ScalarEvolution.cpp revision 081c34b725980f995be9080eaec24cd3dfaaf065
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_BEGIN(ScalarEvolution, "scalar-evolution", 107 "Scalar Evolution Analysis", false, true) 108INITIALIZE_PASS_DEPENDENCY(LoopInfo) 109INITIALIZE_PASS_DEPENDENCY(DominatorTree) 110INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 111 "Scalar Evolution Analysis", false, true) 112char ScalarEvolution::ID = 0; 113 114//===----------------------------------------------------------------------===// 115// SCEV class definitions 116//===----------------------------------------------------------------------===// 117 118//===----------------------------------------------------------------------===// 119// Implementation of the SCEV class. 120// 121 122SCEV::~SCEV() {} 123 124void SCEV::dump() const { 125 print(dbgs()); 126 dbgs() << '\n'; 127} 128 129bool SCEV::isZero() const { 130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 131 return SC->getValue()->isZero(); 132 return false; 133} 134 135bool SCEV::isOne() const { 136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 137 return SC->getValue()->isOne(); 138 return false; 139} 140 141bool SCEV::isAllOnesValue() const { 142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 143 return SC->getValue()->isAllOnesValue(); 144 return false; 145} 146 147SCEVCouldNotCompute::SCEVCouldNotCompute() : 148 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 149 150bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { 151 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 152 return false; 153} 154 155const Type *SCEVCouldNotCompute::getType() const { 156 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 157 return 0; 158} 159 160bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { 161 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 162 return false; 163} 164 165bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { 166 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 167 return false; 168} 169 170void SCEVCouldNotCompute::print(raw_ostream &OS) const { 171 OS << "***COULDNOTCOMPUTE***"; 172} 173 174bool SCEVCouldNotCompute::classof(const SCEV *S) { 175 return S->getSCEVType() == scCouldNotCompute; 176} 177 178const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 179 FoldingSetNodeID ID; 180 ID.AddInteger(scConstant); 181 ID.AddPointer(V); 182 void *IP = 0; 183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 184 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 185 UniqueSCEVs.InsertNode(S, IP); 186 return S; 187} 188 189const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 190 return getConstant(ConstantInt::get(getContext(), Val)); 191} 192 193const SCEV * 194ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 195 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 196 return getConstant(ConstantInt::get(ITy, V, isSigned)); 197} 198 199const Type *SCEVConstant::getType() const { return V->getType(); } 200 201void SCEVConstant::print(raw_ostream &OS) const { 202 WriteAsOperand(OS, V, false); 203} 204 205SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 206 unsigned SCEVTy, const SCEV *op, const Type *ty) 207 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 208 209bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 210 return Op->dominates(BB, DT); 211} 212 213bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 214 return Op->properlyDominates(BB, DT); 215} 216 217SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 218 const SCEV *op, const Type *ty) 219 : SCEVCastExpr(ID, scTruncate, op, ty) { 220 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 221 (Ty->isIntegerTy() || Ty->isPointerTy()) && 222 "Cannot truncate non-integer value!"); 223} 224 225void SCEVTruncateExpr::print(raw_ostream &OS) const { 226 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 227} 228 229SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 230 const SCEV *op, const Type *ty) 231 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 232 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 233 (Ty->isIntegerTy() || Ty->isPointerTy()) && 234 "Cannot zero extend non-integer value!"); 235} 236 237void SCEVZeroExtendExpr::print(raw_ostream &OS) const { 238 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 239} 240 241SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 242 const SCEV *op, const Type *ty) 243 : SCEVCastExpr(ID, scSignExtend, op, ty) { 244 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 245 (Ty->isIntegerTy() || Ty->isPointerTy()) && 246 "Cannot sign extend non-integer value!"); 247} 248 249void SCEVSignExtendExpr::print(raw_ostream &OS) const { 250 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; 251} 252 253void SCEVCommutativeExpr::print(raw_ostream &OS) const { 254 const char *OpStr = getOperationStr(); 255 OS << "("; 256 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 257 OS << **I; 258 if (llvm::next(I) != E) 259 OS << OpStr; 260 } 261 OS << ")"; 262} 263 264bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 265 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 266 if (!(*I)->dominates(BB, DT)) 267 return false; 268 return true; 269} 270 271bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 272 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 273 if (!(*I)->properlyDominates(BB, DT)) 274 return false; 275 return true; 276} 277 278bool SCEVNAryExpr::isLoopInvariant(const Loop *L) const { 279 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 280 if (!(*I)->isLoopInvariant(L)) 281 return false; 282 return true; 283} 284 285// hasComputableLoopEvolution - N-ary expressions have computable loop 286// evolutions iff they have at least one operand that varies with the loop, 287// but that all varying operands are computable. 288bool SCEVNAryExpr::hasComputableLoopEvolution(const Loop *L) const { 289 bool HasVarying = false; 290 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 291 const SCEV *S = *I; 292 if (!S->isLoopInvariant(L)) { 293 if (S->hasComputableLoopEvolution(L)) 294 HasVarying = true; 295 else 296 return false; 297 } 298 } 299 return HasVarying; 300} 301 302bool SCEVNAryExpr::hasOperand(const SCEV *O) const { 303 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { 304 const SCEV *S = *I; 305 if (O == S || S->hasOperand(O)) 306 return true; 307 } 308 return false; 309} 310 311bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 312 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); 313} 314 315bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 316 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); 317} 318 319void SCEVUDivExpr::print(raw_ostream &OS) const { 320 OS << "(" << *LHS << " /u " << *RHS << ")"; 321} 322 323const Type *SCEVUDivExpr::getType() const { 324 // In most cases the types of LHS and RHS will be the same, but in some 325 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't 326 // depend on the type for correctness, but handling types carefully can 327 // avoid extra casts in the SCEVExpander. The LHS is more likely to be 328 // a pointer type than the RHS, so use the RHS' type here. 329 return RHS->getType(); 330} 331 332bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { 333 // Add recurrences are never invariant in the function-body (null loop). 334 if (!QueryLoop) 335 return false; 336 337 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. 338 if (QueryLoop->contains(L)) 339 return false; 340 341 // This recurrence is invariant w.r.t. QueryLoop if L contains QueryLoop. 342 if (L->contains(QueryLoop)) 343 return true; 344 345 // This recurrence is variant w.r.t. QueryLoop if any of its operands 346 // are variant. 347 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) 348 if (!(*I)->isLoopInvariant(QueryLoop)) 349 return false; 350 351 // Otherwise it's loop-invariant. 352 return true; 353} 354 355bool 356SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { 357 return DT->dominates(L->getHeader(), BB) && 358 SCEVNAryExpr::dominates(BB, DT); 359} 360 361bool 362SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 363 // This uses a "dominates" query instead of "properly dominates" query because 364 // the instruction which produces the addrec's value is a PHI, and a PHI 365 // effectively properly dominates its entire containing block. 366 return DT->dominates(L->getHeader(), BB) && 367 SCEVNAryExpr::properlyDominates(BB, DT); 368} 369 370void SCEVAddRecExpr::print(raw_ostream &OS) const { 371 OS << "{" << *Operands[0]; 372 for (unsigned i = 1, e = NumOperands; i != e; ++i) 373 OS << ",+," << *Operands[i]; 374 OS << "}<"; 375 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 376 OS << ">"; 377} 378 379void SCEVUnknown::deleted() { 380 // Clear this SCEVUnknown from ValuesAtScopes. 381 SE->ValuesAtScopes.erase(this); 382 383 // Remove this SCEVUnknown from the uniquing map. 384 SE->UniqueSCEVs.RemoveNode(this); 385 386 // Release the value. 387 setValPtr(0); 388} 389 390void SCEVUnknown::allUsesReplacedWith(Value *New) { 391 // Clear this SCEVUnknown from ValuesAtScopes. 392 SE->ValuesAtScopes.erase(this); 393 394 // Remove this SCEVUnknown from the uniquing map. 395 SE->UniqueSCEVs.RemoveNode(this); 396 397 // Update this SCEVUnknown to point to the new value. This is needed 398 // because there may still be outstanding SCEVs which still point to 399 // this SCEVUnknown. 400 setValPtr(New); 401} 402 403bool SCEVUnknown::isLoopInvariant(const Loop *L) const { 404 // All non-instruction values are loop invariant. All instructions are loop 405 // invariant if they are not contained in the specified loop. 406 // Instructions are never considered invariant in the function body 407 // (null loop) because they are defined within the "loop". 408 if (Instruction *I = dyn_cast<Instruction>(getValue())) 409 return L && !L->contains(I); 410 return true; 411} 412 413bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { 414 if (Instruction *I = dyn_cast<Instruction>(getValue())) 415 return DT->dominates(I->getParent(), BB); 416 return true; 417} 418 419bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { 420 if (Instruction *I = dyn_cast<Instruction>(getValue())) 421 return DT->properlyDominates(I->getParent(), BB); 422 return true; 423} 424 425const Type *SCEVUnknown::getType() const { 426 return getValue()->getType(); 427} 428 429bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 430 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 431 if (VCE->getOpcode() == Instruction::PtrToInt) 432 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 433 if (CE->getOpcode() == Instruction::GetElementPtr && 434 CE->getOperand(0)->isNullValue() && 435 CE->getNumOperands() == 2) 436 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 437 if (CI->isOne()) { 438 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 439 ->getElementType(); 440 return true; 441 } 442 443 return false; 444} 445 446bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 447 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 448 if (VCE->getOpcode() == Instruction::PtrToInt) 449 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 450 if (CE->getOpcode() == Instruction::GetElementPtr && 451 CE->getOperand(0)->isNullValue()) { 452 const Type *Ty = 453 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 454 if (const StructType *STy = dyn_cast<StructType>(Ty)) 455 if (!STy->isPacked() && 456 CE->getNumOperands() == 3 && 457 CE->getOperand(1)->isNullValue()) { 458 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 459 if (CI->isOne() && 460 STy->getNumElements() == 2 && 461 STy->getElementType(0)->isIntegerTy(1)) { 462 AllocTy = STy->getElementType(1); 463 return true; 464 } 465 } 466 } 467 468 return false; 469} 470 471bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 472 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 473 if (VCE->getOpcode() == Instruction::PtrToInt) 474 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 475 if (CE->getOpcode() == Instruction::GetElementPtr && 476 CE->getNumOperands() == 3 && 477 CE->getOperand(0)->isNullValue() && 478 CE->getOperand(1)->isNullValue()) { 479 const Type *Ty = 480 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 481 // Ignore vector types here so that ScalarEvolutionExpander doesn't 482 // emit getelementptrs that index into vectors. 483 if (Ty->isStructTy() || Ty->isArrayTy()) { 484 CTy = Ty; 485 FieldNo = CE->getOperand(2); 486 return true; 487 } 488 } 489 490 return false; 491} 492 493void SCEVUnknown::print(raw_ostream &OS) const { 494 const Type *AllocTy; 495 if (isSizeOf(AllocTy)) { 496 OS << "sizeof(" << *AllocTy << ")"; 497 return; 498 } 499 if (isAlignOf(AllocTy)) { 500 OS << "alignof(" << *AllocTy << ")"; 501 return; 502 } 503 504 const Type *CTy; 505 Constant *FieldNo; 506 if (isOffsetOf(CTy, FieldNo)) { 507 OS << "offsetof(" << *CTy << ", "; 508 WriteAsOperand(OS, FieldNo, false); 509 OS << ")"; 510 return; 511 } 512 513 // Otherwise just print it normally. 514 WriteAsOperand(OS, getValue(), false); 515} 516 517//===----------------------------------------------------------------------===// 518// SCEV Utilities 519//===----------------------------------------------------------------------===// 520 521namespace { 522 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 523 /// than the complexity of the RHS. This comparator is used to canonicalize 524 /// expressions. 525 class SCEVComplexityCompare { 526 const LoopInfo *const LI; 527 public: 528 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 529 530 // Return true or false if LHS is less than, or at least RHS, respectively. 531 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 532 return compare(LHS, RHS) < 0; 533 } 534 535 // Return negative, zero, or positive, if LHS is less than, equal to, or 536 // greater than RHS, respectively. A three-way result allows recursive 537 // comparisons to be more efficient. 538 int compare(const SCEV *LHS, const SCEV *RHS) const { 539 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 540 if (LHS == RHS) 541 return 0; 542 543 // Primarily, sort the SCEVs by their getSCEVType(). 544 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 545 if (LType != RType) 546 return (int)LType - (int)RType; 547 548 // Aside from the getSCEVType() ordering, the particular ordering 549 // isn't very important except that it's beneficial to be consistent, 550 // so that (a + b) and (b + a) don't end up as different expressions. 551 switch (LType) { 552 case scUnknown: { 553 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 554 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 555 556 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 557 // not as complete as it could be. 558 const Value *LV = LU->getValue(), *RV = RU->getValue(); 559 560 // Order pointer values after integer values. This helps SCEVExpander 561 // form GEPs. 562 bool LIsPointer = LV->getType()->isPointerTy(), 563 RIsPointer = RV->getType()->isPointerTy(); 564 if (LIsPointer != RIsPointer) 565 return (int)LIsPointer - (int)RIsPointer; 566 567 // Compare getValueID values. 568 unsigned LID = LV->getValueID(), 569 RID = RV->getValueID(); 570 if (LID != RID) 571 return (int)LID - (int)RID; 572 573 // Sort arguments by their position. 574 if (const Argument *LA = dyn_cast<Argument>(LV)) { 575 const Argument *RA = cast<Argument>(RV); 576 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 577 return (int)LArgNo - (int)RArgNo; 578 } 579 580 // For instructions, compare their loop depth, and their operand 581 // count. This is pretty loose. 582 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 583 const Instruction *RInst = cast<Instruction>(RV); 584 585 // Compare loop depths. 586 const BasicBlock *LParent = LInst->getParent(), 587 *RParent = RInst->getParent(); 588 if (LParent != RParent) { 589 unsigned LDepth = LI->getLoopDepth(LParent), 590 RDepth = LI->getLoopDepth(RParent); 591 if (LDepth != RDepth) 592 return (int)LDepth - (int)RDepth; 593 } 594 595 // Compare the number of operands. 596 unsigned LNumOps = LInst->getNumOperands(), 597 RNumOps = RInst->getNumOperands(); 598 return (int)LNumOps - (int)RNumOps; 599 } 600 601 return 0; 602 } 603 604 case scConstant: { 605 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 606 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 607 608 // Compare constant values. 609 const APInt &LA = LC->getValue()->getValue(); 610 const APInt &RA = RC->getValue()->getValue(); 611 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 612 if (LBitWidth != RBitWidth) 613 return (int)LBitWidth - (int)RBitWidth; 614 return LA.ult(RA) ? -1 : 1; 615 } 616 617 case scAddRecExpr: { 618 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 619 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 620 621 // Compare addrec loop depths. 622 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 623 if (LLoop != RLoop) { 624 unsigned LDepth = LLoop->getLoopDepth(), 625 RDepth = RLoop->getLoopDepth(); 626 if (LDepth != RDepth) 627 return (int)LDepth - (int)RDepth; 628 } 629 630 // Addrec complexity grows with operand count. 631 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 632 if (LNumOps != RNumOps) 633 return (int)LNumOps - (int)RNumOps; 634 635 // Lexicographically compare. 636 for (unsigned i = 0; i != LNumOps; ++i) { 637 long X = compare(LA->getOperand(i), RA->getOperand(i)); 638 if (X != 0) 639 return X; 640 } 641 642 return 0; 643 } 644 645 case scAddExpr: 646 case scMulExpr: 647 case scSMaxExpr: 648 case scUMaxExpr: { 649 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 650 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 651 652 // Lexicographically compare n-ary expressions. 653 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 654 for (unsigned i = 0; i != LNumOps; ++i) { 655 if (i >= RNumOps) 656 return 1; 657 long X = compare(LC->getOperand(i), RC->getOperand(i)); 658 if (X != 0) 659 return X; 660 } 661 return (int)LNumOps - (int)RNumOps; 662 } 663 664 case scUDivExpr: { 665 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 666 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 667 668 // Lexicographically compare udiv expressions. 669 long X = compare(LC->getLHS(), RC->getLHS()); 670 if (X != 0) 671 return X; 672 return compare(LC->getRHS(), RC->getRHS()); 673 } 674 675 case scTruncate: 676 case scZeroExtend: 677 case scSignExtend: { 678 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 679 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 680 681 // Compare cast expressions by operand. 682 return compare(LC->getOperand(), RC->getOperand()); 683 } 684 685 default: 686 break; 687 } 688 689 llvm_unreachable("Unknown SCEV kind!"); 690 return 0; 691 } 692 }; 693} 694 695/// GroupByComplexity - Given a list of SCEV objects, order them by their 696/// complexity, and group objects of the same complexity together by value. 697/// When this routine is finished, we know that any duplicates in the vector are 698/// consecutive and that complexity is monotonically increasing. 699/// 700/// Note that we go take special precautions to ensure that we get deterministic 701/// results from this routine. In other words, we don't want the results of 702/// this to depend on where the addresses of various SCEV objects happened to 703/// land in memory. 704/// 705static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 706 LoopInfo *LI) { 707 if (Ops.size() < 2) return; // Noop 708 if (Ops.size() == 2) { 709 // This is the common case, which also happens to be trivially simple. 710 // Special case it. 711 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 712 if (SCEVComplexityCompare(LI)(RHS, LHS)) 713 std::swap(LHS, RHS); 714 return; 715 } 716 717 // Do the rough sort by complexity. 718 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 719 720 // Now that we are sorted by complexity, group elements of the same 721 // complexity. Note that this is, at worst, N^2, but the vector is likely to 722 // be extremely short in practice. Note that we take this approach because we 723 // do not want to depend on the addresses of the objects we are grouping. 724 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 725 const SCEV *S = Ops[i]; 726 unsigned Complexity = S->getSCEVType(); 727 728 // If there are any objects of the same complexity and same value as this 729 // one, group them. 730 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 731 if (Ops[j] == S) { // Found a duplicate. 732 // Move it to immediately after i'th element. 733 std::swap(Ops[i+1], Ops[j]); 734 ++i; // no need to rescan it. 735 if (i == e-2) return; // Done! 736 } 737 } 738 } 739} 740 741 742 743//===----------------------------------------------------------------------===// 744// Simple SCEV method implementations 745//===----------------------------------------------------------------------===// 746 747/// BinomialCoefficient - Compute BC(It, K). The result has width W. 748/// Assume, K > 0. 749static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 750 ScalarEvolution &SE, 751 const Type* ResultTy) { 752 // Handle the simplest case efficiently. 753 if (K == 1) 754 return SE.getTruncateOrZeroExtend(It, ResultTy); 755 756 // We are using the following formula for BC(It, K): 757 // 758 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 759 // 760 // Suppose, W is the bitwidth of the return value. We must be prepared for 761 // overflow. Hence, we must assure that the result of our computation is 762 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 763 // safe in modular arithmetic. 764 // 765 // However, this code doesn't use exactly that formula; the formula it uses 766 // is something like the following, where T is the number of factors of 2 in 767 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 768 // exponentiation: 769 // 770 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 771 // 772 // This formula is trivially equivalent to the previous formula. However, 773 // this formula can be implemented much more efficiently. The trick is that 774 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 775 // arithmetic. To do exact division in modular arithmetic, all we have 776 // to do is multiply by the inverse. Therefore, this step can be done at 777 // width W. 778 // 779 // The next issue is how to safely do the division by 2^T. The way this 780 // is done is by doing the multiplication step at a width of at least W + T 781 // bits. This way, the bottom W+T bits of the product are accurate. Then, 782 // when we perform the division by 2^T (which is equivalent to a right shift 783 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 784 // truncated out after the division by 2^T. 785 // 786 // In comparison to just directly using the first formula, this technique 787 // is much more efficient; using the first formula requires W * K bits, 788 // but this formula less than W + K bits. Also, the first formula requires 789 // a division step, whereas this formula only requires multiplies and shifts. 