExtTy = 1959 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1960 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1961 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1962 if (const SCEVConstant *Step = 1963 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1964 if (!Step->getValue()->getValue() 1965 .urem(RHSC->getValue()->getValue()) && 1966 getZeroExtendExpr(AR, ExtTy) == 1967 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1968 getZeroExtendExpr(Step, ExtTy), 1969 AR->getLoop())) { 1970 SmallVector<const SCEV *, 4> Operands; 1971 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1972 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1973 return getAddRecExpr(Operands, AR->getLoop()); 1974 } 1975 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1976 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1977 SmallVector<const SCEV *, 4> Operands; 1978 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1979 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1980 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1981 // Find an operand that's safely divisible. 1982 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1983 const SCEV *Op = M->getOperand(i); 1984 const SCEV *Div = getUDivExpr(Op, RHSC); 1985 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1986 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1987 M->op_end()); 1988 Operands[i] = Div; 1989 return getMulExpr(Operands); 1990 } 1991 } 1992 } 1993 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1994 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1995 SmallVector<const SCEV *, 4> Operands; 1996 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1997 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1998 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1999 Operands.clear(); 2000 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2001 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2002 if (isa<SCEVUDivExpr>(Op) || 2003 getMulExpr(Op, RHS) != A->getOperand(i)) 2004 break; 2005 Operands.push_back(Op); 2006 } 2007 if (Operands.size() == A->getNumOperands()) 2008 return getAddExpr(Operands); 2009 } 2010 } 2011 2012 // Fold if both operands are constant. 2013 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2014 Constant *LHSCV = LHSC->getValue(); 2015 Constant *RHSCV = RHSC->getValue(); 2016 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2017 RHSCV))); 2018 } 2019 } 2020 } 2021 2022 FoldingSetNodeID ID; 2023 ID.AddInteger(scUDivExpr); 2024 ID.AddPointer(LHS); 2025 ID.AddPointer(RHS); 2026 void *IP = 0; 2027 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2028 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2029 LHS, RHS); 2030 UniqueSCEVs.InsertNode(S, IP); 2031 return S; 2032} 2033 2034 2035/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2036/// Simplify the expression as much as possible. 2037const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2038 const SCEV *Step, const Loop *L, 2039 bool HasNUW, bool HasNSW) { 2040 SmallVector<const SCEV *, 4> Operands; 2041 Operands.push_back(Start); 2042 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2043 if (StepChrec->getLoop() == L) { 2044 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2045 return getAddRecExpr(Operands, L); 2046 } 2047 2048 Operands.push_back(Step); 2049 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2050} 2051 2052/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2053/// Simplify the expression as much as possible. 2054const SCEV * 2055ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2056 const Loop *L, 2057 bool HasNUW, bool HasNSW) { 2058 if (Operands.size() == 1) return Operands[0]; 2059#ifndef NDEBUG 2060 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2061 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2062 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2063 "SCEVAddRecExpr operand types don't match!"); 2064#endif 2065 2066 if (Operands.back()->isZero()) { 2067 Operands.pop_back(); 2068 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2069 } 2070 2071 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2072 // use that information to infer NUW and NSW flags. However, computing a 2073 // BE count requires calling getAddRecExpr, so we may not yet have a 2074 // meaningful BE count at this point (and if we don't, we'd be stuck 2075 // with a SCEVCouldNotCompute as the cached BE count). 2076 2077 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2078 if (!HasNUW && HasNSW) { 2079 bool All = true; 2080 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2081 E = Operands.end(); I != E; ++I) 2082 if (!isKnownNonNegative(*I)) { 2083 All = false; 2084 break; 2085 } 2086 if (All) HasNUW = true; 2087 } 2088 2089 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2090 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2091 const Loop *NestedLoop = NestedAR->getLoop(); 2092 if (L->contains(NestedLoop) ? 2093 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2094 (!NestedLoop->contains(L) && 2095 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2096 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2097 NestedAR->op_end()); 2098 Operands[0] = NestedAR->getStart(); 2099 // AddRecs require their operands be loop-invariant with respect to their 2100 // loops. Don't perform this transformation if it would break this 2101 // requirement. 2102 bool AllInvariant = true; 2103 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2104 if (!Operands[i]->isLoopInvariant(L)) { 2105 AllInvariant = false; 2106 break; 2107 } 2108 if (AllInvariant) { 2109 NestedOperands[0] = getAddRecExpr(Operands, L); 2110 AllInvariant = true; 2111 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2112 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2113 AllInvariant = false; 2114 break; 2115 } 2116 if (AllInvariant) 2117 // Ok, both add recurrences are valid after the transformation. 2118 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2119 } 2120 // Reset Operands to its original state. 2121 Operands[0] = NestedAR; 2122 } 2123 } 2124 2125 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2126 // already have one, otherwise create a new one. 2127 FoldingSetNodeID ID; 2128 ID.AddInteger(scAddRecExpr); 2129 ID.AddInteger(Operands.size()); 2130 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2131 ID.AddPointer(Operands[i]); 2132 ID.AddPointer(L); 2133 void *IP = 0; 2134 SCEVAddRecExpr *S = 2135 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2136 if (!S) { 2137 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2138 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2139 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2140 O, Operands.size(), L); 2141 UniqueSCEVs.InsertNode(S, IP); 2142 } 2143 if (HasNUW) S->setHasNoUnsignedWrap(true); 2144 if (HasNSW) S->setHasNoSignedWrap(true); 2145 return S; 2146} 2147 2148const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2149 const SCEV *RHS) { 2150 SmallVector<const SCEV *, 2> Ops; 2151 Ops.push_back(LHS); 2152 Ops.push_back(RHS); 2153 return getSMaxExpr(Ops); 2154} 2155 2156const SCEV * 2157ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2158 assert(!Ops.empty() && "Cannot get empty smax!"); 2159 if (Ops.size() == 1) return Ops[0]; 2160#ifndef NDEBUG 2161 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2162 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2163 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2164 "SCEVSMaxExpr operand types don't match!"); 2165#endif 2166 2167 // Sort by complexity, this groups all similar expression types together. 2168 GroupByComplexity(Ops, LI); 2169 2170 // If there are any constants, fold them together. 2171 unsigned Idx = 0; 2172 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2173 ++Idx; 2174 assert(Idx < Ops.size()); 2175 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2176 // We found two constants, fold them together! 2177 ConstantInt *Fold = ConstantInt::get(getContext(), 2178 APIntOps::smax(LHSC->getValue()->getValue(), 2179 RHSC->getValue()->getValue())); 2180 Ops[0] = getConstant(Fold); 2181 Ops.erase(Ops.begin()+1); // Erase the folded element 2182 if (Ops.size() == 1) return Ops[0]; 2183 LHSC = cast<SCEVConstant>(Ops[0]); 2184 } 2185 2186 // If we are left with a constant minimum-int, strip it off. 2187 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2188 Ops.erase(Ops.begin()); 2189 --Idx; 2190 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2191 // If we have an smax with a constant maximum-int, it will always be 2192 // maximum-int. 2193 return Ops[0]; 2194 } 2195 2196 if (Ops.size() == 1) return Ops[0]; 2197 } 2198 2199 // Find the first SMax 2200 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2201 ++Idx; 2202 2203 // Check to see if one of the operands is an SMax. If so, expand its operands 2204 // onto our operand list, and recurse to simplify. 2205 if (Idx < Ops.size()) { 2206 bool DeletedSMax = false; 2207 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2208 Ops.erase(Ops.begin()+Idx); 2209 Ops.append(SMax->op_begin(), SMax->op_end()); 2210 DeletedSMax = true; 2211 } 2212 2213 if (DeletedSMax) 2214 return getSMaxExpr(Ops); 2215 } 2216 2217 // Okay, check to see if the same value occurs in the operand list twice. If 2218 // so, delete one. Since we sorted the list, these values are required to 2219 // be adjacent. 2220 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2221 // X smax Y smax Y --> X smax Y 2222 // X smax Y --> X, if X is always greater than Y 2223 if (Ops[i] == Ops[i+1] || 2224 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2225 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2226 --i; --e; 2227 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2228 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2229 --i; --e; 2230 } 2231 2232 if (Ops.size() == 1) return Ops[0]; 2233 2234 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2235 2236 // Okay, it looks like we really DO need an smax expr. Check to see if we 2237 // already have one, otherwise create a new one. 2238 FoldingSetNodeID ID; 2239 ID.AddInteger(scSMaxExpr); 2240 ID.AddInteger(Ops.size()); 2241 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2242 ID.AddPointer(Ops[i]); 2243 void *IP = 0; 2244 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2245 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2246 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2247 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2248 O, Ops.size()); 2249 UniqueSCEVs.InsertNode(S, IP); 2250 return S; 2251} 2252 2253const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2254 const SCEV *RHS) { 2255 SmallVector<const SCEV *, 2> Ops; 2256 Ops.push_back(LHS); 2257 Ops.push_back(RHS); 2258 return getUMaxExpr(Ops); 2259} 2260 2261const SCEV * 2262ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2263 assert(!Ops.empty() && "Cannot get empty umax!"); 2264 if (Ops.size() == 1) return Ops[0]; 2265#ifndef NDEBUG 2266 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2267 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2268 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2269 "SCEVUMaxExpr operand types don't match!"); 2270#endif 2271 2272 // Sort by complexity, this groups all similar expression types together. 2273 GroupByComplexity(Ops, LI); 2274 2275 // If there are any constants, fold them together. 2276 unsigned Idx = 0; 2277 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2278 ++Idx; 2279 assert(Idx < Ops.size()); 2280 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2281 // We found two constants, fold them together! 2282 ConstantInt *Fold = ConstantInt::get(getContext(), 2283 APIntOps::umax(LHSC->getValue()->getValue(), 2284 RHSC->getValue()->getValue())); 2285 Ops[0] = getConstant(Fold); 2286 Ops.erase(Ops.begin()+1); // Erase the folded element 2287 if (Ops.size() == 1) return Ops[0]; 2288 LHSC = cast<SCEVConstant>(Ops[0]); 2289 } 2290 2291 // If we are left with a constant minimum-int, strip it off. 2292 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2293 Ops.erase(Ops.begin()); 2294 --Idx; 2295 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2296 // If we have an umax with a constant maximum-int, it will always be 2297 // maximum-int. 2298 return Ops[0]; 2299 } 2300 2301 if (Ops.size() == 1) return Ops[0]; 2302 } 2303 2304 // Find the first UMax 2305 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2306 ++Idx; 2307 2308 // Check to see if one of the operands is a UMax. If so, expand its operands 2309 // onto our operand list, and recurse to simplify. 2310 if (Idx < Ops.size()) { 2311 bool DeletedUMax = false; 2312 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2313 Ops.erase(Ops.begin()+Idx); 2314 Ops.append(UMax->op_begin(), UMax->op_end()); 2315 DeletedUMax = true; 2316 } 2317 2318 if (DeletedUMax) 2319 return getUMaxExpr(Ops); 2320 } 2321 2322 // Okay, check to see if the same value occurs in the operand list twice. If 2323 // so, delete one. Since we sorted the list, these values are required to 2324 // be adjacent. 2325 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2326 // X umax Y umax Y --> X umax Y 2327 // X umax Y --> X, if X is always greater than Y 2328 if (Ops[i] == Ops[i+1] || 2329 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2330 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2331 --i; --e; 2332 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2333 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2334 --i; --e; 2335 } 2336 2337 if (Ops.size() == 1) return Ops[0]; 2338 2339 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2340 2341 // Okay, it looks like we really DO need a umax expr. Check to see if we 2342 // already have one, otherwise create a new one. 2343 FoldingSetNodeID ID; 2344 ID.AddInteger(scUMaxExpr); 2345 ID.AddInteger(Ops.size()); 2346 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2347 ID.AddPointer(Ops[i]); 2348 void *IP = 0; 2349 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2350 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2351 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2352 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2353 O, Ops.size()); 2354 UniqueSCEVs.InsertNode(S, IP); 2355 return S; 2356} 2357 2358const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2359 const SCEV *RHS) { 2360 // ~smax(~x, ~y) == smin(x, y). 2361 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2362} 2363 2364const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2365 const SCEV *RHS) { 2366 // ~umax(~x, ~y) == umin(x, y) 2367 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2368} 2369 2370const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2371 // If we have TargetData, we can bypass creating a target-independent 2372 // constant expression and then folding it back into a ConstantInt. 2373 // This is just a compile-time optimization. 2374 if (TD) 2375 return getConstant(TD->getIntPtrType(getContext()), 2376 TD->getTypeAllocSize(AllocTy)); 2377 2378 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2379 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2380 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2381 C = Folded; 2382 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2383 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2384} 2385 2386const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2387 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2388 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2389 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2390 C = Folded; 2391 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2392 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2393} 2394 2395const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2396 unsigned FieldNo) { 2397 // If we have TargetData, we can bypass creating a target-independent 2398 // constant expression and then folding it back into a ConstantInt. 2399 // This is just a compile-time optimization. 2400 if (TD) 2401 return getConstant(TD->getIntPtrType(getContext()), 2402 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2403 2404 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2405 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2406 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2407 C = Folded; 2408 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2409 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2410} 2411 2412const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2413 Constant *FieldNo) { 2414 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2415 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2416 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2417 C = Folded; 2418 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2419 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2420} 2421 2422const SCEV *ScalarEvolution::getUnknown(Value *V) { 2423 // Don't attempt to do anything other than create a SCEVUnknown object 2424 // here. createSCEV only calls getUnknown after checking for all other 2425 // interesting possibilities, and any other code that calls getUnknown 2426 // is doing so in order to hide a value from SCEV canonicalization. 2427 2428 FoldingSetNodeID ID; 2429 ID.AddInteger(scUnknown); 2430 ID.AddPointer(V); 2431 void *IP = 0; 2432 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2433 assert(cast<SCEVUnknown>(S)->getValue() == V && 2434 "Stale SCEVUnknown in uniquing map!"); 2435 return S; 2436 } 2437 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2438 FirstUnknown); 2439 FirstUnknown = cast<SCEVUnknown>(S); 2440 UniqueSCEVs.InsertNode(S, IP); 2441 return S; 2442} 2443 2444//===----------------------------------------------------------------------===// 2445// Basic SCEV Analysis and PHI Idiom Recognition Code 2446// 2447 2448/// isSCEVable - Test if values of the given type are analyzable within 2449/// the SCEV framework. This primarily includes integer types, and it 2450/// can optionally include pointer types if the ScalarEvolution class 2451/// has access to target-specific information. 2452bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2453 // Integers and pointers are always SCEVable. 2454 return Ty->isIntegerTy() || Ty->isPointerTy(); 2455} 2456 2457/// getTypeSizeInBits - Return the size in bits of the specified type, 2458/// for which isSCEVable must return true. 2459uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2460 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2461 2462 // If we have a TargetData, use it! 2463 if (TD) 2464 return TD->getTypeSizeInBits(Ty); 2465 2466 // Integer types have fixed sizes. 