ScalarEvolution.cpp revision 67ef74e0e5863e32e4d581d5e197bf00cccddd01
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 (unsigned i = 0, e = getNumOperands(); i != e; ++i) 344 if (!getOperand(i)->isLoopInvariant(QueryLoop)) 345 return false; 346 347 // Otherwise it's loop-invariant. 348 return true; 349} 350 351bool 352SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 353 return DT->dominates(L->getHeader(), BB) && 354 SCEVNAryExpr::dominates(BB, DT); 355} 356 357bool 358SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 359 // This uses a "dominates" query instead of "properly dominates" query because 360 // the instruction which produces the addrec's value is a PHI, and a PHI 361 // effectively properly dominates its entire containing block. 362 return DT->dominates(L->getHeader(), BB) && 363 SCEVNAryExpr::properlyDominates(BB, DT); 364} 365 366void SCEVAddRecExpr::print(raw_ostream &OS) const { 367 OS << "{" << *Operands[0]; 368 for (unsigned i = 1, e = NumOperands; i != e; ++i) 369 OS << ",+," << *Operands[i]; 370 OS << "}<"; 371 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 372 OS << ">"; 373} 374 375void SCEVUnknown::deleted() { 376 // Clear this SCEVUnknown from ValuesAtScopes. 377 SE->ValuesAtScopes.erase(this); 378 379 // Remove this SCEVUnknown from the uniquing map. 380 SE->UniqueSCEVs.RemoveNode(this); 381 382 // Release the value. 383 setValPtr(0); 384} 385 386void SCEVUnknown::allUsesReplacedWith(Value *New) { 387 // Clear this SCEVUnknown from ValuesAtScopes. 388 SE->ValuesAtScopes.erase(this); 389 390 // Remove this SCEVUnknown from the uniquing map. 391 SE->UniqueSCEVs.RemoveNode(this); 392 393 // Update this SCEVUnknown to point to the new value. This is needed 394 // because there may still be outstanding SCEVs which still point to 395 // this SCEVUnknown. 396 setValPtr(New); 397} 398 399bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 400 // All non-instruction values are loop invariant. All instructions are loop 401 // invariant if they are not contained in the specified loop. 402 // Instructions are never considered invariant in the function body 403 // (null loop) because they are defined within the "loop". 404 if (Instruction *I = dyn_cast<Instruction>(getValue())) 405 return L && !L->contains(I); 406 return true; 407} 408 409bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 410 if (Instruction *I = dyn_cast<Instruction>(getValue())) 411 return DT->dominates(I->getParent(), BB); 412 return true; 413} 414 415bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 416 if (Instruction *I = dyn_cast<Instruction>(getValue())) 417 return DT->properlyDominates(I->getParent(), BB); 418 return true; 419} 420 421const Type *SCEVUnknown::getType() const { 422 return getValue()->getType(); 423} 424 425bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 426 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 427 if (VCE->getOpcode() == Instruction::PtrToInt) 428 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 429 if (CE->getOpcode() == Instruction::GetElementPtr && 430 CE->getOperand(0)->isNullValue() && 431 CE->getNumOperands() == 2) 432 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 433 if (CI->isOne()) { 434 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 435 ->getElementType(); 436 return true; 437 } 438 439 return false; 440} 441 442bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 443 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 444 if (VCE->getOpcode() == Instruction::PtrToInt) 445 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 446 if (CE->getOpcode() == Instruction::GetElementPtr && 447 CE->getOperand(0)->isNullValue()) { 448 const Type *Ty = 449 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 450 if (const StructType *STy = dyn_cast<StructType>(Ty)) 451 if (!STy->isPacked() && 452 CE->getNumOperands() == 3 && 453 CE->getOperand(1)->isNullValue()) { 454 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 455 if (CI->isOne() && 456 STy->getNumElements() == 2 && 457 STy->getElementType(0)->isIntegerTy(1)) { 458 AllocTy = STy->getElementType(1); 459 return true; 460 } 461 } 462 } 463 464 return false; 465} 466 467bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 468 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 469 if (VCE->getOpcode() == Instruction::PtrToInt) 470 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 471 if (CE->getOpcode() == Instruction::GetElementPtr && 472 CE->getNumOperands() == 3 && 473 CE->getOperand(0)->isNullValue() && 474 CE->getOperand(1)->isNullValue()) { 475 const Type *Ty = 476 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 477 // Ignore vector types here so that ScalarEvolutionExpander doesn't 478 // emit getelementptrs that index into vectors. 479 if (Ty->isStructTy() || Ty->isArrayTy()) { 480 CTy = Ty; 481 FieldNo = CE->getOperand(2); 482 return true; 483 } 484 } 485 486 return false; 487} 488 489void SCEVUnknown::print(raw_ostream &OS) const { 490 const Type *AllocTy; 491 if (isSizeOf(AllocTy)) { 492 OS << "sizeof(" << *AllocTy << ")"; 493 return; 494 } 495 if (isAlignOf(AllocTy)) { 496 OS << "alignof(" << *AllocTy << ")"; 497 return; 498 } 499 500 const Type *CTy; 501 Constant *FieldNo; 502 if (isOffsetOf(CTy, FieldNo)) { 503 OS << "offsetof(" << *CTy << ", "; 504 WriteAsOperand(OS, FieldNo, false); 505 OS << ")"; 506 return; 507 } 508 509 // Otherwise just print it normally. 510 WriteAsOperand(OS, getValue(), false); 511} 512 513//===----------------------------------------------------------------------===// 514// SCEV Utilities 515//===----------------------------------------------------------------------===// 516 517namespace { 518 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 519 /// than the complexity of the RHS. This comparator is used to canonicalize 520 /// expressions. 521 class SCEVComplexityCompare { 522 const LoopInfo *const LI; 523 public: 524 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 525 526 // Return true or false if LHS is less than, or at least RHS, respectively. 527 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 528 return compare(LHS, RHS) < 0; 529 } 530 531 // Return negative, zero, or positive, if LHS is less than, equal to, or 532 // greater than RHS, respectively. A three-way result allows recursive 533 // comparisons to be more efficient. 534 int compare(const SCEV *LHS, const SCEV *RHS) const { 535 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 536 if (LHS == RHS) 537 return 0; 538 539 // Primarily, sort the SCEVs by their getSCEVType(). 540 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 541 if (LType != RType) 542 return (int)LType - (int)RType; 543 544 // Aside from the getSCEVType() ordering, the particular ordering 545 // isn't very important except that it's beneficial to be consistent, 546 // so that (a + b) and (b + a) don't end up as different expressions. 547 switch (LType) { 548 case scUnknown: { 549 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 550 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 551 552 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 553 // not as complete as it could be. 554 const Value *LV = LU->getValue(), *RV = RU->getValue(); 555 556 // Order pointer values after integer values. This helps SCEVExpander 557 // form GEPs. 558 bool LIsPointer = LV->getType()->isPointerTy(), 559 RIsPointer = RV->getType()->isPointerTy(); 560 if (LIsPointer != RIsPointer) 561 return (int)LIsPointer - (int)RIsPointer; 562 563 // Compare getValueID values. 564 unsigned LID = LV->getValueID(), 565 RID = RV->getValueID(); 566 if (LID != RID) 567 return (int)LID - (int)RID; 568 569 // Sort arguments by their position. 570 if (const Argument *LA = dyn_cast<Argument>(LV)) { 571 const Argument *RA = cast<Argument>(RV); 572 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 573 return (int)LArgNo - (int)RArgNo; 574 } 575 576 // For instructions, compare their loop depth, and their operand 577 // count. This is pretty loose. 578 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 579 const Instruction *RInst = cast<Instruction>(RV); 580 581 // Compare loop depths. 582 const BasicBlock *LParent = LInst->getParent(), 583 *RParent = RInst->getParent(); 584 if (LParent != RParent) { 585 unsigned LDepth = LI->getLoopDepth(LParent), 586 RDepth = LI->getLoopDepth(RParent); 587 if (LDepth != RDepth) 588 return (int)LDepth - (int)RDepth; 589 } 590 591 // Compare the number of operands. 592 unsigned LNumOps = LInst->getNumOperands(), 593 RNumOps = RInst->getNumOperands(); 594 return (int)LNumOps - (int)RNumOps; 595 } 596 597 return 0; 598 } 599 600 case scConstant: { 601 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 602 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 603 604 // Compare constant values. 605 const APInt &LA = LC->getValue()->getValue(); 606 const APInt &RA = RC->getValue()->getValue(); 607 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 608 if (LBitWidth != RBitWidth) 609 return (int)LBitWidth - (int)RBitWidth; 610 return LA.ult(RA) ? -1 : 1; 611 } 612 613 case scAddRecExpr: { 614 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 615 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 616 617 // Compare addrec loop depths. 618 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 619 if (LLoop != RLoop) { 620 unsigned LDepth = LLoop->getLoopDepth(), 621 RDepth = RLoop->getLoopDepth(); 622 if (LDepth != RDepth) 623 return (int)LDepth - (int)RDepth; 624 } 625 626 // Addrec complexity grows with operand count. 627 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 628 if (LNumOps != RNumOps) 629 return (int)LNumOps - (int)RNumOps; 630 631 // Lexicographically compare. 632 for (unsigned i = 0; i != LNumOps; ++i) { 633 long X = compare(LA->getOperand(i), RA->getOperand(i)); 634 if (X != 0) 635 return X; 636 } 637 638 return 0; 639 } 640 641 case scAddExpr: 642 case scMulExpr: 643 case scSMaxExpr: 644 case scUMaxExpr: { 645 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 646 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 647 648 // Lexicographically compare n-ary expressions. 649 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 650 for (unsigned i = 0; i != LNumOps; ++i) { 651 if (i >= RNumOps) 652 return 1; 653 long X = compare(LC->getOperand(i), RC->getOperand(i)); 654 if (X != 0) 655 return X; 656 } 657 return (int)LNumOps - (int)RNumOps; 658 } 659 660 case scUDivExpr: { 661 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 662 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 663 664 // Lexicographically compare udiv expressions. 665 long X = compare(LC->getLHS(), RC->getLHS()); 666 if (X != 0) 667 return X; 668 return compare(LC->getRHS(), RC->getRHS()); 669 } 670 671 case scTruncate: 672 case scZeroExtend: 673 case scSignExtend: { 674 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 675 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 676 677 // Compare cast expressions by operand. 678 return compare(LC->getOperand(), RC->getOperand()); 679 } 680 681 default: 682 break; 683 } 684 685 llvm_unreachable("Unknown SCEV kind!"); 686 return 0; 687 } 688 }; 689} 690 691/// GroupByComplexity - Given a list of SCEV objects, order them by their 692/// complexity, and group objects of the same complexity together by value. 693/// When this routine is finished, we know that any duplicates in the vector are 694/// consecutive and that complexity is monotonically increasing. 695/// 696/// Note that we go take special precautions to ensure that we get deterministic 697/// results from this routine. In other words, we don't want the results of 698/// this to depend on where the addresses of various SCEV objects happened to 699/// land in memory. 700/// 701static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 702 LoopInfo *LI) { 703 if (Ops.size() < 2) return; // Noop 704 if (Ops.size() == 2) { 705 // This is the common case, which also happens to be trivially simple. 706 // Special case it. 707 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) 708 std::swap(Ops[0], Ops[1]); 709 return; 710 } 711 712 // Do the rough sort by complexity. 713 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 714 715 // Now that we are sorted by complexity, group elements of the same 716 // complexity. Note that this is, at worst, N^2, but the vector is likely to 717 // be extremely short in practice. Note that we take this approach because we 718 // do not want to depend on the addresses of the objects we are grouping. 719 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 720 const SCEV *S = Ops[i]; 721 unsigned Complexity = S->getSCEVType(); 722 723 // If there are any objects of the same complexity and same value as this 724 // one, group them. 725 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 726 if (Ops[j] == S) { // Found a duplicate. 727 // Move it to immediately after i'th element. 728 std::swap(Ops[i+1], Ops[j]); 729 ++i; // no need to rescan it. 730 if (i == e-2) return; // Done! 731 } 732 } 733 } 734} 735 736 737 738//===----------------------------------------------------------------------===// 739// Simple SCEV method implementations 740//===----------------------------------------------------------------------===// 741 742/// BinomialCoefficient - Compute BC(It, K). The result has width W. 743/// Assume, K > 0. 744static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 745 ScalarEvolution &SE, 746 const Type* ResultTy) { 747 // Handle the simplest case efficiently. 748 if (K == 1) 749 return SE.getTruncateOrZeroExtend(It, ResultTy); 750 751 // We are using the following formula for BC(It, K): 752 // 753 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 754 // 755 // Suppose, W is the bitwidth of the return value. We must be prepared for 756 // overflow. Hence, we must assure that the result of our computation is 757 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 758 // safe in modular arithmetic. 759 // 760 // However, this code doesn't use exactly that formula; the formula it uses 761 // is something like the following, where T is the number of factors of 2 in 762 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 763 // exponentiation: 764 // 765 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 766 // 767 // This formula is trivially equivalent to the previous formula. However, 768 // this formula can be implemented much more efficiently. The trick is that 769 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 770 // arithmetic. To do exact division in modular arithmetic, all we have 771 // to do is multiply by the inverse. Therefore, this step can be done at 772 // width W. 773 // 774 // The next issue is how to safely do the division by 2^T. The way this 775 // is done is by doing the multiplication step at a width of at least W + T 776 // bits. This way, the bottom W+T bits of the product are accurate. Then, 777 // when we perform the division by 2^T (which is equivalent to a right shift 778 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 779 // truncated out after the division by 2^T. 780 // 781 // In comparison to just directly using the first formula, this technique 782 // is much more efficient; using the first formula requires W * K bits, 783 // but this formula less than W + K bits. Also, the first formula requires 784 // a division step, whereas this formula only requires multiplies and shifts. 785 // 786 // It doesn't matter whether the subtraction step is done in the calculation 787 // width or the input iteration count's width; if the subtraction overflows, 788 // the result must be zero anyway. We prefer here to do it in the width of 789 // the induction variable because it helps a lot for certain cases; CodeGen 790 // isn't smart enough to ignore the overflow, which leads to much less 791 // efficient code if the width of the subtraction is wider than the native 792 // register width. 793 // 794 // (It's possible to not widen at all by pulling out factors of 2 before 795 // the multiplication; for example, K=2 can be calculated as 796 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 797 // extra arithmetic, so it's not an obvious win, and it gets 798 // much more complicated for K > 3.) 799 800 // Protection from insane SCEVs; this bound is conservative, 801 // but it probably doesn't matter. 802 if (K > 1000) 803 return SE.getCouldNotCompute(); 804 805 unsigned W = SE.getTypeSizeInBits(ResultTy); 806 807 // Calculate K! / 2^T and T; we divide out the factors of two before 808 // multiplying for calculating K! / 2^T to avoid overflow. 809 // Other overflow doesn't matter because we only care about the bottom 810 // W bits of the result. 811 APInt OddFactorial(W, 1); 812 unsigned T = 1; 813 for (unsigned i = 3; i <= K; ++i) { 814 APInt Mult(W, i); 815 unsigned TwoFactors = Mult.countTrailingZeros(); 816 T += TwoFactors; 817 Mult = Mult.lshr(TwoFactors); 818 OddFactorial *= Mult; 819 } 820 821 // We need at least W + T bits for the multiplication step 822 unsigned CalculationBits = W + T; 823 824 // Calculate 2^T, at width T+W. 825 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 826 827 // Calculate the multiplicative inverse of K! / 2^T; 828 // this multiplication factor will perform the exact division by 829 // K! / 2^T. 830 APInt Mod = APInt::getSignedMinValue(W+1); 831 APInt MultiplyFactor = OddFactorial.zext(W+1); 832 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 833 MultiplyFactor = MultiplyFactor.trunc(W); 834 835 // Calculate the product, at width T+W 836 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 837 CalculationBits); 838 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 839 for (unsigned i = 1; i != K; ++i) { 840 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 841 Dividend = SE.getMulExpr(Dividend, 842 SE.getTruncateOrZeroExtend(S, CalculationTy)); 843 } 844 845 // Divide by 2^T 846 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 847 848 // Truncate the result, and divide by K! / 2^T. 849 850 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 851 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 852} 853 854/// evaluateAtIteration - Return the value of this chain of recurrences at 855/// the specified iteration number. We can evaluate this recurrence by 856/// multiplying each element in the chain by the binomial coefficient 857/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 858/// 859/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 860/// 861/// where BC(It, k) stands for binomial coefficient. 862/// 863const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 864 ScalarEvolution &SE) const { 865 const SCEV *Result = getStart(); 866 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 867 // The computation is correct in the face of overflow provided that the 868 // multiplication is performed _after_ the evaluation of the binomial 869 // coefficient. 870 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 871 if (isa<SCEVCouldNotCompute>(Coeff)) 872 return Coeff; 873 874 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 875 } 876 return Result; 877} 878 879//===----------------------------------------------------------------------===// 880// SCEV Expression folder implementations 881//===----------------------------------------------------------------------===// 882 883const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 884 const Type *Ty) { 885 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 886 "This is not a truncating conversion!"); 887 assert(isSCEVable(Ty) && 888 "This is not a conversion to a SCEVable type!"); 889 Ty = getEffectiveSCEVType(Ty); 890 891 FoldingSetNodeID ID; 892 ID.AddInteger(scTruncate); 893 ID.AddPointer(Op); 894 ID.AddPointer(Ty); 895 void *IP = 0; 896 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 897 898 // Fold if the operand is constant. 899 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 900 return getConstant( 901 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 902 getEffectiveSCEVType(Ty)))); 903 904 // trunc(trunc(x)) --> trunc(x) 905 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 906 return getTruncateExpr(ST->getOperand(), Ty); 907 908 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 909 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 910 return getTruncateOrSignExtend(SS->getOperand(), Ty); 911 912 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 913 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 914 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 915 916 // If the input value is a chrec scev, truncate the chrec's operands. 917 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 918 SmallVector<const SCEV *, 4> Operands; 919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 920 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 921 return getAddRecExpr(Operands, AddRec->getLoop()); 922 } 923 924 // As a special case, fold trunc(undef) to undef. We don't want to 925 // know too much about SCEVUnknowns, but this special case is handy 926 // and harmless. 927 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 928 if (isa<UndefValue>(U->getValue())) 929 return getSCEV(UndefValue::get(Ty)); 930 931 // The cast wasn't folded; create an explicit cast node. We can reuse 932 // the existing insert position since if we get here, we won't have 933 // made any changes which would invalidate it. 934 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 935 Op, Ty); 936 UniqueSCEVs.InsertNode(S, IP); 937 return S; 938} 939 940const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 941 const Type *Ty) { 942 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 943 "This is not an extending conversion!"); 944 assert(isSCEVable(Ty) && 945 "This is not a conversion to a SCEVable type!"); 946 Ty = getEffectiveSCEVType(Ty); 947 948 // Fold if the operand is constant. 949 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 950 return getConstant( 951 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 952 getEffectiveSCEVType(Ty)))); 953 954 // zext(zext(x)) --> zext(x) 955 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 956 return getZeroExtendExpr(SZ->getOperand(), Ty); 957 958 // Before doing any expensive analysis, check to see if we've already 959 // computed a SCEV for this Op and Ty. 960 FoldingSetNodeID ID; 961 ID.AddInteger(scZeroExtend); 962 ID.AddPointer(Op); 963 ID.AddPointer(Ty); 964 void *IP = 0; 965 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 966 967 // If the input value is a chrec scev, and we can prove that the value 968 // did not overflow the old, smaller, value, we can zero extend all of the 969 // operands (often constants). This allows analysis of something like 970 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 971 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 972 if (AR->isAffine()) { 973 const SCEV *Start = AR->getStart(); 974 const SCEV *Step = AR->getStepRecurrence(*this); 975 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 976 const Loop *L = AR->getLoop(); 977 978 // If we have special knowledge that this addrec won't overflow, 979 // we don't need to do any further analysis. 980 if (AR->hasNoUnsignedWrap()) 981 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 982 getZeroExtendExpr(Step, Ty), 983 L); 984 985 // Check whether the backedge-taken count is SCEVCouldNotCompute. 986 // Note that this serves two purposes: It filters out loops that are 987 // simply not analyzable, and it covers the case where this code is 988 // being called from within backedge-taken count analysis, such that 989 // attempting to ask for the backedge-taken count would likely result 990 // in infinite recursion. In the later case, the analysis code will 991 // cope with a conservative value, and it will take care to purge 992 // that value once it has finished. 993 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 994 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 995 // Manually compute the final value for AR, checking for 996 // overflow. 997 998 // Check whether the backedge-taken count can be losslessly casted to 999 // the addrec's type. The count is always unsigned. 1000 const SCEV *CastedMaxBECount = 1001 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1002 const SCEV *RecastedMaxBECount = 1003 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1004 if (MaxBECount == RecastedMaxBECount) { 1005 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1006 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1007 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1008 const SCEV *Add = getAddExpr(Start, ZMul); 1009 const SCEV *OperandExtendedAdd = 1010 getAddExpr(getZeroExtendExpr(Start, WideTy), 1011 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1012 getZeroExtendExpr(Step, WideTy))); 1013 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1014 // Return the expression with the addrec on the outside. 1015 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1016 getZeroExtendExpr(Step, Ty), 1017 L); 1018 1019 // Similar to above, only this time treat the step value as signed. 1020 // This covers loops that count down. 1021 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1022 Add = getAddExpr(Start, SMul); 1023 OperandExtendedAdd = 1024 getAddExpr(getZeroExtendExpr(Start, WideTy), 1025 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1026 getSignExtendExpr(Step, WideTy))); 1027 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1028 // Return the expression with the addrec on the outside. 1029 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1030 getSignExtendExpr(Step, Ty), 1031 L); 1032 } 1033 1034 // If the backedge is guarded by a comparison with the pre-inc value 1035 // the addrec is safe. Also, if the entry is guarded by a comparison 1036 // with the start value and the backedge is guarded by a comparison 1037 // with the post-inc value, the addrec is safe. 1038 if (isKnownPositive(Step)) { 1039 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1040 getUnsignedRange(Step).getUnsignedMax()); 1041 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1042 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1043 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1044 AR->getPostIncExpr(*this), N))) 1045 // Return the expression with the addrec on the outside. 