ScalarEvolution.cpp revision d578a40853ab54f6172c2ca350626edacc45846c
1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// 2// 3// The LLVM Compiler Infrastructure 4// 5// This file is distributed under the University of Illinois Open Source 6// License. See LICENSE.TXT for details. 7// 8//===----------------------------------------------------------------------===// 9// 10// This file contains the implementation of the scalar evolution analysis 11// engine, which is used primarily to analyze expressions involving induction 12// variables in loops. 13// 14// There are several aspects to this library. First is the representation of 15// scalar expressions, which are represented as subclasses of the SCEV class. 16// These classes are used to represent certain types of subexpressions that we 17// can handle. We only create one SCEV of a particular shape, so 18// pointer-comparisons for equality are legal. 19// 20// One important aspect of the SCEV objects is that they are never cyclic, even 21// if there is a cycle in the dataflow for an expression (ie, a PHI node). If 22// the PHI node is one of the idioms that we can represent (e.g., a polynomial 23// recurrence) then we represent it directly as a recurrence node, otherwise we 24// represent it as a SCEVUnknown node. 25// 26// In addition to being able to represent expressions of various types, we also 27// have folders that are used to build the *canonical* representation for a 28// particular expression. These folders are capable of using a variety of 29// rewrite rules to simplify the expressions. 30// 31// Once the folders are defined, we can implement the more interesting 32// higher-level code, such as the code that recognizes PHI nodes of various 33// types, computes the execution count of a loop, etc. 34// 35// TODO: We should use these routines and value representations to implement 36// dependence analysis! 37// 38//===----------------------------------------------------------------------===// 39// 40// There are several good references for the techniques used in this analysis. 41// 42// Chains of recurrences -- a method to expedite the evaluation 43// of closed-form functions 44// Olaf Bachmann, Paul S. Wang, Eugene V. Zima 45// 46// On computational properties of chains of recurrences 47// Eugene V. Zima 48// 49// Symbolic Evaluation of Chains of Recurrences for Loop Optimization 50// Robert A. van Engelen 51// 52// Efficient Symbolic Analysis for Optimizing Compilers 53// Robert A. van Engelen 54// 55// Using the chains of recurrences algebra for data dependence testing and 56// induction variable substitution 57// MS Thesis, Johnie Birch 58// 59//===----------------------------------------------------------------------===// 60 61#define DEBUG_TYPE "scalar-evolution" 62#include "llvm/Analysis/ScalarEvolutionExpressions.h" 63#include "llvm/Constants.h" 64#include "llvm/DerivedTypes.h" 65#include "llvm/GlobalVariable.h" 66#include "llvm/GlobalAlias.h" 67#include "llvm/Instructions.h" 68#include "llvm/LLVMContext.h" 69#include "llvm/Operator.h" 70#include "llvm/Analysis/ConstantFolding.h" 71#include "llvm/Analysis/Dominators.h" 72#include "llvm/Analysis/LoopInfo.h" 73#include "llvm/Analysis/ValueTracking.h" 74#include "llvm/Assembly/Writer.h" 75#include "llvm/Target/TargetData.h" 76#include "llvm/Support/CommandLine.h" 77#include "llvm/Support/ConstantRange.h" 78#include "llvm/Support/Debug.h" 79#include "llvm/Support/ErrorHandling.h" 80#include "llvm/Support/GetElementPtrTypeIterator.h" 81#include "llvm/Support/InstIterator.h" 82#include "llvm/Support/MathExtras.h" 83#include "llvm/Support/raw_ostream.h" 84#include "llvm/ADT/Statistic.h" 85#include "llvm/ADT/STLExtras.h" 86#include "llvm/ADT/SmallPtrSet.h" 87#include <algorithm> 88using namespace llvm; 89 90STATISTIC(NumArrayLenItCounts, 91 "Number of trip counts computed with array length"); 92STATISTIC(NumTripCountsComputed, 93 "Number of loops with predictable loop counts"); 94STATISTIC(NumTripCountsNotComputed, 95 "Number of loops without predictable loop counts"); 96STATISTIC(NumBruteForceTripCountsComputed, 97 "Number of loops with trip counts computed by force"); 98 99static cl::opt<unsigned> 100MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 101 cl::desc("Maximum number of iterations SCEV will " 102 "symbolically execute a constant " 103 "derived loop"), 104 cl::init(100)); 105 106INITIALIZE_PASS(ScalarEvolution, "scalar-evolution", 107 "Scalar Evolution Analysis", false, true); 108char ScalarEvolution::ID = 0; 109 110//===----------------------------------------------------------------------===// 111// SCEV class definitions 112//===----------------------------------------------------------------------===// 113 114//===----------------------------------------------------------------------===// 115// Implementation of the SCEV class. 116// 117 118SCEV::~SCEV() {} 119 120void SCEV::dump() const { 121 print(dbgs()); 122 dbgs() << '\n'; 123} 124 125bool SCEV::isZero() const { 126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 127 return SC->getValue()->isZero(); 128 return false; 129} 130 131bool SCEV::isOne() const { 132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 133 return SC->getValue()->isOne(); 134 return false; 135} 136 137bool SCEV::isAllOnesValue() const { 138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 139 return SC->getValue()->isAllOnesValue(); 140 return false; 141} 142 143SCEVCouldNotCompute::SCEVCouldNotCompute() : 144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 145 146bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 148 return false; 149} 150 151const Type *SCEVCouldNotCompute::getType() const { 152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 153 return 0; 154} 155 156bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 158 return false; 159} 160 161bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 163 return false; 164} 165 166void SCEVCouldNotCompute::print(raw_ostream &OS) const { 167 OS << "***COULDNOTCOMPUTE***"; 168} 169 170bool SCEVCouldNotCompute::classof(const SCEV *S) { 171 return S->getSCEVType() == scCouldNotCompute; 172} 173 174const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 175 FoldingSetNodeID ID; 176 ID.AddInteger(scConstant); 177 ID.AddPointer(V); 178 void *IP = 0; 179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 181 UniqueSCEVs.InsertNode(S, IP); 182 return S; 183} 184 185const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 186 return getConstant(ConstantInt::get(getContext(), Val)); 187} 188 189const SCEV * 190ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 192 return getConstant(ConstantInt::get(ITy, V, isSigned)); 193} 194 195const Type *SCEVConstant::getType() const { return V->getType(); } 196 197void SCEVConstant::print(raw_ostream &OS) const { 198 WriteAsOperand(OS, V, false); 199} 200 201SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 202 unsigned SCEVTy, const SCEV *op, const Type *ty) 203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 204 205bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 206 return Op->dominates(BB, DT); 207} 208 209bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->properlyDominates(BB, DT); 211} 212 213SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 214 const SCEV *op, const Type *ty) 215 : SCEVCastExpr(ID, scTruncate, op, ty) { 216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 217 (Ty->isIntegerTy() || Ty->isPointerTy()) && 218 "Cannot truncate non-integer value!"); 219} 220 221void SCEVTruncateExpr::print(raw_ostream &OS) const { 222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 223} 224 225SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 226 const SCEV *op, const Type *ty) 227 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 229 (Ty->isIntegerTy() || Ty->isPointerTy()) && 230 "Cannot zero extend non-integer value!"); 231} 232 233void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 235} 236 237SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 238 const SCEV *op, const Type *ty) 239 : SCEVCastExpr(ID, scSignExtend, op, ty) { 240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 241 (Ty->isIntegerTy() || Ty->isPointerTy()) && 242 "Cannot sign extend non-integer value!"); 243} 244 245void SCEVSignExtendExpr::print(raw_ostream &OS) const { 246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 247} 248 249void SCEVCommutativeExpr::print(raw_ostream &OS) const { 250 const char *OpStr = getOperationStr(); 251 OS << "("; 252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 253 OS << **I; 254 if (llvm::next(I) != E) 255 OS << OpStr; 256 } 257 OS << ")"; 258} 259 260bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 261 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 262 if (!(*I)->dominates(BB, DT)) 263 return false; 264 return true; 265} 266 267bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 268 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 269 if (!(*I)->properlyDominates(BB, DT)) 270 return false; 271 return true; 272} 273 274bool SCEVNAryExpr::isLoopInvariant(const Loop *L) const { 275 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 276 if (!(*I)->isLoopInvariant(L)) 277 return false; 278 return true; 279} 280 281// hasComputableLoopEvolution - N-ary expressions have computable loop 282// evolutions iff they have at least one operand that varies with the loop, 283// but that all varying operands are computable. 284bool SCEVNAryExpr::hasComputableLoopEvolution(const Loop *L) const { 285 bool HasVarying = false; 286 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 287 const SCEV *S = *I; 288 if (!S->isLoopInvariant(L)) { 289 if (S->hasComputableLoopEvolution(L)) 290 HasVarying = true; 291 else 292 return false; 293 } 294 } 295 return HasVarying; 296} 297 298bool SCEVNAryExpr::hasOperand(const SCEV *O) const { 299 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 300 const SCEV *S = *I; 301 if (O == S || S->hasOperand(O)) 302 return true; 303 } 304 return false; 305} 306 307bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 308 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 309} 310 311bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 312 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 313} 314 315void SCEVUDivExpr::print(raw_ostream &OS) const { 316 OS << "(" << *LHS << " /u " << *RHS << ")"; 317} 318 319const Type *SCEVUDivExpr::getType() const { 320 // In most cases the types of LHS and RHS will be the same, but in some 321 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 322 // depend on the type for correctness, but handling types carefully can 323 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 324 // a pointer type than the RHS, so use the RHS' type here. 325 return RHS->getType(); 326} 327 328bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 329 // Add recurrences are never invariant in the function-body (null loop). 330 if (!QueryLoop) 331 return false; 332 333 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 334 if (QueryLoop->contains(L)) 335 return false; 336 337 // This recurrence is invariant w.r.t. QueryLoop if L contains QueryLoop. 338 if (L->contains(QueryLoop)) 339 return true; 340 341 // This recurrence is variant w.r.t. QueryLoop if any of its operands 342 // are variant. 343 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 344 if (!(*I)->isLoopInvariant(QueryLoop)) 345 return false; 346 347 // Otherwise it's loop-invariant. 348 return true; 349} 350 351bool 352SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 353 return DT->dominates(L->getHeader(), BB) && 354 SCEVNAryExpr::dominates(BB, DT); 355} 356 357bool 358SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 359 // This uses a "dominates" query instead of "properly dominates" query because 360 // the instruction which produces the addrec's value is a PHI, and a PHI 361 // effectively properly dominates its entire containing block. 362 return DT->dominates(L->getHeader(), BB) && 363 SCEVNAryExpr::properlyDominates(BB, DT); 364} 365 366void SCEVAddRecExpr::print(raw_ostream &OS) const { 367 OS << "{" << *Operands[0]; 368 for (unsigned i = 1, e = NumOperands; i != e; ++i) 369 OS << ",+," << *Operands[i]; 370 OS << "}<"; 371 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 372 OS << ">"; 373} 374 375void SCEVUnknown::deleted() { 376 // Clear this SCEVUnknown from ValuesAtScopes. 377 SE->ValuesAtScopes.erase(this); 378 379 // Remove this SCEVUnknown from the uniquing map. 380 SE->UniqueSCEVs.RemoveNode(this); 381 382 // Release the value. 383 setValPtr(0); 384} 385 386void SCEVUnknown::allUsesReplacedWith(Value *New) { 387 // Clear this SCEVUnknown from ValuesAtScopes. 388 SE->ValuesAtScopes.erase(this); 389 390 // Remove this SCEVUnknown from the uniquing map. 391 SE->UniqueSCEVs.RemoveNode(this); 392 393 // Update this SCEVUnknown to point to the new value. This is needed 394 // because there may still be outstanding SCEVs which still point to 395 // this SCEVUnknown. 396 setValPtr(New); 397} 398 399bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 400 // All non-instruction values are loop invariant. All instructions are loop 401 // invariant if they are not contained in the specified loop. 402 // Instructions are never considered invariant in the function body 403 // (null loop) because they are defined within the "loop". 404 if (Instruction *I = dyn_cast<Instruction>(getValue())) 405 return L && !L->contains(I); 406 return true; 407} 408 409bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 410 if (Instruction *I = dyn_cast<Instruction>(getValue())) 411 return DT->dominates(I->getParent(), BB); 412 return true; 413} 414 415bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 416 if (Instruction *I = dyn_cast<Instruction>(getValue())) 417 return DT->properlyDominates(I->getParent(), BB); 418 return true; 419} 420 421const Type *SCEVUnknown::getType() const { 422 return getValue()->getType(); 423} 424 425bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 426 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 427 if (VCE->getOpcode() == Instruction::PtrToInt) 428 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 429 if (CE->getOpcode() == Instruction::GetElementPtr && 430 CE->getOperand(0)->isNullValue() && 431 CE->getNumOperands() == 2) 432 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 433 if (CI->isOne()) { 434 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 435 ->getElementType(); 436 return true; 437 } 438 439 return false; 440} 441 442bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 443 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 444 if (VCE->getOpcode() == Instruction::PtrToInt) 445 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 446 if (CE->getOpcode() == Instruction::GetElementPtr && 447 CE->getOperand(0)->isNullValue()) { 448 const Type *Ty = 449 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 450 if (const StructType *STy = dyn_cast<StructType>(Ty)) 451 if (!STy->isPacked() && 452 CE->getNumOperands() == 3 && 453 CE->getOperand(1)->isNullValue()) { 454 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 455 if (CI->isOne() && 456 STy->getNumElements() == 2 && 457 STy->getElementType(0)->isIntegerTy(1)) { 458 AllocTy = STy->getElementType(1); 459 return true; 460 } 461 } 462 } 463 464 return false; 465} 466 467bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 468 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 469 if (VCE->getOpcode() == Instruction::PtrToInt) 470 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 471 if (CE->getOpcode() == Instruction::GetElementPtr && 472 CE->getNumOperands() == 3 && 473 CE->getOperand(0)->isNullValue() && 474 CE->getOperand(1)->isNullValue()) { 475 const Type *Ty = 476 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 477 // Ignore vector types here so that ScalarEvolutionExpander doesn't 478 // emit getelementptrs that index into vectors. 479 if (Ty->isStructTy() || Ty->isArrayTy()) { 480 CTy = Ty; 481 FieldNo = CE->getOperand(2); 482 return true; 483 } 484 } 485 486 return false; 487} 488 489void SCEVUnknown::print(raw_ostream &OS) const { 490 const Type *AllocTy; 491 if (isSizeOf(AllocTy)) { 492 OS << "sizeof(" << *AllocTy << ")"; 493 return; 494 } 495 if (isAlignOf(AllocTy)) { 496 OS << "alignof(" << *AllocTy << ")"; 497 return; 498 } 499 500 const Type *CTy; 501 Constant *FieldNo; 502 if (isOffsetOf(CTy, FieldNo)) { 503 OS << "offsetof(" << *CTy << ", "; 504 WriteAsOperand(OS, FieldNo, false); 505 OS << ")"; 506 return; 507 } 508 509 // Otherwise just print it normally. 510 WriteAsOperand(OS, getValue(), false); 511} 512 513//===----------------------------------------------------------------------===// 514// SCEV Utilities 515//===----------------------------------------------------------------------===// 516 517namespace { 518 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 519 /// than the complexity of the RHS. This comparator is used to canonicalize 520 /// expressions. 521 class SCEVComplexityCompare { 522 const LoopInfo *const LI; 523 public: 524 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 525 526 // Return true or false if LHS is less than, or at least RHS, respectively. 527 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 528 return compare(LHS, RHS) < 0; 529 } 530 531 // Return negative, zero, or positive, if LHS is less than, equal to, or 532 // greater than RHS, respectively. A three-way result allows recursive 533 // comparisons to be more efficient. 534 int compare(const SCEV *LHS, const SCEV *RHS) const { 535 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 536 if (LHS == RHS) 537 return 0; 538 539 // Primarily, sort the SCEVs by their getSCEVType(). 540 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 541 if (LType != RType) 542 return (int)LType - (int)RType; 543 544 // Aside from the getSCEVType() ordering, the particular ordering 545 // isn't very important except that it's beneficial to be consistent, 546 // so that (a + b) and (b + a) don't end up as different expressions. 547 switch (LType) { 548 case scUnknown: { 549 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 550 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 551 552 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 553 // not as complete as it could be. 554 const Value *LV = LU->getValue(), *RV = RU->getValue(); 555 556 // Order pointer values after integer values. This helps SCEVExpander 557 // form GEPs. 558 bool LIsPointer = LV->getType()->isPointerTy(), 559 RIsPointer = RV->getType()->isPointerTy(); 560 if (LIsPointer != RIsPointer) 561 return (int)LIsPointer - (int)RIsPointer; 562 563 // Compare getValueID values. 564 unsigned LID = LV->getValueID(), 565 RID = RV->getValueID(); 566 if (LID != RID) 567 return (int)LID - (int)RID; 568 569 // Sort arguments by their position. 570 if (const Argument *LA = dyn_cast<Argument>(LV)) { 571 const Argument *RA = cast<Argument>(RV); 572 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 573 return (int)LArgNo - (int)RArgNo; 574 } 575 576 // For instructions, compare their loop depth, and their operand 577 // count. This is pretty loose. 578 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 579 const Instruction *RInst = cast<Instruction>(RV); 580 581 // Compare loop depths. 582 const BasicBlock *LParent = LInst->getParent(), 583 *RParent = RInst->getParent(); 584 if (LParent != RParent) { 585 unsigned LDepth = LI->getLoopDepth(LParent), 586 RDepth = LI->getLoopDepth(RParent); 587 if (LDepth != RDepth) 588 return (int)LDepth - (int)RDepth; 589 } 590 591 // Compare the number of operands. 592 unsigned LNumOps = LInst->getNumOperands(), 593 RNumOps = RInst->getNumOperands(); 594 return (int)LNumOps - (int)RNumOps; 595 } 596 597 return 0; 598 } 599 600 case scConstant: { 601 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 602 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 603 604 // Compare constant values. 605 const APInt &LA = LC->getValue()->getValue(); 606 const APInt &RA = RC->getValue()->getValue(); 607 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 608 if (LBitWidth != RBitWidth) 609 return (int)LBitWidth - (int)RBitWidth; 610 return LA.ult(RA) ? -1 : 1; 611 } 612 613 case scAddRecExpr: { 614 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 615 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 616 617 // Compare addrec loop depths. 618 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 619 if (LLoop != RLoop) { 620 unsigned LDepth = LLoop->getLoopDepth(), 621 RDepth = RLoop->getLoopDepth(); 622 if (LDepth != RDepth) 623 return (int)LDepth - (int)RDepth; 624 } 625 626 // Addrec complexity grows with operand count. 627 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 628 if (LNumOps != RNumOps) 629 return (int)LNumOps - (int)RNumOps; 630 631 // Lexicographically compare. 632 for (unsigned i = 0; i != LNumOps; ++i) { 633 long X = compare(LA->getOperand(i), RA->getOperand(i)); 634 if (X != 0) 635 return X; 636 } 637 638 return 0; 639 } 640 641 case scAddExpr: 642 case scMulExpr: 643 case scSMaxExpr: 644 case scUMaxExpr: { 645 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 646 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 647 648 // Lexicographically compare n-ary expressions. 649 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 650 for (unsigned i = 0; i != LNumOps; ++i) { 651 if (i >= RNumOps) 652 return 1; 653 long X = compare(LC->getOperand(i), RC->getOperand(i)); 654 if (X != 0) 655 return X; 656 } 657 return (int)LNumOps - (int)RNumOps; 658 } 659 660 case scUDivExpr: { 661 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 662 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 663 664 // Lexicographically compare udiv expressions. 665 long X = compare(LC->getLHS(), RC->getLHS()); 666 if (X != 0) 667 return X; 668 return compare(LC->getRHS(), RC->getRHS()); 669 } 670 671 case scTruncate: 672 case scZeroExtend: 673 case scSignExtend: { 674 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 675 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 676 677 // Compare cast expressions by operand. 678 return compare(LC->getOperand(), RC->getOperand()); 679 } 680 681 default: 682 break; 683 } 684 685 llvm_unreachable("Unknown SCEV kind!"); 686 return 0; 687 } 688 }; 689} 690 691/// GroupByComplexity - Given a list of SCEV objects, order them by their 692/// complexity, and group objects of the same complexity together by value. 693/// When this routine is finished, we know that any duplicates in the vector are 694/// consecutive and that complexity is monotonically increasing. 695/// 696/// Note that we go take special precautions to ensure that we get deterministic 697/// results from this routine. In other words, we don't want the results of 698/// this to depend on where the addresses of various SCEV objects happened to 699/// land in memory. 700/// 701static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 702 LoopInfo *LI) { 703 if (Ops.size() < 2) return; // Noop 704 if (Ops.size() == 2) { 705 // This is the common case, which also happens to be trivially simple. 706 // Special case it. 707 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 708 if (SCEVComplexityCompare(LI)(RHS, LHS)) 709 std::swap(LHS, RHS); 710 return; 711 } 712 713 // Do the rough sort by complexity. 714 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 715 716 // Now that we are sorted by complexity, group elements of the same 717 // complexity. Note that this is, at worst, N^2, but the vector is likely to 718 // be extremely short in practice. Note that we take this approach because we 719 // do not want to depend on the addresses of the objects we are grouping. 720 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 721 const SCEV *S = Ops[i]; 722 unsigned Complexity = S->getSCEVType(); 723 724 // If there are any objects of the same complexity and same value as this 725 // one, group them. 726 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 727 if (Ops[j] == S) { // Found a duplicate. 728 // Move it to immediately after i'th element. 729 std::swap(Ops[i+1], Ops[j]); 730 ++i; // no need to rescan it. 731 if (i == e-2) return; // Done! 732 } 733 } 734 } 735} 736 737 738 739//===----------------------------------------------------------------------===// 740// Simple SCEV method implementations 741//===----------------------------------------------------------------------===// 742 743/// BinomialCoefficient - Compute BC(It, K). The result has width W. 744/// Assume, K > 0. 745static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 746 ScalarEvolution &SE, 747 const Type* ResultTy) { 748 // Handle the simplest case efficiently. 749 if (K == 1) 750 return SE.getTruncateOrZeroExtend(It, ResultTy); 751 752 // We are using the following formula for BC(It, K): 753 // 754 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 755 // 756 // Suppose, W is the bitwidth of the return value. We must be prepared for 757 // overflow. Hence, we must assure that the result of our computation is 758 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 759 // safe in modular arithmetic. 760 // 761 // However, this code doesn't use exactly that formula; the formula it uses 762 // is something like the following, where T is the number of factors of 2 in 763 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 764 // exponentiation: 765 // 766 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 767 // 768 // This formula is trivially equivalent to the previous formula. However, 769 // this formula can be implemented much more efficiently. The trick is that 770 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 771 // arithmetic. To do exact division in modular arithmetic, all we have 772 // to do is multiply by the inverse. Therefore, this step can be done at 773 // width W. 774 // 775 // The next issue is how to safely do the division by 2^T. The way this 776 // is done is by doing the multiplication step at a width of at least W + T 777 // bits. This way, the bottom W+T bits of the product are accurate. Then, 778 // when we perform the division by 2^T (which is equivalent to a right shift 779 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 780 // truncated out after the division by 2^T. 781 // 782 // In comparison to just directly using the first formula, this technique 783 // is much more efficient; using the first formula requires W * K bits, 784 // but this formula less than W + K bits. Also, the first formula requires 785 // a division step, whereas this formula only requires multiplies and shifts. 786 // 787 // It doesn't matter whether the subtraction step is done in the calculation 788 // width or the input iteration count's width; if the subtraction overflows, 789 // the result must be zero anyway. We prefer here to do it in the width of 790 // the induction variable because it helps a lot for certain cases; CodeGen 791 // isn't smart enough to ignore the overflow, which leads to much less 792 // efficient code if the width of the subtraction is wider than the native 793 // register width. 794 // 795 // (It's possible to not widen at all by pulling out factors of 2 before 796 // the multiplication; for example, K=2 can be calculated as 797 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 798 // extra arithmetic, so it's not an obvious win, and it gets 799 // much more complicated for K > 3.) 800 801 // Protection from insane SCEVs; this bound is conservative, 802 // but it probably doesn't matter. 803 if (K > 1000) 804 return SE.getCouldNotCompute(); 805 806 unsigned W = SE.getTypeSizeInBits(ResultTy); 807 808 // Calculate K! / 2^T and T; we divide out the factors of two before 809 // multiplying for calculating K! / 2^T to avoid overflow. 810 // Other overflow doesn't matter because we only care about the bottom 811 // W bits of the result. 