2467 if (Ty->isIntegerTy()) 2468 return Ty->getPrimitiveSizeInBits(); 2469 2470 // The only other support type is pointer. Without TargetData, conservatively 2471 // assume pointers are 64-bit. 2472 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2473 return 64; 2474} 2475 2476/// getEffectiveSCEVType - Return a type with the same bitwidth as 2477/// the given type and which represents how SCEV will treat the given 2478/// type, for which isSCEVable must return true. For pointer types, 2479/// this is the pointer-sized integer type. 2480const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2481 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2482 2483 if (Ty->isIntegerTy()) 2484 return Ty; 2485 2486 // The only other support type is pointer. 2487 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2488 if (TD) return TD->getIntPtrType(getContext()); 2489 2490 // Without TargetData, conservatively assume pointers are 64-bit. 2491 return Type::getInt64Ty(getContext()); 2492} 2493 2494const SCEV *ScalarEvolution::getCouldNotCompute() { 2495 return &CouldNotCompute; 2496} 2497 2498/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2499/// expression and create a new one. 2500const SCEV *ScalarEvolution::getSCEV(Value *V) { 2501 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2502 2503 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2504 if (I != ValueExprMap.end()) return I->second; 2505 const SCEV *S = createSCEV(V); 2506 2507 // The process of creating a SCEV for V may have caused other SCEVs 2508 // to have been created, so it's necessary to insert the new entry 2509 // from scratch, rather than trying to remember the insert position 2510 // above. 2511 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2512 return S; 2513} 2514 2515/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2516/// 2517const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2518 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2519 return getConstant( 2520 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2521 2522 const Type *Ty = V->getType(); 2523 Ty = getEffectiveSCEVType(Ty); 2524 return getMulExpr(V, 2525 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2526} 2527 2528/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2529const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2530 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2531 return getConstant( 2532 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2533 2534 const Type *Ty = V->getType(); 2535 Ty = getEffectiveSCEVType(Ty); 2536 const SCEV *AllOnes = 2537 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2538 return getMinusSCEV(AllOnes, V); 2539} 2540 2541/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2542/// 2543const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2544 const SCEV *RHS) { 2545 // Fast path: X - X --> 0. 2546 if (LHS == RHS) 2547 return getConstant(LHS->getType(), 0); 2548 2549 // X - Y --> X + -Y 2550 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2551} 2552 2553/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2554/// input value to the specified type. If the type must be extended, it is zero 2555/// extended. 2556const SCEV * 2557ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2558 const Type *Ty) { 2559 const Type *SrcTy = V->getType(); 2560 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2561 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2562 "Cannot truncate or zero extend with non-integer arguments!"); 2563 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2564 return V; // No conversion 2565 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2566 return getTruncateExpr(V, Ty); 2567 return getZeroExtendExpr(V, Ty); 2568} 2569 2570/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2571/// input value to the specified type. If the type must be extended, it is sign 2572/// extended. 2573const SCEV * 2574ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2575 const Type *Ty) { 2576 const Type *SrcTy = V->getType(); 2577 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2578 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2579 "Cannot truncate or zero extend with non-integer arguments!"); 2580 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2581 return V; // No conversion 2582 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2583 return getTruncateExpr(V, Ty); 2584 return getSignExtendExpr(V, Ty); 2585} 2586 2587/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2588/// input value to the specified type. If the type must be extended, it is zero 2589/// extended. The conversion must not be narrowing. 2590const SCEV * 2591ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2592 const Type *SrcTy = V->getType(); 2593 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2594 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2595 "Cannot noop or zero extend with non-integer arguments!"); 2596 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2597 "getNoopOrZeroExtend cannot truncate!"); 2598 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2599 return V; // No conversion 2600 return getZeroExtendExpr(V, Ty); 2601} 2602 2603/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2604/// input value to the specified type. If the type must be extended, it is sign 2605/// extended. The conversion must not be narrowing. 2606const SCEV * 2607ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2608 const Type *SrcTy = V->getType(); 2609 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2610 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2611 "Cannot noop or sign extend with non-integer arguments!"); 2612 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2613 "getNoopOrSignExtend cannot truncate!"); 2614 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2615 return V; // No conversion 2616 return getSignExtendExpr(V, Ty); 2617} 2618 2619/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2620/// the input value to the specified type. If the type must be extended, 2621/// it is extended with unspecified bits. The conversion must not be 2622/// narrowing. 2623const SCEV * 2624ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2625 const Type *SrcTy = V->getType(); 2626 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2627 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2628 "Cannot noop or any extend with non-integer arguments!"); 2629 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2630 "getNoopOrAnyExtend cannot truncate!"); 2631 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2632 return V; // No conversion 2633 return getAnyExtendExpr(V, Ty); 2634} 2635 2636/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2637/// input value to the specified type. The conversion must not be widening. 2638const SCEV * 2639ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2640 const Type *SrcTy = V->getType(); 2641 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2642 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2643 "Cannot truncate or noop with non-integer arguments!"); 2644 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2645 "getTruncateOrNoop cannot extend!"); 2646 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2647 return V; // No conversion 2648 return getTruncateExpr(V, Ty); 2649} 2650 2651/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2652/// the types using zero-extension, and then perform a umax operation 2653/// with them. 2654const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2655 const SCEV *RHS) { 2656 const SCEV *PromotedLHS = LHS; 2657 const SCEV *PromotedRHS = RHS; 2658 2659 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2660 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2661 else 2662 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2663 2664 return getUMaxExpr(PromotedLHS, PromotedRHS); 2665} 2666 2667/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2668/// the types using zero-extension, and then perform a umin operation 2669/// with them. 2670const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2671 const SCEV *RHS) { 2672 const SCEV *PromotedLHS = LHS; 2673 const SCEV *PromotedRHS = RHS; 2674 2675 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2676 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2677 else 2678 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2679 2680 return getUMinExpr(PromotedLHS, PromotedRHS); 2681} 2682 2683/// PushDefUseChildren - Push users of the given Instruction 2684/// onto the given Worklist. 2685static void 2686PushDefUseChildren(Instruction *I, 2687 SmallVectorImpl<Instruction *> &Worklist) { 2688 // Push the def-use children onto the Worklist stack. 2689 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2690 UI != UE; ++UI) 2691 Worklist.push_back(cast<Instruction>(*UI)); 2692} 2693 2694/// ForgetSymbolicValue - This looks up computed SCEV values for all 2695/// instructions that depend on the given instruction and removes them from 2696/// the ValueExprMapType map if they reference SymName. This is used during PHI 2697/// resolution. 2698void 2699ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2700 SmallVector<Instruction *, 16> Worklist; 2701 PushDefUseChildren(PN, Worklist); 2702 2703 SmallPtrSet<Instruction *, 8> Visited; 2704 Visited.insert(PN); 2705 while (!Worklist.empty()) { 2706 Instruction *I = Worklist.pop_back_val(); 2707 if (!Visited.insert(I)) continue; 2708 2709 ValueExprMapType::iterator It = 2710 ValueExprMap.find(static_cast<Value *>(I)); 2711 if (It != ValueExprMap.end()) { 2712 // Short-circuit the def-use traversal if the symbolic name 2713 // ceases to appear in expressions. 2714 if (It->second != SymName && !It->second->hasOperand(SymName)) 2715 continue; 2716 2717 // SCEVUnknown for a PHI either means that it has an unrecognized 2718 // structure, it's a PHI that's in the progress of being computed 2719 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2720 // additional loop trip count information isn't going to change anything. 2721 // In the second case, createNodeForPHI will perform the necessary 2722 // updates on its own when it gets to that point. In the third, we do 2723 // want to forget the SCEVUnknown. 2724 if (!isa<PHINode>(I) || 2725 !isa<SCEVUnknown>(It->second) || 2726 (I != PN && It->second == SymName)) { 2727 ValuesAtScopes.erase(It->second); 2728 ValueExprMap.erase(It); 2729 } 2730 } 2731 2732 PushDefUseChildren(I, Worklist); 2733 } 2734} 2735 2736/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2737/// a loop header, making it a potential recurrence, or it doesn't. 2738/// 2739const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2740 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2741 if (L->getHeader() == PN->getParent()) { 2742 // The loop may have multiple entrances or multiple exits; we can analyze 2743 // this phi as an addrec if it has a unique entry value and a unique 2744 // backedge value. 2745 Value *BEValueV = 0, *StartValueV = 0; 2746 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2747 Value *V = PN->getIncomingValue(i); 2748 if (L->contains(PN->getIncomingBlock(i))) { 2749 if (!BEValueV) { 2750 BEValueV = V; 2751 } else if (BEValueV != V) { 2752 BEValueV = 0; 2753 break; 2754 } 2755 } else if (!StartValueV) { 2756 StartValueV = V; 2757 } else if (StartValueV != V) { 2758 StartValueV = 0; 2759 break; 2760 } 2761 } 2762 if (BEValueV && StartValueV) { 2763 // While we are analyzing this PHI node, handle its value symbolically. 2764 const SCEV *SymbolicName = getUnknown(PN); 2765 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2766 "PHI node already processed?"); 2767 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2768 2769 // Using this symbolic name for the PHI, analyze the value coming around 2770 // the back-edge. 2771 const SCEV *BEValue = getSCEV(BEValueV); 2772 2773 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2774 // has a special value for the first iteration of the loop. 2775 2776 // If the value coming around the backedge is an add with the symbolic 2777 // value we just inserted, then we found a simple induction variable! 2778 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2779 // If there is a single occurrence of the symbolic value, replace it 2780 // with a recurrence. 2781 unsigned FoundIndex = Add->getNumOperands(); 2782 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2783 if (Add->getOperand(i) == SymbolicName) 2784 if (FoundIndex == e) { 2785 FoundIndex = i; 2786 break; 2787 } 2788 2789 if (FoundIndex != Add->getNumOperands()) { 2790 // Create an add with everything but the specified operand. 2791 SmallVector<const SCEV *, 8> Ops; 2792 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2793 if (i != FoundIndex) 2794 Ops.push_back(Add->getOperand(i)); 2795 const SCEV *Accum = getAddExpr(Ops); 2796 2797 // This is not a valid addrec if the step amount is varying each 2798 // loop iteration, but is not itself an addrec in this loop. 2799 if (Accum->isLoopInvariant(L) || 2800 (isa<SCEVAddRecExpr>(Accum) && 2801 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2802 bool HasNUW = false; 2803 bool HasNSW = false; 2804 2805 // If the increment doesn't overflow, then neither the addrec nor 2806 // the post-increment will overflow. 2807 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2808 if (OBO->hasNoUnsignedWrap()) 2809 HasNUW = true; 2810 if (OBO->hasNoSignedWrap()) 2811 HasNSW = true; 2812 } 2813 2814 const SCEV *StartVal = getSCEV(StartValueV); 2815 const SCEV *PHISCEV = 2816 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2817 2818 // Since the no-wrap flags are on the increment, they apply to the 2819 // post-incremented value as well. 2820 if (Accum->isLoopInvariant(L)) 2821 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2822 Accum, L, HasNUW, HasNSW); 2823 2824 // Okay, for the entire analysis of this edge we assumed the PHI 2825 // to be symbolic. We now need to go back and purge all of the 2826 // entries for the scalars that use the symbolic expression. 2827 ForgetSymbolicName(PN, SymbolicName); 2828 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2829 return PHISCEV; 2830 } 2831 } 2832 } else if (const SCEVAddRecExpr *AddRec = 2833 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2834 // Otherwise, this could be a loop like this: 2835 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2836 // In this case, j = {1,+,1} and BEValue is j. 2837 // Because the other in-value of i (0) fits the evolution of BEValue 2838 // i really is an addrec evolution. 2839 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2840 const SCEV *StartVal = getSCEV(StartValueV); 2841 2842 // If StartVal = j.start - j.stride, we can use StartVal as the 2843 // initial step of the addrec evolution. 2844 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2845 AddRec->getOperand(1))) { 2846 const SCEV *PHISCEV = 2847 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2848 2849 // Okay, for the entire analysis of this edge we assumed the PHI 2850 // to be symbolic. We now need to go back and purge all of the 2851 // entries for the scalars that use the symbolic expression. 2852 ForgetSymbolicName(PN, SymbolicName); 2853 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2854 return PHISCEV; 2855 } 2856 } 2857 } 2858 } 2859 } 2860 2861 // If the PHI has a single incoming value, follow that value, unless the 2862 // PHI's incoming blocks are in a different loop, in which case doing so 2863 // risks breaking LCSSA form. Instcombine would normally zap these, but 2864 // it doesn't have DominatorTree information, so it may miss cases. 2865 if (Value *V = PN->hasConstantValue(DT)) { 2866 bool AllSameLoop = true; 2867 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2868 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2869 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2870 AllSameLoop = false; 2871 break; 2872 } 2873 if (AllSameLoop) 2874 return getSCEV(V); 2875 } 2876 2877 // If it's not a loop phi, we can't handle it yet. 2878 return getUnknown(PN); 2879} 2880 2881/// createNodeForGEP - Expand GEP instructions into add and multiply 2882/// operations. This allows them to be analyzed by regular SCEV code. 2883/// 2884const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2885 2886 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2887 // Add expression, because the Instruction may be guarded by control flow 2888 // and the no-overflow bits may not be valid for the expression in any 2889 // context. 2890 2891 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2892 Value *Base = GEP->getOperand(0); 2893 // Don't attempt to analyze GEPs over unsized objects. 2894 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2895 return getUnknown(GEP); 2896 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2897 gep_type_iterator GTI = gep_type_begin(GEP); 2898 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2899 E = GEP->op_end(); 2900 I != E; ++I) { 2901 Value *Index = *I; 2902 // Compute the (potentially symbolic) offset in bytes for this index. 2903 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2904 // For a struct, add the member offset. 2905 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2906 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2907 2908 // Add the field offset to the running total offset. 2909 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2910 } else { 2911 // For an array, add the element offset, explicitly scaled. 2912 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2913 const SCEV *IndexS = getSCEV(Index); 2914 // Getelementptr indices are signed. 2915 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2916 2917 // Multiply the index by the element size to compute the element offset. 2918 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2919 2920 // Add the element offset to the running total offset. 2921 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2922 } 2923 } 2924 2925 // Get the SCEV for the GEP base. 2926 const SCEV *BaseS = getSCEV(Base); 2927 2928 // Add the total offset from all the GEP indices to the base. 2929 return getAddExpr(BaseS, TotalOffset); 2930} 2931 2932/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2933/// guaranteed to end in (at every loop iteration). It is, at the same time, 2934/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2935/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2936uint32_t 2937ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2938 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2939 return C->getValue()->getValue().countTrailingZeros(); 2940 2941 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2942 return std::min(GetMinTrailingZeros(T->getOperand()), 2943 (uint32_t)getTypeSizeInBits(T->getType())); 2944 2945 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2946 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2947 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2948 getTypeSizeInBits(E->getType()) : OpRes; 2949 } 2950 2951 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2952 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2953 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2954 getTypeSizeInBits(E->getType()) : OpRes; 2955 } 2956 2957 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2958 // The result is the min of all operands results. 