1046 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1047 getZeroExtendExpr(Step, Ty), 1048 L); 1049 } else if (isKnownNegative(Step)) { 1050 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1051 getSignedRange(Step).getSignedMin()); 1052 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1053 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1054 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1055 AR->getPostIncExpr(*this), N))) 1056 // Return the expression with the addrec on the outside. 1057 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1058 getSignExtendExpr(Step, Ty), 1059 L); 1060 } 1061 } 1062 } 1063 1064 // The cast wasn't folded; create an explicit cast node. 1065 // Recompute the insert position, as it may have been invalidated. 1066 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1067 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1068 Op, Ty); 1069 UniqueSCEVs.InsertNode(S, IP); 1070 return S; 1071} 1072 1073const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1074 const Type *Ty) { 1075 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1076 "This is not an extending conversion!"); 1077 assert(isSCEVable(Ty) && 1078 "This is not a conversion to a SCEVable type!"); 1079 Ty = getEffectiveSCEVType(Ty); 1080 1081 // Fold if the operand is constant. 1082 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1083 return getConstant( 1084 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1085 getEffectiveSCEVType(Ty)))); 1086 1087 // sext(sext(x)) --> sext(x) 1088 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1089 return getSignExtendExpr(SS->getOperand(), Ty); 1090 1091 // Before doing any expensive analysis, check to see if we've already 1092 // computed a SCEV for this Op and Ty. 1093 FoldingSetNodeID ID; 1094 ID.AddInteger(scSignExtend); 1095 ID.AddPointer(Op); 1096 ID.AddPointer(Ty); 1097 void *IP = 0; 1098 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1099 1100 // If the input value is a chrec scev, and we can prove that the value 1101 // did not overflow the old, smaller, value, we can sign extend all of the 1102 // operands (often constants). This allows analysis of something like 1103 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1104 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1105 if (AR->isAffine()) { 1106 const SCEV *Start = AR->getStart(); 1107 const SCEV *Step = AR->getStepRecurrence(*this); 1108 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1109 const Loop *L = AR->getLoop(); 1110 1111 // If we have special knowledge that this addrec won't overflow, 1112 // we don't need to do any further analysis. 1113 if (AR->hasNoSignedWrap()) 1114 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1115 getSignExtendExpr(Step, Ty), 1116 L); 1117 1118 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1119 // Note that this serves two purposes: It filters out loops that are 1120 // simply not analyzable, and it covers the case where this code is 1121 // being called from within backedge-taken count analysis, such that 1122 // attempting to ask for the backedge-taken count would likely result 1123 // in infinite recursion. In the later case, the analysis code will 1124 // cope with a conservative value, and it will take care to purge 1125 // that value once it has finished. 1126 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1127 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1128 // Manually compute the final value for AR, checking for 1129 // overflow. 1130 1131 // Check whether the backedge-taken count can be losslessly casted to 1132 // the addrec's type. The count is always unsigned. 1133 const SCEV *CastedMaxBECount = 1134 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1135 const SCEV *RecastedMaxBECount = 1136 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1137 if (MaxBECount == RecastedMaxBECount) { 1138 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1139 // Check whether Start+Step*MaxBECount has no signed overflow. 1140 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1141 const SCEV *Add = getAddExpr(Start, SMul); 1142 const SCEV *OperandExtendedAdd = 1143 getAddExpr(getSignExtendExpr(Start, WideTy), 1144 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1145 getSignExtendExpr(Step, WideTy))); 1146 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1147 // Return the expression with the addrec on the outside. 1148 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1149 getSignExtendExpr(Step, Ty), 1150 L); 1151 1152 // Similar to above, only this time treat the step value as unsigned. 1153 // This covers loops that count up with an unsigned step. 1154 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1155 Add = getAddExpr(Start, UMul); 1156 OperandExtendedAdd = 1157 getAddExpr(getSignExtendExpr(Start, WideTy), 1158 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1159 getZeroExtendExpr(Step, WideTy))); 1160 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1161 // Return the expression with the addrec on the outside. 1162 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1163 getZeroExtendExpr(Step, Ty), 1164 L); 1165 } 1166 1167 // If the backedge is guarded by a comparison with the pre-inc value 1168 // the addrec is safe. Also, if the entry is guarded by a comparison 1169 // with the start value and the backedge is guarded by a comparison 1170 // with the post-inc value, the addrec is safe. 1171 if (isKnownPositive(Step)) { 1172 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1173 getSignedRange(Step).getSignedMax()); 1174 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1175 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1176 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1177 AR->getPostIncExpr(*this), N))) 1178 // Return the expression with the addrec on the outside. 1179 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1180 getSignExtendExpr(Step, Ty), 1181 L); 1182 } else if (isKnownNegative(Step)) { 1183 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1184 getSignedRange(Step).getSignedMin()); 1185 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1186 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1187 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1188 AR->getPostIncExpr(*this), N))) 1189 // Return the expression with the addrec on the outside. 1190 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1191 getSignExtendExpr(Step, Ty), 1192 L); 1193 } 1194 } 1195 } 1196 1197 // The cast wasn't folded; create an explicit cast node. 1198 // Recompute the insert position, as it may have been invalidated. 1199 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1200 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1201 Op, Ty); 1202 UniqueSCEVs.InsertNode(S, IP); 1203 return S; 1204} 1205 1206/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1207/// unspecified bits out to the given type. 1208/// 1209const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1210 const Type *Ty) { 1211 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1212 "This is not an extending conversion!"); 1213 assert(isSCEVable(Ty) && 1214 "This is not a conversion to a SCEVable type!"); 1215 Ty = getEffectiveSCEVType(Ty); 1216 1217 // Sign-extend negative constants. 1218 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1219 if (SC->getValue()->getValue().isNegative()) 1220 return getSignExtendExpr(Op, Ty); 1221 1222 // Peel off a truncate cast. 1223 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1224 const SCEV *NewOp = T->getOperand(); 1225 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1226 return getAnyExtendExpr(NewOp, Ty); 1227 return getTruncateOrNoop(NewOp, Ty); 1228 } 1229 1230 // Next try a zext cast. If the cast is folded, use it. 1231 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1232 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1233 return ZExt; 1234 1235 // Next try a sext cast. If the cast is folded, use it. 1236 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1237 if (!isa<SCEVSignExtendExpr>(SExt)) 1238 return SExt; 1239 1240 // Force the cast to be folded into the operands of an addrec. 1241 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1242 SmallVector<const SCEV *, 4> Ops; 1243 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1244 I != E; ++I) 1245 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1246 return getAddRecExpr(Ops, AR->getLoop()); 1247 } 1248 1249 // As a special case, fold anyext(undef) to undef. We don't want to 1250 // know too much about SCEVUnknowns, but this special case is handy 1251 // and harmless. 1252 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1253 if (isa<UndefValue>(U->getValue())) 1254 return getSCEV(UndefValue::get(Ty)); 1255 1256 // If the expression is obviously signed, use the sext cast value. 1257 if (isa<SCEVSMaxExpr>(Op)) 1258 return SExt; 1259 1260 // Absent any other information, use the zext cast value. 1261 return ZExt; 1262} 1263 1264/// CollectAddOperandsWithScales - Process the given Ops list, which is 1265/// a list of operands to be added under the given scale, update the given 1266/// map. This is a helper function for getAddRecExpr. As an example of 1267/// what it does, given a sequence of operands that would form an add 1268/// expression like this: 1269/// 1270/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1271/// 1272/// where A and B are constants, update the map with these values: 1273/// 1274/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1275/// 1276/// and add 13 + A*B*29 to AccumulatedConstant. 1277/// This will allow getAddRecExpr to produce this: 1278/// 1279/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1280/// 1281/// This form often exposes folding opportunities that are hidden in 1282/// the original operand list. 1283/// 1284/// Return true iff it appears that any interesting folding opportunities 1285/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1286/// the common case where no interesting opportunities are present, and 1287/// is also used as a check to avoid infinite recursion. 1288/// 1289static bool 1290CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1291 SmallVector<const SCEV *, 8> &NewOps, 1292 APInt &AccumulatedConstant, 1293 const SCEV *const *Ops, size_t NumOperands, 1294 const APInt &Scale, 1295 ScalarEvolution &SE) { 1296 bool Interesting = false; 1297 1298 // Iterate over the add operands. They are sorted, with constants first. 1299 unsigned i = 0; 1300 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1301 ++i; 1302 // Pull a buried constant out to the outside. 1303 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1304 Interesting = true; 1305 AccumulatedConstant += Scale * C->getValue()->getValue(); 1306 } 1307 1308 // Next comes everything else. We're especially interested in multiplies 1309 // here, but they're in the middle, so just visit the rest with one loop. 1310 for (; i != NumOperands; ++i) { 1311 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1312 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1313 APInt NewScale = 1314 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1315 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1316 // A multiplication of a constant with another add; recurse. 1317 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1318 Interesting |= 1319 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1320 Add->op_begin(), Add->getNumOperands(), 1321 NewScale, SE); 1322 } else { 1323 // A multiplication of a constant with some other value. Update 1324 // the map. 1325 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1326 const SCEV *Key = SE.getMulExpr(MulOps); 1327 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1328 M.insert(std::make_pair(Key, NewScale)); 1329 if (Pair.second) { 1330 NewOps.push_back(Pair.first->first); 1331 } else { 1332 Pair.first->second += NewScale; 1333 // The map already had an entry for this value, which may indicate 1334 // a folding opportunity. 1335 Interesting = true; 1336 } 1337 } 1338 } else { 1339 // An ordinary operand. Update the map. 1340 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1341 M.insert(std::make_pair(Ops[i], Scale)); 1342 if (Pair.second) { 1343 NewOps.push_back(Pair.first->first); 1344 } else { 1345 Pair.first->second += Scale; 1346 // The map already had an entry for this value, which may indicate 1347 // a folding opportunity. 1348 Interesting = true; 1349 } 1350 } 1351 } 1352 1353 return Interesting; 1354} 1355 1356namespace { 1357 struct APIntCompare { 1358 bool operator()(const APInt &LHS, const APInt &RHS) const { 1359 return LHS.ult(RHS); 1360 } 1361 }; 1362} 1363 1364/// getAddExpr - Get a canonical add expression, or something simpler if 1365/// possible. 1366const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1367 bool HasNUW, bool HasNSW) { 1368 assert(!Ops.empty() && "Cannot get empty add!"); 1369 if (Ops.size() == 1) return Ops[0]; 1370#ifndef NDEBUG 1371 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1372 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1373 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1374 "SCEVAddExpr operand types don't match!"); 1375#endif 1376 1377 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1378 if (!HasNUW && HasNSW) { 1379 bool All = true; 1380 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1381 E = Ops.end(); I != E; ++I) 1382 if (!isKnownNonNegative(*I)) { 1383 All = false; 1384 break; 1385 } 1386 if (All) HasNUW = true; 1387 } 1388 1389 // Sort by complexity, this groups all similar expression types together. 1390 GroupByComplexity(Ops, LI); 1391 1392 // If there are any constants, fold them together. 1393 unsigned Idx = 0; 1394 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1395 ++Idx; 1396 assert(Idx < Ops.size()); 1397 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1398 // We found two constants, fold them together! 1399 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1400 RHSC->getValue()->getValue()); 1401 if (Ops.size() == 2) return Ops[0]; 1402 Ops.erase(Ops.begin()+1); // Erase the folded element 1403 LHSC = cast<SCEVConstant>(Ops[0]); 1404 } 1405 1406 // If we are left with a constant zero being added, strip it off. 1407 if (LHSC->getValue()->isZero()) { 1408 Ops.erase(Ops.begin()); 1409 --Idx; 1410 } 1411 1412 if (Ops.size() == 1) return Ops[0]; 1413 } 1414 1415 // Okay, check to see if the same value occurs in the operand list twice. If 1416 // so, merge them together into an multiply expression. Since we sorted the 1417 // list, these values are required to be adjacent. 1418 const Type *Ty = Ops[0]->getType(); 1419 bool FoundMatch = false; 1420 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 1421 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1422 // Found a match, merge the two values into a multiply, and add any 1423 // remaining values to the result. 1424 const SCEV *Two = getConstant(Ty, 2); 1425 const SCEV *Mul = getMulExpr(Two, Ops[i]); 1426 if (Ops.size() == 2) 1427 return Mul; 1428 Ops[i] = Mul; 1429 Ops.erase(Ops.begin()+i+1); 1430 --i; --e; 1431 FoundMatch = true; 1432 } 1433 if (FoundMatch) 1434 return getAddExpr(Ops, HasNUW, HasNSW); 1435 1436 // Check for truncates. If all the operands are truncated from the same 1437 // type, see if factoring out the truncate would permit the result to be 1438 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1439 // if the contents of the resulting outer trunc fold to something simple. 1440 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1441 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1442 const Type *DstType = Trunc->getType(); 1443 const Type *SrcType = Trunc->getOperand()->getType(); 1444 SmallVector<const SCEV *, 8> LargeOps; 1445 bool Ok = true; 1446 // Check all the operands to see if they can be represented in the 1447 // source type of the truncate. 1448 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1449 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1450 if (T->getOperand()->getType() != SrcType) { 1451 Ok = false; 1452 break; 1453 } 1454 LargeOps.push_back(T->getOperand()); 1455 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1456 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1457 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1458 SmallVector<const SCEV *, 8> LargeMulOps; 1459 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1460 if (const SCEVTruncateExpr *T = 1461 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1462 if (T->getOperand()->getType() != SrcType) { 1463 Ok = false; 1464 break; 1465 } 1466 LargeMulOps.push_back(T->getOperand()); 1467 } else if (const SCEVConstant *C = 1468 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1469 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1470 } else { 1471 Ok = false; 1472 break; 1473 } 1474 } 1475 if (Ok) 1476 LargeOps.push_back(getMulExpr(LargeMulOps)); 1477 } else { 1478 Ok = false; 1479 break; 1480 } 1481 } 1482 if (Ok) { 1483 // Evaluate the expression in the larger type. 1484 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1485 // If it folds to something simple, use it. Otherwise, don't. 1486 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1487 return getTruncateExpr(Fold, DstType); 1488 } 1489 } 1490 1491 // Skip past any other cast SCEVs. 1492 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1493 ++Idx; 1494 1495 // If there are add operands they would be next. 1496 if (Idx < Ops.size()) { 1497 bool DeletedAdd = false; 1498 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1499 // If we have an add, expand the add operands onto the end of the operands 1500 // list. 1501 Ops.erase(Ops.begin()+Idx); 1502 Ops.append(Add->op_begin(), Add->op_end()); 1503 DeletedAdd = true; 1504 } 1505 1506 // If we deleted at least one add, we added operands to the end of the list, 1507 // and they are not necessarily sorted. Recurse to resort and resimplify 1508 // any operands we just acquired. 1509 if (DeletedAdd) 1510 return getAddExpr(Ops); 1511 } 1512 1513 // Skip over the add expression until we get to a multiply. 1514 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1515 ++Idx; 1516 1517 // Check to see if there are any folding opportunities present with 1518 // operands multiplied by constant values. 1519 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1520 uint64_t BitWidth = getTypeSizeInBits(Ty); 1521 DenseMap<const SCEV *, APInt> M; 1522 SmallVector<const SCEV *, 8> NewOps; 1523 APInt AccumulatedConstant(BitWidth, 0); 1524 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1525 Ops.data(), Ops.size(), 1526 APInt(BitWidth, 1), *this)) { 1527 // Some interesting folding opportunity is present, so its worthwhile to 1528 // re-generate the operands list. Group the operands by constant scale, 1529 // to avoid multiplying by the same constant scale multiple times. 1530 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1531 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1532 E = NewOps.end(); I != E; ++I) 1533 MulOpLists[M.find(*I)->second].push_back(*I); 1534 // Re-generate the operands list. 1535 Ops.clear(); 1536 if (AccumulatedConstant != 0) 1537 Ops.push_back(getConstant(AccumulatedConstant)); 1538 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1539 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1540 if (I->first != 0) 1541 Ops.push_back(getMulExpr(getConstant(I->first), 1542 getAddExpr(I->second))); 1543 if (Ops.empty()) 1544 return getConstant(Ty, 0); 1545 if (Ops.size() == 1) 1546 return Ops[0]; 1547 return getAddExpr(Ops); 1548 } 1549 } 1550 1551 // If we are adding something to a multiply expression, make sure the 1552 // something is not already an operand of the multiply. If so, merge it into 1553 // the multiply. 1554 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1555 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1556 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1557 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1558 if (isa<SCEVConstant>(MulOpSCEV)) 1559 continue; 1560 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1561 if (MulOpSCEV == Ops[AddOp]) { 1562 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1563 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1564 if (Mul->getNumOperands() != 2) { 1565 // If the multiply has more than two operands, we must get the 1566 // Y*Z term. 1567 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1568 Mul->op_begin()+MulOp); 1569 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1570 InnerMul = getMulExpr(MulOps); 1571 } 1572 const SCEV *One = getConstant(Ty, 1); 1573 const SCEV *AddOne = getAddExpr(One, InnerMul); 1574 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1575 if (Ops.size() == 2) return OuterMul; 1576 if (AddOp < Idx) { 1577 Ops.erase(Ops.begin()+AddOp); 1578 Ops.erase(Ops.begin()+Idx-1); 1579 } else { 1580 Ops.erase(Ops.begin()+Idx); 1581 Ops.erase(Ops.begin()+AddOp-1); 1582 } 1583 Ops.push_back(OuterMul); 1584 return getAddExpr(Ops); 1585 } 1586 1587 // Check this multiply against other multiplies being added together. 1588 bool AnyFold = false; 1589 for (unsigned OtherMulIdx = Idx+1; 1590 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1591 ++OtherMulIdx) { 1592 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1593 // If MulOp occurs in OtherMul, we can fold the two multiplies 1594 // together. 1595 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1596 OMulOp != e; ++OMulOp) 1597 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1598 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1599 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1600 if (Mul->getNumOperands() != 2) { 1601 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1602 Mul->op_begin()+MulOp); 1603 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1604 InnerMul1 = getMulExpr(MulOps); 1605 } 1606 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1607 if (OtherMul->getNumOperands() != 2) { 1608 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1609 OtherMul->op_begin()+OMulOp); 1610 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1611 InnerMul2 = getMulExpr(MulOps); 1612 } 1613 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1614 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1615 if (Ops.size() == 2) return OuterMul; 1616 Ops[Idx] = OuterMul; 1617 Ops.erase(Ops.begin()+OtherMulIdx); 1618 OtherMulIdx = Idx; 1619 AnyFold = true; 1620 } 1621 } 1622 if (AnyFold) 1623 return getAddExpr(Ops); 1624 } 1625 } 1626 1627 // If there are any add recurrences in the operands list, see if any other 1628 // added values are loop invariant. If so, we can fold them into the 1629 // recurrence. 1630 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1631 ++Idx; 1632 1633 // Scan over all recurrences, trying to fold loop invariants into them. 1634 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1635 // Scan all of the other operands to this add and add them to the vector if 1636 // they are loop invariant w.r.t. the recurrence. 1637 SmallVector<const SCEV *, 8> LIOps; 1638 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1639 const Loop *AddRecLoop = AddRec->getLoop(); 1640 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1641 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1642 LIOps.push_back(Ops[i]); 1643 Ops.erase(Ops.begin()+i); 1644 --i; --e; 1645 } 1646 1647 // If we found some loop invariants, fold them into the recurrence. 1648 if (!LIOps.empty()) { 1649 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1650 LIOps.push_back(AddRec->getStart()); 1651 1652 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1653 AddRec->op_end()); 1654 AddRecOps[0] = getAddExpr(LIOps); 1655 1656 // Build the new addrec. Propagate the NUW and NSW flags if both the 1657 // outer add and the inner addrec are guaranteed to have no overflow. 1658 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1659 HasNUW && AddRec->hasNoUnsignedWrap(), 1660 HasNSW && AddRec->hasNoSignedWrap()); 1661 1662 // If all of the other operands were loop invariant, we are done. 1663 if (Ops.size() == 1) return NewRec; 1664 1665 // Otherwise, add the folded AddRec by the non-liv parts. 1666 for (unsigned i = 0;; ++i) 1667 if (Ops[i] == AddRec) { 1668 Ops[i] = NewRec; 1669 break; 1670 } 1671 return getAddExpr(Ops); 1672 } 1673 1674 // Okay, if there weren't any loop invariants to be folded, check to see if 1675 // there are multiple AddRec's with the same loop induction variable being 1676 // added together. If so, we can fold them. 1677 for (unsigned OtherIdx = Idx+1; 1678 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1679 if (OtherIdx != Idx) { 1680 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1681 if (AddRecLoop == OtherAddRec->getLoop()) { 1682 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} 1683 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), 1684 AddRec->op_end()); 1685 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { 1686 if (i >= NewOps.size()) { 1687 NewOps.append(OtherAddRec->op_begin()+i, 1688 OtherAddRec->op_end()); 1689 break; 1690 } 1691 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); 1692 } 1693 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop); 1694 1695 if (Ops.size() == 2) return NewAddRec; 1696 1697 Ops.erase(Ops.begin()+Idx); 1698 Ops.erase(Ops.begin()+OtherIdx-1); 1699 Ops.push_back(NewAddRec); 1700 return getAddExpr(Ops); 1701 } 1702 } 1703 1704 // Otherwise couldn't fold anything into this recurrence. Move onto the 1705 // next one. 1706 } 1707 1708 // Okay, it looks like we really DO need an add expr. Check to see if we 1709 // already have one, otherwise create a new one. 1710 FoldingSetNodeID ID; 1711 ID.AddInteger(scAddExpr); 1712 ID.AddInteger(Ops.size()); 1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1714 ID.AddPointer(Ops[i]); 1715 void *IP = 0; 1716 SCEVAddExpr *S = 1717 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1718 if (!S) { 1719 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1720 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1721 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1722 O, Ops.size()); 1723 UniqueSCEVs.InsertNode(S, IP); 1724 } 1725 if (HasNUW) S->setHasNoUnsignedWrap(true); 1726 if (HasNSW) S->setHasNoSignedWrap(true); 1727 return S; 1728} 1729 1730/// getMulExpr - Get a canonical multiply expression, or something simpler if 1731/// possible. 