812 APInt OddFactorial(W, 1); 813 unsigned T = 1; 814 for (unsigned i = 3; i <= K; ++i) { 815 APInt Mult(W, i); 816 unsigned TwoFactors = Mult.countTrailingZeros(); 817 T += TwoFactors; 818 Mult = Mult.lshr(TwoFactors); 819 OddFactorial *= Mult; 820 } 821 822 // We need at least W + T bits for the multiplication step 823 unsigned CalculationBits = W + T; 824 825 // Calculate 2^T, at width T+W. 826 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 827 828 // Calculate the multiplicative inverse of K! / 2^T; 829 // this multiplication factor will perform the exact division by 830 // K! / 2^T. 831 APInt Mod = APInt::getSignedMinValue(W+1); 832 APInt MultiplyFactor = OddFactorial.zext(W+1); 833 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 834 MultiplyFactor = MultiplyFactor.trunc(W); 835 836 // Calculate the product, at width T+W 837 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 838 CalculationBits); 839 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 840 for (unsigned i = 1; i != K; ++i) { 841 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 842 Dividend = SE.getMulExpr(Dividend, 843 SE.getTruncateOrZeroExtend(S, CalculationTy)); 844 } 845 846 // Divide by 2^T 847 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 848 849 // Truncate the result, and divide by K! / 2^T. 850 851 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 852 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 853} 854 855/// evaluateAtIteration - Return the value of this chain of recurrences at 856/// the specified iteration number. We can evaluate this recurrence by 857/// multiplying each element in the chain by the binomial coefficient 858/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 859/// 860/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 861/// 862/// where BC(It, k) stands for binomial coefficient. 863/// 864const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 865 ScalarEvolution &SE) const { 866 const SCEV *Result = getStart(); 867 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 868 // The computation is correct in the face of overflow provided that the 869 // multiplication is performed _after_ the evaluation of the binomial 870 // coefficient. 871 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 872 if (isa<SCEVCouldNotCompute>(Coeff)) 873 return Coeff; 874 875 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 876 } 877 return Result; 878} 879 880//===----------------------------------------------------------------------===// 881// SCEV Expression folder implementations 882//===----------------------------------------------------------------------===// 883 884const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 885 const Type *Ty) { 886 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 887 "This is not a truncating conversion!"); 888 assert(isSCEVable(Ty) && 889 "This is not a conversion to a SCEVable type!"); 890 Ty = getEffectiveSCEVType(Ty); 891 892 FoldingSetNodeID ID; 893 ID.AddInteger(scTruncate); 894 ID.AddPointer(Op); 895 ID.AddPointer(Ty); 896 void *IP = 0; 897 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 898 899 // Fold if the operand is constant. 900 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 901 return getConstant( 902 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 903 getEffectiveSCEVType(Ty)))); 904 905 // trunc(trunc(x)) --> trunc(x) 906 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 907 return getTruncateExpr(ST->getOperand(), Ty); 908 909 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 910 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 911 return getTruncateOrSignExtend(SS->getOperand(), Ty); 912 913 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 915 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 916 917 // If the input value is a chrec scev, truncate the chrec's operands. 918 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 919 SmallVector<const SCEV *, 4> Operands; 920 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 921 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 922 return getAddRecExpr(Operands, AddRec->getLoop()); 923 } 924 925 // As a special case, fold trunc(undef) to undef. We don't want to 926 // know too much about SCEVUnknowns, but this special case is handy 927 // and harmless. 928 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 929 if (isa<UndefValue>(U->getValue())) 930 return getSCEV(UndefValue::get(Ty)); 931 932 // The cast wasn't folded; create an explicit cast node. We can reuse 933 // the existing insert position since if we get here, we won't have 934 // made any changes which would invalidate it. 935 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 936 Op, Ty); 937 UniqueSCEVs.InsertNode(S, IP); 938 return S; 939} 940 941const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 942 const Type *Ty) { 943 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 944 "This is not an extending conversion!"); 945 assert(isSCEVable(Ty) && 946 "This is not a conversion to a SCEVable type!"); 947 Ty = getEffectiveSCEVType(Ty); 948 949 // Fold if the operand is constant. 950 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 951 return getConstant( 952 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 953 getEffectiveSCEVType(Ty)))); 954 955 // zext(zext(x)) --> zext(x) 956 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 957 return getZeroExtendExpr(SZ->getOperand(), Ty); 958 959 // Before doing any expensive analysis, check to see if we've already 960 // computed a SCEV for this Op and Ty. 961 FoldingSetNodeID ID; 962 ID.AddInteger(scZeroExtend); 963 ID.AddPointer(Op); 964 ID.AddPointer(Ty); 965 void *IP = 0; 966 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 967 968 // If the input value is a chrec scev, and we can prove that the value 969 // did not overflow the old, smaller, value, we can zero extend all of the 970 // operands (often constants). This allows analysis of something like 971 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 972 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 973 if (AR->isAffine()) { 974 const SCEV *Start = AR->getStart(); 975 const SCEV *Step = AR->getStepRecurrence(*this); 976 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 977 const Loop *L = AR->getLoop(); 978 979 // If we have special knowledge that this addrec won't overflow, 980 // we don't need to do any further analysis. 981 if (AR->hasNoUnsignedWrap()) 982 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 983 getZeroExtendExpr(Step, Ty), 984 L); 985 986 // Check whether the backedge-taken count is SCEVCouldNotCompute. 987 // Note that this serves two purposes: It filters out loops that are 988 // simply not analyzable, and it covers the case where this code is 989 // being called from within backedge-taken count analysis, such that 990 // attempting to ask for the backedge-taken count would likely result 991 // in infinite recursion. In the later case, the analysis code will 992 // cope with a conservative value, and it will take care to purge 993 // that value once it has finished. 994 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 995 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 996 // Manually compute the final value for AR, checking for 997 // overflow. 998 999 // Check whether the backedge-taken count can be losslessly casted to 1000 // the addrec's type. The count is always unsigned. 1001 const SCEV *CastedMaxBECount = 1002 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1003 const SCEV *RecastedMaxBECount = 1004 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1005 if (MaxBECount == RecastedMaxBECount) { 1006 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1007 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1008 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1009 const SCEV *Add = getAddExpr(Start, ZMul); 1010 const SCEV *OperandExtendedAdd = 1011 getAddExpr(getZeroExtendExpr(Start, WideTy), 1012 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1013 getZeroExtendExpr(Step, WideTy))); 1014 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1015 // Return the expression with the addrec on the outside. 1016 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1017 getZeroExtendExpr(Step, Ty), 1018 L); 1019 1020 // Similar to above, only this time treat the step value as signed. 1021 // This covers loops that count down. 1022 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1023 Add = getAddExpr(Start, SMul); 1024 OperandExtendedAdd = 1025 getAddExpr(getZeroExtendExpr(Start, WideTy), 1026 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1027 getSignExtendExpr(Step, WideTy))); 1028 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1029 // Return the expression with the addrec on the outside. 1030 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1031 getSignExtendExpr(Step, Ty), 1032 L); 1033 } 1034 1035 // If the backedge is guarded by a comparison with the pre-inc value 1036 // the addrec is safe. Also, if the entry is guarded by a comparison 1037 // with the start value and the backedge is guarded by a comparison 1038 // with the post-inc value, the addrec is safe. 1039 if (isKnownPositive(Step)) { 1040 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1041 getUnsignedRange(Step).getUnsignedMax()); 1042 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1043 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1044 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1045 AR->getPostIncExpr(*this), N))) 1046 // Return the expression with the addrec on the outside. 1047 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1048 getZeroExtendExpr(Step, Ty), 1049 L); 1050 } else if (isKnownNegative(Step)) { 1051 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1052 getSignedRange(Step).getSignedMin()); 1053 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1054 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1055 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1056 AR->getPostIncExpr(*this), N))) 1057 // Return the expression with the addrec on the outside. 1058 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1059 getSignExtendExpr(Step, Ty), 1060 L); 1061 } 1062 } 1063 } 1064 1065 // The cast wasn't folded; create an explicit cast node. 1066 // Recompute the insert position, as it may have been invalidated. 1067 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1068 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1069 Op, Ty); 1070 UniqueSCEVs.InsertNode(S, IP); 1071 return S; 1072} 1073 1074const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1075 const Type *Ty) { 1076 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1077 "This is not an extending conversion!"); 1078 assert(isSCEVable(Ty) && 1079 "This is not a conversion to a SCEVable type!"); 1080 Ty = getEffectiveSCEVType(Ty); 1081 1082 // Fold if the operand is constant. 1083 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1084 return getConstant( 1085 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1086 getEffectiveSCEVType(Ty)))); 1087 1088 // sext(sext(x)) --> sext(x) 1089 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1090 return getSignExtendExpr(SS->getOperand(), Ty); 1091 1092 // Before doing any expensive analysis, check to see if we've already 1093 // computed a SCEV for this Op and Ty. 1094 FoldingSetNodeID ID; 1095 ID.AddInteger(scSignExtend); 1096 ID.AddPointer(Op); 1097 ID.AddPointer(Ty); 1098 void *IP = 0; 1099 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1100 1101 // If the input value is a chrec scev, and we can prove that the value 1102 // did not overflow the old, smaller, value, we can sign extend all of the 1103 // operands (often constants). This allows analysis of something like 1104 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1105 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1106 if (AR->isAffine()) { 1107 const SCEV *Start = AR->getStart(); 1108 const SCEV *Step = AR->getStepRecurrence(*this); 1109 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1110 const Loop *L = AR->getLoop(); 1111 1112 // If we have special knowledge that this addrec won't overflow, 1113 // we don't need to do any further analysis. 1114 if (AR->hasNoSignedWrap()) 1115 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1116 getSignExtendExpr(Step, Ty), 1117 L); 1118 1119 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1120 // Note that this serves two purposes: It filters out loops that are 1121 // simply not analyzable, and it covers the case where this code is 1122 // being called from within backedge-taken count analysis, such that 1123 // attempting to ask for the backedge-taken count would likely result 1124 // in infinite recursion. In the later case, the analysis code will 1125 // cope with a conservative value, and it will take care to purge 1126 // that value once it has finished. 1127 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1128 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1129 // Manually compute the final value for AR, checking for 1130 // overflow. 1131 1132 // Check whether the backedge-taken count can be losslessly casted to 1133 // the addrec's type. The count is always unsigned. 1134 const SCEV *CastedMaxBECount = 1135 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1136 const SCEV *RecastedMaxBECount = 1137 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1138 if (MaxBECount == RecastedMaxBECount) { 1139 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1140 // Check whether Start+Step*MaxBECount has no signed overflow. 1141 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1142 const SCEV *Add = getAddExpr(Start, SMul); 1143 const SCEV *OperandExtendedAdd = 1144 getAddExpr(getSignExtendExpr(Start, WideTy), 1145 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1146 getSignExtendExpr(Step, WideTy))); 1147 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1148 // Return the expression with the addrec on the outside. 1149 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1150 getSignExtendExpr(Step, Ty), 1151 L); 1152 1153 // Similar to above, only this time treat the step value as unsigned. 1154 // This covers loops that count up with an unsigned step. 1155 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1156 Add = getAddExpr(Start, UMul); 1157 OperandExtendedAdd = 1158 getAddExpr(getSignExtendExpr(Start, WideTy), 1159 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1160 getZeroExtendExpr(Step, WideTy))); 1161 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1162 // Return the expression with the addrec on the outside. 1163 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1164 getZeroExtendExpr(Step, Ty), 1165 L); 1166 } 1167 1168 // If the backedge is guarded by a comparison with the pre-inc value 1169 // the addrec is safe. Also, if the entry is guarded by a comparison 1170 // with the start value and the backedge is guarded by a comparison 1171 // with the post-inc value, the addrec is safe. 1172 if (isKnownPositive(Step)) { 1173 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1174 getSignedRange(Step).getSignedMax()); 1175 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1176 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1177 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1178 AR->getPostIncExpr(*this), N))) 1179 // Return the expression with the addrec on the outside. 1180 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1181 getSignExtendExpr(Step, Ty), 1182 L); 1183 } else if (isKnownNegative(Step)) { 1184 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1185 getSignedRange(Step).getSignedMin()); 1186 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1187 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1188 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1189 AR->getPostIncExpr(*this), N))) 1190 // Return the expression with the addrec on the outside. 1191 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1192 getSignExtendExpr(Step, Ty), 1193 L); 1194 } 1195 } 1196 } 1197 1198 // The cast wasn't folded; create an explicit cast node. 1199 // Recompute the insert position, as it may have been invalidated. 1200 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1201 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1202 Op, Ty); 1203 UniqueSCEVs.InsertNode(S, IP); 1204 return S; 1205} 1206 1207/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1208/// unspecified bits out to the given type. 1209/// 1210const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1211 const Type *Ty) { 1212 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1213 "This is not an extending conversion!"); 1214 assert(isSCEVable(Ty) && 1215 "This is not a conversion to a SCEVable type!"); 1216 Ty = getEffectiveSCEVType(Ty); 1217 1218 // Sign-extend negative constants. 1219 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1220 if (SC->getValue()->getValue().isNegative()) 1221 return getSignExtendExpr(Op, Ty); 1222 1223 // Peel off a truncate cast. 1224 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1225 const SCEV *NewOp = T->getOperand(); 1226 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1227 return getAnyExtendExpr(NewOp, Ty); 1228 return getTruncateOrNoop(NewOp, Ty); 1229 } 1230 1231 // Next try a zext cast. If the cast is folded, use it. 1232 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1233 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1234 return ZExt; 1235 1236 // Next try a sext cast. If the cast is folded, use it. 1237 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1238 if (!isa<SCEVSignExtendExpr>(SExt)) 1239 return SExt; 1240 1241 // Force the cast to be folded into the operands of an addrec. 1242 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1243 SmallVector<const SCEV *, 4> Ops; 1244 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1245 I != E; ++I) 1246 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1247 return getAddRecExpr(Ops, AR->getLoop()); 1248 } 1249 1250 // As a special case, fold anyext(undef) to undef. We don't want to 1251 // know too much about SCEVUnknowns, but this special case is handy 1252 // and harmless. 1253 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1254 if (isa<UndefValue>(U->getValue())) 1255 return getSCEV(UndefValue::get(Ty)); 1256 1257 // If the expression is obviously signed, use the sext cast value. 1258 if (isa<SCEVSMaxExpr>(Op)) 1259 return SExt; 1260 1261 // Absent any other information, use the zext cast value. 1262 return ZExt; 1263} 1264 1265/// CollectAddOperandsWithScales - Process the given Ops list, which is 1266/// a list of operands to be added under the given scale, update the given 1267/// map. This is a helper function for getAddRecExpr. As an example of 1268/// what it does, given a sequence of operands that would form an add 1269/// expression like this: 1270/// 1271/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1272/// 1273/// where A and B are constants, update the map with these values: 1274/// 1275/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1276/// 1277/// and add 13 + A*B*29 to AccumulatedConstant. 1278/// This will allow getAddRecExpr to produce this: 1279/// 1280/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1281/// 1282/// This form often exposes folding opportunities that are hidden in 1283/// the original operand list. 1284/// 1285/// Return true iff it appears that any interesting folding opportunities 1286/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1287/// the common case where no interesting opportunities are present, and 1288/// is also used as a check to avoid infinite recursion. 1289/// 1290static bool 1291CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1292 SmallVector<const SCEV *, 8> &NewOps, 1293 APInt &AccumulatedConstant, 1294 const SCEV *const *Ops, size_t NumOperands, 1295 const APInt &Scale, 1296 ScalarEvolution &SE) { 1297 bool Interesting = false; 1298 1299 // Iterate over the add operands. They are sorted, with constants first. 1300 unsigned i = 0; 1301 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1302 ++i; 1303 // Pull a buried constant out to the outside. 1304 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1305 Interesting = true; 1306 AccumulatedConstant += Scale * C->getValue()->getValue(); 1307 } 1308 1309 // Next comes everything else. We're especially interested in multiplies 1310 // here, but they're in the middle, so just visit the rest with one loop. 1311 for (; i != NumOperands; ++i) { 1312 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1313 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1314 APInt NewScale = 1315 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1316 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1317 // A multiplication of a constant with another add; recurse. 1318 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1319 Interesting |= 1320 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1321 Add->op_begin(), Add->getNumOperands(), 1322 NewScale, SE); 1323 } else { 1324 // A multiplication of a constant with some other value. Update 1325 // the map. 1326 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1327 const SCEV *Key = SE.getMulExpr(MulOps); 1328 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1329 M.insert(std::make_pair(Key, NewScale)); 1330 if (Pair.second) { 1331 NewOps.push_back(Pair.first->first); 1332 } else { 1333 Pair.first->second += NewScale; 1334 // The map already had an entry for this value, which may indicate 1335 // a folding opportunity. 1336 Interesting = true; 1337 } 1338 } 1339 } else { 1340 // An ordinary operand. Update the map. 1341 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1342 M.insert(std::make_pair(Ops[i], Scale)); 1343 if (Pair.second) { 1344 NewOps.push_back(Pair.first->first); 1345 } else { 1346 Pair.first->second += Scale; 1347 // The map already had an entry for this value, which may indicate 1348 // a folding opportunity. 1349 Interesting = true; 1350 } 1351 } 1352 } 1353 1354 return Interesting; 1355} 1356 1357namespace { 1358 struct APIntCompare { 1359 bool operator()(const APInt &LHS, const APInt &RHS) const { 1360 return LHS.ult(RHS); 1361 } 1362 }; 1363} 1364 1365/// getAddExpr - Get a canonical add expression, or something simpler if 1366/// possible. 1367const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1368 bool HasNUW, bool HasNSW) { 1369 assert(!Ops.empty() && "Cannot get empty add!"); 1370 if (Ops.size() == 1) return Ops[0]; 1371#ifndef NDEBUG 1372 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1373 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1374 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1375 "SCEVAddExpr operand types don't match!"); 1376#endif 1377 1378 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1379 if (!HasNUW && HasNSW) { 1380 bool All = true; 1381 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1382 E = Ops.end(); I != E; ++I) 1383 if (!isKnownNonNegative(*I)) { 1384 All = false; 1385 break; 1386 } 1387 if (All) HasNUW = true; 1388 } 1389 1390 // Sort by complexity, this groups all similar expression types together. 1391 GroupByComplexity(Ops, LI); 1392 1393 // If there are any constants, fold them together. 1394 unsigned Idx = 0; 1395 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1396 ++Idx; 1397 assert(Idx < Ops.size()); 1398 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1399 // We found two constants, fold them together! 1400 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1401 RHSC->getValue()->getValue()); 1402 if (Ops.size() == 2) return Ops[0]; 1403 Ops.erase(Ops.begin()+1); // Erase the folded element 1404 LHSC = cast<SCEVConstant>(Ops[0]); 1405 } 1406 1407 // If we are left with a constant zero being added, strip it off. 1408 if (LHSC->getValue()->isZero()) { 1409 Ops.erase(Ops.begin()); 1410 --Idx; 1411 } 1412 1413 if (Ops.size() == 1) return Ops[0]; 1414 } 1415 1416 // Okay, check to see if the same value occurs in the operand list more than 1417 // once. If so, merge them together into an multiply expression. Since we 1418 // sorted the list, these values are required to be adjacent. 1419 const Type *Ty = Ops[0]->getType(); 1420 bool FoundMatch = false; 1421 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1422 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1423 // Scan ahead to count how many equal operands there are. 1424 unsigned Count = 2; 1425 while (i+Count != e && Ops[i+Count] == Ops[i]) 1426 ++Count; 1427 // Merge the values into a multiply. 1428 const SCEV *Scale = getConstant(Ty, Count); 1429 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1430 if (Ops.size() == Count) 1431 return Mul; 1432 Ops[i] = Mul; 1433 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1434 --i; e -= Count - 1; 1435 FoundMatch = true; 1436 } 1437 if (FoundMatch) 1438 return getAddExpr(Ops, HasNUW, HasNSW); 1439 1440 // Check for truncates. If all the operands are truncated from the same 1441 // type, see if factoring out the truncate would permit the result to be 1442 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1443 // if the contents of the resulting outer trunc fold to something simple. 1444 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1445 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1446 const Type *DstType = Trunc->getType(); 1447 const Type *SrcType = Trunc->getOperand()->getType(); 1448 SmallVector<const SCEV *, 8> LargeOps; 1449 bool Ok = true; 1450 // Check all the operands to see if they can be represented in the 1451 // source type of the truncate. 1452 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1453 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1454 if (T->getOperand()->getType() != SrcType) { 1455 Ok = false; 1456 break; 1457 } 1458 LargeOps.push_back(T->getOperand()); 1459 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1460 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1461 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1462 SmallVector<const SCEV *, 8> LargeMulOps; 1463 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1464 if (const SCEVTruncateExpr *T = 1465 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1466 if (T->getOperand()->getType() != SrcType) { 1467 Ok = false; 1468 break; 1469 } 1470 LargeMulOps.push_back(T->getOperand()); 1471 } else if (const SCEVConstant *C = 1472 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1473 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1474 } else { 1475 Ok = false; 1476 break; 1477 } 1478 } 1479 if (Ok) 1480 LargeOps.push_back(getMulExpr(LargeMulOps)); 1481 } else { 1482 Ok = false; 1483 break; 1484 } 1485 } 1486 if (Ok) { 1487 // Evaluate the expression in the larger type. 1488 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1489 // If it folds to something simple, use it. Otherwise, don't. 1490 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1491 return getTruncateExpr(Fold, DstType); 1492 } 1493 } 1494 1495 // Skip past any other cast SCEVs. 1496 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1497 ++Idx; 1498 1499 // If there are add operands they would be next. 1500 if (Idx < Ops.size()) { 1501 bool DeletedAdd = false; 1502 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1503 // If we have an add, expand the add operands onto the end of the operands 1504 // list. 1505 Ops.erase(Ops.begin()+Idx); 1506 Ops.append(Add->op_begin(), Add->op_end()); 1507 DeletedAdd = true; 1508 } 1509 1510 // If we deleted at least one add, we added operands to the end of the list, 1511 // and they are not necessarily sorted. Recurse to resort and resimplify 1512 // any operands we just acquired. 1513 if (DeletedAdd) 1514 return getAddExpr(Ops); 1515 } 1516 1517 // Skip over the add expression until we get to a multiply. 