2959 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2960 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2961 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2962 return MinOpRes; 2963 } 2964 2965 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2966 // The result is the sum of all operands results. 2967 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2968 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2969 for (unsigned i = 1, e = M->getNumOperands(); 2970 SumOpRes != BitWidth && i != e; ++i) 2971 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2972 BitWidth); 2973 return SumOpRes; 2974 } 2975 2976 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2977 // The result is the min of all operands results. 2978 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2979 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2980 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2981 return MinOpRes; 2982 } 2983 2984 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2985 // The result is the min of all operands results. 2986 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2987 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2988 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2989 return MinOpRes; 2990 } 2991 2992 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2993 // The result is the min of all operands results. 2994 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2995 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2996 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2997 return MinOpRes; 2998 } 2999 3000 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3001 // For a SCEVUnknown, ask ValueTracking. 3002 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3003 APInt Mask = APInt::getAllOnesValue(BitWidth); 3004 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3005 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3006 return Zeros.countTrailingOnes(); 3007 } 3008 3009 // SCEVUDivExpr 3010 return 0; 3011} 3012 3013/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3014/// 3015ConstantRange 3016ScalarEvolution::getUnsignedRange(const SCEV *S) { 3017 3018 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3019 return ConstantRange(C->getValue()->getValue()); 3020 3021 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3022 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3023 3024 // If the value has known zeros, the maximum unsigned value will have those 3025 // known zeros as well. 3026 uint32_t TZ = GetMinTrailingZeros(S); 3027 if (TZ != 0) 3028 ConservativeResult = 3029 ConstantRange(APInt::getMinValue(BitWidth), 3030 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3031 3032 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3033 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3034 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3035 X = X.add(getUnsignedRange(Add->getOperand(i))); 3036 return ConservativeResult.intersectWith(X); 3037 } 3038 3039 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3040 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3041 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3042 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3043 return ConservativeResult.intersectWith(X); 3044 } 3045 3046 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3047 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3048 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3049 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3050 return ConservativeResult.intersectWith(X); 3051 } 3052 3053 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3054 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3055 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3056 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3057 return ConservativeResult.intersectWith(X); 3058 } 3059 3060 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3061 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3062 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3063 return ConservativeResult.intersectWith(X.udiv(Y)); 3064 } 3065 3066 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3067 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3068 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3069 } 3070 3071 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3072 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3073 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3074 } 3075 3076 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3077 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3078 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3079 } 3080 3081 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3082 // If there's no unsigned wrap, the value will never be less than its 3083 // initial value. 3084 if (AddRec->hasNoUnsignedWrap()) 3085 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3086 if (!C->getValue()->isZero()) 3087 ConservativeResult = 3088 ConservativeResult.intersectWith( 3089 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3090 3091 // TODO: non-affine addrec 3092 if (AddRec->isAffine()) { 3093 const Type *Ty = AddRec->getType(); 3094 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3095 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3096 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3097 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3098 3099 const SCEV *Start = AddRec->getStart(); 3100 const SCEV *Step = AddRec->getStepRecurrence(*this); 3101 3102 ConstantRange StartRange = getUnsignedRange(Start); 3103 ConstantRange StepRange = getSignedRange(Step); 3104 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3105 ConstantRange EndRange = 3106 StartRange.add(MaxBECountRange.multiply(StepRange)); 3107 3108 // Check for overflow. This must be done with ConstantRange arithmetic 3109 // because we could be called from within the ScalarEvolution overflow 3110 // checking code. 3111 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3112 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3113 ConstantRange ExtMaxBECountRange = 3114 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3115 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3116 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3117 ExtEndRange) 3118 return ConservativeResult; 3119 3120 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3121 EndRange.getUnsignedMin()); 3122 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3123 EndRange.getUnsignedMax()); 3124 if (Min.isMinValue() && Max.isMaxValue()) 3125 return ConservativeResult; 3126 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3127 } 3128 } 3129 3130 return ConservativeResult; 3131 } 3132 3133 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3134 // For a SCEVUnknown, ask ValueTracking. 3135 APInt Mask = APInt::getAllOnesValue(BitWidth); 3136 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3137 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3138 if (Ones == ~Zeros + 1) 3139 return ConservativeResult; 3140 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3141 } 3142 3143 return ConservativeResult; 3144} 3145 3146/// getSignedRange - Determine the signed range for a particular SCEV. 3147/// 3148ConstantRange 3149ScalarEvolution::getSignedRange(const SCEV *S) { 3150 3151 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3152 return ConstantRange(C->getValue()->getValue()); 3153 3154 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3155 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3156 3157 // If the value has known zeros, the maximum signed value will have those 3158 // known zeros as well. 3159 uint32_t TZ = GetMinTrailingZeros(S); 3160 if (TZ != 0) 3161 ConservativeResult = 3162 ConstantRange(APInt::getSignedMinValue(BitWidth), 3163 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3164 3165 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3166 ConstantRange X = getSignedRange(Add->getOperand(0)); 3167 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3168 X = X.add(getSignedRange(Add->getOperand(i))); 3169 return ConservativeResult.intersectWith(X); 3170 } 3171 3172 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3173 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3174 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3175 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3176 return ConservativeResult.intersectWith(X); 3177 } 3178 3179 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3180 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3181 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3182 X = X.smax(getSignedRange(SMax->getOperand(i))); 3183 return ConservativeResult.intersectWith(X); 3184 } 3185 3186 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3187 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3188 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3189 X = X.umax(getSignedRange(UMax->getOperand(i))); 3190 return ConservativeResult.intersectWith(X); 3191 } 3192 3193 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3194 ConstantRange X = getSignedRange(UDiv->getLHS()); 3195 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3196 return ConservativeResult.intersectWith(X.udiv(Y)); 3197 } 3198 3199 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3200 ConstantRange X = getSignedRange(ZExt->getOperand()); 3201 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3202 } 3203 3204 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3205 ConstantRange X = getSignedRange(SExt->getOperand()); 3206 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3207 } 3208 3209 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3210 ConstantRange X = getSignedRange(Trunc->getOperand()); 3211 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3212 } 3213 3214 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3215 // If there's no signed wrap, and all the operands have the same sign or 3216 // zero, the value won't ever change sign. 3217 if (AddRec->hasNoSignedWrap()) { 3218 bool AllNonNeg = true; 3219 bool AllNonPos = true; 3220 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3221 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3222 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3223 } 3224 if (AllNonNeg) 3225 ConservativeResult = ConservativeResult.intersectWith( 3226 ConstantRange(APInt(BitWidth, 0), 3227 APInt::getSignedMinValue(BitWidth))); 3228 else if (AllNonPos) 3229 ConservativeResult = ConservativeResult.intersectWith( 3230 ConstantRange(APInt::getSignedMinValue(BitWidth), 3231 APInt(BitWidth, 1))); 3232 } 3233 3234 // TODO: non-affine addrec 3235 if (AddRec->isAffine()) { 3236 const Type *Ty = AddRec->getType(); 3237 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3238 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3239 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3240 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3241 3242 const SCEV *Start = AddRec->getStart(); 3243 const SCEV *Step = AddRec->getStepRecurrence(*this); 3244 3245 ConstantRange StartRange = getSignedRange(Start); 3246 ConstantRange StepRange = getSignedRange(Step); 3247 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3248 ConstantRange EndRange = 3249 StartRange.add(MaxBECountRange.multiply(StepRange)); 3250 3251 // Check for overflow. This must be done with ConstantRange arithmetic 3252 // because we could be called from within the ScalarEvolution overflow 3253 // checking code. 3254 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3255 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3256 ConstantRange ExtMaxBECountRange = 3257 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3258 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3259 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3260 ExtEndRange) 3261 return ConservativeResult; 3262 3263 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3264 EndRange.getSignedMin()); 3265 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3266 EndRange.getSignedMax()); 3267 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3268 return ConservativeResult; 3269 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3270 } 3271 } 3272 3273 return ConservativeResult; 3274 } 3275 3276 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3277 // For a SCEVUnknown, ask ValueTracking. 3278 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3279 return ConservativeResult; 3280 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3281 if (NS == 1) 3282 return ConservativeResult; 3283 return ConservativeResult.intersectWith( 3284 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3285 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3286 } 3287 3288 return ConservativeResult; 3289} 3290 3291/// createSCEV - We know that there is no SCEV for the specified value. 3292/// Analyze the expression. 3293/// 3294const SCEV *ScalarEvolution::createSCEV(Value *V) { 3295 if (!isSCEVable(V->getType())) 3296 return getUnknown(V); 3297 3298 unsigned Opcode = Instruction::UserOp1; 3299 if (Instruction *I = dyn_cast<Instruction>(V)) { 3300 Opcode = I->getOpcode(); 3301 3302 // Don't attempt to analyze instructions in blocks that aren't 3303 // reachable. Such instructions don't matter, and they aren't required 3304 // to obey basic rules for definitions dominating uses which this 3305 // analysis depends on. 3306 if (!DT->isReachableFromEntry(I->getParent())) 3307 return getUnknown(V); 3308 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3309 Opcode = CE->getOpcode(); 3310 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3311 return getConstant(CI); 3312 else if (isa<ConstantPointerNull>(V)) 3313 return getConstant(V->getType(), 0); 3314 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3315 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3316 else 3317 return getUnknown(V); 3318 3319 Operator *U = cast<Operator>(V); 3320 switch (Opcode) { 3321 case Instruction::Add: { 3322 // The simple thing to do would be to just call getSCEV on both operands 3323 // and call getAddExpr with the result. However if we're looking at a 3324 // bunch of things all added together, this can be quite inefficient, 3325 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3326 // Instead, gather up all the operands and make a single getAddExpr call. 3327 // LLVM IR canonical form means we need only traverse the left operands. 3328 SmallVector<const SCEV *, 4> AddOps; 3329 AddOps.push_back(getSCEV(U->getOperand(1))); 3330 for (Value *Op = U->getOperand(0); 3331 Op->getValueID() == Instruction::Add + Value::InstructionVal; 3332 Op = U->getOperand(0)) { 3333 U = cast<Operator>(Op); 3334 AddOps.push_back(getSCEV(U->getOperand(1))); 3335 } 3336 AddOps.push_back(getSCEV(U->getOperand(0))); 3337 return getAddExpr(AddOps); 3338 } 3339 case Instruction::Mul: { 3340 // See the Add code above. 3341 SmallVector<const SCEV *, 4> MulOps; 3342 MulOps.push_back(getSCEV(U->getOperand(1))); 3343 for (Value *Op = U->getOperand(0); 3344 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3345 Op = U->getOperand(0)) { 3346 U = cast<Operator>(Op); 3347 MulOps.push_back(getSCEV(U->getOperand(1))); 3348 } 3349 MulOps.push_back(getSCEV(U->getOperand(0))); 3350 return getMulExpr(MulOps); 3351 } 3352 case Instruction::UDiv: 3353 return getUDivExpr(getSCEV(U->getOperand(0)), 3354 getSCEV(U->getOperand(1))); 3355 case Instruction::Sub: 3356 return getMinusSCEV(getSCEV(U->getOperand(0)), 3357 getSCEV(U->getOperand(1))); 3358 case Instruction::And: 3359 // For an expression like x&255 that merely masks off the high bits, 3360 // use zext(trunc(x)) as the SCEV expression. 3361 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3362 if (CI->isNullValue()) 3363 return getSCEV(U->getOperand(1)); 3364 if (CI->isAllOnesValue()) 3365 return getSCEV(U->getOperand(0)); 3366 const APInt &A = CI->getValue(); 3367 3368 // Instcombine's ShrinkDemandedConstant may strip bits out of 3369 // constants, obscuring what would otherwise be a low-bits mask. 3370 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3371 // knew about to reconstruct a low-bits mask value. 3372 unsigned LZ = A.countLeadingZeros(); 3373 unsigned BitWidth = A.getBitWidth(); 3374 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3375 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3376 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3377 3378 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3379 3380 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3381 return 3382 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3383 IntegerType::get(getContext(), BitWidth - LZ)), 3384 U->getType()); 3385 } 3386 break; 3387 3388 case Instruction::Or: 3389 // If the RHS of the Or is a constant, we may have something like: 3390 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3391 // optimizations will transparently handle this case. 3392 // 3393 // In order for this transformation to be safe, the LHS must be of the 3394 // form X*(2^n) and the Or constant must be less than 2^n. 3395 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3396 const SCEV *LHS = getSCEV(U->getOperand(0)); 3397 const APInt &CIVal = CI->getValue(); 3398 if (GetMinTrailingZeros(LHS) >= 3399 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3400 // Build a plain add SCEV. 3401 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3402 // If the LHS of the add was an addrec and it has no-wrap flags, 3403 // transfer the no-wrap flags, since an or won't introduce a wrap. 3404 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3405 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3406 if (OldAR->hasNoUnsignedWrap()) 3407 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3408 if (OldAR->hasNoSignedWrap()) 3409 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3410 } 3411 return S; 3412 } 3413 } 3414 break; 3415 case Instruction::Xor: 3416 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3417 // If the RHS of the xor is a signbit, then this is just an add. 3418 // Instcombine turns add of signbit into xor as a strength reduction step. 3419 if (CI->getValue().isSignBit()) 3420 return getAddExpr(getSCEV(U->getOperand(0)), 3421 getSCEV(U->getOperand(1))); 3422 3423 // If the RHS of xor is -1, then this is a not operation. 