1732const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1733 bool HasNUW, bool HasNSW) { 1734 assert(!Ops.empty() && "Cannot get empty mul!"); 1735 if (Ops.size() == 1) return Ops[0]; 1736#ifndef NDEBUG 1737 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1738 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1739 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1740 "SCEVMulExpr operand types don't match!"); 1741#endif 1742 1743 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1744 if (!HasNUW && HasNSW) { 1745 bool All = true; 1746 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1747 E = Ops.end(); I != E; ++I) 1748 if (!isKnownNonNegative(*I)) { 1749 All = false; 1750 break; 1751 } 1752 if (All) HasNUW = true; 1753 } 1754 1755 // Sort by complexity, this groups all similar expression types together. 1756 GroupByComplexity(Ops, LI); 1757 1758 // If there are any constants, fold them together. 1759 unsigned Idx = 0; 1760 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1761 1762 // C1*(C2+V) -> C1*C2 + C1*V 1763 if (Ops.size() == 2) 1764 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1765 if (Add->getNumOperands() == 2 && 1766 isa<SCEVConstant>(Add->getOperand(0))) 1767 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1768 getMulExpr(LHSC, Add->getOperand(1))); 1769 1770 ++Idx; 1771 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1772 // We found two constants, fold them together! 1773 ConstantInt *Fold = ConstantInt::get(getContext(), 1774 LHSC->getValue()->getValue() * 1775 RHSC->getValue()->getValue()); 1776 Ops[0] = getConstant(Fold); 1777 Ops.erase(Ops.begin()+1); // Erase the folded element 1778 if (Ops.size() == 1) return Ops[0]; 1779 LHSC = cast<SCEVConstant>(Ops[0]); 1780 } 1781 1782 // If we are left with a constant one being multiplied, strip it off. 1783 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1784 Ops.erase(Ops.begin()); 1785 --Idx; 1786 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1787 // If we have a multiply of zero, it will always be zero. 1788 return Ops[0]; 1789 } else if (Ops[0]->isAllOnesValue()) { 1790 // If we have a mul by -1 of an add, try distributing the -1 among the 1791 // add operands. 1792 if (Ops.size() == 2) 1793 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1794 SmallVector<const SCEV *, 4> NewOps; 1795 bool AnyFolded = false; 1796 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1797 I != E; ++I) { 1798 const SCEV *Mul = getMulExpr(Ops[0], *I); 1799 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1800 NewOps.push_back(Mul); 1801 } 1802 if (AnyFolded) 1803 return getAddExpr(NewOps); 1804 } 1805 } 1806 1807 if (Ops.size() == 1) 1808 return Ops[0]; 1809 } 1810 1811 // Skip over the add expression until we get to a multiply. 1812 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1813 ++Idx; 1814 1815 // If there are mul operands inline them all into this expression. 1816 if (Idx < Ops.size()) { 1817 bool DeletedMul = false; 1818 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1819 // If we have an mul, expand the mul operands onto the end of the operands 1820 // list. 1821 Ops.erase(Ops.begin()+Idx); 1822 Ops.append(Mul->op_begin(), Mul->op_end()); 1823 DeletedMul = true; 1824 } 1825 1826 // If we deleted at least one mul, we added operands to the end of the list, 1827 // and they are not necessarily sorted. Recurse to resort and resimplify 1828 // any operands we just acquired. 1829 if (DeletedMul) 1830 return getMulExpr(Ops); 1831 } 1832 1833 // If there are any add recurrences in the operands list, see if any other 1834 // added values are loop invariant. If so, we can fold them into the 1835 // recurrence. 1836 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1837 ++Idx; 1838 1839 // Scan over all recurrences, trying to fold loop invariants into them. 1840 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1841 // Scan all of the other operands to this mul and add them to the vector if 1842 // they are loop invariant w.r.t. the recurrence. 1843 SmallVector<const SCEV *, 8> LIOps; 1844 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1845 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1846 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { 1847 LIOps.push_back(Ops[i]); 1848 Ops.erase(Ops.begin()+i); 1849 --i; --e; 1850 } 1851 1852 // If we found some loop invariants, fold them into the recurrence. 1853 if (!LIOps.empty()) { 1854 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1855 SmallVector<const SCEV *, 4> NewOps; 1856 NewOps.reserve(AddRec->getNumOperands()); 1857 const SCEV *Scale = getMulExpr(LIOps); 1858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1859 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1860 1861 // Build the new addrec. Propagate the NUW and NSW flags if both the 1862 // outer mul and the inner addrec are guaranteed to have no overflow. 1863 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), 1864 HasNUW && AddRec->hasNoUnsignedWrap(), 1865 HasNSW && AddRec->hasNoSignedWrap()); 1866 1867 // If all of the other operands were loop invariant, we are done. 1868 if (Ops.size() == 1) return NewRec; 1869 1870 // Otherwise, multiply the folded AddRec by the non-liv parts. 1871 for (unsigned i = 0;; ++i) 1872 if (Ops[i] == AddRec) { 1873 Ops[i] = NewRec; 1874 break; 1875 } 1876 return getMulExpr(Ops); 1877 } 1878 1879 // Okay, if there weren't any loop invariants to be folded, check to see if 1880 // there are multiple AddRec's with the same loop induction variable being 1881 // multiplied together. If so, we can fold them. 1882 for (unsigned OtherIdx = Idx+1; 1883 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) 1884 if (OtherIdx != Idx) { 1885 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); 1886 if (AddRec->getLoop() == OtherAddRec->getLoop()) { 1887 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} 1888 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1889 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1890 const SCEV *B = F->getStepRecurrence(*this); 1891 const SCEV *D = G->getStepRecurrence(*this); 1892 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1893 getMulExpr(G, B), 1894 getMulExpr(B, D)); 1895 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1896 F->getLoop()); 1897 if (Ops.size() == 2) return NewAddRec; 1898 1899 Ops.erase(Ops.begin()+Idx); 1900 Ops.erase(Ops.begin()+OtherIdx-1); 1901 Ops.push_back(NewAddRec); 1902 return getMulExpr(Ops); 1903 } 1904 } 1905 1906 // Otherwise couldn't fold anything into this recurrence. Move onto the 1907 // next one. 1908 } 1909 1910 // Okay, it looks like we really DO need an mul expr. Check to see if we 1911 // already have one, otherwise create a new one. 1912 FoldingSetNodeID ID; 1913 ID.AddInteger(scMulExpr); 1914 ID.AddInteger(Ops.size()); 1915 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1916 ID.AddPointer(Ops[i]); 1917 void *IP = 0; 1918 SCEVMulExpr *S = 1919 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1920 if (!S) { 1921 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1922 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1923 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1924 O, Ops.size()); 1925 UniqueSCEVs.InsertNode(S, IP); 1926 } 1927 if (HasNUW) S->setHasNoUnsignedWrap(true); 1928 if (HasNSW) S->setHasNoSignedWrap(true); 1929 return S; 1930} 1931 1932/// getUDivExpr - Get a canonical unsigned division expression, or something 1933/// simpler if possible. 1934const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1935 const SCEV *RHS) { 1936 assert(getEffectiveSCEVType(LHS->getType()) == 1937 getEffectiveSCEVType(RHS->getType()) && 1938 "SCEVUDivExpr operand types don't match!"); 1939 1940 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1941 if (RHSC->getValue()->equalsInt(1)) 1942 return LHS; // X udiv 1 --> x 1943 // If the denominator is zero, the result of the udiv is undefined. Don't 1944 // try to analyze it, because the resolution chosen here may differ from 1945 // the resolution chosen in other parts of the compiler. 1946 if (!RHSC->getValue()->isZero()) { 1947 // Determine if the division can be folded into the operands of 1948 // its operands. 1949 // TODO: Generalize this to non-constants by using known-bits information. 1950 const Type *Ty = LHS->getType(); 1951 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1952 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1953 // For non-power-of-two values, effectively round the value up to the 1954 // nearest power of two. 1955 if (!RHSC->getValue()->getValue().isPowerOf2()) 1956 ++MaxShiftAmt; 1957 const IntegerType *ExtTy = 1958 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1959 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1960 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1961 if (const SCEVConstant *Step = 1962 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1963 if (!Step->getValue()->getValue() 1964 .urem(RHSC->getValue()->getValue()) && 1965 getZeroExtendExpr(AR, ExtTy) == 1966 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1967 getZeroExtendExpr(Step, ExtTy), 1968 AR->getLoop())) { 1969 SmallVector<const SCEV *, 4> Operands; 1970 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1971 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1972 return getAddRecExpr(Operands, AR->getLoop()); 1973 } 1974 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1975 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1976 SmallVector<const SCEV *, 4> Operands; 1977 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1978 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1979 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1980 // Find an operand that's safely divisible. 1981 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1982 const SCEV *Op = M->getOperand(i); 1983 const SCEV *Div = getUDivExpr(Op, RHSC); 1984 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1985 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1986 M->op_end()); 1987 Operands[i] = Div; 1988 return getMulExpr(Operands); 1989 } 1990 } 1991 } 1992 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1993 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1994 SmallVector<const SCEV *, 4> Operands; 1995 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1996 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1997 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1998 Operands.clear(); 1999 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2000 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2001 if (isa<SCEVUDivExpr>(Op) || 2002 getMulExpr(Op, RHS) != A->getOperand(i)) 2003 break; 2004 Operands.push_back(Op); 2005 } 2006 if (Operands.size() == A->getNumOperands()) 2007 return getAddExpr(Operands); 2008 } 2009 } 2010 2011 // Fold if both operands are constant. 2012 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2013 Constant *LHSCV = LHSC->getValue(); 2014 Constant *RHSCV = RHSC->getValue(); 2015 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2016 RHSCV))); 2017 } 2018 } 2019 } 2020 2021 FoldingSetNodeID ID; 2022 ID.AddInteger(scUDivExpr); 2023 ID.AddPointer(LHS); 2024 ID.AddPointer(RHS); 2025 void *IP = 0; 2026 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2027 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2028 LHS, RHS); 2029 UniqueSCEVs.InsertNode(S, IP); 2030 return S; 2031} 2032 2033 2034/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2035/// Simplify the expression as much as possible. 2036const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2037 const SCEV *Step, const Loop *L, 2038 bool HasNUW, bool HasNSW) { 2039 SmallVector<const SCEV *, 4> Operands; 2040 Operands.push_back(Start); 2041 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2042 if (StepChrec->getLoop() == L) { 2043 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2044 return getAddRecExpr(Operands, L); 2045 } 2046 2047 Operands.push_back(Step); 2048 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2049} 2050 2051/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2052/// Simplify the expression as much as possible. 2053const SCEV * 2054ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2055 const Loop *L, 2056 bool HasNUW, bool HasNSW) { 2057 if (Operands.size() == 1) return Operands[0]; 2058#ifndef NDEBUG 2059 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2060 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2061 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2062 "SCEVAddRecExpr operand types don't match!"); 2063#endif 2064 2065 if (Operands.back()->isZero()) { 2066 Operands.pop_back(); 2067 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2068 } 2069 2070 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2071 // use that information to infer NUW and NSW flags. However, computing a 2072 // BE count requires calling getAddRecExpr, so we may not yet have a 2073 // meaningful BE count at this point (and if we don't, we'd be stuck 2074 // with a SCEVCouldNotCompute as the cached BE count). 2075 2076 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2077 if (!HasNUW && HasNSW) { 2078 bool All = true; 2079 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2080 E = Operands.end(); I != E; ++I) 2081 if (!isKnownNonNegative(*I)) { 2082 All = false; 2083 break; 2084 } 2085 if (All) HasNUW = true; 2086 } 2087 2088 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2089 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2090 const Loop *NestedLoop = NestedAR->getLoop(); 2091 if (L->contains(NestedLoop) ? 2092 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2093 (!NestedLoop->contains(L) && 2094 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2095 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2096 NestedAR->op_end()); 2097 Operands[0] = NestedAR->getStart(); 2098 // AddRecs require their operands be loop-invariant with respect to their 2099 // loops. Don't perform this transformation if it would break this 2100 // requirement. 2101 bool AllInvariant = true; 2102 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2103 if (!Operands[i]->isLoopInvariant(L)) { 2104 AllInvariant = false; 2105 break; 2106 } 2107 if (AllInvariant) { 2108 NestedOperands[0] = getAddRecExpr(Operands, L); 2109 AllInvariant = true; 2110 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2111 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2112 AllInvariant = false; 2113 break; 2114 } 2115 if (AllInvariant) 2116 // Ok, both add recurrences are valid after the transformation. 2117 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2118 } 2119 // Reset Operands to its original state. 2120 Operands[0] = NestedAR; 2121 } 2122 } 2123 2124 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2125 // already have one, otherwise create a new one. 2126 FoldingSetNodeID ID; 2127 ID.AddInteger(scAddRecExpr); 2128 ID.AddInteger(Operands.size()); 2129 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2130 ID.AddPointer(Operands[i]); 2131 ID.AddPointer(L); 2132 void *IP = 0; 2133 SCEVAddRecExpr *S = 2134 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2135 if (!S) { 2136 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2137 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2138 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2139 O, Operands.size(), L); 2140 UniqueSCEVs.InsertNode(S, IP); 2141 } 2142 if (HasNUW) S->setHasNoUnsignedWrap(true); 2143 if (HasNSW) S->setHasNoSignedWrap(true); 2144 return S; 2145} 2146 2147const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2148 const SCEV *RHS) { 2149 SmallVector<const SCEV *, 2> Ops; 2150 Ops.push_back(LHS); 2151 Ops.push_back(RHS); 2152 return getSMaxExpr(Ops); 2153} 2154 2155const SCEV * 2156ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2157 assert(!Ops.empty() && "Cannot get empty smax!"); 2158 if (Ops.size() == 1) return Ops[0]; 2159#ifndef NDEBUG 2160 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2161 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2162 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2163 "SCEVSMaxExpr operand types don't match!"); 2164#endif 2165 2166 // Sort by complexity, this groups all similar expression types together. 2167 GroupByComplexity(Ops, LI); 2168 2169 // If there are any constants, fold them together. 2170 unsigned Idx = 0; 2171 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2172 ++Idx; 2173 assert(Idx < Ops.size()); 2174 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2175 // We found two constants, fold them together! 2176 ConstantInt *Fold = ConstantInt::get(getContext(), 2177 APIntOps::smax(LHSC->getValue()->getValue(), 2178 RHSC->getValue()->getValue())); 2179 Ops[0] = getConstant(Fold); 2180 Ops.erase(Ops.begin()+1); // Erase the folded element 2181 if (Ops.size() == 1) return Ops[0]; 2182 LHSC = cast<SCEVConstant>(Ops[0]); 2183 } 2184 2185 // If we are left with a constant minimum-int, strip it off. 2186 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2187 Ops.erase(Ops.begin()); 2188 --Idx; 2189 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2190 // If we have an smax with a constant maximum-int, it will always be 2191 // maximum-int. 2192 return Ops[0]; 2193 } 2194 2195 if (Ops.size() == 1) return Ops[0]; 2196 } 2197 2198 // Find the first SMax 2199 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2200 ++Idx; 2201 2202 // Check to see if one of the operands is an SMax. If so, expand its operands 2203 // onto our operand list, and recurse to simplify. 2204 if (Idx < Ops.size()) { 2205 bool DeletedSMax = false; 2206 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2207 Ops.erase(Ops.begin()+Idx); 2208 Ops.append(SMax->op_begin(), SMax->op_end()); 2209 DeletedSMax = true; 2210 } 2211 2212 if (DeletedSMax) 2213 return getSMaxExpr(Ops); 2214 } 2215 2216 // Okay, check to see if the same value occurs in the operand list twice. If 2217 // so, delete one. Since we sorted the list, these values are required to 2218 // be adjacent. 2219 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2220 // X smax Y smax Y --> X smax Y 2221 // X smax Y --> X, if X is always greater than Y 2222 if (Ops[i] == Ops[i+1] || 2223 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2224 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2225 --i; --e; 2226 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2227 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2228 --i; --e; 2229 } 2230 2231 if (Ops.size() == 1) return Ops[0]; 2232 2233 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2234 2235 // Okay, it looks like we really DO need an smax expr. Check to see if we 2236 // already have one, otherwise create a new one. 2237 FoldingSetNodeID ID; 2238 ID.AddInteger(scSMaxExpr); 2239 ID.AddInteger(Ops.size()); 2240 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2241 ID.AddPointer(Ops[i]); 2242 void *IP = 0; 2243 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2244 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2245 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2246 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2247 O, Ops.size()); 2248 UniqueSCEVs.InsertNode(S, IP); 2249 return S; 2250} 2251 2252const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2253 const SCEV *RHS) { 2254 SmallVector<const SCEV *, 2> Ops; 2255 Ops.push_back(LHS); 2256 Ops.push_back(RHS); 2257 return getUMaxExpr(Ops); 2258} 2259 2260const SCEV * 2261ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2262 assert(!Ops.empty() && "Cannot get empty umax!"); 2263 if (Ops.size() == 1) return Ops[0]; 2264#ifndef NDEBUG 2265 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2266 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2267 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2268 "SCEVUMaxExpr operand types don't match!"); 2269#endif 2270 2271 // Sort by complexity, this groups all similar expression types together. 2272 GroupByComplexity(Ops, LI); 2273 2274 // If there are any constants, fold them together. 2275 unsigned Idx = 0; 2276 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2277 ++Idx; 2278 assert(Idx < Ops.size()); 2279 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2280 // We found two constants, fold them together! 2281 ConstantInt *Fold = ConstantInt::get(getContext(), 2282 APIntOps::umax(LHSC->getValue()->getValue(), 2283 RHSC->getValue()->getValue())); 2284 Ops[0] = getConstant(Fold); 2285 Ops.erase(Ops.begin()+1); // Erase the folded element 2286 if (Ops.size() == 1) return Ops[0]; 2287 LHSC = cast<SCEVConstant>(Ops[0]); 2288 } 2289 2290 // If we are left with a constant minimum-int, strip it off. 2291 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2292 Ops.erase(Ops.begin()); 2293 --Idx; 2294 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2295 // If we have an umax with a constant maximum-int, it will always be 2296 // maximum-int. 2297 return Ops[0]; 2298 } 2299 2300 if (Ops.size() == 1) return Ops[0]; 2301 } 2302 2303 // Find the first UMax 2304 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2305 ++Idx; 2306 2307 // Check to see if one of the operands is a UMax. If so, expand its operands 2308 // onto our operand list, and recurse to simplify. 2309 if (Idx < Ops.size()) { 2310 bool DeletedUMax = false; 2311 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2312 Ops.erase(Ops.begin()+Idx); 2313 Ops.append(UMax->op_begin(), UMax->op_end()); 2314 DeletedUMax = true; 2315 } 2316 2317 if (DeletedUMax) 2318 return getUMaxExpr(Ops); 2319 } 2320 2321 // Okay, check to see if the same value occurs in the operand list twice. If 2322 // so, delete one. Since we sorted the list, these values are required to 2323 // be adjacent. 2324 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2325 // X umax Y umax Y --> X umax Y 2326 // X umax Y --> X, if X is always greater than Y 2327 if (Ops[i] == Ops[i+1] || 2328 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2329 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2330 --i; --e; 2331 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2332 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2333 --i; --e; 2334 } 2335 2336 if (Ops.size() == 1) return Ops[0]; 2337 2338 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2339 2340 // Okay, it looks like we really DO need a umax expr. Check to see if we 2341 // already have one, otherwise create a new one. 2342 FoldingSetNodeID ID; 2343 ID.AddInteger(scUMaxExpr); 2344 ID.AddInteger(Ops.size()); 2345 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2346 ID.AddPointer(Ops[i]); 2347 void *IP = 0; 2348 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2349 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2350 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2351 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2352 O, Ops.size()); 2353 UniqueSCEVs.InsertNode(S, IP); 2354 return S; 2355} 2356 2357const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2358 const SCEV *RHS) { 2359 // ~smax(~x, ~y) == smin(x, y). 2360 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2361} 2362 2363const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2364 const SCEV *RHS) { 2365 // ~umax(~x, ~y) == umin(x, y) 2366 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2367} 2368 2369const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2370 // If we have TargetData, we can bypass creating a target-independent 2371 // constant expression and then folding it back into a ConstantInt. 2372 // This is just a compile-time optimization. 2373 if (TD) 2374 return getConstant(TD->getIntPtrType(getContext()), 2375 TD->getTypeAllocSize(AllocTy)); 2376 2377 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2378 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2379 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2380 C = Folded; 2381 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2382 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2383} 2384 2385const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2386 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2387 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2388 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2389 C = Folded; 2390 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2391 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2392} 2393 2394const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2395 unsigned FieldNo) { 2396 // If we have TargetData, we can bypass creating a target-independent 2397 // constant expression and then folding it back into a ConstantInt. 2398 // This is just a compile-time optimization. 2399 if (TD) 2400 return getConstant(TD->getIntPtrType(getContext()), 2401 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2402 2403 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2404 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2405 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2406 C = Folded; 2407 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2408 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2409} 2410 2411const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2412 Constant *FieldNo) { 2413 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2414 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2415 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2416 C = Folded; 2417 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2418 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2419} 2420 2421const SCEV *ScalarEvolution::getUnknown(Value *V) { 2422 // Don't attempt to do anything other than create a SCEVUnknown object 2423 // here. createSCEV only calls getUnknown after checking for all other 2424 // interesting possibilities, and any other code that calls getUnknown 2425 // is doing so in order to hide a value from SCEV canonicalization. 2426 2427 FoldingSetNodeID ID; 2428 ID.AddInteger(scUnknown); 2429 ID.AddPointer(V); 2430 void *IP = 0; 2431 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2432 assert(cast<SCEVUnknown>(S)->getValue() == V && 2433 "Stale SCEVUnknown in uniquing map!"); 2434 return S; 2435 } 2436 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2437 FirstUnknown); 2438 FirstUnknown = cast<SCEVUnknown>(S); 2439 UniqueSCEVs.InsertNode(S, IP); 2440 return S; 2441} 2442 2443//===----------------------------------------------------------------------===// 2444// Basic SCEV Analysis and PHI Idiom Recognition Code 2445// 2446 2447/// isSCEVable - Test if values of the given type are analyzable within 2448/// the SCEV framework. This primarily includes integer types, and it 2449/// can optionally include pointer types if the ScalarEvolution class 2450/// has access to target-specific information. 