ScalarEvolution.cpp revision 212904
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 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 708 if (SCEVComplexityCompare(LI)(RHS, LHS)) 709 std::swap(LHS, RHS); 710 return; 711 } 712 713 // Do the rough sort by complexity. 714 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 715 716 // Now that we are sorted by complexity, group elements of the same 717 // complexity. Note that this is, at worst, N^2, but the vector is likely to 718 // be extremely short in practice. Note that we take this approach because we 719 // do not want to depend on the addresses of the objects we are grouping. 720 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 721 const SCEV *S = Ops[i]; 722 unsigned Complexity = S->getSCEVType(); 723 724 // If there are any objects of the same complexity and same value as this 725 // one, group them. 726 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 727 if (Ops[j] == S) { // Found a duplicate. 728 // Move it to immediately after i'th element. 729 std::swap(Ops[i+1], Ops[j]); 730 ++i; // no need to rescan it. 731 if (i == e-2) return; // Done! 732 } 733 } 734 } 735} 736 737 738 739//===----------------------------------------------------------------------===// 740// Simple SCEV method implementations 741//===----------------------------------------------------------------------===// 742 743/// BinomialCoefficient - Compute BC(It, K). The result has width W. 744/// Assume, K > 0. 745static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 746 ScalarEvolution &SE, 747 const Type* ResultTy) { 748 // Handle the simplest case efficiently. 749 if (K == 1) 750 return SE.getTruncateOrZeroExtend(It, ResultTy); 751 752 // We are using the following formula for BC(It, K): 753 // 754 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 755 // 756 // Suppose, W is the bitwidth of the return value. We must be prepared for 757 // overflow. Hence, we must assure that the result of our computation is 758 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 759 // safe in modular arithmetic. 760 // 761 // However, this code doesn't use exactly that formula; the formula it uses 762 // is something like the following, where T is the number of factors of 2 in 763 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 764 // exponentiation: 765 // 766 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 767 // 768 // This formula is trivially equivalent to the previous formula. However, 769 // this formula can be implemented much more efficiently. The trick is that 770 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 771 // arithmetic. To do exact division in modular arithmetic, all we have 772 // to do is multiply by the inverse. Therefore, this step can be done at 773 // width W. 774 // 775 // The next issue is how to safely do the division by 2^T. The way this 776 // is done is by doing the multiplication step at a width of at least W + T 777 // bits. This way, the bottom W+T bits of the product are accurate. Then, 778 // when we perform the division by 2^T (which is equivalent to a right shift 779 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 780 // truncated out after the division by 2^T. 781 // 782 // In comparison to just directly using the first formula, this technique 783 // is much more efficient; using the first formula requires W * K bits, 784 // but this formula less than W + K bits. Also, the first formula requires 785 // a division step, whereas this formula only requires multiplies and shifts. 786 // 787 // It doesn't matter whether the subtraction step is done in the calculation 788 // width or the input iteration count's width; if the subtraction overflows, 789 // the result must be zero anyway. We prefer here to do it in the width of 790 // the induction variable because it helps a lot for certain cases; CodeGen 791 // isn't smart enough to ignore the overflow, which leads to much less 792 // efficient code if the width of the subtraction is wider than the native 793 // register width. 794 // 795 // (It's possible to not widen at all by pulling out factors of 2 before 796 // the multiplication; for example, K=2 can be calculated as 797 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 798 // extra arithmetic, so it's not an obvious win, and it gets 799 // much more complicated for K > 3.) 800 801 // Protection from insane SCEVs; this bound is conservative, 802 // but it probably doesn't matter. 803 if (K > 1000) 804 return SE.getCouldNotCompute(); 805 806 unsigned W = SE.getTypeSizeInBits(ResultTy); 807 808 // Calculate K! / 2^T and T; we divide out the factors of two before 809 // multiplying for calculating K! / 2^T to avoid overflow. 810 // Other overflow doesn't matter because we only care about the bottom 811 // W bits of the result. 812 APInt OddFactorial(W, 1); 813 unsigned T = 1; 814 for (unsigned i = 3; i <= K; ++i) { 815 APInt Mult(W, i); 816 unsigned TwoFactors = Mult.countTrailingZeros(); 817 T += TwoFactors; 818 Mult = Mult.lshr(TwoFactors); 819 OddFactorial *= Mult; 820 } 821 822 // We need at least W + T bits for the multiplication step 823 unsigned CalculationBits = W + T; 824 825 // Calculate 2^T, at width T+W. 826 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 827 828 // Calculate the multiplicative inverse of K! / 2^T; 829 // this multiplication factor will perform the exact division by 830 // K! / 2^T. 831 APInt Mod = APInt::getSignedMinValue(W+1); 832 APInt MultiplyFactor = OddFactorial.zext(W+1); 833 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 834 MultiplyFactor = MultiplyFactor.trunc(W); 835 836 // Calculate the product, at width T+W 837 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 838 CalculationBits); 839 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 840 for (unsigned i = 1; i != K; ++i) { 841 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 842 Dividend = SE.getMulExpr(Dividend, 843 SE.getTruncateOrZeroExtend(S, CalculationTy)); 844 } 845 846 // Divide by 2^T 847 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 848 849 // Truncate the result, and divide by K! / 2^T. 850 851 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 852 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 853} 854 855/// evaluateAtIteration - Return the value of this chain of recurrences at 856/// the specified iteration number. We can evaluate this recurrence by 857/// multiplying each element in the chain by the binomial coefficient 858/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 859/// 860/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 861/// 862/// where BC(It, k) stands for binomial coefficient. 863/// 864const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 865 ScalarEvolution &SE) const { 866 const SCEV *Result = getStart(); 867 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 868 // The computation is correct in the face of overflow provided that the 869 // multiplication is performed _after_ the evaluation of the binomial 870 // coefficient. 871 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 872 if (isa<SCEVCouldNotCompute>(Coeff)) 873 return Coeff; 874 875 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 876 } 877 return Result; 878} 879 880//===----------------------------------------------------------------------===// 881// SCEV Expression folder implementations 882//===----------------------------------------------------------------------===// 883 884const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 885 const Type *Ty) { 886 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 887 "This is not a truncating conversion!"); 888 assert(isSCEVable(Ty) && 889 "This is not a conversion to a SCEVable type!"); 890 Ty = getEffectiveSCEVType(Ty); 891 892 FoldingSetNodeID ID; 893 ID.AddInteger(scTruncate); 894 ID.AddPointer(Op); 895 ID.AddPointer(Ty); 896 void *IP = 0; 897 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 898 899 // Fold if the operand is constant. 900 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 901 return getConstant( 902 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 903 getEffectiveSCEVType(Ty)))); 904 905 // trunc(trunc(x)) --> trunc(x) 906 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 907 return getTruncateExpr(ST->getOperand(), Ty); 908 909 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 910 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 911 return getTruncateOrSignExtend(SS->getOperand(), Ty); 912 913 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 915 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 916 917 // If the input value is a chrec scev, truncate the chrec's operands. 918 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 919 SmallVector<const SCEV *, 4> Operands; 920 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 921 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 922 return getAddRecExpr(Operands, AddRec->getLoop()); 923 } 924 925 // As a special case, fold trunc(undef) to undef. We don't want to 926 // know too much about SCEVUnknowns, but this special case is handy 927 // and harmless. 928 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 929 if (isa<UndefValue>(U->getValue())) 930 return getSCEV(UndefValue::get(Ty)); 931 932 // The cast wasn't folded; create an explicit cast node. We can reuse 933 // the existing insert position since if we get here, we won't have 934 // made any changes which would invalidate it. 935 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 936 Op, Ty); 937 UniqueSCEVs.InsertNode(S, IP); 938 return S; 939} 940 941const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 942 const Type *Ty) { 943 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 944 "This is not an extending conversion!"); 945 assert(isSCEVable(Ty) && 946 "This is not a conversion to a SCEVable type!"); 947 Ty = getEffectiveSCEVType(Ty); 948 949 // Fold if the operand is constant. 950 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 951 return getConstant( 952 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 953 getEffectiveSCEVType(Ty)))); 954 955 // zext(zext(x)) --> zext(x) 956 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 957 return getZeroExtendExpr(SZ->getOperand(), Ty); 958 959 // Before doing any expensive analysis, check to see if we've already 960 // computed a SCEV for this Op and Ty. 961 FoldingSetNodeID ID; 962 ID.AddInteger(scZeroExtend); 963 ID.AddPointer(Op); 964 ID.AddPointer(Ty); 965 void *IP = 0; 966 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 967 968 // If the input value is a chrec scev, and we can prove that the value 969 // did not overflow the old, smaller, value, we can zero extend all of the 970 // operands (often constants). This allows analysis of something like 971 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 972 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 973 if (AR->isAffine()) { 974 const SCEV *Start = AR->getStart(); 975 const SCEV *Step = AR->getStepRecurrence(*this); 976 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 977 const Loop *L = AR->getLoop(); 978 979 // If we have special knowledge that this addrec won't overflow, 980 // we don't need to do any further analysis. 981 if (AR->hasNoUnsignedWrap()) 982 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 983 getZeroExtendExpr(Step, Ty), 984 L); 985 986 // Check whether the backedge-taken count is SCEVCouldNotCompute. 987 // Note that this serves two purposes: It filters out loops that are 988 // simply not analyzable, and it covers the case where this code is 989 // being called from within backedge-taken count analysis, such that 990 // attempting to ask for the backedge-taken count would likely result 991 // in infinite recursion. In the later case, the analysis code will 992 // cope with a conservative value, and it will take care to purge 993 // that value once it has finished. 994 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 995 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 996 // Manually compute the final value for AR, checking for 997 // overflow. 998 999 // Check whether the backedge-taken count can be losslessly casted to 1000 // the addrec's type. The count is always unsigned. 1001 const SCEV *CastedMaxBECount = 1002 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1003 const SCEV *RecastedMaxBECount = 1004 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1005 if (MaxBECount == RecastedMaxBECount) { 1006 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1007 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1008 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1009 const SCEV *Add = getAddExpr(Start, ZMul); 1010 const SCEV *OperandExtendedAdd = 1011 getAddExpr(getZeroExtendExpr(Start, WideTy), 1012 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1013 getZeroExtendExpr(Step, WideTy))); 1014 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1015 // Return the expression with the addrec on the outside. 1016 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1017 getZeroExtendExpr(Step, Ty), 1018 L); 1019 1020 // Similar to above, only this time treat the step value as signed. 1021 // This covers loops that count down. 1022 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1023 Add = getAddExpr(Start, SMul); 1024 OperandExtendedAdd = 1025 getAddExpr(getZeroExtendExpr(Start, WideTy), 1026 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1027 getSignExtendExpr(Step, WideTy))); 1028 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1029 // Return the expression with the addrec on the outside. 1030 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1031 getSignExtendExpr(Step, Ty), 1032 L); 1033 } 1034 1035 // If the backedge is guarded by a comparison with the pre-inc value 1036 // the addrec is safe. Also, if the entry is guarded by a comparison 1037 // with the start value and the backedge is guarded by a comparison 1038 // with the post-inc value, the addrec is safe. 1039 if (isKnownPositive(Step)) { 1040 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1041 getUnsignedRange(Step).getUnsignedMax()); 1042 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1043 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1044 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1045 AR->getPostIncExpr(*this), N))) 1046 // Return the expression with the addrec on the outside. 1047 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1048 getZeroExtendExpr(Step, Ty), 1049 L); 1050 } else if (isKnownNegative(Step)) { 1051 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1052 getSignedRange(Step).getSignedMin()); 1053 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1054 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1055 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1056 AR->getPostIncExpr(*this), N))) 1057 // Return the expression with the addrec on the outside. 1058 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1059 getSignExtendExpr(Step, Ty), 1060 L); 1061 } 1062 } 1063 } 1064 1065 // The cast wasn't folded; create an explicit cast node. 1066 // Recompute the insert position, as it may have been invalidated. 1067 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1068 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1069 Op, Ty); 1070 UniqueSCEVs.InsertNode(S, IP); 1071 return S; 1072} 1073 1074const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1075 const Type *Ty) { 1076 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1077 "This is not an extending conversion!"); 1078 assert(isSCEVable(Ty) && 1079 "This is not a conversion to a SCEVable type!"); 1080 Ty = getEffectiveSCEVType(Ty); 1081 1082 // Fold if the operand is constant. 1083 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1084 return getConstant( 1085 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1086 getEffectiveSCEVType(Ty)))); 1087 1088 // sext(sext(x)) --> sext(x) 1089 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1090 return getSignExtendExpr(SS->getOperand(), Ty); 1091 1092 // Before doing any expensive analysis, check to see if we've already 1093 // computed a SCEV for this Op and Ty. 1094 FoldingSetNodeID ID; 1095 ID.AddInteger(scSignExtend); 1096 ID.AddPointer(Op); 1097 ID.AddPointer(Ty); 1098 void *IP = 0; 1099 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1100 1101 // If the input value is a chrec scev, and we can prove that the value 1102 // did not overflow the old, smaller, value, we can sign extend all of the 1103 // operands (often constants). This allows analysis of something like 1104 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1105 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1106 if (AR->isAffine()) { 1107 const SCEV *Start = AR->getStart(); 1108 const SCEV *Step = AR->getStepRecurrence(*this); 1109 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1110 const Loop *L = AR->getLoop(); 1111 1112 // If we have special knowledge that this addrec won't overflow, 1113 // we don't need to do any further analysis. 1114 if (AR->hasNoSignedWrap()) 1115 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1116 getSignExtendExpr(Step, Ty), 1117 L); 1118 1119 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1120 // Note that this serves two purposes: It filters out loops that are 1121 // simply not analyzable, and it covers the case where this code is 1122 // being called from within backedge-taken count analysis, such that 1123 // attempting to ask for the backedge-taken count would likely result 1124 // in infinite recursion. In the later case, the analysis code will 1125 // cope with a conservative value, and it will take care to purge 1126 // that value once it has finished. 1127 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1128 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1129 // Manually compute the final value for AR, checking for 1130 // overflow. 1131 1132 // Check whether the backedge-taken count can be losslessly casted to 1133 // the addrec's type. The count is always unsigned. 1134 const SCEV *CastedMaxBECount = 1135 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1136 const SCEV *RecastedMaxBECount = 1137 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1138 if (MaxBECount == RecastedMaxBECount) { 1139 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1140 // Check whether Start+Step*MaxBECount has no signed overflow. 1141 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1142 const SCEV *Add = getAddExpr(Start, SMul); 1143 const SCEV *OperandExtendedAdd = 1144 getAddExpr(getSignExtendExpr(Start, WideTy), 1145 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1146 getSignExtendExpr(Step, WideTy))); 1147 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1148 // Return the expression with the addrec on the outside. 1149 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1150 getSignExtendExpr(Step, Ty), 1151 L); 1152 1153 // Similar to above, only this time treat the step value as unsigned. 1154 // This covers loops that count up with an unsigned step. 1155 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1156 Add = getAddExpr(Start, UMul); 1157 OperandExtendedAdd = 1158 getAddExpr(getSignExtendExpr(Start, WideTy), 1159 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1160 getZeroExtendExpr(Step, WideTy))); 1161 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1162 // Return the expression with the addrec on the outside. 1163 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1164 getZeroExtendExpr(Step, Ty), 1165 L); 1166 } 1167 1168 // If the backedge is guarded by a comparison with the pre-inc value 1169 // the addrec is safe. Also, if the entry is guarded by a comparison 1170 // with the start value and the backedge is guarded by a comparison 1171 // with the post-inc value, the addrec is safe. 1172 if (isKnownPositive(Step)) { 1173 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1174 getSignedRange(Step).getSignedMax()); 1175 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1176 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1177 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1178 AR->getPostIncExpr(*this), N))) 1179 // Return the expression with the addrec on the outside. 1180 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1181 getSignExtendExpr(Step, Ty), 1182 L); 1183 } else if (isKnownNegative(Step)) { 1184 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1185 getSignedRange(Step).getSignedMin()); 1186 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1187 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1188 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1189 AR->getPostIncExpr(*this), N))) 1190 // Return the expression with the addrec on the outside. 1191 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1192 getSignExtendExpr(Step, Ty), 1193 L); 1194 } 1195 } 1196 } 1197 1198 // The cast wasn't folded; create an explicit cast node. 1199 // Recompute the insert position, as it may have been invalidated. 1200 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1201 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1202 Op, Ty); 1203 UniqueSCEVs.InsertNode(S, IP); 1204 return S; 1205} 1206 1207/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1208/// unspecified bits out to the given type. 1209/// 1210const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1211 const Type *Ty) { 1212 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1213 "This is not an extending conversion!"); 1214 assert(isSCEVable(Ty) && 1215 "This is not a conversion to a SCEVable type!"); 1216 Ty = getEffectiveSCEVType(Ty); 1217 1218 // Sign-extend negative constants. 1219 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1220 if (SC->getValue()->getValue().isNegative()) 1221 return getSignExtendExpr(Op, Ty); 1222 1223 // Peel off a truncate cast. 1224 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1225 const SCEV *NewOp = T->getOperand(); 1226 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1227 return getAnyExtendExpr(NewOp, Ty); 1228 return getTruncateOrNoop(NewOp, Ty); 1229 } 1230 1231 // Next try a zext cast. If the cast is folded, use it. 1232 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1233 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1234 return ZExt; 1235 1236 // Next try a sext cast. If the cast is folded, use it. 1237 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1238 if (!isa<SCEVSignExtendExpr>(SExt)) 1239 return SExt; 1240 1241 // Force the cast to be folded into the operands of an addrec. 1242 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1243 SmallVector<const SCEV *, 4> Ops; 1244 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1245 I != E; ++I) 1246 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1247 return getAddRecExpr(Ops, AR->getLoop()); 1248 } 1249 1250 // As a special case, fold anyext(undef) to undef. We don't want to 1251 // know too much about SCEVUnknowns, but this special case is handy 1252 // and harmless. 1253 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1254 if (isa<UndefValue>(U->getValue())) 1255 return getSCEV(UndefValue::get(Ty)); 1256 1257 // If the expression is obviously signed, use the sext cast value. 1258 if (isa<SCEVSMaxExpr>(Op)) 1259 return SExt; 1260 1261 // Absent any other information, use the zext cast value. 1262 return ZExt; 1263} 1264 1265/// CollectAddOperandsWithScales - Process the given Ops list, which is 1266/// a list of operands to be added under the given scale, update the given 1267/// map. This is a helper function for getAddRecExpr. As an example of 1268/// what it does, given a sequence of operands that would form an add 1269/// expression like this: 1270/// 1271/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1272/// 1273/// where A and B are constants, update the map with these values: 1274/// 1275/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1276/// 1277/// and add 13 + A*B*29 to AccumulatedConstant. 1278/// This will allow getAddRecExpr to produce this: 1279/// 1280/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1281/// 1282/// This form often exposes folding opportunities that are hidden in 1283/// the original operand list. 1284/// 1285/// Return true iff it appears that any interesting folding opportunities 1286/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1287/// the common case where no interesting opportunities are present, and 1288/// is also used as a check to avoid infinite recursion. 1289/// 1290static bool 1291CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1292 SmallVector<const SCEV *, 8> &NewOps, 1293 APInt &AccumulatedConstant, 1294 const SCEV *const *Ops, size_t NumOperands, 1295 const APInt &Scale, 1296 ScalarEvolution &SE) { 1297 bool Interesting = false; 1298 1299 // Iterate over the add operands. They are sorted, with constants first. 