3424 if (CI->isAllOnesValue()) 3425 return getNotSCEV(getSCEV(U->getOperand(0))); 3426 3427 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3428 // This is a variant of the check for xor with -1, and it handles 3429 // the case where instcombine has trimmed non-demanded bits out 3430 // of an xor with -1. 3431 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3432 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3433 if (BO->getOpcode() == Instruction::And && 3434 LCI->getValue() == CI->getValue()) 3435 if (const SCEVZeroExtendExpr *Z = 3436 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3437 const Type *UTy = U->getType(); 3438 const SCEV *Z0 = Z->getOperand(); 3439 const Type *Z0Ty = Z0->getType(); 3440 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3441 3442 // If C is a low-bits mask, the zero extend is serving to 3443 // mask off the high bits. Complement the operand and 3444 // re-apply the zext. 3445 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3446 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3447 3448 // If C is a single bit, it may be in the sign-bit position 3449 // before the zero-extend. In this case, represent the xor 3450 // using an add, which is equivalent, and re-apply the zext. 3451 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3452 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3453 Trunc.isSignBit()) 3454 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3455 UTy); 3456 } 3457 } 3458 break; 3459 3460 case Instruction::Shl: 3461 // Turn shift left of a constant amount into a multiply. 3462 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3463 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3464 3465 // If the shift count is not less than the bitwidth, the result of 3466 // the shift is undefined. Don't try to analyze it, because the 3467 // resolution chosen here may differ from the resolution chosen in 3468 // other parts of the compiler. 3469 if (SA->getValue().uge(BitWidth)) 3470 break; 3471 3472 Constant *X = ConstantInt::get(getContext(), 3473 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3474 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3475 } 3476 break; 3477 3478 case Instruction::LShr: 3479 // Turn logical shift right of a constant into a unsigned divide. 3480 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3481 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3482 3483 // If the shift count is not less than the bitwidth, the result of 3484 // the shift is undefined. Don't try to analyze it, because the 3485 // resolution chosen here may differ from the resolution chosen in 3486 // other parts of the compiler. 3487 if (SA->getValue().uge(BitWidth)) 3488 break; 3489 3490 Constant *X = ConstantInt::get(getContext(), 3491 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3492 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3493 } 3494 break; 3495 3496 case Instruction::AShr: 3497 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3498 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3499 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3500 if (L->getOpcode() == Instruction::Shl && 3501 L->getOperand(1) == U->getOperand(1)) { 3502 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3503 3504 // If the shift count is not less than the bitwidth, the result of 3505 // the shift is undefined. Don't try to analyze it, because the 3506 // resolution chosen here may differ from the resolution chosen in 3507 // other parts of the compiler. 3508 if (CI->getValue().uge(BitWidth)) 3509 break; 3510 3511 uint64_t Amt = BitWidth - CI->getZExtValue(); 3512 if (Amt == BitWidth) 3513 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3514 return 3515 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3516 IntegerType::get(getContext(), 3517 Amt)), 3518 U->getType()); 3519 } 3520 break; 3521 3522 case Instruction::Trunc: 3523 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3524 3525 case Instruction::ZExt: 3526 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3527 3528 case Instruction::SExt: 3529 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3530 3531 case Instruction::BitCast: 3532 // BitCasts are no-op casts so we just eliminate the cast. 3533 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3534 return getSCEV(U->getOperand(0)); 3535 break; 3536 3537 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3538 // lead to pointer expressions which cannot safely be expanded to GEPs, 3539 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3540 // simplifying integer expressions. 3541 3542 case Instruction::GetElementPtr: 3543 return createNodeForGEP(cast<GEPOperator>(U)); 3544 3545 case Instruction::PHI: 3546 return createNodeForPHI(cast<PHINode>(U)); 3547 3548 case Instruction::Select: 3549 // This could be a smax or umax that was lowered earlier. 3550 // Try to recover it. 3551 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3552 Value *LHS = ICI->getOperand(0); 3553 Value *RHS = ICI->getOperand(1); 3554 switch (ICI->getPredicate()) { 3555 case ICmpInst::ICMP_SLT: 3556 case ICmpInst::ICMP_SLE: 3557 std::swap(LHS, RHS); 3558 // fall through 3559 case ICmpInst::ICMP_SGT: 3560 case ICmpInst::ICMP_SGE: 3561 // a >s b ? a+x : b+x -> smax(a, b)+x 3562 // a >s b ? b+x : a+x -> smin(a, b)+x 3563 if (LHS->getType() == U->getType()) { 3564 const SCEV *LS = getSCEV(LHS); 3565 const SCEV *RS = getSCEV(RHS); 3566 const SCEV *LA = getSCEV(U->getOperand(1)); 3567 const SCEV *RA = getSCEV(U->getOperand(2)); 3568 const SCEV *LDiff = getMinusSCEV(LA, LS); 3569 const SCEV *RDiff = getMinusSCEV(RA, RS); 3570 if (LDiff == RDiff) 3571 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3572 LDiff = getMinusSCEV(LA, RS); 3573 RDiff = getMinusSCEV(RA, LS); 3574 if (LDiff == RDiff) 3575 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3576 } 3577 break; 3578 case ICmpInst::ICMP_ULT: 3579 case ICmpInst::ICMP_ULE: 3580 std::swap(LHS, RHS); 3581 // fall through 3582 case ICmpInst::ICMP_UGT: 3583 case ICmpInst::ICMP_UGE: 3584 // a >u b ? a+x : b+x -> umax(a, b)+x 3585 // a >u b ? b+x : a+x -> umin(a, b)+x 3586 if (LHS->getType() == U->getType()) { 3587 const SCEV *LS = getSCEV(LHS); 3588 const SCEV *RS = getSCEV(RHS); 3589 const SCEV *LA = getSCEV(U->getOperand(1)); 3590 const SCEV *RA = getSCEV(U->getOperand(2)); 3591 const SCEV *LDiff = getMinusSCEV(LA, LS); 3592 const SCEV *RDiff = getMinusSCEV(RA, RS); 3593 if (LDiff == RDiff) 3594 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3595 LDiff = getMinusSCEV(LA, RS); 3596 RDiff = getMinusSCEV(RA, LS); 3597 if (LDiff == RDiff) 3598 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3599 } 3600 break; 3601 case ICmpInst::ICMP_NE: 3602 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3603 if (LHS->getType() == U->getType() && 3604 isa<ConstantInt>(RHS) && 3605 cast<ConstantInt>(RHS)->isZero()) { 3606 const SCEV *One = getConstant(LHS->getType(), 1); 3607 const SCEV *LS = getSCEV(LHS); 3608 const SCEV *LA = getSCEV(U->getOperand(1)); 3609 const SCEV *RA = getSCEV(U->getOperand(2)); 3610 const SCEV *LDiff = getMinusSCEV(LA, LS); 3611 const SCEV *RDiff = getMinusSCEV(RA, One); 3612 if (LDiff == RDiff) 3613 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3614 } 3615 break; 3616 case ICmpInst::ICMP_EQ: 3617 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3618 if (LHS->getType() == U->getType() && 3619 isa<ConstantInt>(RHS) && 3620 cast<ConstantInt>(RHS)->isZero()) { 3621 const SCEV *One = getConstant(LHS->getType(), 1); 3622 const SCEV *LS = getSCEV(LHS); 3623 const SCEV *LA = getSCEV(U->getOperand(1)); 3624 const SCEV *RA = getSCEV(U->getOperand(2)); 3625 const SCEV *LDiff = getMinusSCEV(LA, One); 3626 const SCEV *RDiff = getMinusSCEV(RA, LS); 3627 if (LDiff == RDiff) 3628 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3629 } 3630 break; 3631 default: 3632 break; 3633 } 3634 } 3635 3636 default: // We cannot analyze this expression. 3637 break; 3638 } 3639 3640 return getUnknown(V); 3641} 3642 3643 3644 3645//===----------------------------------------------------------------------===// 3646// Iteration Count Computation Code 3647// 3648 3649/// getBackedgeTakenCount - If the specified loop has a predictable 3650/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3651/// object. The backedge-taken count is the number of times the loop header 3652/// will be branched to from within the loop. This is one less than the 3653/// trip count of the loop, since it doesn't count the first iteration, 3654/// when the header is branched to from outside the loop. 3655/// 3656/// Note that it is not valid to call this method on a loop without a 3657/// loop-invariant backedge-taken count (see 3658/// hasLoopInvariantBackedgeTakenCount). 3659/// 3660const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3661 return getBackedgeTakenInfo(L).Exact; 3662} 3663 3664/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3665/// return the least SCEV value that is known never to be less than the 3666/// actual backedge taken count. 3667const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3668 return getBackedgeTakenInfo(L).Max; 3669} 3670 3671/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3672/// onto the given Worklist. 3673static void 3674PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3675 BasicBlock *Header = L->getHeader(); 3676 3677 // Push all Loop-header PHIs onto the Worklist stack. 3678 for (BasicBlock::iterator I = Header->begin(); 3679 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3680 Worklist.push_back(PN); 3681} 3682 3683const ScalarEvolution::BackedgeTakenInfo & 3684ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3685 // Initially insert a CouldNotCompute for this loop. If the insertion 3686 // succeeds, proceed to actually compute a backedge-taken count and 3687 // update the value. The temporary CouldNotCompute value tells SCEV 3688 // code elsewhere that it shouldn't attempt to request a new 3689 // backedge-taken count, which could result in infinite recursion. 3690 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3691 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3692 if (Pair.second) { 3693 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3694 if (BECount.Exact != getCouldNotCompute()) { 3695 assert(BECount.Exact->isLoopInvariant(L) && 3696 BECount.Max->isLoopInvariant(L) && 3697 "Computed backedge-taken count isn't loop invariant for loop!"); 3698 ++NumTripCountsComputed; 3699 3700 // Update the value in the map. 3701 Pair.first->second = BECount; 3702 } else { 3703 if (BECount.Max != getCouldNotCompute()) 3704 // Update the value in the map. 3705 Pair.first->second = BECount; 3706 if (isa<PHINode>(L->getHeader()->begin())) 3707 // Only count loops that have phi nodes as not being computable. 3708 ++NumTripCountsNotComputed; 3709 } 3710 3711 // Now that we know more about the trip count for this loop, forget any 3712 // existing SCEV values for PHI nodes in this loop since they are only 3713 // conservative estimates made without the benefit of trip count 3714 // information. This is similar to the code in forgetLoop, except that 3715 // it handles SCEVUnknown PHI nodes specially. 3716 if (BECount.hasAnyInfo()) { 3717 SmallVector<Instruction *, 16> Worklist; 3718 PushLoopPHIs(L, Worklist); 3719 3720 SmallPtrSet<Instruction *, 8> Visited; 3721 while (!Worklist.empty()) { 3722 Instruction *I = Worklist.pop_back_val(); 3723 if (!Visited.insert(I)) continue; 3724 3725 ValueExprMapType::iterator It = 3726 ValueExprMap.find(static_cast<Value *>(I)); 3727 if (It != ValueExprMap.end()) { 3728 // SCEVUnknown for a PHI either means that it has an unrecognized 3729 // structure, or it's a PHI that's in the progress of being computed 3730 // by createNodeForPHI. In the former case, additional loop trip 3731 // count information isn't going to change anything. In the later 3732 // case, createNodeForPHI will perform the necessary updates on its 3733 // own when it gets to that point. 3734 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3735 ValuesAtScopes.erase(It->second); 3736 ValueExprMap.erase(It); 3737 } 3738 if (PHINode *PN = dyn_cast<PHINode>(I)) 3739 ConstantEvolutionLoopExitValue.erase(PN); 3740 } 3741 3742 PushDefUseChildren(I, Worklist); 3743 } 3744 } 3745 } 3746 return Pair.first->second; 3747} 3748 3749/// forgetLoop - This method should be called by the client when it has 3750/// changed a loop in a way that may effect ScalarEvolution's ability to 3751/// compute a trip count, or if the loop is deleted. 3752void ScalarEvolution::forgetLoop(const Loop *L) { 3753 // Drop any stored trip count value. 3754 BackedgeTakenCounts.erase(L); 3755 3756 // Drop information about expressions based on loop-header PHIs. 3757 SmallVector<Instruction *, 16> Worklist; 3758 PushLoopPHIs(L, Worklist); 3759 3760 SmallPtrSet<Instruction *, 8> Visited; 3761 while (!Worklist.empty()) { 3762 Instruction *I = Worklist.pop_back_val(); 3763 if (!Visited.insert(I)) continue; 3764 3765 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3766 if (It != ValueExprMap.end()) { 3767 ValuesAtScopes.erase(It->second); 3768 ValueExprMap.erase(It); 3769 if (PHINode *PN = dyn_cast<PHINode>(I)) 3770 ConstantEvolutionLoopExitValue.erase(PN); 3771 } 3772 3773 PushDefUseChildren(I, Worklist); 3774 } 3775} 3776 3777/// forgetValue - This method should be called by the client when it has 3778/// changed a value in a way that may effect its value, or which may 3779/// disconnect it from a def-use chain linking it to a loop. 3780void ScalarEvolution::forgetValue(Value *V) { 3781 Instruction *I = dyn_cast<Instruction>(V); 3782 if (!I) return; 3783 3784 // Drop information about expressions based on loop-header PHIs. 3785 SmallVector<Instruction *, 16> Worklist; 3786 Worklist.push_back(I); 3787 3788 SmallPtrSet<Instruction *, 8> Visited; 3789 while (!Worklist.empty()) { 3790 I = Worklist.pop_back_val(); 3791 if (!Visited.insert(I)) continue; 3792 3793 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3794 if (It != ValueExprMap.end()) { 3795 ValuesAtScopes.erase(It->second); 3796 ValueExprMap.erase(It); 3797 if (PHINode *PN = dyn_cast<PHINode>(I)) 3798 ConstantEvolutionLoopExitValue.erase(PN); 3799 } 3800 3801 PushDefUseChildren(I, Worklist); 3802 } 3803} 3804 3805/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3806/// of the specified loop will execute. 3807ScalarEvolution::BackedgeTakenInfo 3808ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3809 SmallVector<BasicBlock *, 8> ExitingBlocks; 3810 L->getExitingBlocks(ExitingBlocks); 3811 3812 // Examine all exits and pick the most conservative values. 3813 const SCEV *BECount = getCouldNotCompute(); 3814 const SCEV *MaxBECount = getCouldNotCompute(); 3815 bool CouldNotComputeBECount = false; 3816 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3817 BackedgeTakenInfo NewBTI = 3818 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3819 3820 if (NewBTI.Exact == getCouldNotCompute()) { 3821 // We couldn't compute an exact value for this exit, so 3822 // we won't be able to compute an exact value for the loop. 3823 CouldNotComputeBECount = true; 3824 BECount = getCouldNotCompute(); 3825 } else if (!CouldNotComputeBECount) { 3826 if (BECount == getCouldNotCompute()) 3827 BECount = NewBTI.Exact; 3828 else 3829 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3830 } 3831 if (MaxBECount == getCouldNotCompute()) 3832 MaxBECount = NewBTI.Max; 3833 else if (NewBTI.Max != getCouldNotCompute()) 3834 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3835 } 3836 3837 return BackedgeTakenInfo(BECount, MaxBECount); 3838} 3839 3840/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3841/// of the specified loop will execute if it exits via the specified block. 3842ScalarEvolution::BackedgeTakenInfo 3843ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3844 BasicBlock *ExitingBlock) { 3845 3846 // Okay, we've chosen an exiting block. See what condition causes us to 3847 // exit at this block. 3848 // 3849 // FIXME: we should be able to handle switch instructions (with a single exit) 3850 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3851 if (ExitBr == 0) return getCouldNotCompute(); 3852 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3853 3854 // At this point, we know we have a conditional branch that determines whether 3855 // the loop is exited. However, we don't know if the branch is executed each 3856 // time through the loop. If not, then the execution count of the branch will 3857 // not be equal to the trip count of the loop. 3858 // 3859 // Currently we check for this by checking to see if the Exit branch goes to 3860 // the loop header. If so, we know it will always execute the same number of 3861 // times as the loop. We also handle the case where the exit block *is* the 3862 // loop header. This is common for un-rotated loops. 3863 // 3864 // If both of those tests fail, walk up the unique predecessor chain to the 3865 // header, stopping if there is an edge that doesn't exit the loop. If the 3866 // header is reached, the execution count of the branch will be equal to the 3867 // trip count of the loop. 3868 // 3869 // More extensive analysis could be done to handle more cases here. 3870 // 3871 if (ExitBr->getSuccessor(0) != L->getHeader() && 3872 ExitBr->getSuccessor(1) != L->getHeader() && 3873 ExitBr->getParent() != L->getHeader()) { 3874 // The simple checks failed, try climbing the unique predecessor chain 3875 // up to the header. 3876 bool Ok = false; 3877 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3878 BasicBlock *Pred = BB->getUniquePredecessor(); 3879 if (!Pred) 3880 return getCouldNotCompute(); 3881 TerminatorInst *PredTerm = Pred->getTerminator(); 3882 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3883 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3884 if (PredSucc == BB) 3885 continue; 3886 // If the predecessor has a successor that isn't BB and isn't 3887 // outside the loop, assume the worst. 3888 if (L->contains(PredSucc)) 3889 return getCouldNotCompute(); 3890 } 3891 if (Pred == L->getHeader()) { 3892 Ok = true; 3893 break; 3894 } 3895 BB = Pred; 3896 } 3897 if (!Ok) 3898 return getCouldNotCompute(); 3899 } 3900 3901 // Proceed to the next level to examine the exit condition expression. 