2451bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2452 // Integers and pointers are always SCEVable. 2453 return Ty->isIntegerTy() || Ty->isPointerTy(); 2454} 2455 2456/// getTypeSizeInBits - Return the size in bits of the specified type, 2457/// for which isSCEVable must return true. 2458uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2459 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2460 2461 // If we have a TargetData, use it! 2462 if (TD) 2463 return TD->getTypeSizeInBits(Ty); 2464 2465 // Integer types have fixed sizes. 2466 if (Ty->isIntegerTy()) 2467 return Ty->getPrimitiveSizeInBits(); 2468 2469 // The only other support type is pointer. Without TargetData, conservatively 2470 // assume pointers are 64-bit. 2471 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2472 return 64; 2473} 2474 2475/// getEffectiveSCEVType - Return a type with the same bitwidth as 2476/// the given type and which represents how SCEV will treat the given 2477/// type, for which isSCEVable must return true. For pointer types, 2478/// this is the pointer-sized integer type. 2479const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2480 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2481 2482 if (Ty->isIntegerTy()) 2483 return Ty; 2484 2485 // The only other support type is pointer. 2486 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2487 if (TD) return TD->getIntPtrType(getContext()); 2488 2489 // Without TargetData, conservatively assume pointers are 64-bit. 2490 return Type::getInt64Ty(getContext()); 2491} 2492 2493const SCEV *ScalarEvolution::getCouldNotCompute() { 2494 return &CouldNotCompute; 2495} 2496 2497/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2498/// expression and create a new one. 2499const SCEV *ScalarEvolution::getSCEV(Value *V) { 2500 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2501 2502 std::map<SCEVCallbackVH, const SCEV *>::const_iterator I = Scalars.find(V); 2503 if (I != Scalars.end()) return I->second; 2504 const SCEV *S = createSCEV(V); 2505 2506 // The process of creating a SCEV for V may have caused other SCEVs 2507 // to have been created, so it's necessary to insert the new entry 2508 // from scratch, rather than trying to remember the insert position 2509 // above. 2510 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2511 return S; 2512} 2513 2514/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2515/// 2516const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2517 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2518 return getConstant( 2519 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2520 2521 const Type *Ty = V->getType(); 2522 Ty = getEffectiveSCEVType(Ty); 2523 return getMulExpr(V, 2524 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2525} 2526 2527/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2528const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2529 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2530 return getConstant( 2531 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2532 2533 const Type *Ty = V->getType(); 2534 Ty = getEffectiveSCEVType(Ty); 2535 const SCEV *AllOnes = 2536 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2537 return getMinusSCEV(AllOnes, V); 2538} 2539 2540/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2541/// 2542const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2543 const SCEV *RHS) { 2544 // Fast path: X - X --> 0. 2545 if (LHS == RHS) 2546 return getConstant(LHS->getType(), 0); 2547 2548 // X - Y --> X + -Y 2549 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2550} 2551 2552/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2553/// input value to the specified type. If the type must be extended, it is zero 2554/// extended. 2555const SCEV * 2556ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2557 const Type *Ty) { 2558 const Type *SrcTy = V->getType(); 2559 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2560 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2561 "Cannot truncate or zero extend with non-integer arguments!"); 2562 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2563 return V; // No conversion 2564 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2565 return getTruncateExpr(V, Ty); 2566 return getZeroExtendExpr(V, Ty); 2567} 2568 2569/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2570/// input value to the specified type. If the type must be extended, it is sign 2571/// extended. 2572const SCEV * 2573ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2574 const Type *Ty) { 2575 const Type *SrcTy = V->getType(); 2576 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2577 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2578 "Cannot truncate or zero extend with non-integer arguments!"); 2579 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2580 return V; // No conversion 2581 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2582 return getTruncateExpr(V, Ty); 2583 return getSignExtendExpr(V, Ty); 2584} 2585 2586/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2587/// input value to the specified type. If the type must be extended, it is zero 2588/// extended. The conversion must not be narrowing. 2589const SCEV * 2590ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2591 const Type *SrcTy = V->getType(); 2592 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2593 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2594 "Cannot noop or zero extend with non-integer arguments!"); 2595 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2596 "getNoopOrZeroExtend cannot truncate!"); 2597 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2598 return V; // No conversion 2599 return getZeroExtendExpr(V, Ty); 2600} 2601 2602/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2603/// input value to the specified type. If the type must be extended, it is sign 2604/// extended. The conversion must not be narrowing. 2605const SCEV * 2606ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2607 const Type *SrcTy = V->getType(); 2608 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2609 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2610 "Cannot noop or sign extend with non-integer arguments!"); 2611 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2612 "getNoopOrSignExtend cannot truncate!"); 2613 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2614 return V; // No conversion 2615 return getSignExtendExpr(V, Ty); 2616} 2617 2618/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2619/// the input value to the specified type. If the type must be extended, 2620/// it is extended with unspecified bits. The conversion must not be 2621/// narrowing. 2622const SCEV * 2623ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2624 const Type *SrcTy = V->getType(); 2625 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2626 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2627 "Cannot noop or any extend with non-integer arguments!"); 2628 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2629 "getNoopOrAnyExtend cannot truncate!"); 2630 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2631 return V; // No conversion 2632 return getAnyExtendExpr(V, Ty); 2633} 2634 2635/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2636/// input value to the specified type. The conversion must not be widening. 2637const SCEV * 2638ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2639 const Type *SrcTy = V->getType(); 2640 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2641 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2642 "Cannot truncate or noop with non-integer arguments!"); 2643 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2644 "getTruncateOrNoop cannot extend!"); 2645 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2646 return V; // No conversion 2647 return getTruncateExpr(V, Ty); 2648} 2649 2650/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2651/// the types using zero-extension, and then perform a umax operation 2652/// with them. 2653const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2654 const SCEV *RHS) { 2655 const SCEV *PromotedLHS = LHS; 2656 const SCEV *PromotedRHS = RHS; 2657 2658 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2659 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2660 else 2661 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2662 2663 return getUMaxExpr(PromotedLHS, PromotedRHS); 2664} 2665 2666/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2667/// the types using zero-extension, and then perform a umin operation 2668/// with them. 2669const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2670 const SCEV *RHS) { 2671 const SCEV *PromotedLHS = LHS; 2672 const SCEV *PromotedRHS = RHS; 2673 2674 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2675 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2676 else 2677 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2678 2679 return getUMinExpr(PromotedLHS, PromotedRHS); 2680} 2681 2682/// PushDefUseChildren - Push users of the given Instruction 2683/// onto the given Worklist. 2684static void 2685PushDefUseChildren(Instruction *I, 2686 SmallVectorImpl<Instruction *> &Worklist) { 2687 // Push the def-use children onto the Worklist stack. 2688 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2689 UI != UE; ++UI) 2690 Worklist.push_back(cast<Instruction>(*UI)); 2691} 2692 2693/// ForgetSymbolicValue - This looks up computed SCEV values for all 2694/// instructions that depend on the given instruction and removes them from 2695/// the Scalars map if they reference SymName. This is used during PHI 2696/// resolution. 2697void 2698ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2699 SmallVector<Instruction *, 16> Worklist; 2700 PushDefUseChildren(PN, Worklist); 2701 2702 SmallPtrSet<Instruction *, 8> Visited; 2703 Visited.insert(PN); 2704 while (!Worklist.empty()) { 2705 Instruction *I = Worklist.pop_back_val(); 2706 if (!Visited.insert(I)) continue; 2707 2708 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 2709 Scalars.find(static_cast<Value *>(I)); 2710 if (It != Scalars.end()) { 2711 // Short-circuit the def-use traversal if the symbolic name 2712 // ceases to appear in expressions. 2713 if (It->second != SymName && !It->second->hasOperand(SymName)) 2714 continue; 2715 2716 // SCEVUnknown for a PHI either means that it has an unrecognized 2717 // structure, it's a PHI that's in the progress of being computed 2718 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2719 // additional loop trip count information isn't going to change anything. 2720 // In the second case, createNodeForPHI will perform the necessary 2721 // updates on its own when it gets to that point. In the third, we do 2722 // want to forget the SCEVUnknown. 2723 if (!isa<PHINode>(I) || 2724 !isa<SCEVUnknown>(It->second) || 2725 (I != PN && It->second == SymName)) { 2726 ValuesAtScopes.erase(It->second); 2727 Scalars.erase(It); 2728 } 2729 } 2730 2731 PushDefUseChildren(I, Worklist); 2732 } 2733} 2734 2735/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2736/// a loop header, making it a potential recurrence, or it doesn't. 2737/// 2738const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2739 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2740 if (L->getHeader() == PN->getParent()) { 2741 // The loop may have multiple entrances or multiple exits; we can analyze 2742 // this phi as an addrec if it has a unique entry value and a unique 2743 // backedge value. 2744 Value *BEValueV = 0, *StartValueV = 0; 2745 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2746 Value *V = PN->getIncomingValue(i); 2747 if (L->contains(PN->getIncomingBlock(i))) { 2748 if (!BEValueV) { 2749 BEValueV = V; 2750 } else if (BEValueV != V) { 2751 BEValueV = 0; 2752 break; 2753 } 2754 } else if (!StartValueV) { 2755 StartValueV = V; 2756 } else if (StartValueV != V) { 2757 StartValueV = 0; 2758 break; 2759 } 2760 } 2761 if (BEValueV && StartValueV) { 2762 // While we are analyzing this PHI node, handle its value symbolically. 2763 const SCEV *SymbolicName = getUnknown(PN); 2764 assert(Scalars.find(PN) == Scalars.end() && 2765 "PHI node already processed?"); 2766 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2767 2768 // Using this symbolic name for the PHI, analyze the value coming around 2769 // the back-edge. 2770 const SCEV *BEValue = getSCEV(BEValueV); 2771 2772 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2773 // has a special value for the first iteration of the loop. 2774 2775 // If the value coming around the backedge is an add with the symbolic 2776 // value we just inserted, then we found a simple induction variable! 2777 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2778 // If there is a single occurrence of the symbolic value, replace it 2779 // with a recurrence. 2780 unsigned FoundIndex = Add->getNumOperands(); 2781 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2782 if (Add->getOperand(i) == SymbolicName) 2783 if (FoundIndex == e) { 2784 FoundIndex = i; 2785 break; 2786 } 2787 2788 if (FoundIndex != Add->getNumOperands()) { 2789 // Create an add with everything but the specified operand. 2790 SmallVector<const SCEV *, 8> Ops; 2791 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2792 if (i != FoundIndex) 2793 Ops.push_back(Add->getOperand(i)); 2794 const SCEV *Accum = getAddExpr(Ops); 2795 2796 // This is not a valid addrec if the step amount is varying each 2797 // loop iteration, but is not itself an addrec in this loop. 2798 if (Accum->isLoopInvariant(L) || 2799 (isa<SCEVAddRecExpr>(Accum) && 2800 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2801 bool HasNUW = false; 2802 bool HasNSW = false; 2803 2804 // If the increment doesn't overflow, then neither the addrec nor 2805 // the post-increment will overflow. 2806 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2807 if (OBO->hasNoUnsignedWrap()) 2808 HasNUW = true; 2809 if (OBO->hasNoSignedWrap()) 2810 HasNSW = true; 2811 } 2812 2813 const SCEV *StartVal = getSCEV(StartValueV); 2814 const SCEV *PHISCEV = 2815 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2816 2817 // Since the no-wrap flags are on the increment, they apply to the 2818 // post-incremented value as well. 2819 if (Accum->isLoopInvariant(L)) 2820 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2821 Accum, L, HasNUW, HasNSW); 2822 2823 // Okay, for the entire analysis of this edge we assumed the PHI 2824 // to be symbolic. We now need to go back and purge all of the 2825 // entries for the scalars that use the symbolic expression. 2826 ForgetSymbolicName(PN, SymbolicName); 2827 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2828 return PHISCEV; 2829 } 2830 } 2831 } else if (const SCEVAddRecExpr *AddRec = 2832 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2833 // Otherwise, this could be a loop like this: 2834 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2835 // In this case, j = {1,+,1} and BEValue is j. 2836 // Because the other in-value of i (0) fits the evolution of BEValue 2837 // i really is an addrec evolution. 2838 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2839 const SCEV *StartVal = getSCEV(StartValueV); 2840 2841 // If StartVal = j.start - j.stride, we can use StartVal as the 2842 // initial step of the addrec evolution. 2843 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2844 AddRec->getOperand(1))) { 2845 const SCEV *PHISCEV = 2846 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2847 2848 // Okay, for the entire analysis of this edge we assumed the PHI 2849 // to be symbolic. We now need to go back and purge all of the 2850 // entries for the scalars that use the symbolic expression. 2851 ForgetSymbolicName(PN, SymbolicName); 2852 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; 2853 return PHISCEV; 2854 } 2855 } 2856 } 2857 } 2858 } 2859 2860 // If the PHI has a single incoming value, follow that value, unless the 2861 // PHI's incoming blocks are in a different loop, in which case doing so 2862 // risks breaking LCSSA form. Instcombine would normally zap these, but 2863 // it doesn't have DominatorTree information, so it may miss cases. 2864 if (Value *V = PN->hasConstantValue(DT)) { 2865 bool AllSameLoop = true; 2866 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2867 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2868 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2869 AllSameLoop = false; 2870 break; 2871 } 2872 if (AllSameLoop) 2873 return getSCEV(V); 2874 } 2875 2876 // If it's not a loop phi, we can't handle it yet. 2877 return getUnknown(PN); 2878} 2879 2880/// createNodeForGEP - Expand GEP instructions into add and multiply 2881/// operations. This allows them to be analyzed by regular SCEV code. 2882/// 2883const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2884 2885 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2886 // Add expression, because the Instruction may be guarded by control flow 2887 // and the no-overflow bits may not be valid for the expression in any 2888 // context. 2889 2890 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2891 Value *Base = GEP->getOperand(0); 2892 // Don't attempt to analyze GEPs over unsized objects. 2893 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2894 return getUnknown(GEP); 2895 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2896 gep_type_iterator GTI = gep_type_begin(GEP); 2897 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2898 E = GEP->op_end(); 2899 I != E; ++I) { 2900 Value *Index = *I; 2901 // Compute the (potentially symbolic) offset in bytes for this index. 2902 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2903 // For a struct, add the member offset. 2904 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2905 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2906 2907 // Add the field offset to the running total offset. 2908 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2909 } else { 2910 // For an array, add the element offset, explicitly scaled. 2911 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2912 const SCEV *IndexS = getSCEV(Index); 2913 // Getelementptr indices are signed. 2914 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2915 2916 // Multiply the index by the element size to compute the element offset. 2917 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2918 2919 // Add the element offset to the running total offset. 2920 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2921 } 2922 } 2923 2924 // Get the SCEV for the GEP base. 2925 const SCEV *BaseS = getSCEV(Base); 2926 2927 // Add the total offset from all the GEP indices to the base. 2928 return getAddExpr(BaseS, TotalOffset); 2929} 2930 2931/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2932/// guaranteed to end in (at every loop iteration). It is, at the same time, 2933/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2934/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2935uint32_t 2936ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2937 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2938 return C->getValue()->getValue().countTrailingZeros(); 2939 2940 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2941 return std::min(GetMinTrailingZeros(T->getOperand()), 2942 (uint32_t)getTypeSizeInBits(T->getType())); 2943 2944 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2945 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2946 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2947 getTypeSizeInBits(E->getType()) : OpRes; 2948 } 2949 2950 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(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 SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2957 // The result is the min of all operands results. 2958 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2959 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2960 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2961 return MinOpRes; 2962 } 2963 2964 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2965 // The result is the sum of all operands results. 2966 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2967 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2968 for (unsigned i = 1, e = M->getNumOperands(); 2969 SumOpRes != BitWidth && i != e; ++i) 2970 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2971 BitWidth); 2972 return SumOpRes; 2973 } 2974 2975 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2976 // The result is the min of all operands results. 2977 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2978 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2979 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2980 return MinOpRes; 2981 } 2982 2983 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2984 // The result is the min of all operands results. 2985 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2986 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2987 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2988 return MinOpRes; 2989 } 2990 2991 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2992 // The result is the min of all operands results. 2993 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2994 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2995 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2996 return MinOpRes; 2997 } 2998 2999 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3000 // For a SCEVUnknown, ask ValueTracking. 3001 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3002 APInt Mask = APInt::getAllOnesValue(BitWidth); 3003 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3004 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3005 return Zeros.countTrailingOnes(); 3006 } 3007 3008 // SCEVUDivExpr 3009 return 0; 3010} 3011 3012/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3013/// 3014ConstantRange 3015ScalarEvolution::getUnsignedRange(const SCEV *S) { 3016 3017 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3018 return ConstantRange(C->getValue()->getValue()); 3019 3020 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3021 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3022 3023 // If the value has known zeros, the maximum unsigned value will have those 3024 // known zeros as well. 3025 uint32_t TZ = GetMinTrailingZeros(S); 3026 if (TZ != 0) 3027 ConservativeResult = 3028 ConstantRange(APInt::getMinValue(BitWidth), 3029 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3030 3031 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3032 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3033 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3034 X = X.add(getUnsignedRange(Add->getOperand(i))); 3035 return ConservativeResult.intersectWith(X); 3036 } 3037 3038 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3039 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3040 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3041 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3042 return ConservativeResult.intersectWith(X); 3043 } 3044 3045 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3046 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3047 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3048 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3049 return ConservativeResult.intersectWith(X); 3050 } 3051 3052 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3053 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3054 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3055 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3056 return ConservativeResult.intersectWith(X); 3057 } 3058 3059 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3060 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3061 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3062 return ConservativeResult.intersectWith(X.udiv(Y)); 3063 } 3064 3065 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3066 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3067 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3068 } 3069 3070 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3071 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3072 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3073 } 3074 3075 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3076 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3077 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3078 } 3079 3080 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3081 // If there's no unsigned wrap, the value will never be less than its 3082 // initial value. 3083 if (AddRec->hasNoUnsignedWrap()) 3084 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3085 if (!C->getValue()->isZero()) 3086 ConservativeResult = 3087 ConservativeResult.intersectWith( 3088 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3089 3090 // TODO: non-affine addrec 3091 if (AddRec->isAffine()) { 3092 const Type *Ty = AddRec->getType(); 3093 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3094 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3095 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3096 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3097 3098 const SCEV *Start = AddRec->getStart(); 3099 const SCEV *Step = AddRec->getStepRecurrence(*this); 3100 3101 ConstantRange StartRange = getUnsignedRange(Start); 3102 ConstantRange StepRange = getSignedRange(Step); 3103 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3104 ConstantRange EndRange = 3105 StartRange.add(MaxBECountRange.multiply(StepRange)); 3106 3107 // Check for overflow. This must be done with ConstantRange arithmetic 3108 // because we could be called from within the ScalarEvolution overflow 3109 // checking code. 3110 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3111 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3112 ConstantRange ExtMaxBECountRange = 3113 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3114 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3115 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3116 ExtEndRange) 3117 return ConservativeResult; 3118 3119 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3120 EndRange.getUnsignedMin()); 3121 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3122 EndRange.getUnsignedMax()); 3123 if (Min.isMinValue() && Max.isMaxValue()) 3124 return ConservativeResult; 3125 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3126 } 3127 } 3128 3129 return ConservativeResult; 3130 } 3131 3132 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3133 // For a SCEVUnknown, ask ValueTracking. 