1300 unsigned i = 0; 1301 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1302 ++i; 1303 // Pull a buried constant out to the outside. 1304 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1305 Interesting = true; 1306 AccumulatedConstant += Scale * C->getValue()->getValue(); 1307 } 1308 1309 // Next comes everything else. We're especially interested in multiplies 1310 // here, but they're in the middle, so just visit the rest with one loop. 1311 for (; i != NumOperands; ++i) { 1312 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1313 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1314 APInt NewScale = 1315 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1316 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1317 // A multiplication of a constant with another add; recurse. 1318 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1319 Interesting |= 1320 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1321 Add->op_begin(), Add->getNumOperands(), 1322 NewScale, SE); 1323 } else { 1324 // A multiplication of a constant with some other value. Update 1325 // the map. 1326 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1327 const SCEV *Key = SE.getMulExpr(MulOps); 1328 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1329 M.insert(std::make_pair(Key, NewScale)); 1330 if (Pair.second) { 1331 NewOps.push_back(Pair.first->first); 1332 } else { 1333 Pair.first->second += NewScale; 1334 // The map already had an entry for this value, which may indicate 1335 // a folding opportunity. 1336 Interesting = true; 1337 } 1338 } 1339 } else { 1340 // An ordinary operand. Update the map. 1341 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1342 M.insert(std::make_pair(Ops[i], Scale)); 1343 if (Pair.second) { 1344 NewOps.push_back(Pair.first->first); 1345 } else { 1346 Pair.first->second += Scale; 1347 // The map already had an entry for this value, which may indicate 1348 // a folding opportunity. 1349 Interesting = true; 1350 } 1351 } 1352 } 1353 1354 return Interesting; 1355} 1356 1357namespace { 1358 struct APIntCompare { 1359 bool operator()(const APInt &LHS, const APInt &RHS) const { 1360 return LHS.ult(RHS); 1361 } 1362 }; 1363} 1364 1365/// getAddExpr - Get a canonical add expression, or something simpler if 1366/// possible. 1367const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1368 bool HasNUW, bool HasNSW) { 1369 assert(!Ops.empty() && "Cannot get empty add!"); 1370 if (Ops.size() == 1) return Ops[0]; 1371#ifndef NDEBUG 1372 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1373 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1374 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1375 "SCEVAddExpr operand types don't match!"); 1376#endif 1377 1378 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1379 if (!HasNUW && HasNSW) { 1380 bool All = true; 1381 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1382 E = Ops.end(); I != E; ++I) 1383 if (!isKnownNonNegative(*I)) { 1384 All = false; 1385 break; 1386 } 1387 if (All) HasNUW = true; 1388 } 1389 1390 // Sort by complexity, this groups all similar expression types together. 1391 GroupByComplexity(Ops, LI); 1392 1393 // If there are any constants, fold them together. 1394 unsigned Idx = 0; 1395 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1396 ++Idx; 1397 assert(Idx < Ops.size()); 1398 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1399 // We found two constants, fold them together! 1400 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1401 RHSC->getValue()->getValue()); 1402 if (Ops.size() == 2) return Ops[0]; 1403 Ops.erase(Ops.begin()+1); // Erase the folded element 1404 LHSC = cast<SCEVConstant>(Ops[0]); 1405 } 1406 1407 // If we are left with a constant zero being added, strip it off. 1408 if (LHSC->getValue()->isZero()) { 1409 Ops.erase(Ops.begin()); 1410 --Idx; 1411 } 1412 1413 if (Ops.size() == 1) return Ops[0]; 1414 } 1415 1416 // Okay, check to see if the same value occurs in the operand list more than 1417 // once. If so, merge them together into an multiply expression. Since we 1418 // sorted the list, these values are required to be adjacent. 1419 const Type *Ty = Ops[0]->getType(); 1420 bool FoundMatch = false; 1421 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1422 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1423 // Scan ahead to count how many equal operands there are. 1424 unsigned Count = 2; 1425 while (i+Count != e && Ops[i+Count] == Ops[i]) 1426 ++Count; 1427 // Merge the values into a multiply. 1428 const SCEV *Scale = getConstant(Ty, Count); 1429 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1430 if (Ops.size() == Count) 1431 return Mul; 1432 Ops[i] = Mul; 1433 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1434 --i; e -= Count - 1; 1435 FoundMatch = true; 1436 } 1437 if (FoundMatch) 1438 return getAddExpr(Ops, HasNUW, HasNSW); 1439 1440 // Check for truncates. If all the operands are truncated from the same 1441 // type, see if factoring out the truncate would permit the result to be 1442 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1443 // if the contents of the resulting outer trunc fold to something simple. 1444 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1445 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1446 const Type *DstType = Trunc->getType(); 1447 const Type *SrcType = Trunc->getOperand()->getType(); 1448 SmallVector<const SCEV *, 8> LargeOps; 1449 bool Ok = true; 1450 // Check all the operands to see if they can be represented in the 1451 // source type of the truncate. 1452 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1453 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1454 if (T->getOperand()->getType() != SrcType) { 1455 Ok = false; 1456 break; 1457 } 1458 LargeOps.push_back(T->getOperand()); 1459 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1460 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1461 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1462 SmallVector<const SCEV *, 8> LargeMulOps; 1463 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1464 if (const SCEVTruncateExpr *T = 1465 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1466 if (T->getOperand()->getType() != SrcType) { 1467 Ok = false; 1468 break; 1469 } 1470 LargeMulOps.push_back(T->getOperand()); 1471 } else if (const SCEVConstant *C = 1472 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1473 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1474 } else { 1475 Ok = false; 1476 break; 1477 } 1478 } 1479 if (Ok) 1480 LargeOps.push_back(getMulExpr(LargeMulOps)); 1481 } else { 1482 Ok = false; 1483 break; 1484 } 1485 } 1486 if (Ok) { 1487 // Evaluate the expression in the larger type. 1488 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1489 // If it folds to something simple, use it. Otherwise, don't. 1490 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1491 return getTruncateExpr(Fold, DstType); 1492 } 1493 } 1494 1495 // Skip past any other cast SCEVs. 1496 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1497 ++Idx; 1498 1499 // If there are add operands they would be next. 1500 if (Idx < Ops.size()) { 1501 bool DeletedAdd = false; 1502 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1503 // If we have an add, expand the add operands onto the end of the operands 1504 // list. 1505 Ops.erase(Ops.begin()+Idx); 1506 Ops.append(Add->op_begin(), Add->op_end()); 1507 DeletedAdd = true; 1508 } 1509 1510 // If we deleted at least one add, we added operands to the end of the list, 1511 // and they are not necessarily sorted. Recurse to resort and resimplify 1512 // any operands we just acquired. 1513 if (DeletedAdd) 1514 return getAddExpr(Ops); 1515 } 1516 1517 // Skip over the add expression until we get to a multiply. 1518 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1519 ++Idx; 1520 1521 // Check to see if there are any folding opportunities present with 1522 // operands multiplied by constant values. 1523 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1524 uint64_t BitWidth = getTypeSizeInBits(Ty); 1525 DenseMap<const SCEV *, APInt> M; 1526 SmallVector<const SCEV *, 8> NewOps; 1527 APInt AccumulatedConstant(BitWidth, 0); 1528 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1529 Ops.data(), Ops.size(), 1530 APInt(BitWidth, 1), *this)) { 1531 // Some interesting folding opportunity is present, so its worthwhile to 1532 // re-generate the operands list. Group the operands by constant scale, 1533 // to avoid multiplying by the same constant scale multiple times. 1534 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1535 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1536 E = NewOps.end(); I != E; ++I) 1537 MulOpLists[M.find(*I)->second].push_back(*I); 1538 // Re-generate the operands list. 1539 Ops.clear(); 1540 if (AccumulatedConstant != 0) 1541 Ops.push_back(getConstant(AccumulatedConstant)); 1542 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1543 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1544 if (I->first != 0) 1545 Ops.push_back(getMulExpr(getConstant(I->first), 1546 getAddExpr(I->second))); 1547 if (Ops.empty()) 1548 return getConstant(Ty, 0); 1549 if (Ops.size() == 1) 1550 return Ops[0]; 1551 return getAddExpr(Ops); 1552 } 1553 } 1554 1555 // If we are adding something to a multiply expression, make sure the 1556 // something is not already an operand of the multiply. If so, merge it into 1557 // the multiply. 1558 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1559 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1560 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1561 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1562 if (isa<SCEVConstant>(MulOpSCEV)) 1563 continue; 1564 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1565 if (MulOpSCEV == Ops[AddOp]) { 1566 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1567 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1568 if (Mul->getNumOperands() != 2) { 1569 // If the multiply has more than two operands, we must get the 1570 // Y*Z term. 1571 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1572 Mul->op_begin()+MulOp); 1573 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1574 InnerMul = getMulExpr(MulOps); 1575 } 1576 const SCEV *One = getConstant(Ty, 1); 1577 const SCEV *AddOne = getAddExpr(One, InnerMul); 1578 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1579 if (Ops.size() == 2) return OuterMul; 1580 if (AddOp < Idx) { 1581 Ops.erase(Ops.begin()+AddOp); 1582 Ops.erase(Ops.begin()+Idx-1); 1583 } else { 1584 Ops.erase(Ops.begin()+Idx); 1585 Ops.erase(Ops.begin()+AddOp-1); 1586 } 1587 Ops.push_back(OuterMul); 1588 return getAddExpr(Ops); 1589 } 1590 1591 // Check this multiply against other multiplies being added together. 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.erase(Ops.begin()+Idx); 1620 Ops.erase(Ops.begin()+OtherMulIdx-1); 1621 Ops.push_back(OuterMul); 1622 return getAddExpr(Ops); 1623 } 1624 } 1625 } 1626 } 1627 1628 // If there are any add recurrences in the operands list, see if any other 1629 // added values are loop invariant. If so, we can fold them into the 1630 // recurrence. 1631 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1632 ++Idx; 1633 1634 // Scan over all recurrences, trying to fold loop invariants into them. 1635 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1636 // Scan all of the other operands to this add and add them to the vector if 1637 // they are loop invariant w.r.t. the recurrence. 1638 SmallVector<const SCEV *, 8> LIOps; 1639 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1640 const Loop *AddRecLoop = AddRec->getLoop(); 1641 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1642 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1643 LIOps.push_back(Ops[i]); 1644 Ops.erase(Ops.begin()+i); 1645 --i; --e; 1646 } 1647 1648 // If we found some loop invariants, fold them into the recurrence. 1649 if (!LIOps.empty()) { 1650 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1651 LIOps.push_back(AddRec->getStart()); 1652 1653 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1654 AddRec->op_end()); 1655 AddRecOps[0] = getAddExpr(LIOps); 1656 1657 // Build the new addrec. Propagate the NUW and NSW flags if both the 1658 // outer add and the inner addrec are guaranteed to have no overflow. 1659 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1660 HasNUW && AddRec->hasNoUnsignedWrap(), 1661 HasNSW && AddRec->hasNoSignedWrap()); 1662 1663 // If all of the other operands were loop invariant, we are done. 1664 if (Ops.size() == 1) return NewRec; 1665 1666 // Otherwise, add the folded AddRec by the non-liv parts. 1667 for (unsigned i = 0;; ++i) 1668 if (Ops[i] == AddRec) { 1669 Ops[i] = NewRec; 1670 break; 1671 } 1672 return getAddExpr(Ops); 1673 } 1674 1675 // Okay, if there weren't any loop invariants to be folded, check to see if 1676 // there are multiple AddRec's with the same loop induction variable being 1677 // added together. If so, we can fold them. 1678 for (unsigned OtherIdx = Idx+1; 1679 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1680 ++OtherIdx) 1681 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1682 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1683 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1684 AddRec->op_end()); 1685 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1686 ++OtherIdx) 1687 if (const SCEVAddRecExpr *OtherAddRec = 1688 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1689 if (OtherAddRec->getLoop() == AddRecLoop) { 1690 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1691 i != e; ++i) { 1692 if (i >= AddRecOps.size()) { 1693 AddRecOps.append(OtherAddRec->op_begin()+i, 1694 OtherAddRec->op_end()); 1695 break; 1696 } 1697 AddRecOps[i] = getAddExpr(AddRecOps[i], 1698 OtherAddRec->getOperand(i)); 1699 } 1700 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1701 } 1702 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1703 return getAddExpr(Ops); 1704 } 1705 1706 // Otherwise couldn't fold anything into this recurrence. Move onto the 1707 // next one. 1708 } 1709 1710 // Okay, it looks like we really DO need an add expr. Check to see if we 1711 // already have one, otherwise create a new one. 1712 FoldingSetNodeID ID; 1713 ID.AddInteger(scAddExpr); 1714 ID.AddInteger(Ops.size()); 1715 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1716 ID.AddPointer(Ops[i]); 1717 void *IP = 0; 1718 SCEVAddExpr *S = 1719 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1720 if (!S) { 1721 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1722 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1723 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1724 O, Ops.size()); 1725 UniqueSCEVs.InsertNode(S, IP); 1726 } 1727 if (HasNUW) S->setHasNoUnsignedWrap(true); 1728 if (HasNSW) S->setHasNoSignedWrap(true); 1729 return S; 1730} 1731 1732/// getMulExpr - Get a canonical multiply expression, or something simpler if 1733/// possible. 1734const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1735 bool HasNUW, bool HasNSW) { 1736 assert(!Ops.empty() && "Cannot get empty mul!"); 1737 if (Ops.size() == 1) return Ops[0]; 1738#ifndef NDEBUG 1739 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1740 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1741 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1742 "SCEVMulExpr operand types don't match!"); 1743#endif 1744 1745 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1746 if (!HasNUW && HasNSW) { 1747 bool All = true; 1748 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1749 E = Ops.end(); I != E; ++I) 1750 if (!isKnownNonNegative(*I)) { 1751 All = false; 1752 break; 1753 } 1754 if (All) HasNUW = true; 1755 } 1756 1757 // Sort by complexity, this groups all similar expression types together. 1758 GroupByComplexity(Ops, LI); 1759 1760 // If there are any constants, fold them together. 1761 unsigned Idx = 0; 1762 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1763 1764 // C1*(C2+V) -> C1*C2 + C1*V 1765 if (Ops.size() == 2) 1766 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1767 if (Add->getNumOperands() == 2 && 1768 isa<SCEVConstant>(Add->getOperand(0))) 1769 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1770 getMulExpr(LHSC, Add->getOperand(1))); 1771 1772 ++Idx; 1773 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1774 // We found two constants, fold them together! 1775 ConstantInt *Fold = ConstantInt::get(getContext(), 1776 LHSC->getValue()->getValue() * 1777 RHSC->getValue()->getValue()); 1778 Ops[0] = getConstant(Fold); 1779 Ops.erase(Ops.begin()+1); // Erase the folded element 1780 if (Ops.size() == 1) return Ops[0]; 1781 LHSC = cast<SCEVConstant>(Ops[0]); 1782 } 1783 1784 // If we are left with a constant one being multiplied, strip it off. 1785 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1786 Ops.erase(Ops.begin()); 1787 --Idx; 1788 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1789 // If we have a multiply of zero, it will always be zero. 1790 return Ops[0]; 1791 } else if (Ops[0]->isAllOnesValue()) { 1792 // If we have a mul by -1 of an add, try distributing the -1 among the 1793 // add operands. 1794 if (Ops.size() == 2) 1795 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1796 SmallVector<const SCEV *, 4> NewOps; 1797 bool AnyFolded = false; 1798 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1799 I != E; ++I) { 1800 const SCEV *Mul = getMulExpr(Ops[0], *I); 1801 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1802 NewOps.push_back(Mul); 1803 } 1804 if (AnyFolded) 1805 return getAddExpr(NewOps); 1806 } 1807 } 1808 1809 if (Ops.size() == 1) 1810 return Ops[0]; 1811 } 1812 1813 // Skip over the add expression until we get to a multiply. 1814 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1815 ++Idx; 1816 1817 // If there are mul operands inline them all into this expression. 1818 if (Idx < Ops.size()) { 1819 bool DeletedMul = false; 1820 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1821 // If we have an mul, expand the mul operands onto the end of the operands 1822 // list. 1823 Ops.erase(Ops.begin()+Idx); 1824 Ops.append(Mul->op_begin(), Mul->op_end()); 1825 DeletedMul = true; 1826 } 1827 1828 // If we deleted at least one mul, we added operands to the end of the list, 1829 // and they are not necessarily sorted. Recurse to resort and resimplify 1830 // any operands we just acquired. 1831 if (DeletedMul) 1832 return getMulExpr(Ops); 1833 } 1834 1835 // If there are any add recurrences in the operands list, see if any other 1836 // added values are loop invariant. If so, we can fold them into the 1837 // recurrence. 1838 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1839 ++Idx; 1840 1841 // Scan over all recurrences, trying to fold loop invariants into them. 1842 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1843 // Scan all of the other operands to this mul and add them to the vector if 1844 // they are loop invariant w.r.t. the recurrence. 1845 SmallVector<const SCEV *, 8> LIOps; 1846 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1847 const Loop *AddRecLoop = AddRec->getLoop(); 1848 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1849 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1850 LIOps.push_back(Ops[i]); 1851 Ops.erase(Ops.begin()+i); 1852 --i; --e; 1853 } 1854 1855 // If we found some loop invariants, fold them into the recurrence. 1856 if (!LIOps.empty()) { 1857 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1858 SmallVector<const SCEV *, 4> NewOps; 1859 NewOps.reserve(AddRec->getNumOperands()); 1860 const SCEV *Scale = getMulExpr(LIOps); 1861 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1862 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1863 1864 // Build the new addrec. Propagate the NUW and NSW flags if both the 1865 // outer mul and the inner addrec are guaranteed to have no overflow. 1866 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, 1867 HasNUW && AddRec->hasNoUnsignedWrap(), 1868 HasNSW && AddRec->hasNoSignedWrap()); 1869 1870 // If all of the other operands were loop invariant, we are done. 1871 if (Ops.size() == 1) return NewRec; 1872 1873 // Otherwise, multiply the folded AddRec by the non-liv parts. 1874 for (unsigned i = 0;; ++i) 1875 if (Ops[i] == AddRec) { 1876 Ops[i] = NewRec; 1877 break; 1878 } 1879 return getMulExpr(Ops); 1880 } 1881 1882 // Okay, if there weren't any loop invariants to be folded, check to see if 1883 // there are multiple AddRec's with the same loop induction variable being 1884 // multiplied together. If so, we can fold them. 1885 for (unsigned OtherIdx = Idx+1; 1886 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1887 ++OtherIdx) 1888 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1889 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1890 // {A*C,+,F*D + G*B + B*D}<L> 1891 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1892 ++OtherIdx) 1893 if (const SCEVAddRecExpr *OtherAddRec = 1894 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1895 if (OtherAddRec->getLoop() == AddRecLoop) { 1896 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1897 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1898 const SCEV *B = F->getStepRecurrence(*this); 1899 const SCEV *D = G->getStepRecurrence(*this); 1900 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1901 getMulExpr(G, B), 1902 getMulExpr(B, D)); 1903 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1904 F->getLoop()); 1905 if (Ops.size() == 2) return NewAddRec; 1906 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1907 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1908 } 1909 return getMulExpr(Ops); 1910 } 1911 1912 // Otherwise couldn't fold anything into this recurrence. Move onto the 1913 // next one. 1914 } 1915 1916 // Okay, it looks like we really DO need an mul expr. Check to see if we 1917 // already have one, otherwise create a new one. 1918 FoldingSetNodeID ID; 1919 ID.AddInteger(scMulExpr); 1920 ID.AddInteger(Ops.size()); 1921 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1922 ID.AddPointer(Ops[i]); 1923 void *IP = 0; 1924 SCEVMulExpr *S = 1925 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1926 if (!S) { 1927 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1928 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1929 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1930 O, Ops.size()); 1931 UniqueSCEVs.InsertNode(S, IP); 1932 } 1933 if (HasNUW) S->setHasNoUnsignedWrap(true); 1934 if (HasNSW) S->setHasNoSignedWrap(true); 1935 return S; 1936} 1937 1938/// getUDivExpr - Get a canonical unsigned division expression, or something 1939/// simpler if possible. 1940const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1941 const SCEV *RHS) { 1942 assert(getEffectiveSCEVType(LHS->getType()) == 1943 getEffectiveSCEVType(RHS->getType()) && 1944 "SCEVUDivExpr operand types don't match!"); 1945 1946 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1947 if (RHSC->getValue()->equalsInt(1)) 1948 return LHS; // X udiv 1 --> x 1949 // If the denominator is zero, the result of the udiv is undefined. Don't 1950 // try to analyze it, because the resolution chosen here may differ from 1951 // the resolution chosen in other parts of the compiler. 1952 if (!RHSC->getValue()->isZero()) { 1953 // Determine if the division can be folded into the operands of 1954 // its operands. 1955 // TODO: Generalize this to non-constants by using known-bits information. 1956 const Type *Ty = LHS->getType(); 1957 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1958 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1959 // For non-power-of-two values, effectively round the value up to the 1960 // nearest power of two. 1961 if (!RHSC->getValue()->getValue().isPowerOf2()) 1962 ++MaxShiftAmt; 1963 const IntegerType *ExtTy = 1964 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1965 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1966 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1967 if (const SCEVConstant *Step = 1968 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1969 if (!Step->getValue()->getValue() 1970 .urem(RHSC->getValue()->getValue()) && 1971 getZeroExtendExpr(AR, ExtTy) == 1972 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1973 getZeroExtendExpr(Step, ExtTy), 1974 AR->getLoop())) { 1975 SmallVector<const SCEV *, 4> Operands; 1976 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1977 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1978 return getAddRecExpr(Operands, AR->getLoop()); 1979 } 1980 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1981 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1982 SmallVector<const SCEV *, 4> Operands; 1983 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1984 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1985 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1986 // Find an operand that's safely divisible. 