790 // 791 // It doesn't matter whether the subtraction step is done in the calculation 792 // width or the input iteration count's width; if the subtraction overflows, 793 // the result must be zero anyway. We prefer here to do it in the width of 794 // the induction variable because it helps a lot for certain cases; CodeGen 795 // isn't smart enough to ignore the overflow, which leads to much less 796 // efficient code if the width of the subtraction is wider than the native 797 // register width. 798 // 799 // (It's possible to not widen at all by pulling out factors of 2 before 800 // the multiplication; for example, K=2 can be calculated as 801 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 802 // extra arithmetic, so it's not an obvious win, and it gets 803 // much more complicated for K > 3.) 804 805 // Protection from insane SCEVs; this bound is conservative, 806 // but it probably doesn't matter. 807 if (K > 1000) 808 return SE.getCouldNotCompute(); 809 810 unsigned W = SE.getTypeSizeInBits(ResultTy); 811 812 // Calculate K! / 2^T and T; we divide out the factors of two before 813 // multiplying for calculating K! / 2^T to avoid overflow. 814 // Other overflow doesn't matter because we only care about the bottom 815 // W bits of the result. 816 APInt OddFactorial(W, 1); 817 unsigned T = 1; 818 for (unsigned i = 3; i <= K; ++i) { 819 APInt Mult(W, i); 820 unsigned TwoFactors = Mult.countTrailingZeros(); 821 T += TwoFactors; 822 Mult = Mult.lshr(TwoFactors); 823 OddFactorial *= Mult; 824 } 825 826 // We need at least W + T bits for the multiplication step 827 unsigned CalculationBits = W + T; 828 829 // Calculate 2^T, at width T+W. 830 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 831 832 // Calculate the multiplicative inverse of K! / 2^T; 833 // this multiplication factor will perform the exact division by 834 // K! / 2^T. 835 APInt Mod = APInt::getSignedMinValue(W+1); 836 APInt MultiplyFactor = OddFactorial.zext(W+1); 837 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 838 MultiplyFactor = MultiplyFactor.trunc(W); 839 840 // Calculate the product, at width T+W 841 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 842 CalculationBits); 843 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 844 for (unsigned i = 1; i != K; ++i) { 845 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 846 Dividend = SE.getMulExpr(Dividend, 847 SE.getTruncateOrZeroExtend(S, CalculationTy)); 848 } 849 850 // Divide by 2^T 851 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 852 853 // Truncate the result, and divide by K! / 2^T. 854 855 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 856 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 857} 858 859/// evaluateAtIteration - Return the value of this chain of recurrences at 860/// the specified iteration number. We can evaluate this recurrence by 861/// multiplying each element in the chain by the binomial coefficient 862/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 863/// 864/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 865/// 866/// where BC(It, k) stands for binomial coefficient. 867/// 868const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 869 ScalarEvolution &SE) const { 870 const SCEV *Result = getStart(); 871 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 872 // The computation is correct in the face of overflow provided that the 873 // multiplication is performed _after_ the evaluation of the binomial 874 // coefficient. 875 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 876 if (isa<SCEVCouldNotCompute>(Coeff)) 877 return Coeff; 878 879 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 880 } 881 return Result; 882} 883 884//===----------------------------------------------------------------------===// 885// SCEV Expression folder implementations 886//===----------------------------------------------------------------------===// 887 888const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 889 const Type *Ty) { 890 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 891 "This is not a truncating conversion!"); 892 assert(isSCEVable(Ty) && 893 "This is not a conversion to a SCEVable type!"); 894 Ty = getEffectiveSCEVType(Ty); 895 896 FoldingSetNodeID ID; 897 ID.AddInteger(scTruncate); 898 ID.AddPointer(Op); 899 ID.AddPointer(Ty); 900 void *IP = 0; 901 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 902 903 // Fold if the operand is constant. 904 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 905 return getConstant( 906 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 907 getEffectiveSCEVType(Ty)))); 908 909 // trunc(trunc(x)) --> trunc(x) 910 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 911 return getTruncateExpr(ST->getOperand(), Ty); 912 913 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 914 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 915 return getTruncateOrSignExtend(SS->getOperand(), Ty); 916 917 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 918 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 919 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 920 921 // If the input value is a chrec scev, truncate the chrec's operands. 922 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 923 SmallVector<const SCEV *, 4> Operands; 924 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 925 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 926 return getAddRecExpr(Operands, AddRec->getLoop()); 927 } 928 929 // As a special case, fold trunc(undef) to undef. We don't want to 930 // know too much about SCEVUnknowns, but this special case is handy 931 // and harmless. 932 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 933 if (isa<UndefValue>(U->getValue())) 934 return getSCEV(UndefValue::get(Ty)); 935 936 // The cast wasn't folded; create an explicit cast node. We can reuse 937 // the existing insert position since if we get here, we won't have 938 // made any changes which would invalidate it. 939 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 940 Op, Ty); 941 UniqueSCEVs.InsertNode(S, IP); 942 return S; 943} 944 945const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 946 const Type *Ty) { 947 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 948 "This is not an extending conversion!"); 949 assert(isSCEVable(Ty) && 950 "This is not a conversion to a SCEVable type!"); 951 Ty = getEffectiveSCEVType(Ty); 952 953 // Fold if the operand is constant. 954 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 955 return getConstant( 956 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 957 getEffectiveSCEVType(Ty)))); 958 959 // zext(zext(x)) --> zext(x) 960 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 961 return getZeroExtendExpr(SZ->getOperand(), Ty); 962 963 // Before doing any expensive analysis, check to see if we've already 964 // computed a SCEV for this Op and Ty. 965 FoldingSetNodeID ID; 966 ID.AddInteger(scZeroExtend); 967 ID.AddPointer(Op); 968 ID.AddPointer(Ty); 969 void *IP = 0; 970 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 971 972 // If the input value is a chrec scev, and we can prove that the value 973 // did not overflow the old, smaller, value, we can zero extend all of the 974 // operands (often constants). This allows analysis of something like 975 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 976 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 977 if (AR->isAffine()) { 978 const SCEV *Start = AR->getStart(); 979 const SCEV *Step = AR->getStepRecurrence(*this); 980 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 981 const Loop *L = AR->getLoop(); 982 983 // If we have special knowledge that this addrec won't overflow, 984 // we don't need to do any further analysis. 985 if (AR->hasNoUnsignedWrap()) 986 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 987 getZeroExtendExpr(Step, Ty), 988 L); 989 990 // Check whether the backedge-taken count is SCEVCouldNotCompute. 991 // Note that this serves two purposes: It filters out loops that are 992 // simply not analyzable, and it covers the case where this code is 993 // being called from within backedge-taken count analysis, such that 994 // attempting to ask for the backedge-taken count would likely result 995 // in infinite recursion. In the later case, the analysis code will 996 // cope with a conservative value, and it will take care to purge 997 // that value once it has finished. 998 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 999 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1000 // Manually compute the final value for AR, checking for 1001 // overflow. 1002 1003 // Check whether the backedge-taken count can be losslessly casted to 1004 // the addrec's type. The count is always unsigned. 1005 const SCEV *CastedMaxBECount = 1006 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1007 const SCEV *RecastedMaxBECount = 1008 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1009 if (MaxBECount == RecastedMaxBECount) { 1010 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1011 // Check whether Start+Step*MaxBECount has no unsigned overflow. 1012 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 1013 const SCEV *Add = getAddExpr(Start, ZMul); 1014 const SCEV *OperandExtendedAdd = 1015 getAddExpr(getZeroExtendExpr(Start, WideTy), 1016 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1017 getZeroExtendExpr(Step, WideTy))); 1018 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1019 // Return the expression with the addrec on the outside. 1020 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1021 getZeroExtendExpr(Step, Ty), 1022 L); 1023 1024 // Similar to above, only this time treat the step value as signed. 1025 // This covers loops that count down. 1026 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1027 Add = getAddExpr(Start, SMul); 1028 OperandExtendedAdd = 1029 getAddExpr(getZeroExtendExpr(Start, WideTy), 1030 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1031 getSignExtendExpr(Step, WideTy))); 1032 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 1033 // Return the expression with the addrec on the outside. 1034 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1035 getSignExtendExpr(Step, Ty), 1036 L); 1037 } 1038 1039 // If the backedge is guarded by a comparison with the pre-inc value 1040 // the addrec is safe. Also, if the entry is guarded by a comparison 1041 // with the start value and the backedge is guarded by a comparison 1042 // with the post-inc value, the addrec is safe. 1043 if (isKnownPositive(Step)) { 1044 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1045 getUnsignedRange(Step).getUnsignedMax()); 1046 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1047 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1048 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1049 AR->getPostIncExpr(*this), N))) 1050 // Return the expression with the addrec on the outside. 1051 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1052 getZeroExtendExpr(Step, Ty), 1053 L); 1054 } else if (isKnownNegative(Step)) { 1055 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1056 getSignedRange(Step).getSignedMin()); 1057 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1058 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1059 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1060 AR->getPostIncExpr(*this), N))) 1061 // Return the expression with the addrec on the outside. 1062 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1063 getSignExtendExpr(Step, Ty), 1064 L); 1065 } 1066 } 1067 } 1068 1069 // The cast wasn't folded; create an explicit cast node. 1070 // Recompute the insert position, as it may have been invalidated. 1071 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1072 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1073 Op, Ty); 1074 UniqueSCEVs.InsertNode(S, IP); 1075 return S; 1076} 1077 1078const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1079 const Type *Ty) { 1080 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1081 "This is not an extending conversion!"); 1082 assert(isSCEVable(Ty) && 1083 "This is not a conversion to a SCEVable type!"); 1084 Ty = getEffectiveSCEVType(Ty); 1085 1086 // Fold if the operand is constant. 1087 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1088 return getConstant( 1089 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1090 getEffectiveSCEVType(Ty)))); 1091 1092 // sext(sext(x)) --> sext(x) 1093 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1094 return getSignExtendExpr(SS->getOperand(), Ty); 1095 1096 // Before doing any expensive analysis, check to see if we've already 1097 // computed a SCEV for this Op and Ty. 1098 FoldingSetNodeID ID; 1099 ID.AddInteger(scSignExtend); 1100 ID.AddPointer(Op); 1101 ID.AddPointer(Ty); 1102 void *IP = 0; 1103 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1104 1105 // If the input value is a chrec scev, and we can prove that the value 1106 // did not overflow the old, smaller, value, we can sign extend all of the 1107 // operands (often constants). This allows analysis of something like 1108 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1109 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1110 if (AR->isAffine()) { 1111 const SCEV *Start = AR->getStart(); 1112 const SCEV *Step = AR->getStepRecurrence(*this); 1113 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1114 const Loop *L = AR->getLoop(); 1115 1116 // If we have special knowledge that this addrec won't overflow, 1117 // we don't need to do any further analysis. 1118 if (AR->hasNoSignedWrap()) 1119 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1120 getSignExtendExpr(Step, Ty), 1121 L); 1122 1123 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1124 // Note that this serves two purposes: It filters out loops that are 1125 // simply not analyzable, and it covers the case where this code is 1126 // being called from within backedge-taken count analysis, such that 1127 // attempting to ask for the backedge-taken count would likely result 1128 // in infinite recursion. In the later case, the analysis code will 1129 // cope with a conservative value, and it will take care to purge 1130 // that value once it has finished. 1131 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1132 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1133 // Manually compute the final value for AR, checking for 1134 // overflow. 1135 1136 // Check whether the backedge-taken count can be losslessly casted to 1137 // the addrec's type. The count is always unsigned. 1138 const SCEV *CastedMaxBECount = 1139 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1140 const SCEV *RecastedMaxBECount = 1141 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1142 if (MaxBECount == RecastedMaxBECount) { 1143 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1144 // Check whether Start+Step*MaxBECount has no signed overflow. 1145 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1146 const SCEV *Add = getAddExpr(Start, SMul); 1147 const SCEV *OperandExtendedAdd = 1148 getAddExpr(getSignExtendExpr(Start, WideTy), 1149 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1150 getSignExtendExpr(Step, WideTy))); 1151 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1152 // Return the expression with the addrec on the outside. 1153 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1154 getSignExtendExpr(Step, Ty), 1155 L); 1156 1157 // Similar to above, only this time treat the step value as unsigned. 1158 // This covers loops that count up with an unsigned step. 1159 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1160 Add = getAddExpr(Start, UMul); 1161 OperandExtendedAdd = 1162 getAddExpr(getSignExtendExpr(Start, WideTy), 1163 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1164 getZeroExtendExpr(Step, WideTy))); 1165 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1166 // Return the expression with the addrec on the outside. 1167 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1168 getZeroExtendExpr(Step, Ty), 1169 L); 1170 } 1171 1172 // If the backedge is guarded by a comparison with the pre-inc value 1173 // the addrec is safe. Also, if the entry is guarded by a comparison 1174 // with the start value and the backedge is guarded by a comparison 1175 // with the post-inc value, the addrec is safe. 1176 if (isKnownPositive(Step)) { 1177 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1178 getSignedRange(Step).getSignedMax()); 1179 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1180 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1181 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1182 AR->getPostIncExpr(*this), N))) 1183 // Return the expression with the addrec on the outside. 1184 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1185 getSignExtendExpr(Step, Ty), 1186 L); 1187 } else if (isKnownNegative(Step)) { 1188 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1189 getSignedRange(Step).getSignedMin()); 1190 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1191 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1192 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1193 AR->getPostIncExpr(*this), N))) 1194 // Return the expression with the addrec on the outside. 1195 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1196 getSignExtendExpr(Step, Ty), 1197 L); 1198 } 1199 } 1200 } 1201 1202 // The cast wasn't folded; create an explicit cast node. 1203 // Recompute the insert position, as it may have been invalidated. 1204 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1205 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1206 Op, Ty); 1207 UniqueSCEVs.InsertNode(S, IP); 1208 return S; 1209} 1210 1211/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1212/// unspecified bits out to the given type. 1213/// 1214const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1215 const Type *Ty) { 1216 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1217 "This is not an extending conversion!"); 1218 assert(isSCEVable(Ty) && 1219 "This is not a conversion to a SCEVable type!"); 1220 Ty = getEffectiveSCEVType(Ty); 1221 1222 // Sign-extend negative constants. 1223 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1224 if (SC->getValue()->getValue().isNegative()) 1225 return getSignExtendExpr(Op, Ty); 1226 1227 // Peel off a truncate cast. 1228 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1229 const SCEV *NewOp = T->getOperand(); 1230 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1231 return getAnyExtendExpr(NewOp, Ty); 1232 return getTruncateOrNoop(NewOp, Ty); 1233 } 1234 1235 // Next try a zext cast. If the cast is folded, use it. 1236 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1237 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1238 return ZExt; 1239 1240 // Next try a sext cast. If the cast is folded, use it. 1241 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1242 if (!isa<SCEVSignExtendExpr>(SExt)) 1243 return SExt; 1244 1245 // Force the cast to be folded into the operands of an addrec. 1246 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1247 SmallVector<const SCEV *, 4> Ops; 1248 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1249 I != E; ++I) 1250 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1251 return getAddRecExpr(Ops, AR->getLoop()); 1252 } 1253 1254 // As a special case, fold anyext(undef) to undef. We don't want to 1255 // know too much about SCEVUnknowns, but this special case is handy 1256 // and harmless. 1257 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1258 if (isa<UndefValue>(U->getValue())) 1259 return getSCEV(UndefValue::get(Ty)); 1260 1261 // If the expression is obviously signed, use the sext cast value. 1262 if (isa<SCEVSMaxExpr>(Op)) 1263 return SExt; 1264 1265 // Absent any other information, use the zext cast value. 1266 return ZExt; 1267} 1268 1269/// CollectAddOperandsWithScales - Process the given Ops list, which is 1270/// a list of operands to be added under the given scale, update the given 1271/// map. This is a helper function for getAddRecExpr. As an example of 1272/// what it does, given a sequence of operands that would form an add 1273/// expression like this: 1274/// 1275/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1276/// 1277/// where A and B are constants, update the map with these values: 1278/// 1279/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1280/// 1281/// and add 13 + A*B*29 to AccumulatedConstant. 1282/// This will allow getAddRecExpr to produce this: 1283/// 1284/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1285/// 1286/// This form often exposes folding opportunities that are hidden in 1287/// the original operand list. 1288/// 1289/// Return true iff it appears that any interesting folding opportunities 1290/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1291/// the common case where no interesting opportunities are present, and 1292/// is also used as a check to avoid infinite recursion. 1293/// 1294static bool 1295CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1296 SmallVector<const SCEV *, 8> &NewOps, 1297 APInt &AccumulatedConstant, 1298 const SCEV *const *Ops, size_t NumOperands, 1299 const APInt &Scale, 1300 ScalarEvolution &SE) { 1301 bool Interesting = false; 1302 1303 // Iterate over the add operands. They are sorted, with constants first. 1304 unsigned i = 0; 1305 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1306 ++i; 1307 // Pull a buried constant out to the outside. 