1518 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1519 ++Idx; 1520 1521 // Check to see if there are any folding opportunities present with 1522 // operands multiplied by constant values. 1523 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1524 uint64_t BitWidth = getTypeSizeInBits(Ty); 1525 DenseMap<const SCEV *, APInt> M; 1526 SmallVector<const SCEV *, 8> NewOps; 1527 APInt AccumulatedConstant(BitWidth, 0); 1528 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1529 Ops.data(), Ops.size(), 1530 APInt(BitWidth, 1), *this)) { 1531 // Some interesting folding opportunity is present, so its worthwhile to 1532 // re-generate the operands list. Group the operands by constant scale, 1533 // to avoid multiplying by the same constant scale multiple times. 1534 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1535 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1536 E = NewOps.end(); I != E; ++I) 1537 MulOpLists[M.find(*I)->second].push_back(*I); 1538 // Re-generate the operands list. 1539 Ops.clear(); 1540 if (AccumulatedConstant != 0) 1541 Ops.push_back(getConstant(AccumulatedConstant)); 1542 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1543 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1544 if (I->first != 0) 1545 Ops.push_back(getMulExpr(getConstant(I->first), 1546 getAddExpr(I->second))); 1547 if (Ops.empty()) 1548 return getConstant(Ty, 0); 1549 if (Ops.size() == 1) 1550 return Ops[0]; 1551 return getAddExpr(Ops); 1552 } 1553 } 1554 1555 // If we are adding something to a multiply expression, make sure the 1556 // something is not already an operand of the multiply. If so, merge it into 1557 // the multiply. 1558 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1559 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1560 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1561 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1562 if (isa<SCEVConstant>(MulOpSCEV)) 1563 continue; 1564 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1565 if (MulOpSCEV == Ops[AddOp]) { 1566 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1567 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1568 if (Mul->getNumOperands() != 2) { 1569 // If the multiply has more than two operands, we must get the 1570 // Y*Z term. 1571 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1572 Mul->op_begin()+MulOp); 1573 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1574 InnerMul = getMulExpr(MulOps); 1575 } 1576 const SCEV *One = getConstant(Ty, 1); 1577 const SCEV *AddOne = getAddExpr(One, InnerMul); 1578 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1579 if (Ops.size() == 2) return OuterMul; 1580 if (AddOp < Idx) { 1581 Ops.erase(Ops.begin()+AddOp); 1582 Ops.erase(Ops.begin()+Idx-1); 1583 } else { 1584 Ops.erase(Ops.begin()+Idx); 1585 Ops.erase(Ops.begin()+AddOp-1); 1586 } 1587 Ops.push_back(OuterMul); 1588 return getAddExpr(Ops); 1589 } 1590 1591 // Check this multiply against other multiplies being added together. 1592 bool AnyFold = false; 1593 for (unsigned OtherMulIdx = Idx+1; 1594 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1595 ++OtherMulIdx) { 1596 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1597 // If MulOp occurs in OtherMul, we can fold the two multiplies 1598 // together. 1599 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1600 OMulOp != e; ++OMulOp) 1601 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1602 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1603 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1604 if (Mul->getNumOperands() != 2) { 1605 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1606 Mul->op_begin()+MulOp); 1607 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1608 InnerMul1 = getMulExpr(MulOps); 1609 } 1610 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1611 if (OtherMul->getNumOperands() != 2) { 1612 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1613 OtherMul->op_begin()+OMulOp); 1614 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1615 InnerMul2 = getMulExpr(MulOps); 1616 } 1617 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1618 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1619 if (Ops.size() == 2) return OuterMul; 1620 Ops[Idx] = OuterMul; 1621 Ops.erase(Ops.begin()+OtherMulIdx); 1622 OtherMulIdx = Idx; 1623 AnyFold = true; 1624 } 1625 } 1626 if (AnyFold) 1627 return getAddExpr(Ops); 1628 } 1629 } 1630 1631 // If there are any add recurrences in the operands list, see if any other 1632 // added values are loop invariant. If so, we can fold them into the 1633 // recurrence. 1634 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1635 ++Idx; 1636 1637 // Scan over all recurrences, trying to fold loop invariants into them. 1638 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1639 // Scan all of the other operands to this add and add them to the vector if 1640 // they are loop invariant w.r.t. the recurrence. 1641 SmallVector<const SCEV *, 8> LIOps; 1642 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1643 const Loop *AddRecLoop = AddRec->getLoop(); 1644 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1645 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1646 LIOps.push_back(Ops[i]); 1647 Ops.erase(Ops.begin()+i); 1648 --i; --e; 1649 } 1650 1651 // If we found some loop invariants, fold them into the recurrence. 1652 if (!LIOps.empty()) { 1653 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1654 LIOps.push_back(AddRec->getStart()); 1655 1656 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1657 AddRec->op_end()); 1658 AddRecOps[0] = getAddExpr(LIOps); 1659 1660 // Build the new addrec. Propagate the NUW and NSW flags if both the 1661 // outer add and the inner addrec are guaranteed to have no overflow. 1662 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1663 HasNUW && AddRec->hasNoUnsignedWrap(), 1664 HasNSW && AddRec->hasNoSignedWrap()); 1665 1666 // If all of the other operands were loop invariant, we are done. 1667 if (Ops.size() == 1) return NewRec; 1668 1669 // Otherwise, add the folded AddRec by the non-liv parts. 1670 for (unsigned i = 0;; ++i) 1671 if (Ops[i] == AddRec) { 1672 Ops[i] = NewRec; 1673 break; 1674 } 1675 return getAddExpr(Ops); 1676 } 1677 1678 // Okay, if there weren't any loop invariants to be folded, check to see if 1679 // there are multiple AddRec's with the same loop induction variable being 1680 // added together. If so, we can fold them. 1681 for (unsigned OtherIdx = Idx+1; 1682 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1683 ++OtherIdx) 1684 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1685 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1686 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1687 AddRec->op_end()); 1688 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1689 ++OtherIdx) 1690 if (const SCEVAddRecExpr *OtherAddRec = 1691 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1692 if (OtherAddRec->getLoop() == AddRecLoop) { 1693 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1694 i != e; ++i) { 1695 if (i >= AddRecOps.size()) { 1696 AddRecOps.append(OtherAddRec->op_begin()+i, 1697 OtherAddRec->op_end()); 1698 break; 1699 } 1700 AddRecOps[i] = getAddExpr(AddRecOps[i], 1701 OtherAddRec->getOperand(i)); 1702 } 1703 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1704 } 1705 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1706 return getAddExpr(Ops); 1707 } 1708 1709 // Otherwise couldn't fold anything into this recurrence. Move onto the 1710 // next one. 1711 } 1712 1713 // Okay, it looks like we really DO need an add expr. Check to see if we 1714 // already have one, otherwise create a new one. 1715 FoldingSetNodeID ID; 1716 ID.AddInteger(scAddExpr); 1717 ID.AddInteger(Ops.size()); 1718 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1719 ID.AddPointer(Ops[i]); 1720 void *IP = 0; 1721 SCEVAddExpr *S = 1722 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1723 if (!S) { 1724 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1725 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1726 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1727 O, Ops.size()); 1728 UniqueSCEVs.InsertNode(S, IP); 1729 } 1730 if (HasNUW) S->setHasNoUnsignedWrap(true); 1731 if (HasNSW) S->setHasNoSignedWrap(true); 1732 return S; 1733} 1734 1735/// getMulExpr - Get a canonical multiply expression, or something simpler if 1736/// possible. 1737const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1738 bool HasNUW, bool HasNSW) { 1739 assert(!Ops.empty() && "Cannot get empty mul!"); 1740 if (Ops.size() == 1) return Ops[0]; 1741#ifndef NDEBUG 1742 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1743 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1744 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1745 "SCEVMulExpr operand types don't match!"); 1746#endif 1747 1748 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1749 if (!HasNUW && HasNSW) { 1750 bool All = true; 1751 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1752 E = Ops.end(); I != E; ++I) 1753 if (!isKnownNonNegative(*I)) { 1754 All = false; 1755 break; 1756 } 1757 if (All) HasNUW = true; 1758 } 1759 1760 // Sort by complexity, this groups all similar expression types together. 1761 GroupByComplexity(Ops, LI); 1762 1763 // If there are any constants, fold them together. 1764 unsigned Idx = 0; 1765 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1766 1767 // C1*(C2+V) -> C1*C2 + C1*V 1768 if (Ops.size() == 2) 1769 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1770 if (Add->getNumOperands() == 2 && 1771 isa<SCEVConstant>(Add->getOperand(0))) 1772 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1773 getMulExpr(LHSC, Add->getOperand(1))); 1774 1775 ++Idx; 1776 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1777 // We found two constants, fold them together! 1778 ConstantInt *Fold = ConstantInt::get(getContext(), 1779 LHSC->getValue()->getValue() * 1780 RHSC->getValue()->getValue()); 1781 Ops[0] = getConstant(Fold); 1782 Ops.erase(Ops.begin()+1); // Erase the folded element 1783 if (Ops.size() == 1) return Ops[0]; 1784 LHSC = cast<SCEVConstant>(Ops[0]); 1785 } 1786 1787 // If we are left with a constant one being multiplied, strip it off. 1788 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1789 Ops.erase(Ops.begin()); 1790 --Idx; 1791 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1792 // If we have a multiply of zero, it will always be zero. 1793 return Ops[0]; 1794 } else if (Ops[0]->isAllOnesValue()) { 1795 // If we have a mul by -1 of an add, try distributing the -1 among the 1796 // add operands. 1797 if (Ops.size() == 2) 1798 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1799 SmallVector<const SCEV *, 4> NewOps; 1800 bool AnyFolded = false; 1801 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1802 I != E; ++I) { 1803 const SCEV *Mul = getMulExpr(Ops[0], *I); 1804 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1805 NewOps.push_back(Mul); 1806 } 1807 if (AnyFolded) 1808 return getAddExpr(NewOps); 1809 } 1810 } 1811 1812 if (Ops.size() == 1) 1813 return Ops[0]; 1814 } 1815 1816 // Skip over the add expression until we get to a multiply. 1817 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1818 ++Idx; 1819 1820 // If there are mul operands inline them all into this expression. 1821 if (Idx < Ops.size()) { 1822 bool DeletedMul = false; 1823 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1824 // If we have an mul, expand the mul operands onto the end of the operands 1825 // list. 1826 Ops.erase(Ops.begin()+Idx); 1827 Ops.append(Mul->op_begin(), Mul->op_end()); 1828 DeletedMul = true; 1829 } 1830 1831 // If we deleted at least one mul, we added operands to the end of the list, 1832 // and they are not necessarily sorted. Recurse to resort and resimplify 1833 // any operands we just acquired. 1834 if (DeletedMul) 1835 return getMulExpr(Ops); 1836 } 1837 1838 // If there are any add recurrences in the operands list, see if any other 1839 // added values are loop invariant. If so, we can fold them into the 1840 // recurrence. 1841 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1842 ++Idx; 1843 1844 // Scan over all recurrences, trying to fold loop invariants into them. 1845 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1846 // Scan all of the other operands to this mul and add them to the vector if 1847 // they are loop invariant w.r.t. the recurrence. 1848 SmallVector<const SCEV *, 8> LIOps; 1849 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1850 const Loop *AddRecLoop = AddRec->getLoop(); 1851 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1852 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1853 LIOps.push_back(Ops[i]); 1854 Ops.erase(Ops.begin()+i); 1855 --i; --e; 1856 } 1857 1858 // If we found some loop invariants, fold them into the recurrence. 1859 if (!LIOps.empty()) { 1860 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1861 SmallVector<const SCEV *, 4> NewOps; 1862 NewOps.reserve(AddRec->getNumOperands()); 1863 const SCEV *Scale = getMulExpr(LIOps); 1864 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1865 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1866 1867 // Build the new addrec. Propagate the NUW and NSW flags if both the 1868 // outer mul and the inner addrec are guaranteed to have no overflow. 1869 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, 1870 HasNUW && AddRec->hasNoUnsignedWrap(), 1871 HasNSW && AddRec->hasNoSignedWrap()); 1872 1873 // If all of the other operands were loop invariant, we are done. 1874 if (Ops.size() == 1) return NewRec; 1875 1876 // Otherwise, multiply the folded AddRec by the non-liv parts. 1877 for (unsigned i = 0;; ++i) 1878 if (Ops[i] == AddRec) { 1879 Ops[i] = NewRec; 1880 break; 1881 } 1882 return getMulExpr(Ops); 1883 } 1884 1885 // Okay, if there weren't any loop invariants to be folded, check to see if 1886 // there are multiple AddRec's with the same loop induction variable being 1887 // multiplied together. If so, we can fold them. 1888 for (unsigned OtherIdx = Idx+1; 1889 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1890 ++OtherIdx) 1891 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1892 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1893 // {A*C,+,F*D + G*B + B*D}<L> 1894 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1895 ++OtherIdx) 1896 if (const SCEVAddRecExpr *OtherAddRec = 1897 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1898 if (OtherAddRec->getLoop() == AddRecLoop) { 1899 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1900 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1901 const SCEV *B = F->getStepRecurrence(*this); 1902 const SCEV *D = G->getStepRecurrence(*this); 1903 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1904 getMulExpr(G, B), 1905 getMulExpr(B, D)); 1906 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1907 F->getLoop()); 1908 if (Ops.size() == 2) return NewAddRec; 1909 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1910 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1911 } 1912 return getMulExpr(Ops); 1913 } 1914 1915 // Otherwise couldn't fold anything into this recurrence. Move onto the 1916 // next one. 1917 } 1918 1919 // Okay, it looks like we really DO need an mul expr. Check to see if we 1920 // already have one, otherwise create a new one. 1921 FoldingSetNodeID ID; 1922 ID.AddInteger(scMulExpr); 1923 ID.AddInteger(Ops.size()); 1924 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1925 ID.AddPointer(Ops[i]); 1926 void *IP = 0; 1927 SCEVMulExpr *S = 1928 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1929 if (!S) { 1930 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1931 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1932 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1933 O, Ops.size()); 1934 UniqueSCEVs.InsertNode(S, IP); 1935 } 1936 if (HasNUW) S->setHasNoUnsignedWrap(true); 1937 if (HasNSW) S->setHasNoSignedWrap(true); 1938 return S; 1939} 1940 1941/// getUDivExpr - Get a canonical unsigned division expression, or something 1942/// simpler if possible. 1943const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1944 const SCEV *RHS) { 1945 assert(getEffectiveSCEVType(LHS->getType()) == 1946 getEffectiveSCEVType(RHS->getType()) && 1947 "SCEVUDivExpr operand types don't match!"); 1948 1949 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1950 if (RHSC->getValue()->equalsInt(1)) 1951 return LHS; // X udiv 1 --> x 1952 // If the denominator is zero, the result of the udiv is undefined. Don't 1953 // try to analyze it, because the resolution chosen here may differ from 1954 // the resolution chosen in other parts of the compiler. 1955 if (!RHSC->getValue()->isZero()) { 1956 // Determine if the division can be folded into the operands of 1957 // its operands. 1958 // TODO: Generalize this to non-constants by using known-bits information. 1959 const Type *Ty = LHS->getType(); 1960 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1961 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1962 // For non-power-of-two values, effectively round the value up to the 1963 // nearest power of two. 1964 if (!RHSC->getValue()->getValue().isPowerOf2()) 1965 ++MaxShiftAmt; 1966 const IntegerType *ExtTy = 1967 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1968 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1969 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1970 if (const SCEVConstant *Step = 1971 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1972 if (!Step->getValue()->getValue() 1973 .urem(RHSC->getValue()->getValue()) && 1974 getZeroExtendExpr(AR, ExtTy) == 1975 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1976 getZeroExtendExpr(Step, ExtTy), 1977 AR->getLoop())) { 1978 SmallVector<const SCEV *, 4> Operands; 1979 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1980 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1981 return getAddRecExpr(Operands, AR->getLoop()); 1982 } 1983 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1984 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1985 SmallVector<const SCEV *, 4> Operands; 1986 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1987 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1988 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1989 // Find an operand that's safely divisible. 1990 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1991 const SCEV *Op = M->getOperand(i); 1992 const SCEV *Div = getUDivExpr(Op, RHSC); 1993 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1994 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1995 M->op_end()); 1996 Operands[i] = Div; 1997 return getMulExpr(Operands); 1998 } 1999 } 2000 } 2001 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2002 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 2003 SmallVector<const SCEV *, 4> Operands; 2004 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2005 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2006 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2007 Operands.clear(); 2008 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2009 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2010 if (isa<SCEVUDivExpr>(Op) || 2011 getMulExpr(Op, RHS) != A->getOperand(i)) 2012 break; 2013 Operands.push_back(Op); 2014 } 2015 if (Operands.size() == A->getNumOperands()) 2016 return getAddExpr(Operands); 2017 } 2018 } 2019 2020 // Fold if both operands are constant. 2021 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2022 Constant *LHSCV = LHSC->getValue(); 2023 Constant *RHSCV = RHSC->getValue(); 2024 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2025 RHSCV))); 2026 } 2027 } 2028 } 2029 2030 FoldingSetNodeID ID; 2031 ID.AddInteger(scUDivExpr); 2032 ID.AddPointer(LHS); 2033 ID.AddPointer(RHS); 2034 void *IP = 0; 2035 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2036 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2037 LHS, RHS); 2038 UniqueSCEVs.InsertNode(S, IP); 2039 return S; 2040} 2041 2042 2043/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2044/// Simplify the expression as much as possible. 2045const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2046 const SCEV *Step, const Loop *L, 2047 bool HasNUW, bool HasNSW) { 2048 SmallVector<const SCEV *, 4> Operands; 2049 Operands.push_back(Start); 2050 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2051 if (StepChrec->getLoop() == L) { 2052 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2053 return getAddRecExpr(Operands, L); 2054 } 2055 2056 Operands.push_back(Step); 2057 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2058} 2059 2060/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2061/// Simplify the expression as much as possible. 2062const SCEV * 2063ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2064 const Loop *L, 2065 bool HasNUW, bool HasNSW) { 2066 if (Operands.size() == 1) return Operands[0]; 2067#ifndef NDEBUG 2068 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2069 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2070 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2071 "SCEVAddRecExpr operand types don't match!"); 2072#endif 2073 2074 if (Operands.back()->isZero()) { 2075 Operands.pop_back(); 2076 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2077 } 2078 2079 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2080 // use that information to infer NUW and NSW flags. However, computing a 2081 // BE count requires calling getAddRecExpr, so we may not yet have a 2082 // meaningful BE count at this point (and if we don't, we'd be stuck 2083 // with a SCEVCouldNotCompute as the cached BE count). 2084 2085 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2086 if (!HasNUW && HasNSW) { 2087 bool All = true; 2088 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2089 E = Operands.end(); I != E; ++I) 2090 if (!isKnownNonNegative(*I)) { 2091 All = false; 2092 break; 2093 } 2094 if (All) HasNUW = true; 2095 } 2096 2097 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2098 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2099 const Loop *NestedLoop = NestedAR->getLoop(); 2100 if (L->contains(NestedLoop) ? 2101 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2102 (!NestedLoop->contains(L) && 2103 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2104 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2105 NestedAR->op_end()); 2106 Operands[0] = NestedAR->getStart(); 2107 // AddRecs require their operands be loop-invariant with respect to their 2108 // loops. Don't perform this transformation if it would break this 2109 // requirement. 2110 bool AllInvariant = true; 2111 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2112 if (!Operands[i]->isLoopInvariant(L)) { 2113 AllInvariant = false; 2114 break; 2115 } 2116 if (AllInvariant) { 2117 NestedOperands[0] = getAddRecExpr(Operands, L); 2118 AllInvariant = true; 2119 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2120 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2121 AllInvariant = false; 2122 break; 2123 } 2124 if (AllInvariant) 2125 // Ok, both add recurrences are valid after the transformation. 2126 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2127 } 2128 // Reset Operands to its original state. 2129 Operands[0] = NestedAR; 2130 } 2131 } 2132 2133 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2134 // already have one, otherwise create a new one. 2135 FoldingSetNodeID ID; 2136 ID.AddInteger(scAddRecExpr); 2137 ID.AddInteger(Operands.size()); 2138 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2139 ID.AddPointer(Operands[i]); 2140 ID.AddPointer(L); 2141 void *IP = 0; 2142 SCEVAddRecExpr *S = 2143 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2144 if (!S) { 2145 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2146 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2147 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2148 O, Operands.size(), L); 2149 UniqueSCEVs.InsertNode(S, IP); 2150 } 2151 if (HasNUW) S->setHasNoUnsignedWrap(true); 2152 if (HasNSW) S->setHasNoSignedWrap(true); 2153 return S; 2154} 2155 2156const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2157 const SCEV *RHS) { 2158 SmallVector<const SCEV *, 2> Ops; 2159 Ops.push_back(LHS); 2160 Ops.push_back(RHS); 2161 return getSMaxExpr(Ops); 2162} 2163 2164const SCEV * 2165ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2166 assert(!Ops.empty() && "Cannot get empty smax!"); 2167 if (Ops.size() == 1) return Ops[0]; 2168#ifndef NDEBUG 2169 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2170 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2171 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2172 "SCEVSMaxExpr operand types don't match!"); 2173#endif 2174 2175 // Sort by complexity, this groups all similar expression types together. 2176 GroupByComplexity(Ops, LI); 2177 2178 // If there are any constants, fold them together. 2179 unsigned Idx = 0; 2180 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2181 ++Idx; 2182 assert(Idx < Ops.size()); 2183 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2184 // We found two constants, fold them together! 2185 ConstantInt *Fold = ConstantInt::get(getContext(), 2186 APIntOps::smax(LHSC->getValue()->getValue(), 2187 RHSC->getValue()->getValue())); 2188 Ops[0] = getConstant(Fold); 2189 Ops.erase(Ops.begin()+1); // Erase the folded element 2190 if (Ops.size() == 1) return Ops[0]; 2191 LHSC = cast<SCEVConstant>(Ops[0]); 2192 } 2193 2194 // If we are left with a constant minimum-int, strip it off. 2195 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2196 Ops.erase(Ops.begin()); 2197 --Idx; 2198 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2199 // If we have an smax with a constant maximum-int, it will always be 2200 // maximum-int. 2201 return Ops[0]; 2202 } 2203 2204 if (Ops.size() == 1) return Ops[0]; 2205 } 2206 2207 // Find the first SMax 2208 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2209 ++Idx; 2210 2211 // Check to see if one of the operands is an SMax. If so, expand its operands 2212 // onto our operand list, and recurse to simplify. 2213 if (Idx < Ops.size()) { 2214 bool DeletedSMax = false; 2215 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2216 Ops.erase(Ops.begin()+Idx); 2217 Ops.append(SMax->op_begin(), SMax->op_end()); 2218 DeletedSMax = true; 2219 } 2220 2221 if (DeletedSMax) 2222 return getSMaxExpr(Ops); 2223 } 2224 2225 // Okay, check to see if the same value occurs in the operand list twice. If 2226 // so, delete one. Since we sorted the list, these values are required to 2227 // be adjacent. 2228 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2229 // X smax Y smax Y --> X smax Y 2230 // X smax Y --> X, if X is always greater than Y 2231 if (Ops[i] == Ops[i+1] || 2232 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2233 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2234 --i; --e; 2235 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2236 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2237 --i; --e; 2238 } 2239 2240 if (Ops.size() == 1) return Ops[0]; 2241 2242 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2243 2244 // Okay, it looks like we really DO need an smax expr. Check to see if we 2245 // already have one, otherwise create a new one. 2246 FoldingSetNodeID ID; 2247 ID.AddInteger(scSMaxExpr); 2248 ID.AddInteger(Ops.size()); 2249 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2250 ID.AddPointer(Ops[i]); 2251 void *IP = 0; 2252 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2253 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2254 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2255 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2256 O, Ops.size()); 2257 UniqueSCEVs.InsertNode(S, IP); 2258 return S; 2259} 2260 2261const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2262 const SCEV *RHS) { 2263 SmallVector<const SCEV *, 2> Ops; 2264 Ops.push_back(LHS); 2265 Ops.push_back(RHS); 2266 return getUMaxExpr(Ops); 2267} 2268 2269const SCEV * 2270ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2271 assert(!Ops.empty() && "Cannot get empty umax!"); 2272 if (Ops.size() == 1) return Ops[0]; 2273#ifndef NDEBUG 2274 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2275 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2276 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2277 "SCEVUMaxExpr operand types don't match!"); 2278#endif 2279 2280 // Sort by complexity, this groups all similar expression types together. 