1987 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1988 const SCEV *Op = M->getOperand(i); 1989 const SCEV *Div = getUDivExpr(Op, RHSC); 1990 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1991 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1992 M->op_end()); 1993 Operands[i] = Div; 1994 return getMulExpr(Operands); 1995 } 1996 } 1997 } 1998 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1999 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 2000 SmallVector<const SCEV *, 4> Operands; 2001 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2002 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2003 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2004 Operands.clear(); 2005 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2006 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2007 if (isa<SCEVUDivExpr>(Op) || 2008 getMulExpr(Op, RHS) != A->getOperand(i)) 2009 break; 2010 Operands.push_back(Op); 2011 } 2012 if (Operands.size() == A->getNumOperands()) 2013 return getAddExpr(Operands); 2014 } 2015 } 2016 2017 // Fold if both operands are constant. 2018 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2019 Constant *LHSCV = LHSC->getValue(); 2020 Constant *RHSCV = RHSC->getValue(); 2021 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2022 RHSCV))); 2023 } 2024 } 2025 } 2026 2027 FoldingSetNodeID ID; 2028 ID.AddInteger(scUDivExpr); 2029 ID.AddPointer(LHS); 2030 ID.AddPointer(RHS); 2031 void *IP = 0; 2032 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2033 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2034 LHS, RHS); 2035 UniqueSCEVs.InsertNode(S, IP); 2036 return S; 2037} 2038 2039 2040/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2041/// Simplify the expression as much as possible. 2042const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2043 const SCEV *Step, const Loop *L, 2044 bool HasNUW, bool HasNSW) { 2045 SmallVector<const SCEV *, 4> Operands; 2046 Operands.push_back(Start); 2047 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2048 if (StepChrec->getLoop() == L) { 2049 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2050 return getAddRecExpr(Operands, L); 2051 } 2052 2053 Operands.push_back(Step); 2054 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2055} 2056 2057/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2058/// Simplify the expression as much as possible. 2059const SCEV * 2060ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2061 const Loop *L, 2062 bool HasNUW, bool HasNSW) { 2063 if (Operands.size() == 1) return Operands[0]; 2064#ifndef NDEBUG 2065 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2066 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2067 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2068 "SCEVAddRecExpr operand types don't match!"); 2069#endif 2070 2071 if (Operands.back()->isZero()) { 2072 Operands.pop_back(); 2073 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2074 } 2075 2076 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2077 // use that information to infer NUW and NSW flags. However, computing a 2078 // BE count requires calling getAddRecExpr, so we may not yet have a 2079 // meaningful BE count at this point (and if we don't, we'd be stuck 2080 // with a SCEVCouldNotCompute as the cached BE count). 2081 2082 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2083 if (!HasNUW && HasNSW) { 2084 bool All = true; 2085 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2086 E = Operands.end(); I != E; ++I) 2087 if (!isKnownNonNegative(*I)) { 2088 All = false; 2089 break; 2090 } 2091 if (All) HasNUW = true; 2092 } 2093 2094 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2095 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2096 const Loop *NestedLoop = NestedAR->getLoop(); 2097 if (L->contains(NestedLoop) ? 2098 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2099 (!NestedLoop->contains(L) && 2100 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2101 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2102 NestedAR->op_end()); 2103 Operands[0] = NestedAR->getStart(); 2104 // AddRecs require their operands be loop-invariant with respect to their 2105 // loops. Don't perform this transformation if it would break this 2106 // requirement. 2107 bool AllInvariant = true; 2108 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2109 if (!Operands[i]->isLoopInvariant(L)) { 2110 AllInvariant = false; 2111 break; 2112 } 2113 if (AllInvariant) { 2114 NestedOperands[0] = getAddRecExpr(Operands, L); 2115 AllInvariant = true; 2116 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2117 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2118 AllInvariant = false; 2119 break; 2120 } 2121 if (AllInvariant) 2122 // Ok, both add recurrences are valid after the transformation. 2123 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2124 } 2125 // Reset Operands to its original state. 2126 Operands[0] = NestedAR; 2127 } 2128 } 2129 2130 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2131 // already have one, otherwise create a new one. 2132 FoldingSetNodeID ID; 2133 ID.AddInteger(scAddRecExpr); 2134 ID.AddInteger(Operands.size()); 2135 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2136 ID.AddPointer(Operands[i]); 2137 ID.AddPointer(L); 2138 void *IP = 0; 2139 SCEVAddRecExpr *S = 2140 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2141 if (!S) { 2142 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2143 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2144 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2145 O, Operands.size(), L); 2146 UniqueSCEVs.InsertNode(S, IP); 2147 } 2148 if (HasNUW) S->setHasNoUnsignedWrap(true); 2149 if (HasNSW) S->setHasNoSignedWrap(true); 2150 return S; 2151} 2152 2153const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2154 const SCEV *RHS) { 2155 SmallVector<const SCEV *, 2> Ops; 2156 Ops.push_back(LHS); 2157 Ops.push_back(RHS); 2158 return getSMaxExpr(Ops); 2159} 2160 2161const SCEV * 2162ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2163 assert(!Ops.empty() && "Cannot get empty smax!"); 2164 if (Ops.size() == 1) return Ops[0]; 2165#ifndef NDEBUG 2166 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2167 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2168 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2169 "SCEVSMaxExpr operand types don't match!"); 2170#endif 2171 2172 // Sort by complexity, this groups all similar expression types together. 2173 GroupByComplexity(Ops, LI); 2174 2175 // If there are any constants, fold them together. 2176 unsigned Idx = 0; 2177 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2178 ++Idx; 2179 assert(Idx < Ops.size()); 2180 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2181 // We found two constants, fold them together! 2182 ConstantInt *Fold = ConstantInt::get(getContext(), 2183 APIntOps::smax(LHSC->getValue()->getValue(), 2184 RHSC->getValue()->getValue())); 2185 Ops[0] = getConstant(Fold); 2186 Ops.erase(Ops.begin()+1); // Erase the folded element 2187 if (Ops.size() == 1) return Ops[0]; 2188 LHSC = cast<SCEVConstant>(Ops[0]); 2189 } 2190 2191 // If we are left with a constant minimum-int, strip it off. 2192 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2193 Ops.erase(Ops.begin()); 2194 --Idx; 2195 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2196 // If we have an smax with a constant maximum-int, it will always be 2197 // maximum-int. 2198 return Ops[0]; 2199 } 2200 2201 if (Ops.size() == 1) return Ops[0]; 2202 } 2203 2204 // Find the first SMax 2205 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2206 ++Idx; 2207 2208 // Check to see if one of the operands is an SMax. If so, expand its operands 2209 // onto our operand list, and recurse to simplify. 2210 if (Idx < Ops.size()) { 2211 bool DeletedSMax = false; 2212 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2213 Ops.erase(Ops.begin()+Idx); 2214 Ops.append(SMax->op_begin(), SMax->op_end()); 2215 DeletedSMax = true; 2216 } 2217 2218 if (DeletedSMax) 2219 return getSMaxExpr(Ops); 2220 } 2221 2222 // Okay, check to see if the same value occurs in the operand list twice. If 2223 // so, delete one. Since we sorted the list, these values are required to 2224 // be adjacent. 2225 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2226 // X smax Y smax Y --> X smax Y 2227 // X smax Y --> X, if X is always greater than Y 2228 if (Ops[i] == Ops[i+1] || 2229 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2230 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2231 --i; --e; 2232 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2233 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2234 --i; --e; 2235 } 2236 2237 if (Ops.size() == 1) return Ops[0]; 2238 2239 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2240 2241 // Okay, it looks like we really DO need an smax expr. Check to see if we 2242 // already have one, otherwise create a new one. 2243 FoldingSetNodeID ID; 2244 ID.AddInteger(scSMaxExpr); 2245 ID.AddInteger(Ops.size()); 2246 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2247 ID.AddPointer(Ops[i]); 2248 void *IP = 0; 2249 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2250 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2251 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2252 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2253 O, Ops.size()); 2254 UniqueSCEVs.InsertNode(S, IP); 2255 return S; 2256} 2257 2258const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2259 const SCEV *RHS) { 2260 SmallVector<const SCEV *, 2> Ops; 2261 Ops.push_back(LHS); 2262 Ops.push_back(RHS); 2263 return getUMaxExpr(Ops); 2264} 2265 2266const SCEV * 2267ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2268 assert(!Ops.empty() && "Cannot get empty umax!"); 2269 if (Ops.size() == 1) return Ops[0]; 2270#ifndef NDEBUG 2271 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2272 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2273 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2274 "SCEVUMaxExpr operand types don't match!"); 2275#endif 2276 2277 // Sort by complexity, this groups all similar expression types together. 2278 GroupByComplexity(Ops, LI); 2279 2280 // If there are any constants, fold them together. 2281 unsigned Idx = 0; 2282 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2283 ++Idx; 2284 assert(Idx < Ops.size()); 2285 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2286 // We found two constants, fold them together! 2287 ConstantInt *Fold = ConstantInt::get(getContext(), 2288 APIntOps::umax(LHSC->getValue()->getValue(), 2289 RHSC->getValue()->getValue())); 2290 Ops[0] = getConstant(Fold); 2291 Ops.erase(Ops.begin()+1); // Erase the folded element 2292 if (Ops.size() == 1) return Ops[0]; 2293 LHSC = cast<SCEVConstant>(Ops[0]); 2294 } 2295 2296 // If we are left with a constant minimum-int, strip it off. 2297 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2298 Ops.erase(Ops.begin()); 2299 --Idx; 2300 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2301 // If we have an umax with a constant maximum-int, it will always be 2302 // maximum-int. 2303 return Ops[0]; 2304 } 2305 2306 if (Ops.size() == 1) return Ops[0]; 2307 } 2308 2309 // Find the first UMax 2310 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2311 ++Idx; 2312 2313 // Check to see if one of the operands is a UMax. If so, expand its operands 2314 // onto our operand list, and recurse to simplify. 2315 if (Idx < Ops.size()) { 2316 bool DeletedUMax = false; 2317 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2318 Ops.erase(Ops.begin()+Idx); 2319 Ops.append(UMax->op_begin(), UMax->op_end()); 2320 DeletedUMax = true; 2321 } 2322 2323 if (DeletedUMax) 2324 return getUMaxExpr(Ops); 2325 } 2326 2327 // Okay, check to see if the same value occurs in the operand list twice. If 2328 // so, delete one. Since we sorted the list, these values are required to 2329 // be adjacent. 2330 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2331 // X umax Y umax Y --> X umax Y 2332 // X umax Y --> X, if X is always greater than Y 2333 if (Ops[i] == Ops[i+1] || 2334 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2335 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2336 --i; --e; 2337 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2338 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2339 --i; --e; 2340 } 2341 2342 if (Ops.size() == 1) return Ops[0]; 2343 2344 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2345 2346 // Okay, it looks like we really DO need a umax expr. Check to see if we 2347 // already have one, otherwise create a new one. 2348 FoldingSetNodeID ID; 2349 ID.AddInteger(scUMaxExpr); 2350 ID.AddInteger(Ops.size()); 2351 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2352 ID.AddPointer(Ops[i]); 2353 void *IP = 0; 2354 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2355 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2356 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2357 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2358 O, Ops.size()); 2359 UniqueSCEVs.InsertNode(S, IP); 2360 return S; 2361} 2362 2363const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2364 const SCEV *RHS) { 2365 // ~smax(~x, ~y) == smin(x, y). 2366 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2367} 2368 2369const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2370 const SCEV *RHS) { 2371 // ~umax(~x, ~y) == umin(x, y) 2372 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2373} 2374 2375const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2376 // If we have TargetData, we can bypass creating a target-independent 2377 // constant expression and then folding it back into a ConstantInt. 2378 // This is just a compile-time optimization. 2379 if (TD) 2380 return getConstant(TD->getIntPtrType(getContext()), 2381 TD->getTypeAllocSize(AllocTy)); 2382 2383 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2385 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2386 C = Folded; 2387 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2388 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2389} 2390 2391const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2392 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2393 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2394 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2395 C = Folded; 2396 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2397 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2398} 2399 2400const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2401 unsigned FieldNo) { 2402 // If we have TargetData, we can bypass creating a target-independent 2403 // constant expression and then folding it back into a ConstantInt. 2404 // This is just a compile-time optimization. 2405 if (TD) 2406 return getConstant(TD->getIntPtrType(getContext()), 2407 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2408 2409 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2410 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2411 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2412 C = Folded; 2413 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2414 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2415} 2416 2417const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2418 Constant *FieldNo) { 2419 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2420 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2421 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2422 C = Folded; 2423 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2424 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2425} 2426 2427const SCEV *ScalarEvolution::getUnknown(Value *V) { 2428 // Don't attempt to do anything other than create a SCEVUnknown object 2429 // here. createSCEV only calls getUnknown after checking for all other 2430 // interesting possibilities, and any other code that calls getUnknown 2431 // is doing so in order to hide a value from SCEV canonicalization. 2432 2433 FoldingSetNodeID ID; 2434 ID.AddInteger(scUnknown); 2435 ID.AddPointer(V); 2436 void *IP = 0; 2437 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2438 assert(cast<SCEVUnknown>(S)->getValue() == V && 2439 "Stale SCEVUnknown in uniquing map!"); 2440 return S; 2441 } 2442 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2443 FirstUnknown); 2444 FirstUnknown = cast<SCEVUnknown>(S); 2445 UniqueSCEVs.InsertNode(S, IP); 2446 return S; 2447} 2448 2449//===----------------------------------------------------------------------===// 2450// Basic SCEV Analysis and PHI Idiom Recognition Code 2451// 2452 2453/// isSCEVable - Test if values of the given type are analyzable within 2454/// the SCEV framework. This primarily includes integer types, and it 2455/// can optionally include pointer types if the ScalarEvolution class 2456/// has access to target-specific information. 2457bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2458 // Integers and pointers are always SCEVable. 2459 return Ty->isIntegerTy() || Ty->isPointerTy(); 2460} 2461 2462/// getTypeSizeInBits - Return the size in bits of the specified type, 2463/// for which isSCEVable must return true. 2464uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2465 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2466 2467 // If we have a TargetData, use it! 2468 if (TD) 2469 return TD->getTypeSizeInBits(Ty); 2470 2471 // Integer types have fixed sizes. 2472 if (Ty->isIntegerTy()) 2473 return Ty->getPrimitiveSizeInBits(); 2474 2475 // The only other support type is pointer. Without TargetData, conservatively 2476 // assume pointers are 64-bit. 2477 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2478 return 64; 2479} 2480 2481/// getEffectiveSCEVType - Return a type with the same bitwidth as 2482/// the given type and which represents how SCEV will treat the given 2483/// type, for which isSCEVable must return true. For pointer types, 2484/// this is the pointer-sized integer type. 2485const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2486 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2487 2488 if (Ty->isIntegerTy()) 2489 return Ty; 2490 2491 // The only other support type is pointer. 2492 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2493 if (TD) return TD->getIntPtrType(getContext()); 2494 2495 // Without TargetData, conservatively assume pointers are 64-bit. 2496 return Type::getInt64Ty(getContext()); 2497} 2498 2499const SCEV *ScalarEvolution::getCouldNotCompute() { 2500 return &CouldNotCompute; 2501} 2502 2503/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2504/// expression and create a new one. 2505const SCEV *ScalarEvolution::getSCEV(Value *V) { 2506 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2507 2508 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2509 if (I != ValueExprMap.end()) return I->second; 2510 const SCEV *S = createSCEV(V); 2511 2512 // The process of creating a SCEV for V may have caused other SCEVs 2513 // to have been created, so it's necessary to insert the new entry 2514 // from scratch, rather than trying to remember the insert position 2515 // above. 2516 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2517 return S; 2518} 2519 2520/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2521/// 2522const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2523 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2524 return getConstant( 2525 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2526 2527 const Type *Ty = V->getType(); 2528 Ty = getEffectiveSCEVType(Ty); 2529 return getMulExpr(V, 2530 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2531} 2532 2533/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2534const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2535 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2536 return getConstant( 2537 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2538 2539 const Type *Ty = V->getType(); 2540 Ty = getEffectiveSCEVType(Ty); 2541 const SCEV *AllOnes = 2542 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2543 return getMinusSCEV(AllOnes, V); 2544} 2545 2546/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2547/// 2548const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2549 const SCEV *RHS) { 2550 // Fast path: X - X --> 0. 2551 if (LHS == RHS) 2552 return getConstant(LHS->getType(), 0); 2553 2554 // X - Y --> X + -Y 2555 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2556} 2557 2558/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2559/// input value to the specified type. If the type must be extended, it is zero 2560/// extended. 2561const SCEV * 2562ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2563 const Type *Ty) { 2564 const Type *SrcTy = V->getType(); 2565 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2566 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2567 "Cannot truncate or zero extend with non-integer arguments!"); 2568 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2569 return V; // No conversion 2570 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2571 return getTruncateExpr(V, Ty); 2572 return getZeroExtendExpr(V, Ty); 2573} 2574 2575/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2576/// input value to the specified type. If the type must be extended, it is sign 2577/// extended. 2578const SCEV * 2579ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2580 const Type *Ty) { 2581 const Type *SrcTy = V->getType(); 2582 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2583 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2584 "Cannot truncate or zero extend with non-integer arguments!"); 2585 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2586 return V; // No conversion 2587 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2588 return getTruncateExpr(V, Ty); 2589 return getSignExtendExpr(V, Ty); 2590} 2591 2592/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2593/// input value to the specified type. If the type must be extended, it is zero 2594/// extended. The conversion must not be narrowing. 2595const SCEV * 2596ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2597 const Type *SrcTy = V->getType(); 2598 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2599 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2600 "Cannot noop or zero extend with non-integer arguments!"); 2601 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2602 "getNoopOrZeroExtend cannot truncate!"); 2603 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2604 return V; // No conversion 2605 return getZeroExtendExpr(V, Ty); 2606} 2607 2608/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2609/// input value to the specified type. If the type must be extended, it is sign 2610/// extended. The conversion must not be narrowing. 2611const SCEV * 2612ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2613 const Type *SrcTy = V->getType(); 2614 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2615 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2616 "Cannot noop or sign extend with non-integer arguments!"); 2617 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2618 "getNoopOrSignExtend cannot truncate!"); 2619 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2620 return V; // No conversion 2621 return getSignExtendExpr(V, Ty); 2622} 2623 2624/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2625/// the input value to the specified type. If the type must be extended, 2626/// it is extended with unspecified bits. The conversion must not be 2627/// narrowing. 2628const SCEV * 2629ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2630 const Type *SrcTy = V->getType(); 2631 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2632 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2633 "Cannot noop or any extend with non-integer arguments!"); 2634 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2635 "getNoopOrAnyExtend cannot truncate!"); 2636 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2637 return V; // No conversion 2638 return getAnyExtendExpr(V, Ty); 2639} 2640 2641/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2642/// input value to the specified type. The conversion must not be widening. 