1308 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1309 Interesting = true; 1310 AccumulatedConstant += Scale * C->getValue()->getValue(); 1311 } 1312 1313 // Next comes everything else. We're especially interested in multiplies 1314 // here, but they're in the middle, so just visit the rest with one loop. 1315 for (; i != NumOperands; ++i) { 1316 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1317 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1318 APInt NewScale = 1319 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1320 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1321 // A multiplication of a constant with another add; recurse. 1322 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1323 Interesting |= 1324 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1325 Add->op_begin(), Add->getNumOperands(), 1326 NewScale, SE); 1327 } else { 1328 // A multiplication of a constant with some other value. Update 1329 // the map. 1330 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1331 const SCEV *Key = SE.getMulExpr(MulOps); 1332 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1333 M.insert(std::make_pair(Key, NewScale)); 1334 if (Pair.second) { 1335 NewOps.push_back(Pair.first->first); 1336 } else { 1337 Pair.first->second += NewScale; 1338 // The map already had an entry for this value, which may indicate 1339 // a folding opportunity. 1340 Interesting = true; 1341 } 1342 } 1343 } else { 1344 // An ordinary operand. Update the map. 1345 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1346 M.insert(std::make_pair(Ops[i], Scale)); 1347 if (Pair.second) { 1348 NewOps.push_back(Pair.first->first); 1349 } else { 1350 Pair.first->second += Scale; 1351 // The map already had an entry for this value, which may indicate 1352 // a folding opportunity. 1353 Interesting = true; 1354 } 1355 } 1356 } 1357 1358 return Interesting; 1359} 1360 1361namespace { 1362 struct APIntCompare { 1363 bool operator()(const APInt &LHS, const APInt &RHS) const { 1364 return LHS.ult(RHS); 1365 } 1366 }; 1367} 1368 1369/// getAddExpr - Get a canonical add expression, or something simpler if 1370/// possible. 1371const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1372 bool HasNUW, bool HasNSW) { 1373 assert(!Ops.empty() && "Cannot get empty add!"); 1374 if (Ops.size() == 1) return Ops[0]; 1375#ifndef NDEBUG 1376 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1377 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1378 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1379 "SCEVAddExpr operand types don't match!"); 1380#endif 1381 1382 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1383 if (!HasNUW && HasNSW) { 1384 bool All = true; 1385 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1386 E = Ops.end(); I != E; ++I) 1387 if (!isKnownNonNegative(*I)) { 1388 All = false; 1389 break; 1390 } 1391 if (All) HasNUW = true; 1392 } 1393 1394 // Sort by complexity, this groups all similar expression types together. 1395 GroupByComplexity(Ops, LI); 1396 1397 // If there are any constants, fold them together. 1398 unsigned Idx = 0; 1399 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1400 ++Idx; 1401 assert(Idx < Ops.size()); 1402 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1403 // We found two constants, fold them together! 1404 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1405 RHSC->getValue()->getValue()); 1406 if (Ops.size() == 2) return Ops[0]; 1407 Ops.erase(Ops.begin()+1); // Erase the folded element 1408 LHSC = cast<SCEVConstant>(Ops[0]); 1409 } 1410 1411 // If we are left with a constant zero being added, strip it off. 1412 if (LHSC->getValue()->isZero()) { 1413 Ops.erase(Ops.begin()); 1414 --Idx; 1415 } 1416 1417 if (Ops.size() == 1) return Ops[0]; 1418 } 1419 1420 // Okay, check to see if the same value occurs in the operand list more than 1421 // once. If so, merge them together into an multiply expression. Since we 1422 // sorted the list, these values are required to be adjacent. 1423 const Type *Ty = Ops[0]->getType(); 1424 bool FoundMatch = false; 1425 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1426 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1427 // Scan ahead to count how many equal operands there are. 1428 unsigned Count = 2; 1429 while (i+Count != e && Ops[i+Count] == Ops[i]) 1430 ++Count; 1431 // Merge the values into a multiply. 1432 const SCEV *Scale = getConstant(Ty, Count); 1433 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1434 if (Ops.size() == Count) 1435 return Mul; 1436 Ops[i] = Mul; 1437 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1438 --i; e -= Count - 1; 1439 FoundMatch = true; 1440 } 1441 if (FoundMatch) 1442 return getAddExpr(Ops, HasNUW, HasNSW); 1443 1444 // Check for truncates. If all the operands are truncated from the same 1445 // type, see if factoring out the truncate would permit the result to be 1446 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1447 // if the contents of the resulting outer trunc fold to something simple. 1448 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1449 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1450 const Type *DstType = Trunc->getType(); 1451 const Type *SrcType = Trunc->getOperand()->getType(); 1452 SmallVector<const SCEV *, 8> LargeOps; 1453 bool Ok = true; 1454 // Check all the operands to see if they can be represented in the 1455 // source type of the truncate. 1456 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1457 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1458 if (T->getOperand()->getType() != SrcType) { 1459 Ok = false; 1460 break; 1461 } 1462 LargeOps.push_back(T->getOperand()); 1463 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1464 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1465 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1466 SmallVector<const SCEV *, 8> LargeMulOps; 1467 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1468 if (const SCEVTruncateExpr *T = 1469 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1470 if (T->getOperand()->getType() != SrcType) { 1471 Ok = false; 1472 break; 1473 } 1474 LargeMulOps.push_back(T->getOperand()); 1475 } else if (const SCEVConstant *C = 1476 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1477 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1478 } else { 1479 Ok = false; 1480 break; 1481 } 1482 } 1483 if (Ok) 1484 LargeOps.push_back(getMulExpr(LargeMulOps)); 1485 } else { 1486 Ok = false; 1487 break; 1488 } 1489 } 1490 if (Ok) { 1491 // Evaluate the expression in the larger type. 1492 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1493 // If it folds to something simple, use it. Otherwise, don't. 1494 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1495 return getTruncateExpr(Fold, DstType); 1496 } 1497 } 1498 1499 // Skip past any other cast SCEVs. 1500 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1501 ++Idx; 1502 1503 // If there are add operands they would be next. 1504 if (Idx < Ops.size()) { 1505 bool DeletedAdd = false; 1506 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1507 // If we have an add, expand the add operands onto the end of the operands 1508 // list. 1509 Ops.erase(Ops.begin()+Idx); 1510 Ops.append(Add->op_begin(), Add->op_end()); 1511 DeletedAdd = true; 1512 } 1513 1514 // If we deleted at least one add, we added operands to the end of the list, 1515 // and they are not necessarily sorted. Recurse to resort and resimplify 1516 // any operands we just acquired. 1517 if (DeletedAdd) 1518 return getAddExpr(Ops); 1519 } 1520 1521 // Skip over the add expression until we get to a multiply. 1522 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1523 ++Idx; 1524 1525 // Check to see if there are any folding opportunities present with 1526 // operands multiplied by constant values. 1527 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1528 uint64_t BitWidth = getTypeSizeInBits(Ty); 1529 DenseMap<const SCEV *, APInt> M; 1530 SmallVector<const SCEV *, 8> NewOps; 1531 APInt AccumulatedConstant(BitWidth, 0); 1532 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1533 Ops.data(), Ops.size(), 1534 APInt(BitWidth, 1), *this)) { 1535 // Some interesting folding opportunity is present, so its worthwhile to 1536 // re-generate the operands list. Group the operands by constant scale, 1537 // to avoid multiplying by the same constant scale multiple times. 1538 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1539 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1540 E = NewOps.end(); I != E; ++I) 1541 MulOpLists[M.find(*I)->second].push_back(*I); 1542 // Re-generate the operands list. 1543 Ops.clear(); 1544 if (AccumulatedConstant != 0) 1545 Ops.push_back(getConstant(AccumulatedConstant)); 1546 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1547 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1548 if (I->first != 0) 1549 Ops.push_back(getMulExpr(getConstant(I->first), 1550 getAddExpr(I->second))); 1551 if (Ops.empty()) 1552 return getConstant(Ty, 0); 1553 if (Ops.size() == 1) 1554 return Ops[0]; 1555 return getAddExpr(Ops); 1556 } 1557 } 1558 1559 // If we are adding something to a multiply expression, make sure the 1560 // something is not already an operand of the multiply. If so, merge it into 1561 // the multiply. 1562 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1563 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1564 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1565 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1566 if (isa<SCEVConstant>(MulOpSCEV)) 1567 continue; 1568 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1569 if (MulOpSCEV == Ops[AddOp]) { 1570 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1571 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1572 if (Mul->getNumOperands() != 2) { 1573 // If the multiply has more than two operands, we must get the 1574 // Y*Z term. 1575 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1576 Mul->op_begin()+MulOp); 1577 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1578 InnerMul = getMulExpr(MulOps); 1579 } 1580 const SCEV *One = getConstant(Ty, 1); 1581 const SCEV *AddOne = getAddExpr(One, InnerMul); 1582 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1583 if (Ops.size() == 2) return OuterMul; 1584 if (AddOp < Idx) { 1585 Ops.erase(Ops.begin()+AddOp); 1586 Ops.erase(Ops.begin()+Idx-1); 1587 } else { 1588 Ops.erase(Ops.begin()+Idx); 1589 Ops.erase(Ops.begin()+AddOp-1); 1590 } 1591 Ops.push_back(OuterMul); 1592 return getAddExpr(Ops); 1593 } 1594 1595 // Check this multiply against other multiplies being added together. 1596 for (unsigned OtherMulIdx = Idx+1; 1597 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1598 ++OtherMulIdx) { 1599 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1600 // If MulOp occurs in OtherMul, we can fold the two multiplies 1601 // together. 1602 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1603 OMulOp != e; ++OMulOp) 1604 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1605 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1606 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1607 if (Mul->getNumOperands() != 2) { 1608 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1609 Mul->op_begin()+MulOp); 1610 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1611 InnerMul1 = getMulExpr(MulOps); 1612 } 1613 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1614 if (OtherMul->getNumOperands() != 2) { 1615 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1616 OtherMul->op_begin()+OMulOp); 1617 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1618 InnerMul2 = getMulExpr(MulOps); 1619 } 1620 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1621 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1622 if (Ops.size() == 2) return OuterMul; 1623 Ops.erase(Ops.begin()+Idx); 1624 Ops.erase(Ops.begin()+OtherMulIdx-1); 1625 Ops.push_back(OuterMul); 1626 return getAddExpr(Ops); 1627 } 1628 } 1629 } 1630 } 1631 1632 // If there are any add recurrences in the operands list, see if any other 1633 // added values are loop invariant. If so, we can fold them into the 1634 // recurrence. 1635 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1636 ++Idx; 1637 1638 // Scan over all recurrences, trying to fold loop invariants into them. 1639 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1640 // Scan all of the other operands to this add and add them to the vector if 1641 // they are loop invariant w.r.t. the recurrence. 1642 SmallVector<const SCEV *, 8> LIOps; 1643 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1644 const Loop *AddRecLoop = AddRec->getLoop(); 1645 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1646 if (Ops[i]->isLoopInvariant(AddRecLoop)) { 1647 LIOps.push_back(Ops[i]); 1648 Ops.erase(Ops.begin()+i); 1649 --i; --e; 1650 } 1651 1652 // If we found some loop invariants, fold them into the recurrence. 1653 if (!LIOps.empty()) { 1654 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1655 LIOps.push_back(AddRec->getStart()); 1656 1657 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1658 AddRec->op_end()); 1659 AddRecOps[0] = getAddExpr(LIOps); 1660 1661 // Build the new addrec. Propagate the NUW and NSW flags if both the 1662 // outer add and the inner addrec are guaranteed to have no overflow. 1663 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1664 HasNUW && AddRec->hasNoUnsignedWrap(), 1665 HasNSW && AddRec->hasNoSignedWrap()); 1666 1667 // If all of the other operands were loop invariant, we are done. 1668 if (Ops.size() == 1) return NewRec; 1669 1670 // Otherwise, add the folded AddRec by the non-liv parts. 1671 for (unsigned i = 0;; ++i) 1672 if (Ops[i] == AddRec) { 1673 Ops[i] = NewRec; 1674 break; 1675 } 1676 return getAddExpr(Ops); 1677 } 1678 1679 // Okay, if there weren't any loop invariants to be folded, check to see if 1680 // there are multiple AddRec's with the same loop induction variable being 1681 // added together. If so, we can fold them. 1682 for (unsigned OtherIdx = Idx+1; 1683 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1684 ++OtherIdx) 1685 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1686 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1687 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1688 AddRec->op_end()); 1689 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1690 ++OtherIdx) 1691 if (const SCEVAddRecExpr *OtherAddRec = 1692 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1693 if (OtherAddRec->getLoop() == AddRecLoop) { 1694 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1695 i != e; ++i) { 1696 if (i >= AddRecOps.size()) { 1697 AddRecOps.append(OtherAddRec->op_begin()+i, 1698 OtherAddRec->op_end()); 1699 break; 1700 } 1701 AddRecOps[i] = getAddExpr(AddRecOps[i], 1702 OtherAddRec->getOperand(i)); 1703 } 1704 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1705 } 1706 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1707 return getAddExpr(Ops); 1708 } 1709 1710 // Otherwise couldn't fold anything into this recurrence. Move onto the 1711 // next one. 1712 } 1713 1714 // Okay, it looks like we really DO need an add expr. Check to see if we 1715 // already have one, otherwise create a new one. 1716 FoldingSetNodeID ID; 1717 ID.AddInteger(scAddExpr); 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 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1924 ID.AddPointer(Ops[i]); 1925 void *IP = 0; 1926 SCEVMulExpr *S = 1927 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1928 if (!S) { 1929 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1930 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1931 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1932 O, Ops.size()); 1933 UniqueSCEVs.InsertNode(S, IP); 1934 } 1935 if (HasNUW) S->setHasNoUnsignedWrap(true); 1936 if (HasNSW) S->setHasNoSignedWrap(true); 1937 return S; 1938} 1939 1940/// getUDivExpr - Get a canonical unsigned division expression, or something 1941/// simpler if possible. 1942const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1943 const SCEV *RHS) { 1944 assert(getEffectiveSCEVType(LHS->getType()) == 1945 getEffectiveSCEVType(RHS->getType()) && 1946 "SCEVUDivExpr operand types don't match!"); 1947 1948 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1949 if (RHSC->getValue()->equalsInt(1)) 1950 return LHS; // X udiv 1 --> x 1951 // If the denominator is zero, the result of the udiv is undefined. Don't 1952 // try to analyze it, because the resolution chosen here may differ from 1953 // the resolution chosen in other parts of the compiler. 1954 if (!RHSC->getValue()->isZero()) { 1955 // Determine if the division can be folded into the operands of 1956 // its operands. 1957 // TODO: Generalize this to non-constants by using known-bits information. 1958 const Type *Ty = LHS->getType(); 1959 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1960 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1961 // For non-power-of-two values, effectively round the value up to the 1962 // nearest power of two. 1963 if (!RHSC->getValue()->getValue().isPowerOf2()) 1964 ++MaxShiftAmt; 1965 const IntegerType *ExtTy = 1966 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1967 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1968 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1969 if (const SCEVConstant *Step = 1970 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1971 if (!Step->getValue()->getValue() 1972 .urem(RHSC->getValue()->getValue()) && 1973 getZeroExtendExpr(AR, ExtTy) == 1974 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1975 getZeroExtendExpr(Step, ExtTy), 1976 AR->getLoop())) { 1977 SmallVector<const SCEV *, 4> Operands; 1978 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1979 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1980 return getAddRecExpr(Operands, AR->getLoop()); 1981 } 1982 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1983 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1984 SmallVector<const SCEV *, 4> Operands; 1985 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1986 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1987 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1988 // Find an operand that's safely divisible. 1989 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1990 const SCEV *Op = M->getOperand(i); 1991 const SCEV *Div = getUDivExpr(Op, RHSC); 1992 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1993 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1994 M->op_end()); 1995 Operands[i] = Div; 1996 return getMulExpr(Operands); 1997 } 1998 } 1999 } 2000 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2001 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 2002 SmallVector<const SCEV *, 4> Operands; 2003 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2004 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2005 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2006 Operands.clear(); 2007 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2008 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2009 if (isa<SCEVUDivExpr>(Op) || 2010 getMulExpr(Op, RHS) != A->getOperand(i)) 2011 break; 2012 Operands.push_back(Op); 2013 } 2014 if (Operands.size() == A->getNumOperands()) 2015 return getAddExpr(Operands); 2016 } 2017 } 2018 2019 // Fold if both operands are constant. 2020 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2021 Constant *LHSCV = LHSC->getValue(); 2022 Constant *RHSCV = RHSC->getValue(); 2023 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2024 RHSCV))); 2025 } 2026 } 2027 } 2028 2029 FoldingSetNodeID ID; 2030 ID.AddInteger(scUDivExpr); 2031 ID.AddPointer(LHS); 2032 ID.AddPointer(RHS); 2033 void *IP = 0; 2034 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2035 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2036 LHS, RHS); 2037 UniqueSCEVs.InsertNode(S, IP); 2038 return S; 2039} 2040 2041 2042/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2043/// Simplify the expression as much as possible. 2044const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 2045 const SCEV *Step, const Loop *L, 2046 bool HasNUW, bool HasNSW) { 2047 SmallVector<const SCEV *, 4> Operands; 2048 Operands.push_back(Start); 2049 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2050 if (StepChrec->getLoop() == L) { 2051 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2052 return getAddRecExpr(Operands, L); 2053 } 2054 2055 Operands.push_back(Step); 2056 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 2057} 2058 2059/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2060/// Simplify the expression as much as possible. 2061const SCEV * 2062ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2063 const Loop *L, 2064 bool HasNUW, bool HasNSW) { 2065 if (Operands.size() == 1) return Operands[0]; 2066#ifndef NDEBUG 2067 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2068 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2069 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2070 "SCEVAddRecExpr operand types don't match!"); 2071#endif 2072 2073 if (Operands.back()->isZero()) { 2074 Operands.pop_back(); 2075 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2076 } 2077 2078 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2079 // use that information to infer NUW and NSW flags. However, computing a 2080 // BE count requires calling getAddRecExpr, so we may not yet have a 2081 // meaningful BE count at this point (and if we don't, we'd be stuck 2082 // with a SCEVCouldNotCompute as the cached BE count). 2083 2084 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2085 if (!HasNUW && HasNSW) { 2086 bool All = true; 2087 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2088 E = Operands.end(); I != E; ++I) 2089 if (!isKnownNonNegative(*I)) { 2090 All = false; 2091 break; 2092 } 2093 if (All) HasNUW = true; 2094 } 2095 2096 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2097 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2098 const Loop *NestedLoop = NestedAR->getLoop(); 2099 if (L->contains(NestedLoop) ? 2100 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2101 (!NestedLoop->contains(L) && 2102 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2103 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2104 NestedAR->op_end()); 2105 Operands[0] = NestedAR->getStart(); 2106 // AddRecs require their operands be loop-invariant with respect to their 2107 // loops. Don't perform this transformation if it would break this 2108 // requirement. 