3902 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3903 ExitBr->getSuccessor(0), 3904 ExitBr->getSuccessor(1)); 3905} 3906 3907/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3908/// backedge of the specified loop will execute if its exit condition 3909/// were a conditional branch of ExitCond, TBB, and FBB. 3910ScalarEvolution::BackedgeTakenInfo 3911ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3912 Value *ExitCond, 3913 BasicBlock *TBB, 3914 BasicBlock *FBB) { 3915 // Check if the controlling expression for this loop is an And or Or. 3916 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3917 if (BO->getOpcode() == Instruction::And) { 3918 // Recurse on the operands of the and. 3919 BackedgeTakenInfo BTI0 = 3920 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3921 BackedgeTakenInfo BTI1 = 3922 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3923 const SCEV *BECount = getCouldNotCompute(); 3924 const SCEV *MaxBECount = getCouldNotCompute(); 3925 if (L->contains(TBB)) { 3926 // Both conditions must be true for the loop to continue executing. 3927 // Choose the less conservative count. 3928 if (BTI0.Exact == getCouldNotCompute() || 3929 BTI1.Exact == getCouldNotCompute()) 3930 BECount = getCouldNotCompute(); 3931 else 3932 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3933 if (BTI0.Max == getCouldNotCompute()) 3934 MaxBECount = BTI1.Max; 3935 else if (BTI1.Max == getCouldNotCompute()) 3936 MaxBECount = BTI0.Max; 3937 else 3938 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3939 } else { 3940 // Both conditions must be true at the same time for the loop to exit. 3941 // For now, be conservative. 3942 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3943 if (BTI0.Max == BTI1.Max) 3944 MaxBECount = BTI0.Max; 3945 if (BTI0.Exact == BTI1.Exact) 3946 BECount = BTI0.Exact; 3947 } 3948 3949 return BackedgeTakenInfo(BECount, MaxBECount); 3950 } 3951 if (BO->getOpcode() == Instruction::Or) { 3952 // Recurse on the operands of the or. 3953 BackedgeTakenInfo BTI0 = 3954 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3955 BackedgeTakenInfo BTI1 = 3956 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3957 const SCEV *BECount = getCouldNotCompute(); 3958 const SCEV *MaxBECount = getCouldNotCompute(); 3959 if (L->contains(FBB)) { 3960 // Both conditions must be false for the loop to continue executing. 3961 // Choose the less conservative count. 3962 if (BTI0.Exact == getCouldNotCompute() || 3963 BTI1.Exact == getCouldNotCompute()) 3964 BECount = getCouldNotCompute(); 3965 else 3966 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3967 if (BTI0.Max == getCouldNotCompute()) 3968 MaxBECount = BTI1.Max; 3969 else if (BTI1.Max == getCouldNotCompute()) 3970 MaxBECount = BTI0.Max; 3971 else 3972 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3973 } else { 3974 // Both conditions must be false at the same time for the loop to exit. 3975 // For now, be conservative. 3976 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3977 if (BTI0.Max == BTI1.Max) 3978 MaxBECount = BTI0.Max; 3979 if (BTI0.Exact == BTI1.Exact) 3980 BECount = BTI0.Exact; 3981 } 3982 3983 return BackedgeTakenInfo(BECount, MaxBECount); 3984 } 3985 } 3986 3987 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3988 // Proceed to the next level to examine the icmp. 3989 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3990 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3991 3992 // Check for a constant condition. These are normally stripped out by 3993 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3994 // preserve the CFG and is temporarily leaving constant conditions 3995 // in place. 3996 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3997 if (L->contains(FBB) == !CI->getZExtValue()) 3998 // The backedge is always taken. 3999 return getCouldNotCompute(); 4000 else 4001 // The backedge is never taken. 4002 return getConstant(CI->getType(), 0); 4003 } 4004 4005 // If it's not an integer or pointer comparison then compute it the hard way. 4006 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4007} 4008 4009/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4010/// backedge of the specified loop will execute if its exit condition 4011/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4012ScalarEvolution::BackedgeTakenInfo 4013ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4014 ICmpInst *ExitCond, 4015 BasicBlock *TBB, 4016 BasicBlock *FBB) { 4017 4018 // If the condition was exit on true, convert the condition to exit on false 4019 ICmpInst::Predicate Cond; 4020 if (!L->contains(FBB)) 4021 Cond = ExitCond->getPredicate(); 4022 else 4023 Cond = ExitCond->getInversePredicate(); 4024 4025 // Handle common loops like: for (X = "string"; *X; ++X) 4026 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4027 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4028 BackedgeTakenInfo ItCnt = 4029 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4030 if (ItCnt.hasAnyInfo()) 4031 return ItCnt; 4032 } 4033 4034 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4035 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4036 4037 // Try to evaluate any dependencies out of the loop. 4038 LHS = getSCEVAtScope(LHS, L); 4039 RHS = getSCEVAtScope(RHS, L); 4040 4041 // At this point, we would like to compute how many iterations of the 4042 // loop the predicate will return true for these inputs. 4043 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 4044 // If there is a loop-invariant, force it into the RHS. 4045 std::swap(LHS, RHS); 4046 Cond = ICmpInst::getSwappedPredicate(Cond); 4047 } 4048 4049 // Simplify the operands before analyzing them. 4050 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4051 4052 // If we have a comparison of a chrec against a constant, try to use value 4053 // ranges to answer this query. 4054 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4055 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4056 if (AddRec->getLoop() == L) { 4057 // Form the constant range. 4058 ConstantRange CompRange( 4059 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4060 4061 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4062 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4063 } 4064 4065 switch (Cond) { 4066 case ICmpInst::ICMP_NE: { // while (X != Y) 4067 // Convert to: while (X-Y != 0) 4068 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4069 if (BTI.hasAnyInfo()) return BTI; 4070 break; 4071 } 4072 case ICmpInst::ICMP_EQ: { // while (X == Y) 4073 // Convert to: while (X-Y == 0) 4074 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4075 if (BTI.hasAnyInfo()) return BTI; 4076 break; 4077 } 4078 case ICmpInst::ICMP_SLT: { 4079 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4080 if (BTI.hasAnyInfo()) return BTI; 4081 break; 4082 } 4083 case ICmpInst::ICMP_SGT: { 4084 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4085 getNotSCEV(RHS), L, true); 4086 if (BTI.hasAnyInfo()) return BTI; 4087 break; 4088 } 4089 case ICmpInst::ICMP_ULT: { 4090 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4091 if (BTI.hasAnyInfo()) return BTI; 4092 break; 4093 } 4094 case ICmpInst::ICMP_UGT: { 4095 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4096 getNotSCEV(RHS), L, false); 4097 if (BTI.hasAnyInfo()) return BTI; 4098 break; 4099 } 4100 default: 4101#if 0 4102 dbgs() << "ComputeBackedgeTakenCount "; 4103 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4104 dbgs() << "[unsigned] "; 4105 dbgs() << *LHS << " " 4106 << Instruction::getOpcodeName(Instruction::ICmp) 4107 << " " << *RHS << "\n"; 4108#endif 4109 break; 4110 } 4111 return 4112 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4113} 4114 4115static ConstantInt * 4116EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4117 ScalarEvolution &SE) { 4118 const SCEV *InVal = SE.getConstant(C); 4119 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4120 assert(isa<SCEVConstant>(Val) && 4121 "Evaluation of SCEV at constant didn't fold correctly?"); 4122 return cast<SCEVConstant>(Val)->getValue(); 4123} 4124 4125/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4126/// and a GEP expression (missing the pointer index) indexing into it, return 4127/// the addressed element of the initializer or null if the index expression is 4128/// invalid. 4129static Constant * 4130GetAddressedElementFromGlobal(GlobalVariable *GV, 4131 const std::vector<ConstantInt*> &Indices) { 4132 Constant *Init = GV->getInitializer(); 4133 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4134 uint64_t Idx = Indices[i]->getZExtValue(); 4135 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4136 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4137 Init = cast<Constant>(CS->getOperand(Idx)); 4138 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4139 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4140 Init = cast<Constant>(CA->getOperand(Idx)); 4141 } else if (isa<ConstantAggregateZero>(Init)) { 4142 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4143 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4144 Init = Constant::getNullValue(STy->getElementType(Idx)); 4145 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4146 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4147 Init = Constant::getNullValue(ATy->getElementType()); 4148 } else { 4149 llvm_unreachable("Unknown constant aggregate type!"); 4150 } 4151 return 0; 4152 } else { 4153 return 0; // Unknown initializer type 4154 } 4155 } 4156 return Init; 4157} 4158 4159/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4160/// 'icmp op load X, cst', try to see if we can compute the backedge 4161/// execution count. 4162ScalarEvolution::BackedgeTakenInfo 4163ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4164 LoadInst *LI, 4165 Constant *RHS, 4166 const Loop *L, 4167 ICmpInst::Predicate predicate) { 4168 if (LI->isVolatile()) return getCouldNotCompute(); 4169 4170 // Check to see if the loaded pointer is a getelementptr of a global. 4171 // TODO: Use SCEV instead of manually grubbing with GEPs. 4172 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4173 if (!GEP) return getCouldNotCompute(); 4174 4175 // Make sure that it is really a constant global we are gepping, with an 4176 // initializer, and make sure the first IDX is really 0. 4177 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4178 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4179 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4180 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4181 return getCouldNotCompute(); 4182 4183 // Okay, we allow one non-constant index into the GEP instruction. 4184 Value *VarIdx = 0; 4185 std::vector<ConstantInt*> Indexes; 4186 unsigned VarIdxNum = 0; 4187 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4188 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4189 Indexes.push_back(CI); 4190 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4191 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4192 VarIdx = GEP->getOperand(i); 4193 VarIdxNum = i-2; 4194 Indexes.push_back(0); 4195 } 4196 4197 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4198 // Check to see if X is a loop variant variable value now. 4199 const SCEV *Idx = getSCEV(VarIdx); 4200 Idx = getSCEVAtScope(Idx, L); 4201 4202 // We can only recognize very limited forms of loop index expressions, in 4203 // particular, only affine AddRec's like {C1,+,C2}. 4204 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4205 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4206 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4207 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4208 return getCouldNotCompute(); 4209 4210 unsigned MaxSteps = MaxBruteForceIterations; 4211 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4212 ConstantInt *ItCst = ConstantInt::get( 4213 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4214 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4215 4216 // Form the GEP offset. 4217 Indexes[VarIdxNum] = Val; 4218 4219 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4220 if (Result == 0) break; // Cannot compute! 4221 4222 // Evaluate the condition for this iteration. 4223 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4224 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4225 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4226#if 0 4227 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4228 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4229 << "***\n"; 4230#endif 4231 ++NumArrayLenItCounts; 4232 return getConstant(ItCst); // Found terminating iteration! 4233 } 4234 } 4235 return getCouldNotCompute(); 4236} 4237 4238 4239/// CanConstantFold - Return true if we can constant fold an instruction of the 4240/// specified type, assuming that all operands were constants. 4241static bool CanConstantFold(const Instruction *I) { 4242 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4243 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4244 return true; 4245 4246 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4247 if (const Function *F = CI->getCalledFunction()) 4248 return canConstantFoldCallTo(F); 4249 return false; 4250} 4251 4252/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4253/// in the loop that V is derived from. We allow arbitrary operations along the 4254/// way, but the operands of an operation must either be constants or a value 4255/// derived from a constant PHI. If this expression does not fit with these 4256/// constraints, return null. 4257static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4258 // If this is not an instruction, or if this is an instruction outside of the 4259 // loop, it can't be derived from a loop PHI. 4260 Instruction *I = dyn_cast<Instruction>(V); 4261 if (I == 0 || !L->contains(I)) return 0; 4262 4263 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4264 if (L->getHeader() == I->getParent()) 4265 return PN; 4266 else 4267 // We don't currently keep track of the control flow needed to evaluate 4268 // PHIs, so we cannot handle PHIs inside of loops. 4269 return 0; 4270 } 4271 4272 // If we won't be able to constant fold this expression even if the operands 4273 // are constants, return early. 4274 if (!CanConstantFold(I)) return 0; 4275 4276 // Otherwise, we can evaluate this instruction if all of its operands are 4277 // constant or derived from a PHI node themselves. 4278 PHINode *PHI = 0; 4279 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4280 if (!isa<Constant>(I->getOperand(Op))) { 4281 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4282 if (P == 0) return 0; // Not evolving from PHI 4283 if (PHI == 0) 4284 PHI = P; 4285 else if (PHI != P) 4286 return 0; // Evolving from multiple different PHIs. 4287 } 4288 4289 // This is a expression evolving from a constant PHI! 4290 return PHI; 4291} 4292 4293/// EvaluateExpression - Given an expression that passes the 4294/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4295/// in the loop has the value PHIVal. If we can't fold this expression for some 4296/// reason, return null. 4297static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4298 const TargetData *TD) { 4299 if (isa<PHINode>(V)) return PHIVal; 4300 if (Constant *C = dyn_cast<Constant>(V)) return C; 4301 Instruction *I = cast<Instruction>(V); 4302 4303 std::vector<Constant*> Operands(I->getNumOperands()); 4304 4305 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4306 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4307 if (Operands[i] == 0) return 0; 4308 } 4309 4310 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4311 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4312 Operands[1], TD); 4313 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4314 &Operands[0], Operands.size(), TD); 4315} 4316 4317/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4318/// in the header of its containing loop, we know the loop executes a 4319/// constant number of times, and the PHI node is just a recurrence 4320/// involving constants, fold it. 4321Constant * 4322ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4323 const APInt &BEs, 4324 const Loop *L) { 4325 std::map<PHINode*, Constant*>::const_iterator I = 4326 ConstantEvolutionLoopExitValue.find(PN); 4327 if (I != ConstantEvolutionLoopExitValue.end()) 4328 return I->second; 4329 4330 if (BEs.ugt(MaxBruteForceIterations)) 4331 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4332 4333 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4334 4335 // Since the loop is canonicalized, the PHI node must have two entries. One 4336 // entry must be a constant (coming in from outside of the loop), and the 4337 // second must be derived from the same PHI. 4338 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4339 Constant *StartCST = 4340 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4341 if (StartCST == 0) 4342 return RetVal = 0; // Must be a constant. 4343 4344 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4345 if (getConstantEvolvingPHI(BEValue, L) != PN && 4346 !isa<Constant>(BEValue)) 4347 return RetVal = 0; // Not derived from same PHI. 4348 4349 // Execute the loop symbolically to determine the exit value. 4350 if (BEs.getActiveBits() >= 32) 4351 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4352 4353 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4354 unsigned IterationNum = 0; 4355 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4356 if (IterationNum == NumIterations) 4357 return RetVal = PHIVal; // Got exit value! 4358 4359 // Compute the value of the PHI node for the next iteration. 4360 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4361 if (NextPHI == PHIVal) 4362 return RetVal = NextPHI; // Stopped evolving! 4363 if (NextPHI == 0) 4364 return 0; // Couldn't evaluate! 4365 PHIVal = NextPHI; 4366 } 4367} 4368 4369/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4370/// constant number of times (the condition evolves only from constants), 4371/// try to evaluate a few iterations of the loop until we get the exit 4372/// condition gets a value of ExitWhen (true or false). If we cannot 4373/// evaluate the trip count of the loop, return getCouldNotCompute(). 4374const SCEV * 4375ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4376 Value *Cond, 4377 bool ExitWhen) { 4378 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4379 if (PN == 0) return getCouldNotCompute(); 4380 4381 // If the loop is canonicalized, the PHI will have exactly two entries. 