2643const SCEV * 2644ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2645 const Type *SrcTy = V->getType(); 2646 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2647 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2648 "Cannot truncate or noop with non-integer arguments!"); 2649 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2650 "getTruncateOrNoop cannot extend!"); 2651 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2652 return V; // No conversion 2653 return getTruncateExpr(V, Ty); 2654} 2655 2656/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2657/// the types using zero-extension, and then perform a umax operation 2658/// with them. 2659const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2660 const SCEV *RHS) { 2661 const SCEV *PromotedLHS = LHS; 2662 const SCEV *PromotedRHS = RHS; 2663 2664 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2665 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2666 else 2667 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2668 2669 return getUMaxExpr(PromotedLHS, PromotedRHS); 2670} 2671 2672/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2673/// the types using zero-extension, and then perform a umin operation 2674/// with them. 2675const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2676 const SCEV *RHS) { 2677 const SCEV *PromotedLHS = LHS; 2678 const SCEV *PromotedRHS = RHS; 2679 2680 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2681 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2682 else 2683 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2684 2685 return getUMinExpr(PromotedLHS, PromotedRHS); 2686} 2687 2688/// PushDefUseChildren - Push users of the given Instruction 2689/// onto the given Worklist. 2690static void 2691PushDefUseChildren(Instruction *I, 2692 SmallVectorImpl<Instruction *> &Worklist) { 2693 // Push the def-use children onto the Worklist stack. 2694 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2695 UI != UE; ++UI) 2696 Worklist.push_back(cast<Instruction>(*UI)); 2697} 2698 2699/// ForgetSymbolicValue - This looks up computed SCEV values for all 2700/// instructions that depend on the given instruction and removes them from 2701/// the ValueExprMapType map if they reference SymName. This is used during PHI 2702/// resolution. 2703void 2704ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2705 SmallVector<Instruction *, 16> Worklist; 2706 PushDefUseChildren(PN, Worklist); 2707 2708 SmallPtrSet<Instruction *, 8> Visited; 2709 Visited.insert(PN); 2710 while (!Worklist.empty()) { 2711 Instruction *I = Worklist.pop_back_val(); 2712 if (!Visited.insert(I)) continue; 2713 2714 ValueExprMapType::iterator It = 2715 ValueExprMap.find(static_cast<Value *>(I)); 2716 if (It != ValueExprMap.end()) { 2717 // Short-circuit the def-use traversal if the symbolic name 2718 // ceases to appear in expressions. 2719 if (It->second != SymName && !It->second->hasOperand(SymName)) 2720 continue; 2721 2722 // SCEVUnknown for a PHI either means that it has an unrecognized 2723 // structure, it's a PHI that's in the progress of being computed 2724 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2725 // additional loop trip count information isn't going to change anything. 2726 // In the second case, createNodeForPHI will perform the necessary 2727 // updates on its own when it gets to that point. In the third, we do 2728 // want to forget the SCEVUnknown. 2729 if (!isa<PHINode>(I) || 2730 !isa<SCEVUnknown>(It->second) || 2731 (I != PN && It->second == SymName)) { 2732 ValuesAtScopes.erase(It->second); 2733 ValueExprMap.erase(It); 2734 } 2735 } 2736 2737 PushDefUseChildren(I, Worklist); 2738 } 2739} 2740 2741/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2742/// a loop header, making it a potential recurrence, or it doesn't. 2743/// 2744const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2745 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2746 if (L->getHeader() == PN->getParent()) { 2747 // The loop may have multiple entrances or multiple exits; we can analyze 2748 // this phi as an addrec if it has a unique entry value and a unique 2749 // backedge value. 2750 Value *BEValueV = 0, *StartValueV = 0; 2751 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2752 Value *V = PN->getIncomingValue(i); 2753 if (L->contains(PN->getIncomingBlock(i))) { 2754 if (!BEValueV) { 2755 BEValueV = V; 2756 } else if (BEValueV != V) { 2757 BEValueV = 0; 2758 break; 2759 } 2760 } else if (!StartValueV) { 2761 StartValueV = V; 2762 } else if (StartValueV != V) { 2763 StartValueV = 0; 2764 break; 2765 } 2766 } 2767 if (BEValueV && StartValueV) { 2768 // While we are analyzing this PHI node, handle its value symbolically. 2769 const SCEV *SymbolicName = getUnknown(PN); 2770 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2771 "PHI node already processed?"); 2772 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2773 2774 // Using this symbolic name for the PHI, analyze the value coming around 2775 // the back-edge. 2776 const SCEV *BEValue = getSCEV(BEValueV); 2777 2778 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2779 // has a special value for the first iteration of the loop. 2780 2781 // If the value coming around the backedge is an add with the symbolic 2782 // value we just inserted, then we found a simple induction variable! 2783 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2784 // If there is a single occurrence of the symbolic value, replace it 2785 // with a recurrence. 2786 unsigned FoundIndex = Add->getNumOperands(); 2787 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2788 if (Add->getOperand(i) == SymbolicName) 2789 if (FoundIndex == e) { 2790 FoundIndex = i; 2791 break; 2792 } 2793 2794 if (FoundIndex != Add->getNumOperands()) { 2795 // Create an add with everything but the specified operand. 2796 SmallVector<const SCEV *, 8> Ops; 2797 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2798 if (i != FoundIndex) 2799 Ops.push_back(Add->getOperand(i)); 2800 const SCEV *Accum = getAddExpr(Ops); 2801 2802 // This is not a valid addrec if the step amount is varying each 2803 // loop iteration, but is not itself an addrec in this loop. 2804 if (Accum->isLoopInvariant(L) || 2805 (isa<SCEVAddRecExpr>(Accum) && 2806 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2807 bool HasNUW = false; 2808 bool HasNSW = false; 2809 2810 // If the increment doesn't overflow, then neither the addrec nor 2811 // the post-increment will overflow. 2812 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2813 if (OBO->hasNoUnsignedWrap()) 2814 HasNUW = true; 2815 if (OBO->hasNoSignedWrap()) 2816 HasNSW = true; 2817 } 2818 2819 const SCEV *StartVal = getSCEV(StartValueV); 2820 const SCEV *PHISCEV = 2821 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2822 2823 // Since the no-wrap flags are on the increment, they apply to the 2824 // post-incremented value as well. 2825 if (Accum->isLoopInvariant(L)) 2826 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2827 Accum, L, HasNUW, HasNSW); 2828 2829 // Okay, for the entire analysis of this edge we assumed the PHI 2830 // to be symbolic. We now need to go back and purge all of the 2831 // entries for the scalars that use the symbolic expression. 2832 ForgetSymbolicName(PN, SymbolicName); 2833 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2834 return PHISCEV; 2835 } 2836 } 2837 } else if (const SCEVAddRecExpr *AddRec = 2838 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2839 // Otherwise, this could be a loop like this: 2840 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2841 // In this case, j = {1,+,1} and BEValue is j. 2842 // Because the other in-value of i (0) fits the evolution of BEValue 2843 // i really is an addrec evolution. 2844 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2845 const SCEV *StartVal = getSCEV(StartValueV); 2846 2847 // If StartVal = j.start - j.stride, we can use StartVal as the 2848 // initial step of the addrec evolution. 2849 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2850 AddRec->getOperand(1))) { 2851 const SCEV *PHISCEV = 2852 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2853 2854 // Okay, for the entire analysis of this edge we assumed the PHI 2855 // to be symbolic. We now need to go back and purge all of the 2856 // entries for the scalars that use the symbolic expression. 2857 ForgetSymbolicName(PN, SymbolicName); 2858 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2859 return PHISCEV; 2860 } 2861 } 2862 } 2863 } 2864 } 2865 2866 // If the PHI has a single incoming value, follow that value, unless the 2867 // PHI's incoming blocks are in a different loop, in which case doing so 2868 // risks breaking LCSSA form. Instcombine would normally zap these, but 2869 // it doesn't have DominatorTree information, so it may miss cases. 2870 if (Value *V = PN->hasConstantValue(DT)) { 2871 bool AllSameLoop = true; 2872 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2873 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2874 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2875 AllSameLoop = false; 2876 break; 2877 } 2878 if (AllSameLoop) 2879 return getSCEV(V); 2880 } 2881 2882 // If it's not a loop phi, we can't handle it yet. 2883 return getUnknown(PN); 2884} 2885 2886/// createNodeForGEP - Expand GEP instructions into add and multiply 2887/// operations. This allows them to be analyzed by regular SCEV code. 2888/// 2889const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2890 2891 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2892 // Add expression, because the Instruction may be guarded by control flow 2893 // and the no-overflow bits may not be valid for the expression in any 2894 // context. 2895 2896 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2897 Value *Base = GEP->getOperand(0); 2898 // Don't attempt to analyze GEPs over unsized objects. 2899 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2900 return getUnknown(GEP); 2901 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2902 gep_type_iterator GTI = gep_type_begin(GEP); 2903 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2904 E = GEP->op_end(); 2905 I != E; ++I) { 2906 Value *Index = *I; 2907 // Compute the (potentially symbolic) offset in bytes for this index. 2908 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2909 // For a struct, add the member offset. 2910 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2911 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2912 2913 // Add the field offset to the running total offset. 2914 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2915 } else { 2916 // For an array, add the element offset, explicitly scaled. 2917 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2918 const SCEV *IndexS = getSCEV(Index); 2919 // Getelementptr indices are signed. 2920 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2921 2922 // Multiply the index by the element size to compute the element offset. 2923 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2924 2925 // Add the element offset to the running total offset. 2926 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2927 } 2928 } 2929 2930 // Get the SCEV for the GEP base. 2931 const SCEV *BaseS = getSCEV(Base); 2932 2933 // Add the total offset from all the GEP indices to the base. 2934 return getAddExpr(BaseS, TotalOffset); 2935} 2936 2937/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2938/// guaranteed to end in (at every loop iteration). It is, at the same time, 2939/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2940/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2941uint32_t 2942ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2943 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2944 return C->getValue()->getValue().countTrailingZeros(); 2945 2946 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2947 return std::min(GetMinTrailingZeros(T->getOperand()), 2948 (uint32_t)getTypeSizeInBits(T->getType())); 2949 2950 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2951 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2952 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2953 getTypeSizeInBits(E->getType()) : OpRes; 2954 } 2955 2956 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2957 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2958 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2959 getTypeSizeInBits(E->getType()) : OpRes; 2960 } 2961 2962 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2963 // The result is the min of all operands results. 2964 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2965 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2966 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2967 return MinOpRes; 2968 } 2969 2970 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2971 // The result is the sum of all operands results. 2972 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2973 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2974 for (unsigned i = 1, e = M->getNumOperands(); 2975 SumOpRes != BitWidth && i != e; ++i) 2976 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2977 BitWidth); 2978 return SumOpRes; 2979 } 2980 2981 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2982 // The result is the min of all operands results. 2983 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2984 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2985 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2986 return MinOpRes; 2987 } 2988 2989 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2990 // The result is the min of all operands results. 2991 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2992 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2993 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2994 return MinOpRes; 2995 } 2996 2997 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2998 // The result is the min of all operands results. 2999 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3000 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3001 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3002 return MinOpRes; 3003 } 3004 3005 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3006 // For a SCEVUnknown, ask ValueTracking. 3007 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3008 APInt Mask = APInt::getAllOnesValue(BitWidth); 3009 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3010 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3011 return Zeros.countTrailingOnes(); 3012 } 3013 3014 // SCEVUDivExpr 3015 return 0; 3016} 3017 3018/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3019/// 3020ConstantRange 3021ScalarEvolution::getUnsignedRange(const SCEV *S) { 3022 3023 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3024 return ConstantRange(C->getValue()->getValue()); 3025 3026 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3027 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3028 3029 // If the value has known zeros, the maximum unsigned value will have those 3030 // known zeros as well. 3031 uint32_t TZ = GetMinTrailingZeros(S); 3032 if (TZ != 0) 3033 ConservativeResult = 3034 ConstantRange(APInt::getMinValue(BitWidth), 3035 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3036 3037 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3038 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3039 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3040 X = X.add(getUnsignedRange(Add->getOperand(i))); 3041 return ConservativeResult.intersectWith(X); 3042 } 3043 3044 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3045 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3046 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3047 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3048 return ConservativeResult.intersectWith(X); 3049 } 3050 3051 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3052 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3053 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3054 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3055 return ConservativeResult.intersectWith(X); 3056 } 3057 3058 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3059 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3060 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3061 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3062 return ConservativeResult.intersectWith(X); 3063 } 3064 3065 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3066 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3067 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3068 return ConservativeResult.intersectWith(X.udiv(Y)); 3069 } 3070 3071 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3072 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3073 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3074 } 3075 3076 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3077 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3078 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3079 } 3080 3081 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3082 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3083 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3084 } 3085 3086 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3087 // If there's no unsigned wrap, the value will never be less than its 3088 // initial value. 3089 if (AddRec->hasNoUnsignedWrap()) 3090 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3091 if (!C->getValue()->isZero()) 3092 ConservativeResult = 3093 ConservativeResult.intersectWith( 3094 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3095 3096 // TODO: non-affine addrec 3097 if (AddRec->isAffine()) { 3098 const Type *Ty = AddRec->getType(); 3099 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3100 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3101 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3102 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3103 3104 const SCEV *Start = AddRec->getStart(); 3105 const SCEV *Step = AddRec->getStepRecurrence(*this); 3106 3107 ConstantRange StartRange = getUnsignedRange(Start); 3108 ConstantRange StepRange = getSignedRange(Step); 3109 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3110 ConstantRange EndRange = 3111 StartRange.add(MaxBECountRange.multiply(StepRange)); 3112 3113 // Check for overflow. This must be done with ConstantRange arithmetic 3114 // because we could be called from within the ScalarEvolution overflow 3115 // checking code. 3116 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3117 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3118 ConstantRange ExtMaxBECountRange = 3119 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3120 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3121 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3122 ExtEndRange) 3123 return ConservativeResult; 3124 3125 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3126 EndRange.getUnsignedMin()); 3127 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3128 EndRange.getUnsignedMax()); 3129 if (Min.isMinValue() && Max.isMaxValue()) 3130 return ConservativeResult; 3131 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3132 } 3133 } 3134 3135 return ConservativeResult; 3136 } 3137 3138 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3139 // For a SCEVUnknown, ask ValueTracking. 3140 APInt Mask = APInt::getAllOnesValue(BitWidth); 3141 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3142 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3143 if (Ones == ~Zeros + 1) 3144 return ConservativeResult; 3145 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3146 } 3147 3148 return ConservativeResult; 3149} 3150 3151/// getSignedRange - Determine the signed range for a particular SCEV. 3152/// 3153ConstantRange 3154ScalarEvolution::getSignedRange(const SCEV *S) { 3155 3156 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3157 return ConstantRange(C->getValue()->getValue()); 3158 3159 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3160 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3161 3162 // If the value has known zeros, the maximum signed value will have those 3163 // known zeros as well. 3164 uint32_t TZ = GetMinTrailingZeros(S); 3165 if (TZ != 0) 3166 ConservativeResult = 3167 ConstantRange(APInt::getSignedMinValue(BitWidth), 3168 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3169 3170 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3171 ConstantRange X = getSignedRange(Add->getOperand(0)); 3172 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3173 X = X.add(getSignedRange(Add->getOperand(i))); 3174 return ConservativeResult.intersectWith(X); 3175 } 3176 3177 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3178 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3179 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3180 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3181 return ConservativeResult.intersectWith(X); 3182 } 3183 3184 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3185 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3186 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3187 X = X.smax(getSignedRange(SMax->getOperand(i))); 3188 return ConservativeResult.intersectWith(X); 3189 } 3190 3191 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3192 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3193 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3194 X = X.umax(getSignedRange(UMax->getOperand(i))); 3195 return ConservativeResult.intersectWith(X); 3196 } 3197 3198 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3199 ConstantRange X = getSignedRange(UDiv->getLHS()); 3200 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3201 return ConservativeResult.intersectWith(X.udiv(Y)); 3202 } 3203 3204 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3205 ConstantRange X = getSignedRange(ZExt->getOperand()); 3206 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3207 } 3208 3209 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3210 ConstantRange X = getSignedRange(SExt->getOperand()); 3211 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3212 } 3213 3214 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3215 ConstantRange X = getSignedRange(Trunc->getOperand()); 3216 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3217 } 3218 3219 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3220 // If there's no signed wrap, and all the operands have the same sign or 3221 // zero, the value won't ever change sign. 3222 if (AddRec->hasNoSignedWrap()) { 3223 bool AllNonNeg = true; 3224 bool AllNonPos = true; 3225 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3226 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3227 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3228 } 3229 if (AllNonNeg) 3230 ConservativeResult = ConservativeResult.intersectWith( 3231 ConstantRange(APInt(BitWidth, 0), 3232 APInt::getSignedMinValue(BitWidth))); 3233 else if (AllNonPos) 3234 ConservativeResult = ConservativeResult.intersectWith( 3235 ConstantRange(APInt::getSignedMinValue(BitWidth), 3236 APInt(BitWidth, 1))); 3237 } 3238 3239 // TODO: non-affine addrec 3240 if (AddRec->isAffine()) { 3241 const Type *Ty = AddRec->getType(); 3242 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3243 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3244 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3245 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3246 3247 const SCEV *Start = AddRec->getStart(); 3248 const SCEV *Step = AddRec->getStepRecurrence(*this); 3249 3250 ConstantRange StartRange = getSignedRange(Start); 3251 ConstantRange StepRange = getSignedRange(Step); 3252 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3253 ConstantRange EndRange = 3254 StartRange.add(MaxBECountRange.multiply(StepRange)); 3255 3256 // Check for overflow. This must be done with ConstantRange arithmetic 3257 // because we could be called from within the ScalarEvolution overflow 3258 // checking code. 3259 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3260 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3261 ConstantRange ExtMaxBECountRange = 3262 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3263 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3264 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3265 ExtEndRange) 3266 return ConservativeResult; 3267 3268 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3269 EndRange.getSignedMin()); 3270 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3271 EndRange.getSignedMax()); 3272 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3273 return ConservativeResult; 3274 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3275 } 3276 } 3277 3278 return ConservativeResult; 3279 } 3280 3281 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3282 // For a SCEVUnknown, ask ValueTracking. 