2109 bool AllInvariant = true; 2110 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2111 if (!Operands[i]->isLoopInvariant(L)) { 2112 AllInvariant = false; 2113 break; 2114 } 2115 if (AllInvariant) { 2116 NestedOperands[0] = getAddRecExpr(Operands, L); 2117 AllInvariant = true; 2118 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2119 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { 2120 AllInvariant = false; 2121 break; 2122 } 2123 if (AllInvariant) 2124 // Ok, both add recurrences are valid after the transformation. 2125 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2126 } 2127 // Reset Operands to its original state. 2128 Operands[0] = NestedAR; 2129 } 2130 } 2131 2132 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2133 // already have one, otherwise create a new one. 2134 FoldingSetNodeID ID; 2135 ID.AddInteger(scAddRecExpr); 2136 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2137 ID.AddPointer(Operands[i]); 2138 ID.AddPointer(L); 2139 void *IP = 0; 2140 SCEVAddRecExpr *S = 2141 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2142 if (!S) { 2143 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2144 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2145 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2146 O, Operands.size(), L); 2147 UniqueSCEVs.InsertNode(S, IP); 2148 } 2149 if (HasNUW) S->setHasNoUnsignedWrap(true); 2150 if (HasNSW) S->setHasNoSignedWrap(true); 2151 return S; 2152} 2153 2154const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2155 const SCEV *RHS) { 2156 SmallVector<const SCEV *, 2> Ops; 2157 Ops.push_back(LHS); 2158 Ops.push_back(RHS); 2159 return getSMaxExpr(Ops); 2160} 2161 2162const SCEV * 2163ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2164 assert(!Ops.empty() && "Cannot get empty smax!"); 2165 if (Ops.size() == 1) return Ops[0]; 2166#ifndef NDEBUG 2167 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2168 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2169 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2170 "SCEVSMaxExpr operand types don't match!"); 2171#endif 2172 2173 // Sort by complexity, this groups all similar expression types together. 2174 GroupByComplexity(Ops, LI); 2175 2176 // If there are any constants, fold them together. 2177 unsigned Idx = 0; 2178 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2179 ++Idx; 2180 assert(Idx < Ops.size()); 2181 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2182 // We found two constants, fold them together! 2183 ConstantInt *Fold = ConstantInt::get(getContext(), 2184 APIntOps::smax(LHSC->getValue()->getValue(), 2185 RHSC->getValue()->getValue())); 2186 Ops[0] = getConstant(Fold); 2187 Ops.erase(Ops.begin()+1); // Erase the folded element 2188 if (Ops.size() == 1) return Ops[0]; 2189 LHSC = cast<SCEVConstant>(Ops[0]); 2190 } 2191 2192 // If we are left with a constant minimum-int, strip it off. 2193 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2194 Ops.erase(Ops.begin()); 2195 --Idx; 2196 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2197 // If we have an smax with a constant maximum-int, it will always be 2198 // maximum-int. 2199 return Ops[0]; 2200 } 2201 2202 if (Ops.size() == 1) return Ops[0]; 2203 } 2204 2205 // Find the first SMax 2206 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2207 ++Idx; 2208 2209 // Check to see if one of the operands is an SMax. If so, expand its operands 2210 // onto our operand list, and recurse to simplify. 2211 if (Idx < Ops.size()) { 2212 bool DeletedSMax = false; 2213 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2214 Ops.erase(Ops.begin()+Idx); 2215 Ops.append(SMax->op_begin(), SMax->op_end()); 2216 DeletedSMax = true; 2217 } 2218 2219 if (DeletedSMax) 2220 return getSMaxExpr(Ops); 2221 } 2222 2223 // Okay, check to see if the same value occurs in the operand list twice. If 2224 // so, delete one. Since we sorted the list, these values are required to 2225 // be adjacent. 2226 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2227 // X smax Y smax Y --> X smax Y 2228 // X smax Y --> X, if X is always greater than Y 2229 if (Ops[i] == Ops[i+1] || 2230 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2231 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2232 --i; --e; 2233 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2234 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2235 --i; --e; 2236 } 2237 2238 if (Ops.size() == 1) return Ops[0]; 2239 2240 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2241 2242 // Okay, it looks like we really DO need an smax expr. Check to see if we 2243 // already have one, otherwise create a new one. 2244 FoldingSetNodeID ID; 2245 ID.AddInteger(scSMaxExpr); 2246 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2247 ID.AddPointer(Ops[i]); 2248 void *IP = 0; 2249 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2250 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2251 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2252 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2253 O, Ops.size()); 2254 UniqueSCEVs.InsertNode(S, IP); 2255 return S; 2256} 2257 2258const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2259 const SCEV *RHS) { 2260 SmallVector<const SCEV *, 2> Ops; 2261 Ops.push_back(LHS); 2262 Ops.push_back(RHS); 2263 return getUMaxExpr(Ops); 2264} 2265 2266const SCEV * 2267ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2268 assert(!Ops.empty() && "Cannot get empty umax!"); 2269 if (Ops.size() == 1) return Ops[0]; 2270#ifndef NDEBUG 2271 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2272 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2273 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2274 "SCEVUMaxExpr operand types don't match!"); 2275#endif 2276 2277 // Sort by complexity, this groups all similar expression types together. 2278 GroupByComplexity(Ops, LI); 2279 2280 // If there are any constants, fold them together. 2281 unsigned Idx = 0; 2282 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2283 ++Idx; 2284 assert(Idx < Ops.size()); 2285 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2286 // We found two constants, fold them together! 2287 ConstantInt *Fold = ConstantInt::get(getContext(), 2288 APIntOps::umax(LHSC->getValue()->getValue(), 2289 RHSC->getValue()->getValue())); 2290 Ops[0] = getConstant(Fold); 2291 Ops.erase(Ops.begin()+1); // Erase the folded element 2292 if (Ops.size() == 1) return Ops[0]; 2293 LHSC = cast<SCEVConstant>(Ops[0]); 2294 } 2295 2296 // If we are left with a constant minimum-int, strip it off. 2297 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2298 Ops.erase(Ops.begin()); 2299 --Idx; 2300 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2301 // If we have an umax with a constant maximum-int, it will always be 2302 // maximum-int. 2303 return Ops[0]; 2304 } 2305 2306 if (Ops.size() == 1) return Ops[0]; 2307 } 2308 2309 // Find the first UMax 2310 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2311 ++Idx; 2312 2313 // Check to see if one of the operands is a UMax. If so, expand its operands 2314 // onto our operand list, and recurse to simplify. 2315 if (Idx < Ops.size()) { 2316 bool DeletedUMax = false; 2317 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2318 Ops.erase(Ops.begin()+Idx); 2319 Ops.append(UMax->op_begin(), UMax->op_end()); 2320 DeletedUMax = true; 2321 } 2322 2323 if (DeletedUMax) 2324 return getUMaxExpr(Ops); 2325 } 2326 2327 // Okay, check to see if the same value occurs in the operand list twice. If 2328 // so, delete one. Since we sorted the list, these values are required to 2329 // be adjacent. 2330 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2331 // X umax Y umax Y --> X umax Y 2332 // X umax Y --> X, if X is always greater than Y 2333 if (Ops[i] == Ops[i+1] || 2334 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2335 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2336 --i; --e; 2337 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2338 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2339 --i; --e; 2340 } 2341 2342 if (Ops.size() == 1) return Ops[0]; 2343 2344 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2345 2346 // Okay, it looks like we really DO need a umax expr. Check to see if we 2347 // already have one, otherwise create a new one. 2348 FoldingSetNodeID ID; 2349 ID.AddInteger(scUMaxExpr); 2350 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2351 ID.AddPointer(Ops[i]); 2352 void *IP = 0; 2353 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2354 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2355 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2356 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2357 O, Ops.size()); 2358 UniqueSCEVs.InsertNode(S, IP); 2359 return S; 2360} 2361 2362const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2363 const SCEV *RHS) { 2364 // ~smax(~x, ~y) == smin(x, y). 2365 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2366} 2367 2368const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2369 const SCEV *RHS) { 2370 // ~umax(~x, ~y) == umin(x, y) 2371 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2372} 2373 2374const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2375 // If we have TargetData, we can bypass creating a target-independent 2376 // constant expression and then folding it back into a ConstantInt. 2377 // This is just a compile-time optimization. 2378 if (TD) 2379 return getConstant(TD->getIntPtrType(getContext()), 2380 TD->getTypeAllocSize(AllocTy)); 2381 2382 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2383 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2384 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2385 C = Folded; 2386 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2387 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2388} 2389 2390const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2391 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2393 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2394 C = Folded; 2395 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2396 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2397} 2398 2399const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2400 unsigned FieldNo) { 2401 // If we have TargetData, we can bypass creating a target-independent 2402 // constant expression and then folding it back into a ConstantInt. 2403 // This is just a compile-time optimization. 2404 if (TD) 2405 return getConstant(TD->getIntPtrType(getContext()), 2406 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2407 2408 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2410 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2411 C = Folded; 2412 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2413 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2414} 2415 2416const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2417 Constant *FieldNo) { 2418 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2419 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2420 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2421 C = Folded; 2422 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2423 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2424} 2425 2426const SCEV *ScalarEvolution::getUnknown(Value *V) { 2427 // Don't attempt to do anything other than create a SCEVUnknown object 2428 // here. createSCEV only calls getUnknown after checking for all other 2429 // interesting possibilities, and any other code that calls getUnknown 2430 // is doing so in order to hide a value from SCEV canonicalization. 2431 2432 FoldingSetNodeID ID; 2433 ID.AddInteger(scUnknown); 2434 ID.AddPointer(V); 2435 void *IP = 0; 2436 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2437 assert(cast<SCEVUnknown>(S)->getValue() == V && 2438 "Stale SCEVUnknown in uniquing map!"); 2439 return S; 2440 } 2441 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2442 FirstUnknown); 2443 FirstUnknown = cast<SCEVUnknown>(S); 2444 UniqueSCEVs.InsertNode(S, IP); 2445 return S; 2446} 2447 2448//===----------------------------------------------------------------------===// 2449// Basic SCEV Analysis and PHI Idiom Recognition Code 2450// 2451 2452/// isSCEVable - Test if values of the given type are analyzable within 2453/// the SCEV framework. This primarily includes integer types, and it 2454/// can optionally include pointer types if the ScalarEvolution class 2455/// has access to target-specific information. 2456bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2457 // Integers and pointers are always SCEVable. 2458 return Ty->isIntegerTy() || Ty->isPointerTy(); 2459} 2460 2461/// getTypeSizeInBits - Return the size in bits of the specified type, 2462/// for which isSCEVable must return true. 2463uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2464 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2465 2466 // If we have a TargetData, use it! 2467 if (TD) 2468 return TD->getTypeSizeInBits(Ty); 2469 2470 // Integer types have fixed sizes. 2471 if (Ty->isIntegerTy()) 2472 return Ty->getPrimitiveSizeInBits(); 2473 2474 // The only other support type is pointer. Without TargetData, conservatively 2475 // assume pointers are 64-bit. 2476 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2477 return 64; 2478} 2479 2480/// getEffectiveSCEVType - Return a type with the same bitwidth as 2481/// the given type and which represents how SCEV will treat the given 2482/// type, for which isSCEVable must return true. For pointer types, 2483/// this is the pointer-sized integer type. 2484const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2485 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2486 2487 if (Ty->isIntegerTy()) 2488 return Ty; 2489 2490 // The only other support type is pointer. 2491 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2492 if (TD) return TD->getIntPtrType(getContext()); 2493 2494 // Without TargetData, conservatively assume pointers are 64-bit. 2495 return Type::getInt64Ty(getContext()); 2496} 2497 2498const SCEV *ScalarEvolution::getCouldNotCompute() { 2499 return &CouldNotCompute; 2500} 2501 2502/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2503/// expression and create a new one. 2504const SCEV *ScalarEvolution::getSCEV(Value *V) { 2505 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2506 2507 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2508 if (I != ValueExprMap.end()) return I->second; 2509 const SCEV *S = createSCEV(V); 2510 2511 // The process of creating a SCEV for V may have caused other SCEVs 2512 // to have been created, so it's necessary to insert the new entry 2513 // from scratch, rather than trying to remember the insert position 2514 // above. 2515 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2516 return S; 2517} 2518 2519/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2520/// 2521const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2522 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2523 return getConstant( 2524 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2525 2526 const Type *Ty = V->getType(); 2527 Ty = getEffectiveSCEVType(Ty); 2528 return getMulExpr(V, 2529 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2530} 2531 2532/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2533const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2534 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2535 return getConstant( 2536 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2537 2538 const Type *Ty = V->getType(); 2539 Ty = getEffectiveSCEVType(Ty); 2540 const SCEV *AllOnes = 2541 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2542 return getMinusSCEV(AllOnes, V); 2543} 2544 2545/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. 2546/// 2547const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, 2548 const SCEV *RHS) { 2549 // Fast path: X - X --> 0. 2550 if (LHS == RHS) 2551 return getConstant(LHS->getType(), 0); 2552 2553 // X - Y --> X + -Y 2554 return getAddExpr(LHS, getNegativeSCEV(RHS)); 2555} 2556 2557/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2558/// input value to the specified type. If the type must be extended, it is zero 2559/// extended. 2560const SCEV * 2561ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, 2562 const Type *Ty) { 2563 const Type *SrcTy = V->getType(); 2564 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2565 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2566 "Cannot truncate or zero extend with non-integer arguments!"); 2567 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2568 return V; // No conversion 2569 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2570 return getTruncateExpr(V, Ty); 2571 return getZeroExtendExpr(V, Ty); 2572} 2573 2574/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2575/// input value to the specified type. If the type must be extended, it is sign 2576/// extended. 2577const SCEV * 2578ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2579 const Type *Ty) { 2580 const Type *SrcTy = V->getType(); 2581 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2582 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2583 "Cannot truncate or zero extend with non-integer arguments!"); 2584 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2585 return V; // No conversion 2586 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2587 return getTruncateExpr(V, Ty); 2588 return getSignExtendExpr(V, Ty); 2589} 2590 2591/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2592/// input value to the specified type. If the type must be extended, it is zero 2593/// extended. The conversion must not be narrowing. 2594const SCEV * 2595ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2596 const Type *SrcTy = V->getType(); 2597 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2598 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2599 "Cannot noop or zero extend with non-integer arguments!"); 2600 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2601 "getNoopOrZeroExtend cannot truncate!"); 2602 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2603 return V; // No conversion 2604 return getZeroExtendExpr(V, Ty); 2605} 2606 2607/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2608/// input value to the specified type. If the type must be extended, it is sign 2609/// extended. The conversion must not be narrowing. 2610const SCEV * 2611ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2612 const Type *SrcTy = V->getType(); 2613 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2614 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2615 "Cannot noop or sign extend with non-integer arguments!"); 2616 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2617 "getNoopOrSignExtend cannot truncate!"); 2618 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2619 return V; // No conversion 2620 return getSignExtendExpr(V, Ty); 2621} 2622 2623/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2624/// the input value to the specified type. If the type must be extended, 2625/// it is extended with unspecified bits. The conversion must not be 2626/// narrowing. 2627const SCEV * 2628ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2629 const Type *SrcTy = V->getType(); 2630 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2631 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2632 "Cannot noop or any extend with non-integer arguments!"); 2633 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2634 "getNoopOrAnyExtend cannot truncate!"); 2635 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2636 return V; // No conversion 2637 return getAnyExtendExpr(V, Ty); 2638} 2639 2640/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2641/// input value to the specified type. The conversion must not be widening. 2642const SCEV * 2643ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2644 const Type *SrcTy = V->getType(); 2645 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2646 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2647 "Cannot truncate or noop with non-integer arguments!"); 2648 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2649 "getTruncateOrNoop cannot extend!"); 2650 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2651 return V; // No conversion 2652 return getTruncateExpr(V, Ty); 2653} 2654 2655/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2656/// the types using zero-extension, and then perform a umax operation 2657/// with them. 2658const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2659 const SCEV *RHS) { 2660 const SCEV *PromotedLHS = LHS; 2661 const SCEV *PromotedRHS = RHS; 2662 2663 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2664 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2665 else 2666 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2667 2668 return getUMaxExpr(PromotedLHS, PromotedRHS); 2669} 2670 2671/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2672/// the types using zero-extension, and then perform a umin operation 2673/// with them. 2674const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2675 const SCEV *RHS) { 2676 const SCEV *PromotedLHS = LHS; 2677 const SCEV *PromotedRHS = RHS; 2678 2679 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2680 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2681 else 2682 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2683 2684 return getUMinExpr(PromotedLHS, PromotedRHS); 2685} 2686 2687/// PushDefUseChildren - Push users of the given Instruction 2688/// onto the given Worklist. 2689static void 2690PushDefUseChildren(Instruction *I, 2691 SmallVectorImpl<Instruction *> &Worklist) { 2692 // Push the def-use children onto the Worklist stack. 2693 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2694 UI != UE; ++UI) 2695 Worklist.push_back(cast<Instruction>(*UI)); 2696} 2697 2698/// ForgetSymbolicValue - This looks up computed SCEV values for all 2699/// instructions that depend on the given instruction and removes them from 2700/// the ValueExprMapType map if they reference SymName. This is used during PHI 2701/// resolution. 