4382 // That's the only form we support here. 4383 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4384 4385 // One entry must be a constant (coming in from outside of the loop), and the 4386 // second must be derived from the same PHI. 4387 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4388 Constant *StartCST = 4389 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4390 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4391 4392 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4393 if (getConstantEvolvingPHI(BEValue, L) != PN && 4394 !isa<Constant>(BEValue)) 4395 return getCouldNotCompute(); // Not derived from same PHI. 4396 4397 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4398 // the loop symbolically to determine when the condition gets a value of 4399 // "ExitWhen". 4400 unsigned IterationNum = 0; 4401 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4402 for (Constant *PHIVal = StartCST; 4403 IterationNum != MaxIterations; ++IterationNum) { 4404 ConstantInt *CondVal = 4405 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4406 4407 // Couldn't symbolically evaluate. 4408 if (!CondVal) return getCouldNotCompute(); 4409 4410 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4411 ++NumBruteForceTripCountsComputed; 4412 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4413 } 4414 4415 // Compute the value of the PHI node for the next iteration. 4416 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4417 if (NextPHI == 0 || NextPHI == PHIVal) 4418 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4419 PHIVal = NextPHI; 4420 } 4421 4422 // Too many iterations were needed to evaluate. 4423 return getCouldNotCompute(); 4424} 4425 4426/// getSCEVAtScope - Return a SCEV expression for the specified value 4427/// at the specified scope in the program. The L value specifies a loop 4428/// nest to evaluate the expression at, where null is the top-level or a 4429/// specified loop is immediately inside of the loop. 4430/// 4431/// This method can be used to compute the exit value for a variable defined 4432/// in a loop by querying what the value will hold in the parent loop. 4433/// 4434/// In the case that a relevant loop exit value cannot be computed, the 4435/// original value V is returned. 4436const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4437 // Check to see if we've folded this expression at this loop before. 4438 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4439 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4440 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4441 if (!Pair.second) 4442 return Pair.first->second ? Pair.first->second : V; 4443 4444 // Otherwise compute it. 4445 const SCEV *C = computeSCEVAtScope(V, L); 4446 ValuesAtScopes[V][L] = C; 4447 return C; 4448} 4449 4450const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4451 if (isa<SCEVConstant>(V)) return V; 4452 4453 // If this instruction is evolved from a constant-evolving PHI, compute the 4454 // exit value from the loop without using SCEVs. 4455 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4456 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4457 const Loop *LI = (*this->LI)[I->getParent()]; 4458 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4459 if (PHINode *PN = dyn_cast<PHINode>(I)) 4460 if (PN->getParent() == LI->getHeader()) { 4461 // Okay, there is no closed form solution for the PHI node. Check 4462 // to see if the loop that contains it has a known backedge-taken 4463 // count. If so, we may be able to force computation of the exit 4464 // value. 4465 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4466 if (const SCEVConstant *BTCC = 4467 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4468 // Okay, we know how many times the containing loop executes. If 4469 // this is a constant evolving PHI node, get the final value at 4470 // the specified iteration number. 4471 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4472 BTCC->getValue()->getValue(), 4473 LI); 4474 if (RV) return getSCEV(RV); 4475 } 4476 } 4477 4478 // Okay, this is an expression that we cannot symbolically evaluate 4479 // into a SCEV. Check to see if it's possible to symbolically evaluate 4480 // the arguments into constants, and if so, try to constant propagate the 4481 // result. This is particularly useful for computing loop exit values. 4482 if (CanConstantFold(I)) { 4483 SmallVector<Constant *, 4> Operands; 4484 bool MadeImprovement = false; 4485 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4486 Value *Op = I->getOperand(i); 4487 if (Constant *C = dyn_cast<Constant>(Op)) { 4488 Operands.push_back(C); 4489 continue; 4490 } 4491 4492 // If any of the operands is non-constant and if they are 4493 // non-integer and non-pointer, don't even try to analyze them 4494 // with scev techniques. 4495 if (!isSCEVable(Op->getType())) 4496 return V; 4497 4498 const SCEV *OrigV = getSCEV(Op); 4499 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4500 MadeImprovement |= OrigV != OpV; 4501 4502 Constant *C = 0; 4503 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4504 C = SC->getValue(); 4505 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4506 C = dyn_cast<Constant>(SU->getValue()); 4507 if (!C) return V; 4508 if (C->getType() != Op->getType()) 4509 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4510 Op->getType(), 4511 false), 4512 C, Op->getType()); 4513 Operands.push_back(C); 4514 } 4515 4516 // Check to see if getSCEVAtScope actually made an improvement. 4517 if (MadeImprovement) { 4518 Constant *C = 0; 4519 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4520 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4521 Operands[0], Operands[1], TD); 4522 else 4523 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4524 &Operands[0], Operands.size(), TD); 4525 if (!C) return V; 4526 return getSCEV(C); 4527 } 4528 } 4529 } 4530 4531 // This is some other type of SCEVUnknown, just return it. 4532 return V; 4533 } 4534 4535 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4536 // Avoid performing the look-up in the common case where the specified 4537 // expression has no loop-variant portions. 4538 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4539 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4540 if (OpAtScope != Comm->getOperand(i)) { 4541 // Okay, at least one of these operands is loop variant but might be 4542 // foldable. Build a new instance of the folded commutative expression. 4543 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4544 Comm->op_begin()+i); 4545 NewOps.push_back(OpAtScope); 4546 4547 for (++i; i != e; ++i) { 4548 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4549 NewOps.push_back(OpAtScope); 4550 } 4551 if (isa<SCEVAddExpr>(Comm)) 4552 return getAddExpr(NewOps); 4553 if (isa<SCEVMulExpr>(Comm)) 4554 return getMulExpr(NewOps); 4555 if (isa<SCEVSMaxExpr>(Comm)) 4556 return getSMaxExpr(NewOps); 4557 if (isa<SCEVUMaxExpr>(Comm)) 4558 return getUMaxExpr(NewOps); 4559 llvm_unreachable("Unknown commutative SCEV type!"); 4560 } 4561 } 4562 // If we got here, all operands are loop invariant. 4563 return Comm; 4564 } 4565 4566 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4567 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4568 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4569 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4570 return Div; // must be loop invariant 4571 return getUDivExpr(LHS, RHS); 4572 } 4573 4574 // If this is a loop recurrence for a loop that does not contain L, then we 4575 // are dealing with the final value computed by the loop. 4576 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4577 // First, attempt to evaluate each operand. 4578 // Avoid performing the look-up in the common case where the specified 4579 // expression has no loop-variant portions. 4580 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4581 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4582 if (OpAtScope == AddRec->getOperand(i)) 4583 continue; 4584 4585 // Okay, at least one of these operands is loop variant but might be 4586 // foldable. Build a new instance of the folded commutative expression. 4587 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4588 AddRec->op_begin()+i); 4589 NewOps.push_back(OpAtScope); 4590 for (++i; i != e; ++i) 4591 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4592 4593 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4594 break; 4595 } 4596 4597 // If the scope is outside the addrec's loop, evaluate it by using the 4598 // loop exit value of the addrec. 4599 if (!AddRec->getLoop()->contains(L)) { 4600 // To evaluate this recurrence, we need to know how many times the AddRec 4601 // loop iterates. Compute this now. 4602 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4603 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4604 4605 // Then, evaluate the AddRec. 4606 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4607 } 4608 4609 return AddRec; 4610 } 4611 4612 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4613 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4614 if (Op == Cast->getOperand()) 4615 return Cast; // must be loop invariant 4616 return getZeroExtendExpr(Op, Cast->getType()); 4617 } 4618 4619 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4620 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4621 if (Op == Cast->getOperand()) 4622 return Cast; // must be loop invariant 4623 return getSignExtendExpr(Op, Cast->getType()); 4624 } 4625 4626 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4627 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4628 if (Op == Cast->getOperand()) 4629 return Cast; // must be loop invariant 4630 return getTruncateExpr(Op, Cast->getType()); 4631 } 4632 4633 llvm_unreachable("Unknown SCEV type!"); 4634 return 0; 4635} 4636 4637/// getSCEVAtScope - This is a convenience function which does 4638/// getSCEVAtScope(getSCEV(V), L). 4639const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4640 return getSCEVAtScope(getSCEV(V), L); 4641} 4642 4643/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4644/// following equation: 4645/// 4646/// A * X = B (mod N) 4647/// 4648/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4649/// A and B isn't important. 4650/// 4651/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4652static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4653 ScalarEvolution &SE) { 4654 uint32_t BW = A.getBitWidth(); 4655 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4656 assert(A != 0 && "A must be non-zero."); 4657 4658 // 1. D = gcd(A, N) 4659 // 4660 // The gcd of A and N may have only one prime factor: 2. The number of 4661 // trailing zeros in A is its multiplicity 4662 uint32_t Mult2 = A.countTrailingZeros(); 4663 // D = 2^Mult2 4664 4665 // 2. Check if B is divisible by D. 4666 // 4667 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4668 // is not less than multiplicity of this prime factor for D. 4669 if (B.countTrailingZeros() < Mult2) 4670 return SE.getCouldNotCompute(); 4671 4672 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4673 // modulo (N / D). 4674 // 4675 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4676 // bit width during computations. 4677 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4678 APInt Mod(BW + 1, 0); 4679 Mod.set(BW - Mult2); // Mod = N / D 4680 APInt I = AD.multiplicativeInverse(Mod); 4681 4682 // 4. Compute the minimum unsigned root of the equation: 4683 // I * (B / D) mod (N / D) 4684 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4685 4686 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4687 // bits. 4688 return SE.getConstant(Result.trunc(BW)); 4689} 4690 4691/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4692/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4693/// might be the same) or two SCEVCouldNotCompute objects. 4694/// 4695static std::pair<const SCEV *,const SCEV *> 4696SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4697 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4698 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4699 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4700 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4701 4702 // We currently can only solve this if the coefficients are constants. 4703 if (!LC || !MC || !NC) { 4704 const SCEV *CNC = SE.getCouldNotCompute(); 4705 return std::make_pair(CNC, CNC); 4706 } 4707 4708 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4709 const APInt &L = LC->getValue()->getValue(); 4710 const APInt &M = MC->getValue()->getValue(); 4711 const APInt &N = NC->getValue()->getValue(); 4712 APInt Two(BitWidth, 2); 4713 APInt Four(BitWidth, 4); 4714 4715 { 4716 using namespace APIntOps; 4717 const APInt& C = L; 4718 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4719 // The B coefficient is M-N/2 4720 APInt B(M); 4721 B -= sdiv(N,Two); 4722 4723 // The A coefficient is N/2 4724 APInt A(N.sdiv(Two)); 4725 4726 // Compute the B^2-4ac term. 4727 APInt SqrtTerm(B); 4728 SqrtTerm *= B; 4729 SqrtTerm -= Four * (A * C); 4730 4731 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4732 // integer value or else APInt::sqrt() will assert. 4733 APInt SqrtVal(SqrtTerm.sqrt()); 4734 4735 // Compute the two solutions for the quadratic formula. 4736 // The divisions must be performed as signed divisions. 4737 APInt NegB(-B); 4738 APInt TwoA( A << 1 ); 4739 if (TwoA.isMinValue()) { 4740 const SCEV *CNC = SE.getCouldNotCompute(); 4741 return std::make_pair(CNC, CNC); 4742 } 4743 4744 LLVMContext &Context = SE.getContext(); 4745 4746 ConstantInt *Solution1 = 4747 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4748 ConstantInt *Solution2 = 4749 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4750 4751 return std::make_pair(SE.getConstant(Solution1), 4752 SE.getConstant(Solution2)); 4753 } // end APIntOps namespace 4754} 4755 4756/// HowFarToZero - Return the number of times a backedge comparing the specified 4757/// value to zero will execute. If not computable, return CouldNotCompute. 4758ScalarEvolution::BackedgeTakenInfo 4759ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4760 // If the value is a constant 4761 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4762 // If the value is already zero, the branch will execute zero times. 4763 if (C->getValue()->isZero()) return C; 4764 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4765 } 4766 4767 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4768 if (!AddRec || AddRec->getLoop() != L) 4769 return getCouldNotCompute(); 4770 4771 if (AddRec->isAffine()) { 4772 // If this is an affine expression, the execution count of this branch is 4773 // the minimum unsigned root of the following equation: 4774 // 4775 // Start + Step*N = 0 (mod 2^BW) 4776 // 4777 // equivalent to: 4778 // 4779 // Step*N = -Start (mod 2^BW) 4780 // 4781 // where BW is the common bit width of Start and Step. 4782 4783 // Get the initial value for the loop. 4784 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4785 L->getParentLoop()); 4786 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4787 L->getParentLoop()); 4788 4789 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4790 // For now we handle only constant steps. 4791 4792 // First, handle unitary steps. 4793 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4794 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4795 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4796 return Start; // N = Start (as unsigned) 4797 4798 // Then, try to solve the above equation provided that Start is constant. 4799 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4800 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4801 -StartC->getValue()->getValue(), 4802 *this); 4803 } 4804 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4805 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4806 // the quadratic equation to solve it. 4807 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4808 *this); 4809 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4810 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4811 if (R1) { 4812#if 0 4813 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4814 << " sol#2: " << *R2 << "\n"; 4815#endif 4816 // Pick the smallest positive root value. 4817 if (ConstantInt *CB = 4818 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4819 R1->getValue(), R2->getValue()))) { 4820 if (CB->getZExtValue() == false) 4821 std::swap(R1, R2); // R1 is the minimum root now. 4822 4823 // We can only use this value if the chrec ends up with an exact zero 4824 // value at this index. When solving for "X*X != 5", for example, we 4825 // should not accept a root of 2. 4826 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4827 if (Val->isZero()) 4828 return R1; // We found a quadratic root! 4829 } 4830 } 4831 } 4832 4833 return getCouldNotCompute(); 4834} 4835 4836/// HowFarToNonZero - Return the number of times a backedge checking the 4837/// specified value for nonzero will execute. If not computable, return 4838/// CouldNotCompute 4839ScalarEvolution::BackedgeTakenInfo 4840ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4841 // Loops that look like: while (X == 0) are very strange indeed. We don't 4842 // handle them yet except for the trivial case. This could be expanded in the 4843 // future as needed. 4844 4845 // If the value is a constant, check to see if it is known to be non-zero 4846 // already. If so, the backedge will execute zero times. 4847 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4848 if (!C->getValue()->isNullValue()) 4849 return getConstant(C->getType(), 0); 4850 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4851 } 4852 4853 // We could implement others, but I really doubt anyone writes loops like 4854 // this, and if they did, they would already be constant folded. 4855 return getCouldNotCompute(); 4856} 4857 4858/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4859/// (which may not be an immediate predecessor) which has exactly one 4860/// successor from which BB is reachable, or null if no such block is 4861/// found. 4862/// 4863std::pair<BasicBlock *, BasicBlock *> 4864ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4865 // If the block has a unique predecessor, then there is no path from the 4866 // predecessor to the block that does not go through the direct edge 4867 // from the predecessor to the block. 4868 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4869 return std::make_pair(Pred, BB); 4870 4871 // A loop's header is defined to be a block that dominates the loop. 4872 // If the header has a unique predecessor outside the loop, it must be 4873 // a block that has exactly one successor that can reach the loop. 4874 if (Loop *L = LI->getLoopFor(BB)) 4875 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4876 4877 return std::pair<BasicBlock *, BasicBlock *>(); 4878} 4879 4880/// HasSameValue - SCEV structural equivalence is usually sufficient for 4881/// testing whether two expressions are equal, however for the purposes of 4882/// looking for a condition guarding a loop, it can be useful to be a little 4883/// more general, since a front-end may have replicated the controlling 4884/// expression. 