3134 APInt Mask = APInt::getAllOnesValue(BitWidth); 3135 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3136 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3137 if (Ones == ~Zeros + 1) 3138 return ConservativeResult; 3139 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3140 } 3141 3142 return ConservativeResult; 3143} 3144 3145/// getSignedRange - Determine the signed range for a particular SCEV. 3146/// 3147ConstantRange 3148ScalarEvolution::getSignedRange(const SCEV *S) { 3149 3150 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3151 return ConstantRange(C->getValue()->getValue()); 3152 3153 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3154 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3155 3156 // If the value has known zeros, the maximum signed value will have those 3157 // known zeros as well. 3158 uint32_t TZ = GetMinTrailingZeros(S); 3159 if (TZ != 0) 3160 ConservativeResult = 3161 ConstantRange(APInt::getSignedMinValue(BitWidth), 3162 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3163 3164 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3165 ConstantRange X = getSignedRange(Add->getOperand(0)); 3166 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3167 X = X.add(getSignedRange(Add->getOperand(i))); 3168 return ConservativeResult.intersectWith(X); 3169 } 3170 3171 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3172 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3173 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3174 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3175 return ConservativeResult.intersectWith(X); 3176 } 3177 3178 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3179 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3180 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3181 X = X.smax(getSignedRange(SMax->getOperand(i))); 3182 return ConservativeResult.intersectWith(X); 3183 } 3184 3185 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3186 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3187 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3188 X = X.umax(getSignedRange(UMax->getOperand(i))); 3189 return ConservativeResult.intersectWith(X); 3190 } 3191 3192 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3193 ConstantRange X = getSignedRange(UDiv->getLHS()); 3194 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3195 return ConservativeResult.intersectWith(X.udiv(Y)); 3196 } 3197 3198 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3199 ConstantRange X = getSignedRange(ZExt->getOperand()); 3200 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3201 } 3202 3203 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3204 ConstantRange X = getSignedRange(SExt->getOperand()); 3205 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3206 } 3207 3208 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3209 ConstantRange X = getSignedRange(Trunc->getOperand()); 3210 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3211 } 3212 3213 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3214 // If there's no signed wrap, and all the operands have the same sign or 3215 // zero, the value won't ever change sign. 3216 if (AddRec->hasNoSignedWrap()) { 3217 bool AllNonNeg = true; 3218 bool AllNonPos = true; 3219 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3220 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3221 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3222 } 3223 if (AllNonNeg) 3224 ConservativeResult = ConservativeResult.intersectWith( 3225 ConstantRange(APInt(BitWidth, 0), 3226 APInt::getSignedMinValue(BitWidth))); 3227 else if (AllNonPos) 3228 ConservativeResult = ConservativeResult.intersectWith( 3229 ConstantRange(APInt::getSignedMinValue(BitWidth), 3230 APInt(BitWidth, 1))); 3231 } 3232 3233 // TODO: non-affine addrec 3234 if (AddRec->isAffine()) { 3235 const Type *Ty = AddRec->getType(); 3236 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3237 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3238 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3239 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3240 3241 const SCEV *Start = AddRec->getStart(); 3242 const SCEV *Step = AddRec->getStepRecurrence(*this); 3243 3244 ConstantRange StartRange = getSignedRange(Start); 3245 ConstantRange StepRange = getSignedRange(Step); 3246 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3247 ConstantRange EndRange = 3248 StartRange.add(MaxBECountRange.multiply(StepRange)); 3249 3250 // Check for overflow. This must be done with ConstantRange arithmetic 3251 // because we could be called from within the ScalarEvolution overflow 3252 // checking code. 3253 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3254 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3255 ConstantRange ExtMaxBECountRange = 3256 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3257 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3258 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3259 ExtEndRange) 3260 return ConservativeResult; 3261 3262 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3263 EndRange.getSignedMin()); 3264 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3265 EndRange.getSignedMax()); 3266 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3267 return ConservativeResult; 3268 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3269 } 3270 } 3271 3272 return ConservativeResult; 3273 } 3274 3275 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3276 // For a SCEVUnknown, ask ValueTracking. 3277 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3278 return ConservativeResult; 3279 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3280 if (NS == 1) 3281 return ConservativeResult; 3282 return ConservativeResult.intersectWith( 3283 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3284 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3285 } 3286 3287 return ConservativeResult; 3288} 3289 3290/// createSCEV - We know that there is no SCEV for the specified value. 3291/// Analyze the expression. 3292/// 3293const SCEV *ScalarEvolution::createSCEV(Value *V) { 3294 if (!isSCEVable(V->getType())) 3295 return getUnknown(V); 3296 3297 unsigned Opcode = Instruction::UserOp1; 3298 if (Instruction *I = dyn_cast<Instruction>(V)) { 3299 Opcode = I->getOpcode(); 3300 3301 // Don't attempt to analyze instructions in blocks that aren't 3302 // reachable. Such instructions don't matter, and they aren't required 3303 // to obey basic rules for definitions dominating uses which this 3304 // analysis depends on. 3305 if (!DT->isReachableFromEntry(I->getParent())) 3306 return getUnknown(V); 3307 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3308 Opcode = CE->getOpcode(); 3309 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3310 return getConstant(CI); 3311 else if (isa<ConstantPointerNull>(V)) 3312 return getConstant(V->getType(), 0); 3313 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3314 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3315 else 3316 return getUnknown(V); 3317 3318 Operator *U = cast<Operator>(V); 3319 switch (Opcode) { 3320 case Instruction::Add: { 3321 // The simple thing to do would be to just call getSCEV on both operands 3322 // and call getAddExpr with the result. However if we're looking at a 3323 // bunch of things all added together, this can be quite inefficient, 3324 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3325 // Instead, gather up all the operands and make a single getAddExpr call. 3326 // LLVM IR canonical form means we need only traverse the left operands. 3327 SmallVector<const SCEV *, 4> AddOps; 3328 AddOps.push_back(getSCEV(U->getOperand(1))); 3329 for (Value *Op = U->getOperand(0); 3330 Op->getValueID() == Instruction::Add + Value::InstructionVal; 3331 Op = U->getOperand(0)) { 3332 U = cast<Operator>(Op); 3333 AddOps.push_back(getSCEV(U->getOperand(1))); 3334 } 3335 AddOps.push_back(getSCEV(U->getOperand(0))); 3336 return getAddExpr(AddOps); 3337 } 3338 case Instruction::Mul: { 3339 // See the Add code above. 3340 SmallVector<const SCEV *, 4> MulOps; 3341 MulOps.push_back(getSCEV(U->getOperand(1))); 3342 for (Value *Op = U->getOperand(0); 3343 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3344 Op = U->getOperand(0)) { 3345 U = cast<Operator>(Op); 3346 MulOps.push_back(getSCEV(U->getOperand(1))); 3347 } 3348 MulOps.push_back(getSCEV(U->getOperand(0))); 3349 return getMulExpr(MulOps); 3350 } 3351 case Instruction::UDiv: 3352 return getUDivExpr(getSCEV(U->getOperand(0)), 3353 getSCEV(U->getOperand(1))); 3354 case Instruction::Sub: 3355 return getMinusSCEV(getSCEV(U->getOperand(0)), 3356 getSCEV(U->getOperand(1))); 3357 case Instruction::And: 3358 // For an expression like x&255 that merely masks off the high bits, 3359 // use zext(trunc(x)) as the SCEV expression. 3360 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3361 if (CI->isNullValue()) 3362 return getSCEV(U->getOperand(1)); 3363 if (CI->isAllOnesValue()) 3364 return getSCEV(U->getOperand(0)); 3365 const APInt &A = CI->getValue(); 3366 3367 // Instcombine's ShrinkDemandedConstant may strip bits out of 3368 // constants, obscuring what would otherwise be a low-bits mask. 3369 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3370 // knew about to reconstruct a low-bits mask value. 3371 unsigned LZ = A.countLeadingZeros(); 3372 unsigned BitWidth = A.getBitWidth(); 3373 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3374 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3375 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3376 3377 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3378 3379 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3380 return 3381 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3382 IntegerType::get(getContext(), BitWidth - LZ)), 3383 U->getType()); 3384 } 3385 break; 3386 3387 case Instruction::Or: 3388 // If the RHS of the Or is a constant, we may have something like: 3389 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3390 // optimizations will transparently handle this case. 3391 // 3392 // In order for this transformation to be safe, the LHS must be of the 3393 // form X*(2^n) and the Or constant must be less than 2^n. 3394 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3395 const SCEV *LHS = getSCEV(U->getOperand(0)); 3396 const APInt &CIVal = CI->getValue(); 3397 if (GetMinTrailingZeros(LHS) >= 3398 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3399 // Build a plain add SCEV. 3400 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3401 // If the LHS of the add was an addrec and it has no-wrap flags, 3402 // transfer the no-wrap flags, since an or won't introduce a wrap. 3403 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3404 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3405 if (OldAR->hasNoUnsignedWrap()) 3406 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3407 if (OldAR->hasNoSignedWrap()) 3408 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3409 } 3410 return S; 3411 } 3412 } 3413 break; 3414 case Instruction::Xor: 3415 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3416 // If the RHS of the xor is a signbit, then this is just an add. 3417 // Instcombine turns add of signbit into xor as a strength reduction step. 3418 if (CI->getValue().isSignBit()) 3419 return getAddExpr(getSCEV(U->getOperand(0)), 3420 getSCEV(U->getOperand(1))); 3421 3422 // If the RHS of xor is -1, then this is a not operation. 3423 if (CI->isAllOnesValue()) 3424 return getNotSCEV(getSCEV(U->getOperand(0))); 3425 3426 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3427 // This is a variant of the check for xor with -1, and it handles 3428 // the case where instcombine has trimmed non-demanded bits out 3429 // of an xor with -1. 3430 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3431 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3432 if (BO->getOpcode() == Instruction::And && 3433 LCI->getValue() == CI->getValue()) 3434 if (const SCEVZeroExtendExpr *Z = 3435 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3436 const Type *UTy = U->getType(); 3437 const SCEV *Z0 = Z->getOperand(); 3438 const Type *Z0Ty = Z0->getType(); 3439 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3440 3441 // If C is a low-bits mask, the zero extend is serving to 3442 // mask off the high bits. Complement the operand and 3443 // re-apply the zext. 3444 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3445 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3446 3447 // If C is a single bit, it may be in the sign-bit position 3448 // before the zero-extend. In this case, represent the xor 3449 // using an add, which is equivalent, and re-apply the zext. 3450 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3451 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3452 Trunc.isSignBit()) 3453 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3454 UTy); 3455 } 3456 } 3457 break; 3458 3459 case Instruction::Shl: 3460 // Turn shift left of a constant amount into a multiply. 3461 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3462 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3463 3464 // If the shift count is not less than the bitwidth, the result of 3465 // the shift is undefined. Don't try to analyze it, because the 3466 // resolution chosen here may differ from the resolution chosen in 3467 // other parts of the compiler. 3468 if (SA->getValue().uge(BitWidth)) 3469 break; 3470 3471 Constant *X = ConstantInt::get(getContext(), 3472 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3473 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3474 } 3475 break; 3476 3477 case Instruction::LShr: 3478 // Turn logical shift right of a constant into a unsigned divide. 3479 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3480 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3481 3482 // If the shift count is not less than the bitwidth, the result of 3483 // the shift is undefined. Don't try to analyze it, because the 3484 // resolution chosen here may differ from the resolution chosen in 3485 // other parts of the compiler. 3486 if (SA->getValue().uge(BitWidth)) 3487 break; 3488 3489 Constant *X = ConstantInt::get(getContext(), 3490 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3491 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3492 } 3493 break; 3494 3495 case Instruction::AShr: 3496 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3497 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3498 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3499 if (L->getOpcode() == Instruction::Shl && 3500 L->getOperand(1) == U->getOperand(1)) { 3501 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3502 3503 // If the shift count is not less than the bitwidth, the result of 3504 // the shift is undefined. Don't try to analyze it, because the 3505 // resolution chosen here may differ from the resolution chosen in 3506 // other parts of the compiler. 3507 if (CI->getValue().uge(BitWidth)) 3508 break; 3509 3510 uint64_t Amt = BitWidth - CI->getZExtValue(); 3511 if (Amt == BitWidth) 3512 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3513 return 3514 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3515 IntegerType::get(getContext(), 3516 Amt)), 3517 U->getType()); 3518 } 3519 break; 3520 3521 case Instruction::Trunc: 3522 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3523 3524 case Instruction::ZExt: 3525 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3526 3527 case Instruction::SExt: 3528 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3529 3530 case Instruction::BitCast: 3531 // BitCasts are no-op casts so we just eliminate the cast. 3532 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3533 return getSCEV(U->getOperand(0)); 3534 break; 3535 3536 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3537 // lead to pointer expressions which cannot safely be expanded to GEPs, 3538 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3539 // simplifying integer expressions. 3540 3541 case Instruction::GetElementPtr: 3542 return createNodeForGEP(cast<GEPOperator>(U)); 3543 3544 case Instruction::PHI: 3545 return createNodeForPHI(cast<PHINode>(U)); 3546 3547 case Instruction::Select: 3548 // This could be a smax or umax that was lowered earlier. 3549 // Try to recover it. 3550 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3551 Value *LHS = ICI->getOperand(0); 3552 Value *RHS = ICI->getOperand(1); 3553 switch (ICI->getPredicate()) { 3554 case ICmpInst::ICMP_SLT: 3555 case ICmpInst::ICMP_SLE: 3556 std::swap(LHS, RHS); 3557 // fall through 3558 case ICmpInst::ICMP_SGT: 3559 case ICmpInst::ICMP_SGE: 3560 // a >s b ? a+x : b+x -> smax(a, b)+x 3561 // a >s b ? b+x : a+x -> smin(a, b)+x 3562 if (LHS->getType() == U->getType()) { 3563 const SCEV *LS = getSCEV(LHS); 3564 const SCEV *RS = getSCEV(RHS); 3565 const SCEV *LA = getSCEV(U->getOperand(1)); 3566 const SCEV *RA = getSCEV(U->getOperand(2)); 3567 const SCEV *LDiff = getMinusSCEV(LA, LS); 3568 const SCEV *RDiff = getMinusSCEV(RA, RS); 3569 if (LDiff == RDiff) 3570 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3571 LDiff = getMinusSCEV(LA, RS); 3572 RDiff = getMinusSCEV(RA, LS); 3573 if (LDiff == RDiff) 3574 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3575 } 3576 break; 3577 case ICmpInst::ICMP_ULT: 3578 case ICmpInst::ICMP_ULE: 3579 std::swap(LHS, RHS); 3580 // fall through 3581 case ICmpInst::ICMP_UGT: 3582 case ICmpInst::ICMP_UGE: 3583 // a >u b ? a+x : b+x -> umax(a, b)+x 3584 // a >u b ? b+x : a+x -> umin(a, b)+x 3585 if (LHS->getType() == U->getType()) { 3586 const SCEV *LS = getSCEV(LHS); 3587 const SCEV *RS = getSCEV(RHS); 3588 const SCEV *LA = getSCEV(U->getOperand(1)); 3589 const SCEV *RA = getSCEV(U->getOperand(2)); 3590 const SCEV *LDiff = getMinusSCEV(LA, LS); 3591 const SCEV *RDiff = getMinusSCEV(RA, RS); 3592 if (LDiff == RDiff) 3593 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3594 LDiff = getMinusSCEV(LA, RS); 3595 RDiff = getMinusSCEV(RA, LS); 3596 if (LDiff == RDiff) 3597 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3598 } 3599 break; 3600 case ICmpInst::ICMP_NE: 3601 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3602 if (LHS->getType() == U->getType() && 3603 isa<ConstantInt>(RHS) && 3604 cast<ConstantInt>(RHS)->isZero()) { 3605 const SCEV *One = getConstant(LHS->getType(), 1); 3606 const SCEV *LS = getSCEV(LHS); 3607 const SCEV *LA = getSCEV(U->getOperand(1)); 3608 const SCEV *RA = getSCEV(U->getOperand(2)); 3609 const SCEV *LDiff = getMinusSCEV(LA, LS); 3610 const SCEV *RDiff = getMinusSCEV(RA, One); 3611 if (LDiff == RDiff) 3612 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3613 } 3614 break; 3615 case ICmpInst::ICMP_EQ: 3616 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3617 if (LHS->getType() == U->getType() && 3618 isa<ConstantInt>(RHS) && 3619 cast<ConstantInt>(RHS)->isZero()) { 3620 const SCEV *One = getConstant(LHS->getType(), 1); 3621 const SCEV *LS = getSCEV(LHS); 3622 const SCEV *LA = getSCEV(U->getOperand(1)); 3623 const SCEV *RA = getSCEV(U->getOperand(2)); 3624 const SCEV *LDiff = getMinusSCEV(LA, One); 3625 const SCEV *RDiff = getMinusSCEV(RA, LS); 3626 if (LDiff == RDiff) 3627 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3628 } 3629 break; 3630 default: 3631 break; 3632 } 3633 } 3634 3635 default: // We cannot analyze this expression. 3636 break; 3637 } 3638 3639 return getUnknown(V); 3640} 3641 3642 3643 3644//===----------------------------------------------------------------------===// 3645// Iteration Count Computation Code 3646// 3647 3648/// getBackedgeTakenCount - If the specified loop has a predictable 3649/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3650/// object. The backedge-taken count is the number of times the loop header 3651/// will be branched to from within the loop. This is one less than the 3652/// trip count of the loop, since it doesn't count the first iteration, 3653/// when the header is branched to from outside the loop. 3654/// 3655/// Note that it is not valid to call this method on a loop without a 3656/// loop-invariant backedge-taken count (see 3657/// hasLoopInvariantBackedgeTakenCount). 3658/// 3659const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3660 return getBackedgeTakenInfo(L).Exact; 3661} 3662 3663/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3664/// return the least SCEV value that is known never to be less than the 3665/// actual backedge taken count. 3666const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3667 return getBackedgeTakenInfo(L).Max; 3668} 3669 3670/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3671/// onto the given Worklist. 3672static void 3673PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3674 BasicBlock *Header = L->getHeader(); 3675 3676 // Push all Loop-header PHIs onto the Worklist stack. 3677 for (BasicBlock::iterator I = Header->begin(); 3678 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3679 Worklist.push_back(PN); 3680} 3681 3682const ScalarEvolution::BackedgeTakenInfo & 3683ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3684 // Initially insert a CouldNotCompute for this loop. If the insertion 3685 // succeeds, proceed to actually compute a backedge-taken count and 3686 // update the value. The temporary CouldNotCompute value tells SCEV 3687 // code elsewhere that it shouldn't attempt to request a new 3688 // backedge-taken count, which could result in infinite recursion. 3689 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3690 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3691 if (Pair.second) { 3692 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3693 if (BECount.Exact != getCouldNotCompute()) { 3694 assert(BECount.Exact->isLoopInvariant(L) && 3695 BECount.Max->isLoopInvariant(L) && 3696 "Computed backedge-taken count isn't loop invariant for loop!"); 3697 ++NumTripCountsComputed; 3698 3699 // Update the value in the map. 3700 Pair.first->second = BECount; 3701 } else { 3702 if (BECount.Max != getCouldNotCompute()) 3703 // Update the value in the map. 3704 Pair.first->second = BECount; 3705 if (isa<PHINode>(L->getHeader()->begin())) 3706 // Only count loops that have phi nodes as not being computable. 3707 ++NumTripCountsNotComputed; 3708 } 3709 3710 // Now that we know more about the trip count for this loop, forget any 3711 // existing SCEV values for PHI nodes in this loop since they are only 3712 // conservative estimates made without the benefit of trip count 3713 // information. This is similar to the code in forgetLoop, except that 3714 // it handles SCEVUnknown PHI nodes specially. 3715 if (BECount.hasAnyInfo()) { 3716 SmallVector<Instruction *, 16> Worklist; 3717 PushLoopPHIs(L, Worklist); 3718 3719 SmallPtrSet<Instruction *, 8> Visited; 3720 while (!Worklist.empty()) { 3721 Instruction *I = Worklist.pop_back_val(); 3722 if (!Visited.insert(I)) continue; 3723 3724 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3725 Scalars.find(static_cast<Value *>(I)); 3726 if (It != Scalars.end()) { 3727 // SCEVUnknown for a PHI either means that it has an unrecognized 3728 // structure, or it's a PHI that's in the progress of being computed 3729 // by createNodeForPHI. In the former case, additional loop trip 3730 // count information isn't going to change anything. In the later 3731 // case, createNodeForPHI will perform the necessary updates on its 3732 // own when it gets to that point. 3733 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3734 ValuesAtScopes.erase(It->second); 3735 Scalars.erase(It); 3736 } 3737 if (PHINode *PN = dyn_cast<PHINode>(I)) 3738 ConstantEvolutionLoopExitValue.erase(PN); 3739 } 3740 3741 PushDefUseChildren(I, Worklist); 3742 } 3743 } 3744 } 3745 return Pair.first->second; 3746} 3747 3748/// forgetLoop - This method should be called by the client when it has 3749/// changed a loop in a way that may effect ScalarEvolution's ability to 3750/// compute a trip count, or if the loop is deleted. 3751void ScalarEvolution::forgetLoop(const Loop *L) { 3752 // Drop any stored trip count value. 3753 BackedgeTakenCounts.erase(L); 3754 3755 // Drop information about expressions based on loop-header PHIs. 3756 SmallVector<Instruction *, 16> Worklist; 3757 PushLoopPHIs(L, Worklist); 3758 3759 SmallPtrSet<Instruction *, 8> Visited; 3760 while (!Worklist.empty()) { 3761 Instruction *I = Worklist.pop_back_val(); 3762 if (!Visited.insert(I)) continue; 3763 3764 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3765 Scalars.find(static_cast<Value *>(I)); 3766 if (It != Scalars.end()) { 3767 ValuesAtScopes.erase(It->second); 3768 Scalars.erase(It); 3769 if (PHINode *PN = dyn_cast<PHINode>(I)) 3770 ConstantEvolutionLoopExitValue.erase(PN); 3771 } 3772 3773 PushDefUseChildren(I, Worklist); 3774 } 3775} 3776 3777/// forgetValue - This method should be called by the client when it has 3778/// changed a value in a way that may effect its value, or which may 3779/// disconnect it from a def-use chain linking it to a loop. 3780void ScalarEvolution::forgetValue(Value *V) { 3781 Instruction *I = dyn_cast<Instruction>(V); 3782 if (!I) return; 3783 3784 // Drop information about expressions based on loop-header PHIs. 3785 SmallVector<Instruction *, 16> Worklist; 3786 Worklist.push_back(I); 3787 3788 SmallPtrSet<Instruction *, 8> Visited; 3789 while (!Worklist.empty()) { 3790 I = Worklist.pop_back_val(); 3791 if (!Visited.insert(I)) continue; 3792 3793 std::map<SCEVCallbackVH, const SCEV *>::iterator It = 3794 Scalars.find(static_cast<Value *>(I)); 3795 if (It != Scalars.end()) { 3796 ValuesAtScopes.erase(It->second); 3797 Scalars.erase(It); 3798 if (PHINode *PN = dyn_cast<PHINode>(I)) 3799 ConstantEvolutionLoopExitValue.erase(PN); 3800 } 3801 3802 PushDefUseChildren(I, Worklist); 3803 } 3804} 3805 3806/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3807/// of the specified loop will execute. 