2702void 2703ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2704 SmallVector<Instruction *, 16> Worklist; 2705 PushDefUseChildren(PN, Worklist); 2706 2707 SmallPtrSet<Instruction *, 8> Visited; 2708 Visited.insert(PN); 2709 while (!Worklist.empty()) { 2710 Instruction *I = Worklist.pop_back_val(); 2711 if (!Visited.insert(I)) continue; 2712 2713 ValueExprMapType::iterator It = 2714 ValueExprMap.find(static_cast<Value *>(I)); 2715 if (It != ValueExprMap.end()) { 2716 // Short-circuit the def-use traversal if the symbolic name 2717 // ceases to appear in expressions. 2718 if (It->second != SymName && !It->second->hasOperand(SymName)) 2719 continue; 2720 2721 // SCEVUnknown for a PHI either means that it has an unrecognized 2722 // structure, it's a PHI that's in the progress of being computed 2723 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2724 // additional loop trip count information isn't going to change anything. 2725 // In the second case, createNodeForPHI will perform the necessary 2726 // updates on its own when it gets to that point. In the third, we do 2727 // want to forget the SCEVUnknown. 2728 if (!isa<PHINode>(I) || 2729 !isa<SCEVUnknown>(It->second) || 2730 (I != PN && It->second == SymName)) { 2731 ValuesAtScopes.erase(It->second); 2732 ValueExprMap.erase(It); 2733 } 2734 } 2735 2736 PushDefUseChildren(I, Worklist); 2737 } 2738} 2739 2740/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2741/// a loop header, making it a potential recurrence, or it doesn't. 2742/// 2743const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2744 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2745 if (L->getHeader() == PN->getParent()) { 2746 // The loop may have multiple entrances or multiple exits; we can analyze 2747 // this phi as an addrec if it has a unique entry value and a unique 2748 // backedge value. 2749 Value *BEValueV = 0, *StartValueV = 0; 2750 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2751 Value *V = PN->getIncomingValue(i); 2752 if (L->contains(PN->getIncomingBlock(i))) { 2753 if (!BEValueV) { 2754 BEValueV = V; 2755 } else if (BEValueV != V) { 2756 BEValueV = 0; 2757 break; 2758 } 2759 } else if (!StartValueV) { 2760 StartValueV = V; 2761 } else if (StartValueV != V) { 2762 StartValueV = 0; 2763 break; 2764 } 2765 } 2766 if (BEValueV && StartValueV) { 2767 // While we are analyzing this PHI node, handle its value symbolically. 2768 const SCEV *SymbolicName = getUnknown(PN); 2769 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2770 "PHI node already processed?"); 2771 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2772 2773 // Using this symbolic name for the PHI, analyze the value coming around 2774 // the back-edge. 2775 const SCEV *BEValue = getSCEV(BEValueV); 2776 2777 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2778 // has a special value for the first iteration of the loop. 2779 2780 // If the value coming around the backedge is an add with the symbolic 2781 // value we just inserted, then we found a simple induction variable! 2782 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2783 // If there is a single occurrence of the symbolic value, replace it 2784 // with a recurrence. 2785 unsigned FoundIndex = Add->getNumOperands(); 2786 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2787 if (Add->getOperand(i) == SymbolicName) 2788 if (FoundIndex == e) { 2789 FoundIndex = i; 2790 break; 2791 } 2792 2793 if (FoundIndex != Add->getNumOperands()) { 2794 // Create an add with everything but the specified operand. 2795 SmallVector<const SCEV *, 8> Ops; 2796 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2797 if (i != FoundIndex) 2798 Ops.push_back(Add->getOperand(i)); 2799 const SCEV *Accum = getAddExpr(Ops); 2800 2801 // This is not a valid addrec if the step amount is varying each 2802 // loop iteration, but is not itself an addrec in this loop. 2803 if (Accum->isLoopInvariant(L) || 2804 (isa<SCEVAddRecExpr>(Accum) && 2805 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2806 bool HasNUW = false; 2807 bool HasNSW = false; 2808 2809 // If the increment doesn't overflow, then neither the addrec nor 2810 // the post-increment will overflow. 2811 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2812 if (OBO->hasNoUnsignedWrap()) 2813 HasNUW = true; 2814 if (OBO->hasNoSignedWrap()) 2815 HasNSW = true; 2816 } 2817 2818 const SCEV *StartVal = getSCEV(StartValueV); 2819 const SCEV *PHISCEV = 2820 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2821 2822 // Since the no-wrap flags are on the increment, they apply to the 2823 // post-incremented value as well. 2824 if (Accum->isLoopInvariant(L)) 2825 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2826 Accum, L, HasNUW, HasNSW); 2827 2828 // Okay, for the entire analysis of this edge we assumed the PHI 2829 // to be symbolic. We now need to go back and purge all of the 2830 // entries for the scalars that use the symbolic expression. 2831 ForgetSymbolicName(PN, SymbolicName); 2832 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2833 return PHISCEV; 2834 } 2835 } 2836 } else if (const SCEVAddRecExpr *AddRec = 2837 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2838 // Otherwise, this could be a loop like this: 2839 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2840 // In this case, j = {1,+,1} and BEValue is j. 2841 // Because the other in-value of i (0) fits the evolution of BEValue 2842 // i really is an addrec evolution. 2843 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2844 const SCEV *StartVal = getSCEV(StartValueV); 2845 2846 // If StartVal = j.start - j.stride, we can use StartVal as the 2847 // initial step of the addrec evolution. 2848 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2849 AddRec->getOperand(1))) { 2850 const SCEV *PHISCEV = 2851 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2852 2853 // Okay, for the entire analysis of this edge we assumed the PHI 2854 // to be symbolic. We now need to go back and purge all of the 2855 // entries for the scalars that use the symbolic expression. 2856 ForgetSymbolicName(PN, SymbolicName); 2857 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2858 return PHISCEV; 2859 } 2860 } 2861 } 2862 } 2863 } 2864 2865 // If the PHI has a single incoming value, follow that value, unless the 2866 // PHI's incoming blocks are in a different loop, in which case doing so 2867 // risks breaking LCSSA form. Instcombine would normally zap these, but 2868 // it doesn't have DominatorTree information, so it may miss cases. 2869 if (Value *V = PN->hasConstantValue(DT)) { 2870 bool AllSameLoop = true; 2871 Loop *PNLoop = LI->getLoopFor(PN->getParent()); 2872 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) 2873 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { 2874 AllSameLoop = false; 2875 break; 2876 } 2877 if (AllSameLoop) 2878 return getSCEV(V); 2879 } 2880 2881 // If it's not a loop phi, we can't handle it yet. 2882 return getUnknown(PN); 2883} 2884 2885/// createNodeForGEP - Expand GEP instructions into add and multiply 2886/// operations. This allows them to be analyzed by regular SCEV code. 2887/// 2888const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2889 2890 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2891 // Add expression, because the Instruction may be guarded by control flow 2892 // and the no-overflow bits may not be valid for the expression in any 2893 // context. 2894 2895 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2896 Value *Base = GEP->getOperand(0); 2897 // Don't attempt to analyze GEPs over unsized objects. 2898 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2899 return getUnknown(GEP); 2900 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2901 gep_type_iterator GTI = gep_type_begin(GEP); 2902 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2903 E = GEP->op_end(); 2904 I != E; ++I) { 2905 Value *Index = *I; 2906 // Compute the (potentially symbolic) offset in bytes for this index. 2907 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2908 // For a struct, add the member offset. 2909 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2910 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2911 2912 // Add the field offset to the running total offset. 2913 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2914 } else { 2915 // For an array, add the element offset, explicitly scaled. 2916 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2917 const SCEV *IndexS = getSCEV(Index); 2918 // Getelementptr indices are signed. 2919 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2920 2921 // Multiply the index by the element size to compute the element offset. 2922 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2923 2924 // Add the element offset to the running total offset. 2925 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2926 } 2927 } 2928 2929 // Get the SCEV for the GEP base. 2930 const SCEV *BaseS = getSCEV(Base); 2931 2932 // Add the total offset from all the GEP indices to the base. 2933 return getAddExpr(BaseS, TotalOffset); 2934} 2935 2936/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2937/// guaranteed to end in (at every loop iteration). It is, at the same time, 2938/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2939/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2940uint32_t 2941ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2942 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2943 return C->getValue()->getValue().countTrailingZeros(); 2944 2945 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2946 return std::min(GetMinTrailingZeros(T->getOperand()), 2947 (uint32_t)getTypeSizeInBits(T->getType())); 2948 2949 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2950 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2951 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2952 getTypeSizeInBits(E->getType()) : OpRes; 2953 } 2954 2955 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2956 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2957 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2958 getTypeSizeInBits(E->getType()) : OpRes; 2959 } 2960 2961 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2962 // The result is the min of all operands results. 2963 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2964 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2965 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2966 return MinOpRes; 2967 } 2968 2969 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2970 // The result is the sum of all operands results. 2971 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2972 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2973 for (unsigned i = 1, e = M->getNumOperands(); 2974 SumOpRes != BitWidth && i != e; ++i) 2975 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2976 BitWidth); 2977 return SumOpRes; 2978 } 2979 2980 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2981 // The result is the min of all operands results. 2982 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2983 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2984 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2985 return MinOpRes; 2986 } 2987 2988 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2989 // The result is the min of all operands results. 2990 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2991 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2992 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2993 return MinOpRes; 2994 } 2995 2996 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2997 // The result is the min of all operands results. 2998 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2999 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3000 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3001 return MinOpRes; 3002 } 3003 3004 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3005 // For a SCEVUnknown, ask ValueTracking. 3006 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3007 APInt Mask = APInt::getAllOnesValue(BitWidth); 3008 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3009 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3010 return Zeros.countTrailingOnes(); 3011 } 3012 3013 // SCEVUDivExpr 3014 return 0; 3015} 3016 3017/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3018/// 3019ConstantRange 3020ScalarEvolution::getUnsignedRange(const SCEV *S) { 3021 3022 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3023 return ConstantRange(C->getValue()->getValue()); 3024 3025 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3026 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3027 3028 // If the value has known zeros, the maximum unsigned value will have those 3029 // known zeros as well. 3030 uint32_t TZ = GetMinTrailingZeros(S); 3031 if (TZ != 0) 3032 ConservativeResult = 3033 ConstantRange(APInt::getMinValue(BitWidth), 3034 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3035 3036 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3037 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3038 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3039 X = X.add(getUnsignedRange(Add->getOperand(i))); 3040 return ConservativeResult.intersectWith(X); 3041 } 3042 3043 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3044 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3045 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3046 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3047 return ConservativeResult.intersectWith(X); 3048 } 3049 3050 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3051 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3052 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3053 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3054 return ConservativeResult.intersectWith(X); 3055 } 3056 3057 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3058 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3059 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3060 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3061 return ConservativeResult.intersectWith(X); 3062 } 3063 3064 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3065 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3066 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3067 return ConservativeResult.intersectWith(X.udiv(Y)); 3068 } 3069 3070 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3071 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3072 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3073 } 3074 3075 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3076 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3077 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3078 } 3079 3080 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3081 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3082 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3083 } 3084 3085 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3086 // If there's no unsigned wrap, the value will never be less than its 3087 // initial value. 3088 if (AddRec->hasNoUnsignedWrap()) 3089 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3090 if (!C->getValue()->isZero()) 3091 ConservativeResult = 3092 ConservativeResult.intersectWith( 3093 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3094 3095 // TODO: non-affine addrec 3096 if (AddRec->isAffine()) { 3097 const Type *Ty = AddRec->getType(); 3098 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3099 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3100 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3101 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3102 3103 const SCEV *Start = AddRec->getStart(); 3104 const SCEV *Step = AddRec->getStepRecurrence(*this); 3105 3106 ConstantRange StartRange = getUnsignedRange(Start); 3107 ConstantRange StepRange = getSignedRange(Step); 3108 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3109 ConstantRange EndRange = 3110 StartRange.add(MaxBECountRange.multiply(StepRange)); 3111 3112 // Check for overflow. This must be done with ConstantRange arithmetic 3113 // because we could be called from within the ScalarEvolution overflow 3114 // checking code. 3115 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3116 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3117 ConstantRange ExtMaxBECountRange = 3118 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3119 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3120 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3121 ExtEndRange) 3122 return ConservativeResult; 3123 3124 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3125 EndRange.getUnsignedMin()); 3126 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3127 EndRange.getUnsignedMax()); 3128 if (Min.isMinValue() && Max.isMaxValue()) 3129 return ConservativeResult; 3130 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3131 } 3132 } 3133 3134 return ConservativeResult; 3135 } 3136 3137 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3138 // For a SCEVUnknown, ask ValueTracking. 3139 APInt Mask = APInt::getAllOnesValue(BitWidth); 3140 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3141 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3142 if (Ones == ~Zeros + 1) 3143 return ConservativeResult; 3144 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); 3145 } 3146 3147 return ConservativeResult; 3148} 3149 3150/// getSignedRange - Determine the signed range for a particular SCEV. 3151/// 3152ConstantRange 3153ScalarEvolution::getSignedRange(const SCEV *S) { 3154 3155 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3156 return ConstantRange(C->getValue()->getValue()); 3157 3158 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3159 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3160 3161 // If the value has known zeros, the maximum signed value will have those 3162 // known zeros as well. 3163 uint32_t TZ = GetMinTrailingZeros(S); 3164 if (TZ != 0) 3165 ConservativeResult = 3166 ConstantRange(APInt::getSignedMinValue(BitWidth), 3167 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3168 3169 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3170 ConstantRange X = getSignedRange(Add->getOperand(0)); 3171 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3172 X = X.add(getSignedRange(Add->getOperand(i))); 3173 return ConservativeResult.intersectWith(X); 3174 } 3175 3176 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3177 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3178 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3179 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3180 return ConservativeResult.intersectWith(X); 3181 } 3182 3183 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3184 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3185 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3186 X = X.smax(getSignedRange(SMax->getOperand(i))); 3187 return ConservativeResult.intersectWith(X); 3188 } 3189 3190 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3191 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3192 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3193 X = X.umax(getSignedRange(UMax->getOperand(i))); 3194 return ConservativeResult.intersectWith(X); 3195 } 3196 3197 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3198 ConstantRange X = getSignedRange(UDiv->getLHS()); 3199 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3200 return ConservativeResult.intersectWith(X.udiv(Y)); 3201 } 3202 3203 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3204 ConstantRange X = getSignedRange(ZExt->getOperand()); 3205 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); 3206 } 3207 3208 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3209 ConstantRange X = getSignedRange(SExt->getOperand()); 3210 return ConservativeResult.intersectWith(X.signExtend(BitWidth)); 3211 } 3212 3213 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3214 ConstantRange X = getSignedRange(Trunc->getOperand()); 3215 return ConservativeResult.intersectWith(X.truncate(BitWidth)); 3216 } 3217 3218 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3219 // If there's no signed wrap, and all the operands have the same sign or 3220 // zero, the value won't ever change sign. 3221 if (AddRec->hasNoSignedWrap()) { 3222 bool AllNonNeg = true; 3223 bool AllNonPos = true; 3224 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3225 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3226 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3227 } 3228 if (AllNonNeg) 3229 ConservativeResult = ConservativeResult.intersectWith( 3230 ConstantRange(APInt(BitWidth, 0), 3231 APInt::getSignedMinValue(BitWidth))); 3232 else if (AllNonPos) 3233 ConservativeResult = ConservativeResult.intersectWith( 3234 ConstantRange(APInt::getSignedMinValue(BitWidth), 3235 APInt(BitWidth, 1))); 3236 } 3237 3238 // TODO: non-affine addrec 3239 if (AddRec->isAffine()) { 3240 const Type *Ty = AddRec->getType(); 3241 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3242 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3243 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3244 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3245 3246 const SCEV *Start = AddRec->getStart(); 3247 const SCEV *Step = AddRec->getStepRecurrence(*this); 3248 3249 ConstantRange StartRange = getSignedRange(Start); 3250 ConstantRange StepRange = getSignedRange(Step); 3251 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3252 ConstantRange EndRange = 3253 StartRange.add(MaxBECountRange.multiply(StepRange)); 3254 3255 // Check for overflow. This must be done with ConstantRange arithmetic 3256 // because we could be called from within the ScalarEvolution overflow 3257 // checking code. 3258 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3259 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3260 ConstantRange ExtMaxBECountRange = 3261 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3262 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3263 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3264 ExtEndRange) 3265 return ConservativeResult; 3266 3267 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3268 EndRange.getSignedMin()); 3269 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3270 EndRange.getSignedMax()); 3271 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3272 return ConservativeResult; 3273 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); 3274 } 3275 } 3276 3277 return ConservativeResult; 3278 } 3279 3280 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3281 // For a SCEVUnknown, ask ValueTracking. 