2281 GroupByComplexity(Ops, LI); 2282 2283 // If there are any constants, fold them together. 2284 unsigned Idx = 0; 2285 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2286 ++Idx; 2287 assert(Idx < Ops.size()); 2288 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2289 // We found two constants, fold them together! 2290 ConstantInt *Fold = ConstantInt::get(getContext(), 2291 APIntOps::umax(LHSC->getValue()->getValue(), 2292 RHSC->getValue()->getValue())); 2293 Ops[0] = getConstant(Fold); 2294 Ops.erase(Ops.begin()+1); // Erase the folded element 2295 if (Ops.size() == 1) return Ops[0]; 2296 LHSC = cast<SCEVConstant>(Ops[0]); 2297 } 2298 2299 // If we are left with a constant minimum-int, strip it off. 2300 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2301 Ops.erase(Ops.begin()); 2302 --Idx; 2303 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2304 // If we have an umax with a constant maximum-int, it will always be 2305 // maximum-int. 2306 return Ops[0]; 2307 } 2308 2309 if (Ops.size() == 1) return Ops[0]; 2310 } 2311 2312 // Find the first UMax 2313 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2314 ++Idx; 2315 2316 // Check to see if one of the operands is a UMax. If so, expand its operands 2317 // onto our operand list, and recurse to simplify. 2318 if (Idx < Ops.size()) { 2319 bool DeletedUMax = false; 2320 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2321 Ops.erase(Ops.begin()+Idx); 2322 Ops.append(UMax->op_begin(), UMax->op_end()); 2323 DeletedUMax = true; 2324 } 2325 2326 if (DeletedUMax) 2327 return getUMaxExpr(Ops); 2328 } 2329 2330 // Okay, check to see if the same value occurs in the operand list twice. If 2331 // so, delete one. Since we sorted the list, these values are required to 2332 // be adjacent. 2333 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2334 // X umax Y umax Y --> X umax Y 2335 // X umax Y --> X, if X is always greater than Y 2336 if (Ops[i] == Ops[i+1] || 2337 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2338 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2339 --i; --e; 2340 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2341 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2342 --i; --e; 2343 } 2344 2345 if (Ops.size() == 1) return Ops[0]; 2346 2347 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2348 2349 // Okay, it looks like we really DO need a umax expr. Check to see if we 2350 // already have one, otherwise create a new one. 2351 FoldingSetNodeID ID; 2352 ID.AddInteger(scUMaxExpr); 2353 ID.AddInteger(Ops.size()); 2354 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2355 ID.AddPointer(Ops[i]); 2356 void *IP = 0; 2357 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2358 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2359 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2360 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2361 O, Ops.size()); 2362 UniqueSCEVs.InsertNode(S, IP); 2363 return S; 2364} 2365 2366const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2367 const SCEV *RHS) { 2368 // ~smax(~x, ~y) == smin(x, y). 2369 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2370} 2371 2372const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2373 const SCEV *RHS) { 2374 // ~umax(~x, ~y) == umin(x, y) 2375 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2376} 2377 2378const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2379 // If we have TargetData, we can bypass creating a target-independent 2380 // constant expression and then folding it back into a ConstantInt. 2381 // This is just a compile-time optimization. 2382 if (TD) 2383 return getConstant(TD->getIntPtrType(getContext()), 2384 TD->getTypeAllocSize(AllocTy)); 2385 2386 Constant *C = ConstantExpr::getSizeOf(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::getAlignOfExpr(const Type *AllocTy) { 2395 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2396 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2397 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2398 C = Folded; 2399 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2400 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2401} 2402 2403const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2404 unsigned FieldNo) { 2405 // If we have TargetData, we can bypass creating a target-independent 2406 // constant expression and then folding it back into a ConstantInt. 2407 // This is just a compile-time optimization. 2408 if (TD) 2409 return getConstant(TD->getIntPtrType(getContext()), 2410 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2411 2412 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2413 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2414 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2415 C = Folded; 2416 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2417 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2418} 2419 2420const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2421 Constant *FieldNo) { 2422 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2423 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2424 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2425 C = Folded; 2426 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2427 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2428} 2429 2430const SCEV *ScalarEvolution::getUnknown(Value *V) { 2431 // Don't attempt to do anything other than create a SCEVUnknown object 2432 // here. createSCEV only calls getUnknown after checking for all other 2433 // interesting possibilities, and any other code that calls getUnknown 2434 // is doing so in order to hide a value from SCEV canonicalization. 2435 2436 FoldingSetNodeID ID; 2437 ID.AddInteger(scUnknown); 2438 ID.AddPointer(V); 2439 void *IP = 0; 2440 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2441 assert(cast<SCEVUnknown>(S)->getValue() == V && 2442 "Stale SCEVUnknown in uniquing map!"); 2443 return S; 2444 } 2445 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2446 FirstUnknown); 2447 FirstUnknown = cast<SCEVUnknown>(S); 2448 UniqueSCEVs.InsertNode(S, IP); 2449 return S; 2450} 2451 2452//===----------------------------------------------------------------------===// 2453// Basic SCEV Analysis and PHI Idiom Recognition Code 2454// 2455 2456/// isSCEVable - Test if values of the given type are analyzable within 2457/// the SCEV framework. This primarily includes integer types, and it 2458/// can optionally include pointer types if the ScalarEvolution class 2459/// has access to target-specific information. 2460bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2461 // Integers and pointers are always SCEVable. 2462 return Ty->isIntegerTy() || Ty->isPointerTy(); 2463} 2464 2465/// getTypeSizeInBits - Return the size in bits of the specified type, 2466/// for which isSCEVable must return true. 2467uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2468 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2469 2470 // If we have a TargetData, use it! 2471 if (TD) 2472 return TD->getTypeSizeInBits(Ty); 2473 2474 // Integer types have fixed sizes. 2475 if (Ty->isIntegerTy()) 2476 return Ty->getPrimitiveSizeInBits(); 2477 2478 // The only other support type is pointer. Without TargetData, conservatively 2479 // assume pointers are 64-bit. 2480 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2481 return 64; 2482} 2483 2484/// getEffectiveSCEVType - Return a type with the same bitwidth as 2485/// the given type and which represents how SCEV will treat the given 2486/// type, for which isSCEVable must return true. For pointer types, 2487/// this is the pointer-sized integer type. 2488const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2489 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2490 2491 if (Ty->isIntegerTy()) 2492 return Ty; 2493 2494 // The only other support type is pointer. 2495 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2496 if (TD) return TD->getIntPtrType(getContext()); 2497 2498 // Without TargetData, conservatively assume pointers are 64-bit. 2499 return Type::getInt64Ty(getContext()); 2500} 2501 2502const SCEV *ScalarEvolution::getCouldNotCompute() { 2503 return &CouldNotCompute; 2504} 2505 2506/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2507/// expression and create a new one. 2508const SCEV *ScalarEvolution::getSCEV(Value *V) { 2509 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2510 2511 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2512 if (I != ValueExprMap.end()) return I->second; 2513 const SCEV *S = createSCEV(V); 2514 2515 // The process of creating a SCEV for V may have caused other SCEVs 2516 // to have been created, so it's necessary to insert the new entry 2517 // from scratch, rather than trying to remember the insert position 2518 // above. 2519 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2520 return S; 2521} 2522 2523/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2524/// 2525const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2526 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2527 return getConstant( 2528 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2529 2530 const Type *Ty = V->getType(); 2531 Ty = getEffectiveSCEVType(Ty); 2532 return getMulExpr(V, 2533 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2534} 2535 2536/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2537const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2538 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2539 return getConstant( 2540 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2541 2542 const Type *Ty = V->getType(); 2543 Ty = getEffectiveSCEVType(Ty); 2544 const SCEV *AllOnes = 2545 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2546 return getMinusSCEV(AllOnes, V); 2547} 2548 2549/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2550/// 2551const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2552 const SCEV *RHS) { 2553 // Fast path: X - X --> 0. 2554 if (LHS == RHS) 2555 return getConstant(LHS->getType(), 0); 2556 2557 // X - Y --> X + -Y 2558 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2559} 2560 2561/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2562/// input value to the specified type. If the type must be extended, it is zero 2563/// extended. 2564const SCEV * 2565ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2566 const Type *Ty) { 2567 const Type *SrcTy = V->getType(); 2568 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2569 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2570 "Cannot truncate or zero extend with non-integer arguments!"); 2571 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2572 return V; // No conversion 2573 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2574 return getTruncateExpr(V, Ty); 2575 return getZeroExtendExpr(V, Ty); 2576} 2577 2578/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2579/// input value to the specified type. If the type must be extended, it is sign 2580/// extended. 2581const SCEV * 2582ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2583 const Type *Ty) { 2584 const Type *SrcTy = V->getType(); 2585 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2586 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2587 "Cannot truncate or zero extend with non-integer arguments!"); 2588 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2589 return V; // No conversion 2590 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2591 return getTruncateExpr(V, Ty); 2592 return getSignExtendExpr(V, Ty); 2593} 2594 2595/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2596/// input value to the specified type. If the type must be extended, it is zero 2597/// extended. The conversion must not be narrowing. 2598const SCEV * 2599ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2600 const Type *SrcTy = V->getType(); 2601 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2602 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2603 "Cannot noop or zero extend with non-integer arguments!"); 2604 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2605 "getNoopOrZeroExtend cannot truncate!"); 2606 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2607 return V; // No conversion 2608 return getZeroExtendExpr(V, Ty); 2609} 2610 2611/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2612/// input value to the specified type. If the type must be extended, it is sign 2613/// extended. The conversion must not be narrowing. 2614const SCEV * 2615ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2616 const Type *SrcTy = V->getType(); 2617 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2618 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2619 "Cannot noop or sign extend with non-integer arguments!"); 2620 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2621 "getNoopOrSignExtend cannot truncate!"); 2622 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2623 return V; // No conversion 2624 return getSignExtendExpr(V, Ty); 2625} 2626 2627/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2628/// the input value to the specified type. If the type must be extended, 2629/// it is extended with unspecified bits. The conversion must not be 2630/// narrowing. 2631const SCEV * 2632ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2633 const Type *SrcTy = V->getType(); 2634 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2635 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2636 "Cannot noop or any extend with non-integer arguments!"); 2637 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2638 "getNoopOrAnyExtend cannot truncate!"); 2639 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2640 return V; // No conversion 2641 return getAnyExtendExpr(V, Ty); 2642} 2643 2644/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2645/// input value to the specified type. The conversion must not be widening. 2646const SCEV * 2647ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2648 const Type *SrcTy = V->getType(); 2649 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2650 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2651 "Cannot truncate or noop with non-integer arguments!"); 2652 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2653 "getTruncateOrNoop cannot extend!"); 2654 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2655 return V; // No conversion 2656 return getTruncateExpr(V, Ty); 2657} 2658 2659/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2660/// the types using zero-extension, and then perform a umax operation 2661/// with them. 2662const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2663 const SCEV *RHS) { 2664 const SCEV *PromotedLHS = LHS; 2665 const SCEV *PromotedRHS = RHS; 2666 2667 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2668 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2669 else 2670 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2671 2672 return getUMaxExpr(PromotedLHS, PromotedRHS); 2673} 2674 2675/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2676/// the types using zero-extension, and then perform a umin operation 2677/// with them. 2678const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2679 const SCEV *RHS) { 2680 const SCEV *PromotedLHS = LHS; 2681 const SCEV *PromotedRHS = RHS; 2682 2683 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2684 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2685 else 2686 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2687 2688 return getUMinExpr(PromotedLHS, PromotedRHS); 2689} 2690 2691/// PushDefUseChildren - Push users of the given Instruction 2692/// onto the given Worklist. 2693static void 2694PushDefUseChildren(Instruction *I, 2695 SmallVectorImpl<Instruction *> &Worklist) { 2696 // Push the def-use children onto the Worklist stack. 2697 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2698 UI != UE; ++UI) 2699 Worklist.push_back(cast<Instruction>(*UI)); 2700} 2701 2702/// ForgetSymbolicValue - This looks up computed SCEV values for all 2703/// instructions that depend on the given instruction and removes them from 2704/// the ValueExprMapType map if they reference SymName. This is used during PHI 2705/// resolution. 2706void 2707ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2708 SmallVector<Instruction *, 16> Worklist; 2709 PushDefUseChildren(PN, Worklist); 2710 2711 SmallPtrSet<Instruction *, 8> Visited; 2712 Visited.insert(PN); 2713 while (!Worklist.empty()) { 2714 Instruction *I = Worklist.pop_back_val(); 2715 if (!Visited.insert(I)) continue; 2716 2717 ValueExprMapType::iterator It = 2718 ValueExprMap.find(static_cast<Value *>(I)); 2719 if (It != ValueExprMap.end()) { 2720 // Short-circuit the def-use traversal if the symbolic name 2721 // ceases to appear in expressions. 2722 if (It->second != SymName && !It->second->hasOperand(SymName)) 2723 continue; 2724 2725 // SCEVUnknown for a PHI either means that it has an unrecognized 2726 // structure, it's a PHI that's in the progress of being computed 2727 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2728 // additional loop trip count information isn't going to change anything. 2729 // In the second case, createNodeForPHI will perform the necessary 2730 // updates on its own when it gets to that point. In the third, we do 2731 // want to forget the SCEVUnknown. 2732 if (!isa<PHINode>(I) || 2733 !isa<SCEVUnknown>(It->second) || 2734 (I != PN && It->second == SymName)) { 2735 ValuesAtScopes.erase(It->second); 2736 ValueExprMap.erase(It); 2737 } 2738 } 2739 2740 PushDefUseChildren(I, Worklist); 2741 } 2742} 2743 2744/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2745/// a loop header, making it a potential recurrence, or it doesn't. 2746/// 2747const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2748 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2749 if (L->getHeader() == PN->getParent()) { 2750 // The loop may have multiple entrances or multiple exits; we can analyze 2751 // this phi as an addrec if it has a unique entry value and a unique 2752 // backedge value. 2753 Value *BEValueV = 0, *StartValueV = 0; 2754 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2755 Value *V = PN->getIncomingValue(i); 2756 if (L->contains(PN->getIncomingBlock(i))) { 2757 if (!BEValueV) { 2758 BEValueV = V; 2759 } else if (BEValueV != V) { 2760 BEValueV = 0; 2761 break; 2762 } 2763 } else if (!StartValueV) { 2764 StartValueV = V; 2765 } else if (StartValueV != V) { 2766 StartValueV = 0; 2767 break; 2768 } 2769 } 2770 if (BEValueV && StartValueV) { 2771 // While we are analyzing this PHI node, handle its value symbolically. 2772 const SCEV *SymbolicName = getUnknown(PN); 2773 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2774 "PHI node already processed?"); 2775 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2776 2777 // Using this symbolic name for the PHI, analyze the value coming around 2778 // the back-edge. 2779 const SCEV *BEValue = getSCEV(BEValueV); 2780 2781 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2782 // has a special value for the first iteration of the loop. 2783 2784 // If the value coming around the backedge is an add with the symbolic 2785 // value we just inserted, then we found a simple induction variable! 2786 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2787 // If there is a single occurrence of the symbolic value, replace it 2788 // with a recurrence. 2789 unsigned FoundIndex = Add->getNumOperands(); 2790 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2791 if (Add->getOperand(i) == SymbolicName) 2792 if (FoundIndex == e) { 2793 FoundIndex = i; 2794 break; 2795 } 2796 2797 if (FoundIndex != Add->getNumOperands()) { 2798 // Create an add with everything but the specified operand. 2799 SmallVector<const SCEV *, 8> Ops; 2800 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2801 if (i != FoundIndex) 2802 Ops.push_back(Add->getOperand(i)); 2803 const SCEV *Accum = getAddExpr(Ops); 2804 2805 // This is not a valid addrec if the step amount is varying each 2806 // loop iteration, but is not itself an addrec in this loop. 2807 if (Accum->isLoopInvariant(L) || 2808 (isa<SCEVAddRecExpr>(Accum) && 2809 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2810 bool HasNUW = false; 2811 bool HasNSW = false; 2812 2813 // If the increment doesn't overflow, then neither the addrec nor 2814 // the post-increment will overflow. 2815 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2816 if (OBO->hasNoUnsignedWrap()) 2817 HasNUW = true; 2818 if (OBO->hasNoSignedWrap()) 2819 HasNSW = true; 2820 } 2821 2822 const SCEV *StartVal = getSCEV(StartValueV); 2823 const SCEV *PHISCEV = 2824 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2825 2826 // Since the no-wrap flags are on the increment, they apply to the 2827 // post-incremented value as well. 2828 if (Accum->isLoopInvariant(L)) 2829 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2830 Accum, L, HasNUW, HasNSW); 2831 2832 // Okay, for the entire analysis of this edge we assumed the PHI 2833 // to be symbolic. We now need to go back and purge all of the 2834 // entries for the scalars that use the symbolic expression. 2835 ForgetSymbolicName(PN, SymbolicName); 2836 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2837 return PHISCEV; 2838 } 2839 } 2840 } else if (const SCEVAddRecExpr *AddRec = 2841 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2842 // Otherwise, this could be a loop like this: 2843 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2844 // In this case, j = {1,+,1} and BEValue is j. 2845 // Because the other in-value of i (0) fits the evolution of BEValue 2846 // i really is an addrec evolution. 2847 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2848 const SCEV *StartVal = getSCEV(StartValueV); 2849 2850 // If StartVal = j.start - j.stride, we can use StartVal as the 2851 // initial step of the addrec evolution. 2852 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2853 AddRec->getOperand(1))) { 2854 const SCEV *PHISCEV = 2855 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2856 2857 // Okay, for the entire analysis of this edge we assumed the PHI 2858 // to be symbolic. We now need to go back and purge all of the 2859 // entries for the scalars that use the symbolic expression. 2860 ForgetSymbolicName(PN, SymbolicName); 2861 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2862 return PHISCEV; 2863 } 2864 } 2865 } 2866 } 2867 } 2868 2869 // If the PHI has a single incoming value, follow that value, unless the 2870 // PHI's incoming blocks are in a different loop, in which case doing so 2871 // risks breaking LCSSA form. Instcombine would normally zap these, but 2872 // it doesn't have DominatorTree information, so it may miss cases. 2873 if (Value *V = PN->hasConstantValue(DT)) { 2874 bool AllSameLoop = true; 2875 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2876 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2877 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2878 AllSameLoop = false; 2879 break; 2880 } 2881 if (AllSameLoop) 2882 return getSCEV(V); 2883 } 2884 2885 // If it's not a loop phi, we can't handle it yet. 2886 return getUnknown(PN); 2887} 2888 2889/// createNodeForGEP - Expand GEP instructions into add and multiply 2890/// operations. This allows them to be analyzed by regular SCEV code. 2891/// 2892const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2893 2894 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2895 // Add expression, because the Instruction may be guarded by control flow 2896 // and the no-overflow bits may not be valid for the expression in any 2897 // context. 2898 2899 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2900 Value *Base = GEP->getOperand(0); 2901 // Don't attempt to analyze GEPs over unsized objects. 2902 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2903 return getUnknown(GEP); 2904 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2905 gep_type_iterator GTI = gep_type_begin(GEP); 2906 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2907 E = GEP->op_end(); 2908 I != E; ++I) { 2909 Value *Index = *I; 2910 // Compute the (potentially symbolic) offset in bytes for this index. 2911 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2912 // For a struct, add the member offset. 2913 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2914 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2915 2916 // Add the field offset to the running total offset. 2917 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2918 } else { 2919 // For an array, add the element offset, explicitly scaled. 2920 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2921 const SCEV *IndexS = getSCEV(Index); 2922 // Getelementptr indices are signed. 2923 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2924 2925 // Multiply the index by the element size to compute the element offset. 2926 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2927 2928 // Add the element offset to the running total offset. 2929 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2930 } 2931 } 2932 2933 // Get the SCEV for the GEP base. 2934 const SCEV *BaseS = getSCEV(Base); 2935 2936 // Add the total offset from all the GEP indices to the base. 2937 return getAddExpr(BaseS, TotalOffset); 2938} 2939 2940/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2941/// guaranteed to end in (at every loop iteration). It is, at the same time, 2942/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2943/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2944uint32_t 2945ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2946 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2947 return C->getValue()->getValue().countTrailingZeros(); 2948 2949 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2950 return std::min(GetMinTrailingZeros(T->getOperand()), 2951 (uint32_t)getTypeSizeInBits(T->getType())); 2952 2953 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2954 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2955 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2956 getTypeSizeInBits(E->getType()) : OpRes; 2957 } 2958 2959 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2960 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2961 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2962 getTypeSizeInBits(E->getType()) : OpRes; 2963 } 2964 2965 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2966 // The result is the min of all operands results. 2967 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2968 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2969 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2970 return MinOpRes; 2971 } 2972 2973 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2974 // The result is the sum of all operands results. 