4885/// 4886static bool HasSameValue(const SCEV *A, const SCEV *B) { 4887 // Quick check to see if they are the same SCEV. 4888 if (A == B) return true; 4889 4890 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4891 // two different instructions with the same value. Check for this case. 4892 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4893 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4894 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4895 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4896 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4897 return true; 4898 4899 // Otherwise assume they may have a different value. 4900 return false; 4901} 4902 4903/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4904/// predicate Pred. Return true iff any changes were made. 4905/// 4906bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4907 const SCEV *&LHS, const SCEV *&RHS) { 4908 bool Changed = false; 4909 4910 // Canonicalize a constant to the right side. 4911 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4912 // Check for both operands constant. 4913 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4914 if (ConstantExpr::getICmp(Pred, 4915 LHSC->getValue(), 4916 RHSC->getValue())->isNullValue()) 4917 goto trivially_false; 4918 else 4919 goto trivially_true; 4920 } 4921 // Otherwise swap the operands to put the constant on the right. 4922 std::swap(LHS, RHS); 4923 Pred = ICmpInst::getSwappedPredicate(Pred); 4924 Changed = true; 4925 } 4926 4927 // If we're comparing an addrec with a value which is loop-invariant in the 4928 // addrec's loop, put the addrec on the left. Also make a dominance check, 4929 // as both operands could be addrecs loop-invariant in each other's loop. 4930 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4931 const Loop *L = AR->getLoop(); 4932 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4933 std::swap(LHS, RHS); 4934 Pred = ICmpInst::getSwappedPredicate(Pred); 4935 Changed = true; 4936 } 4937 } 4938 4939 // If there's a constant operand, canonicalize comparisons with boundary 4940 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4941 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4942 const APInt &RA = RC->getValue()->getValue(); 4943 switch (Pred) { 4944 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4945 case ICmpInst::ICMP_EQ: 4946 case ICmpInst::ICMP_NE: 4947 break; 4948 case ICmpInst::ICMP_UGE: 4949 if ((RA - 1).isMinValue()) { 4950 Pred = ICmpInst::ICMP_NE; 4951 RHS = getConstant(RA - 1); 4952 Changed = true; 4953 break; 4954 } 4955 if (RA.isMaxValue()) { 4956 Pred = ICmpInst::ICMP_EQ; 4957 Changed = true; 4958 break; 4959 } 4960 if (RA.isMinValue()) goto trivially_true; 4961 4962 Pred = ICmpInst::ICMP_UGT; 4963 RHS = getConstant(RA - 1); 4964 Changed = true; 4965 break; 4966 case ICmpInst::ICMP_ULE: 4967 if ((RA + 1).isMaxValue()) { 4968 Pred = ICmpInst::ICMP_NE; 4969 RHS = getConstant(RA + 1); 4970 Changed = true; 4971 break; 4972 } 4973 if (RA.isMinValue()) { 4974 Pred = ICmpInst::ICMP_EQ; 4975 Changed = true; 4976 break; 4977 } 4978 if (RA.isMaxValue()) goto trivially_true; 4979 4980 Pred = ICmpInst::ICMP_ULT; 4981 RHS = getConstant(RA + 1); 4982 Changed = true; 4983 break; 4984 case ICmpInst::ICMP_SGE: 4985 if ((RA - 1).isMinSignedValue()) { 4986 Pred = ICmpInst::ICMP_NE; 4987 RHS = getConstant(RA - 1); 4988 Changed = true; 4989 break; 4990 } 4991 if (RA.isMaxSignedValue()) { 4992 Pred = ICmpInst::ICMP_EQ; 4993 Changed = true; 4994 break; 4995 } 4996 if (RA.isMinSignedValue()) goto trivially_true; 4997 4998 Pred = ICmpInst::ICMP_SGT; 4999 RHS = getConstant(RA - 1); 5000 Changed = true; 5001 break; 5002 case ICmpInst::ICMP_SLE: 5003 if ((RA + 1).isMaxSignedValue()) { 5004 Pred = ICmpInst::ICMP_NE; 5005 RHS = getConstant(RA + 1); 5006 Changed = true; 5007 break; 5008 } 5009 if (RA.isMinSignedValue()) { 5010 Pred = ICmpInst::ICMP_EQ; 5011 Changed = true; 5012 break; 5013 } 5014 if (RA.isMaxSignedValue()) goto trivially_true; 5015 5016 Pred = ICmpInst::ICMP_SLT; 5017 RHS = getConstant(RA + 1); 5018 Changed = true; 5019 break; 5020 case ICmpInst::ICMP_UGT: 5021 if (RA.isMinValue()) { 5022 Pred = ICmpInst::ICMP_NE; 5023 Changed = true; 5024 break; 5025 } 5026 if ((RA + 1).isMaxValue()) { 5027 Pred = ICmpInst::ICMP_EQ; 5028 RHS = getConstant(RA + 1); 5029 Changed = true; 5030 break; 5031 } 5032 if (RA.isMaxValue()) goto trivially_false; 5033 break; 5034 case ICmpInst::ICMP_ULT: 5035 if (RA.isMaxValue()) { 5036 Pred = ICmpInst::ICMP_NE; 5037 Changed = true; 5038 break; 5039 } 5040 if ((RA - 1).isMinValue()) { 5041 Pred = ICmpInst::ICMP_EQ; 5042 RHS = getConstant(RA - 1); 5043 Changed = true; 5044 break; 5045 } 5046 if (RA.isMinValue()) goto trivially_false; 5047 break; 5048 case ICmpInst::ICMP_SGT: 5049 if (RA.isMinSignedValue()) { 5050 Pred = ICmpInst::ICMP_NE; 5051 Changed = true; 5052 break; 5053 } 5054 if ((RA + 1).isMaxSignedValue()) { 5055 Pred = ICmpInst::ICMP_EQ; 5056 RHS = getConstant(RA + 1); 5057 Changed = true; 5058 break; 5059 } 5060 if (RA.isMaxSignedValue()) goto trivially_false; 5061 break; 5062 case ICmpInst::ICMP_SLT: 5063 if (RA.isMaxSignedValue()) { 5064 Pred = ICmpInst::ICMP_NE; 5065 Changed = true; 5066 break; 5067 } 5068 if ((RA - 1).isMinSignedValue()) { 5069 Pred = ICmpInst::ICMP_EQ; 5070 RHS = getConstant(RA - 1); 5071 Changed = true; 5072 break; 5073 } 5074 if (RA.isMinSignedValue()) goto trivially_false; 5075 break; 5076 } 5077 } 5078 5079 // Check for obvious equality. 5080 if (HasSameValue(LHS, RHS)) { 5081 if (ICmpInst::isTrueWhenEqual(Pred)) 5082 goto trivially_true; 5083 if (ICmpInst::isFalseWhenEqual(Pred)) 5084 goto trivially_false; 5085 } 5086 5087 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5088 // adding or subtracting 1 from one of the operands. 5089 switch (Pred) { 5090 case ICmpInst::ICMP_SLE: 5091 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5092 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5093 /*HasNUW=*/false, /*HasNSW=*/true); 5094 Pred = ICmpInst::ICMP_SLT; 5095 Changed = true; 5096 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5097 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5098 /*HasNUW=*/false, /*HasNSW=*/true); 5099 Pred = ICmpInst::ICMP_SLT; 5100 Changed = true; 5101 } 5102 break; 5103 case ICmpInst::ICMP_SGE: 5104 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5105 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5106 /*HasNUW=*/false, /*HasNSW=*/true); 5107 Pred = ICmpInst::ICMP_SGT; 5108 Changed = true; 5109 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5110 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5111 /*HasNUW=*/false, /*HasNSW=*/true); 5112 Pred = ICmpInst::ICMP_SGT; 5113 Changed = true; 5114 } 5115 break; 5116 case ICmpInst::ICMP_ULE: 5117 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5118 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5119 /*HasNUW=*/true, /*HasNSW=*/false); 5120 Pred = ICmpInst::ICMP_ULT; 5121 Changed = true; 5122 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5123 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5124 /*HasNUW=*/true, /*HasNSW=*/false); 5125 Pred = ICmpInst::ICMP_ULT; 5126 Changed = true; 5127 } 5128 break; 5129 case ICmpInst::ICMP_UGE: 5130 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5131 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5132 /*HasNUW=*/true, /*HasNSW=*/false); 5133 Pred = ICmpInst::ICMP_UGT; 5134 Changed = true; 5135 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5136 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5137 /*HasNUW=*/true, /*HasNSW=*/false); 5138 Pred = ICmpInst::ICMP_UGT; 5139 Changed = true; 5140 } 5141 break; 5142 default: 5143 break; 5144 } 5145 5146 // TODO: More simplifications are possible here. 5147 5148 return Changed; 5149 5150trivially_true: 5151 // Return 0 == 0. 5152 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5153 Pred = ICmpInst::ICMP_EQ; 5154 return true; 5155 5156trivially_false: 5157 // Return 0 != 0. 5158 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5159 Pred = ICmpInst::ICMP_NE; 5160 return true; 5161} 5162 5163bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5164 return getSignedRange(S).getSignedMax().isNegative(); 5165} 5166 5167bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5168 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5169} 5170 5171bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5172 return !getSignedRange(S).getSignedMin().isNegative(); 5173} 5174 5175bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5176 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5177} 5178 5179bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5180 return isKnownNegative(S) || isKnownPositive(S); 5181} 5182 5183bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5184 const SCEV *LHS, const SCEV *RHS) { 5185 // Canonicalize the inputs first. 5186 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5187 5188 // If LHS or RHS is an addrec, check to see if the condition is true in 5189 // every iteration of the loop. 5190 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5191 if (isLoopEntryGuardedByCond( 5192 AR->getLoop(), Pred, AR->getStart(), RHS) && 5193 isLoopBackedgeGuardedByCond( 5194 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5195 return true; 5196 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5197 if (isLoopEntryGuardedByCond( 5198 AR->getLoop(), Pred, LHS, AR->getStart()) && 5199 isLoopBackedgeGuardedByCond( 5200 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5201 return true; 5202 5203 // Otherwise see what can be done with known constant ranges. 5204 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5205} 5206 5207bool 5208ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5209 const SCEV *LHS, const SCEV *RHS) { 5210 if (HasSameValue(LHS, RHS)) 5211 return ICmpInst::isTrueWhenEqual(Pred); 5212 5213 // This code is split out from isKnownPredicate because it is called from 5214 // within isLoopEntryGuardedByCond. 5215 switch (Pred) { 5216 default: 5217 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5218 break; 5219 case ICmpInst::ICMP_SGT: 5220 Pred = ICmpInst::ICMP_SLT; 5221 std::swap(LHS, RHS); 5222 case ICmpInst::ICMP_SLT: { 5223 ConstantRange LHSRange = getSignedRange(LHS); 5224 ConstantRange RHSRange = getSignedRange(RHS); 5225 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5226 return true; 5227 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5228 return false; 5229 break; 5230 } 5231 case ICmpInst::ICMP_SGE: 5232 Pred = ICmpInst::ICMP_SLE; 5233 std::swap(LHS, RHS); 5234 case ICmpInst::ICMP_SLE: { 5235 ConstantRange LHSRange = getSignedRange(LHS); 5236 ConstantRange RHSRange = getSignedRange(RHS); 5237 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5238 return true; 5239 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5240 return false; 5241 break; 5242 } 5243 case ICmpInst::ICMP_UGT: 5244 Pred = ICmpInst::ICMP_ULT; 5245 std::swap(LHS, RHS); 5246 case ICmpInst::ICMP_ULT: { 5247 ConstantRange LHSRange = getUnsignedRange(LHS); 5248 ConstantRange RHSRange = getUnsignedRange(RHS); 5249 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5250 return true; 5251 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5252 return false; 5253 break; 5254 } 5255 case ICmpInst::ICMP_UGE: 5256 Pred = ICmpInst::ICMP_ULE; 5257 std::swap(LHS, RHS); 5258 case ICmpInst::ICMP_ULE: { 5259 ConstantRange LHSRange = getUnsignedRange(LHS); 5260 ConstantRange RHSRange = getUnsignedRange(RHS); 5261 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5262 return true; 5263 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5264 return false; 5265 break; 5266 } 5267 case ICmpInst::ICMP_NE: { 5268 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5269 return true; 5270 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5271 return true; 5272 5273 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5274 if (isKnownNonZero(Diff)) 5275 return true; 5276 break; 5277 } 5278 case ICmpInst::ICMP_EQ: 5279 // The check at the top of the function catches the case where 5280 // the values are known to be equal. 5281 break; 5282 } 5283 return false; 5284} 5285 5286/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5287/// protected by a conditional between LHS and RHS. This is used to 5288/// to eliminate casts. 5289bool 5290ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5291 ICmpInst::Predicate Pred, 5292 const SCEV *LHS, const SCEV *RHS) { 5293 // Interpret a null as meaning no loop, where there is obviously no guard 5294 // (interprocedural conditions notwithstanding). 5295 if (!L) return true; 5296 5297 BasicBlock *Latch = L->getLoopLatch(); 5298 if (!Latch) 5299 return false; 5300 5301 BranchInst *LoopContinuePredicate = 5302 dyn_cast<BranchInst>(Latch->getTerminator()); 5303 if (!LoopContinuePredicate || 5304 LoopContinuePredicate->isUnconditional()) 5305 return false; 5306 5307 return isImpliedCond(Pred, LHS, RHS, 5308 LoopContinuePredicate->getCondition(), 5309 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5310} 5311 5312/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5313/// by a conditional between LHS and RHS. This is used to help avoid max 5314/// expressions in loop trip counts, and to eliminate casts. 5315bool 5316ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5317 ICmpInst::Predicate Pred, 5318 const SCEV *LHS, const SCEV *RHS) { 5319 // Interpret a null as meaning no loop, where there is obviously no guard 5320 // (interprocedural conditions notwithstanding). 5321 if (!L) return false; 5322 5323 // Starting at the loop predecessor, climb up the predecessor chain, as long 5324 // as there are predecessors that can be found that have unique successors 5325 // leading to the original header. 5326 for (std::pair<BasicBlock *, BasicBlock *> 5327 Pair(L->getLoopPredecessor(), L->getHeader()); 5328 Pair.first; 5329 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5330 5331 BranchInst *LoopEntryPredicate = 5332 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5333 if (!LoopEntryPredicate || 5334 LoopEntryPredicate->isUnconditional()) 5335 continue; 5336 5337 if (isImpliedCond(Pred, LHS, RHS, 5338 LoopEntryPredicate->getCondition(), 5339 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5340 return true; 5341 } 5342 5343 return false; 5344} 5345 5346/// isImpliedCond - Test whether the condition described by Pred, LHS, 5347/// and RHS is true whenever the given Cond value evaluates to true. 5348bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5349 const SCEV *LHS, const SCEV *RHS, 5350 Value *FoundCondValue, 5351 bool Inverse) { 5352 // Recursively handle And and Or conditions. 5353 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5354 if (BO->getOpcode() == Instruction::And) { 5355 if (!Inverse) 5356 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5357 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5358 } else if (BO->getOpcode() == Instruction::Or) { 5359 if (Inverse) 5360 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5361 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5362 } 5363 } 5364 5365 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5366 if (!ICI) return false; 5367 5368 // Bail if the ICmp's operands' types are wider than the needed type 5369 // before attempting to call getSCEV on them. This avoids infinite 5370 // recursion, since the analysis of widening casts can require loop 5371 // exit condition information for overflow checking, which would 5372 // lead back here. 5373 if (getTypeSizeInBits(LHS->getType()) < 5374 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5375 return false; 5376 5377 // Now that we found a conditional branch that dominates the loop, check to 5378 // see if it is the comparison we are looking for. 5379 ICmpInst::Predicate FoundPred; 5380 if (Inverse) 5381 FoundPred = ICI->getInversePredicate(); 5382 else 5383 FoundPred = ICI->getPredicate(); 5384 5385 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5386 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5387 5388 // Balance the types. The case where FoundLHS' type is wider than 5389 // LHS' type is checked for above. 5390 if (getTypeSizeInBits(LHS->getType()) > 5391 getTypeSizeInBits(FoundLHS->getType())) { 5392 if (CmpInst::isSigned(Pred)) { 5393 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5394 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5395 } else { 5396 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5397 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5398 } 5399 } 5400 5401 // Canonicalize the query to match the way instcombine will have 5402 // canonicalized the comparison. 5403 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5404 if (LHS == RHS) 5405 return CmpInst::isTrueWhenEqual(Pred); 5406 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5407 if (FoundLHS == FoundRHS) 5408 return CmpInst::isFalseWhenEqual(Pred); 5409 5410 // Check to see if we can make the LHS or RHS match. 5411 if (LHS == FoundRHS || RHS == FoundLHS) { 5412 if (isa<SCEVConstant>(RHS)) { 5413 std::swap(FoundLHS, FoundRHS); 5414 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5415 } else { 5416 std::swap(LHS, RHS); 5417 Pred = ICmpInst::getSwappedPredicate(Pred); 5418 } 5419 } 5420 5421 // Check whether the found predicate is the same as the desired predicate. 5422 if (FoundPred == Pred) 5423 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5424 5425 // Check whether swapping the found predicate makes it the same as the 5426 // desired predicate. 5427 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5428 if (isa<SCEVConstant>(RHS)) 5429 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5430 else 5431 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5432 RHS, LHS, FoundLHS, FoundRHS); 5433 } 5434 5435 // Check whether the actual condition is beyond sufficient. 5436 if (FoundPred == ICmpInst::ICMP_EQ) 5437 if (ICmpInst::isTrueWhenEqual(Pred)) 5438 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5439 return true; 5440 if (Pred == ICmpInst::ICMP_NE) 5441 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5442 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5443 return true; 5444 5445 // Otherwise assume the worst. 