3282 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3283 return ConservativeResult; 3284 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3285 if (NS == 1) 3286 return ConservativeResult; 3287 return ConservativeResult.intersectWith( 3288 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3289 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); 3290 } 3291 3292 return ConservativeResult; 3293} 3294 3295/// createSCEV - We know that there is no SCEV for the specified value. 3296/// Analyze the expression. 3297/// 3298const SCEV *ScalarEvolution::createSCEV(Value *V) { 3299 if (!isSCEVable(V->getType())) 3300 return getUnknown(V); 3301 3302 unsigned Opcode = Instruction::UserOp1; 3303 if (Instruction *I = dyn_cast<Instruction>(V)) { 3304 Opcode = I->getOpcode(); 3305 3306 // Don't attempt to analyze instructions in blocks that aren't 3307 // reachable. Such instructions don't matter, and they aren't required 3308 // to obey basic rules for definitions dominating uses which this 3309 // analysis depends on. 3310 if (!DT->isReachableFromEntry(I->getParent())) 3311 return getUnknown(V); 3312 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3313 Opcode = CE->getOpcode(); 3314 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3315 return getConstant(CI); 3316 else if (isa<ConstantPointerNull>(V)) 3317 return getConstant(V->getType(), 0); 3318 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3319 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3320 else 3321 return getUnknown(V); 3322 3323 Operator *U = cast<Operator>(V); 3324 switch (Opcode) { 3325 case Instruction::Add: { 3326 // The simple thing to do would be to just call getSCEV on both operands 3327 // and call getAddExpr with the result. However if we're looking at a 3328 // bunch of things all added together, this can be quite inefficient, 3329 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3330 // Instead, gather up all the operands and make a single getAddExpr call. 3331 // LLVM IR canonical form means we need only traverse the left operands. 3332 SmallVector<const SCEV *, 4> AddOps; 3333 AddOps.push_back(getSCEV(U->getOperand(1))); 3334 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3335 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3336 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3337 break; 3338 U = cast<Operator>(Op); 3339 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3340 if (Opcode == Instruction::Sub) 3341 AddOps.push_back(getNegativeSCEV(Op1)); 3342 else 3343 AddOps.push_back(Op1); 3344 } 3345 AddOps.push_back(getSCEV(U->getOperand(0))); 3346 return getAddExpr(AddOps); 3347 } 3348 case Instruction::Mul: { 3349 // See the Add code above. 3350 SmallVector<const SCEV *, 4> MulOps; 3351 MulOps.push_back(getSCEV(U->getOperand(1))); 3352 for (Value *Op = U->getOperand(0); 3353 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3354 Op = U->getOperand(0)) { 3355 U = cast<Operator>(Op); 3356 MulOps.push_back(getSCEV(U->getOperand(1))); 3357 } 3358 MulOps.push_back(getSCEV(U->getOperand(0))); 3359 return getMulExpr(MulOps); 3360 } 3361 case Instruction::UDiv: 3362 return getUDivExpr(getSCEV(U->getOperand(0)), 3363 getSCEV(U->getOperand(1))); 3364 case Instruction::Sub: 3365 return getMinusSCEV(getSCEV(U->getOperand(0)), 3366 getSCEV(U->getOperand(1))); 3367 case Instruction::And: 3368 // For an expression like x&255 that merely masks off the high bits, 3369 // use zext(trunc(x)) as the SCEV expression. 3370 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3371 if (CI->isNullValue()) 3372 return getSCEV(U->getOperand(1)); 3373 if (CI->isAllOnesValue()) 3374 return getSCEV(U->getOperand(0)); 3375 const APInt &A = CI->getValue(); 3376 3377 // Instcombine's ShrinkDemandedConstant may strip bits out of 3378 // constants, obscuring what would otherwise be a low-bits mask. 3379 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3380 // knew about to reconstruct a low-bits mask value. 3381 unsigned LZ = A.countLeadingZeros(); 3382 unsigned BitWidth = A.getBitWidth(); 3383 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3384 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3385 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3386 3387 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3388 3389 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3390 return 3391 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3392 IntegerType::get(getContext(), BitWidth - LZ)), 3393 U->getType()); 3394 } 3395 break; 3396 3397 case Instruction::Or: 3398 // If the RHS of the Or is a constant, we may have something like: 3399 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3400 // optimizations will transparently handle this case. 3401 // 3402 // In order for this transformation to be safe, the LHS must be of the 3403 // form X*(2^n) and the Or constant must be less than 2^n. 3404 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3405 const SCEV *LHS = getSCEV(U->getOperand(0)); 3406 const APInt &CIVal = CI->getValue(); 3407 if (GetMinTrailingZeros(LHS) >= 3408 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3409 // Build a plain add SCEV. 3410 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3411 // If the LHS of the add was an addrec and it has no-wrap flags, 3412 // transfer the no-wrap flags, since an or won't introduce a wrap. 3413 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3414 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3415 if (OldAR->hasNoUnsignedWrap()) 3416 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3417 if (OldAR->hasNoSignedWrap()) 3418 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3419 } 3420 return S; 3421 } 3422 } 3423 break; 3424 case Instruction::Xor: 3425 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3426 // If the RHS of the xor is a signbit, then this is just an add. 3427 // Instcombine turns add of signbit into xor as a strength reduction step. 3428 if (CI->getValue().isSignBit()) 3429 return getAddExpr(getSCEV(U->getOperand(0)), 3430 getSCEV(U->getOperand(1))); 3431 3432 // If the RHS of xor is -1, then this is a not operation. 3433 if (CI->isAllOnesValue()) 3434 return getNotSCEV(getSCEV(U->getOperand(0))); 3435 3436 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3437 // This is a variant of the check for xor with -1, and it handles 3438 // the case where instcombine has trimmed non-demanded bits out 3439 // of an xor with -1. 3440 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3441 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3442 if (BO->getOpcode() == Instruction::And && 3443 LCI->getValue() == CI->getValue()) 3444 if (const SCEVZeroExtendExpr *Z = 3445 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3446 const Type *UTy = U->getType(); 3447 const SCEV *Z0 = Z->getOperand(); 3448 const Type *Z0Ty = Z0->getType(); 3449 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3450 3451 // If C is a low-bits mask, the zero extend is serving to 3452 // mask off the high bits. Complement the operand and 3453 // re-apply the zext. 3454 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3455 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3456 3457 // If C is a single bit, it may be in the sign-bit position 3458 // before the zero-extend. In this case, represent the xor 3459 // using an add, which is equivalent, and re-apply the zext. 3460 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); 3461 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3462 Trunc.isSignBit()) 3463 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3464 UTy); 3465 } 3466 } 3467 break; 3468 3469 case Instruction::Shl: 3470 // Turn shift left of a constant amount into a multiply. 3471 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3472 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3473 3474 // If the shift count is not less than the bitwidth, the result of 3475 // the shift is undefined. Don't try to analyze it, because the 3476 // resolution chosen here may differ from the resolution chosen in 3477 // other parts of the compiler. 3478 if (SA->getValue().uge(BitWidth)) 3479 break; 3480 3481 Constant *X = ConstantInt::get(getContext(), 3482 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3483 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3484 } 3485 break; 3486 3487 case Instruction::LShr: 3488 // Turn logical shift right of a constant into a unsigned divide. 3489 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3490 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3491 3492 // If the shift count is not less than the bitwidth, the result of 3493 // the shift is undefined. Don't try to analyze it, because the 3494 // resolution chosen here may differ from the resolution chosen in 3495 // other parts of the compiler. 3496 if (SA->getValue().uge(BitWidth)) 3497 break; 3498 3499 Constant *X = ConstantInt::get(getContext(), 3500 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3501 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3502 } 3503 break; 3504 3505 case Instruction::AShr: 3506 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3507 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3508 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3509 if (L->getOpcode() == Instruction::Shl && 3510 L->getOperand(1) == U->getOperand(1)) { 3511 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3512 3513 // If the shift count is not less than the bitwidth, the result of 3514 // the shift is undefined. Don't try to analyze it, because the 3515 // resolution chosen here may differ from the resolution chosen in 3516 // other parts of the compiler. 3517 if (CI->getValue().uge(BitWidth)) 3518 break; 3519 3520 uint64_t Amt = BitWidth - CI->getZExtValue(); 3521 if (Amt == BitWidth) 3522 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3523 return 3524 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3525 IntegerType::get(getContext(), 3526 Amt)), 3527 U->getType()); 3528 } 3529 break; 3530 3531 case Instruction::Trunc: 3532 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3533 3534 case Instruction::ZExt: 3535 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3536 3537 case Instruction::SExt: 3538 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3539 3540 case Instruction::BitCast: 3541 // BitCasts are no-op casts so we just eliminate the cast. 3542 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3543 return getSCEV(U->getOperand(0)); 3544 break; 3545 3546 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3547 // lead to pointer expressions which cannot safely be expanded to GEPs, 3548 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3549 // simplifying integer expressions. 3550 3551 case Instruction::GetElementPtr: 3552 return createNodeForGEP(cast<GEPOperator>(U)); 3553 3554 case Instruction::PHI: 3555 return createNodeForPHI(cast<PHINode>(U)); 3556 3557 case Instruction::Select: 3558 // This could be a smax or umax that was lowered earlier. 3559 // Try to recover it. 3560 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3561 Value *LHS = ICI->getOperand(0); 3562 Value *RHS = ICI->getOperand(1); 3563 switch (ICI->getPredicate()) { 3564 case ICmpInst::ICMP_SLT: 3565 case ICmpInst::ICMP_SLE: 3566 std::swap(LHS, RHS); 3567 // fall through 3568 case ICmpInst::ICMP_SGT: 3569 case ICmpInst::ICMP_SGE: 3570 // a >s b ? a+x : b+x -> smax(a, b)+x 3571 // a >s b ? b+x : a+x -> smin(a, b)+x 3572 if (LHS->getType() == U->getType()) { 3573 const SCEV *LS = getSCEV(LHS); 3574 const SCEV *RS = getSCEV(RHS); 3575 const SCEV *LA = getSCEV(U->getOperand(1)); 3576 const SCEV *RA = getSCEV(U->getOperand(2)); 3577 const SCEV *LDiff = getMinusSCEV(LA, LS); 3578 const SCEV *RDiff = getMinusSCEV(RA, RS); 3579 if (LDiff == RDiff) 3580 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3581 LDiff = getMinusSCEV(LA, RS); 3582 RDiff = getMinusSCEV(RA, LS); 3583 if (LDiff == RDiff) 3584 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3585 } 3586 break; 3587 case ICmpInst::ICMP_ULT: 3588 case ICmpInst::ICMP_ULE: 3589 std::swap(LHS, RHS); 3590 // fall through 3591 case ICmpInst::ICMP_UGT: 3592 case ICmpInst::ICMP_UGE: 3593 // a >u b ? a+x : b+x -> umax(a, b)+x 3594 // a >u b ? b+x : a+x -> umin(a, b)+x 3595 if (LHS->getType() == U->getType()) { 3596 const SCEV *LS = getSCEV(LHS); 3597 const SCEV *RS = getSCEV(RHS); 3598 const SCEV *LA = getSCEV(U->getOperand(1)); 3599 const SCEV *RA = getSCEV(U->getOperand(2)); 3600 const SCEV *LDiff = getMinusSCEV(LA, LS); 3601 const SCEV *RDiff = getMinusSCEV(RA, RS); 3602 if (LDiff == RDiff) 3603 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3604 LDiff = getMinusSCEV(LA, RS); 3605 RDiff = getMinusSCEV(RA, LS); 3606 if (LDiff == RDiff) 3607 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3608 } 3609 break; 3610 case ICmpInst::ICMP_NE: 3611 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3612 if (LHS->getType() == U->getType() && 3613 isa<ConstantInt>(RHS) && 3614 cast<ConstantInt>(RHS)->isZero()) { 3615 const SCEV *One = getConstant(LHS->getType(), 1); 3616 const SCEV *LS = getSCEV(LHS); 3617 const SCEV *LA = getSCEV(U->getOperand(1)); 3618 const SCEV *RA = getSCEV(U->getOperand(2)); 3619 const SCEV *LDiff = getMinusSCEV(LA, LS); 3620 const SCEV *RDiff = getMinusSCEV(RA, One); 3621 if (LDiff == RDiff) 3622 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3623 } 3624 break; 3625 case ICmpInst::ICMP_EQ: 3626 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3627 if (LHS->getType() == U->getType() && 3628 isa<ConstantInt>(RHS) && 3629 cast<ConstantInt>(RHS)->isZero()) { 3630 const SCEV *One = getConstant(LHS->getType(), 1); 3631 const SCEV *LS = getSCEV(LHS); 3632 const SCEV *LA = getSCEV(U->getOperand(1)); 3633 const SCEV *RA = getSCEV(U->getOperand(2)); 3634 const SCEV *LDiff = getMinusSCEV(LA, One); 3635 const SCEV *RDiff = getMinusSCEV(RA, LS); 3636 if (LDiff == RDiff) 3637 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3638 } 3639 break; 3640 default: 3641 break; 3642 } 3643 } 3644 3645 default: // We cannot analyze this expression. 3646 break; 3647 } 3648 3649 return getUnknown(V); 3650} 3651 3652 3653 3654//===----------------------------------------------------------------------===// 3655// Iteration Count Computation Code 3656// 3657 3658/// getBackedgeTakenCount - If the specified loop has a predictable 3659/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3660/// object. The backedge-taken count is the number of times the loop header 3661/// will be branched to from within the loop. This is one less than the 3662/// trip count of the loop, since it doesn't count the first iteration, 3663/// when the header is branched to from outside the loop. 3664/// 3665/// Note that it is not valid to call this method on a loop without a 3666/// loop-invariant backedge-taken count (see 3667/// hasLoopInvariantBackedgeTakenCount). 3668/// 3669const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3670 return getBackedgeTakenInfo(L).Exact; 3671} 3672 3673/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3674/// return the least SCEV value that is known never to be less than the 3675/// actual backedge taken count. 3676const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3677 return getBackedgeTakenInfo(L).Max; 3678} 3679 3680/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3681/// onto the given Worklist. 3682static void 3683PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3684 BasicBlock *Header = L->getHeader(); 3685 3686 // Push all Loop-header PHIs onto the Worklist stack. 3687 for (BasicBlock::iterator I = Header->begin(); 3688 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3689 Worklist.push_back(PN); 3690} 3691 3692const ScalarEvolution::BackedgeTakenInfo & 3693ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3694 // Initially insert a CouldNotCompute for this loop. If the insertion 3695 // succeeds, proceed to actually compute a backedge-taken count and 3696 // update the value. The temporary CouldNotCompute value tells SCEV 3697 // code elsewhere that it shouldn't attempt to request a new 3698 // backedge-taken count, which could result in infinite recursion. 3699 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3700 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3701 if (Pair.second) { 3702 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3703 if (BECount.Exact != getCouldNotCompute()) { 3704 assert(BECount.Exact->isLoopInvariant(L) && 3705 BECount.Max->isLoopInvariant(L) && 3706 "Computed backedge-taken count isn't loop invariant for loop!"); 3707 ++NumTripCountsComputed; 3708 3709 // Update the value in the map. 3710 Pair.first->second = BECount; 3711 } else { 3712 if (BECount.Max != getCouldNotCompute()) 3713 // Update the value in the map. 3714 Pair.first->second = BECount; 3715 if (isa<PHINode>(L->getHeader()->begin())) 3716 // Only count loops that have phi nodes as not being computable. 3717 ++NumTripCountsNotComputed; 3718 } 3719 3720 // Now that we know more about the trip count for this loop, forget any 3721 // existing SCEV values for PHI nodes in this loop since they are only 3722 // conservative estimates made without the benefit of trip count 3723 // information. This is similar to the code in forgetLoop, except that 3724 // it handles SCEVUnknown PHI nodes specially. 3725 if (BECount.hasAnyInfo()) { 3726 SmallVector<Instruction *, 16> Worklist; 3727 PushLoopPHIs(L, Worklist); 3728 3729 SmallPtrSet<Instruction *, 8> Visited; 3730 while (!Worklist.empty()) { 3731 Instruction *I = Worklist.pop_back_val(); 3732 if (!Visited.insert(I)) continue; 3733 3734 ValueExprMapType::iterator It = 3735 ValueExprMap.find(static_cast<Value *>(I)); 3736 if (It != ValueExprMap.end()) { 3737 // SCEVUnknown for a PHI either means that it has an unrecognized 3738 // structure, or it's a PHI that's in the progress of being computed 3739 // by createNodeForPHI. In the former case, additional loop trip 3740 // count information isn't going to change anything. In the later 3741 // case, createNodeForPHI will perform the necessary updates on its 3742 // own when it gets to that point. 3743 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { 3744 ValuesAtScopes.erase(It->second); 3745 ValueExprMap.erase(It); 3746 } 3747 if (PHINode *PN = dyn_cast<PHINode>(I)) 3748 ConstantEvolutionLoopExitValue.erase(PN); 3749 } 3750 3751 PushDefUseChildren(I, Worklist); 3752 } 3753 } 3754 } 3755 return Pair.first->second; 3756} 3757 3758/// forgetLoop - This method should be called by the client when it has 3759/// changed a loop in a way that may effect ScalarEvolution's ability to 3760/// compute a trip count, or if the loop is deleted. 3761void ScalarEvolution::forgetLoop(const Loop *L) { 3762 // Drop any stored trip count value. 3763 BackedgeTakenCounts.erase(L); 3764 3765 // Drop information about expressions based on loop-header PHIs. 3766 SmallVector<Instruction *, 16> Worklist; 3767 PushLoopPHIs(L, Worklist); 3768 3769 SmallPtrSet<Instruction *, 8> Visited; 3770 while (!Worklist.empty()) { 3771 Instruction *I = Worklist.pop_back_val(); 3772 if (!Visited.insert(I)) continue; 3773 3774 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3775 if (It != ValueExprMap.end()) { 3776 ValuesAtScopes.erase(It->second); 3777 ValueExprMap.erase(It); 3778 if (PHINode *PN = dyn_cast<PHINode>(I)) 3779 ConstantEvolutionLoopExitValue.erase(PN); 3780 } 3781 3782 PushDefUseChildren(I, Worklist); 3783 } 3784} 3785 3786/// forgetValue - This method should be called by the client when it has 3787/// changed a value in a way that may effect its value, or which may 3788/// disconnect it from a def-use chain linking it to a loop. 3789void ScalarEvolution::forgetValue(Value *V) { 3790 Instruction *I = dyn_cast<Instruction>(V); 3791 if (!I) return; 3792 3793 // Drop information about expressions based on loop-header PHIs. 3794 SmallVector<Instruction *, 16> Worklist; 3795 Worklist.push_back(I); 3796 3797 SmallPtrSet<Instruction *, 8> Visited; 3798 while (!Worklist.empty()) { 3799 I = Worklist.pop_back_val(); 3800 if (!Visited.insert(I)) continue; 3801 3802 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3803 if (It != ValueExprMap.end()) { 3804 ValuesAtScopes.erase(It->second); 3805 ValueExprMap.erase(It); 3806 if (PHINode *PN = dyn_cast<PHINode>(I)) 3807 ConstantEvolutionLoopExitValue.erase(PN); 3808 } 3809 3810 PushDefUseChildren(I, Worklist); 3811 } 3812} 3813 3814/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3815/// of the specified loop will execute. 3816ScalarEvolution::BackedgeTakenInfo 3817ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3818 SmallVector<BasicBlock *, 8> ExitingBlocks; 3819 L->getExitingBlocks(ExitingBlocks); 3820 3821 // Examine all exits and pick the most conservative values. 3822 const SCEV *BECount = getCouldNotCompute(); 3823 const SCEV *MaxBECount = getCouldNotCompute(); 3824 bool CouldNotComputeBECount = false; 3825 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3826 BackedgeTakenInfo NewBTI = 3827 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3828 3829 if (NewBTI.Exact == getCouldNotCompute()) { 3830 // We couldn't compute an exact value for this exit, so 3831 // we won't be able to compute an exact value for the loop. 3832 CouldNotComputeBECount = true; 3833 BECount = getCouldNotCompute(); 3834 } else if (!CouldNotComputeBECount) { 3835 if (BECount == getCouldNotCompute()) 3836 BECount = NewBTI.Exact; 3837 else 3838 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3839 } 3840 if (MaxBECount == getCouldNotCompute()) 3841 MaxBECount = NewBTI.Max; 3842 else if (NewBTI.Max != getCouldNotCompute()) 3843 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3844 } 3845 3846 return BackedgeTakenInfo(BECount, MaxBECount); 3847} 3848 3849/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3850/// of the specified loop will execute if it exits via the specified block. 