2975 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2976 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2977 for (unsigned i = 1, e = M->getNumOperands(); 2978 SumOpRes != BitWidth && i != e; ++i) 2979 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2980 BitWidth); 2981 return SumOpRes; 2982 } 2983 2984 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2985 // The result is the min of all operands results. 2986 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2987 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2988 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2989 return MinOpRes; 2990 } 2991 2992 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2993 // The result is the min of all operands results. 2994 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2995 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2996 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2997 return MinOpRes; 2998 } 2999 3000 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3001 // The result is the min of all operands results. 3002 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3003 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3004 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3005 return MinOpRes; 3006 } 3007 3008 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3009 // For a SCEVUnknown, ask ValueTracking. 3010 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3011 APInt Mask = APInt::getAllOnesValue(BitWidth); 3012 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3013 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3014 return Zeros.countTrailingOnes(); 3015 } 3016 3017 // SCEVUDivExpr 3018 return 0; 3019} 3020 3021/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3022/// 3023ConstantRange 3024ScalarEvolution::getUnsignedRange(const SCEV *S) { 3025 3026 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3027 return ConstantRange(C->getValue()->getValue()); 3028 3029 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3030 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3031 3032 // If the value has known zeros, the maximum unsigned value will have those 3033 // known zeros as well. 3034 uint32_t TZ = GetMinTrailingZeros(S); 3035 if (TZ != 0) 3036 ConservativeResult = 3037 ConstantRange(APInt::getMinValue(BitWidth), 3038 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3039 3040 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3041 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3042 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3043 X = X.add(getUnsignedRange(Add->getOperand(i))); 3044 return ConservativeResult.intersectWith(X); 3045 } 3046 3047 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3048 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3049 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3050 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3051 return ConservativeResult.intersectWith(X); 3052 } 3053 3054 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3055 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3056 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3057 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3058 return ConservativeResult.intersectWith(X); 3059 } 3060 3061 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3062 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3063 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3064 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3065 return ConservativeResult.intersectWith(X); 3066 } 3067 3068 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3069 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3070 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3071 return ConservativeResult.intersectWith(X.udiv(Y)); 3072 } 3073 3074 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3075 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3076 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3077 } 3078 3079 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3080 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3081 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3082 } 3083 3084 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3085 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3086 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3087 } 3088 3089 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3090 // If there's no unsigned wrap, the value will never be less than its 3091 // initial value. 3092 if (AddRec->hasNoUnsignedWrap()) 3093 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3094 if (!C->getValue()->isZero()) 3095 ConservativeResult = 3096 ConservativeResult.intersectWith( 3097 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3098 3099 // TODO: non-affine addrec 3100 if (AddRec->isAffine()) { 3101 const Type *Ty = AddRec->getType(); 3102 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3103 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3104 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3105 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3106 3107 const SCEV *Start = AddRec->getStart(); 3108 const SCEV *Step = AddRec->getStepRecurrence(*this); 3109 3110 ConstantRange StartRange = getUnsignedRange(Start); 3111 ConstantRange StepRange = getSignedRange(Step); 3112 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3113 ConstantRange EndRange = 3114 StartRange.add(MaxBECountRange.multiply(StepRange)); 3115 3116 // Check for overflow. This must be done with ConstantRange arithmetic 3117 // because we could be called from within the ScalarEvolution overflow 3118 // checking code. 3119 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3120 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3121 ConstantRange ExtMaxBECountRange = 3122 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3123 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3124 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3125 ExtEndRange) 3126 return ConservativeResult; 3127 3128 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3129 EndRange.getUnsignedMin()); 3130 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3131 EndRange.getUnsignedMax()); 3132 if (Min.isMinValue() && Max.isMaxValue()) 3133 return ConservativeResult; 3134 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3135 } 3136 } 3137 3138 return ConservativeResult; 3139 } 3140 3141 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3142 // For a SCEVUnknown, ask ValueTracking. 3143 APInt Mask = APInt::getAllOnesValue(BitWidth); 3144 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3145 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3146 if (Ones == ~Zeros + 1) 3147 return ConservativeResult; 3148 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3149 } 3150 3151 return ConservativeResult; 3152} 3153 3154/// getSignedRange - Determine the signed range for a particular SCEV. 3155/// 3156ConstantRange 3157ScalarEvolution::getSignedRange(const SCEV *S) { 3158 3159 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3160 return ConstantRange(C->getValue()->getValue()); 3161 3162 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3163 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3164 3165 // If the value has known zeros, the maximum signed value will have those 3166 // known zeros as well. 3167 uint32_t TZ = GetMinTrailingZeros(S); 3168 if (TZ != 0) 3169 ConservativeResult = 3170 ConstantRange(APInt::getSignedMinValue(BitWidth), 3171 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3172 3173 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3174 ConstantRange X = getSignedRange(Add->getOperand(0)); 3175 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3176 X = X.add(getSignedRange(Add->getOperand(i))); 3177 return ConservativeResult.intersectWith(X); 3178 } 3179 3180 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3181 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3182 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3183 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3184 return ConservativeResult.intersectWith(X); 3185 } 3186 3187 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3188 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3189 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3190 X = X.smax(getSignedRange(SMax->getOperand(i))); 3191 return ConservativeResult.intersectWith(X); 3192 } 3193 3194 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3195 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3196 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3197 X = X.umax(getSignedRange(UMax->getOperand(i))); 3198 return ConservativeResult.intersectWith(X); 3199 } 3200 3201 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3202 ConstantRange X = getSignedRange(UDiv->getLHS()); 3203 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3204 return ConservativeResult.intersectWith(X.udiv(Y)); 3205 } 3206 3207 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3208 ConstantRange X = getSignedRange(ZExt->getOperand()); 3209 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3210 } 3211 3212 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3213 ConstantRange X = getSignedRange(SExt->getOperand()); 3214 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3215 } 3216 3217 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3218 ConstantRange X = getSignedRange(Trunc->getOperand()); 3219 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3220 } 3221 3222 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3223 // If there's no signed wrap, and all the operands have the same sign or 3224 // zero, the value won't ever change sign. 3225 if (AddRec->hasNoSignedWrap()) { 3226 bool AllNonNeg = true; 3227 bool AllNonPos = true; 3228 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3229 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3230 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3231 } 3232 if (AllNonNeg) 3233 ConservativeResult = ConservativeResult.intersectWith( 3234 ConstantRange(APInt(BitWidth, 0), 3235 APInt::getSignedMinValue(BitWidth))); 3236 else if (AllNonPos) 3237 ConservativeResult = ConservativeResult.intersectWith( 3238 ConstantRange(APInt::getSignedMinValue(BitWidth), 3239 APInt(BitWidth, 1))); 3240 } 3241 3242 // TODO: non-affine addrec 3243 if (AddRec->isAffine()) { 3244 const Type *Ty = AddRec->getType(); 3245 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3246 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3247 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3248 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3249 3250 const SCEV *Start = AddRec->getStart(); 3251 const SCEV *Step = AddRec->getStepRecurrence(*this); 3252 3253 ConstantRange StartRange = getSignedRange(Start); 3254 ConstantRange StepRange = getSignedRange(Step); 3255 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3256 ConstantRange EndRange = 3257 StartRange.add(MaxBECountRange.multiply(StepRange)); 3258 3259 // Check for overflow. This must be done with ConstantRange arithmetic 3260 // because we could be called from within the ScalarEvolution overflow 3261 // checking code. 3262 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3263 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3264 ConstantRange ExtMaxBECountRange = 3265 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3266 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3267 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3268 ExtEndRange) 3269 return ConservativeResult; 3270 3271 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3272 EndRange.getSignedMin()); 3273 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3274 EndRange.getSignedMax()); 3275 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3276 return ConservativeResult; 3277 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3278 } 3279 } 3280 3281 return ConservativeResult; 3282 } 3283 3284 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3285 // For a SCEVUnknown, ask ValueTracking. 3286 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3287 return ConservativeResult; 3288 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3289 if (NS == 1) 3290 return ConservativeResult; 3291 return ConservativeResult.intersectWith( 3292 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3293 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3294 } 3295 3296 return ConservativeResult; 3297} 3298 3299/// createSCEV - We know that there is no SCEV for the specified value. 3300/// Analyze the expression. 3301/// 3302const SCEV *ScalarEvolution::createSCEV(Value *V) { 3303 if (!isSCEVable(V->getType())) 3304 return getUnknown(V); 3305 3306 unsigned Opcode = Instruction::UserOp1; 3307 if (Instruction *I = dyn_cast<Instruction>(V)) { 3308 Opcode = I->getOpcode(); 3309 3310 // Don't attempt to analyze instructions in blocks that aren't 3311 // reachable. Such instructions don't matter, and they aren't required 3312 // to obey basic rules for definitions dominating uses which this 3313 // analysis depends on. 3314 if (!DT->isReachableFromEntry(I->getParent())) 3315 return getUnknown(V); 3316 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3317 Opcode = CE->getOpcode(); 3318 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3319 return getConstant(CI); 3320 else if (isa<ConstantPointerNull>(V)) 3321 return getConstant(V->getType(), 0); 3322 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3323 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3324 else 3325 return getUnknown(V); 3326 3327 Operator *U = cast<Operator>(V); 3328 switch (Opcode) { 3329 case Instruction::Add: { 3330 // The simple thing to do would be to just call getSCEV on both operands 3331 // and call getAddExpr with the result. However if we're looking at a 3332 // bunch of things all added together, this can be quite inefficient, 3333 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3334 // Instead, gather up all the operands and make a single getAddExpr call. 3335 // LLVM IR canonical form means we need only traverse the left operands. 3336 SmallVector<const SCEV *, 4> AddOps; 3337 AddOps.push_back(getSCEV(U->getOperand(1))); 3338 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3339 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3340 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3341 break; 3342 U = cast<Operator>(Op); 3343 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3344 if (Opcode == Instruction::Sub) 3345 AddOps.push_back(getNegativeSCEV(Op1)); 3346 else 3347 AddOps.push_back(Op1); 3348 } 3349 AddOps.push_back(getSCEV(U->getOperand(0))); 3350 return getAddExpr(AddOps); 3351 } 3352 case Instruction::Mul: { 3353 // See the Add code above. 3354 SmallVector<const SCEV *, 4> MulOps; 3355 MulOps.push_back(getSCEV(U->getOperand(1))); 3356 for (Value *Op = U->getOperand(0); 3357 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3358 Op = U->getOperand(0)) { 3359 U = cast<Operator>(Op); 3360 MulOps.push_back(getSCEV(U->getOperand(1))); 3361 } 3362 MulOps.push_back(getSCEV(U->getOperand(0))); 3363 return getMulExpr(MulOps); 3364 } 3365 case Instruction::UDiv: 3366 return getUDivExpr(getSCEV(U->getOperand(0)), 3367 getSCEV(U->getOperand(1))); 3368 case Instruction::Sub: 3369 return getMinusSCEV(getSCEV(U->getOperand(0)), 3370 getSCEV(U->getOperand(1))); 3371 case Instruction::And: 3372 // For an expression like x&255 that merely masks off the high bits, 3373 // use zext(trunc(x)) as the SCEV expression. 3374 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3375 if (CI->isNullValue()) 3376 return getSCEV(U->getOperand(1)); 3377 if (CI->isAllOnesValue()) 3378 return getSCEV(U->getOperand(0)); 3379 const APInt &A = CI->getValue(); 3380 3381 // Instcombine's ShrinkDemandedConstant may strip bits out of 3382 // constants, obscuring what would otherwise be a low-bits mask. 3383 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3384 // knew about to reconstruct a low-bits mask value. 3385 unsigned LZ = A.countLeadingZeros(); 3386 unsigned BitWidth = A.getBitWidth(); 3387 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3388 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3389 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3390 3391 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3392 3393 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3394 return 3395 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3396 IntegerType::get(getContext(), BitWidth - LZ)), 3397 U->getType()); 3398 } 3399 break; 3400 3401 case Instruction::Or: 3402 // If the RHS of the Or is a constant, we may have something like: 3403 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3404 // optimizations will transparently handle this case. 3405 // 3406 // In order for this transformation to be safe, the LHS must be of the 3407 // form X*(2^n) and the Or constant must be less than 2^n. 3408 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3409 const SCEV *LHS = getSCEV(U->getOperand(0)); 3410 const APInt &CIVal = CI->getValue(); 3411 if (GetMinTrailingZeros(LHS) >= 3412 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3413 // Build a plain add SCEV. 3414 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3415 // If the LHS of the add was an addrec and it has no-wrap flags, 3416 // transfer the no-wrap flags, since an or won't introduce a wrap. 3417 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3418 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3419 if (OldAR->hasNoUnsignedWrap()) 3420 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3421 if (OldAR->hasNoSignedWrap()) 3422 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3423 } 3424 return S; 3425 } 3426 } 3427 break; 3428 case Instruction::Xor: 3429 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3430 // If the RHS of the xor is a signbit, then this is just an add. 3431 // Instcombine turns add of signbit into xor as a strength reduction step. 3432 if (CI->getValue().isSignBit()) 3433 return getAddExpr(getSCEV(U->getOperand(0)), 3434 getSCEV(U->getOperand(1))); 3435 3436 // If the RHS of xor is -1, then this is a not operation. 3437 if (CI->isAllOnesValue()) 3438 return getNotSCEV(getSCEV(U->getOperand(0))); 3439 3440 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3441 // This is a variant of the check for xor with -1, and it handles 3442 // the case where instcombine has trimmed non-demanded bits out 3443 // of an xor with -1. 3444 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3445 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3446 if (BO->getOpcode() == Instruction::And && 3447 LCI->getValue() == CI->getValue()) 3448 if (const SCEVZeroExtendExpr *Z = 3449 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3450 const Type *UTy = U->getType(); 3451 const SCEV *Z0 = Z->getOperand(); 3452 const Type *Z0Ty = Z0->getType(); 3453 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3454 3455 // If C is a low-bits mask, the zero extend is serving to 3456 // mask off the high bits. Complement the operand and 3457 // re-apply the zext. 3458 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3459 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3460 3461 // If C is a single bit, it may be in the sign-bit position 3462 // before the zero-extend. In this case, represent the xor 3463 // using an add, which is equivalent, and re-apply the zext. 3464 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3465 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3466 Trunc.isSignBit()) 3467 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3468 UTy); 3469 } 3470 } 3471 break; 3472 3473 case Instruction::Shl: 3474 // Turn shift left of a constant amount into a multiply. 3475 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3476 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3477 3478 // If the shift count is not less than the bitwidth, the result of 3479 // the shift is undefined. Don't try to analyze it, because the 3480 // resolution chosen here may differ from the resolution chosen in 3481 // other parts of the compiler. 3482 if (SA->getValue().uge(BitWidth)) 3483 break; 3484 3485 Constant *X = ConstantInt::get(getContext(), 3486 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3487 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3488 } 3489 break; 3490 3491 case Instruction::LShr: 3492 // Turn logical shift right of a constant into a unsigned divide. 3493 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3494 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3495 3496 // If the shift count is not less than the bitwidth, the result of 3497 // the shift is undefined. Don't try to analyze it, because the 3498 // resolution chosen here may differ from the resolution chosen in 3499 // other parts of the compiler. 3500 if (SA->getValue().uge(BitWidth)) 3501 break; 3502 3503 Constant *X = ConstantInt::get(getContext(), 3504 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3505 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3506 } 3507 break; 3508 3509 case Instruction::AShr: 3510 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3511 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3512 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3513 if (L->getOpcode() == Instruction::Shl && 3514 L->getOperand(1) == U->getOperand(1)) { 3515 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3516 3517 // If the shift count is not less than the bitwidth, the result of 3518 // the shift is undefined. Don't try to analyze it, because the 3519 // resolution chosen here may differ from the resolution chosen in 3520 // other parts of the compiler. 3521 if (CI->getValue().uge(BitWidth)) 3522 break; 3523 3524 uint64_t Amt = BitWidth - CI->getZExtValue(); 3525 if (Amt == BitWidth) 3526 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3527 return 3528 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3529 IntegerType::get(getContext(), 3530 Amt)), 3531 U->getType()); 3532 } 3533 break; 3534 3535 case Instruction::Trunc: 3536 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3537 3538 case Instruction::ZExt: 3539 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3540 3541 case Instruction::SExt: 3542 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3543 3544 case Instruction::BitCast: 3545 // BitCasts are no-op casts so we just eliminate the cast. 3546 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3547 return getSCEV(U->getOperand(0)); 3548 break; 3549 3550 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3551 // lead to pointer expressions which cannot safely be expanded to GEPs, 3552 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3553 // simplifying integer expressions. 3554 3555 case Instruction::GetElementPtr: 3556 return createNodeForGEP(cast<GEPOperator>(U)); 3557 3558 case Instruction::PHI: 3559 return createNodeForPHI(cast<PHINode>(U)); 3560 3561 case Instruction::Select: 3562 // This could be a smax or umax that was lowered earlier. 3563 // Try to recover it. 3564 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3565 Value *LHS = ICI->getOperand(0); 3566 Value *RHS = ICI->getOperand(1); 3567 switch (ICI->getPredicate()) { 3568 case ICmpInst::ICMP_SLT: 3569 case ICmpInst::ICMP_SLE: 3570 std::swap(LHS, RHS); 3571 // fall through 3572 case ICmpInst::ICMP_SGT: 3573 case ICmpInst::ICMP_SGE: 3574 // a >s b ? a+x : b+x -> smax(a, b)+x 3575 // a >s b ? b+x : a+x -> smin(a, b)+x 3576 if (LHS->getType() == U->getType()) { 3577 const SCEV *LS = getSCEV(LHS); 3578 const SCEV *RS = getSCEV(RHS); 3579 const SCEV *LA = getSCEV(U->getOperand(1)); 3580 const SCEV *RA = getSCEV(U->getOperand(2)); 3581 const SCEV *LDiff = getMinusSCEV(LA, LS); 3582 const SCEV *RDiff = getMinusSCEV(RA, RS); 3583 if (LDiff == RDiff) 3584 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3585 LDiff = getMinusSCEV(LA, RS); 3586 RDiff = getMinusSCEV(RA, LS); 3587 if (LDiff == RDiff) 3588 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3589 } 3590 break; 3591 case ICmpInst::ICMP_ULT: 3592 case ICmpInst::ICMP_ULE: 3593 std::swap(LHS, RHS); 3594 // fall through 3595 case ICmpInst::ICMP_UGT: 3596 case ICmpInst::ICMP_UGE: 3597 // a >u b ? a+x : b+x -> umax(a, b)+x 3598 // a >u b ? b+x : a+x -> umin(a, b)+x 3599 if (LHS->getType() == U->getType()) { 3600 const SCEV *LS = getSCEV(LHS); 3601 const SCEV *RS = getSCEV(RHS); 3602 const SCEV *LA = getSCEV(U->getOperand(1)); 3603 const SCEV *RA = getSCEV(U->getOperand(2)); 3604 const SCEV *LDiff = getMinusSCEV(LA, LS); 3605 const SCEV *RDiff = getMinusSCEV(RA, RS); 3606 if (LDiff == RDiff) 3607 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3608 LDiff = getMinusSCEV(LA, RS); 3609 RDiff = getMinusSCEV(RA, LS); 3610 if (LDiff == RDiff) 3611 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3612 } 3613 break; 3614 case ICmpInst::ICMP_NE: 3615 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3616 if (LHS->getType() == U->getType() && 3617 isa<ConstantInt>(RHS) && 3618 cast<ConstantInt>(RHS)->isZero()) { 3619 const SCEV *One = getConstant(LHS->getType(), 1); 3620 const SCEV *LS = getSCEV(LHS); 3621 const SCEV *LA = getSCEV(U->getOperand(1)); 3622 const SCEV *RA = getSCEV(U->getOperand(2)); 3623 const SCEV *LDiff = getMinusSCEV(LA, LS); 3624 const SCEV *RDiff = getMinusSCEV(RA, One); 3625 if (LDiff == RDiff) 3626 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3627 } 3628 break; 3629 case ICmpInst::ICMP_EQ: 3630 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3631 if (LHS->getType() == U->getType() && 3632 isa<ConstantInt>(RHS) && 3633 cast<ConstantInt>(RHS)->isZero()) { 3634 const SCEV *One = getConstant(LHS->getType(), 1); 3635 const SCEV *LS = getSCEV(LHS); 3636 const SCEV *LA = getSCEV(U->getOperand(1)); 3637 const SCEV *RA = getSCEV(U->getOperand(2)); 3638 const SCEV *LDiff = getMinusSCEV(LA, One); 3639 const SCEV *RDiff = getMinusSCEV(RA, LS); 3640 if (LDiff == RDiff) 3641 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3642 } 3643 break; 3644 default: 3645 break; 3646 } 3647 } 3648 3649 default: // We cannot analyze this expression. 3650 break; 3651 } 3652 3653 return getUnknown(V); 3654} 3655 3656 3657 3658//===----------------------------------------------------------------------===// 3659// Iteration Count Computation Code 3660// 3661 3662/// getBackedgeTakenCount - If the specified loop has a predictable 3663/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3664/// object. The backedge-taken count is the number of times the loop header 3665/// will be branched to from within the loop. This is one less than the 3666/// trip count of the loop, since it doesn't count the first iteration, 3667/// when the header is branched to from outside the loop. 3668/// 3669/// Note that it is not valid to call this method on a loop without a 3670/// loop-invariant backedge-taken count (see 3671/// hasLoopInvariantBackedgeTakenCount). 3672/// 3673const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3674 return getBackedgeTakenInfo(L).Exact; 3675} 3676 3677/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3678/// return the least SCEV value that is known never to be less than the 3679/// actual backedge taken count. 3680const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3681 return getBackedgeTakenInfo(L).Max; 3682} 3683 3684/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3685/// onto the given Worklist. 3686static void 3687PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3688 BasicBlock *Header = L->getHeader(); 3689 3690 // Push all Loop-header PHIs onto the Worklist stack. 3691 for (BasicBlock::iterator I = Header->begin(); 3692 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3693 Worklist.push_back(PN); 3694} 3695 3696const ScalarEvolution::BackedgeTakenInfo & 3697ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3698 // Initially insert a CouldNotCompute for this loop. If the insertion 3699 // succeeds, proceed to actually compute a backedge-taken count and 3700 // update the value. The temporary CouldNotCompute value tells SCEV 3701 // code elsewhere that it shouldn't attempt to request a new 3702 // backedge-taken count, which could result in infinite recursion. 