3283 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3284 return ConservativeResult; 3285 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3286 if (NS == 1) 3287 return ConservativeResult; 3288 return ConservativeResult.intersectWith( 3289 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3290 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3291 } 3292 3293 return ConservativeResult; 3294} 3295 3296/// createSCEV - We know that there is no SCEV for the specified value. 3297/// Analyze the expression. 3298/// 3299const SCEV *ScalarEvolution::createSCEV(Value *V) { 3300 if (!isSCEVable(V->getType())) 3301 return getUnknown(V); 3302 3303 unsigned Opcode = Instruction::UserOp1; 3304 if (Instruction *I = dyn_cast<Instruction>(V)) { 3305 Opcode = I->getOpcode(); 3306 3307 // Don't attempt to analyze instructions in blocks that aren't 3308 // reachable. Such instructions don't matter, and they aren't required 3309 // to obey basic rules for definitions dominating uses which this 3310 // analysis depends on. 3311 if (!DT->isReachableFromEntry(I->getParent())) 3312 return getUnknown(V); 3313 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3314 Opcode = CE->getOpcode(); 3315 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3316 return getConstant(CI); 3317 else if (isa<ConstantPointerNull>(V)) 3318 return getConstant(V->getType(), 0); 3319 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3320 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3321 else 3322 return getUnknown(V); 3323 3324 Operator *U = cast<Operator>(V); 3325 switch (Opcode) { 3326 case Instruction::Add: { 3327 // The simple thing to do would be to just call getSCEV on both operands 3328 // and call getAddExpr with the result. However if we're looking at a 3329 // bunch of things all added together, this can be quite inefficient, 3330 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3331 // Instead, gather up all the operands and make a single getAddExpr call. 3332 // LLVM IR canonical form means we need only traverse the left operands. 3333 SmallVector<const SCEV *, 4> AddOps; 3334 AddOps.push_back(getSCEV(U->getOperand(1))); 3335 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3336 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3337 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3338 break; 3339 U = cast<Operator>(Op); 3340 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3341 if (Opcode == Instruction::Sub) 3342 AddOps.push_back(getNegativeSCEV(Op1)); 3343 else 3344 AddOps.push_back(Op1); 3345 } 3346 AddOps.push_back(getSCEV(U->getOperand(0))); 3347 return getAddExpr(AddOps); 3348 } 3349 case Instruction::Mul: { 3350 // See the Add code above. 3351 SmallVector<const SCEV *, 4> MulOps; 3352 MulOps.push_back(getSCEV(U->getOperand(1))); 3353 for (Value *Op = U->getOperand(0); 3354 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3355 Op = U->getOperand(0)) { 3356 U = cast<Operator>(Op); 3357 MulOps.push_back(getSCEV(U->getOperand(1))); 3358 } 3359 MulOps.push_back(getSCEV(U->getOperand(0))); 3360 return getMulExpr(MulOps); 3361 } 3362 case Instruction::UDiv: 3363 return getUDivExpr(getSCEV(U->getOperand(0)), 3364 getSCEV(U->getOperand(1))); 3365 case Instruction::Sub: 3366 return getMinusSCEV(getSCEV(U->getOperand(0)), 3367 getSCEV(U->getOperand(1))); 3368 case Instruction::And: 3369 // For an expression like x&255 that merely masks off the high bits, 3370 // use zext(trunc(x)) as the SCEV expression. 3371 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3372 if (CI->isNullValue()) 3373 return getSCEV(U->getOperand(1)); 3374 if (CI->isAllOnesValue()) 3375 return getSCEV(U->getOperand(0)); 3376 const APInt &A = CI->getValue(); 3377 3378 // Instcombine's ShrinkDemandedConstant may strip bits out of 3379 // constants, obscuring what would otherwise be a low-bits mask. 3380 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3381 // knew about to reconstruct a low-bits mask value. 3382 unsigned LZ = A.countLeadingZeros(); 3383 unsigned BitWidth = A.getBitWidth(); 3384 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3385 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3386 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3387 3388 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3389 3390 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3391 return 3392 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3393 IntegerType::get(getContext(), BitWidth - LZ)), 3394 U->getType()); 3395 } 3396 break; 3397 3398 case Instruction::Or: 3399 // If the RHS of the Or is a constant, we may have something like: 3400 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3401 // optimizations will transparently handle this case. 3402 // 3403 // In order for this transformation to be safe, the LHS must be of the 3404 // form X*(2^n) and the Or constant must be less than 2^n. 3405 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3406 const SCEV *LHS = getSCEV(U->getOperand(0)); 3407 const APInt &CIVal = CI->getValue(); 3408 if (GetMinTrailingZeros(LHS) >= 3409 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3410 // Build a plain add SCEV. 3411 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3412 // If the LHS of the add was an addrec and it has no-wrap flags, 3413 // transfer the no-wrap flags, since an or won't introduce a wrap. 3414 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3415 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3416 if (OldAR->hasNoUnsignedWrap()) 3417 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3418 if (OldAR->hasNoSignedWrap()) 3419 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3420 } 3421 return S; 3422 } 3423 } 3424 break; 3425 case Instruction::Xor: 3426 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3427 // If the RHS of the xor is a signbit, then this is just an add. 3428 // Instcombine turns add of signbit into xor as a strength reduction step. 3429 if (CI->getValue().isSignBit()) 3430 return getAddExpr(getSCEV(U->getOperand(0)), 3431 getSCEV(U->getOperand(1))); 3432 3433 // If the RHS of xor is -1, then this is a not operation. 3434 if (CI->isAllOnesValue()) 3435 return getNotSCEV(getSCEV(U->getOperand(0))); 3436 3437 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3438 // This is a variant of the check for xor with -1, and it handles 3439 // the case where instcombine has trimmed non-demanded bits out 3440 // of an xor with -1. 3441 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3442 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3443 if (BO->getOpcode() == Instruction::And && 3444 LCI->getValue() == CI->getValue()) 3445 if (const SCEVZeroExtendExpr *Z = 3446 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3447 const Type *UTy = U->getType(); 3448 const SCEV *Z0 = Z->getOperand(); 3449 const Type *Z0Ty = Z0->getType(); 3450 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3451 3452 // If C is a low-bits mask, the zero extend is serving to 3453 // mask off the high bits. Complement the operand and 3454 // re-apply the zext. 3455 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3456 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3457 3458 // If C is a single bit, it may be in the sign-bit position 3459 // before the zero-extend. In this case, represent the xor 3460 // using an add, which is equivalent, and re-apply the zext. 3461 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3462 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3463 Trunc.isSignBit()) 3464 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3465 UTy); 3466 } 3467 } 3468 break; 3469 3470 case Instruction::Shl: 3471 // Turn shift left of a constant amount into a multiply. 3472 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3473 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3474 3475 // If the shift count is not less than the bitwidth, the result of 3476 // the shift is undefined. Don't try to analyze it, because the 3477 // resolution chosen here may differ from the resolution chosen in 3478 // other parts of the compiler. 3479 if (SA->getValue().uge(BitWidth)) 3480 break; 3481 3482 Constant *X = ConstantInt::get(getContext(), 3483 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3484 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3485 } 3486 break; 3487 3488 case Instruction::LShr: 3489 // Turn logical shift right of a constant into a unsigned divide. 3490 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3491 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3492 3493 // If the shift count is not less than the bitwidth, the result of 3494 // the shift is undefined. Don't try to analyze it, because the 3495 // resolution chosen here may differ from the resolution chosen in 3496 // other parts of the compiler. 3497 if (SA->getValue().uge(BitWidth)) 3498 break; 3499 3500 Constant *X = ConstantInt::get(getContext(), 3501 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3502 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3503 } 3504 break; 3505 3506 case Instruction::AShr: 3507 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3508 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3509 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3510 if (L->getOpcode() == Instruction::Shl && 3511 L->getOperand(1) == U->getOperand(1)) { 3512 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3513 3514 // If the shift count is not less than the bitwidth, the result of 3515 // the shift is undefined. Don't try to analyze it, because the 3516 // resolution chosen here may differ from the resolution chosen in 3517 // other parts of the compiler. 3518 if (CI->getValue().uge(BitWidth)) 3519 break; 3520 3521 uint64_t Amt = BitWidth - CI->getZExtValue(); 3522 if (Amt == BitWidth) 3523 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3524 return 3525 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3526 IntegerType::get(getContext(), 3527 Amt)), 3528 U->getType()); 3529 } 3530 break; 3531 3532 case Instruction::Trunc: 3533 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3534 3535 case Instruction::ZExt: 3536 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3537 3538 case Instruction::SExt: 3539 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3540 3541 case Instruction::BitCast: 3542 // BitCasts are no-op casts so we just eliminate the cast. 3543 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3544 return getSCEV(U->getOperand(0)); 3545 break; 3546 3547 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3548 // lead to pointer expressions which cannot safely be expanded to GEPs, 3549 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3550 // simplifying integer expressions. 3551 3552 case Instruction::GetElementPtr: 3553 return createNodeForGEP(cast<GEPOperator>(U)); 3554 3555 case Instruction::PHI: 3556 return createNodeForPHI(cast<PHINode>(U)); 3557 3558 case Instruction::Select: 3559 // This could be a smax or umax that was lowered earlier. 3560 // Try to recover it. 3561 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3562 Value *LHS = ICI->getOperand(0); 3563 Value *RHS = ICI->getOperand(1); 3564 switch (ICI->getPredicate()) { 3565 case ICmpInst::ICMP_SLT: 3566 case ICmpInst::ICMP_SLE: 3567 std::swap(LHS, RHS); 3568 // fall through 3569 case ICmpInst::ICMP_SGT: 3570 case ICmpInst::ICMP_SGE: 3571 // a >s b ? a+x : b+x -> smax(a, b)+x 3572 // a >s b ? b+x : a+x -> smin(a, b)+x 3573 if (LHS->getType() == U->getType()) { 3574 const SCEV *LS = getSCEV(LHS); 3575 const SCEV *RS = getSCEV(RHS); 3576 const SCEV *LA = getSCEV(U->getOperand(1)); 3577 const SCEV *RA = getSCEV(U->getOperand(2)); 3578 const SCEV *LDiff = getMinusSCEV(LA, LS); 3579 const SCEV *RDiff = getMinusSCEV(RA, RS); 3580 if (LDiff == RDiff) 3581 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3582 LDiff = getMinusSCEV(LA, RS); 3583 RDiff = getMinusSCEV(RA, LS); 3584 if (LDiff == RDiff) 3585 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3586 } 3587 break; 3588 case ICmpInst::ICMP_ULT: 3589 case ICmpInst::ICMP_ULE: 3590 std::swap(LHS, RHS); 3591 // fall through 3592 case ICmpInst::ICMP_UGT: 3593 case ICmpInst::ICMP_UGE: 3594 // a >u b ? a+x : b+x -> umax(a, b)+x 3595 // a >u b ? b+x : a+x -> umin(a, b)+x 3596 if (LHS->getType() == U->getType()) { 3597 const SCEV *LS = getSCEV(LHS); 3598 const SCEV *RS = getSCEV(RHS); 3599 const SCEV *LA = getSCEV(U->getOperand(1)); 3600 const SCEV *RA = getSCEV(U->getOperand(2)); 3601 const SCEV *LDiff = getMinusSCEV(LA, LS); 3602 const SCEV *RDiff = getMinusSCEV(RA, RS); 3603 if (LDiff == RDiff) 3604 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3605 LDiff = getMinusSCEV(LA, RS); 3606 RDiff = getMinusSCEV(RA, LS); 3607 if (LDiff == RDiff) 3608 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3609 } 3610 break; 3611 case ICmpInst::ICMP_NE: 3612 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3613 if (LHS->getType() == U->getType() && 3614 isa<ConstantInt>(RHS) && 3615 cast<ConstantInt>(RHS)->isZero()) { 3616 const SCEV *One = getConstant(LHS->getType(), 1); 3617 const SCEV *LS = getSCEV(LHS); 3618 const SCEV *LA = getSCEV(U->getOperand(1)); 3619 const SCEV *RA = getSCEV(U->getOperand(2)); 3620 const SCEV *LDiff = getMinusSCEV(LA, LS); 3621 const SCEV *RDiff = getMinusSCEV(RA, One); 3622 if (LDiff == RDiff) 3623 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3624 } 3625 break; 3626 case ICmpInst::ICMP_EQ: 3627 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3628 if (LHS->getType() == U->getType() && 3629 isa<ConstantInt>(RHS) && 3630 cast<ConstantInt>(RHS)->isZero()) { 3631 const SCEV *One = getConstant(LHS->getType(), 1); 3632 const SCEV *LS = getSCEV(LHS); 3633 const SCEV *LA = getSCEV(U->getOperand(1)); 3634 const SCEV *RA = getSCEV(U->getOperand(2)); 3635 const SCEV *LDiff = getMinusSCEV(LA, One); 3636 const SCEV *RDiff = getMinusSCEV(RA, LS); 3637 if (LDiff == RDiff) 3638 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3639 } 3640 break; 3641 default: 3642 break; 3643 } 3644 } 3645 3646 default: // We cannot analyze this expression. 3647 break; 3648 } 3649 3650 return getUnknown(V); 3651} 3652 3653 3654 3655//===----------------------------------------------------------------------===// 3656// Iteration Count Computation Code 3657// 3658 3659/// getBackedgeTakenCount - If the specified loop has a predictable 3660/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3661/// object. The backedge-taken count is the number of times the loop header 3662/// will be branched to from within the loop. This is one less than the 3663/// trip count of the loop, since it doesn't count the first iteration, 3664/// when the header is branched to from outside the loop. 3665/// 3666/// Note that it is not valid to call this method on a loop without a 3667/// loop-invariant backedge-taken count (see 3668/// hasLoopInvariantBackedgeTakenCount). 3669/// 3670const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3671 return getBackedgeTakenInfo(L).Exact; 3672} 3673 3674/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3675/// return the least SCEV value that is known never to be less than the 3676/// actual backedge taken count. 3677const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3678 return getBackedgeTakenInfo(L).Max; 3679} 3680 3681/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3682/// onto the given Worklist. 3683static void 3684PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3685 BasicBlock *Header = L->getHeader(); 3686 3687 // Push all Loop-header PHIs onto the Worklist stack. 3688 for (BasicBlock::iterator I = Header->begin(); 3689 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3690 Worklist.push_back(PN); 3691} 3692 3693const ScalarEvolution::BackedgeTakenInfo & 3694ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3695 // Initially insert a CouldNotCompute for this loop. If the insertion 3696 // succeeds, proceed to actually compute a backedge-taken count and 3697 // update the value. The temporary CouldNotCompute value tells SCEV 3698 // code elsewhere that it shouldn't attempt to request a new 3699 // backedge-taken count, which could result in infinite recursion. 3700 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3701 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3702 if (Pair.second) { 3703 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3704 if (BECount.Exact != getCouldNotCompute()) { 3705 assert(BECount.Exact->isLoopInvariant(L) && 3706 BECount.Max->isLoopInvariant(L) && 3707 "Computed backedge-taken count isn't loop invariant for loop!"); 3708 ++NumTripCountsComputed; 3709 3710 // Update the value in the map. 3711 Pair.first->second = BECount; 3712 } else { 3713 if (BECount.Max != getCouldNotCompute()) 3714 // Update the value in the map. 3715 Pair.first->second = BECount; 3716 if (isa<PHINode>(L->getHeader()->begin())) 3717 // Only count loops that have phi nodes as not being computable. 3718 ++NumTripCountsNotComputed; 3719 } 3720 3721 // Now that we know more about the trip count for this loop, forget any 3722 // existing SCEV values for PHI nodes in this loop since they are only 3723 // conservative estimates made without the benefit of trip count 3724 // information. This is similar to the code in forgetLoop, except that 3725 // it handles SCEVUnknown PHI nodes specially. 3726 if (BECount.hasAnyInfo()) { 3727 SmallVector<Instruction *, 16> Worklist; 3728 PushLoopPHIs(L, Worklist); 3729 3730 SmallPtrSet<Instruction *, 8> Visited; 3731 while (!Worklist.empty()) { 3732 Instruction *I = Worklist.pop_back_val(); 3733 if (!Visited.insert(I)) continue; 3734 3735 ValueExprMapType::iterator It = 3736 ValueExprMap.find(static_cast<Value *>(I)); 3737 if (It != ValueExprMap.end()) { 3738 // SCEVUnknown for a PHI either means that it has an unrecognized 3739 // structure, or it's a PHI that's in the progress of being computed 3740 // by createNodeForPHI. In the former case, additional loop trip 3741 // count information isn't going to change anything. In the later 3742 // case, createNodeForPHI will perform the necessary updates on its 3743 // own when it gets to that point. 3744 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3745 ValuesAtScopes.erase(It->second); 3746 ValueExprMap.erase(It); 3747 } 3748 if (PHINode *PN = dyn_cast<PHINode>(I)) 3749 ConstantEvolutionLoopExitValue.erase(PN); 3750 } 3751 3752 PushDefUseChildren(I, Worklist); 3753 } 3754 } 3755 } 3756 return Pair.first->second; 3757} 3758 3759/// forgetLoop - This method should be called by the client when it has 3760/// changed a loop in a way that may effect ScalarEvolution's ability to 3761/// compute a trip count, or if the loop is deleted. 3762void ScalarEvolution::forgetLoop(const Loop *L) { 3763 // Drop any stored trip count value. 3764 BackedgeTakenCounts.erase(L); 3765 3766 // Drop information about expressions based on loop-header PHIs. 3767 SmallVector<Instruction *, 16> Worklist; 3768 PushLoopPHIs(L, Worklist); 3769 3770 SmallPtrSet<Instruction *, 8> Visited; 3771 while (!Worklist.empty()) { 3772 Instruction *I = Worklist.pop_back_val(); 3773 if (!Visited.insert(I)) continue; 3774 3775 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3776 if (It != ValueExprMap.end()) { 3777 ValuesAtScopes.erase(It->second); 3778 ValueExprMap.erase(It); 3779 if (PHINode *PN = dyn_cast<PHINode>(I)) 3780 ConstantEvolutionLoopExitValue.erase(PN); 3781 } 3782 3783 PushDefUseChildren(I, Worklist); 3784 } 3785} 3786 3787/// forgetValue - This method should be called by the client when it has 3788/// changed a value in a way that may effect its value, or which may 3789/// disconnect it from a def-use chain linking it to a loop. 3790void ScalarEvolution::forgetValue(Value *V) { 3791 Instruction *I = dyn_cast<Instruction>(V); 3792 if (!I) return; 3793 3794 // Drop information about expressions based on loop-header PHIs. 3795 SmallVector<Instruction *, 16> Worklist; 3796 Worklist.push_back(I); 3797 3798 SmallPtrSet<Instruction *, 8> Visited; 3799 while (!Worklist.empty()) { 3800 I = Worklist.pop_back_val(); 3801 if (!Visited.insert(I)) continue; 3802 3803 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3804 if (It != ValueExprMap.end()) { 3805 ValuesAtScopes.erase(It->second); 3806 ValueExprMap.erase(It); 3807 if (PHINode *PN = dyn_cast<PHINode>(I)) 3808 ConstantEvolutionLoopExitValue.erase(PN); 3809 } 3810 3811 PushDefUseChildren(I, Worklist); 3812 } 3813} 3814 3815/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3816/// of the specified loop will execute. 3817ScalarEvolution::BackedgeTakenInfo 3818ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3819 SmallVector<BasicBlock *, 8> ExitingBlocks; 3820 L->getExitingBlocks(ExitingBlocks); 3821 3822 // Examine all exits and pick the most conservative values. 3823 const SCEV *BECount = getCouldNotCompute(); 3824 const SCEV *MaxBECount = getCouldNotCompute(); 3825 bool CouldNotComputeBECount = false; 3826 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3827 BackedgeTakenInfo NewBTI = 3828 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3829 3830 if (NewBTI.Exact == getCouldNotCompute()) { 3831 // We couldn't compute an exact value for this exit, so 3832 // we won't be able to compute an exact value for the loop. 3833 CouldNotComputeBECount = true; 3834 BECount = getCouldNotCompute(); 3835 } else if (!CouldNotComputeBECount) { 3836 if (BECount == getCouldNotCompute()) 3837 BECount = NewBTI.Exact; 3838 else 3839 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3840 } 3841 if (MaxBECount == getCouldNotCompute()) 3842 MaxBECount = NewBTI.Max; 3843 else if (NewBTI.Max != getCouldNotCompute()) 3844 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3845 } 3846 3847 return BackedgeTakenInfo(BECount, MaxBECount); 3848} 3849 3850/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3851/// of the specified loop will execute if it exits via the specified block. 3852ScalarEvolution::BackedgeTakenInfo 3853ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3854 BasicBlock *ExitingBlock) { 3855 3856 // Okay, we've chosen an exiting block. See what condition causes us to 3857 // exit at this block. 3858 // 3859 // FIXME: we should be able to handle switch instructions (with a single exit) 3860 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3861 if (ExitBr == 0) return getCouldNotCompute(); 3862 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3863 3864 // At this point, we know we have a conditional branch that determines whether 3865 // the loop is exited. However, we don't know if the branch is executed each 3866 // time through the loop. If not, then the execution count of the branch will 3867 // not be equal to the trip count of the loop. 3868 // 3869 // Currently we check for this by checking to see if the Exit branch goes to 3870 // the loop header. If so, we know it will always execute the same number of 3871 // times as the loop. We also handle the case where the exit block *is* the 3872 // loop header. This is common for un-rotated loops. 3873 // 3874 // If both of those tests fail, walk up the unique predecessor chain to the 3875 // header, stopping if there is an edge that doesn't exit the loop. If the 3876 // header is reached, the execution count of the branch will be equal to the 3877 // trip count of the loop. 3878 // 3879 // More extensive analysis could be done to handle more cases here. 3880 // 3881 if (ExitBr->getSuccessor(0) != L->getHeader() && 3882 ExitBr->getSuccessor(1) != L->getHeader() && 3883 ExitBr->getParent() != L->getHeader()) { 3884 // The simple checks failed, try climbing the unique predecessor chain 3885 // up to the header. 3886 bool Ok = false; 3887 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3888 BasicBlock *Pred = BB->getUniquePredecessor(); 3889 if (!Pred) 3890 return getCouldNotCompute(); 3891 TerminatorInst *PredTerm = Pred->getTerminator(); 3892 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3893 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3894 if (PredSucc == BB) 3895 continue; 3896 // If the predecessor has a successor that isn't BB and isn't 3897 // outside the loop, assume the worst. 3898 if (L->contains(PredSucc)) 3899 return getCouldNotCompute(); 3900 } 3901 if (Pred == L->getHeader()) { 3902 Ok = true; 3903 break; 3904 } 3905 BB = Pred; 3906 } 3907 if (!Ok) 3908 return getCouldNotCompute(); 3909 } 3910 3911 // Proceed to the next level to examine the exit condition expression. 3912 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3913 ExitBr->getSuccessor(0), 3914 ExitBr->getSuccessor(1)); 3915} 3916 3917/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3918/// backedge of the specified loop will execute if its exit condition 3919/// were a conditional branch of ExitCond, TBB, and FBB. 3920ScalarEvolution::BackedgeTakenInfo 3921ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3922 Value *ExitCond, 3923 BasicBlock *TBB, 3924 BasicBlock *FBB) { 3925 // Check if the controlling expression for this loop is an And or Or. 3926 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3927 if (BO->getOpcode() == Instruction::And) { 3928 // Recurse on the operands of the and. 3929 BackedgeTakenInfo BTI0 = 3930 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3931 BackedgeTakenInfo BTI1 = 3932 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3933 const SCEV *BECount = getCouldNotCompute(); 3934 const SCEV *MaxBECount = getCouldNotCompute(); 3935 if (L->contains(TBB)) { 3936 // Both conditions must be true for the loop to continue executing. 