3851ScalarEvolution::BackedgeTakenInfo 3852ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3853 BasicBlock *ExitingBlock) { 3854 3855 // Okay, we've chosen an exiting block. See what condition causes us to 3856 // exit at this block. 3857 // 3858 // FIXME: we should be able to handle switch instructions (with a single exit) 3859 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3860 if (ExitBr == 0) return getCouldNotCompute(); 3861 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3862 3863 // At this point, we know we have a conditional branch that determines whether 3864 // the loop is exited. However, we don't know if the branch is executed each 3865 // time through the loop. If not, then the execution count of the branch will 3866 // not be equal to the trip count of the loop. 3867 // 3868 // Currently we check for this by checking to see if the Exit branch goes to 3869 // the loop header. If so, we know it will always execute the same number of 3870 // times as the loop. We also handle the case where the exit block *is* the 3871 // loop header. This is common for un-rotated loops. 3872 // 3873 // If both of those tests fail, walk up the unique predecessor chain to the 3874 // header, stopping if there is an edge that doesn't exit the loop. If the 3875 // header is reached, the execution count of the branch will be equal to the 3876 // trip count of the loop. 3877 // 3878 // More extensive analysis could be done to handle more cases here. 3879 // 3880 if (ExitBr->getSuccessor(0) != L->getHeader() && 3881 ExitBr->getSuccessor(1) != L->getHeader() && 3882 ExitBr->getParent() != L->getHeader()) { 3883 // The simple checks failed, try climbing the unique predecessor chain 3884 // up to the header. 3885 bool Ok = false; 3886 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3887 BasicBlock *Pred = BB->getUniquePredecessor(); 3888 if (!Pred) 3889 return getCouldNotCompute(); 3890 TerminatorInst *PredTerm = Pred->getTerminator(); 3891 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3892 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3893 if (PredSucc == BB) 3894 continue; 3895 // If the predecessor has a successor that isn't BB and isn't 3896 // outside the loop, assume the worst. 3897 if (L->contains(PredSucc)) 3898 return getCouldNotCompute(); 3899 } 3900 if (Pred == L->getHeader()) { 3901 Ok = true; 3902 break; 3903 } 3904 BB = Pred; 3905 } 3906 if (!Ok) 3907 return getCouldNotCompute(); 3908 } 3909 3910 // Proceed to the next level to examine the exit condition expression. 3911 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3912 ExitBr->getSuccessor(0), 3913 ExitBr->getSuccessor(1)); 3914} 3915 3916/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3917/// backedge of the specified loop will execute if its exit condition 3918/// were a conditional branch of ExitCond, TBB, and FBB. 3919ScalarEvolution::BackedgeTakenInfo 3920ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3921 Value *ExitCond, 3922 BasicBlock *TBB, 3923 BasicBlock *FBB) { 3924 // Check if the controlling expression for this loop is an And or Or. 3925 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3926 if (BO->getOpcode() == Instruction::And) { 3927 // Recurse on the operands of the and. 3928 BackedgeTakenInfo BTI0 = 3929 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3930 BackedgeTakenInfo BTI1 = 3931 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3932 const SCEV *BECount = getCouldNotCompute(); 3933 const SCEV *MaxBECount = getCouldNotCompute(); 3934 if (L->contains(TBB)) { 3935 // Both conditions must be true for the loop to continue executing. 3936 // Choose the less conservative count. 3937 if (BTI0.Exact == getCouldNotCompute() || 3938 BTI1.Exact == getCouldNotCompute()) 3939 BECount = getCouldNotCompute(); 3940 else 3941 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3942 if (BTI0.Max == getCouldNotCompute()) 3943 MaxBECount = BTI1.Max; 3944 else if (BTI1.Max == getCouldNotCompute()) 3945 MaxBECount = BTI0.Max; 3946 else 3947 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3948 } else { 3949 // Both conditions must be true at the same time for the loop to exit. 3950 // For now, be conservative. 3951 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3952 if (BTI0.Max == BTI1.Max) 3953 MaxBECount = BTI0.Max; 3954 if (BTI0.Exact == BTI1.Exact) 3955 BECount = BTI0.Exact; 3956 } 3957 3958 return BackedgeTakenInfo(BECount, MaxBECount); 3959 } 3960 if (BO->getOpcode() == Instruction::Or) { 3961 // Recurse on the operands of the or. 3962 BackedgeTakenInfo BTI0 = 3963 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3964 BackedgeTakenInfo BTI1 = 3965 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3966 const SCEV *BECount = getCouldNotCompute(); 3967 const SCEV *MaxBECount = getCouldNotCompute(); 3968 if (L->contains(FBB)) { 3969 // Both conditions must be false for the loop to continue executing. 3970 // Choose the less conservative count. 3971 if (BTI0.Exact == getCouldNotCompute() || 3972 BTI1.Exact == getCouldNotCompute()) 3973 BECount = getCouldNotCompute(); 3974 else 3975 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3976 if (BTI0.Max == getCouldNotCompute()) 3977 MaxBECount = BTI1.Max; 3978 else if (BTI1.Max == getCouldNotCompute()) 3979 MaxBECount = BTI0.Max; 3980 else 3981 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3982 } else { 3983 // Both conditions must be false at the same time for the loop to exit. 3984 // For now, be conservative. 3985 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3986 if (BTI0.Max == BTI1.Max) 3987 MaxBECount = BTI0.Max; 3988 if (BTI0.Exact == BTI1.Exact) 3989 BECount = BTI0.Exact; 3990 } 3991 3992 return BackedgeTakenInfo(BECount, MaxBECount); 3993 } 3994 } 3995 3996 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3997 // Proceed to the next level to examine the icmp. 3998 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3999 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 4000 4001 // Check for a constant condition. These are normally stripped out by 4002 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4003 // preserve the CFG and is temporarily leaving constant conditions 4004 // in place. 4005 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4006 if (L->contains(FBB) == !CI->getZExtValue()) 4007 // The backedge is always taken. 4008 return getCouldNotCompute(); 4009 else 4010 // The backedge is never taken. 4011 return getConstant(CI->getType(), 0); 4012 } 4013 4014 // If it's not an integer or pointer comparison then compute it the hard way. 4015 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4016} 4017 4018/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4019/// backedge of the specified loop will execute if its exit condition 4020/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4021ScalarEvolution::BackedgeTakenInfo 4022ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4023 ICmpInst *ExitCond, 4024 BasicBlock *TBB, 4025 BasicBlock *FBB) { 4026 4027 // If the condition was exit on true, convert the condition to exit on false 4028 ICmpInst::Predicate Cond; 4029 if (!L->contains(FBB)) 4030 Cond = ExitCond->getPredicate(); 4031 else 4032 Cond = ExitCond->getInversePredicate(); 4033 4034 // Handle common loops like: for (X = "string"; *X; ++X) 4035 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4036 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4037 BackedgeTakenInfo ItCnt = 4038 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4039 if (ItCnt.hasAnyInfo()) 4040 return ItCnt; 4041 } 4042 4043 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4044 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4045 4046 // Try to evaluate any dependencies out of the loop. 4047 LHS = getSCEVAtScope(LHS, L); 4048 RHS = getSCEVAtScope(RHS, L); 4049 4050 // At this point, we would like to compute how many iterations of the 4051 // loop the predicate will return true for these inputs. 4052 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { 4053 // If there is a loop-invariant, force it into the RHS. 4054 std::swap(LHS, RHS); 4055 Cond = ICmpInst::getSwappedPredicate(Cond); 4056 } 4057 4058 // Simplify the operands before analyzing them. 4059 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4060 4061 // If we have a comparison of a chrec against a constant, try to use value 4062 // ranges to answer this query. 4063 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4064 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4065 if (AddRec->getLoop() == L) { 4066 // Form the constant range. 4067 ConstantRange CompRange( 4068 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4069 4070 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4071 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4072 } 4073 4074 switch (Cond) { 4075 case ICmpInst::ICMP_NE: { // while (X != Y) 4076 // Convert to: while (X-Y != 0) 4077 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4078 if (BTI.hasAnyInfo()) return BTI; 4079 break; 4080 } 4081 case ICmpInst::ICMP_EQ: { // while (X == Y) 4082 // Convert to: while (X-Y == 0) 4083 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4084 if (BTI.hasAnyInfo()) return BTI; 4085 break; 4086 } 4087 case ICmpInst::ICMP_SLT: { 4088 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4089 if (BTI.hasAnyInfo()) return BTI; 4090 break; 4091 } 4092 case ICmpInst::ICMP_SGT: { 4093 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4094 getNotSCEV(RHS), L, true); 4095 if (BTI.hasAnyInfo()) return BTI; 4096 break; 4097 } 4098 case ICmpInst::ICMP_ULT: { 4099 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4100 if (BTI.hasAnyInfo()) return BTI; 4101 break; 4102 } 4103 case ICmpInst::ICMP_UGT: { 4104 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4105 getNotSCEV(RHS), L, false); 4106 if (BTI.hasAnyInfo()) return BTI; 4107 break; 4108 } 4109 default: 4110#if 0 4111 dbgs() << "ComputeBackedgeTakenCount "; 4112 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4113 dbgs() << "[unsigned] "; 4114 dbgs() << *LHS << " " 4115 << Instruction::getOpcodeName(Instruction::ICmp) 4116 << " " << *RHS << "\n"; 4117#endif 4118 break; 4119 } 4120 return 4121 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4122} 4123 4124static ConstantInt * 4125EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4126 ScalarEvolution &SE) { 4127 const SCEV *InVal = SE.getConstant(C); 4128 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4129 assert(isa<SCEVConstant>(Val) && 4130 "Evaluation of SCEV at constant didn't fold correctly?"); 4131 return cast<SCEVConstant>(Val)->getValue(); 4132} 4133 4134/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4135/// and a GEP expression (missing the pointer index) indexing into it, return 4136/// the addressed element of the initializer or null if the index expression is 4137/// invalid. 4138static Constant * 4139GetAddressedElementFromGlobal(GlobalVariable *GV, 4140 const std::vector<ConstantInt*> &Indices) { 4141 Constant *Init = GV->getInitializer(); 4142 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4143 uint64_t Idx = Indices[i]->getZExtValue(); 4144 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4145 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4146 Init = cast<Constant>(CS->getOperand(Idx)); 4147 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4148 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4149 Init = cast<Constant>(CA->getOperand(Idx)); 4150 } else if (isa<ConstantAggregateZero>(Init)) { 4151 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4152 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4153 Init = Constant::getNullValue(STy->getElementType(Idx)); 4154 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4155 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4156 Init = Constant::getNullValue(ATy->getElementType()); 4157 } else { 4158 llvm_unreachable("Unknown constant aggregate type!"); 4159 } 4160 return 0; 4161 } else { 4162 return 0; // Unknown initializer type 4163 } 4164 } 4165 return Init; 4166} 4167 4168/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4169/// 'icmp op load X, cst', try to see if we can compute the backedge 4170/// execution count. 4171ScalarEvolution::BackedgeTakenInfo 4172ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4173 LoadInst *LI, 4174 Constant *RHS, 4175 const Loop *L, 4176 ICmpInst::Predicate predicate) { 4177 if (LI->isVolatile()) return getCouldNotCompute(); 4178 4179 // Check to see if the loaded pointer is a getelementptr of a global. 4180 // TODO: Use SCEV instead of manually grubbing with GEPs. 4181 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4182 if (!GEP) return getCouldNotCompute(); 4183 4184 // Make sure that it is really a constant global we are gepping, with an 4185 // initializer, and make sure the first IDX is really 0. 4186 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4187 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4188 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4189 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4190 return getCouldNotCompute(); 4191 4192 // Okay, we allow one non-constant index into the GEP instruction. 4193 Value *VarIdx = 0; 4194 std::vector<ConstantInt*> Indexes; 4195 unsigned VarIdxNum = 0; 4196 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4197 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4198 Indexes.push_back(CI); 4199 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4200 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4201 VarIdx = GEP->getOperand(i); 4202 VarIdxNum = i-2; 4203 Indexes.push_back(0); 4204 } 4205 4206 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4207 // Check to see if X is a loop variant variable value now. 4208 const SCEV *Idx = getSCEV(VarIdx); 4209 Idx = getSCEVAtScope(Idx, L); 4210 4211 // We can only recognize very limited forms of loop index expressions, in 4212 // particular, only affine AddRec's like {C1,+,C2}. 4213 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4214 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || 4215 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4216 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4217 return getCouldNotCompute(); 4218 4219 unsigned MaxSteps = MaxBruteForceIterations; 4220 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4221 ConstantInt *ItCst = ConstantInt::get( 4222 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4223 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4224 4225 // Form the GEP offset. 4226 Indexes[VarIdxNum] = Val; 4227 4228 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4229 if (Result == 0) break; // Cannot compute! 4230 4231 // Evaluate the condition for this iteration. 4232 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4233 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4234 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4235#if 0 4236 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4237 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4238 << "***\n"; 4239#endif 4240 ++NumArrayLenItCounts; 4241 return getConstant(ItCst); // Found terminating iteration! 4242 } 4243 } 4244 return getCouldNotCompute(); 4245} 4246 4247 4248/// CanConstantFold - Return true if we can constant fold an instruction of the 4249/// specified type, assuming that all operands were constants. 4250static bool CanConstantFold(const Instruction *I) { 4251 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4252 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4253 return true; 4254 4255 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4256 if (const Function *F = CI->getCalledFunction()) 4257 return canConstantFoldCallTo(F); 4258 return false; 4259} 4260 4261/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4262/// in the loop that V is derived from. We allow arbitrary operations along the 4263/// way, but the operands of an operation must either be constants or a value 4264/// derived from a constant PHI. If this expression does not fit with these 4265/// constraints, return null. 4266static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4267 // If this is not an instruction, or if this is an instruction outside of the 4268 // loop, it can't be derived from a loop PHI. 4269 Instruction *I = dyn_cast<Instruction>(V); 4270 if (I == 0 || !L->contains(I)) return 0; 4271 4272 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4273 if (L->getHeader() == I->getParent()) 4274 return PN; 4275 else 4276 // We don't currently keep track of the control flow needed to evaluate 4277 // PHIs, so we cannot handle PHIs inside of loops. 4278 return 0; 4279 } 4280 4281 // If we won't be able to constant fold this expression even if the operands 4282 // are constants, return early. 4283 if (!CanConstantFold(I)) return 0; 4284 4285 // Otherwise, we can evaluate this instruction if all of its operands are 4286 // constant or derived from a PHI node themselves. 4287 PHINode *PHI = 0; 4288 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4289 if (!isa<Constant>(I->getOperand(Op))) { 4290 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4291 if (P == 0) return 0; // Not evolving from PHI 4292 if (PHI == 0) 4293 PHI = P; 4294 else if (PHI != P) 4295 return 0; // Evolving from multiple different PHIs. 4296 } 4297 4298 // This is a expression evolving from a constant PHI! 4299 return PHI; 4300} 4301 4302/// EvaluateExpression - Given an expression that passes the 4303/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4304/// in the loop has the value PHIVal. If we can't fold this expression for some 4305/// reason, return null. 4306static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4307 const TargetData *TD) { 4308 if (isa<PHINode>(V)) return PHIVal; 4309 if (Constant *C = dyn_cast<Constant>(V)) return C; 4310 Instruction *I = cast<Instruction>(V); 4311 4312 std::vector<Constant*> Operands(I->getNumOperands()); 4313 4314 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4315 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4316 if (Operands[i] == 0) return 0; 4317 } 4318 4319 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4320 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4321 Operands[1], TD); 4322 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4323 &Operands[0], Operands.size(), TD); 4324} 4325 4326/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4327/// in the header of its containing loop, we know the loop executes a 4328/// constant number of times, and the PHI node is just a recurrence 4329/// involving constants, fold it. 4330Constant * 4331ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4332 const APInt &BEs, 4333 const Loop *L) { 4334 std::map<PHINode*, Constant*>::const_iterator I = 4335 ConstantEvolutionLoopExitValue.find(PN); 4336 if (I != ConstantEvolutionLoopExitValue.end()) 4337 return I->second; 4338 4339 if (BEs.ugt(MaxBruteForceIterations)) 4340 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4341 4342 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4343 4344 // Since the loop is canonicalized, the PHI node must have two entries. One 4345 // entry must be a constant (coming in from outside of the loop), and the 4346 // second must be derived from the same PHI. 4347 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4348 Constant *StartCST = 4349 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4350 if (StartCST == 0) 4351 return RetVal = 0; // Must be a constant. 4352 4353 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4354 if (getConstantEvolvingPHI(BEValue, L) != PN && 4355 !isa<Constant>(BEValue)) 4356 return RetVal = 0; // Not derived from same PHI. 4357 4358 // Execute the loop symbolically to determine the exit value. 4359 if (BEs.getActiveBits() >= 32) 4360 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4361 4362 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4363 unsigned IterationNum = 0; 4364 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4365 if (IterationNum == NumIterations) 4366 return RetVal = PHIVal; // Got exit value! 4367 4368 // Compute the value of the PHI node for the next iteration. 4369 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4370 if (NextPHI == PHIVal) 4371 return RetVal = NextPHI; // Stopped evolving! 4372 if (NextPHI == 0) 4373 return 0; // Couldn't evaluate! 4374 PHIVal = NextPHI; 4375 } 4376} 4377 4378/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4379/// constant number of times (the condition evolves only from constants), 4380/// try to evaluate a few iterations of the loop until we get the exit 4381/// condition gets a value of ExitWhen (true or false). If we cannot 4382/// evaluate the trip count of the loop, return getCouldNotCompute(). 4383const SCEV * 4384ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4385 Value *Cond, 4386 bool ExitWhen) { 4387 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4388 if (PN == 0) return getCouldNotCompute(); 4389 4390 // If the loop is canonicalized, the PHI will have exactly two entries. 4391 // That's the only form we support here. 4392 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4393 4394 // One entry must be a constant (coming in from outside of the loop), and the 4395 // second must be derived from the same PHI. 4396 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4397 Constant *StartCST = 4398 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4399 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4400 4401 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4402 if (getConstantEvolvingPHI(BEValue, L) != PN && 4403 !isa<Constant>(BEValue)) 4404 return getCouldNotCompute(); // Not derived from same PHI. 4405 4406 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4407 // the loop symbolically to determine when the condition gets a value of 4408 // "ExitWhen". 4409 unsigned IterationNum = 0; 4410 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4411 for (Constant *PHIVal = StartCST; 4412 IterationNum != MaxIterations; ++IterationNum) { 4413 ConstantInt *CondVal = 4414 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4415 4416 // Couldn't symbolically evaluate. 