5446 return false; 5447} 5448 5449/// isImpliedCondOperands - Test whether the condition described by Pred, 5450/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5451/// and FoundRHS is true. 5452bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5453 const SCEV *LHS, const SCEV *RHS, 5454 const SCEV *FoundLHS, 5455 const SCEV *FoundRHS) { 5456 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5457 FoundLHS, FoundRHS) || 5458 // ~x < ~y --> x > y 5459 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5460 getNotSCEV(FoundRHS), 5461 getNotSCEV(FoundLHS)); 5462} 5463 5464/// isImpliedCondOperandsHelper - Test whether the condition described by 5465/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5466/// FoundLHS, and FoundRHS is true. 5467bool 5468ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5469 const SCEV *LHS, const SCEV *RHS, 5470 const SCEV *FoundLHS, 5471 const SCEV *FoundRHS) { 5472 switch (Pred) { 5473 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5474 case ICmpInst::ICMP_EQ: 5475 case ICmpInst::ICMP_NE: 5476 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5477 return true; 5478 break; 5479 case ICmpInst::ICMP_SLT: 5480 case ICmpInst::ICMP_SLE: 5481 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5482 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5483 return true; 5484 break; 5485 case ICmpInst::ICMP_SGT: 5486 case ICmpInst::ICMP_SGE: 5487 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5488 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5489 return true; 5490 break; 5491 case ICmpInst::ICMP_ULT: 5492 case ICmpInst::ICMP_ULE: 5493 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5494 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5495 return true; 5496 break; 5497 case ICmpInst::ICMP_UGT: 5498 case ICmpInst::ICMP_UGE: 5499 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5500 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5501 return true; 5502 break; 5503 } 5504 5505 return false; 5506} 5507 5508/// getBECount - Subtract the end and start values and divide by the step, 5509/// rounding up, to get the number of times the backedge is executed. Return 5510/// CouldNotCompute if an intermediate computation overflows. 5511const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5512 const SCEV *End, 5513 const SCEV *Step, 5514 bool NoWrap) { 5515 assert(!isKnownNegative(Step) && 5516 "This code doesn't handle negative strides yet!"); 5517 5518 const Type *Ty = Start->getType(); 5519 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5520 const SCEV *Diff = getMinusSCEV(End, Start); 5521 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5522 5523 // Add an adjustment to the difference between End and Start so that 5524 // the division will effectively round up. 5525 const SCEV *Add = getAddExpr(Diff, RoundUp); 5526 5527 if (!NoWrap) { 5528 // Check Add for unsigned overflow. 5529 // TODO: More sophisticated things could be done here. 5530 const Type *WideTy = IntegerType::get(getContext(), 5531 getTypeSizeInBits(Ty) + 1); 5532 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5533 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5534 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5535 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5536 return getCouldNotCompute(); 5537 } 5538 5539 return getUDivExpr(Add, Step); 5540} 5541 5542/// HowManyLessThans - Return the number of times a backedge containing the 5543/// specified less-than comparison will execute. If not computable, return 5544/// CouldNotCompute. 5545ScalarEvolution::BackedgeTakenInfo 5546ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5547 const Loop *L, bool isSigned) { 5548 // Only handle: "ADDREC < LoopInvariant". 5549 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5550 5551 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5552 if (!AddRec || AddRec->getLoop() != L) 5553 return getCouldNotCompute(); 5554 5555 // Check to see if we have a flag which makes analysis easy. 5556 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5557 AddRec->hasNoUnsignedWrap(); 5558 5559 if (AddRec->isAffine()) { 5560 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5561 const SCEV *Step = AddRec->getStepRecurrence(*this); 5562 5563 if (Step->isZero()) 5564 return getCouldNotCompute(); 5565 if (Step->isOne()) { 5566 // With unit stride, the iteration never steps past the limit value. 5567 } else if (isKnownPositive(Step)) { 5568 // Test whether a positive iteration can step past the limit 5569 // value and past the maximum value for its type in a single step. 5570 // Note that it's not sufficient to check NoWrap here, because even 5571 // though the value after a wrap is undefined, it's not undefined 5572 // behavior, so if wrap does occur, the loop could either terminate or 5573 // loop infinitely, but in either case, the loop is guaranteed to 5574 // iterate at least until the iteration where the wrapping occurs. 5575 const SCEV *One = getConstant(Step->getType(), 1); 5576 if (isSigned) { 5577 APInt Max = APInt::getSignedMaxValue(BitWidth); 5578 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5579 .slt(getSignedRange(RHS).getSignedMax())) 5580 return getCouldNotCompute(); 5581 } else { 5582 APInt Max = APInt::getMaxValue(BitWidth); 5583 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5584 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5585 return getCouldNotCompute(); 5586 } 5587 } else 5588 // TODO: Handle negative strides here and below. 5589 return getCouldNotCompute(); 5590 5591 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5592 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5593 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5594 // treat m-n as signed nor unsigned due to overflow possibility. 5595 5596 // First, we get the value of the LHS in the first iteration: n 5597 const SCEV *Start = AddRec->getOperand(0); 5598 5599 // Determine the minimum constant start value. 5600 const SCEV *MinStart = getConstant(isSigned ? 5601 getSignedRange(Start).getSignedMin() : 5602 getUnsignedRange(Start).getUnsignedMin()); 5603 5604 // If we know that the condition is true in order to enter the loop, 5605 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5606 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5607 // the division must round up. 5608 const SCEV *End = RHS; 5609 if (!isLoopEntryGuardedByCond(L, 5610 isSigned ? ICmpInst::ICMP_SLT : 5611 ICmpInst::ICMP_ULT, 5612 getMinusSCEV(Start, Step), RHS)) 5613 End = isSigned ? getSMaxExpr(RHS, Start) 5614 : getUMaxExpr(RHS, Start); 5615 5616 // Determine the maximum constant end value. 5617 const SCEV *MaxEnd = getConstant(isSigned ? 5618 getSignedRange(End).getSignedMax() : 5619 getUnsignedRange(End).getUnsignedMax()); 5620 5621 // If MaxEnd is within a step of the maximum integer value in its type, 5622 // adjust it down to the minimum value which would produce the same effect. 5623 // This allows the subsequent ceiling division of (N+(step-1))/step to 5624 // compute the correct value. 5625 const SCEV *StepMinusOne = getMinusSCEV(Step, 5626 getConstant(Step->getType(), 1)); 5627 MaxEnd = isSigned ? 5628 getSMinExpr(MaxEnd, 5629 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5630 StepMinusOne)) : 5631 getUMinExpr(MaxEnd, 5632 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5633 StepMinusOne)); 5634 5635 // Finally, we subtract these two values and divide, rounding up, to get 5636 // the number of times the backedge is executed. 5637 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5638 5639 // The maximum backedge count is similar, except using the minimum start 5640 // value and the maximum end value. 5641 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5642 5643 return BackedgeTakenInfo(BECount, MaxBECount); 5644 } 5645 5646 return getCouldNotCompute(); 5647} 5648 5649/// getNumIterationsInRange - Return the number of iterations of this loop that 5650/// produce values in the specified constant range. Another way of looking at 5651/// this is that it returns the first iteration number where the value is not in 5652/// the condition, thus computing the exit count. If the iteration count can't 5653/// be computed, an instance of SCEVCouldNotCompute is returned. 5654const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5655 ScalarEvolution &SE) const { 5656 if (Range.isFullSet()) // Infinite loop. 5657 return SE.getCouldNotCompute(); 5658 5659 // If the start is a non-zero constant, shift the range to simplify things. 5660 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5661 if (!SC->getValue()->isZero()) { 5662 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5663 Operands[0] = SE.getConstant(SC->getType(), 0); 5664 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5665 if (const SCEVAddRecExpr *ShiftedAddRec = 5666 dyn_cast<SCEVAddRecExpr>(Shifted)) 5667 return ShiftedAddRec->getNumIterationsInRange( 5668 Range.subtract(SC->getValue()->getValue()), SE); 5669 // This is strange and shouldn't happen. 5670 return SE.getCouldNotCompute(); 5671 } 5672 5673 // The only time we can solve this is when we have all constant indices. 5674 // Otherwise, we cannot determine the overflow conditions. 5675 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5676 if (!isa<SCEVConstant>(getOperand(i))) 5677 return SE.getCouldNotCompute(); 5678 5679 5680 // Okay at this point we know that all elements of the chrec are constants and 5681 // that the start element is zero. 5682 5683 // First check to see if the range contains zero. If not, the first 5684 // iteration exits. 5685 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5686 if (!Range.contains(APInt(BitWidth, 0))) 5687 return SE.getConstant(getType(), 0); 5688 5689 if (isAffine()) { 5690 // If this is an affine expression then we have this situation: 5691 // Solve {0,+,A} in Range === Ax in Range 5692 5693 // We know that zero is in the range. If A is positive then we know that 5694 // the upper value of the range must be the first possible exit value. 5695 // If A is negative then the lower of the range is the last possible loop 5696 // value. Also note that we already checked for a full range. 5697 APInt One(BitWidth,1); 5698 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5699 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5700 5701 // The exit value should be (End+A)/A. 5702 APInt ExitVal = (End + A).udiv(A); 5703 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5704 5705 // Evaluate at the exit value. If we really did fall out of the valid 5706 // range, then we computed our trip count, otherwise wrap around or other 5707 // things must have happened. 5708 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5709 if (Range.contains(Val->getValue())) 5710 return SE.getCouldNotCompute(); // Something strange happened 5711 5712 // Ensure that the previous value is in the range. This is a sanity check. 5713 assert(Range.contains( 5714 EvaluateConstantChrecAtConstant(this, 5715 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5716 "Linear scev computation is off in a bad way!"); 5717 return SE.getConstant(ExitValue); 5718 } else if (isQuadratic()) { 5719 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5720 // quadratic equation to solve it. To do this, we must frame our problem in 5721 // terms of figuring out when zero is crossed, instead of when 5722 // Range.getUpper() is crossed. 5723 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5724 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5725 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5726 5727 // Next, solve the constructed addrec 5728 std::pair<const SCEV *,const SCEV *> Roots = 5729 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5730 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5731 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5732 if (R1) { 5733 // Pick the smallest positive root value. 5734 if (ConstantInt *CB = 5735 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5736 R1->getValue(), R2->getValue()))) { 5737 if (CB->getZExtValue() == false) 5738 std::swap(R1, R2); // R1 is the minimum root now. 5739 5740 // Make sure the root is not off by one. The returned iteration should 5741 // not be in the range, but the previous one should be. When solving 5742 // for "X*X < 5", for example, we should not return a root of 2. 5743 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5744 R1->getValue(), 5745 SE); 5746 if (Range.contains(R1Val->getValue())) { 5747 // The next iteration must be out of the range... 5748 ConstantInt *NextVal = 5749 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5750 5751 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5752 if (!Range.contains(R1Val->getValue())) 5753 return SE.getConstant(NextVal); 5754 return SE.getCouldNotCompute(); // Something strange happened 5755 } 5756 5757 // If R1 was not in the range, then it is a good return value. Make 5758 // sure that R1-1 WAS in the range though, just in case. 5759 ConstantInt *NextVal = 5760 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5761 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5762 if (Range.contains(R1Val->getValue())) 5763 return R1; 5764 return SE.getCouldNotCompute(); // Something strange happened 5765 } 5766 } 5767 } 5768 5769 return SE.getCouldNotCompute(); 5770} 5771 5772 5773 5774//===----------------------------------------------------------------------===// 5775// SCEVCallbackVH Class Implementation 5776//===----------------------------------------------------------------------===// 5777 5778void ScalarEvolution::SCEVCallbackVH::deleted() { 5779 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5780 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5781 SE->ConstantEvolutionLoopExitValue.erase(PN); 5782 SE->ValueExprMap.erase(getValPtr()); 5783 // this now dangles! 5784} 5785 5786void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5787 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5788 5789 // Forget all the expressions associated with users of the old value, 5790 // so that future queries will recompute the expressions using the new 5791 // value. 5792 Value *Old = getValPtr(); 5793 SmallVector<User *, 16> Worklist; 5794 SmallPtrSet<User *, 8> Visited; 5795 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5796 UI != UE; ++UI) 5797 Worklist.push_back(*UI); 5798 while (!Worklist.empty()) { 5799 User *U = Worklist.pop_back_val(); 5800 // Deleting the Old value will cause this to dangle. Postpone 5801 // that until everything else is done. 5802 if (U == Old) 5803 continue; 5804 if (!Visited.insert(U)) 5805 continue; 5806 if (PHINode *PN = dyn_cast<PHINode>(U)) 5807 SE->ConstantEvolutionLoopExitValue.erase(PN); 5808 SE->ValueExprMap.erase(U); 5809 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5810 UI != UE; ++UI) 5811 Worklist.push_back(*UI); 5812 } 5813 // Delete the Old value. 5814 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5815 SE->ConstantEvolutionLoopExitValue.erase(PN); 5816 SE->ValueExprMap.erase(Old); 5817 // this now dangles! 5818} 5819 5820ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5821 : CallbackVH(V), SE(se) {} 5822 5823//===----------------------------------------------------------------------===// 5824// ScalarEvolution Class Implementation 5825//===----------------------------------------------------------------------===// 5826 5827ScalarEvolution::ScalarEvolution() 5828 : FunctionPass(ID), FirstUnknown(0) { 5829} 5830 5831bool ScalarEvolution::runOnFunction(Function &F) { 5832 this->F = &F; 5833 LI = &getAnalysis<LoopInfo>(); 5834 TD = getAnalysisIfAvailable<TargetData>(); 5835 DT = &getAnalysis<DominatorTree>(); 5836 return false; 5837} 5838 5839void ScalarEvolution::releaseMemory() { 5840 // Iterate through all the SCEVUnknown instances and call their 5841 // destructors, so that they release their references to their values. 5842 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5843 U->~SCEVUnknown(); 5844 FirstUnknown = 0; 5845 5846 ValueExprMap.clear(); 5847 BackedgeTakenCounts.clear(); 5848 ConstantEvolutionLoopExitValue.clear(); 5849 ValuesAtScopes.clear(); 5850 UniqueSCEVs.clear(); 5851 SCEVAllocator.Reset(); 5852} 5853 5854void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5855 AU.setPreservesAll(); 5856 AU.addRequiredTransitive<LoopInfo>(); 5857 AU.addRequiredTransitive<DominatorTree>(); 5858} 5859 5860bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5861 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5862} 5863 5864static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5865 const Loop *L) { 5866 // Print all inner loops first 5867 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5868 PrintLoopInfo(OS, SE, *I); 5869 5870 OS << "Loop "; 5871 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5872 OS << ": "; 5873 5874 SmallVector<BasicBlock *, 8> ExitBlocks; 5875 L->getExitBlocks(ExitBlocks); 5876 if (ExitBlocks.size() != 1) 5877 OS << "<multiple exits> "; 5878 5879 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5880 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5881 } else { 5882 OS << "Unpredictable backedge-taken count. "; 5883 } 5884 5885 OS << "\n" 5886 "Loop "; 5887 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5888 OS << ": "; 5889 5890 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5891 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5892 } else { 5893 OS << "Unpredictable max backedge-taken count. "; 5894 } 5895 5896 OS << "\n"; 5897} 5898 5899void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5900 // ScalarEvolution's implementation of the print method is to print 5901 // out SCEV values of all instructions that are interesting. Doing 5902 // this potentially causes it to create new SCEV objects though, 5903 // which technically conflicts with the const qualifier. This isn't 5904 // observable from outside the class though, so casting away the 5905 // const isn't dangerous. 5906 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5907 5908 OS << "Classifying expressions for: "; 5909 WriteAsOperand(OS, F, /*PrintType=*/false); 5910 OS << "\n"; 5911 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5912 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5913 OS << *I << '\n'; 5914 OS << " --> "; 5915 const SCEV *SV = SE.getSCEV(&*I); 5916 SV->print(OS); 5917 5918 const Loop *L = LI->getLoopFor((*I).getParent()); 5919 5920 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5921 if (AtUse != SV) { 5922 OS << " --> "; 5923 AtUse->print(OS); 5924 } 5925 5926 if (L) { 5927 OS << "\t\t" "Exits: "; 5928 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5929 if (!ExitValue->isLoopInvariant(L)) { 5930 OS << "<<Unknown>>"; 5931 } else { 5932 OS << *ExitValue; 5933 } 5934 } 5935 5936 OS << "\n"; 5937 } 5938 5939 OS << "Determining loop execution counts for: "; 5940 WriteAsOperand(OS, F, /*PrintType=*/false); 5941 OS << "\n"; 5942 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5943 PrintLoopInfo(OS, &SE, *I); 5944} 5945 5946