3937 // Choose the less conservative count. 3938 if (BTI0.Exact == getCouldNotCompute() || 3939 BTI1.Exact == getCouldNotCompute()) 3940 BECount = getCouldNotCompute(); 3941 else 3942 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3943 if (BTI0.Max == getCouldNotCompute()) 3944 MaxBECount = BTI1.Max; 3945 else if (BTI1.Max == getCouldNotCompute()) 3946 MaxBECount = BTI0.Max; 3947 else 3948 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3949 } else { 3950 // Both conditions must be true at the same time for the loop to exit. 3951 // For now, be conservative. 3952 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3953 if (BTI0.Max == BTI1.Max) 3954 MaxBECount = BTI0.Max; 3955 if (BTI0.Exact == BTI1.Exact) 3956 BECount = BTI0.Exact; 3957 } 3958 3959 return BackedgeTakenInfo(BECount, MaxBECount); 3960 } 3961 if (BO->getOpcode() == Instruction::Or) { 3962 // Recurse on the operands of the or. 3963 BackedgeTakenInfo BTI0 = 3964 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3965 BackedgeTakenInfo BTI1 = 3966 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3967 const SCEV *BECount = getCouldNotCompute(); 3968 const SCEV *MaxBECount = getCouldNotCompute(); 3969 if (L->contains(FBB)) { 3970 // Both conditions must be false for the loop to continue executing. 3971 // Choose the less conservative count. 3972 if (BTI0.Exact == getCouldNotCompute() || 3973 BTI1.Exact == getCouldNotCompute()) 3974 BECount = getCouldNotCompute(); 3975 else 3976 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3977 if (BTI0.Max == getCouldNotCompute()) 3978 MaxBECount = BTI1.Max; 3979 else if (BTI1.Max == getCouldNotCompute()) 3980 MaxBECount = BTI0.Max; 3981 else 3982 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3983 } else { 3984 // Both conditions must be false at the same time for the loop to exit. 3985 // For now, be conservative. 3986 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3987 if (BTI0.Max == BTI1.Max) 3988 MaxBECount = BTI0.Max; 3989 if (BTI0.Exact == BTI1.Exact) 3990 BECount = BTI0.Exact; 3991 } 3992 3993 return BackedgeTakenInfo(BECount, MaxBECount); 3994 } 3995 } 3996 3997 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3998 // Proceed to the next level to examine the icmp. 3999 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4000 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 4001 4002 // Check for a constant condition. These are normally stripped out by 4003 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4004 // preserve the CFG and is temporarily leaving constant conditions 4005 // in place. 4006 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4007 if (L->contains(FBB) == !CI->getZExtValue()) 4008 // The backedge is always taken. 4009 return getCouldNotCompute(); 4010 else 4011 // The backedge is never taken. 4012 return getConstant(CI->getType(), 0); 4013 } 4014 4015 // If it's not an integer or pointer comparison then compute it the hard way. 4016 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4017} 4018 4019/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4020/// backedge of the specified loop will execute if its exit condition 4021/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4022ScalarEvolution::BackedgeTakenInfo 4023ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4024 ICmpInst *ExitCond, 4025 BasicBlock *TBB, 4026 BasicBlock *FBB) { 4027 4028 // If the condition was exit on true, convert the condition to exit on false 4029 ICmpInst::Predicate Cond; 4030 if (!L->contains(FBB)) 4031 Cond = ExitCond->getPredicate(); 4032 else 4033 Cond = ExitCond->getInversePredicate(); 4034 4035 // Handle common loops like: for (X = "string"; *X; ++X) 4036 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4037 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4038 BackedgeTakenInfo ItCnt = 4039 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4040 if (ItCnt.hasAnyInfo()) 4041 return ItCnt; 4042 } 4043 4044 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4045 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4046 4047 // Try to evaluate any dependencies out of the loop. 4048 LHS = getSCEVAtScope(LHS, L); 4049 RHS = getSCEVAtScope(RHS, L); 4050 4051 // At this point, we would like to compute how many iterations of the 4052 // loop the predicate will return true for these inputs. 4053 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 4054 // If there is a loop-invariant, force it into the RHS. 4055 std::swap(LHS, RHS); 4056 Cond = ICmpInst::getSwappedPredicate(Cond); 4057 } 4058 4059 // Simplify the operands before analyzing them. 4060 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4061 4062 // If we have a comparison of a chrec against a constant, try to use value 4063 // ranges to answer this query. 4064 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4065 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4066 if (AddRec->getLoop() == L) { 4067 // Form the constant range. 4068 ConstantRange CompRange( 4069 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4070 4071 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4072 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4073 } 4074 4075 switch (Cond) { 4076 case ICmpInst::ICMP_NE: { // while (X != Y) 4077 // Convert to: while (X-Y != 0) 4078 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4079 if (BTI.hasAnyInfo()) return BTI; 4080 break; 4081 } 4082 case ICmpInst::ICMP_EQ: { // while (X == Y) 4083 // Convert to: while (X-Y == 0) 4084 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4085 if (BTI.hasAnyInfo()) return BTI; 4086 break; 4087 } 4088 case ICmpInst::ICMP_SLT: { 4089 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4090 if (BTI.hasAnyInfo()) return BTI; 4091 break; 4092 } 4093 case ICmpInst::ICMP_SGT: { 4094 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4095 getNotSCEV(RHS), L, true); 4096 if (BTI.hasAnyInfo()) return BTI; 4097 break; 4098 } 4099 case ICmpInst::ICMP_ULT: { 4100 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4101 if (BTI.hasAnyInfo()) return BTI; 4102 break; 4103 } 4104 case ICmpInst::ICMP_UGT: { 4105 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4106 getNotSCEV(RHS), L, false); 4107 if (BTI.hasAnyInfo()) return BTI; 4108 break; 4109 } 4110 default: 4111#if 0 4112 dbgs() << "ComputeBackedgeTakenCount "; 4113 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4114 dbgs() << "[unsigned] "; 4115 dbgs() << *LHS << " " 4116 << Instruction::getOpcodeName(Instruction::ICmp) 4117 << " " << *RHS << "\n"; 4118#endif 4119 break; 4120 } 4121 return 4122 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4123} 4124 4125static ConstantInt * 4126EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4127 ScalarEvolution &SE) { 4128 const SCEV *InVal = SE.getConstant(C); 4129 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4130 assert(isa<SCEVConstant>(Val) && 4131 "Evaluation of SCEV at constant didn't fold correctly?"); 4132 return cast<SCEVConstant>(Val)->getValue(); 4133} 4134 4135/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4136/// and a GEP expression (missing the pointer index) indexing into it, return 4137/// the addressed element of the initializer or null if the index expression is 4138/// invalid. 4139static Constant * 4140GetAddressedElementFromGlobal(GlobalVariable *GV, 4141 const std::vector<ConstantInt*> &Indices) { 4142 Constant *Init = GV->getInitializer(); 4143 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4144 uint64_t Idx = Indices[i]->getZExtValue(); 4145 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4146 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4147 Init = cast<Constant>(CS->getOperand(Idx)); 4148 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4149 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4150 Init = cast<Constant>(CA->getOperand(Idx)); 4151 } else if (isa<ConstantAggregateZero>(Init)) { 4152 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4153 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4154 Init = Constant::getNullValue(STy->getElementType(Idx)); 4155 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4156 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4157 Init = Constant::getNullValue(ATy->getElementType()); 4158 } else { 4159 llvm_unreachable("Unknown constant aggregate type!"); 4160 } 4161 return 0; 4162 } else { 4163 return 0; // Unknown initializer type 4164 } 4165 } 4166 return Init; 4167} 4168 4169/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4170/// 'icmp op load X, cst', try to see if we can compute the backedge 4171/// execution count. 4172ScalarEvolution::BackedgeTakenInfo 4173ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4174 LoadInst *LI, 4175 Constant *RHS, 4176 const Loop *L, 4177 ICmpInst::Predicate predicate) { 4178 if (LI->isVolatile()) return getCouldNotCompute(); 4179 4180 // Check to see if the loaded pointer is a getelementptr of a global. 4181 // TODO: Use SCEV instead of manually grubbing with GEPs. 4182 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4183 if (!GEP) return getCouldNotCompute(); 4184 4185 // Make sure that it is really a constant global we are gepping, with an 4186 // initializer, and make sure the first IDX is really 0. 4187 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4188 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4189 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4190 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4191 return getCouldNotCompute(); 4192 4193 // Okay, we allow one non-constant index into the GEP instruction. 4194 Value *VarIdx = 0; 4195 std::vector<ConstantInt*> Indexes; 4196 unsigned VarIdxNum = 0; 4197 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4198 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4199 Indexes.push_back(CI); 4200 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4201 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4202 VarIdx = GEP->getOperand(i); 4203 VarIdxNum = i-2; 4204 Indexes.push_back(0); 4205 } 4206 4207 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4208 // Check to see if X is a loop variant variable value now. 4209 const SCEV *Idx = getSCEV(VarIdx); 4210 Idx = getSCEVAtScope(Idx, L); 4211 4212 // We can only recognize very limited forms of loop index expressions, in 4213 // particular, only affine AddRec's like {C1,+,C2}. 4214 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4215 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4216 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4217 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4218 return getCouldNotCompute(); 4219 4220 unsigned MaxSteps = MaxBruteForceIterations; 4221 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4222 ConstantInt *ItCst = ConstantInt::get( 4223 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4224 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4225 4226 // Form the GEP offset. 4227 Indexes[VarIdxNum] = Val; 4228 4229 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4230 if (Result == 0) break; // Cannot compute! 4231 4232 // Evaluate the condition for this iteration. 4233 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4234 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4235 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4236#if 0 4237 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4238 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4239 << "***\n"; 4240#endif 4241 ++NumArrayLenItCounts; 4242 return getConstant(ItCst); // Found terminating iteration! 4243 } 4244 } 4245 return getCouldNotCompute(); 4246} 4247 4248 4249/// CanConstantFold - Return true if we can constant fold an instruction of the 4250/// specified type, assuming that all operands were constants. 4251static bool CanConstantFold(const Instruction *I) { 4252 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4253 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4254 return true; 4255 4256 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4257 if (const Function *F = CI->getCalledFunction()) 4258 return canConstantFoldCallTo(F); 4259 return false; 4260} 4261 4262/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4263/// in the loop that V is derived from. We allow arbitrary operations along the 4264/// way, but the operands of an operation must either be constants or a value 4265/// derived from a constant PHI. If this expression does not fit with these 4266/// constraints, return null. 4267static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4268 // If this is not an instruction, or if this is an instruction outside of the 4269 // loop, it can't be derived from a loop PHI. 4270 Instruction *I = dyn_cast<Instruction>(V); 4271 if (I == 0 || !L->contains(I)) return 0; 4272 4273 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4274 if (L->getHeader() == I->getParent()) 4275 return PN; 4276 else 4277 // We don't currently keep track of the control flow needed to evaluate 4278 // PHIs, so we cannot handle PHIs inside of loops. 4279 return 0; 4280 } 4281 4282 // If we won't be able to constant fold this expression even if the operands 4283 // are constants, return early. 4284 if (!CanConstantFold(I)) return 0; 4285 4286 // Otherwise, we can evaluate this instruction if all of its operands are 4287 // constant or derived from a PHI node themselves. 4288 PHINode *PHI = 0; 4289 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4290 if (!isa<Constant>(I->getOperand(Op))) { 4291 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4292 if (P == 0) return 0; // Not evolving from PHI 4293 if (PHI == 0) 4294 PHI = P; 4295 else if (PHI != P) 4296 return 0; // Evolving from multiple different PHIs. 4297 } 4298 4299 // This is a expression evolving from a constant PHI! 4300 return PHI; 4301} 4302 4303/// EvaluateExpression - Given an expression that passes the 4304/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4305/// in the loop has the value PHIVal. If we can't fold this expression for some 4306/// reason, return null. 4307static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4308 const TargetData *TD) { 4309 if (isa<PHINode>(V)) return PHIVal; 4310 if (Constant *C = dyn_cast<Constant>(V)) return C; 4311 Instruction *I = cast<Instruction>(V); 4312 4313 std::vector<Constant*> Operands(I->getNumOperands()); 4314 4315 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4316 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4317 if (Operands[i] == 0) return 0; 4318 } 4319 4320 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4321 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4322 Operands[1], TD); 4323 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4324 &Operands[0], Operands.size(), TD); 4325} 4326 4327/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4328/// in the header of its containing loop, we know the loop executes a 4329/// constant number of times, and the PHI node is just a recurrence 4330/// involving constants, fold it. 4331Constant * 4332ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4333 const APInt &BEs, 4334 const Loop *L) { 4335 std::map<PHINode*, Constant*>::const_iterator I = 4336 ConstantEvolutionLoopExitValue.find(PN); 4337 if (I != ConstantEvolutionLoopExitValue.end()) 4338 return I->second; 4339 4340 if (BEs.ugt(MaxBruteForceIterations)) 4341 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4342 4343 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4344 4345 // Since the loop is canonicalized, the PHI node must have two entries. One 4346 // entry must be a constant (coming in from outside of the loop), and the 4347 // second must be derived from the same PHI. 4348 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4349 Constant *StartCST = 4350 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4351 if (StartCST == 0) 4352 return RetVal = 0; // Must be a constant. 4353 4354 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4355 if (getConstantEvolvingPHI(BEValue, L) != PN && 4356 !isa<Constant>(BEValue)) 4357 return RetVal = 0; // Not derived from same PHI. 4358 4359 // Execute the loop symbolically to determine the exit value. 4360 if (BEs.getActiveBits() >= 32) 4361 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4362 4363 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4364 unsigned IterationNum = 0; 4365 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4366 if (IterationNum == NumIterations) 4367 return RetVal = PHIVal; // Got exit value! 4368 4369 // Compute the value of the PHI node for the next iteration. 4370 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4371 if (NextPHI == PHIVal) 4372 return RetVal = NextPHI; // Stopped evolving! 4373 if (NextPHI == 0) 4374 return 0; // Couldn't evaluate! 4375 PHIVal = NextPHI; 4376 } 4377} 4378 4379/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4380/// constant number of times (the condition evolves only from constants), 4381/// try to evaluate a few iterations of the loop until we get the exit 4382/// condition gets a value of ExitWhen (true or false). If we cannot 4383/// evaluate the trip count of the loop, return getCouldNotCompute(). 4384const SCEV * 4385ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4386 Value *Cond, 4387 bool ExitWhen) { 4388 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4389 if (PN == 0) return getCouldNotCompute(); 4390 4391 // If the loop is canonicalized, the PHI will have exactly two entries. 4392 // That's the only form we support here. 4393 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4394 4395 // One entry must be a constant (coming in from outside of the loop), and the 4396 // second must be derived from the same PHI. 4397 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4398 Constant *StartCST = 4399 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4400 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4401 4402 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4403 if (getConstantEvolvingPHI(BEValue, L) != PN && 4404 !isa<Constant>(BEValue)) 4405 return getCouldNotCompute(); // Not derived from same PHI. 4406 4407 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4408 // the loop symbolically to determine when the condition gets a value of 4409 // "ExitWhen". 4410 unsigned IterationNum = 0; 4411 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4412 for (Constant *PHIVal = StartCST; 4413 IterationNum != MaxIterations; ++IterationNum) { 4414 ConstantInt *CondVal = 4415 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4416 4417 // Couldn't symbolically evaluate. 4418 if (!CondVal) return getCouldNotCompute(); 4419 4420 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4421 ++NumBruteForceTripCountsComputed; 4422 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4423 } 4424 4425 // Compute the value of the PHI node for the next iteration. 4426 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4427 if (NextPHI == 0 || NextPHI == PHIVal) 4428 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4429 PHIVal = NextPHI; 4430 } 4431 4432 // Too many iterations were needed to evaluate. 4433 return getCouldNotCompute(); 4434} 4435 4436/// getSCEVAtScope - Return a SCEV expression for the specified value 4437/// at the specified scope in the program. The L value specifies a loop 4438/// nest to evaluate the expression at, where null is the top-level or a 4439/// specified loop is immediately inside of the loop. 4440/// 4441/// This method can be used to compute the exit value for a variable defined 4442/// in a loop by querying what the value will hold in the parent loop. 4443/// 4444/// In the case that a relevant loop exit value cannot be computed, the 4445/// original value V is returned. 4446const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4447 // Check to see if we've folded this expression at this loop before. 4448 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4449 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4450 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4451 if (!Pair.second) 4452 return Pair.first->second ? Pair.first->second : V; 4453 4454 // Otherwise compute it. 4455 const SCEV *C = computeSCEVAtScope(V, L); 4456 ValuesAtScopes[V][L] = C; 4457 return C; 4458} 4459 4460const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4461 if (isa<SCEVConstant>(V)) return V; 4462 4463 // If this instruction is evolved from a constant-evolving PHI, compute the 4464 // exit value from the loop without using SCEVs. 4465 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4466 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4467 const Loop *LI = (*this->LI)[I->getParent()]; 4468 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4469 if (PHINode *PN = dyn_cast<PHINode>(I)) 4470 if (PN->getParent() == LI->getHeader()) { 4471 // Okay, there is no closed form solution for the PHI node. Check 4472 // to see if the loop that contains it has a known backedge-taken 4473 // count. If so, we may be able to force computation of the exit 4474 // value. 4475 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4476 if (const SCEVConstant *BTCC = 4477 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4478 // Okay, we know how many times the containing loop executes. If 4479 // this is a constant evolving PHI node, get the final value at 4480 // the specified iteration number. 4481 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4482 BTCC->getValue()->getValue(), 4483 LI); 4484 if (RV) return getSCEV(RV); 4485 } 4486 } 4487 4488 // Okay, this is an expression that we cannot symbolically evaluate 4489 // into a SCEV. Check to see if it's possible to symbolically evaluate 4490 // the arguments into constants, and if so, try to constant propagate the 4491 // result. This is particularly useful for computing loop exit values. 4492 if (CanConstantFold(I)) { 4493 SmallVector<Constant *, 4> Operands; 4494 bool MadeImprovement = false; 4495 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4496 Value *Op = I->getOperand(i); 4497 if (Constant *C = dyn_cast<Constant>(Op)) { 4498 Operands.push_back(C); 4499 continue; 4500 } 4501 4502 // If any of the operands is non-constant and if they are 4503 // non-integer and non-pointer, don't even try to analyze them 4504 // with scev techniques. 4505 if (!isSCEVable(Op->getType())) 4506 return V; 4507 4508 const SCEV *OrigV = getSCEV(Op); 4509 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4510 MadeImprovement |= OrigV != OpV; 4511 4512 Constant *C = 0; 4513 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4514 C = SC->getValue(); 4515 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4516 C = dyn_cast<Constant>(SU->getValue()); 4517 if (!C) return V; 4518 if (C->getType() != Op->getType()) 4519 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4520 Op->getType(), 4521 false), 4522 C, Op->getType()); 4523 Operands.push_back(C); 4524 } 4525 4526 // Check to see if getSCEVAtScope actually made an improvement. 4527 if (MadeImprovement) { 4528 Constant *C = 0; 4529 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4530 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4531 Operands[0], Operands[1], TD); 4532 else 4533 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4534 &Operands[0], Operands.size(), TD); 4535 if (!C) return V; 4536 return getSCEV(C); 4537 } 4538 } 4539 } 4540 4541 // This is some other type of SCEVUnknown, just return it. 4542 return V; 4543 } 4544 4545 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4546 // Avoid performing the look-up in the common case where the specified 4547 // expression has no loop-variant portions. 4548 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4549 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4550 if (OpAtScope != Comm->getOperand(i)) { 4551 // Okay, at least one of these operands is loop variant but might be 4552 // foldable. Build a new instance of the folded commutative expression. 4553 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4554 Comm->op_begin()+i); 4555 NewOps.push_back(OpAtScope); 4556 4557 for (++i; i != e; ++i) { 4558 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4559 NewOps.push_back(OpAtScope); 4560 } 4561 if (isa<SCEVAddExpr>(Comm)) 4562 return getAddExpr(NewOps); 4563 if (isa<SCEVMulExpr>(Comm)) 4564 return getMulExpr(NewOps); 4565 if (isa<SCEVSMaxExpr>(Comm)) 4566 return getSMaxExpr(NewOps); 4567 if (isa<SCEVUMaxExpr>(Comm)) 4568 return getUMaxExpr(NewOps); 4569 llvm_unreachable("Unknown commutative SCEV type!"); 4570 } 4571 } 4572 // If we got here, all operands are loop invariant. 