3808ScalarEvolution::BackedgeTakenInfo 3809ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3810 SmallVector<BasicBlock *, 8> ExitingBlocks; 3811 L->getExitingBlocks(ExitingBlocks); 3812 3813 // Examine all exits and pick the most conservative values. 3814 const SCEV *BECount = getCouldNotCompute(); 3815 const SCEV *MaxBECount = getCouldNotCompute(); 3816 bool CouldNotComputeBECount = false; 3817 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3818 BackedgeTakenInfo NewBTI = 3819 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3820 3821 if (NewBTI.Exact == getCouldNotCompute()) { 3822 // We couldn't compute an exact value for this exit, so 3823 // we won't be able to compute an exact value for the loop. 3824 CouldNotComputeBECount = true; 3825 BECount = getCouldNotCompute(); 3826 } else if (!CouldNotComputeBECount) { 3827 if (BECount == getCouldNotCompute()) 3828 BECount = NewBTI.Exact; 3829 else 3830 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3831 } 3832 if (MaxBECount == getCouldNotCompute()) 3833 MaxBECount = NewBTI.Max; 3834 else if (NewBTI.Max != getCouldNotCompute()) 3835 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3836 } 3837 3838 return BackedgeTakenInfo(BECount, MaxBECount); 3839} 3840 3841/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3842/// of the specified loop will execute if it exits via the specified block. 3843ScalarEvolution::BackedgeTakenInfo 3844ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3845 BasicBlock *ExitingBlock) { 3846 3847 // Okay, we've chosen an exiting block. See what condition causes us to 3848 // exit at this block. 3849 // 3850 // FIXME: we should be able to handle switch instructions (with a single exit) 3851 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3852 if (ExitBr == 0) return getCouldNotCompute(); 3853 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3854 3855 // At this point, we know we have a conditional branch that determines whether 3856 // the loop is exited. However, we don't know if the branch is executed each 3857 // time through the loop. If not, then the execution count of the branch will 3858 // not be equal to the trip count of the loop. 3859 // 3860 // Currently we check for this by checking to see if the Exit branch goes to 3861 // the loop header. If so, we know it will always execute the same number of 3862 // times as the loop. We also handle the case where the exit block *is* the 3863 // loop header. This is common for un-rotated loops. 3864 // 3865 // If both of those tests fail, walk up the unique predecessor chain to the 3866 // header, stopping if there is an edge that doesn't exit the loop. If the 3867 // header is reached, the execution count of the branch will be equal to the 3868 // trip count of the loop. 3869 // 3870 // More extensive analysis could be done to handle more cases here. 3871 // 3872 if (ExitBr->getSuccessor(0) != L->getHeader() && 3873 ExitBr->getSuccessor(1) != L->getHeader() && 3874 ExitBr->getParent() != L->getHeader()) { 3875 // The simple checks failed, try climbing the unique predecessor chain 3876 // up to the header. 3877 bool Ok = false; 3878 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3879 BasicBlock *Pred = BB->getUniquePredecessor(); 3880 if (!Pred) 3881 return getCouldNotCompute(); 3882 TerminatorInst *PredTerm = Pred->getTerminator(); 3883 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3884 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3885 if (PredSucc == BB) 3886 continue; 3887 // If the predecessor has a successor that isn't BB and isn't 3888 // outside the loop, assume the worst. 3889 if (L->contains(PredSucc)) 3890 return getCouldNotCompute(); 3891 } 3892 if (Pred == L->getHeader()) { 3893 Ok = true; 3894 break; 3895 } 3896 BB = Pred; 3897 } 3898 if (!Ok) 3899 return getCouldNotCompute(); 3900 } 3901 3902 // Proceed to the next level to examine the exit condition expression. 3903 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3904 ExitBr->getSuccessor(0), 3905 ExitBr->getSuccessor(1)); 3906} 3907 3908/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3909/// backedge of the specified loop will execute if its exit condition 3910/// were a conditional branch of ExitCond, TBB, and FBB. 3911ScalarEvolution::BackedgeTakenInfo 3912ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3913 Value *ExitCond, 3914 BasicBlock *TBB, 3915 BasicBlock *FBB) { 3916 // Check if the controlling expression for this loop is an And or Or. 3917 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3918 if (BO->getOpcode() == Instruction::And) { 3919 // Recurse on the operands of the and. 3920 BackedgeTakenInfo BTI0 = 3921 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3922 BackedgeTakenInfo BTI1 = 3923 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3924 const SCEV *BECount = getCouldNotCompute(); 3925 const SCEV *MaxBECount = getCouldNotCompute(); 3926 if (L->contains(TBB)) { 3927 // Both conditions must be true for the loop to continue executing. 3928 // Choose the less conservative count. 3929 if (BTI0.Exact == getCouldNotCompute() || 3930 BTI1.Exact == getCouldNotCompute()) 3931 BECount = getCouldNotCompute(); 3932 else 3933 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3934 if (BTI0.Max == getCouldNotCompute()) 3935 MaxBECount = BTI1.Max; 3936 else if (BTI1.Max == getCouldNotCompute()) 3937 MaxBECount = BTI0.Max; 3938 else 3939 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3940 } else { 3941 // Both conditions must be true at the same time for the loop to exit. 3942 // For now, be conservative. 3943 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3944 if (BTI0.Max == BTI1.Max) 3945 MaxBECount = BTI0.Max; 3946 if (BTI0.Exact == BTI1.Exact) 3947 BECount = BTI0.Exact; 3948 } 3949 3950 return BackedgeTakenInfo(BECount, MaxBECount); 3951 } 3952 if (BO->getOpcode() == Instruction::Or) { 3953 // Recurse on the operands of the or. 3954 BackedgeTakenInfo BTI0 = 3955 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3956 BackedgeTakenInfo BTI1 = 3957 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3958 const SCEV *BECount = getCouldNotCompute(); 3959 const SCEV *MaxBECount = getCouldNotCompute(); 3960 if (L->contains(FBB)) { 3961 // Both conditions must be false for the loop to continue executing. 3962 // Choose the less conservative count. 3963 if (BTI0.Exact == getCouldNotCompute() || 3964 BTI1.Exact == getCouldNotCompute()) 3965 BECount = getCouldNotCompute(); 3966 else 3967 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3968 if (BTI0.Max == getCouldNotCompute()) 3969 MaxBECount = BTI1.Max; 3970 else if (BTI1.Max == getCouldNotCompute()) 3971 MaxBECount = BTI0.Max; 3972 else 3973 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3974 } else { 3975 // Both conditions must be false at the same time for the loop to exit. 3976 // For now, be conservative. 3977 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3978 if (BTI0.Max == BTI1.Max) 3979 MaxBECount = BTI0.Max; 3980 if (BTI0.Exact == BTI1.Exact) 3981 BECount = BTI0.Exact; 3982 } 3983 3984 return BackedgeTakenInfo(BECount, MaxBECount); 3985 } 3986 } 3987 3988 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3989 // Proceed to the next level to examine the icmp. 3990 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3991 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3992 3993 // Check for a constant condition. These are normally stripped out by 3994 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3995 // preserve the CFG and is temporarily leaving constant conditions 3996 // in place. 3997 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3998 if (L->contains(FBB) == !CI->getZExtValue()) 3999 // The backedge is always taken. 4000 return getCouldNotCompute(); 4001 else 4002 // The backedge is never taken. 4003 return getConstant(CI->getType(), 0); 4004 } 4005 4006 // If it's not an integer or pointer comparison then compute it the hard way. 4007 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4008} 4009 4010/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4011/// backedge of the specified loop will execute if its exit condition 4012/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4013ScalarEvolution::BackedgeTakenInfo 4014ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4015 ICmpInst *ExitCond, 4016 BasicBlock *TBB, 4017 BasicBlock *FBB) { 4018 4019 // If the condition was exit on true, convert the condition to exit on false 4020 ICmpInst::Predicate Cond; 4021 if (!L->contains(FBB)) 4022 Cond = ExitCond->getPredicate(); 4023 else 4024 Cond = ExitCond->getInversePredicate(); 4025 4026 // Handle common loops like: for (X = "string"; *X; ++X) 4027 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4028 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4029 BackedgeTakenInfo ItCnt = 4030 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4031 if (ItCnt.hasAnyInfo()) 4032 return ItCnt; 4033 } 4034 4035 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4036 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4037 4038 // Try to evaluate any dependencies out of the loop. 4039 LHS = getSCEVAtScope(LHS, L); 4040 RHS = getSCEVAtScope(RHS, L); 4041 4042 // At this point, we would like to compute how many iterations of the 4043 // loop the predicate will return true for these inputs. 4044 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 4045 // If there is a loop-invariant, force it into the RHS. 4046 std::swap(LHS, RHS); 4047 Cond = ICmpInst::getSwappedPredicate(Cond); 4048 } 4049 4050 // Simplify the operands before analyzing them. 4051 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4052 4053 // If we have a comparison of a chrec against a constant, try to use value 4054 // ranges to answer this query. 4055 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4056 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4057 if (AddRec->getLoop() == L) { 4058 // Form the constant range. 4059 ConstantRange CompRange( 4060 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4061 4062 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4063 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4064 } 4065 4066 switch (Cond) { 4067 case ICmpInst::ICMP_NE: { // while (X != Y) 4068 // Convert to: while (X-Y != 0) 4069 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4070 if (BTI.hasAnyInfo()) return BTI; 4071 break; 4072 } 4073 case ICmpInst::ICMP_EQ: { // while (X == Y) 4074 // Convert to: while (X-Y == 0) 4075 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4076 if (BTI.hasAnyInfo()) return BTI; 4077 break; 4078 } 4079 case ICmpInst::ICMP_SLT: { 4080 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4081 if (BTI.hasAnyInfo()) return BTI; 4082 break; 4083 } 4084 case ICmpInst::ICMP_SGT: { 4085 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4086 getNotSCEV(RHS), L, true); 4087 if (BTI.hasAnyInfo()) return BTI; 4088 break; 4089 } 4090 case ICmpInst::ICMP_ULT: { 4091 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4092 if (BTI.hasAnyInfo()) return BTI; 4093 break; 4094 } 4095 case ICmpInst::ICMP_UGT: { 4096 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4097 getNotSCEV(RHS), L, false); 4098 if (BTI.hasAnyInfo()) return BTI; 4099 break; 4100 } 4101 default: 4102#if 0 4103 dbgs() << "ComputeBackedgeTakenCount "; 4104 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4105 dbgs() << "[unsigned] "; 4106 dbgs() << *LHS << " " 4107 << Instruction::getOpcodeName(Instruction::ICmp) 4108 << " " << *RHS << "\n"; 4109#endif 4110 break; 4111 } 4112 return 4113 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4114} 4115 4116static ConstantInt * 4117EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4118 ScalarEvolution &SE) { 4119 const SCEV *InVal = SE.getConstant(C); 4120 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4121 assert(isa<SCEVConstant>(Val) && 4122 "Evaluation of SCEV at constant didn't fold correctly?"); 4123 return cast<SCEVConstant>(Val)->getValue(); 4124} 4125 4126/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4127/// and a GEP expression (missing the pointer index) indexing into it, return 4128/// the addressed element of the initializer or null if the index expression is 4129/// invalid. 4130static Constant * 4131GetAddressedElementFromGlobal(GlobalVariable *GV, 4132 const std::vector<ConstantInt*> &Indices) { 4133 Constant *Init = GV->getInitializer(); 4134 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4135 uint64_t Idx = Indices[i]->getZExtValue(); 4136 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4137 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4138 Init = cast<Constant>(CS->getOperand(Idx)); 4139 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4140 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4141 Init = cast<Constant>(CA->getOperand(Idx)); 4142 } else if (isa<ConstantAggregateZero>(Init)) { 4143 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4144 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4145 Init = Constant::getNullValue(STy->getElementType(Idx)); 4146 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4147 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4148 Init = Constant::getNullValue(ATy->getElementType()); 4149 } else { 4150 llvm_unreachable("Unknown constant aggregate type!"); 4151 } 4152 return 0; 4153 } else { 4154 return 0; // Unknown initializer type 4155 } 4156 } 4157 return Init; 4158} 4159 4160/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4161/// 'icmp op load X, cst', try to see if we can compute the backedge 4162/// execution count. 4163ScalarEvolution::BackedgeTakenInfo 4164ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4165 LoadInst *LI, 4166 Constant *RHS, 4167 const Loop *L, 4168 ICmpInst::Predicate predicate) { 4169 if (LI->isVolatile()) return getCouldNotCompute(); 4170 4171 // Check to see if the loaded pointer is a getelementptr of a global. 4172 // TODO: Use SCEV instead of manually grubbing with GEPs. 4173 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4174 if (!GEP) return getCouldNotCompute(); 4175 4176 // Make sure that it is really a constant global we are gepping, with an 4177 // initializer, and make sure the first IDX is really 0. 4178 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4179 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4180 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4181 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4182 return getCouldNotCompute(); 4183 4184 // Okay, we allow one non-constant index into the GEP instruction. 4185 Value *VarIdx = 0; 4186 std::vector<ConstantInt*> Indexes; 4187 unsigned VarIdxNum = 0; 4188 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4189 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4190 Indexes.push_back(CI); 4191 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4192 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4193 VarIdx = GEP->getOperand(i); 4194 VarIdxNum = i-2; 4195 Indexes.push_back(0); 4196 } 4197 4198 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4199 // Check to see if X is a loop variant variable value now. 4200 const SCEV *Idx = getSCEV(VarIdx); 4201 Idx = getSCEVAtScope(Idx, L); 4202 4203 // We can only recognize very limited forms of loop index expressions, in 4204 // particular, only affine AddRec's like {C1,+,C2}. 4205 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4206 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4207 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4208 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4209 return getCouldNotCompute(); 4210 4211 unsigned MaxSteps = MaxBruteForceIterations; 4212 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4213 ConstantInt *ItCst = ConstantInt::get( 4214 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4215 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4216 4217 // Form the GEP offset. 4218 Indexes[VarIdxNum] = Val; 4219 4220 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4221 if (Result == 0) break; // Cannot compute! 4222 4223 // Evaluate the condition for this iteration. 4224 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4225 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4226 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4227#if 0 4228 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4229 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4230 << "***\n"; 4231#endif 4232 ++NumArrayLenItCounts; 4233 return getConstant(ItCst); // Found terminating iteration! 4234 } 4235 } 4236 return getCouldNotCompute(); 4237} 4238 4239 4240/// CanConstantFold - Return true if we can constant fold an instruction of the 4241/// specified type, assuming that all operands were constants. 4242static bool CanConstantFold(const Instruction *I) { 4243 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4244 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4245 return true; 4246 4247 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4248 if (const Function *F = CI->getCalledFunction()) 4249 return canConstantFoldCallTo(F); 4250 return false; 4251} 4252 4253/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4254/// in the loop that V is derived from. We allow arbitrary operations along the 4255/// way, but the operands of an operation must either be constants or a value 4256/// derived from a constant PHI. If this expression does not fit with these 4257/// constraints, return null. 4258static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4259 // If this is not an instruction, or if this is an instruction outside of the 4260 // loop, it can't be derived from a loop PHI. 4261 Instruction *I = dyn_cast<Instruction>(V); 4262 if (I == 0 || !L->contains(I)) return 0; 4263 4264 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4265 if (L->getHeader() == I->getParent()) 4266 return PN; 4267 else 4268 // We don't currently keep track of the control flow needed to evaluate 4269 // PHIs, so we cannot handle PHIs inside of loops. 4270 return 0; 4271 } 4272 4273 // If we won't be able to constant fold this expression even if the operands 4274 // are constants, return early. 4275 if (!CanConstantFold(I)) return 0; 4276 4277 // Otherwise, we can evaluate this instruction if all of its operands are 4278 // constant or derived from a PHI node themselves. 4279 PHINode *PHI = 0; 4280 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4281 if (!isa<Constant>(I->getOperand(Op))) { 4282 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4283 if (P == 0) return 0; // Not evolving from PHI 4284 if (PHI == 0) 4285 PHI = P; 4286 else if (PHI != P) 4287 return 0; // Evolving from multiple different PHIs. 4288 } 4289 4290 // This is a expression evolving from a constant PHI! 4291 return PHI; 4292} 4293 4294/// EvaluateExpression - Given an expression that passes the 4295/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4296/// in the loop has the value PHIVal. If we can't fold this expression for some 4297/// reason, return null. 4298static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4299 const TargetData *TD) { 4300 if (isa<PHINode>(V)) return PHIVal; 4301 if (Constant *C = dyn_cast<Constant>(V)) return C; 4302 Instruction *I = cast<Instruction>(V); 4303 4304 std::vector<Constant*> Operands(I->getNumOperands()); 4305 4306 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4307 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4308 if (Operands[i] == 0) return 0; 4309 } 4310 4311 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4312 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4313 Operands[1], TD); 4314 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4315 &Operands[0], Operands.size(), TD); 4316} 4317 4318/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4319/// in the header of its containing loop, we know the loop executes a 4320/// constant number of times, and the PHI node is just a recurrence 4321/// involving constants, fold it. 4322Constant * 4323ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4324 const APInt &BEs, 4325 const Loop *L) { 4326 std::map<PHINode*, Constant*>::const_iterator I = 4327 ConstantEvolutionLoopExitValue.find(PN); 4328 if (I != ConstantEvolutionLoopExitValue.end()) 4329 return I->second; 4330 4331 if (BEs.ugt(MaxBruteForceIterations)) 4332 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4333 4334 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4335 4336 // Since the loop is canonicalized, the PHI node must have two entries. One 4337 // entry must be a constant (coming in from outside of the loop), and the 4338 // second must be derived from the same PHI. 4339 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4340 Constant *StartCST = 4341 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4342 if (StartCST == 0) 4343 return RetVal = 0; // Must be a constant. 4344 4345 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4346 if (getConstantEvolvingPHI(BEValue, L) != PN && 4347 !isa<Constant>(BEValue)) 4348 return RetVal = 0; // Not derived from same PHI. 4349 4350 // Execute the loop symbolically to determine the exit value. 4351 if (BEs.getActiveBits() >= 32) 4352 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4353 4354 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4355 unsigned IterationNum = 0; 4356 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4357 if (IterationNum == NumIterations) 4358 return RetVal = PHIVal; // Got exit value! 4359 4360 // Compute the value of the PHI node for the next iteration. 4361 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4362 if (NextPHI == PHIVal) 4363 return RetVal = NextPHI; // Stopped evolving! 4364 if (NextPHI == 0) 4365 return 0; // Couldn't evaluate! 4366 PHIVal = NextPHI; 4367 } 4368} 4369 4370/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4371/// constant number of times (the condition evolves only from constants), 4372/// try to evaluate a few iterations of the loop until we get the exit 4373/// condition gets a value of ExitWhen (true or false). If we cannot 4374/// evaluate the trip count of the loop, return getCouldNotCompute(). 4375const SCEV * 4376ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4377 Value *Cond, 4378 bool ExitWhen) { 4379 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4380 if (PN == 0) return getCouldNotCompute(); 4381 4382 // If the loop is canonicalized, the PHI will have exactly two entries. 4383 // That's the only form we support here. 4384 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4385 4386 // One entry must be a constant (coming in from outside of the loop), and the 4387 // second must be derived from the same PHI. 4388 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4389 Constant *StartCST = 4390 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4391 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4392 4393 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4394 if (getConstantEvolvingPHI(BEValue, L) != PN && 4395 !isa<Constant>(BEValue)) 4396 return getCouldNotCompute(); // Not derived from same PHI. 4397 4398 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4399 // the loop symbolically to determine when the condition gets a value of 4400 // "ExitWhen". 4401 unsigned IterationNum = 0; 4402 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4403 for (Constant *PHIVal = StartCST; 4404 IterationNum != MaxIterations; ++IterationNum) { 4405 ConstantInt *CondVal = 4406 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4407 4408 // Couldn't symbolically evaluate. 4409 if (!CondVal) return getCouldNotCompute(); 4410 4411 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4412 ++NumBruteForceTripCountsComputed; 4413 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4414 } 4415 4416 // Compute the value of the PHI node for the next iteration. 4417 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4418 if (NextPHI == 0 || NextPHI == PHIVal) 4419 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4420 PHIVal = NextPHI; 4421 } 4422 4423 // Too many iterations were needed to evaluate. 4424 return getCouldNotCompute(); 4425} 4426 4427/// getSCEVAtScope - Return a SCEV expression for the specified value 4428/// at the specified scope in the program. The L value specifies a loop 4429/// nest to evaluate the expression at, where null is the top-level or a 4430/// specified loop is immediately inside of the loop. 4431/// 4432/// This method can be used to compute the exit value for a variable defined 4433/// in a loop by querying what the value will hold in the parent loop. 4434/// 4435/// In the case that a relevant loop exit value cannot be computed, the 4436/// original value V is returned. 4437const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4438 // Check to see if we've folded this expression at this loop before. 4439 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4440 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4441 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4442 if (!Pair.second) 4443 return Pair.first->second ? Pair.first->second : V; 4444 4445 // Otherwise compute it. 4446 const SCEV *C = computeSCEVAtScope(V, L); 4447 ValuesAtScopes[V][L] = C; 4448 return C; 4449} 4450 4451const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4452 if (isa<SCEVConstant>(V)) return V; 4453 4454 // If this instruction is evolved from a constant-evolving PHI, compute the 4455 // exit value from the loop without using SCEVs. 4456 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4457 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4458 const Loop *LI = (*this->LI)[I->getParent()]; 4459 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4460 if (PHINode *PN = dyn_cast<PHINode>(I)) 4461 if (PN->getParent() == LI->getHeader()) { 4462 // Okay, there is no closed form solution for the PHI node. Check 4463 // to see if the loop that contains it has a known backedge-taken 4464 // count. If so, we may be able to force computation of the exit 4465 // value. 4466 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4467 if (const SCEVConstant *BTCC = 4468 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4469 // Okay, we know how many times the containing loop executes. If 4470 // this is a constant evolving PHI node, get the final value at 4471 // the specified iteration number. 