3703 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3704 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3705 if (Pair.second) { 3706 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3707 if (BECount.Exact != getCouldNotCompute()) { 3708 assert(BECount.Exact->isLoopInvariant(L) && 3709 BECount.Max->isLoopInvariant(L) && 3710 "Computed backedge-taken count isn't loop invariant for loop!"); 3711 ++NumTripCountsComputed; 3712 3713 // Update the value in the map. 3714 Pair.first->second = BECount; 3715 } else { 3716 if (BECount.Max != getCouldNotCompute()) 3717 // Update the value in the map. 3718 Pair.first->second = BECount; 3719 if (isa<PHINode>(L->getHeader()->begin())) 3720 // Only count loops that have phi nodes as not being computable. 3721 ++NumTripCountsNotComputed; 3722 } 3723 3724 // Now that we know more about the trip count for this loop, forget any 3725 // existing SCEV values for PHI nodes in this loop since they are only 3726 // conservative estimates made without the benefit of trip count 3727 // information. This is similar to the code in forgetLoop, except that 3728 // it handles SCEVUnknown PHI nodes specially. 3729 if (BECount.hasAnyInfo()) { 3730 SmallVector<Instruction *, 16> Worklist; 3731 PushLoopPHIs(L, Worklist); 3732 3733 SmallPtrSet<Instruction *, 8> Visited; 3734 while (!Worklist.empty()) { 3735 Instruction *I = Worklist.pop_back_val(); 3736 if (!Visited.insert(I)) continue; 3737 3738 ValueExprMapType::iterator It = 3739 ValueExprMap.find(static_cast<Value *>(I)); 3740 if (It != ValueExprMap.end()) { 3741 // SCEVUnknown for a PHI either means that it has an unrecognized 3742 // structure, or it's a PHI that's in the progress of being computed 3743 // by createNodeForPHI. In the former case, additional loop trip 3744 // count information isn't going to change anything. In the later 3745 // case, createNodeForPHI will perform the necessary updates on its 3746 // own when it gets to that point. 3747 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3748 ValuesAtScopes.erase(It->second); 3749 ValueExprMap.erase(It); 3750 } 3751 if (PHINode *PN = dyn_cast<PHINode>(I)) 3752 ConstantEvolutionLoopExitValue.erase(PN); 3753 } 3754 3755 PushDefUseChildren(I, Worklist); 3756 } 3757 } 3758 } 3759 return Pair.first->second; 3760} 3761 3762/// forgetLoop - This method should be called by the client when it has 3763/// changed a loop in a way that may effect ScalarEvolution's ability to 3764/// compute a trip count, or if the loop is deleted. 3765void ScalarEvolution::forgetLoop(const Loop *L) { 3766 // Drop any stored trip count value. 3767 BackedgeTakenCounts.erase(L); 3768 3769 // Drop information about expressions based on loop-header PHIs. 3770 SmallVector<Instruction *, 16> Worklist; 3771 PushLoopPHIs(L, Worklist); 3772 3773 SmallPtrSet<Instruction *, 8> Visited; 3774 while (!Worklist.empty()) { 3775 Instruction *I = Worklist.pop_back_val(); 3776 if (!Visited.insert(I)) continue; 3777 3778 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3779 if (It != ValueExprMap.end()) { 3780 ValuesAtScopes.erase(It->second); 3781 ValueExprMap.erase(It); 3782 if (PHINode *PN = dyn_cast<PHINode>(I)) 3783 ConstantEvolutionLoopExitValue.erase(PN); 3784 } 3785 3786 PushDefUseChildren(I, Worklist); 3787 } 3788} 3789 3790/// forgetValue - This method should be called by the client when it has 3791/// changed a value in a way that may effect its value, or which may 3792/// disconnect it from a def-use chain linking it to a loop. 3793void ScalarEvolution::forgetValue(Value *V) { 3794 Instruction *I = dyn_cast<Instruction>(V); 3795 if (!I) return; 3796 3797 // Drop information about expressions based on loop-header PHIs. 3798 SmallVector<Instruction *, 16> Worklist; 3799 Worklist.push_back(I); 3800 3801 SmallPtrSet<Instruction *, 8> Visited; 3802 while (!Worklist.empty()) { 3803 I = Worklist.pop_back_val(); 3804 if (!Visited.insert(I)) continue; 3805 3806 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3807 if (It != ValueExprMap.end()) { 3808 ValuesAtScopes.erase(It->second); 3809 ValueExprMap.erase(It); 3810 if (PHINode *PN = dyn_cast<PHINode>(I)) 3811 ConstantEvolutionLoopExitValue.erase(PN); 3812 } 3813 3814 PushDefUseChildren(I, Worklist); 3815 } 3816} 3817 3818/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3819/// of the specified loop will execute. 3820ScalarEvolution::BackedgeTakenInfo 3821ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3822 SmallVector<BasicBlock *, 8> ExitingBlocks; 3823 L->getExitingBlocks(ExitingBlocks); 3824 3825 // Examine all exits and pick the most conservative values. 3826 const SCEV *BECount = getCouldNotCompute(); 3827 const SCEV *MaxBECount = getCouldNotCompute(); 3828 bool CouldNotComputeBECount = false; 3829 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3830 BackedgeTakenInfo NewBTI = 3831 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3832 3833 if (NewBTI.Exact == getCouldNotCompute()) { 3834 // We couldn't compute an exact value for this exit, so 3835 // we won't be able to compute an exact value for the loop. 3836 CouldNotComputeBECount = true; 3837 BECount = getCouldNotCompute(); 3838 } else if (!CouldNotComputeBECount) { 3839 if (BECount == getCouldNotCompute()) 3840 BECount = NewBTI.Exact; 3841 else 3842 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3843 } 3844 if (MaxBECount == getCouldNotCompute()) 3845 MaxBECount = NewBTI.Max; 3846 else if (NewBTI.Max != getCouldNotCompute()) 3847 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3848 } 3849 3850 return BackedgeTakenInfo(BECount, MaxBECount); 3851} 3852 3853/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3854/// of the specified loop will execute if it exits via the specified block. 3855ScalarEvolution::BackedgeTakenInfo 3856ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3857 BasicBlock *ExitingBlock) { 3858 3859 // Okay, we've chosen an exiting block. See what condition causes us to 3860 // exit at this block. 3861 // 3862 // FIXME: we should be able to handle switch instructions (with a single exit) 3863 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3864 if (ExitBr == 0) return getCouldNotCompute(); 3865 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3866 3867 // At this point, we know we have a conditional branch that determines whether 3868 // the loop is exited. However, we don't know if the branch is executed each 3869 // time through the loop. If not, then the execution count of the branch will 3870 // not be equal to the trip count of the loop. 3871 // 3872 // Currently we check for this by checking to see if the Exit branch goes to 3873 // the loop header. If so, we know it will always execute the same number of 3874 // times as the loop. We also handle the case where the exit block *is* the 3875 // loop header. This is common for un-rotated loops. 3876 // 3877 // If both of those tests fail, walk up the unique predecessor chain to the 3878 // header, stopping if there is an edge that doesn't exit the loop. If the 3879 // header is reached, the execution count of the branch will be equal to the 3880 // trip count of the loop. 3881 // 3882 // More extensive analysis could be done to handle more cases here. 3883 // 3884 if (ExitBr->getSuccessor(0) != L->getHeader() && 3885 ExitBr->getSuccessor(1) != L->getHeader() && 3886 ExitBr->getParent() != L->getHeader()) { 3887 // The simple checks failed, try climbing the unique predecessor chain 3888 // up to the header. 3889 bool Ok = false; 3890 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3891 BasicBlock *Pred = BB->getUniquePredecessor(); 3892 if (!Pred) 3893 return getCouldNotCompute(); 3894 TerminatorInst *PredTerm = Pred->getTerminator(); 3895 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3896 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3897 if (PredSucc == BB) 3898 continue; 3899 // If the predecessor has a successor that isn't BB and isn't 3900 // outside the loop, assume the worst. 3901 if (L->contains(PredSucc)) 3902 return getCouldNotCompute(); 3903 } 3904 if (Pred == L->getHeader()) { 3905 Ok = true; 3906 break; 3907 } 3908 BB = Pred; 3909 } 3910 if (!Ok) 3911 return getCouldNotCompute(); 3912 } 3913 3914 // Proceed to the next level to examine the exit condition expression. 3915 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3916 ExitBr->getSuccessor(0), 3917 ExitBr->getSuccessor(1)); 3918} 3919 3920/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3921/// backedge of the specified loop will execute if its exit condition 3922/// were a conditional branch of ExitCond, TBB, and FBB. 3923ScalarEvolution::BackedgeTakenInfo 3924ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3925 Value *ExitCond, 3926 BasicBlock *TBB, 3927 BasicBlock *FBB) { 3928 // Check if the controlling expression for this loop is an And or Or. 3929 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3930 if (BO->getOpcode() == Instruction::And) { 3931 // Recurse on the operands of the and. 3932 BackedgeTakenInfo BTI0 = 3933 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3934 BackedgeTakenInfo BTI1 = 3935 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3936 const SCEV *BECount = getCouldNotCompute(); 3937 const SCEV *MaxBECount = getCouldNotCompute(); 3938 if (L->contains(TBB)) { 3939 // Both conditions must be true for the loop to continue executing. 3940 // Choose the less conservative count. 3941 if (BTI0.Exact == getCouldNotCompute() || 3942 BTI1.Exact == getCouldNotCompute()) 3943 BECount = getCouldNotCompute(); 3944 else 3945 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3946 if (BTI0.Max == getCouldNotCompute()) 3947 MaxBECount = BTI1.Max; 3948 else if (BTI1.Max == getCouldNotCompute()) 3949 MaxBECount = BTI0.Max; 3950 else 3951 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3952 } else { 3953 // Both conditions must be true at the same time for the loop to exit. 3954 // For now, be conservative. 3955 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3956 if (BTI0.Max == BTI1.Max) 3957 MaxBECount = BTI0.Max; 3958 if (BTI0.Exact == BTI1.Exact) 3959 BECount = BTI0.Exact; 3960 } 3961 3962 return BackedgeTakenInfo(BECount, MaxBECount); 3963 } 3964 if (BO->getOpcode() == Instruction::Or) { 3965 // Recurse on the operands of the or. 3966 BackedgeTakenInfo BTI0 = 3967 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3968 BackedgeTakenInfo BTI1 = 3969 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3970 const SCEV *BECount = getCouldNotCompute(); 3971 const SCEV *MaxBECount = getCouldNotCompute(); 3972 if (L->contains(FBB)) { 3973 // Both conditions must be false for the loop to continue executing. 3974 // Choose the less conservative count. 3975 if (BTI0.Exact == getCouldNotCompute() || 3976 BTI1.Exact == getCouldNotCompute()) 3977 BECount = getCouldNotCompute(); 3978 else 3979 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3980 if (BTI0.Max == getCouldNotCompute()) 3981 MaxBECount = BTI1.Max; 3982 else if (BTI1.Max == getCouldNotCompute()) 3983 MaxBECount = BTI0.Max; 3984 else 3985 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3986 } else { 3987 // Both conditions must be false at the same time for the loop to exit. 3988 // For now, be conservative. 3989 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3990 if (BTI0.Max == BTI1.Max) 3991 MaxBECount = BTI0.Max; 3992 if (BTI0.Exact == BTI1.Exact) 3993 BECount = BTI0.Exact; 3994 } 3995 3996 return BackedgeTakenInfo(BECount, MaxBECount); 3997 } 3998 } 3999 4000 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4001 // Proceed to the next level to examine the icmp. 4002 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4003 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 4004 4005 // Check for a constant condition. These are normally stripped out by 4006 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4007 // preserve the CFG and is temporarily leaving constant conditions 4008 // in place. 4009 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4010 if (L->contains(FBB) == !CI->getZExtValue()) 4011 // The backedge is always taken. 4012 return getCouldNotCompute(); 4013 else 4014 // The backedge is never taken. 4015 return getConstant(CI->getType(), 0); 4016 } 4017 4018 // If it's not an integer or pointer comparison then compute it the hard way. 4019 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4020} 4021 4022/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4023/// backedge of the specified loop will execute if its exit condition 4024/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4025ScalarEvolution::BackedgeTakenInfo 4026ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4027 ICmpInst *ExitCond, 4028 BasicBlock *TBB, 4029 BasicBlock *FBB) { 4030 4031 // If the condition was exit on true, convert the condition to exit on false 4032 ICmpInst::Predicate Cond; 4033 if (!L->contains(FBB)) 4034 Cond = ExitCond->getPredicate(); 4035 else 4036 Cond = ExitCond->getInversePredicate(); 4037 4038 // Handle common loops like: for (X = "string"; *X; ++X) 4039 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4040 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4041 BackedgeTakenInfo ItCnt = 4042 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4043 if (ItCnt.hasAnyInfo()) 4044 return ItCnt; 4045 } 4046 4047 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4048 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4049 4050 // Try to evaluate any dependencies out of the loop. 4051 LHS = getSCEVAtScope(LHS, L); 4052 RHS = getSCEVAtScope(RHS, L); 4053 4054 // At this point, we would like to compute how many iterations of the 4055 // loop the predicate will return true for these inputs. 4056 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 4057 // If there is a loop-invariant, force it into the RHS. 4058 std::swap(LHS, RHS); 4059 Cond = ICmpInst::getSwappedPredicate(Cond); 4060 } 4061 4062 // Simplify the operands before analyzing them. 4063 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4064 4065 // If we have a comparison of a chrec against a constant, try to use value 4066 // ranges to answer this query. 4067 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4068 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4069 if (AddRec->getLoop() == L) { 4070 // Form the constant range. 4071 ConstantRange CompRange( 4072 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4073 4074 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4075 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4076 } 4077 4078 switch (Cond) { 4079 case ICmpInst::ICMP_NE: { // while (X != Y) 4080 // Convert to: while (X-Y != 0) 4081 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4082 if (BTI.hasAnyInfo()) return BTI; 4083 break; 4084 } 4085 case ICmpInst::ICMP_EQ: { // while (X == Y) 4086 // Convert to: while (X-Y == 0) 4087 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4088 if (BTI.hasAnyInfo()) return BTI; 4089 break; 4090 } 4091 case ICmpInst::ICMP_SLT: { 4092 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4093 if (BTI.hasAnyInfo()) return BTI; 4094 break; 4095 } 4096 case ICmpInst::ICMP_SGT: { 4097 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4098 getNotSCEV(RHS), L, true); 4099 if (BTI.hasAnyInfo()) return BTI; 4100 break; 4101 } 4102 case ICmpInst::ICMP_ULT: { 4103 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4104 if (BTI.hasAnyInfo()) return BTI; 4105 break; 4106 } 4107 case ICmpInst::ICMP_UGT: { 4108 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4109 getNotSCEV(RHS), L, false); 4110 if (BTI.hasAnyInfo()) return BTI; 4111 break; 4112 } 4113 default: 4114#if 0 4115 dbgs() << "ComputeBackedgeTakenCount "; 4116 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4117 dbgs() << "[unsigned] "; 4118 dbgs() << *LHS << " " 4119 << Instruction::getOpcodeName(Instruction::ICmp) 4120 << " " << *RHS << "\n"; 4121#endif 4122 break; 4123 } 4124 return 4125 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4126} 4127 4128static ConstantInt * 4129EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4130 ScalarEvolution &SE) { 4131 const SCEV *InVal = SE.getConstant(C); 4132 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4133 assert(isa<SCEVConstant>(Val) && 4134 "Evaluation of SCEV at constant didn't fold correctly?"); 4135 return cast<SCEVConstant>(Val)->getValue(); 4136} 4137 4138/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4139/// and a GEP expression (missing the pointer index) indexing into it, return 4140/// the addressed element of the initializer or null if the index expression is 4141/// invalid. 4142static Constant * 4143GetAddressedElementFromGlobal(GlobalVariable *GV, 4144 const std::vector<ConstantInt*> &Indices) { 4145 Constant *Init = GV->getInitializer(); 4146 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4147 uint64_t Idx = Indices[i]->getZExtValue(); 4148 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4149 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4150 Init = cast<Constant>(CS->getOperand(Idx)); 4151 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4152 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4153 Init = cast<Constant>(CA->getOperand(Idx)); 4154 } else if (isa<ConstantAggregateZero>(Init)) { 4155 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4156 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4157 Init = Constant::getNullValue(STy->getElementType(Idx)); 4158 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4159 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4160 Init = Constant::getNullValue(ATy->getElementType()); 4161 } else { 4162 llvm_unreachable("Unknown constant aggregate type!"); 4163 } 4164 return 0; 4165 } else { 4166 return 0; // Unknown initializer type 4167 } 4168 } 4169 return Init; 4170} 4171 4172/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4173/// 'icmp op load X, cst', try to see if we can compute the backedge 4174/// execution count. 4175ScalarEvolution::BackedgeTakenInfo 4176ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4177 LoadInst *LI, 4178 Constant *RHS, 4179 const Loop *L, 4180 ICmpInst::Predicate predicate) { 4181 if (LI->isVolatile()) return getCouldNotCompute(); 4182 4183 // Check to see if the loaded pointer is a getelementptr of a global. 4184 // TODO: Use SCEV instead of manually grubbing with GEPs. 4185 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4186 if (!GEP) return getCouldNotCompute(); 4187 4188 // Make sure that it is really a constant global we are gepping, with an 4189 // initializer, and make sure the first IDX is really 0. 4190 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4191 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4192 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4193 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4194 return getCouldNotCompute(); 4195 4196 // Okay, we allow one non-constant index into the GEP instruction. 4197 Value *VarIdx = 0; 4198 std::vector<ConstantInt*> Indexes; 4199 unsigned VarIdxNum = 0; 4200 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4201 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4202 Indexes.push_back(CI); 4203 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4204 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4205 VarIdx = GEP->getOperand(i); 4206 VarIdxNum = i-2; 4207 Indexes.push_back(0); 4208 } 4209 4210 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4211 // Check to see if X is a loop variant variable value now. 4212 const SCEV *Idx = getSCEV(VarIdx); 4213 Idx = getSCEVAtScope(Idx, L); 4214 4215 // We can only recognize very limited forms of loop index expressions, in 4216 // particular, only affine AddRec's like {C1,+,C2}. 4217 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4218 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4219 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4220 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4221 return getCouldNotCompute(); 4222 4223 unsigned MaxSteps = MaxBruteForceIterations; 4224 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4225 ConstantInt *ItCst = ConstantInt::get( 4226 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4227 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4228 4229 // Form the GEP offset. 4230 Indexes[VarIdxNum] = Val; 4231 4232 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4233 if (Result == 0) break; // Cannot compute! 4234 4235 // Evaluate the condition for this iteration. 4236 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4237 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4238 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4239#if 0 4240 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4241 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4242 << "***\n"; 4243#endif 4244 ++NumArrayLenItCounts; 4245 return getConstant(ItCst); // Found terminating iteration! 4246 } 4247 } 4248 return getCouldNotCompute(); 4249} 4250 4251 4252/// CanConstantFold - Return true if we can constant fold an instruction of the 4253/// specified type, assuming that all operands were constants. 4254static bool CanConstantFold(const Instruction *I) { 4255 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4256 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4257 return true; 4258 4259 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4260 if (const Function *F = CI->getCalledFunction()) 4261 return canConstantFoldCallTo(F); 4262 return false; 4263} 4264 4265/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4266/// in the loop that V is derived from. We allow arbitrary operations along the 4267/// way, but the operands of an operation must either be constants or a value 4268/// derived from a constant PHI. If this expression does not fit with these 4269/// constraints, return null. 4270static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4271 // If this is not an instruction, or if this is an instruction outside of the 4272 // loop, it can't be derived from a loop PHI. 4273 Instruction *I = dyn_cast<Instruction>(V); 4274 if (I == 0 || !L->contains(I)) return 0; 4275 4276 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4277 if (L->getHeader() == I->getParent()) 4278 return PN; 4279 else 4280 // We don't currently keep track of the control flow needed to evaluate 4281 // PHIs, so we cannot handle PHIs inside of loops. 4282 return 0; 4283 } 4284 4285 // If we won't be able to constant fold this expression even if the operands 4286 // are constants, return early. 4287 if (!CanConstantFold(I)) return 0; 4288 4289 // Otherwise, we can evaluate this instruction if all of its operands are 4290 // constant or derived from a PHI node themselves. 4291 PHINode *PHI = 0; 4292 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4293 if (!isa<Constant>(I->getOperand(Op))) { 4294 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4295 if (P == 0) return 0; // Not evolving from PHI 4296 if (PHI == 0) 4297 PHI = P; 4298 else if (PHI != P) 4299 return 0; // Evolving from multiple different PHIs. 4300 } 4301 4302 // This is a expression evolving from a constant PHI! 4303 return PHI; 4304} 4305 4306/// EvaluateExpression - Given an expression that passes the 4307/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4308/// in the loop has the value PHIVal. If we can't fold this expression for some 4309/// reason, return null. 4310static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4311 const TargetData *TD) { 4312 if (isa<PHINode>(V)) return PHIVal; 4313 if (Constant *C = dyn_cast<Constant>(V)) return C; 4314 Instruction *I = cast<Instruction>(V); 4315 4316 std::vector<Constant*> Operands(I->getNumOperands()); 4317 4318 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4319 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4320 if (Operands[i] == 0) return 0; 4321 } 4322 4323 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4324 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4325 Operands[1], TD); 4326 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4327 &Operands[0], Operands.size(), TD); 4328} 4329 4330/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4331/// in the header of its containing loop, we know the loop executes a 4332/// constant number of times, and the PHI node is just a recurrence 4333/// involving constants, fold it. 4334Constant * 4335ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4336 const APInt &BEs, 4337 const Loop *L) { 4338 std::map<PHINode*, Constant*>::const_iterator I = 4339 ConstantEvolutionLoopExitValue.find(PN); 4340 if (I != ConstantEvolutionLoopExitValue.end()) 4341 return I->second; 4342 4343 if (BEs.ugt(MaxBruteForceIterations)) 4344 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4345 4346 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4347 4348 // Since the loop is canonicalized, the PHI node must have two entries. One 4349 // entry must be a constant (coming in from outside of the loop), and the 4350 // second must be derived from the same PHI. 4351 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4352 Constant *StartCST = 4353 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4354 if (StartCST == 0) 4355 return RetVal = 0; // Must be a constant. 4356 4357 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4358 if (getConstantEvolvingPHI(BEValue, L) != PN && 4359 !isa<Constant>(BEValue)) 4360 return RetVal = 0; // Not derived from same PHI. 4361 4362 // Execute the loop symbolically to determine the exit value. 4363 if (BEs.getActiveBits() >= 32) 4364 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4365 4366 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4367 unsigned IterationNum = 0; 4368 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4369 if (IterationNum == NumIterations) 4370 return RetVal = PHIVal; // Got exit value! 4371 4372 // Compute the value of the PHI node for the next iteration. 4373 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4374 if (NextPHI == PHIVal) 4375 return RetVal = NextPHI; // Stopped evolving! 4376 if (NextPHI == 0) 4377 return 0; // Couldn't evaluate! 4378 PHIVal = NextPHI; 4379 } 4380} 4381 4382/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4383/// constant number of times (the condition evolves only from constants), 4384/// try to evaluate a few iterations of the loop until we get the exit 4385/// condition gets a value of ExitWhen (true or false). If we cannot 4386/// evaluate the trip count of the loop, return getCouldNotCompute(). 4387const SCEV * 4388ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4389 Value *Cond, 4390 bool ExitWhen) { 4391 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4392 if (PN == 0) return getCouldNotCompute(); 4393 4394 // If the loop is canonicalized, the PHI will have exactly two entries. 4395 // That's the only form we support here. 4396 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4397 4398 // One entry must be a constant (coming in from outside of the loop), and the 4399 // second must be derived from the same PHI. 4400 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4401 Constant *StartCST = 4402 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4403 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4404 4405 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4406 if (getConstantEvolvingPHI(BEValue, L) != PN && 4407 !isa<Constant>(BEValue)) 4408 return getCouldNotCompute(); // Not derived from same PHI. 4409 4410 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4411 // the loop symbolically to determine when the condition gets a value of 4412 // "ExitWhen". 