4573 return Comm; 4574 } 4575 4576 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4577 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4578 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4579 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4580 return Div; // must be loop invariant 4581 return getUDivExpr(LHS, RHS); 4582 } 4583 4584 // If this is a loop recurrence for a loop that does not contain L, then we 4585 // are dealing with the final value computed by the loop. 4586 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4587 // First, attempt to evaluate each operand. 4588 // Avoid performing the look-up in the common case where the specified 4589 // expression has no loop-variant portions. 4590 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4591 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4592 if (OpAtScope == AddRec->getOperand(i)) 4593 continue; 4594 4595 // Okay, at least one of these operands is loop variant but might be 4596 // foldable. Build a new instance of the folded commutative expression. 4597 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4598 AddRec->op_begin()+i); 4599 NewOps.push_back(OpAtScope); 4600 for (++i; i != e; ++i) 4601 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4602 4603 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4604 break; 4605 } 4606 4607 // If the scope is outside the addrec's loop, evaluate it by using the 4608 // loop exit value of the addrec. 4609 if (!AddRec->getLoop()->contains(L)) { 4610 // To evaluate this recurrence, we need to know how many times the AddRec 4611 // loop iterates. Compute this now. 4612 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4613 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4614 4615 // Then, evaluate the AddRec. 4616 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4617 } 4618 4619 return AddRec; 4620 } 4621 4622 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4623 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4624 if (Op == Cast->getOperand()) 4625 return Cast; // must be loop invariant 4626 return getZeroExtendExpr(Op, Cast->getType()); 4627 } 4628 4629 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4630 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4631 if (Op == Cast->getOperand()) 4632 return Cast; // must be loop invariant 4633 return getSignExtendExpr(Op, Cast->getType()); 4634 } 4635 4636 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4637 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4638 if (Op == Cast->getOperand()) 4639 return Cast; // must be loop invariant 4640 return getTruncateExpr(Op, Cast->getType()); 4641 } 4642 4643 llvm_unreachable("Unknown SCEV type!"); 4644 return 0; 4645} 4646 4647/// getSCEVAtScope - This is a convenience function which does 4648/// getSCEVAtScope(getSCEV(V), L). 4649const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4650 return getSCEVAtScope(getSCEV(V), L); 4651} 4652 4653/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4654/// following equation: 4655/// 4656/// A * X = B (mod N) 4657/// 4658/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4659/// A and B isn't important. 4660/// 4661/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4662static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4663 ScalarEvolution &SE) { 4664 uint32_t BW = A.getBitWidth(); 4665 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4666 assert(A != 0 && "A must be non-zero."); 4667 4668 // 1. D = gcd(A, N) 4669 // 4670 // The gcd of A and N may have only one prime factor: 2. The number of 4671 // trailing zeros in A is its multiplicity 4672 uint32_t Mult2 = A.countTrailingZeros(); 4673 // D = 2^Mult2 4674 4675 // 2. Check if B is divisible by D. 4676 // 4677 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4678 // is not less than multiplicity of this prime factor for D. 4679 if (B.countTrailingZeros() < Mult2) 4680 return SE.getCouldNotCompute(); 4681 4682 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4683 // modulo (N / D). 4684 // 4685 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4686 // bit width during computations. 4687 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4688 APInt Mod(BW + 1, 0); 4689 Mod.set(BW - Mult2); // Mod = N / D 4690 APInt I = AD.multiplicativeInverse(Mod); 4691 4692 // 4. Compute the minimum unsigned root of the equation: 4693 // I * (B / D) mod (N / D) 4694 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4695 4696 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4697 // bits. 4698 return SE.getConstant(Result.trunc(BW)); 4699} 4700 4701/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4702/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4703/// might be the same) or two SCEVCouldNotCompute objects. 4704/// 4705static std::pair<const SCEV *,const SCEV *> 4706SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4707 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4708 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4709 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4710 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4711 4712 // We currently can only solve this if the coefficients are constants. 4713 if (!LC || !MC || !NC) { 4714 const SCEV *CNC = SE.getCouldNotCompute(); 4715 return std::make_pair(CNC, CNC); 4716 } 4717 4718 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4719 const APInt &L = LC->getValue()->getValue(); 4720 const APInt &M = MC->getValue()->getValue(); 4721 const APInt &N = NC->getValue()->getValue(); 4722 APInt Two(BitWidth, 2); 4723 APInt Four(BitWidth, 4); 4724 4725 { 4726 using namespace APIntOps; 4727 const APInt& C = L; 4728 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4729 // The B coefficient is M-N/2 4730 APInt B(M); 4731 B -= sdiv(N,Two); 4732 4733 // The A coefficient is N/2 4734 APInt A(N.sdiv(Two)); 4735 4736 // Compute the B^2-4ac term. 4737 APInt SqrtTerm(B); 4738 SqrtTerm *= B; 4739 SqrtTerm -= Four * (A * C); 4740 4741 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4742 // integer value or else APInt::sqrt() will assert. 4743 APInt SqrtVal(SqrtTerm.sqrt()); 4744 4745 // Compute the two solutions for the quadratic formula. 4746 // The divisions must be performed as signed divisions. 4747 APInt NegB(-B); 4748 APInt TwoA( A << 1 ); 4749 if (TwoA.isMinValue()) { 4750 const SCEV *CNC = SE.getCouldNotCompute(); 4751 return std::make_pair(CNC, CNC); 4752 } 4753 4754 LLVMContext &Context = SE.getContext(); 4755 4756 ConstantInt *Solution1 = 4757 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4758 ConstantInt *Solution2 = 4759 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4760 4761 return std::make_pair(SE.getConstant(Solution1), 4762 SE.getConstant(Solution2)); 4763 } // end APIntOps namespace 4764} 4765 4766/// HowFarToZero - Return the number of times a backedge comparing the specified 4767/// value to zero will execute. If not computable, return CouldNotCompute. 4768ScalarEvolution::BackedgeTakenInfo 4769ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4770 // If the value is a constant 4771 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4772 // If the value is already zero, the branch will execute zero times. 4773 if (C->getValue()->isZero()) return C; 4774 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4775 } 4776 4777 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4778 if (!AddRec || AddRec->getLoop() != L) 4779 return getCouldNotCompute(); 4780 4781 if (AddRec->isAffine()) { 4782 // If this is an affine expression, the execution count of this branch is 4783 // the minimum unsigned root of the following equation: 4784 // 4785 // Start + Step*N = 0 (mod 2^BW) 4786 // 4787 // equivalent to: 4788 // 4789 // Step*N = -Start (mod 2^BW) 4790 // 4791 // where BW is the common bit width of Start and Step. 4792 4793 // Get the initial value for the loop. 4794 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4795 L->getParentLoop()); 4796 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4797 L->getParentLoop()); 4798 4799 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4800 // For now we handle only constant steps. 4801 4802 // First, handle unitary steps. 4803 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4804 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4805 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4806 return Start; // N = Start (as unsigned) 4807 4808 // Then, try to solve the above equation provided that Start is constant. 4809 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4810 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4811 -StartC->getValue()->getValue(), 4812 *this); 4813 } 4814 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4815 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4816 // the quadratic equation to solve it. 4817 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4818 *this); 4819 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4820 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4821 if (R1) { 4822#if 0 4823 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4824 << " sol#2: " << *R2 << "\n"; 4825#endif 4826 // Pick the smallest positive root value. 4827 if (ConstantInt *CB = 4828 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4829 R1->getValue(), R2->getValue()))) { 4830 if (CB->getZExtValue() == false) 4831 std::swap(R1, R2); // R1 is the minimum root now. 4832 4833 // We can only use this value if the chrec ends up with an exact zero 4834 // value at this index. When solving for "X*X != 5", for example, we 4835 // should not accept a root of 2. 4836 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4837 if (Val->isZero()) 4838 return R1; // We found a quadratic root! 4839 } 4840 } 4841 } 4842 4843 return getCouldNotCompute(); 4844} 4845 4846/// HowFarToNonZero - Return the number of times a backedge checking the 4847/// specified value for nonzero will execute. If not computable, return 4848/// CouldNotCompute 4849ScalarEvolution::BackedgeTakenInfo 4850ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4851 // Loops that look like: while (X == 0) are very strange indeed. We don't 4852 // handle them yet except for the trivial case. This could be expanded in the 4853 // future as needed. 4854 4855 // If the value is a constant, check to see if it is known to be non-zero 4856 // already. If so, the backedge will execute zero times. 4857 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4858 if (!C->getValue()->isNullValue()) 4859 return getConstant(C->getType(), 0); 4860 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4861 } 4862 4863 // We could implement others, but I really doubt anyone writes loops like 4864 // this, and if they did, they would already be constant folded. 4865 return getCouldNotCompute(); 4866} 4867 4868/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4869/// (which may not be an immediate predecessor) which has exactly one 4870/// successor from which BB is reachable, or null if no such block is 4871/// found. 4872/// 4873std::pair<BasicBlock *, BasicBlock *> 4874ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4875 // If the block has a unique predecessor, then there is no path from the 4876 // predecessor to the block that does not go through the direct edge 4877 // from the predecessor to the block. 4878 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4879 return std::make_pair(Pred, BB); 4880 4881 // A loop's header is defined to be a block that dominates the loop. 4882 // If the header has a unique predecessor outside the loop, it must be 4883 // a block that has exactly one successor that can reach the loop. 4884 if (Loop *L = LI->getLoopFor(BB)) 4885 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4886 4887 return std::pair<BasicBlock *, BasicBlock *>(); 4888} 4889 4890/// HasSameValue - SCEV structural equivalence is usually sufficient for 4891/// testing whether two expressions are equal, however for the purposes of 4892/// looking for a condition guarding a loop, it can be useful to be a little 4893/// more general, since a front-end may have replicated the controlling 4894/// expression. 4895/// 4896static bool HasSameValue(const SCEV *A, const SCEV *B) { 4897 // Quick check to see if they are the same SCEV. 4898 if (A == B) return true; 4899 4900 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4901 // two different instructions with the same value. Check for this case. 4902 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4903 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4904 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4905 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4906 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4907 return true; 4908 4909 // Otherwise assume they may have a different value. 4910 return false; 4911} 4912 4913/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4914/// predicate Pred. Return true iff any changes were made. 4915/// 4916bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4917 const SCEV *&LHS, const SCEV *&RHS) { 4918 bool Changed = false; 4919 4920 // Canonicalize a constant to the right side. 4921 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4922 // Check for both operands constant. 4923 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4924 if (ConstantExpr::getICmp(Pred, 4925 LHSC->getValue(), 4926 RHSC->getValue())->isNullValue()) 4927 goto trivially_false; 4928 else 4929 goto trivially_true; 4930 } 4931 // Otherwise swap the operands to put the constant on the right. 4932 std::swap(LHS, RHS); 4933 Pred = ICmpInst::getSwappedPredicate(Pred); 4934 Changed = true; 4935 } 4936 4937 // If we're comparing an addrec with a value which is loop-invariant in the 4938 // addrec's loop, put the addrec on the left. Also make a dominance check, 4939 // as both operands could be addrecs loop-invariant in each other's loop. 4940 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4941 const Loop *L = AR->getLoop(); 4942 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4943 std::swap(LHS, RHS); 4944 Pred = ICmpInst::getSwappedPredicate(Pred); 4945 Changed = true; 4946 } 4947 } 4948 4949 // If there's a constant operand, canonicalize comparisons with boundary 4950 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4951 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4952 const APInt &RA = RC->getValue()->getValue(); 4953 switch (Pred) { 4954 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4955 case ICmpInst::ICMP_EQ: 4956 case ICmpInst::ICMP_NE: 4957 break; 4958 case ICmpInst::ICMP_UGE: 4959 if ((RA - 1).isMinValue()) { 4960 Pred = ICmpInst::ICMP_NE; 4961 RHS = getConstant(RA - 1); 4962 Changed = true; 4963 break; 4964 } 4965 if (RA.isMaxValue()) { 4966 Pred = ICmpInst::ICMP_EQ; 4967 Changed = true; 4968 break; 4969 } 4970 if (RA.isMinValue()) goto trivially_true; 4971 4972 Pred = ICmpInst::ICMP_UGT; 4973 RHS = getConstant(RA - 1); 4974 Changed = true; 4975 break; 4976 case ICmpInst::ICMP_ULE: 4977 if ((RA + 1).isMaxValue()) { 4978 Pred = ICmpInst::ICMP_NE; 4979 RHS = getConstant(RA + 1); 4980 Changed = true; 4981 break; 4982 } 4983 if (RA.isMinValue()) { 4984 Pred = ICmpInst::ICMP_EQ; 4985 Changed = true; 4986 break; 4987 } 4988 if (RA.isMaxValue()) goto trivially_true; 4989 4990 Pred = ICmpInst::ICMP_ULT; 4991 RHS = getConstant(RA + 1); 4992 Changed = true; 4993 break; 4994 case ICmpInst::ICMP_SGE: 4995 if ((RA - 1).isMinSignedValue()) { 4996 Pred = ICmpInst::ICMP_NE; 4997 RHS = getConstant(RA - 1); 4998 Changed = true; 4999 break; 5000 } 5001 if (RA.isMaxSignedValue()) { 5002 Pred = ICmpInst::ICMP_EQ; 5003 Changed = true; 5004 break; 5005 } 5006 if (RA.isMinSignedValue()) goto trivially_true; 5007 5008 Pred = ICmpInst::ICMP_SGT; 5009 RHS = getConstant(RA - 1); 5010 Changed = true; 5011 break; 5012 case ICmpInst::ICMP_SLE: 5013 if ((RA + 1).isMaxSignedValue()) { 5014 Pred = ICmpInst::ICMP_NE; 5015 RHS = getConstant(RA + 1); 5016 Changed = true; 5017 break; 5018 } 5019 if (RA.isMinSignedValue()) { 5020 Pred = ICmpInst::ICMP_EQ; 5021 Changed = true; 5022 break; 5023 } 5024 if (RA.isMaxSignedValue()) goto trivially_true; 5025 5026 Pred = ICmpInst::ICMP_SLT; 5027 RHS = getConstant(RA + 1); 5028 Changed = true; 5029 break; 5030 case ICmpInst::ICMP_UGT: 5031 if (RA.isMinValue()) { 5032 Pred = ICmpInst::ICMP_NE; 5033 Changed = true; 5034 break; 5035 } 5036 if ((RA + 1).isMaxValue()) { 5037 Pred = ICmpInst::ICMP_EQ; 5038 RHS = getConstant(RA + 1); 5039 Changed = true; 5040 break; 5041 } 5042 if (RA.isMaxValue()) goto trivially_false; 5043 break; 5044 case ICmpInst::ICMP_ULT: 5045 if (RA.isMaxValue()) { 5046 Pred = ICmpInst::ICMP_NE; 5047 Changed = true; 5048 break; 5049 } 5050 if ((RA - 1).isMinValue()) { 5051 Pred = ICmpInst::ICMP_EQ; 5052 RHS = getConstant(RA - 1); 5053 Changed = true; 5054 break; 5055 } 5056 if (RA.isMinValue()) goto trivially_false; 5057 break; 5058 case ICmpInst::ICMP_SGT: 5059 if (RA.isMinSignedValue()) { 5060 Pred = ICmpInst::ICMP_NE; 5061 Changed = true; 5062 break; 5063 } 5064 if ((RA + 1).isMaxSignedValue()) { 5065 Pred = ICmpInst::ICMP_EQ; 5066 RHS = getConstant(RA + 1); 5067 Changed = true; 5068 break; 5069 } 5070 if (RA.isMaxSignedValue()) goto trivially_false; 5071 break; 5072 case ICmpInst::ICMP_SLT: 5073 if (RA.isMaxSignedValue()) { 5074 Pred = ICmpInst::ICMP_NE; 5075 Changed = true; 5076 break; 5077 } 5078 if ((RA - 1).isMinSignedValue()) { 5079 Pred = ICmpInst::ICMP_EQ; 5080 RHS = getConstant(RA - 1); 5081 Changed = true; 5082 break; 5083 } 5084 if (RA.isMinSignedValue()) goto trivially_false; 5085 break; 5086 } 5087 } 5088 5089 // Check for obvious equality. 5090 if (HasSameValue(LHS, RHS)) { 5091 if (ICmpInst::isTrueWhenEqual(Pred)) 5092 goto trivially_true; 5093 if (ICmpInst::isFalseWhenEqual(Pred)) 5094 goto trivially_false; 5095 } 5096 5097 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5098 // adding or subtracting 1 from one of the operands. 5099 switch (Pred) { 5100 case ICmpInst::ICMP_SLE: 5101 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5102 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5103 /*HasNUW=*/false, /*HasNSW=*/true); 5104 Pred = ICmpInst::ICMP_SLT; 5105 Changed = true; 5106 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5107 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5108 /*HasNUW=*/false, /*HasNSW=*/true); 5109 Pred = ICmpInst::ICMP_SLT; 5110 Changed = true; 5111 } 5112 break; 5113 case ICmpInst::ICMP_SGE: 5114 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5115 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5116 /*HasNUW=*/false, /*HasNSW=*/true); 5117 Pred = ICmpInst::ICMP_SGT; 5118 Changed = true; 5119 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5120 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5121 /*HasNUW=*/false, /*HasNSW=*/true); 5122 Pred = ICmpInst::ICMP_SGT; 5123 Changed = true; 5124 } 5125 break; 5126 case ICmpInst::ICMP_ULE: 5127 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5128 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5129 /*HasNUW=*/true, /*HasNSW=*/false); 5130 Pred = ICmpInst::ICMP_ULT; 5131 Changed = true; 5132 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5133 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5134 /*HasNUW=*/true, /*HasNSW=*/false); 5135 Pred = ICmpInst::ICMP_ULT; 5136 Changed = true; 5137 } 5138 break; 5139 case ICmpInst::ICMP_UGE: 5140 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5141 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5142 /*HasNUW=*/true, /*HasNSW=*/false); 5143 Pred = ICmpInst::ICMP_UGT; 5144 Changed = true; 5145 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5146 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5147 /*HasNUW=*/true, /*HasNSW=*/false); 5148 Pred = ICmpInst::ICMP_UGT; 5149 Changed = true; 5150 } 5151 break; 5152 default: 5153 break; 5154 } 5155 5156 // TODO: More simplifications are possible here. 5157 5158 return Changed; 5159 5160trivially_true: 5161 // Return 0 == 0. 5162 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5163 Pred = ICmpInst::ICMP_EQ; 5164 return true; 5165 5166trivially_false: 5167 // Return 0 != 0. 5168 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5169 Pred = ICmpInst::ICMP_NE; 5170 return true; 5171} 5172 5173bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5174 return getSignedRange(S).getSignedMax().isNegative(); 5175} 5176 5177bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5178 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5179} 5180 5181bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5182 return !getSignedRange(S).getSignedMin().isNegative(); 5183} 5184 5185bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5186 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5187} 5188 5189bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5190 return isKnownNegative(S) || isKnownPositive(S); 5191} 5192 5193bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5194 const SCEV *LHS, const SCEV *RHS) { 5195 // Canonicalize the inputs first. 5196 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5197 5198 // If LHS or RHS is an addrec, check to see if the condition is true in 5199 // every iteration of the loop. 5200 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5201 if (isLoopEntryGuardedByCond( 5202 AR->getLoop(), Pred, AR->getStart(), RHS) && 5203 isLoopBackedgeGuardedByCond( 5204 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5205 return true; 5206 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5207 if (isLoopEntryGuardedByCond( 5208 AR->getLoop(), Pred, LHS, AR->getStart()) && 5209 isLoopBackedgeGuardedByCond( 5210 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5211 return true; 5212 5213 // Otherwise see what can be done with known constant ranges. 5214 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5215} 5216 5217bool 5218ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5219 const SCEV *LHS, const SCEV *RHS) { 5220 if (HasSameValue(LHS, RHS)) 5221 return ICmpInst::isTrueWhenEqual(Pred); 5222 5223 // This code is split out from isKnownPredicate because it is called from 5224 // within isLoopEntryGuardedByCond. 5225 switch (Pred) { 5226 default: 5227 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5228 break; 5229 case ICmpInst::ICMP_SGT: 5230 Pred = ICmpInst::ICMP_SLT; 5231 std::swap(LHS, RHS); 5232 case ICmpInst::ICMP_SLT: { 5233 ConstantRange LHSRange = getSignedRange(LHS); 5234 ConstantRange RHSRange = getSignedRange(RHS); 5235 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5236 return true; 5237 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5238 return false; 5239 break; 5240 } 5241 case ICmpInst::ICMP_SGE: 5242 Pred = ICmpInst::ICMP_SLE; 5243 std::swap(LHS, RHS); 5244 case ICmpInst::ICMP_SLE: { 5245 ConstantRange LHSRange = getSignedRange(LHS); 5246 ConstantRange RHSRange = getSignedRange(RHS); 5247 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5248 return true; 5249 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5250 return false; 5251 break; 5252 } 5253 case ICmpInst::ICMP_UGT: 5254 Pred = ICmpInst::ICMP_ULT; 5255 std::swap(LHS, RHS); 5256 case ICmpInst::ICMP_ULT: { 5257 ConstantRange LHSRange = getUnsignedRange(LHS); 5258 ConstantRange RHSRange = getUnsignedRange(RHS); 5259 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5260 return true; 5261 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5262 return false; 5263 break; 5264 } 5265 case ICmpInst::ICMP_UGE: 5266 Pred = ICmpInst::ICMP_ULE; 5267 std::swap(LHS, RHS); 5268 case ICmpInst::ICMP_ULE: { 5269 ConstantRange LHSRange = getUnsignedRange(LHS); 5270 ConstantRange RHSRange = getUnsignedRange(RHS); 5271 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5272 return true; 5273 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5274 return false; 5275 break; 5276 } 5277 case ICmpInst::ICMP_NE: { 5278 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5279 return true; 5280 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5281 return true; 5282 5283 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5284 if (isKnownNonZero(Diff)) 5285 return true; 5286 break; 5287 } 5288 case ICmpInst::ICMP_EQ: 5289 // The check at the top of the function catches the case where 5290 // the values are known to be equal. 5291 break; 5292 } 5293 return false; 5294} 5295 5296/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5297/// protected by a conditional between LHS and RHS. This is used to 5298/// to eliminate casts. 