4472 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4473 BTCC->getValue()->getValue(), 4474 LI); 4475 if (RV) return getSCEV(RV); 4476 } 4477 } 4478 4479 // Okay, this is an expression that we cannot symbolically evaluate 4480 // into a SCEV. Check to see if it's possible to symbolically evaluate 4481 // the arguments into constants, and if so, try to constant propagate the 4482 // result. This is particularly useful for computing loop exit values. 4483 if (CanConstantFold(I)) { 4484 SmallVector<Constant *, 4> Operands; 4485 bool MadeImprovement = false; 4486 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4487 Value *Op = I->getOperand(i); 4488 if (Constant *C = dyn_cast<Constant>(Op)) { 4489 Operands.push_back(C); 4490 continue; 4491 } 4492 4493 // If any of the operands is non-constant and if they are 4494 // non-integer and non-pointer, don't even try to analyze them 4495 // with scev techniques. 4496 if (!isSCEVable(Op->getType())) 4497 return V; 4498 4499 const SCEV *OrigV = getSCEV(Op); 4500 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4501 MadeImprovement |= OrigV != OpV; 4502 4503 Constant *C = 0; 4504 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4505 C = SC->getValue(); 4506 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4507 C = dyn_cast<Constant>(SU->getValue()); 4508 if (!C) return V; 4509 if (C->getType() != Op->getType()) 4510 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4511 Op->getType(), 4512 false), 4513 C, Op->getType()); 4514 Operands.push_back(C); 4515 } 4516 4517 // Check to see if getSCEVAtScope actually made an improvement. 4518 if (MadeImprovement) { 4519 Constant *C = 0; 4520 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4521 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4522 Operands[0], Operands[1], TD); 4523 else 4524 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4525 &Operands[0], Operands.size(), TD); 4526 if (!C) return V; 4527 return getSCEV(C); 4528 } 4529 } 4530 } 4531 4532 // This is some other type of SCEVUnknown, just return it. 4533 return V; 4534 } 4535 4536 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4537 // Avoid performing the look-up in the common case where the specified 4538 // expression has no loop-variant portions. 4539 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4540 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4541 if (OpAtScope != Comm->getOperand(i)) { 4542 // Okay, at least one of these operands is loop variant but might be 4543 // foldable. Build a new instance of the folded commutative expression. 4544 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4545 Comm->op_begin()+i); 4546 NewOps.push_back(OpAtScope); 4547 4548 for (++i; i != e; ++i) { 4549 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4550 NewOps.push_back(OpAtScope); 4551 } 4552 if (isa<SCEVAddExpr>(Comm)) 4553 return getAddExpr(NewOps); 4554 if (isa<SCEVMulExpr>(Comm)) 4555 return getMulExpr(NewOps); 4556 if (isa<SCEVSMaxExpr>(Comm)) 4557 return getSMaxExpr(NewOps); 4558 if (isa<SCEVUMaxExpr>(Comm)) 4559 return getUMaxExpr(NewOps); 4560 llvm_unreachable("Unknown commutative SCEV type!"); 4561 } 4562 } 4563 // If we got here, all operands are loop invariant. 4564 return Comm; 4565 } 4566 4567 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4568 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4569 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4570 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4571 return Div; // must be loop invariant 4572 return getUDivExpr(LHS, RHS); 4573 } 4574 4575 // If this is a loop recurrence for a loop that does not contain L, then we 4576 // are dealing with the final value computed by the loop. 4577 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4578 // First, attempt to evaluate each operand. 4579 // Avoid performing the look-up in the common case where the specified 4580 // expression has no loop-variant portions. 4581 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4582 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4583 if (OpAtScope == AddRec->getOperand(i)) 4584 continue; 4585 4586 // Okay, at least one of these operands is loop variant but might be 4587 // foldable. Build a new instance of the folded commutative expression. 4588 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4589 AddRec->op_begin()+i); 4590 NewOps.push_back(OpAtScope); 4591 for (++i; i != e; ++i) 4592 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4593 4594 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4595 break; 4596 } 4597 4598 // If the scope is outside the addrec's loop, evaluate it by using the 4599 // loop exit value of the addrec. 4600 if (!AddRec->getLoop()->contains(L)) { 4601 // To evaluate this recurrence, we need to know how many times the AddRec 4602 // loop iterates. Compute this now. 4603 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4604 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4605 4606 // Then, evaluate the AddRec. 4607 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4608 } 4609 4610 return AddRec; 4611 } 4612 4613 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4614 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4615 if (Op == Cast->getOperand()) 4616 return Cast; // must be loop invariant 4617 return getZeroExtendExpr(Op, Cast->getType()); 4618 } 4619 4620 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4621 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4622 if (Op == Cast->getOperand()) 4623 return Cast; // must be loop invariant 4624 return getSignExtendExpr(Op, Cast->getType()); 4625 } 4626 4627 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4628 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4629 if (Op == Cast->getOperand()) 4630 return Cast; // must be loop invariant 4631 return getTruncateExpr(Op, Cast->getType()); 4632 } 4633 4634 llvm_unreachable("Unknown SCEV type!"); 4635 return 0; 4636} 4637 4638/// getSCEVAtScope - This is a convenience function which does 4639/// getSCEVAtScope(getSCEV(V), L). 4640const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4641 return getSCEVAtScope(getSCEV(V), L); 4642} 4643 4644/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4645/// following equation: 4646/// 4647/// A * X = B (mod N) 4648/// 4649/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4650/// A and B isn't important. 4651/// 4652/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4653static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4654 ScalarEvolution &SE) { 4655 uint32_t BW = A.getBitWidth(); 4656 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4657 assert(A != 0 && "A must be non-zero."); 4658 4659 // 1. D = gcd(A, N) 4660 // 4661 // The gcd of A and N may have only one prime factor: 2. The number of 4662 // trailing zeros in A is its multiplicity 4663 uint32_t Mult2 = A.countTrailingZeros(); 4664 // D = 2^Mult2 4665 4666 // 2. Check if B is divisible by D. 4667 // 4668 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4669 // is not less than multiplicity of this prime factor for D. 4670 if (B.countTrailingZeros() < Mult2) 4671 return SE.getCouldNotCompute(); 4672 4673 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4674 // modulo (N / D). 4675 // 4676 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4677 // bit width during computations. 4678 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4679 APInt Mod(BW + 1, 0); 4680 Mod.set(BW - Mult2); // Mod = N / D 4681 APInt I = AD.multiplicativeInverse(Mod); 4682 4683 // 4. Compute the minimum unsigned root of the equation: 4684 // I * (B / D) mod (N / D) 4685 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4686 4687 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4688 // bits. 4689 return SE.getConstant(Result.trunc(BW)); 4690} 4691 4692/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4693/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4694/// might be the same) or two SCEVCouldNotCompute objects. 4695/// 4696static std::pair<const SCEV *,const SCEV *> 4697SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4698 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4699 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4700 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4701 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4702 4703 // We currently can only solve this if the coefficients are constants. 4704 if (!LC || !MC || !NC) { 4705 const SCEV *CNC = SE.getCouldNotCompute(); 4706 return std::make_pair(CNC, CNC); 4707 } 4708 4709 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4710 const APInt &L = LC->getValue()->getValue(); 4711 const APInt &M = MC->getValue()->getValue(); 4712 const APInt &N = NC->getValue()->getValue(); 4713 APInt Two(BitWidth, 2); 4714 APInt Four(BitWidth, 4); 4715 4716 { 4717 using namespace APIntOps; 4718 const APInt& C = L; 4719 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4720 // The B coefficient is M-N/2 4721 APInt B(M); 4722 B -= sdiv(N,Two); 4723 4724 // The A coefficient is N/2 4725 APInt A(N.sdiv(Two)); 4726 4727 // Compute the B^2-4ac term. 4728 APInt SqrtTerm(B); 4729 SqrtTerm *= B; 4730 SqrtTerm -= Four * (A * C); 4731 4732 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4733 // integer value or else APInt::sqrt() will assert. 4734 APInt SqrtVal(SqrtTerm.sqrt()); 4735 4736 // Compute the two solutions for the quadratic formula. 4737 // The divisions must be performed as signed divisions. 4738 APInt NegB(-B); 4739 APInt TwoA( A << 1 ); 4740 if (TwoA.isMinValue()) { 4741 const SCEV *CNC = SE.getCouldNotCompute(); 4742 return std::make_pair(CNC, CNC); 4743 } 4744 4745 LLVMContext &Context = SE.getContext(); 4746 4747 ConstantInt *Solution1 = 4748 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4749 ConstantInt *Solution2 = 4750 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4751 4752 return std::make_pair(SE.getConstant(Solution1), 4753 SE.getConstant(Solution2)); 4754 } // end APIntOps namespace 4755} 4756 4757/// HowFarToZero - Return the number of times a backedge comparing the specified 4758/// value to zero will execute. If not computable, return CouldNotCompute. 4759ScalarEvolution::BackedgeTakenInfo 4760ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4761 // If the value is a constant 4762 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4763 // If the value is already zero, the branch will execute zero times. 4764 if (C->getValue()->isZero()) return C; 4765 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4766 } 4767 4768 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4769 if (!AddRec || AddRec->getLoop() != L) 4770 return getCouldNotCompute(); 4771 4772 if (AddRec->isAffine()) { 4773 // If this is an affine expression, the execution count of this branch is 4774 // the minimum unsigned root of the following equation: 4775 // 4776 // Start + Step*N = 0 (mod 2^BW) 4777 // 4778 // equivalent to: 4779 // 4780 // Step*N = -Start (mod 2^BW) 4781 // 4782 // where BW is the common bit width of Start and Step. 4783 4784 // Get the initial value for the loop. 4785 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4786 L->getParentLoop()); 4787 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4788 L->getParentLoop()); 4789 4790 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4791 // For now we handle only constant steps. 4792 4793 // First, handle unitary steps. 4794 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4795 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4796 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4797 return Start; // N = Start (as unsigned) 4798 4799 // Then, try to solve the above equation provided that Start is constant. 4800 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4801 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4802 -StartC->getValue()->getValue(), 4803 *this); 4804 } 4805 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4806 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4807 // the quadratic equation to solve it. 4808 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4809 *this); 4810 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4811 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4812 if (R1) { 4813#if 0 4814 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4815 << " sol#2: " << *R2 << "\n"; 4816#endif 4817 // Pick the smallest positive root value. 4818 if (ConstantInt *CB = 4819 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4820 R1->getValue(), R2->getValue()))) { 4821 if (CB->getZExtValue() == false) 4822 std::swap(R1, R2); // R1 is the minimum root now. 4823 4824 // We can only use this value if the chrec ends up with an exact zero 4825 // value at this index. When solving for "X*X != 5", for example, we 4826 // should not accept a root of 2. 4827 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4828 if (Val->isZero()) 4829 return R1; // We found a quadratic root! 4830 } 4831 } 4832 } 4833 4834 return getCouldNotCompute(); 4835} 4836 4837/// HowFarToNonZero - Return the number of times a backedge checking the 4838/// specified value for nonzero will execute. If not computable, return 4839/// CouldNotCompute 4840ScalarEvolution::BackedgeTakenInfo 4841ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4842 // Loops that look like: while (X == 0) are very strange indeed. We don't 4843 // handle them yet except for the trivial case. This could be expanded in the 4844 // future as needed. 4845 4846 // If the value is a constant, check to see if it is known to be non-zero 4847 // already. If so, the backedge will execute zero times. 4848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4849 if (!C->getValue()->isNullValue()) 4850 return getConstant(C->getType(), 0); 4851 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4852 } 4853 4854 // We could implement others, but I really doubt anyone writes loops like 4855 // this, and if they did, they would already be constant folded. 4856 return getCouldNotCompute(); 4857} 4858 4859/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4860/// (which may not be an immediate predecessor) which has exactly one 4861/// successor from which BB is reachable, or null if no such block is 4862/// found. 4863/// 4864std::pair<BasicBlock *, BasicBlock *> 4865ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4866 // If the block has a unique predecessor, then there is no path from the 4867 // predecessor to the block that does not go through the direct edge 4868 // from the predecessor to the block. 4869 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4870 return std::make_pair(Pred, BB); 4871 4872 // A loop's header is defined to be a block that dominates the loop. 4873 // If the header has a unique predecessor outside the loop, it must be 4874 // a block that has exactly one successor that can reach the loop. 4875 if (Loop *L = LI->getLoopFor(BB)) 4876 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4877 4878 return std::pair<BasicBlock *, BasicBlock *>(); 4879} 4880 4881/// HasSameValue - SCEV structural equivalence is usually sufficient for 4882/// testing whether two expressions are equal, however for the purposes of 4883/// looking for a condition guarding a loop, it can be useful to be a little 4884/// more general, since a front-end may have replicated the controlling 4885/// expression. 4886/// 4887static bool HasSameValue(const SCEV *A, const SCEV *B) { 4888 // Quick check to see if they are the same SCEV. 4889 if (A == B) return true; 4890 4891 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4892 // two different instructions with the same value. Check for this case. 4893 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4894 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4895 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4896 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4897 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4898 return true; 4899 4900 // Otherwise assume they may have a different value. 4901 return false; 4902} 4903 4904/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4905/// predicate Pred. Return true iff any changes were made. 4906/// 4907bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4908 const SCEV *&LHS, const SCEV *&RHS) { 4909 bool Changed = false; 4910 4911 // Canonicalize a constant to the right side. 4912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4913 // Check for both operands constant. 4914 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4915 if (ConstantExpr::getICmp(Pred, 4916 LHSC->getValue(), 4917 RHSC->getValue())->isNullValue()) 4918 goto trivially_false; 4919 else 4920 goto trivially_true; 4921 } 4922 // Otherwise swap the operands to put the constant on the right. 4923 std::swap(LHS, RHS); 4924 Pred = ICmpInst::getSwappedPredicate(Pred); 4925 Changed = true; 4926 } 4927 4928 // If we're comparing an addrec with a value which is loop-invariant in the 4929 // addrec's loop, put the addrec on the left. Also make a dominance check, 4930 // as both operands could be addrecs loop-invariant in each other's loop. 4931 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4932 const Loop *L = AR->getLoop(); 4933 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4934 std::swap(LHS, RHS); 4935 Pred = ICmpInst::getSwappedPredicate(Pred); 4936 Changed = true; 4937 } 4938 } 4939 4940 // If there's a constant operand, canonicalize comparisons with boundary 4941 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4942 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4943 const APInt &RA = RC->getValue()->getValue(); 4944 switch (Pred) { 4945 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4946 case ICmpInst::ICMP_EQ: 4947 case ICmpInst::ICMP_NE: 4948 break; 4949 case ICmpInst::ICMP_UGE: 4950 if ((RA - 1).isMinValue()) { 4951 Pred = ICmpInst::ICMP_NE; 4952 RHS = getConstant(RA - 1); 4953 Changed = true; 4954 break; 4955 } 4956 if (RA.isMaxValue()) { 4957 Pred = ICmpInst::ICMP_EQ; 4958 Changed = true; 4959 break; 4960 } 4961 if (RA.isMinValue()) goto trivially_true; 4962 4963 Pred = ICmpInst::ICMP_UGT; 4964 RHS = getConstant(RA - 1); 4965 Changed = true; 4966 break; 4967 case ICmpInst::ICMP_ULE: 4968 if ((RA + 1).isMaxValue()) { 4969 Pred = ICmpInst::ICMP_NE; 4970 RHS = getConstant(RA + 1); 4971 Changed = true; 4972 break; 4973 } 4974 if (RA.isMinValue()) { 4975 Pred = ICmpInst::ICMP_EQ; 4976 Changed = true; 4977 break; 4978 } 4979 if (RA.isMaxValue()) goto trivially_true; 4980 4981 Pred = ICmpInst::ICMP_ULT; 4982 RHS = getConstant(RA + 1); 4983 Changed = true; 4984 break; 4985 case ICmpInst::ICMP_SGE: 4986 if ((RA - 1).isMinSignedValue()) { 4987 Pred = ICmpInst::ICMP_NE; 4988 RHS = getConstant(RA - 1); 4989 Changed = true; 4990 break; 4991 } 4992 if (RA.isMaxSignedValue()) { 4993 Pred = ICmpInst::ICMP_EQ; 4994 Changed = true; 4995 break; 4996 } 4997 if (RA.isMinSignedValue()) goto trivially_true; 4998 4999 Pred = ICmpInst::ICMP_SGT; 5000 RHS = getConstant(RA - 1); 5001 Changed = true; 5002 break; 5003 case ICmpInst::ICMP_SLE: 5004 if ((RA + 1).isMaxSignedValue()) { 5005 Pred = ICmpInst::ICMP_NE; 5006 RHS = getConstant(RA + 1); 5007 Changed = true; 5008 break; 5009 } 5010 if (RA.isMinSignedValue()) { 5011 Pred = ICmpInst::ICMP_EQ; 5012 Changed = true; 5013 break; 5014 } 5015 if (RA.isMaxSignedValue()) goto trivially_true; 5016 5017 Pred = ICmpInst::ICMP_SLT; 5018 RHS = getConstant(RA + 1); 5019 Changed = true; 5020 break; 5021 case ICmpInst::ICMP_UGT: 5022 if (RA.isMinValue()) { 5023 Pred = ICmpInst::ICMP_NE; 5024 Changed = true; 5025 break; 5026 } 5027 if ((RA + 1).isMaxValue()) { 5028 Pred = ICmpInst::ICMP_EQ; 5029 RHS = getConstant(RA + 1); 5030 Changed = true; 5031 break; 5032 } 5033 if (RA.isMaxValue()) goto trivially_false; 5034 break; 5035 case ICmpInst::ICMP_ULT: 5036 if (RA.isMaxValue()) { 5037 Pred = ICmpInst::ICMP_NE; 5038 Changed = true; 5039 break; 5040 } 5041 if ((RA - 1).isMinValue()) { 5042 Pred = ICmpInst::ICMP_EQ; 5043 RHS = getConstant(RA - 1); 5044 Changed = true; 5045 break; 5046 } 5047 if (RA.isMinValue()) goto trivially_false; 5048 break; 5049 case ICmpInst::ICMP_SGT: 5050 if (RA.isMinSignedValue()) { 5051 Pred = ICmpInst::ICMP_NE; 5052 Changed = true; 5053 break; 5054 } 5055 if ((RA + 1).isMaxSignedValue()) { 5056 Pred = ICmpInst::ICMP_EQ; 5057 RHS = getConstant(RA + 1); 5058 Changed = true; 5059 break; 5060 } 5061 if (RA.isMaxSignedValue()) goto trivially_false; 5062 break; 5063 case ICmpInst::ICMP_SLT: 5064 if (RA.isMaxSignedValue()) { 5065 Pred = ICmpInst::ICMP_NE; 5066 Changed = true; 5067 break; 5068 } 5069 if ((RA - 1).isMinSignedValue()) { 5070 Pred = ICmpInst::ICMP_EQ; 5071 RHS = getConstant(RA - 1); 5072 Changed = true; 5073 break; 5074 } 5075 if (RA.isMinSignedValue()) goto trivially_false; 5076 break; 5077 } 5078 } 5079 5080 // Check for obvious equality. 5081 if (HasSameValue(LHS, RHS)) { 5082 if (ICmpInst::isTrueWhenEqual(Pred)) 5083 goto trivially_true; 5084 if (ICmpInst::isFalseWhenEqual(Pred)) 5085 goto trivially_false; 5086 } 5087 5088 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5089 // adding or subtracting 1 from one of the operands. 5090 switch (Pred) { 5091 case ICmpInst::ICMP_SLE: 5092 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5093 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5094 /*HasNUW=*/false, /*HasNSW=*/true); 5095 Pred = ICmpInst::ICMP_SLT; 5096 Changed = true; 5097 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5098 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5099 /*HasNUW=*/false, /*HasNSW=*/true); 5100 Pred = ICmpInst::ICMP_SLT; 5101 Changed = true; 5102 } 5103 break; 5104 case ICmpInst::ICMP_SGE: 5105 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5106 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5107 /*HasNUW=*/false, /*HasNSW=*/true); 5108 Pred = ICmpInst::ICMP_SGT; 5109 Changed = true; 5110 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5111 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5112 /*HasNUW=*/false, /*HasNSW=*/true); 5113 Pred = ICmpInst::ICMP_SGT; 5114 Changed = true; 5115 } 5116 break; 5117 case ICmpInst::ICMP_ULE: 5118 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5119 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5120 /*HasNUW=*/true, /*HasNSW=*/false); 5121 Pred = ICmpInst::ICMP_ULT; 5122 Changed = true; 5123 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5124 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5125 /*HasNUW=*/true, /*HasNSW=*/false); 5126 Pred = ICmpInst::ICMP_ULT; 5127 Changed = true; 5128 } 5129 break; 5130 case ICmpInst::ICMP_UGE: 5131 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5132 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5133 /*HasNUW=*/true, /*HasNSW=*/false); 5134 Pred = ICmpInst::ICMP_UGT; 5135 Changed = true; 5136 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5137 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5138 /*HasNUW=*/true, /*HasNSW=*/false); 5139 Pred = ICmpInst::ICMP_UGT; 5140 Changed = true; 5141 } 5142 break; 5143 default: 5144 break; 5145 } 5146 5147 // TODO: More simplifications are possible here. 5148 5149 return Changed; 5150 5151trivially_true: 5152 // Return 0 == 0. 5153 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5154 Pred = ICmpInst::ICMP_EQ; 5155 return true; 5156 5157trivially_false: 5158 // Return 0 != 0. 5159 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5160 Pred = ICmpInst::ICMP_NE; 5161 return true; 5162} 5163 5164bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5165 return getSignedRange(S).getSignedMax().isNegative(); 5166} 5167 5168bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5169 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5170} 5171 5172bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5173 return !getSignedRange(S).getSignedMin().isNegative(); 5174} 5175 5176bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5177 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5178} 5179 5180bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5181 return isKnownNegative(S) || isKnownPositive(S); 5182} 5183 5184bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5185 const SCEV *LHS, const SCEV *RHS) { 5186 // Canonicalize the inputs first. 5187 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5188 5189 // If LHS or RHS is an addrec, check to see if the condition is true in 5190 // every iteration of the loop. 5191 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5192 if (isLoopEntryGuardedByCond( 5193 AR->getLoop(), Pred, AR->getStart(), RHS) && 5194 isLoopBackedgeGuardedByCond( 5195 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5196 return true; 5197 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5198 if (isLoopEntryGuardedByCond( 5199 AR->getLoop(), Pred, LHS, AR->getStart()) && 5200 isLoopBackedgeGuardedByCond( 5201 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5202 return true; 5203 5204 // Otherwise see what can be done with known constant ranges. 5205 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5206} 5207 5208bool 5209ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5210 const SCEV *LHS, const SCEV *RHS) { 5211 if (HasSameValue(LHS, RHS)) 5212 return ICmpInst::isTrueWhenEqual(Pred); 5213 5214 // This code is split out from isKnownPredicate because it is called from 5215 // within isLoopEntryGuardedByCond. 