4413 unsigned IterationNum = 0; 4414 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4415 for (Constant *PHIVal = StartCST; 4416 IterationNum != MaxIterations; ++IterationNum) { 4417 ConstantInt *CondVal = 4418 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4419 4420 // Couldn't symbolically evaluate. 4421 if (!CondVal) return getCouldNotCompute(); 4422 4423 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4424 ++NumBruteForceTripCountsComputed; 4425 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4426 } 4427 4428 // Compute the value of the PHI node for the next iteration. 4429 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4430 if (NextPHI == 0 || NextPHI == PHIVal) 4431 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4432 PHIVal = NextPHI; 4433 } 4434 4435 // Too many iterations were needed to evaluate. 4436 return getCouldNotCompute(); 4437} 4438 4439/// getSCEVAtScope - Return a SCEV expression for the specified value 4440/// at the specified scope in the program. The L value specifies a loop 4441/// nest to evaluate the expression at, where null is the top-level or a 4442/// specified loop is immediately inside of the loop. 4443/// 4444/// This method can be used to compute the exit value for a variable defined 4445/// in a loop by querying what the value will hold in the parent loop. 4446/// 4447/// In the case that a relevant loop exit value cannot be computed, the 4448/// original value V is returned. 4449const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4450 // Check to see if we've folded this expression at this loop before. 4451 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4452 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4453 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4454 if (!Pair.second) 4455 return Pair.first->second ? Pair.first->second : V; 4456 4457 // Otherwise compute it. 4458 const SCEV *C = computeSCEVAtScope(V, L); 4459 ValuesAtScopes[V][L] = C; 4460 return C; 4461} 4462 4463const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4464 if (isa<SCEVConstant>(V)) return V; 4465 4466 // If this instruction is evolved from a constant-evolving PHI, compute the 4467 // exit value from the loop without using SCEVs. 4468 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4469 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4470 const Loop *LI = (*this->LI)[I->getParent()]; 4471 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4472 if (PHINode *PN = dyn_cast<PHINode>(I)) 4473 if (PN->getParent() == LI->getHeader()) { 4474 // Okay, there is no closed form solution for the PHI node. Check 4475 // to see if the loop that contains it has a known backedge-taken 4476 // count. If so, we may be able to force computation of the exit 4477 // value. 4478 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4479 if (const SCEVConstant *BTCC = 4480 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4481 // Okay, we know how many times the containing loop executes. If 4482 // this is a constant evolving PHI node, get the final value at 4483 // the specified iteration number. 4484 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4485 BTCC->getValue()->getValue(), 4486 LI); 4487 if (RV) return getSCEV(RV); 4488 } 4489 } 4490 4491 // Okay, this is an expression that we cannot symbolically evaluate 4492 // into a SCEV. Check to see if it's possible to symbolically evaluate 4493 // the arguments into constants, and if so, try to constant propagate the 4494 // result. This is particularly useful for computing loop exit values. 4495 if (CanConstantFold(I)) { 4496 SmallVector<Constant *, 4> Operands; 4497 bool MadeImprovement = false; 4498 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4499 Value *Op = I->getOperand(i); 4500 if (Constant *C = dyn_cast<Constant>(Op)) { 4501 Operands.push_back(C); 4502 continue; 4503 } 4504 4505 // If any of the operands is non-constant and if they are 4506 // non-integer and non-pointer, don't even try to analyze them 4507 // with scev techniques. 4508 if (!isSCEVable(Op->getType())) 4509 return V; 4510 4511 const SCEV *OrigV = getSCEV(Op); 4512 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4513 MadeImprovement |= OrigV != OpV; 4514 4515 Constant *C = 0; 4516 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4517 C = SC->getValue(); 4518 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4519 C = dyn_cast<Constant>(SU->getValue()); 4520 if (!C) return V; 4521 if (C->getType() != Op->getType()) 4522 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4523 Op->getType(), 4524 false), 4525 C, Op->getType()); 4526 Operands.push_back(C); 4527 } 4528 4529 // Check to see if getSCEVAtScope actually made an improvement. 4530 if (MadeImprovement) { 4531 Constant *C = 0; 4532 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4533 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4534 Operands[0], Operands[1], TD); 4535 else 4536 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4537 &Operands[0], Operands.size(), TD); 4538 if (!C) return V; 4539 return getSCEV(C); 4540 } 4541 } 4542 } 4543 4544 // This is some other type of SCEVUnknown, just return it. 4545 return V; 4546 } 4547 4548 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4549 // Avoid performing the look-up in the common case where the specified 4550 // expression has no loop-variant portions. 4551 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4552 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4553 if (OpAtScope != Comm->getOperand(i)) { 4554 // Okay, at least one of these operands is loop variant but might be 4555 // foldable. Build a new instance of the folded commutative expression. 4556 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4557 Comm->op_begin()+i); 4558 NewOps.push_back(OpAtScope); 4559 4560 for (++i; i != e; ++i) { 4561 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4562 NewOps.push_back(OpAtScope); 4563 } 4564 if (isa<SCEVAddExpr>(Comm)) 4565 return getAddExpr(NewOps); 4566 if (isa<SCEVMulExpr>(Comm)) 4567 return getMulExpr(NewOps); 4568 if (isa<SCEVSMaxExpr>(Comm)) 4569 return getSMaxExpr(NewOps); 4570 if (isa<SCEVUMaxExpr>(Comm)) 4571 return getUMaxExpr(NewOps); 4572 llvm_unreachable("Unknown commutative SCEV type!"); 4573 } 4574 } 4575 // If we got here, all operands are loop invariant. 4576 return Comm; 4577 } 4578 4579 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4580 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4581 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4582 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4583 return Div; // must be loop invariant 4584 return getUDivExpr(LHS, RHS); 4585 } 4586 4587 // If this is a loop recurrence for a loop that does not contain L, then we 4588 // are dealing with the final value computed by the loop. 4589 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4590 // First, attempt to evaluate each operand. 4591 // Avoid performing the look-up in the common case where the specified 4592 // expression has no loop-variant portions. 4593 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4594 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4595 if (OpAtScope == AddRec->getOperand(i)) 4596 continue; 4597 4598 // Okay, at least one of these operands is loop variant but might be 4599 // foldable. Build a new instance of the folded commutative expression. 4600 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4601 AddRec->op_begin()+i); 4602 NewOps.push_back(OpAtScope); 4603 for (++i; i != e; ++i) 4604 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4605 4606 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4607 break; 4608 } 4609 4610 // If the scope is outside the addrec's loop, evaluate it by using the 4611 // loop exit value of the addrec. 4612 if (!AddRec->getLoop()->contains(L)) { 4613 // To evaluate this recurrence, we need to know how many times the AddRec 4614 // loop iterates. Compute this now. 4615 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4616 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4617 4618 // Then, evaluate the AddRec. 4619 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4620 } 4621 4622 return AddRec; 4623 } 4624 4625 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4626 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4627 if (Op == Cast->getOperand()) 4628 return Cast; // must be loop invariant 4629 return getZeroExtendExpr(Op, Cast->getType()); 4630 } 4631 4632 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4633 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4634 if (Op == Cast->getOperand()) 4635 return Cast; // must be loop invariant 4636 return getSignExtendExpr(Op, Cast->getType()); 4637 } 4638 4639 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4640 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4641 if (Op == Cast->getOperand()) 4642 return Cast; // must be loop invariant 4643 return getTruncateExpr(Op, Cast->getType()); 4644 } 4645 4646 llvm_unreachable("Unknown SCEV type!"); 4647 return 0; 4648} 4649 4650/// getSCEVAtScope - This is a convenience function which does 4651/// getSCEVAtScope(getSCEV(V), L). 4652const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4653 return getSCEVAtScope(getSCEV(V), L); 4654} 4655 4656/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4657/// following equation: 4658/// 4659/// A * X = B (mod N) 4660/// 4661/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4662/// A and B isn't important. 4663/// 4664/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4665static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4666 ScalarEvolution &SE) { 4667 uint32_t BW = A.getBitWidth(); 4668 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4669 assert(A != 0 && "A must be non-zero."); 4670 4671 // 1. D = gcd(A, N) 4672 // 4673 // The gcd of A and N may have only one prime factor: 2. The number of 4674 // trailing zeros in A is its multiplicity 4675 uint32_t Mult2 = A.countTrailingZeros(); 4676 // D = 2^Mult2 4677 4678 // 2. Check if B is divisible by D. 4679 // 4680 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4681 // is not less than multiplicity of this prime factor for D. 4682 if (B.countTrailingZeros() < Mult2) 4683 return SE.getCouldNotCompute(); 4684 4685 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4686 // modulo (N / D). 4687 // 4688 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4689 // bit width during computations. 4690 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4691 APInt Mod(BW + 1, 0); 4692 Mod.set(BW - Mult2); // Mod = N / D 4693 APInt I = AD.multiplicativeInverse(Mod); 4694 4695 // 4. Compute the minimum unsigned root of the equation: 4696 // I * (B / D) mod (N / D) 4697 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4698 4699 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4700 // bits. 4701 return SE.getConstant(Result.trunc(BW)); 4702} 4703 4704/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4705/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4706/// might be the same) or two SCEVCouldNotCompute objects. 4707/// 4708static std::pair<const SCEV *,const SCEV *> 4709SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4710 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4711 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4712 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4713 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4714 4715 // We currently can only solve this if the coefficients are constants. 4716 if (!LC || !MC || !NC) { 4717 const SCEV *CNC = SE.getCouldNotCompute(); 4718 return std::make_pair(CNC, CNC); 4719 } 4720 4721 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4722 const APInt &L = LC->getValue()->getValue(); 4723 const APInt &M = MC->getValue()->getValue(); 4724 const APInt &N = NC->getValue()->getValue(); 4725 APInt Two(BitWidth, 2); 4726 APInt Four(BitWidth, 4); 4727 4728 { 4729 using namespace APIntOps; 4730 const APInt& C = L; 4731 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4732 // The B coefficient is M-N/2 4733 APInt B(M); 4734 B -= sdiv(N,Two); 4735 4736 // The A coefficient is N/2 4737 APInt A(N.sdiv(Two)); 4738 4739 // Compute the B^2-4ac term. 4740 APInt SqrtTerm(B); 4741 SqrtTerm *= B; 4742 SqrtTerm -= Four * (A * C); 4743 4744 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4745 // integer value or else APInt::sqrt() will assert. 4746 APInt SqrtVal(SqrtTerm.sqrt()); 4747 4748 // Compute the two solutions for the quadratic formula. 4749 // The divisions must be performed as signed divisions. 4750 APInt NegB(-B); 4751 APInt TwoA( A << 1 ); 4752 if (TwoA.isMinValue()) { 4753 const SCEV *CNC = SE.getCouldNotCompute(); 4754 return std::make_pair(CNC, CNC); 4755 } 4756 4757 LLVMContext &Context = SE.getContext(); 4758 4759 ConstantInt *Solution1 = 4760 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4761 ConstantInt *Solution2 = 4762 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4763 4764 return std::make_pair(SE.getConstant(Solution1), 4765 SE.getConstant(Solution2)); 4766 } // end APIntOps namespace 4767} 4768 4769/// HowFarToZero - Return the number of times a backedge comparing the specified 4770/// value to zero will execute. If not computable, return CouldNotCompute. 4771ScalarEvolution::BackedgeTakenInfo 4772ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4773 // If the value is a constant 4774 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4775 // If the value is already zero, the branch will execute zero times. 4776 if (C->getValue()->isZero()) return C; 4777 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4778 } 4779 4780 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4781 if (!AddRec || AddRec->getLoop() != L) 4782 return getCouldNotCompute(); 4783 4784 if (AddRec->isAffine()) { 4785 // If this is an affine expression, the execution count of this branch is 4786 // the minimum unsigned root of the following equation: 4787 // 4788 // Start + Step*N = 0 (mod 2^BW) 4789 // 4790 // equivalent to: 4791 // 4792 // Step*N = -Start (mod 2^BW) 4793 // 4794 // where BW is the common bit width of Start and Step. 4795 4796 // Get the initial value for the loop. 4797 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4798 L->getParentLoop()); 4799 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4800 L->getParentLoop()); 4801 4802 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4803 // For now we handle only constant steps. 4804 4805 // First, handle unitary steps. 4806 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4807 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4808 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4809 return Start; // N = Start (as unsigned) 4810 4811 // Then, try to solve the above equation provided that Start is constant. 4812 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4813 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4814 -StartC->getValue()->getValue(), 4815 *this); 4816 } 4817 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4818 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4819 // the quadratic equation to solve it. 4820 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4821 *this); 4822 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4823 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4824 if (R1) { 4825#if 0 4826 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4827 << " sol#2: " << *R2 << "\n"; 4828#endif 4829 // Pick the smallest positive root value. 4830 if (ConstantInt *CB = 4831 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4832 R1->getValue(), R2->getValue()))) { 4833 if (CB->getZExtValue() == false) 4834 std::swap(R1, R2); // R1 is the minimum root now. 4835 4836 // We can only use this value if the chrec ends up with an exact zero 4837 // value at this index. When solving for "X*X != 5", for example, we 4838 // should not accept a root of 2. 4839 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4840 if (Val->isZero()) 4841 return R1; // We found a quadratic root! 4842 } 4843 } 4844 } 4845 4846 return getCouldNotCompute(); 4847} 4848 4849/// HowFarToNonZero - Return the number of times a backedge checking the 4850/// specified value for nonzero will execute. If not computable, return 4851/// CouldNotCompute 4852ScalarEvolution::BackedgeTakenInfo 4853ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4854 // Loops that look like: while (X == 0) are very strange indeed. We don't 4855 // handle them yet except for the trivial case. This could be expanded in the 4856 // future as needed. 4857 4858 // If the value is a constant, check to see if it is known to be non-zero 4859 // already. If so, the backedge will execute zero times. 4860 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4861 if (!C->getValue()->isNullValue()) 4862 return getConstant(C->getType(), 0); 4863 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4864 } 4865 4866 // We could implement others, but I really doubt anyone writes loops like 4867 // this, and if they did, they would already be constant folded. 4868 return getCouldNotCompute(); 4869} 4870 4871/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4872/// (which may not be an immediate predecessor) which has exactly one 4873/// successor from which BB is reachable, or null if no such block is 4874/// found. 4875/// 4876std::pair<BasicBlock *, BasicBlock *> 4877ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4878 // If the block has a unique predecessor, then there is no path from the 4879 // predecessor to the block that does not go through the direct edge 4880 // from the predecessor to the block. 4881 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4882 return std::make_pair(Pred, BB); 4883 4884 // A loop's header is defined to be a block that dominates the loop. 4885 // If the header has a unique predecessor outside the loop, it must be 4886 // a block that has exactly one successor that can reach the loop. 4887 if (Loop *L = LI->getLoopFor(BB)) 4888 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4889 4890 return std::pair<BasicBlock *, BasicBlock *>(); 4891} 4892 4893/// HasSameValue - SCEV structural equivalence is usually sufficient for 4894/// testing whether two expressions are equal, however for the purposes of 4895/// looking for a condition guarding a loop, it can be useful to be a little 4896/// more general, since a front-end may have replicated the controlling 4897/// expression. 4898/// 4899static bool HasSameValue(const SCEV *A, const SCEV *B) { 4900 // Quick check to see if they are the same SCEV. 4901 if (A == B) return true; 4902 4903 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4904 // two different instructions with the same value. Check for this case. 4905 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4906 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4907 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4908 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4909 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4910 return true; 4911 4912 // Otherwise assume they may have a different value. 4913 return false; 4914} 4915 4916/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4917/// predicate Pred. Return true iff any changes were made. 4918/// 4919bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4920 const SCEV *&LHS, const SCEV *&RHS) { 4921 bool Changed = false; 4922 4923 // Canonicalize a constant to the right side. 4924 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4925 // Check for both operands constant. 4926 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4927 if (ConstantExpr::getICmp(Pred, 4928 LHSC->getValue(), 4929 RHSC->getValue())->isNullValue()) 4930 goto trivially_false; 4931 else 4932 goto trivially_true; 4933 } 4934 // Otherwise swap the operands to put the constant on the right. 4935 std::swap(LHS, RHS); 4936 Pred = ICmpInst::getSwappedPredicate(Pred); 4937 Changed = true; 4938 } 4939 4940 // If we're comparing an addrec with a value which is loop-invariant in the 4941 // addrec's loop, put the addrec on the left. Also make a dominance check, 4942 // as both operands could be addrecs loop-invariant in each other's loop. 4943 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4944 const Loop *L = AR->getLoop(); 4945 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4946 std::swap(LHS, RHS); 4947 Pred = ICmpInst::getSwappedPredicate(Pred); 4948 Changed = true; 4949 } 4950 } 4951 4952 // If there's a constant operand, canonicalize comparisons with boundary 4953 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4954 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4955 const APInt &RA = RC->getValue()->getValue(); 4956 switch (Pred) { 4957 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4958 case ICmpInst::ICMP_EQ: 4959 case ICmpInst::ICMP_NE: 4960 break; 4961 case ICmpInst::ICMP_UGE: 4962 if ((RA - 1).isMinValue()) { 4963 Pred = ICmpInst::ICMP_NE; 4964 RHS = getConstant(RA - 1); 4965 Changed = true; 4966 break; 4967 } 4968 if (RA.isMaxValue()) { 4969 Pred = ICmpInst::ICMP_EQ; 4970 Changed = true; 4971 break; 4972 } 4973 if (RA.isMinValue()) goto trivially_true; 4974 4975 Pred = ICmpInst::ICMP_UGT; 4976 RHS = getConstant(RA - 1); 4977 Changed = true; 4978 break; 4979 case ICmpInst::ICMP_ULE: 4980 if ((RA + 1).isMaxValue()) { 4981 Pred = ICmpInst::ICMP_NE; 4982 RHS = getConstant(RA + 1); 4983 Changed = true; 4984 break; 4985 } 4986 if (RA.isMinValue()) { 4987 Pred = ICmpInst::ICMP_EQ; 4988 Changed = true; 4989 break; 4990 } 4991 if (RA.isMaxValue()) goto trivially_true; 4992 4993 Pred = ICmpInst::ICMP_ULT; 4994 RHS = getConstant(RA + 1); 4995 Changed = true; 4996 break; 4997 case ICmpInst::ICMP_SGE: 4998 if ((RA - 1).isMinSignedValue()) { 4999 Pred = ICmpInst::ICMP_NE; 5000 RHS = getConstant(RA - 1); 5001 Changed = true; 5002 break; 5003 } 5004 if (RA.isMaxSignedValue()) { 5005 Pred = ICmpInst::ICMP_EQ; 5006 Changed = true; 5007 break; 5008 } 5009 if (RA.isMinSignedValue()) goto trivially_true; 5010 5011 Pred = ICmpInst::ICMP_SGT; 5012 RHS = getConstant(RA - 1); 5013 Changed = true; 5014 break; 5015 case ICmpInst::ICMP_SLE: 5016 if ((RA + 1).isMaxSignedValue()) { 5017 Pred = ICmpInst::ICMP_NE; 5018 RHS = getConstant(RA + 1); 5019 Changed = true; 5020 break; 5021 } 5022 if (RA.isMinSignedValue()) { 5023 Pred = ICmpInst::ICMP_EQ; 5024 Changed = true; 5025 break; 5026 } 5027 if (RA.isMaxSignedValue()) goto trivially_true; 5028 5029 Pred = ICmpInst::ICMP_SLT; 5030 RHS = getConstant(RA + 1); 5031 Changed = true; 5032 break; 5033 case ICmpInst::ICMP_UGT: 5034 if (RA.isMinValue()) { 5035 Pred = ICmpInst::ICMP_NE; 5036 Changed = true; 5037 break; 5038 } 5039 if ((RA + 1).isMaxValue()) { 5040 Pred = ICmpInst::ICMP_EQ; 5041 RHS = getConstant(RA + 1); 5042 Changed = true; 5043 break; 5044 } 5045 if (RA.isMaxValue()) goto trivially_false; 5046 break; 5047 case ICmpInst::ICMP_ULT: 5048 if (RA.isMaxValue()) { 5049 Pred = ICmpInst::ICMP_NE; 5050 Changed = true; 5051 break; 5052 } 5053 if ((RA - 1).isMinValue()) { 5054 Pred = ICmpInst::ICMP_EQ; 5055 RHS = getConstant(RA - 1); 5056 Changed = true; 5057 break; 5058 } 5059 if (RA.isMinValue()) goto trivially_false; 5060 break; 5061 case ICmpInst::ICMP_SGT: 5062 if (RA.isMinSignedValue()) { 5063 Pred = ICmpInst::ICMP_NE; 5064 Changed = true; 5065 break; 5066 } 5067 if ((RA + 1).isMaxSignedValue()) { 5068 Pred = ICmpInst::ICMP_EQ; 5069 RHS = getConstant(RA + 1); 5070 Changed = true; 5071 break; 5072 } 5073 if (RA.isMaxSignedValue()) goto trivially_false; 5074 break; 5075 case ICmpInst::ICMP_SLT: 5076 if (RA.isMaxSignedValue()) { 5077 Pred = ICmpInst::ICMP_NE; 5078 Changed = true; 5079 break; 5080 } 5081 if ((RA - 1).isMinSignedValue()) { 5082 Pred = ICmpInst::ICMP_EQ; 5083 RHS = getConstant(RA - 1); 5084 Changed = true; 5085 break; 5086 } 5087 if (RA.isMinSignedValue()) goto trivially_false; 5088 break; 5089 } 5090 } 5091 5092 // Check for obvious equality. 5093 if (HasSameValue(LHS, RHS)) { 5094 if (ICmpInst::isTrueWhenEqual(Pred)) 5095 goto trivially_true; 5096 if (ICmpInst::isFalseWhenEqual(Pred)) 5097 goto trivially_false; 5098 } 5099 5100 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5101 // adding or subtracting 1 from one of the operands. 5102 switch (Pred) { 5103 case ICmpInst::ICMP_SLE: 5104 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5105 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5106 /*HasNUW=*/false, /*HasNSW=*/true); 5107 Pred = ICmpInst::ICMP_SLT; 5108 Changed = true; 5109 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5110 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5111 /*HasNUW=*/false, /*HasNSW=*/true); 5112 Pred = ICmpInst::ICMP_SLT; 5113 Changed = true; 5114 } 5115 break; 5116 case ICmpInst::ICMP_SGE: 5117 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5118 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5119 /*HasNUW=*/false, /*HasNSW=*/true); 5120 Pred = ICmpInst::ICMP_SGT; 5121 Changed = true; 5122 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5123 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5124 /*HasNUW=*/false, /*HasNSW=*/true); 5125 Pred = ICmpInst::ICMP_SGT; 5126 Changed = true; 5127 } 5128 break; 5129 case ICmpInst::ICMP_ULE: 5130 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5131 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5132 /*HasNUW=*/true, /*HasNSW=*/false); 5133 Pred = ICmpInst::ICMP_ULT; 5134 Changed = true; 5135 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5136 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5137 /*HasNUW=*/true, /*HasNSW=*/false); 5138 Pred = ICmpInst::ICMP_ULT; 5139 Changed = true; 5140 } 5141 break; 5142 case ICmpInst::ICMP_UGE: 5143 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5144 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5145 /*HasNUW=*/true, /*HasNSW=*/false); 5146 Pred = ICmpInst::ICMP_UGT; 5147 Changed = true; 5148 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5149 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5150 /*HasNUW=*/true, /*HasNSW=*/false); 5151 Pred = ICmpInst::ICMP_UGT; 5152 Changed = true; 5153 } 5154 break; 5155 default: 5156 break; 5157 } 5158 5159 // TODO: More simplifications are possible here. 5160 5161 return Changed; 5162 5163trivially_true: 5164 // Return 0 == 0. 5165 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5166 Pred = ICmpInst::ICMP_EQ; 5167 return true; 5168 5169trivially_false: 5170 // Return 0 != 0. 5171 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5172 Pred = ICmpInst::ICMP_NE; 5173 return true; 5174} 5175 5176bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5177 return getSignedRange(S).getSignedMax().isNegative(); 5178} 5179 5180bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5181 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5182} 5183 5184bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5185 return !getSignedRange(S).getSignedMin().isNegative(); 5186} 5187 5188bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5189 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5190} 5191 5192bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5193 return isKnownNegative(S) || isKnownPositive(S); 5194} 5195 5196bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5197 const SCEV *LHS, const SCEV *RHS) { 5198 // Canonicalize the inputs first. 5199 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5200 5201 // If LHS or RHS is an addrec, check to see if the condition is true in 5202 // every iteration of the loop. 5203 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5204 if (isLoopEntryGuardedByCond( 5205 AR->getLoop(), Pred, AR->getStart(), RHS) && 5206 isLoopBackedgeGuardedByCond( 5207 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5208 return true; 5209 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5210 if (isLoopEntryGuardedByCond( 5211 AR->getLoop(), Pred, LHS, AR->getStart()) && 5212 isLoopBackedgeGuardedByCond( 5213 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5214 return true; 5215 5216 // Otherwise see what can be done with known constant ranges. 