5299bool 5300ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5301 ICmpInst::Predicate Pred, 5302 const SCEV *LHS, const SCEV *RHS) { 5303 // Interpret a null as meaning no loop, where there is obviously no guard 5304 // (interprocedural conditions notwithstanding). 5305 if (!L) return true; 5306 5307 BasicBlock *Latch = L->getLoopLatch(); 5308 if (!Latch) 5309 return false; 5310 5311 BranchInst *LoopContinuePredicate = 5312 dyn_cast<BranchInst>(Latch->getTerminator()); 5313 if (!LoopContinuePredicate || 5314 LoopContinuePredicate->isUnconditional()) 5315 return false; 5316 5317 return isImpliedCond(Pred, LHS, RHS, 5318 LoopContinuePredicate->getCondition(), 5319 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5320} 5321 5322/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5323/// by a conditional between LHS and RHS. This is used to help avoid max 5324/// expressions in loop trip counts, and to eliminate casts. 5325bool 5326ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5327 ICmpInst::Predicate Pred, 5328 const SCEV *LHS, const SCEV *RHS) { 5329 // Interpret a null as meaning no loop, where there is obviously no guard 5330 // (interprocedural conditions notwithstanding). 5331 if (!L) return false; 5332 5333 // Starting at the loop predecessor, climb up the predecessor chain, as long 5334 // as there are predecessors that can be found that have unique successors 5335 // leading to the original header. 5336 for (std::pair<BasicBlock *, BasicBlock *> 5337 Pair(L->getLoopPredecessor(), L->getHeader()); 5338 Pair.first; 5339 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5340 5341 BranchInst *LoopEntryPredicate = 5342 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5343 if (!LoopEntryPredicate || 5344 LoopEntryPredicate->isUnconditional()) 5345 continue; 5346 5347 if (isImpliedCond(Pred, LHS, RHS, 5348 LoopEntryPredicate->getCondition(), 5349 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5350 return true; 5351 } 5352 5353 return false; 5354} 5355 5356/// isImpliedCond - Test whether the condition described by Pred, LHS, 5357/// and RHS is true whenever the given Cond value evaluates to true. 5358bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5359 const SCEV *LHS, const SCEV *RHS, 5360 Value *FoundCondValue, 5361 bool Inverse) { 5362 // Recursively handle And and Or conditions. 5363 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5364 if (BO->getOpcode() == Instruction::And) { 5365 if (!Inverse) 5366 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5367 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5368 } else if (BO->getOpcode() == Instruction::Or) { 5369 if (Inverse) 5370 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5371 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5372 } 5373 } 5374 5375 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5376 if (!ICI) return false; 5377 5378 // Bail if the ICmp's operands' types are wider than the needed type 5379 // before attempting to call getSCEV on them. This avoids infinite 5380 // recursion, since the analysis of widening casts can require loop 5381 // exit condition information for overflow checking, which would 5382 // lead back here. 5383 if (getTypeSizeInBits(LHS->getType()) < 5384 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5385 return false; 5386 5387 // Now that we found a conditional branch that dominates the loop, check to 5388 // see if it is the comparison we are looking for. 5389 ICmpInst::Predicate FoundPred; 5390 if (Inverse) 5391 FoundPred = ICI->getInversePredicate(); 5392 else 5393 FoundPred = ICI->getPredicate(); 5394 5395 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5396 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5397 5398 // Balance the types. The case where FoundLHS' type is wider than 5399 // LHS' type is checked for above. 5400 if (getTypeSizeInBits(LHS->getType()) > 5401 getTypeSizeInBits(FoundLHS->getType())) { 5402 if (CmpInst::isSigned(Pred)) { 5403 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5404 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5405 } else { 5406 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5407 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5408 } 5409 } 5410 5411 // Canonicalize the query to match the way instcombine will have 5412 // canonicalized the comparison. 5413 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5414 if (LHS == RHS) 5415 return CmpInst::isTrueWhenEqual(Pred); 5416 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5417 if (FoundLHS == FoundRHS) 5418 return CmpInst::isFalseWhenEqual(Pred); 5419 5420 // Check to see if we can make the LHS or RHS match. 5421 if (LHS == FoundRHS || RHS == FoundLHS) { 5422 if (isa<SCEVConstant>(RHS)) { 5423 std::swap(FoundLHS, FoundRHS); 5424 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5425 } else { 5426 std::swap(LHS, RHS); 5427 Pred = ICmpInst::getSwappedPredicate(Pred); 5428 } 5429 } 5430 5431 // Check whether the found predicate is the same as the desired predicate. 5432 if (FoundPred == Pred) 5433 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5434 5435 // Check whether swapping the found predicate makes it the same as the 5436 // desired predicate. 5437 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5438 if (isa<SCEVConstant>(RHS)) 5439 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5440 else 5441 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5442 RHS, LHS, FoundLHS, FoundRHS); 5443 } 5444 5445 // Check whether the actual condition is beyond sufficient. 5446 if (FoundPred == ICmpInst::ICMP_EQ) 5447 if (ICmpInst::isTrueWhenEqual(Pred)) 5448 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5449 return true; 5450 if (Pred == ICmpInst::ICMP_NE) 5451 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5452 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5453 return true; 5454 5455 // Otherwise assume the worst. 5456 return false; 5457} 5458 5459/// isImpliedCondOperands - Test whether the condition described by Pred, 5460/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5461/// and FoundRHS is true. 5462bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5463 const SCEV *LHS, const SCEV *RHS, 5464 const SCEV *FoundLHS, 5465 const SCEV *FoundRHS) { 5466 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5467 FoundLHS, FoundRHS) || 5468 // ~x < ~y --> x > y 5469 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5470 getNotSCEV(FoundRHS), 5471 getNotSCEV(FoundLHS)); 5472} 5473 5474/// isImpliedCondOperandsHelper - Test whether the condition described by 5475/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5476/// FoundLHS, and FoundRHS is true. 5477bool 5478ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5479 const SCEV *LHS, const SCEV *RHS, 5480 const SCEV *FoundLHS, 5481 const SCEV *FoundRHS) { 5482 switch (Pred) { 5483 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5484 case ICmpInst::ICMP_EQ: 5485 case ICmpInst::ICMP_NE: 5486 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5487 return true; 5488 break; 5489 case ICmpInst::ICMP_SLT: 5490 case ICmpInst::ICMP_SLE: 5491 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5492 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5493 return true; 5494 break; 5495 case ICmpInst::ICMP_SGT: 5496 case ICmpInst::ICMP_SGE: 5497 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5498 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5499 return true; 5500 break; 5501 case ICmpInst::ICMP_ULT: 5502 case ICmpInst::ICMP_ULE: 5503 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5504 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5505 return true; 5506 break; 5507 case ICmpInst::ICMP_UGT: 5508 case ICmpInst::ICMP_UGE: 5509 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5510 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5511 return true; 5512 break; 5513 } 5514 5515 return false; 5516} 5517 5518/// getBECount - Subtract the end and start values and divide by the step, 5519/// rounding up, to get the number of times the backedge is executed. Return 5520/// CouldNotCompute if an intermediate computation overflows. 5521const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5522 const SCEV *End, 5523 const SCEV *Step, 5524 bool NoWrap) { 5525 assert(!isKnownNegative(Step) && 5526 "This code doesn't handle negative strides yet!"); 5527 5528 const Type *Ty = Start->getType(); 5529 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5530 const SCEV *Diff = getMinusSCEV(End, Start); 5531 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5532 5533 // Add an adjustment to the difference between End and Start so that 5534 // the division will effectively round up. 5535 const SCEV *Add = getAddExpr(Diff, RoundUp); 5536 5537 if (!NoWrap) { 5538 // Check Add for unsigned overflow. 5539 // TODO: More sophisticated things could be done here. 5540 const Type *WideTy = IntegerType::get(getContext(), 5541 getTypeSizeInBits(Ty) + 1); 5542 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5543 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5544 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5545 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5546 return getCouldNotCompute(); 5547 } 5548 5549 return getUDivExpr(Add, Step); 5550} 5551 5552/// HowManyLessThans - Return the number of times a backedge containing the 5553/// specified less-than comparison will execute. If not computable, return 5554/// CouldNotCompute. 5555ScalarEvolution::BackedgeTakenInfo 5556ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5557 const Loop *L, bool isSigned) { 5558 // Only handle: "ADDREC < LoopInvariant". 5559 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5560 5561 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5562 if (!AddRec || AddRec->getLoop() != L) 5563 return getCouldNotCompute(); 5564 5565 // Check to see if we have a flag which makes analysis easy. 5566 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5567 AddRec->hasNoUnsignedWrap(); 5568 5569 if (AddRec->isAffine()) { 5570 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5571 const SCEV *Step = AddRec->getStepRecurrence(*this); 5572 5573 if (Step->isZero()) 5574 return getCouldNotCompute(); 5575 if (Step->isOne()) { 5576 // With unit stride, the iteration never steps past the limit value. 5577 } else if (isKnownPositive(Step)) { 5578 // Test whether a positive iteration can step past the limit 5579 // value and past the maximum value for its type in a single step. 5580 // Note that it's not sufficient to check NoWrap here, because even 5581 // though the value after a wrap is undefined, it's not undefined 5582 // behavior, so if wrap does occur, the loop could either terminate or 5583 // loop infinitely, but in either case, the loop is guaranteed to 5584 // iterate at least until the iteration where the wrapping occurs. 5585 const SCEV *One = getConstant(Step->getType(), 1); 5586 if (isSigned) { 5587 APInt Max = APInt::getSignedMaxValue(BitWidth); 5588 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5589 .slt(getSignedRange(RHS).getSignedMax())) 5590 return getCouldNotCompute(); 5591 } else { 5592 APInt Max = APInt::getMaxValue(BitWidth); 5593 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5594 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5595 return getCouldNotCompute(); 5596 } 5597 } else 5598 // TODO: Handle negative strides here and below. 5599 return getCouldNotCompute(); 5600 5601 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5602 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5603 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5604 // treat m-n as signed nor unsigned due to overflow possibility. 5605 5606 // First, we get the value of the LHS in the first iteration: n 5607 const SCEV *Start = AddRec->getOperand(0); 5608 5609 // Determine the minimum constant start value. 5610 const SCEV *MinStart = getConstant(isSigned ? 5611 getSignedRange(Start).getSignedMin() : 5612 getUnsignedRange(Start).getUnsignedMin()); 5613 5614 // If we know that the condition is true in order to enter the loop, 5615 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5616 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5617 // the division must round up. 5618 const SCEV *End = RHS; 5619 if (!isLoopEntryGuardedByCond(L, 5620 isSigned ? ICmpInst::ICMP_SLT : 5621 ICmpInst::ICMP_ULT, 5622 getMinusSCEV(Start, Step), RHS)) 5623 End = isSigned ? getSMaxExpr(RHS, Start) 5624 : getUMaxExpr(RHS, Start); 5625 5626 // Determine the maximum constant end value. 5627 const SCEV *MaxEnd = getConstant(isSigned ? 5628 getSignedRange(End).getSignedMax() : 5629 getUnsignedRange(End).getUnsignedMax()); 5630 5631 // If MaxEnd is within a step of the maximum integer value in its type, 5632 // adjust it down to the minimum value which would produce the same effect. 5633 // This allows the subsequent ceiling division of (N+(step-1))/step to 5634 // compute the correct value. 5635 const SCEV *StepMinusOne = getMinusSCEV(Step, 5636 getConstant(Step->getType(), 1)); 5637 MaxEnd = isSigned ? 5638 getSMinExpr(MaxEnd, 5639 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5640 StepMinusOne)) : 5641 getUMinExpr(MaxEnd, 5642 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5643 StepMinusOne)); 5644 5645 // Finally, we subtract these two values and divide, rounding up, to get 5646 // the number of times the backedge is executed. 5647 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5648 5649 // The maximum backedge count is similar, except using the minimum start 5650 // value and the maximum end value. 5651 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5652 5653 return BackedgeTakenInfo(BECount, MaxBECount); 5654 } 5655 5656 return getCouldNotCompute(); 5657} 5658 5659/// getNumIterationsInRange - Return the number of iterations of this loop that 5660/// produce values in the specified constant range. Another way of looking at 5661/// this is that it returns the first iteration number where the value is not in 5662/// the condition, thus computing the exit count. If the iteration count can't 5663/// be computed, an instance of SCEVCouldNotCompute is returned. 5664const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5665 ScalarEvolution &SE) const { 5666 if (Range.isFullSet()) // Infinite loop. 5667 return SE.getCouldNotCompute(); 5668 5669 // If the start is a non-zero constant, shift the range to simplify things. 5670 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5671 if (!SC->getValue()->isZero()) { 5672 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5673 Operands[0] = SE.getConstant(SC->getType(), 0); 5674 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5675 if (const SCEVAddRecExpr *ShiftedAddRec = 5676 dyn_cast<SCEVAddRecExpr>(Shifted)) 5677 return ShiftedAddRec->getNumIterationsInRange( 5678 Range.subtract(SC->getValue()->getValue()), SE); 5679 // This is strange and shouldn't happen. 5680 return SE.getCouldNotCompute(); 5681 } 5682 5683 // The only time we can solve this is when we have all constant indices. 5684 // Otherwise, we cannot determine the overflow conditions. 5685 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5686 if (!isa<SCEVConstant>(getOperand(i))) 5687 return SE.getCouldNotCompute(); 5688 5689 5690 // Okay at this point we know that all elements of the chrec are constants and 5691 // that the start element is zero. 5692 5693 // First check to see if the range contains zero. If not, the first 5694 // iteration exits. 5695 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5696 if (!Range.contains(APInt(BitWidth, 0))) 5697 return SE.getConstant(getType(), 0); 5698 5699 if (isAffine()) { 5700 // If this is an affine expression then we have this situation: 5701 // Solve {0,+,A} in Range === Ax in Range 5702 5703 // We know that zero is in the range. If A is positive then we know that 5704 // the upper value of the range must be the first possible exit value. 5705 // If A is negative then the lower of the range is the last possible loop 5706 // value. Also note that we already checked for a full range. 5707 APInt One(BitWidth,1); 5708 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5709 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5710 5711 // The exit value should be (End+A)/A. 5712 APInt ExitVal = (End + A).udiv(A); 5713 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5714 5715 // Evaluate at the exit value. If we really did fall out of the valid 5716 // range, then we computed our trip count, otherwise wrap around or other 5717 // things must have happened. 5718 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5719 if (Range.contains(Val->getValue())) 5720 return SE.getCouldNotCompute(); // Something strange happened 5721 5722 // Ensure that the previous value is in the range. This is a sanity check. 5723 assert(Range.contains( 5724 EvaluateConstantChrecAtConstant(this, 5725 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5726 "Linear scev computation is off in a bad way!"); 5727 return SE.getConstant(ExitValue); 5728 } else if (isQuadratic()) { 5729 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5730 // quadratic equation to solve it. To do this, we must frame our problem in 5731 // terms of figuring out when zero is crossed, instead of when 5732 // Range.getUpper() is crossed. 5733 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5734 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5735 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5736 5737 // Next, solve the constructed addrec 5738 std::pair<const SCEV *,const SCEV *> Roots = 5739 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5740 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5741 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5742 if (R1) { 5743 // Pick the smallest positive root value. 5744 if (ConstantInt *CB = 5745 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5746 R1->getValue(), R2->getValue()))) { 5747 if (CB->getZExtValue() == false) 5748 std::swap(R1, R2); // R1 is the minimum root now. 5749 5750 // Make sure the root is not off by one. The returned iteration should 5751 // not be in the range, but the previous one should be. When solving 5752 // for "X*X < 5", for example, we should not return a root of 2. 5753 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5754 R1->getValue(), 5755 SE); 5756 if (Range.contains(R1Val->getValue())) { 5757 // The next iteration must be out of the range... 5758 ConstantInt *NextVal = 5759 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5760 5761 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5762 if (!Range.contains(R1Val->getValue())) 5763 return SE.getConstant(NextVal); 5764 return SE.getCouldNotCompute(); // Something strange happened 5765 } 5766 5767 // If R1 was not in the range, then it is a good return value. Make 5768 // sure that R1-1 WAS in the range though, just in case. 5769 ConstantInt *NextVal = 5770 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5771 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5772 if (Range.contains(R1Val->getValue())) 5773 return R1; 5774 return SE.getCouldNotCompute(); // Something strange happened 5775 } 5776 } 5777 } 5778 5779 return SE.getCouldNotCompute(); 5780} 5781 5782 5783 5784//===----------------------------------------------------------------------===// 5785// SCEVCallbackVH Class Implementation 5786//===----------------------------------------------------------------------===// 5787 5788void ScalarEvolution::SCEVCallbackVH::deleted() { 5789 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5790 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5791 SE->ConstantEvolutionLoopExitValue.erase(PN); 5792 SE->ValueExprMap.erase(getValPtr()); 5793 // this now dangles! 5794} 5795 5796void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5797 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5798 5799 // Forget all the expressions associated with users of the old value, 5800 // so that future queries will recompute the expressions using the new 5801 // value. 5802 Value *Old = getValPtr(); 5803 SmallVector<User *, 16> Worklist; 5804 SmallPtrSet<User *, 8> Visited; 5805 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5806 UI != UE; ++UI) 5807 Worklist.push_back(*UI); 5808 while (!Worklist.empty()) { 5809 User *U = Worklist.pop_back_val(); 5810 // Deleting the Old value will cause this to dangle. Postpone 5811 // that until everything else is done. 5812 if (U == Old) 5813 continue; 5814 if (!Visited.insert(U)) 5815 continue; 5816 if (PHINode *PN = dyn_cast<PHINode>(U)) 5817 SE->ConstantEvolutionLoopExitValue.erase(PN); 5818 SE->ValueExprMap.erase(U); 5819 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5820 UI != UE; ++UI) 5821 Worklist.push_back(*UI); 5822 } 5823 // Delete the Old value. 5824 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5825 SE->ConstantEvolutionLoopExitValue.erase(PN); 5826 SE->ValueExprMap.erase(Old); 5827 // this now dangles! 5828} 5829 5830ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5831 : CallbackVH(V), SE(se) {} 5832 5833//===----------------------------------------------------------------------===// 5834// ScalarEvolution Class Implementation 5835//===----------------------------------------------------------------------===// 5836 5837ScalarEvolution::ScalarEvolution() 5838 : FunctionPass(ID), FirstUnknown(0) { 5839} 5840 5841bool ScalarEvolution::runOnFunction(Function &F) { 5842 this->F = &F; 5843 LI = &getAnalysis<LoopInfo>(); 5844 TD = getAnalysisIfAvailable<TargetData>(); 5845 DT = &getAnalysis<DominatorTree>(); 5846 return false; 5847} 5848 5849void ScalarEvolution::releaseMemory() { 5850 // Iterate through all the SCEVUnknown instances and call their 5851 // destructors, so that they release their references to their values. 5852 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5853 U->~SCEVUnknown(); 5854 FirstUnknown = 0; 5855 5856 ValueExprMap.clear(); 5857 BackedgeTakenCounts.clear(); 5858 ConstantEvolutionLoopExitValue.clear(); 5859 ValuesAtScopes.clear(); 5860 UniqueSCEVs.clear(); 5861 SCEVAllocator.Reset(); 5862} 5863 5864void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5865 AU.setPreservesAll(); 5866 AU.addRequiredTransitive<LoopInfo>(); 5867 AU.addRequiredTransitive<DominatorTree>(); 5868} 5869 5870bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5871 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5872} 5873 5874static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5875 const Loop *L) { 5876 // Print all inner loops first 5877 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5878 PrintLoopInfo(OS, SE, *I); 5879 5880 OS << "Loop "; 5881 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5882 OS << ": "; 5883 5884 SmallVector<BasicBlock *, 8> ExitBlocks; 5885 L->getExitBlocks(ExitBlocks); 5886 if (ExitBlocks.size() != 1) 5887 OS << "<multiple exits> "; 5888 5889 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5890 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5891 } else { 5892 OS << "Unpredictable backedge-taken count. "; 5893 } 5894 5895 OS << "\n" 5896 "Loop "; 5897 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5898 OS << ": "; 5899 5900 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5901 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5902 } else { 5903 OS << "Unpredictable max backedge-taken count. "; 5904 } 5905 5906 OS << "\n"; 5907} 5908 5909void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5910 // ScalarEvolution's implementation of the print method is to print 5911 // out SCEV values of all instructions that are interesting. Doing 5912 // this potentially causes it to create new SCEV objects though, 5913 // which technically conflicts with the const qualifier. This isn't 5914 // observable from outside the class though, so casting away the 5915 // const isn't dangerous. 5916 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5917 5918 OS << "Classifying expressions for: "; 5919 WriteAsOperand(OS, F, /*PrintType=*/false); 5920 OS << "\n"; 5921 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5922 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5923 OS << *I << '\n'; 5924 OS << " --> "; 5925 const SCEV *SV = SE.getSCEV(&*I); 5926 SV->print(OS); 5927 5928 const Loop *L = LI->getLoopFor((*I).getParent()); 5929 5930 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5931 if (AtUse != SV) { 5932 OS << " --> "; 5933 AtUse->print(OS); 5934 } 5935 5936 if (L) { 5937 OS << "\t\t" "Exits: "; 5938 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5939 if (!ExitValue->isLoopInvariant(L)) { 5940 OS << "<<Unknown>>"; 5941 } else { 5942 OS << *ExitValue; 5943 } 5944 } 5945 5946 OS << "\n"; 5947 } 5948 5949 OS << "Determining loop execution counts for: "; 5950 WriteAsOperand(OS, F, /*PrintType=*/false); 5951 OS << "\n"; 5952 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5953 PrintLoopInfo(OS, &SE, *I); 5954} 5955 5956