5216 switch (Pred) { 5217 default: 5218 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5219 break; 5220 case ICmpInst::ICMP_SGT: 5221 Pred = ICmpInst::ICMP_SLT; 5222 std::swap(LHS, RHS); 5223 case ICmpInst::ICMP_SLT: { 5224 ConstantRange LHSRange = getSignedRange(LHS); 5225 ConstantRange RHSRange = getSignedRange(RHS); 5226 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5227 return true; 5228 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5229 return false; 5230 break; 5231 } 5232 case ICmpInst::ICMP_SGE: 5233 Pred = ICmpInst::ICMP_SLE; 5234 std::swap(LHS, RHS); 5235 case ICmpInst::ICMP_SLE: { 5236 ConstantRange LHSRange = getSignedRange(LHS); 5237 ConstantRange RHSRange = getSignedRange(RHS); 5238 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5239 return true; 5240 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5241 return false; 5242 break; 5243 } 5244 case ICmpInst::ICMP_UGT: 5245 Pred = ICmpInst::ICMP_ULT; 5246 std::swap(LHS, RHS); 5247 case ICmpInst::ICMP_ULT: { 5248 ConstantRange LHSRange = getUnsignedRange(LHS); 5249 ConstantRange RHSRange = getUnsignedRange(RHS); 5250 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5251 return true; 5252 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5253 return false; 5254 break; 5255 } 5256 case ICmpInst::ICMP_UGE: 5257 Pred = ICmpInst::ICMP_ULE; 5258 std::swap(LHS, RHS); 5259 case ICmpInst::ICMP_ULE: { 5260 ConstantRange LHSRange = getUnsignedRange(LHS); 5261 ConstantRange RHSRange = getUnsignedRange(RHS); 5262 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5263 return true; 5264 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5265 return false; 5266 break; 5267 } 5268 case ICmpInst::ICMP_NE: { 5269 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5270 return true; 5271 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5272 return true; 5273 5274 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5275 if (isKnownNonZero(Diff)) 5276 return true; 5277 break; 5278 } 5279 case ICmpInst::ICMP_EQ: 5280 // The check at the top of the function catches the case where 5281 // the values are known to be equal. 5282 break; 5283 } 5284 return false; 5285} 5286 5287/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5288/// protected by a conditional between LHS and RHS. This is used to 5289/// to eliminate casts. 5290bool 5291ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5292 ICmpInst::Predicate Pred, 5293 const SCEV *LHS, const SCEV *RHS) { 5294 // Interpret a null as meaning no loop, where there is obviously no guard 5295 // (interprocedural conditions notwithstanding). 5296 if (!L) return true; 5297 5298 BasicBlock *Latch = L->getLoopLatch(); 5299 if (!Latch) 5300 return false; 5301 5302 BranchInst *LoopContinuePredicate = 5303 dyn_cast<BranchInst>(Latch->getTerminator()); 5304 if (!LoopContinuePredicate || 5305 LoopContinuePredicate->isUnconditional()) 5306 return false; 5307 5308 return isImpliedCond(Pred, LHS, RHS, 5309 LoopContinuePredicate->getCondition(), 5310 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5311} 5312 5313/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5314/// by a conditional between LHS and RHS. This is used to help avoid max 5315/// expressions in loop trip counts, and to eliminate casts. 5316bool 5317ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5318 ICmpInst::Predicate Pred, 5319 const SCEV *LHS, const SCEV *RHS) { 5320 // Interpret a null as meaning no loop, where there is obviously no guard 5321 // (interprocedural conditions notwithstanding). 5322 if (!L) return false; 5323 5324 // Starting at the loop predecessor, climb up the predecessor chain, as long 5325 // as there are predecessors that can be found that have unique successors 5326 // leading to the original header. 5327 for (std::pair<BasicBlock *, BasicBlock *> 5328 Pair(L->getLoopPredecessor(), L->getHeader()); 5329 Pair.first; 5330 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5331 5332 BranchInst *LoopEntryPredicate = 5333 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5334 if (!LoopEntryPredicate || 5335 LoopEntryPredicate->isUnconditional()) 5336 continue; 5337 5338 if (isImpliedCond(Pred, LHS, RHS, 5339 LoopEntryPredicate->getCondition(), 5340 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5341 return true; 5342 } 5343 5344 return false; 5345} 5346 5347/// isImpliedCond - Test whether the condition described by Pred, LHS, 5348/// and RHS is true whenever the given Cond value evaluates to true. 5349bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5350 const SCEV *LHS, const SCEV *RHS, 5351 Value *FoundCondValue, 5352 bool Inverse) { 5353 // Recursively handle And and Or conditions. 5354 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5355 if (BO->getOpcode() == Instruction::And) { 5356 if (!Inverse) 5357 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5358 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5359 } else if (BO->getOpcode() == Instruction::Or) { 5360 if (Inverse) 5361 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5362 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5363 } 5364 } 5365 5366 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5367 if (!ICI) return false; 5368 5369 // Bail if the ICmp's operands' types are wider than the needed type 5370 // before attempting to call getSCEV on them. This avoids infinite 5371 // recursion, since the analysis of widening casts can require loop 5372 // exit condition information for overflow checking, which would 5373 // lead back here. 5374 if (getTypeSizeInBits(LHS->getType()) < 5375 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5376 return false; 5377 5378 // Now that we found a conditional branch that dominates the loop, check to 5379 // see if it is the comparison we are looking for. 5380 ICmpInst::Predicate FoundPred; 5381 if (Inverse) 5382 FoundPred = ICI->getInversePredicate(); 5383 else 5384 FoundPred = ICI->getPredicate(); 5385 5386 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5387 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5388 5389 // Balance the types. The case where FoundLHS' type is wider than 5390 // LHS' type is checked for above. 5391 if (getTypeSizeInBits(LHS->getType()) > 5392 getTypeSizeInBits(FoundLHS->getType())) { 5393 if (CmpInst::isSigned(Pred)) { 5394 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5395 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5396 } else { 5397 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5398 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5399 } 5400 } 5401 5402 // Canonicalize the query to match the way instcombine will have 5403 // canonicalized the comparison. 5404 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5405 if (LHS == RHS) 5406 return CmpInst::isTrueWhenEqual(Pred); 5407 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5408 if (FoundLHS == FoundRHS) 5409 return CmpInst::isFalseWhenEqual(Pred); 5410 5411 // Check to see if we can make the LHS or RHS match. 5412 if (LHS == FoundRHS || RHS == FoundLHS) { 5413 if (isa<SCEVConstant>(RHS)) { 5414 std::swap(FoundLHS, FoundRHS); 5415 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5416 } else { 5417 std::swap(LHS, RHS); 5418 Pred = ICmpInst::getSwappedPredicate(Pred); 5419 } 5420 } 5421 5422 // Check whether the found predicate is the same as the desired predicate. 5423 if (FoundPred == Pred) 5424 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5425 5426 // Check whether swapping the found predicate makes it the same as the 5427 // desired predicate. 5428 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5429 if (isa<SCEVConstant>(RHS)) 5430 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5431 else 5432 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5433 RHS, LHS, FoundLHS, FoundRHS); 5434 } 5435 5436 // Check whether the actual condition is beyond sufficient. 5437 if (FoundPred == ICmpInst::ICMP_EQ) 5438 if (ICmpInst::isTrueWhenEqual(Pred)) 5439 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5440 return true; 5441 if (Pred == ICmpInst::ICMP_NE) 5442 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5443 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5444 return true; 5445 5446 // Otherwise assume the worst. 5447 return false; 5448} 5449 5450/// isImpliedCondOperands - Test whether the condition described by Pred, 5451/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5452/// and FoundRHS is true. 5453bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5454 const SCEV *LHS, const SCEV *RHS, 5455 const SCEV *FoundLHS, 5456 const SCEV *FoundRHS) { 5457 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5458 FoundLHS, FoundRHS) || 5459 // ~x < ~y --> x > y 5460 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5461 getNotSCEV(FoundRHS), 5462 getNotSCEV(FoundLHS)); 5463} 5464 5465/// isImpliedCondOperandsHelper - Test whether the condition described by 5466/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5467/// FoundLHS, and FoundRHS is true. 5468bool 5469ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5470 const SCEV *LHS, const SCEV *RHS, 5471 const SCEV *FoundLHS, 5472 const SCEV *FoundRHS) { 5473 switch (Pred) { 5474 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5475 case ICmpInst::ICMP_EQ: 5476 case ICmpInst::ICMP_NE: 5477 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5478 return true; 5479 break; 5480 case ICmpInst::ICMP_SLT: 5481 case ICmpInst::ICMP_SLE: 5482 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5483 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5484 return true; 5485 break; 5486 case ICmpInst::ICMP_SGT: 5487 case ICmpInst::ICMP_SGE: 5488 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5489 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5490 return true; 5491 break; 5492 case ICmpInst::ICMP_ULT: 5493 case ICmpInst::ICMP_ULE: 5494 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5495 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5496 return true; 5497 break; 5498 case ICmpInst::ICMP_UGT: 5499 case ICmpInst::ICMP_UGE: 5500 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5501 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5502 return true; 5503 break; 5504 } 5505 5506 return false; 5507} 5508 5509/// getBECount - Subtract the end and start values and divide by the step, 5510/// rounding up, to get the number of times the backedge is executed. Return 5511/// CouldNotCompute if an intermediate computation overflows. 5512const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5513 const SCEV *End, 5514 const SCEV *Step, 5515 bool NoWrap) { 5516 assert(!isKnownNegative(Step) && 5517 "This code doesn't handle negative strides yet!"); 5518 5519 const Type *Ty = Start->getType(); 5520 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5521 const SCEV *Diff = getMinusSCEV(End, Start); 5522 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5523 5524 // Add an adjustment to the difference between End and Start so that 5525 // the division will effectively round up. 5526 const SCEV *Add = getAddExpr(Diff, RoundUp); 5527 5528 if (!NoWrap) { 5529 // Check Add for unsigned overflow. 5530 // TODO: More sophisticated things could be done here. 5531 const Type *WideTy = IntegerType::get(getContext(), 5532 getTypeSizeInBits(Ty) + 1); 5533 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5534 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5535 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5536 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5537 return getCouldNotCompute(); 5538 } 5539 5540 return getUDivExpr(Add, Step); 5541} 5542 5543/// HowManyLessThans - Return the number of times a backedge containing the 5544/// specified less-than comparison will execute. If not computable, return 5545/// CouldNotCompute. 5546ScalarEvolution::BackedgeTakenInfo 5547ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5548 const Loop *L, bool isSigned) { 5549 // Only handle: "ADDREC < LoopInvariant". 5550 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5551 5552 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5553 if (!AddRec || AddRec->getLoop() != L) 5554 return getCouldNotCompute(); 5555 5556 // Check to see if we have a flag which makes analysis easy. 5557 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5558 AddRec->hasNoUnsignedWrap(); 5559 5560 if (AddRec->isAffine()) { 5561 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5562 const SCEV *Step = AddRec->getStepRecurrence(*this); 5563 5564 if (Step->isZero()) 5565 return getCouldNotCompute(); 5566 if (Step->isOne()) { 5567 // With unit stride, the iteration never steps past the limit value. 5568 } else if (isKnownPositive(Step)) { 5569 // Test whether a positive iteration can step past the limit 5570 // value and past the maximum value for its type in a single step. 5571 // Note that it's not sufficient to check NoWrap here, because even 5572 // though the value after a wrap is undefined, it's not undefined 5573 // behavior, so if wrap does occur, the loop could either terminate or 5574 // loop infinitely, but in either case, the loop is guaranteed to 5575 // iterate at least until the iteration where the wrapping occurs. 5576 const SCEV *One = getConstant(Step->getType(), 1); 5577 if (isSigned) { 5578 APInt Max = APInt::getSignedMaxValue(BitWidth); 5579 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5580 .slt(getSignedRange(RHS).getSignedMax())) 5581 return getCouldNotCompute(); 5582 } else { 5583 APInt Max = APInt::getMaxValue(BitWidth); 5584 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5585 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5586 return getCouldNotCompute(); 5587 } 5588 } else 5589 // TODO: Handle negative strides here and below. 5590 return getCouldNotCompute(); 5591 5592 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5593 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5594 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5595 // treat m-n as signed nor unsigned due to overflow possibility. 5596 5597 // First, we get the value of the LHS in the first iteration: n 5598 const SCEV *Start = AddRec->getOperand(0); 5599 5600 // Determine the minimum constant start value. 5601 const SCEV *MinStart = getConstant(isSigned ? 5602 getSignedRange(Start).getSignedMin() : 5603 getUnsignedRange(Start).getUnsignedMin()); 5604 5605 // If we know that the condition is true in order to enter the loop, 5606 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5607 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5608 // the division must round up. 5609 const SCEV *End = RHS; 5610 if (!isLoopEntryGuardedByCond(L, 5611 isSigned ? ICmpInst::ICMP_SLT : 5612 ICmpInst::ICMP_ULT, 5613 getMinusSCEV(Start, Step), RHS)) 5614 End = isSigned ? getSMaxExpr(RHS, Start) 5615 : getUMaxExpr(RHS, Start); 5616 5617 // Determine the maximum constant end value. 5618 const SCEV *MaxEnd = getConstant(isSigned ? 5619 getSignedRange(End).getSignedMax() : 5620 getUnsignedRange(End).getUnsignedMax()); 5621 5622 // If MaxEnd is within a step of the maximum integer value in its type, 5623 // adjust it down to the minimum value which would produce the same effect. 5624 // This allows the subsequent ceiling division of (N+(step-1))/step to 5625 // compute the correct value. 5626 const SCEV *StepMinusOne = getMinusSCEV(Step, 5627 getConstant(Step->getType(), 1)); 5628 MaxEnd = isSigned ? 5629 getSMinExpr(MaxEnd, 5630 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5631 StepMinusOne)) : 5632 getUMinExpr(MaxEnd, 5633 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5634 StepMinusOne)); 5635 5636 // Finally, we subtract these two values and divide, rounding up, to get 5637 // the number of times the backedge is executed. 5638 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5639 5640 // The maximum backedge count is similar, except using the minimum start 5641 // value and the maximum end value. 5642 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5643 5644 return BackedgeTakenInfo(BECount, MaxBECount); 5645 } 5646 5647 return getCouldNotCompute(); 5648} 5649 5650/// getNumIterationsInRange - Return the number of iterations of this loop that 5651/// produce values in the specified constant range. Another way of looking at 5652/// this is that it returns the first iteration number where the value is not in 5653/// the condition, thus computing the exit count. If the iteration count can't 5654/// be computed, an instance of SCEVCouldNotCompute is returned. 5655const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5656 ScalarEvolution &SE) const { 5657 if (Range.isFullSet()) // Infinite loop. 5658 return SE.getCouldNotCompute(); 5659 5660 // If the start is a non-zero constant, shift the range to simplify things. 5661 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5662 if (!SC->getValue()->isZero()) { 5663 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5664 Operands[0] = SE.getConstant(SC->getType(), 0); 5665 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5666 if (const SCEVAddRecExpr *ShiftedAddRec = 5667 dyn_cast<SCEVAddRecExpr>(Shifted)) 5668 return ShiftedAddRec->getNumIterationsInRange( 5669 Range.subtract(SC->getValue()->getValue()), SE); 5670 // This is strange and shouldn't happen. 5671 return SE.getCouldNotCompute(); 5672 } 5673 5674 // The only time we can solve this is when we have all constant indices. 5675 // Otherwise, we cannot determine the overflow conditions. 5676 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5677 if (!isa<SCEVConstant>(getOperand(i))) 5678 return SE.getCouldNotCompute(); 5679 5680 5681 // Okay at this point we know that all elements of the chrec are constants and 5682 // that the start element is zero. 5683 5684 // First check to see if the range contains zero. If not, the first 5685 // iteration exits. 5686 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5687 if (!Range.contains(APInt(BitWidth, 0))) 5688 return SE.getConstant(getType(), 0); 5689 5690 if (isAffine()) { 5691 // If this is an affine expression then we have this situation: 5692 // Solve {0,+,A} in Range === Ax in Range 5693 5694 // We know that zero is in the range. If A is positive then we know that 5695 // the upper value of the range must be the first possible exit value. 5696 // If A is negative then the lower of the range is the last possible loop 5697 // value. Also note that we already checked for a full range. 5698 APInt One(BitWidth,1); 5699 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5700 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5701 5702 // The exit value should be (End+A)/A. 5703 APInt ExitVal = (End + A).udiv(A); 5704 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5705 5706 // Evaluate at the exit value. If we really did fall out of the valid 5707 // range, then we computed our trip count, otherwise wrap around or other 5708 // things must have happened. 5709 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5710 if (Range.contains(Val->getValue())) 5711 return SE.getCouldNotCompute(); // Something strange happened 5712 5713 // Ensure that the previous value is in the range. This is a sanity check. 5714 assert(Range.contains( 5715 EvaluateConstantChrecAtConstant(this, 5716 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5717 "Linear scev computation is off in a bad way!"); 5718 return SE.getConstant(ExitValue); 5719 } else if (isQuadratic()) { 5720 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5721 // quadratic equation to solve it. To do this, we must frame our problem in 5722 // terms of figuring out when zero is crossed, instead of when 5723 // Range.getUpper() is crossed. 5724 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5725 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5726 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5727 5728 // Next, solve the constructed addrec 5729 std::pair<const SCEV *,const SCEV *> Roots = 5730 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5731 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5732 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5733 if (R1) { 5734 // Pick the smallest positive root value. 5735 if (ConstantInt *CB = 5736 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5737 R1->getValue(), R2->getValue()))) { 5738 if (CB->getZExtValue() == false) 5739 std::swap(R1, R2); // R1 is the minimum root now. 5740 5741 // Make sure the root is not off by one. The returned iteration should 5742 // not be in the range, but the previous one should be. When solving 5743 // for "X*X < 5", for example, we should not return a root of 2. 5744 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5745 R1->getValue(), 5746 SE); 5747 if (Range.contains(R1Val->getValue())) { 5748 // The next iteration must be out of the range... 5749 ConstantInt *NextVal = 5750 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5751 5752 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5753 if (!Range.contains(R1Val->getValue())) 5754 return SE.getConstant(NextVal); 5755 return SE.getCouldNotCompute(); // Something strange happened 5756 } 5757 5758 // If R1 was not in the range, then it is a good return value. Make 5759 // sure that R1-1 WAS in the range though, just in case. 5760 ConstantInt *NextVal = 5761 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5762 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5763 if (Range.contains(R1Val->getValue())) 5764 return R1; 5765 return SE.getCouldNotCompute(); // Something strange happened 5766 } 5767 } 5768 } 5769 5770 return SE.getCouldNotCompute(); 5771} 5772 5773 5774 5775//===----------------------------------------------------------------------===// 5776// SCEVCallbackVH Class Implementation 5777//===----------------------------------------------------------------------===// 5778 5779void ScalarEvolution::SCEVCallbackVH::deleted() { 5780 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5781 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5782 SE->ConstantEvolutionLoopExitValue.erase(PN); 5783 SE->Scalars.erase(getValPtr()); 5784 // this now dangles! 5785} 5786 5787void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5788 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5789 5790 // Forget all the expressions associated with users of the old value, 5791 // so that future queries will recompute the expressions using the new 5792 // value. 5793 Value *Old = getValPtr(); 5794 SmallVector<User *, 16> Worklist; 5795 SmallPtrSet<User *, 8> Visited; 5796 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5797 UI != UE; ++UI) 5798 Worklist.push_back(*UI); 5799 while (!Worklist.empty()) { 5800 User *U = Worklist.pop_back_val(); 5801 // Deleting the Old value will cause this to dangle. Postpone 5802 // that until everything else is done. 5803 if (U == Old) 5804 continue; 5805 if (!Visited.insert(U)) 5806 continue; 5807 if (PHINode *PN = dyn_cast<PHINode>(U)) 5808 SE->ConstantEvolutionLoopExitValue.erase(PN); 5809 SE->Scalars.erase(U); 5810 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5811 UI != UE; ++UI) 5812 Worklist.push_back(*UI); 5813 } 5814 // Delete the Old value. 5815 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5816 SE->ConstantEvolutionLoopExitValue.erase(PN); 5817 SE->Scalars.erase(Old); 5818 // this now dangles! 5819} 5820 5821ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5822 : CallbackVH(V), SE(se) {} 5823 5824//===----------------------------------------------------------------------===// 5825// ScalarEvolution Class Implementation 5826//===----------------------------------------------------------------------===// 5827 5828ScalarEvolution::ScalarEvolution() 5829 : FunctionPass(ID), FirstUnknown(0) { 5830} 5831 5832bool ScalarEvolution::runOnFunction(Function &F) { 5833 this->F = &F; 5834 LI = &getAnalysis<LoopInfo>(); 5835 TD = getAnalysisIfAvailable<TargetData>(); 5836 DT = &getAnalysis<DominatorTree>(); 5837 return false; 5838} 5839 5840void ScalarEvolution::releaseMemory() { 5841 // Iterate through all the SCEVUnknown instances and call their 5842 // destructors, so that they release their references to their values. 5843 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5844 U->~SCEVUnknown(); 5845 FirstUnknown = 0; 5846 5847 Scalars.clear(); 5848 BackedgeTakenCounts.clear(); 5849 ConstantEvolutionLoopExitValue.clear(); 5850 ValuesAtScopes.clear(); 5851 UniqueSCEVs.clear(); 5852 SCEVAllocator.Reset(); 5853} 5854 5855void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5856 AU.setPreservesAll(); 5857 AU.addRequiredTransitive<LoopInfo>(); 5858 AU.addRequiredTransitive<DominatorTree>(); 5859} 5860 5861bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5862 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5863} 5864 5865static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5866 const Loop *L) { 5867 // Print all inner loops first 5868 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5869 PrintLoopInfo(OS, SE, *I); 5870 5871 OS << "Loop "; 5872 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5873 OS << ": "; 5874 5875 SmallVector<BasicBlock *, 8> ExitBlocks; 5876 L->getExitBlocks(ExitBlocks); 5877 if (ExitBlocks.size() != 1) 5878 OS << "<multiple exits> "; 5879 5880 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5881 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5882 } else { 5883 OS << "Unpredictable backedge-taken count. "; 5884 } 5885 5886 OS << "\n" 5887 "Loop "; 5888 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5889 OS << ": "; 5890 5891 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5892 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5893 } else { 5894 OS << "Unpredictable max backedge-taken count. "; 5895 } 5896 5897 OS << "\n"; 5898} 5899 5900void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5901 // ScalarEvolution's implementation of the print method is to print 5902 // out SCEV values of all instructions that are interesting. Doing 5903 // this potentially causes it to create new SCEV objects though, 5904 // which technically conflicts with the const qualifier. This isn't 5905 // observable from outside the class though, so casting away the 5906 // const isn't dangerous. 5907 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5908 5909 OS << "Classifying expressions for: "; 5910 WriteAsOperand(OS, F, /*PrintType=*/false); 5911 OS << "\n"; 5912 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5913 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5914 OS << *I << '\n'; 5915 OS << " --> "; 5916 const SCEV *SV = SE.getSCEV(&*I); 5917 SV->print(OS); 5918 5919 const Loop *L = LI->getLoopFor((*I).getParent()); 5920 5921 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5922 if (AtUse != SV) { 5923 OS << " --> "; 5924 AtUse->print(OS); 5925 } 5926 5927 if (L) { 5928 OS << "\t\t" "Exits: "; 5929 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5930 if (!ExitValue->isLoopInvariant(L)) { 5931 OS << "<<Unknown>>"; 5932 } else { 5933 OS << *ExitValue; 5934 } 5935 } 5936 5937 OS << "\n"; 5938 } 5939 5940 OS << "Determining loop execution counts for: "; 5941 WriteAsOperand(OS, F, /*PrintType=*/false); 5942 OS << "\n"; 5943 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5944 PrintLoopInfo(OS, &SE, *I); 5945} 5946 5947