5217 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5218} 5219 5220bool 5221ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5222 const SCEV *LHS, const SCEV *RHS) { 5223 if (HasSameValue(LHS, RHS)) 5224 return ICmpInst::isTrueWhenEqual(Pred); 5225 5226 // This code is split out from isKnownPredicate because it is called from 5227 // within isLoopEntryGuardedByCond. 5228 switch (Pred) { 5229 default: 5230 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5231 break; 5232 case ICmpInst::ICMP_SGT: 5233 Pred = ICmpInst::ICMP_SLT; 5234 std::swap(LHS, RHS); 5235 case ICmpInst::ICMP_SLT: { 5236 ConstantRange LHSRange = getSignedRange(LHS); 5237 ConstantRange RHSRange = getSignedRange(RHS); 5238 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5239 return true; 5240 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5241 return false; 5242 break; 5243 } 5244 case ICmpInst::ICMP_SGE: 5245 Pred = ICmpInst::ICMP_SLE; 5246 std::swap(LHS, RHS); 5247 case ICmpInst::ICMP_SLE: { 5248 ConstantRange LHSRange = getSignedRange(LHS); 5249 ConstantRange RHSRange = getSignedRange(RHS); 5250 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5251 return true; 5252 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5253 return false; 5254 break; 5255 } 5256 case ICmpInst::ICMP_UGT: 5257 Pred = ICmpInst::ICMP_ULT; 5258 std::swap(LHS, RHS); 5259 case ICmpInst::ICMP_ULT: { 5260 ConstantRange LHSRange = getUnsignedRange(LHS); 5261 ConstantRange RHSRange = getUnsignedRange(RHS); 5262 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5263 return true; 5264 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5265 return false; 5266 break; 5267 } 5268 case ICmpInst::ICMP_UGE: 5269 Pred = ICmpInst::ICMP_ULE; 5270 std::swap(LHS, RHS); 5271 case ICmpInst::ICMP_ULE: { 5272 ConstantRange LHSRange = getUnsignedRange(LHS); 5273 ConstantRange RHSRange = getUnsignedRange(RHS); 5274 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5275 return true; 5276 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5277 return false; 5278 break; 5279 } 5280 case ICmpInst::ICMP_NE: { 5281 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5282 return true; 5283 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5284 return true; 5285 5286 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5287 if (isKnownNonZero(Diff)) 5288 return true; 5289 break; 5290 } 5291 case ICmpInst::ICMP_EQ: 5292 // The check at the top of the function catches the case where 5293 // the values are known to be equal. 5294 break; 5295 } 5296 return false; 5297} 5298 5299/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5300/// protected by a conditional between LHS and RHS. This is used to 5301/// to eliminate casts. 5302bool 5303ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5304 ICmpInst::Predicate Pred, 5305 const SCEV *LHS, const SCEV *RHS) { 5306 // Interpret a null as meaning no loop, where there is obviously no guard 5307 // (interprocedural conditions notwithstanding). 5308 if (!L) return true; 5309 5310 BasicBlock *Latch = L->getLoopLatch(); 5311 if (!Latch) 5312 return false; 5313 5314 BranchInst *LoopContinuePredicate = 5315 dyn_cast<BranchInst>(Latch->getTerminator()); 5316 if (!LoopContinuePredicate || 5317 LoopContinuePredicate->isUnconditional()) 5318 return false; 5319 5320 return isImpliedCond(Pred, LHS, RHS, 5321 LoopContinuePredicate->getCondition(), 5322 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5323} 5324 5325/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5326/// by a conditional between LHS and RHS. This is used to help avoid max 5327/// expressions in loop trip counts, and to eliminate casts. 5328bool 5329ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5330 ICmpInst::Predicate Pred, 5331 const SCEV *LHS, const SCEV *RHS) { 5332 // Interpret a null as meaning no loop, where there is obviously no guard 5333 // (interprocedural conditions notwithstanding). 5334 if (!L) return false; 5335 5336 // Starting at the loop predecessor, climb up the predecessor chain, as long 5337 // as there are predecessors that can be found that have unique successors 5338 // leading to the original header. 5339 for (std::pair<BasicBlock *, BasicBlock *> 5340 Pair(L->getLoopPredecessor(), L->getHeader()); 5341 Pair.first; 5342 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5343 5344 BranchInst *LoopEntryPredicate = 5345 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5346 if (!LoopEntryPredicate || 5347 LoopEntryPredicate->isUnconditional()) 5348 continue; 5349 5350 if (isImpliedCond(Pred, LHS, RHS, 5351 LoopEntryPredicate->getCondition(), 5352 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5353 return true; 5354 } 5355 5356 return false; 5357} 5358 5359/// isImpliedCond - Test whether the condition described by Pred, LHS, 5360/// and RHS is true whenever the given Cond value evaluates to true. 5361bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5362 const SCEV *LHS, const SCEV *RHS, 5363 Value *FoundCondValue, 5364 bool Inverse) { 5365 // Recursively handle And and Or conditions. 5366 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5367 if (BO->getOpcode() == Instruction::And) { 5368 if (!Inverse) 5369 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5370 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5371 } else if (BO->getOpcode() == Instruction::Or) { 5372 if (Inverse) 5373 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5374 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5375 } 5376 } 5377 5378 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5379 if (!ICI) return false; 5380 5381 // Bail if the ICmp's operands' types are wider than the needed type 5382 // before attempting to call getSCEV on them. This avoids infinite 5383 // recursion, since the analysis of widening casts can require loop 5384 // exit condition information for overflow checking, which would 5385 // lead back here. 5386 if (getTypeSizeInBits(LHS->getType()) < 5387 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5388 return false; 5389 5390 // Now that we found a conditional branch that dominates the loop, check to 5391 // see if it is the comparison we are looking for. 5392 ICmpInst::Predicate FoundPred; 5393 if (Inverse) 5394 FoundPred = ICI->getInversePredicate(); 5395 else 5396 FoundPred = ICI->getPredicate(); 5397 5398 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5399 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5400 5401 // Balance the types. The case where FoundLHS' type is wider than 5402 // LHS' type is checked for above. 5403 if (getTypeSizeInBits(LHS->getType()) > 5404 getTypeSizeInBits(FoundLHS->getType())) { 5405 if (CmpInst::isSigned(Pred)) { 5406 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5407 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5408 } else { 5409 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5410 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5411 } 5412 } 5413 5414 // Canonicalize the query to match the way instcombine will have 5415 // canonicalized the comparison. 5416 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5417 if (LHS == RHS) 5418 return CmpInst::isTrueWhenEqual(Pred); 5419 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5420 if (FoundLHS == FoundRHS) 5421 return CmpInst::isFalseWhenEqual(Pred); 5422 5423 // Check to see if we can make the LHS or RHS match. 5424 if (LHS == FoundRHS || RHS == FoundLHS) { 5425 if (isa<SCEVConstant>(RHS)) { 5426 std::swap(FoundLHS, FoundRHS); 5427 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5428 } else { 5429 std::swap(LHS, RHS); 5430 Pred = ICmpInst::getSwappedPredicate(Pred); 5431 } 5432 } 5433 5434 // Check whether the found predicate is the same as the desired predicate. 5435 if (FoundPred == Pred) 5436 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5437 5438 // Check whether swapping the found predicate makes it the same as the 5439 // desired predicate. 5440 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5441 if (isa<SCEVConstant>(RHS)) 5442 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5443 else 5444 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5445 RHS, LHS, FoundLHS, FoundRHS); 5446 } 5447 5448 // Check whether the actual condition is beyond sufficient. 5449 if (FoundPred == ICmpInst::ICMP_EQ) 5450 if (ICmpInst::isTrueWhenEqual(Pred)) 5451 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5452 return true; 5453 if (Pred == ICmpInst::ICMP_NE) 5454 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5455 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5456 return true; 5457 5458 // Otherwise assume the worst. 5459 return false; 5460} 5461 5462/// isImpliedCondOperands - Test whether the condition described by Pred, 5463/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5464/// and FoundRHS is true. 5465bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5466 const SCEV *LHS, const SCEV *RHS, 5467 const SCEV *FoundLHS, 5468 const SCEV *FoundRHS) { 5469 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5470 FoundLHS, FoundRHS) || 5471 // ~x < ~y --> x > y 5472 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5473 getNotSCEV(FoundRHS), 5474 getNotSCEV(FoundLHS)); 5475} 5476 5477/// isImpliedCondOperandsHelper - Test whether the condition described by 5478/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5479/// FoundLHS, and FoundRHS is true. 5480bool 5481ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5482 const SCEV *LHS, const SCEV *RHS, 5483 const SCEV *FoundLHS, 5484 const SCEV *FoundRHS) { 5485 switch (Pred) { 5486 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5487 case ICmpInst::ICMP_EQ: 5488 case ICmpInst::ICMP_NE: 5489 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5490 return true; 5491 break; 5492 case ICmpInst::ICMP_SLT: 5493 case ICmpInst::ICMP_SLE: 5494 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5495 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5496 return true; 5497 break; 5498 case ICmpInst::ICMP_SGT: 5499 case ICmpInst::ICMP_SGE: 5500 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5501 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5502 return true; 5503 break; 5504 case ICmpInst::ICMP_ULT: 5505 case ICmpInst::ICMP_ULE: 5506 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5507 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5508 return true; 5509 break; 5510 case ICmpInst::ICMP_UGT: 5511 case ICmpInst::ICMP_UGE: 5512 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5513 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5514 return true; 5515 break; 5516 } 5517 5518 return false; 5519} 5520 5521/// getBECount - Subtract the end and start values and divide by the step, 5522/// rounding up, to get the number of times the backedge is executed. Return 5523/// CouldNotCompute if an intermediate computation overflows. 5524const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5525 const SCEV *End, 5526 const SCEV *Step, 5527 bool NoWrap) { 5528 assert(!isKnownNegative(Step) && 5529 "This code doesn't handle negative strides yet!"); 5530 5531 const Type *Ty = Start->getType(); 5532 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5533 const SCEV *Diff = getMinusSCEV(End, Start); 5534 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5535 5536 // Add an adjustment to the difference between End and Start so that 5537 // the division will effectively round up. 5538 const SCEV *Add = getAddExpr(Diff, RoundUp); 5539 5540 if (!NoWrap) { 5541 // Check Add for unsigned overflow. 5542 // TODO: More sophisticated things could be done here. 5543 const Type *WideTy = IntegerType::get(getContext(), 5544 getTypeSizeInBits(Ty) + 1); 5545 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5546 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5547 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5548 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5549 return getCouldNotCompute(); 5550 } 5551 5552 return getUDivExpr(Add, Step); 5553} 5554 5555/// HowManyLessThans - Return the number of times a backedge containing the 5556/// specified less-than comparison will execute. If not computable, return 5557/// CouldNotCompute. 5558ScalarEvolution::BackedgeTakenInfo 5559ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5560 const Loop *L, bool isSigned) { 5561 // Only handle: "ADDREC < LoopInvariant". 5562 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5563 5564 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5565 if (!AddRec || AddRec->getLoop() != L) 5566 return getCouldNotCompute(); 5567 5568 // Check to see if we have a flag which makes analysis easy. 5569 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5570 AddRec->hasNoUnsignedWrap(); 5571 5572 if (AddRec->isAffine()) { 5573 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5574 const SCEV *Step = AddRec->getStepRecurrence(*this); 5575 5576 if (Step->isZero()) 5577 return getCouldNotCompute(); 5578 if (Step->isOne()) { 5579 // With unit stride, the iteration never steps past the limit value. 5580 } else if (isKnownPositive(Step)) { 5581 // Test whether a positive iteration can step past the limit 5582 // value and past the maximum value for its type in a single step. 5583 // Note that it's not sufficient to check NoWrap here, because even 5584 // though the value after a wrap is undefined, it's not undefined 5585 // behavior, so if wrap does occur, the loop could either terminate or 5586 // loop infinitely, but in either case, the loop is guaranteed to 5587 // iterate at least until the iteration where the wrapping occurs. 5588 const SCEV *One = getConstant(Step->getType(), 1); 5589 if (isSigned) { 5590 APInt Max = APInt::getSignedMaxValue(BitWidth); 5591 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5592 .slt(getSignedRange(RHS).getSignedMax())) 5593 return getCouldNotCompute(); 5594 } else { 5595 APInt Max = APInt::getMaxValue(BitWidth); 5596 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5597 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5598 return getCouldNotCompute(); 5599 } 5600 } else 5601 // TODO: Handle negative strides here and below. 5602 return getCouldNotCompute(); 5603 5604 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5605 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5606 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5607 // treat m-n as signed nor unsigned due to overflow possibility. 5608 5609 // First, we get the value of the LHS in the first iteration: n 5610 const SCEV *Start = AddRec->getOperand(0); 5611 5612 // Determine the minimum constant start value. 5613 const SCEV *MinStart = getConstant(isSigned ? 5614 getSignedRange(Start).getSignedMin() : 5615 getUnsignedRange(Start).getUnsignedMin()); 5616 5617 // If we know that the condition is true in order to enter the loop, 5618 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5619 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5620 // the division must round up. 5621 const SCEV *End = RHS; 5622 if (!isLoopEntryGuardedByCond(L, 5623 isSigned ? ICmpInst::ICMP_SLT : 5624 ICmpInst::ICMP_ULT, 5625 getMinusSCEV(Start, Step), RHS)) 5626 End = isSigned ? getSMaxExpr(RHS, Start) 5627 : getUMaxExpr(RHS, Start); 5628 5629 // Determine the maximum constant end value. 5630 const SCEV *MaxEnd = getConstant(isSigned ? 5631 getSignedRange(End).getSignedMax() : 5632 getUnsignedRange(End).getUnsignedMax()); 5633 5634 // If MaxEnd is within a step of the maximum integer value in its type, 5635 // adjust it down to the minimum value which would produce the same effect. 5636 // This allows the subsequent ceiling division of (N+(step-1))/step to 5637 // compute the correct value. 5638 const SCEV *StepMinusOne = getMinusSCEV(Step, 5639 getConstant(Step->getType(), 1)); 5640 MaxEnd = isSigned ? 5641 getSMinExpr(MaxEnd, 5642 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5643 StepMinusOne)) : 5644 getUMinExpr(MaxEnd, 5645 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5646 StepMinusOne)); 5647 5648 // Finally, we subtract these two values and divide, rounding up, to get 5649 // the number of times the backedge is executed. 5650 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5651 5652 // The maximum backedge count is similar, except using the minimum start 5653 // value and the maximum end value. 5654 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5655 5656 return BackedgeTakenInfo(BECount, MaxBECount); 5657 } 5658 5659 return getCouldNotCompute(); 5660} 5661 5662/// getNumIterationsInRange - Return the number of iterations of this loop that 5663/// produce values in the specified constant range. Another way of looking at 5664/// this is that it returns the first iteration number where the value is not in 5665/// the condition, thus computing the exit count. If the iteration count can't 5666/// be computed, an instance of SCEVCouldNotCompute is returned. 5667const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5668 ScalarEvolution &SE) const { 5669 if (Range.isFullSet()) // Infinite loop. 5670 return SE.getCouldNotCompute(); 5671 5672 // If the start is a non-zero constant, shift the range to simplify things. 5673 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5674 if (!SC->getValue()->isZero()) { 5675 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5676 Operands[0] = SE.getConstant(SC->getType(), 0); 5677 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5678 if (const SCEVAddRecExpr *ShiftedAddRec = 5679 dyn_cast<SCEVAddRecExpr>(Shifted)) 5680 return ShiftedAddRec->getNumIterationsInRange( 5681 Range.subtract(SC->getValue()->getValue()), SE); 5682 // This is strange and shouldn't happen. 5683 return SE.getCouldNotCompute(); 5684 } 5685 5686 // The only time we can solve this is when we have all constant indices. 5687 // Otherwise, we cannot determine the overflow conditions. 5688 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5689 if (!isa<SCEVConstant>(getOperand(i))) 5690 return SE.getCouldNotCompute(); 5691 5692 5693 // Okay at this point we know that all elements of the chrec are constants and 5694 // that the start element is zero. 5695 5696 // First check to see if the range contains zero. If not, the first 5697 // iteration exits. 5698 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5699 if (!Range.contains(APInt(BitWidth, 0))) 5700 return SE.getConstant(getType(), 0); 5701 5702 if (isAffine()) { 5703 // If this is an affine expression then we have this situation: 5704 // Solve {0,+,A} in Range === Ax in Range 5705 5706 // We know that zero is in the range. If A is positive then we know that 5707 // the upper value of the range must be the first possible exit value. 5708 // If A is negative then the lower of the range is the last possible loop 5709 // value. Also note that we already checked for a full range. 5710 APInt One(BitWidth,1); 5711 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5712 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5713 5714 // The exit value should be (End+A)/A. 5715 APInt ExitVal = (End + A).udiv(A); 5716 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5717 5718 // Evaluate at the exit value. If we really did fall out of the valid 5719 // range, then we computed our trip count, otherwise wrap around or other 5720 // things must have happened. 5721 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5722 if (Range.contains(Val->getValue())) 5723 return SE.getCouldNotCompute(); // Something strange happened 5724 5725 // Ensure that the previous value is in the range. This is a sanity check. 5726 assert(Range.contains( 5727 EvaluateConstantChrecAtConstant(this, 5728 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5729 "Linear scev computation is off in a bad way!"); 5730 return SE.getConstant(ExitValue); 5731 } else if (isQuadratic()) { 5732 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5733 // quadratic equation to solve it. To do this, we must frame our problem in 5734 // terms of figuring out when zero is crossed, instead of when 5735 // Range.getUpper() is crossed. 5736 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5737 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5738 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5739 5740 // Next, solve the constructed addrec 5741 std::pair<const SCEV *,const SCEV *> Roots = 5742 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5743 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5744 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5745 if (R1) { 5746 // Pick the smallest positive root value. 5747 if (ConstantInt *CB = 5748 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5749 R1->getValue(), R2->getValue()))) { 5750 if (CB->getZExtValue() == false) 5751 std::swap(R1, R2); // R1 is the minimum root now. 5752 5753 // Make sure the root is not off by one. The returned iteration should 5754 // not be in the range, but the previous one should be. When solving 5755 // for "X*X < 5", for example, we should not return a root of 2. 5756 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5757 R1->getValue(), 5758 SE); 5759 if (Range.contains(R1Val->getValue())) { 5760 // The next iteration must be out of the range... 5761 ConstantInt *NextVal = 5762 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5763 5764 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5765 if (!Range.contains(R1Val->getValue())) 5766 return SE.getConstant(NextVal); 5767 return SE.getCouldNotCompute(); // Something strange happened 5768 } 5769 5770 // If R1 was not in the range, then it is a good return value. Make 5771 // sure that R1-1 WAS in the range though, just in case. 5772 ConstantInt *NextVal = 5773 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5774 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5775 if (Range.contains(R1Val->getValue())) 5776 return R1; 5777 return SE.getCouldNotCompute(); // Something strange happened 5778 } 5779 } 5780 } 5781 5782 return SE.getCouldNotCompute(); 5783} 5784 5785 5786 5787//===----------------------------------------------------------------------===// 5788// SCEVCallbackVH Class Implementation 5789//===----------------------------------------------------------------------===// 5790 5791void ScalarEvolution::SCEVCallbackVH::deleted() { 5792 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5793 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5794 SE->ConstantEvolutionLoopExitValue.erase(PN); 5795 SE->ValueExprMap.erase(getValPtr()); 5796 // this now dangles! 5797} 5798 5799void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5800 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5801 5802 // Forget all the expressions associated with users of the old value, 5803 // so that future queries will recompute the expressions using the new 5804 // value. 5805 Value *Old = getValPtr(); 5806 SmallVector<User *, 16> Worklist; 5807 SmallPtrSet<User *, 8> Visited; 5808 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5809 UI != UE; ++UI) 5810 Worklist.push_back(*UI); 5811 while (!Worklist.empty()) { 5812 User *U = Worklist.pop_back_val(); 5813 // Deleting the Old value will cause this to dangle. Postpone 5814 // that until everything else is done. 5815 if (U == Old) 5816 continue; 5817 if (!Visited.insert(U)) 5818 continue; 5819 if (PHINode *PN = dyn_cast<PHINode>(U)) 5820 SE->ConstantEvolutionLoopExitValue.erase(PN); 5821 SE->ValueExprMap.erase(U); 5822 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5823 UI != UE; ++UI) 5824 Worklist.push_back(*UI); 5825 } 5826 // Delete the Old value. 5827 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5828 SE->ConstantEvolutionLoopExitValue.erase(PN); 5829 SE->ValueExprMap.erase(Old); 5830 // this now dangles! 5831} 5832 5833ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5834 : CallbackVH(V), SE(se) {} 5835 5836//===----------------------------------------------------------------------===// 5837// ScalarEvolution Class Implementation 5838//===----------------------------------------------------------------------===// 5839 5840ScalarEvolution::ScalarEvolution() 5841 : FunctionPass(ID), FirstUnknown(0) { 5842} 5843 5844bool ScalarEvolution::runOnFunction(Function &F) { 5845 this->F = &F; 5846 LI = &getAnalysis<LoopInfo>(); 5847 TD = getAnalysisIfAvailable<TargetData>(); 5848 DT = &getAnalysis<DominatorTree>(); 5849 return false; 5850} 5851 5852void ScalarEvolution::releaseMemory() { 5853 // Iterate through all the SCEVUnknown instances and call their 5854 // destructors, so that they release their references to their values. 5855 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5856 U->~SCEVUnknown(); 5857 FirstUnknown = 0; 5858 5859 ValueExprMap.clear(); 5860 BackedgeTakenCounts.clear(); 5861 ConstantEvolutionLoopExitValue.clear(); 5862 ValuesAtScopes.clear(); 5863 UniqueSCEVs.clear(); 5864 SCEVAllocator.Reset(); 5865} 5866 5867void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5868 AU.setPreservesAll(); 5869 AU.addRequiredTransitive<LoopInfo>(); 5870 AU.addRequiredTransitive<DominatorTree>(); 5871} 5872 5873bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5874 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5875} 5876 5877static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5878 const Loop *L) { 5879 // Print all inner loops first 5880 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5881 PrintLoopInfo(OS, SE, *I); 5882 5883 OS << "Loop "; 5884 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5885 OS << ": "; 5886 5887 SmallVector<BasicBlock *, 8> ExitBlocks; 5888 L->getExitBlocks(ExitBlocks); 5889 if (ExitBlocks.size() != 1) 5890 OS << "<multiple exits> "; 5891 5892 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5893 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5894 } else { 5895 OS << "Unpredictable backedge-taken count. "; 5896 } 5897 5898 OS << "\n" 5899 "Loop "; 5900 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5901 OS << ": "; 5902 5903 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5904 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5905 } else { 5906 OS << "Unpredictable max backedge-taken count. "; 5907 } 5908 5909 OS << "\n"; 5910} 5911 5912void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5913 // ScalarEvolution's implementation of the print method is to print 5914 // out SCEV values of all instructions that are interesting. Doing 5915 // this potentially causes it to create new SCEV objects though, 5916 // which technically conflicts with the const qualifier. This isn't 5917 // observable from outside the class though, so casting away the 5918 // const isn't dangerous. 5919 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5920 5921 OS << "Classifying expressions for: "; 5922 WriteAsOperand(OS, F, /*PrintType=*/false); 5923 OS << "\n"; 5924 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5925 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5926 OS << *I << '\n'; 5927 OS << " --> "; 5928 const SCEV *SV = SE.getSCEV(&*I); 5929 SV->print(OS); 5930 5931 const Loop *L = LI->getLoopFor((*I).getParent()); 5932 5933 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5934 if (AtUse != SV) { 5935 OS << " --> "; 5936 AtUse->print(OS); 5937 } 5938 5939 if (L) { 5940 OS << "\t\t" "Exits: "; 5941 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5942 if (!ExitValue->isLoopInvariant(L)) { 5943 OS << "<<Unknown>>"; 5944 } else { 5945 OS << *ExitValue; 5946 } 5947 } 5948 5949 OS << "\n"; 5950 } 5951 5952 OS << "Determining loop execution counts for: "; 5953 WriteAsOperand(OS, F, /*PrintType=*/false); 5954 OS << "\n"; 5955 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5956 PrintLoopInfo(OS, &SE, *I); 5957} 5958 5959