4417 if (!CondVal) return getCouldNotCompute(); 4418 4419 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4420 ++NumBruteForceTripCountsComputed; 4421 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4422 } 4423 4424 // Compute the value of the PHI node for the next iteration. 4425 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4426 if (NextPHI == 0 || NextPHI == PHIVal) 4427 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4428 PHIVal = NextPHI; 4429 } 4430 4431 // Too many iterations were needed to evaluate. 4432 return getCouldNotCompute(); 4433} 4434 4435/// getSCEVAtScope - Return a SCEV expression for the specified value 4436/// at the specified scope in the program. The L value specifies a loop 4437/// nest to evaluate the expression at, where null is the top-level or a 4438/// specified loop is immediately inside of the loop. 4439/// 4440/// This method can be used to compute the exit value for a variable defined 4441/// in a loop by querying what the value will hold in the parent loop. 4442/// 4443/// In the case that a relevant loop exit value cannot be computed, the 4444/// original value V is returned. 4445const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4446 // Check to see if we've folded this expression at this loop before. 4447 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4448 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4449 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4450 if (!Pair.second) 4451 return Pair.first->second ? Pair.first->second : V; 4452 4453 // Otherwise compute it. 4454 const SCEV *C = computeSCEVAtScope(V, L); 4455 ValuesAtScopes[V][L] = C; 4456 return C; 4457} 4458 4459const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4460 if (isa<SCEVConstant>(V)) return V; 4461 4462 // If this instruction is evolved from a constant-evolving PHI, compute the 4463 // exit value from the loop without using SCEVs. 4464 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4465 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4466 const Loop *LI = (*this->LI)[I->getParent()]; 4467 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4468 if (PHINode *PN = dyn_cast<PHINode>(I)) 4469 if (PN->getParent() == LI->getHeader()) { 4470 // Okay, there is no closed form solution for the PHI node. Check 4471 // to see if the loop that contains it has a known backedge-taken 4472 // count. If so, we may be able to force computation of the exit 4473 // value. 4474 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4475 if (const SCEVConstant *BTCC = 4476 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4477 // Okay, we know how many times the containing loop executes. If 4478 // this is a constant evolving PHI node, get the final value at 4479 // the specified iteration number. 4480 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4481 BTCC->getValue()->getValue(), 4482 LI); 4483 if (RV) return getSCEV(RV); 4484 } 4485 } 4486 4487 // Okay, this is an expression that we cannot symbolically evaluate 4488 // into a SCEV. Check to see if it's possible to symbolically evaluate 4489 // the arguments into constants, and if so, try to constant propagate the 4490 // result. This is particularly useful for computing loop exit values. 4491 if (CanConstantFold(I)) { 4492 SmallVector<Constant *, 4> Operands; 4493 bool MadeImprovement = false; 4494 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4495 Value *Op = I->getOperand(i); 4496 if (Constant *C = dyn_cast<Constant>(Op)) { 4497 Operands.push_back(C); 4498 continue; 4499 } 4500 4501 // If any of the operands is non-constant and if they are 4502 // non-integer and non-pointer, don't even try to analyze them 4503 // with scev techniques. 4504 if (!isSCEVable(Op->getType())) 4505 return V; 4506 4507 const SCEV *OrigV = getSCEV(Op); 4508 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4509 MadeImprovement |= OrigV != OpV; 4510 4511 Constant *C = 0; 4512 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4513 C = SC->getValue(); 4514 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4515 C = dyn_cast<Constant>(SU->getValue()); 4516 if (!C) return V; 4517 if (C->getType() != Op->getType()) 4518 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4519 Op->getType(), 4520 false), 4521 C, Op->getType()); 4522 Operands.push_back(C); 4523 } 4524 4525 // Check to see if getSCEVAtScope actually made an improvement. 4526 if (MadeImprovement) { 4527 Constant *C = 0; 4528 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4529 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4530 Operands[0], Operands[1], TD); 4531 else 4532 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4533 &Operands[0], Operands.size(), TD); 4534 if (!C) return V; 4535 return getSCEV(C); 4536 } 4537 } 4538 } 4539 4540 // This is some other type of SCEVUnknown, just return it. 4541 return V; 4542 } 4543 4544 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4545 // Avoid performing the look-up in the common case where the specified 4546 // expression has no loop-variant portions. 4547 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4548 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4549 if (OpAtScope != Comm->getOperand(i)) { 4550 // Okay, at least one of these operands is loop variant but might be 4551 // foldable. Build a new instance of the folded commutative expression. 4552 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4553 Comm->op_begin()+i); 4554 NewOps.push_back(OpAtScope); 4555 4556 for (++i; i != e; ++i) { 4557 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4558 NewOps.push_back(OpAtScope); 4559 } 4560 if (isa<SCEVAddExpr>(Comm)) 4561 return getAddExpr(NewOps); 4562 if (isa<SCEVMulExpr>(Comm)) 4563 return getMulExpr(NewOps); 4564 if (isa<SCEVSMaxExpr>(Comm)) 4565 return getSMaxExpr(NewOps); 4566 if (isa<SCEVUMaxExpr>(Comm)) 4567 return getUMaxExpr(NewOps); 4568 llvm_unreachable("Unknown commutative SCEV type!"); 4569 } 4570 } 4571 // If we got here, all operands are loop invariant. 4572 return Comm; 4573 } 4574 4575 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4576 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4577 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4578 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4579 return Div; // must be loop invariant 4580 return getUDivExpr(LHS, RHS); 4581 } 4582 4583 // If this is a loop recurrence for a loop that does not contain L, then we 4584 // are dealing with the final value computed by the loop. 4585 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4586 // First, attempt to evaluate each operand. 4587 // Avoid performing the look-up in the common case where the specified 4588 // expression has no loop-variant portions. 4589 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4590 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4591 if (OpAtScope == AddRec->getOperand(i)) 4592 continue; 4593 4594 // Okay, at least one of these operands is loop variant but might be 4595 // foldable. Build a new instance of the folded commutative expression. 4596 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4597 AddRec->op_begin()+i); 4598 NewOps.push_back(OpAtScope); 4599 for (++i; i != e; ++i) 4600 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4601 4602 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4603 break; 4604 } 4605 4606 // If the scope is outside the addrec's loop, evaluate it by using the 4607 // loop exit value of the addrec. 4608 if (!AddRec->getLoop()->contains(L)) { 4609 // To evaluate this recurrence, we need to know how many times the AddRec 4610 // loop iterates. Compute this now. 4611 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4612 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4613 4614 // Then, evaluate the AddRec. 4615 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4616 } 4617 4618 return AddRec; 4619 } 4620 4621 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4622 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4623 if (Op == Cast->getOperand()) 4624 return Cast; // must be loop invariant 4625 return getZeroExtendExpr(Op, Cast->getType()); 4626 } 4627 4628 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4629 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4630 if (Op == Cast->getOperand()) 4631 return Cast; // must be loop invariant 4632 return getSignExtendExpr(Op, Cast->getType()); 4633 } 4634 4635 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4636 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4637 if (Op == Cast->getOperand()) 4638 return Cast; // must be loop invariant 4639 return getTruncateExpr(Op, Cast->getType()); 4640 } 4641 4642 llvm_unreachable("Unknown SCEV type!"); 4643 return 0; 4644} 4645 4646/// getSCEVAtScope - This is a convenience function which does 4647/// getSCEVAtScope(getSCEV(V), L). 4648const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4649 return getSCEVAtScope(getSCEV(V), L); 4650} 4651 4652/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4653/// following equation: 4654/// 4655/// A * X = B (mod N) 4656/// 4657/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4658/// A and B isn't important. 4659/// 4660/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4661static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4662 ScalarEvolution &SE) { 4663 uint32_t BW = A.getBitWidth(); 4664 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4665 assert(A != 0 && "A must be non-zero."); 4666 4667 // 1. D = gcd(A, N) 4668 // 4669 // The gcd of A and N may have only one prime factor: 2. The number of 4670 // trailing zeros in A is its multiplicity 4671 uint32_t Mult2 = A.countTrailingZeros(); 4672 // D = 2^Mult2 4673 4674 // 2. Check if B is divisible by D. 4675 // 4676 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4677 // is not less than multiplicity of this prime factor for D. 4678 if (B.countTrailingZeros() < Mult2) 4679 return SE.getCouldNotCompute(); 4680 4681 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4682 // modulo (N / D). 4683 // 4684 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4685 // bit width during computations. 4686 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4687 APInt Mod(BW + 1, 0); 4688 Mod.set(BW - Mult2); // Mod = N / D 4689 APInt I = AD.multiplicativeInverse(Mod); 4690 4691 // 4. Compute the minimum unsigned root of the equation: 4692 // I * (B / D) mod (N / D) 4693 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4694 4695 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4696 // bits. 4697 return SE.getConstant(Result.trunc(BW)); 4698} 4699 4700/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4701/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4702/// might be the same) or two SCEVCouldNotCompute objects. 4703/// 4704static std::pair<const SCEV *,const SCEV *> 4705SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4706 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4707 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4708 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4709 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4710 4711 // We currently can only solve this if the coefficients are constants. 4712 if (!LC || !MC || !NC) { 4713 const SCEV *CNC = SE.getCouldNotCompute(); 4714 return std::make_pair(CNC, CNC); 4715 } 4716 4717 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4718 const APInt &L = LC->getValue()->getValue(); 4719 const APInt &M = MC->getValue()->getValue(); 4720 const APInt &N = NC->getValue()->getValue(); 4721 APInt Two(BitWidth, 2); 4722 APInt Four(BitWidth, 4); 4723 4724 { 4725 using namespace APIntOps; 4726 const APInt& C = L; 4727 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4728 // The B coefficient is M-N/2 4729 APInt B(M); 4730 B -= sdiv(N,Two); 4731 4732 // The A coefficient is N/2 4733 APInt A(N.sdiv(Two)); 4734 4735 // Compute the B^2-4ac term. 4736 APInt SqrtTerm(B); 4737 SqrtTerm *= B; 4738 SqrtTerm -= Four * (A * C); 4739 4740 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4741 // integer value or else APInt::sqrt() will assert. 4742 APInt SqrtVal(SqrtTerm.sqrt()); 4743 4744 // Compute the two solutions for the quadratic formula. 4745 // The divisions must be performed as signed divisions. 4746 APInt NegB(-B); 4747 APInt TwoA( A << 1 ); 4748 if (TwoA.isMinValue()) { 4749 const SCEV *CNC = SE.getCouldNotCompute(); 4750 return std::make_pair(CNC, CNC); 4751 } 4752 4753 LLVMContext &Context = SE.getContext(); 4754 4755 ConstantInt *Solution1 = 4756 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4757 ConstantInt *Solution2 = 4758 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4759 4760 return std::make_pair(SE.getConstant(Solution1), 4761 SE.getConstant(Solution2)); 4762 } // end APIntOps namespace 4763} 4764 4765/// HowFarToZero - Return the number of times a backedge comparing the specified 4766/// value to zero will execute. If not computable, return CouldNotCompute. 4767ScalarEvolution::BackedgeTakenInfo 4768ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4769 // If the value is a constant 4770 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4771 // If the value is already zero, the branch will execute zero times. 4772 if (C->getValue()->isZero()) return C; 4773 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4774 } 4775 4776 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4777 if (!AddRec || AddRec->getLoop() != L) 4778 return getCouldNotCompute(); 4779 4780 if (AddRec->isAffine()) { 4781 // If this is an affine expression, the execution count of this branch is 4782 // the minimum unsigned root of the following equation: 4783 // 4784 // Start + Step*N = 0 (mod 2^BW) 4785 // 4786 // equivalent to: 4787 // 4788 // Step*N = -Start (mod 2^BW) 4789 // 4790 // where BW is the common bit width of Start and Step. 4791 4792 // Get the initial value for the loop. 4793 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), 4794 L->getParentLoop()); 4795 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), 4796 L->getParentLoop()); 4797 4798 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { 4799 // For now we handle only constant steps. 4800 4801 // First, handle unitary steps. 4802 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4803 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4804 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4805 return Start; // N = Start (as unsigned) 4806 4807 // Then, try to solve the above equation provided that Start is constant. 4808 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4809 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4810 -StartC->getValue()->getValue(), 4811 *this); 4812 } 4813 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4814 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4815 // the quadratic equation to solve it. 4816 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, 4817 *this); 4818 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4819 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4820 if (R1) { 4821#if 0 4822 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4823 << " sol#2: " << *R2 << "\n"; 4824#endif 4825 // Pick the smallest positive root value. 4826 if (ConstantInt *CB = 4827 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 4828 R1->getValue(), R2->getValue()))) { 4829 if (CB->getZExtValue() == false) 4830 std::swap(R1, R2); // R1 is the minimum root now. 4831 4832 // We can only use this value if the chrec ends up with an exact zero 4833 // value at this index. When solving for "X*X != 5", for example, we 4834 // should not accept a root of 2. 4835 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4836 if (Val->isZero()) 4837 return R1; // We found a quadratic root! 4838 } 4839 } 4840 } 4841 4842 return getCouldNotCompute(); 4843} 4844 4845/// HowFarToNonZero - Return the number of times a backedge checking the 4846/// specified value for nonzero will execute. If not computable, return 4847/// CouldNotCompute 4848ScalarEvolution::BackedgeTakenInfo 4849ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4850 // Loops that look like: while (X == 0) are very strange indeed. We don't 4851 // handle them yet except for the trivial case. This could be expanded in the 4852 // future as needed. 4853 4854 // If the value is a constant, check to see if it is known to be non-zero 4855 // already. If so, the backedge will execute zero times. 4856 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4857 if (!C->getValue()->isNullValue()) 4858 return getConstant(C->getType(), 0); 4859 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4860 } 4861 4862 // We could implement others, but I really doubt anyone writes loops like 4863 // this, and if they did, they would already be constant folded. 4864 return getCouldNotCompute(); 4865} 4866 4867/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4868/// (which may not be an immediate predecessor) which has exactly one 4869/// successor from which BB is reachable, or null if no such block is 4870/// found. 4871/// 4872std::pair<BasicBlock *, BasicBlock *> 4873ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4874 // If the block has a unique predecessor, then there is no path from the 4875 // predecessor to the block that does not go through the direct edge 4876 // from the predecessor to the block. 4877 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4878 return std::make_pair(Pred, BB); 4879 4880 // A loop's header is defined to be a block that dominates the loop. 4881 // If the header has a unique predecessor outside the loop, it must be 4882 // a block that has exactly one successor that can reach the loop. 4883 if (Loop *L = LI->getLoopFor(BB)) 4884 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4885 4886 return std::pair<BasicBlock *, BasicBlock *>(); 4887} 4888 4889/// HasSameValue - SCEV structural equivalence is usually sufficient for 4890/// testing whether two expressions are equal, however for the purposes of 4891/// looking for a condition guarding a loop, it can be useful to be a little 4892/// more general, since a front-end may have replicated the controlling 4893/// expression. 4894/// 4895static bool HasSameValue(const SCEV *A, const SCEV *B) { 4896 // Quick check to see if they are the same SCEV. 4897 if (A == B) return true; 4898 4899 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4900 // two different instructions with the same value. Check for this case. 4901 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4902 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4903 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4904 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4905 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4906 return true; 4907 4908 // Otherwise assume they may have a different value. 4909 return false; 4910} 4911 4912/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4913/// predicate Pred. Return true iff any changes were made. 4914/// 4915bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4916 const SCEV *&LHS, const SCEV *&RHS) { 4917 bool Changed = false; 4918 4919 // Canonicalize a constant to the right side. 4920 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4921 // Check for both operands constant. 4922 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4923 if (ConstantExpr::getICmp(Pred, 4924 LHSC->getValue(), 4925 RHSC->getValue())->isNullValue()) 4926 goto trivially_false; 4927 else 4928 goto trivially_true; 4929 } 4930 // Otherwise swap the operands to put the constant on the right. 4931 std::swap(LHS, RHS); 4932 Pred = ICmpInst::getSwappedPredicate(Pred); 4933 Changed = true; 4934 } 4935 4936 // If we're comparing an addrec with a value which is loop-invariant in the 4937 // addrec's loop, put the addrec on the left. Also make a dominance check, 4938 // as both operands could be addrecs loop-invariant in each other's loop. 4939 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 4940 const Loop *L = AR->getLoop(); 4941 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { 4942 std::swap(LHS, RHS); 4943 Pred = ICmpInst::getSwappedPredicate(Pred); 4944 Changed = true; 4945 } 4946 } 4947 4948 // If there's a constant operand, canonicalize comparisons with boundary 4949 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 4950 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 4951 const APInt &RA = RC->getValue()->getValue(); 4952 switch (Pred) { 4953 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 4954 case ICmpInst::ICMP_EQ: 4955 case ICmpInst::ICMP_NE: 4956 break; 4957 case ICmpInst::ICMP_UGE: 4958 if ((RA - 1).isMinValue()) { 4959 Pred = ICmpInst::ICMP_NE; 4960 RHS = getConstant(RA - 1); 4961 Changed = true; 4962 break; 4963 } 4964 if (RA.isMaxValue()) { 4965 Pred = ICmpInst::ICMP_EQ; 4966 Changed = true; 4967 break; 4968 } 4969 if (RA.isMinValue()) goto trivially_true; 4970 4971 Pred = ICmpInst::ICMP_UGT; 4972 RHS = getConstant(RA - 1); 4973 Changed = true; 4974 break; 4975 case ICmpInst::ICMP_ULE: 4976 if ((RA + 1).isMaxValue()) { 4977 Pred = ICmpInst::ICMP_NE; 4978 RHS = getConstant(RA + 1); 4979 Changed = true; 4980 break; 4981 } 4982 if (RA.isMinValue()) { 4983 Pred = ICmpInst::ICMP_EQ; 4984 Changed = true; 4985 break; 4986 } 4987 if (RA.isMaxValue()) goto trivially_true; 4988 4989 Pred = ICmpInst::ICMP_ULT; 4990 RHS = getConstant(RA + 1); 4991 Changed = true; 4992 break; 4993 case ICmpInst::ICMP_SGE: 4994 if ((RA - 1).isMinSignedValue()) { 4995 Pred = ICmpInst::ICMP_NE; 4996 RHS = getConstant(RA - 1); 4997 Changed = true; 4998 break; 4999 } 5000 if (RA.isMaxSignedValue()) { 5001 Pred = ICmpInst::ICMP_EQ; 5002 Changed = true; 5003 break; 5004 } 5005 if (RA.isMinSignedValue()) goto trivially_true; 5006 5007 Pred = ICmpInst::ICMP_SGT; 5008 RHS = getConstant(RA - 1); 5009 Changed = true; 5010 break; 5011 case ICmpInst::ICMP_SLE: 5012 if ((RA + 1).isMaxSignedValue()) { 5013 Pred = ICmpInst::ICMP_NE; 5014 RHS = getConstant(RA + 1); 5015 Changed = true; 5016 break; 5017 } 5018 if (RA.isMinSignedValue()) { 5019 Pred = ICmpInst::ICMP_EQ; 5020 Changed = true; 5021 break; 5022 } 5023 if (RA.isMaxSignedValue()) goto trivially_true; 5024 5025 Pred = ICmpInst::ICMP_SLT; 5026 RHS = getConstant(RA + 1); 5027 Changed = true; 5028 break; 5029 case ICmpInst::ICMP_UGT: 5030 if (RA.isMinValue()) { 5031 Pred = ICmpInst::ICMP_NE; 5032 Changed = true; 5033 break; 5034 } 5035 if ((RA + 1).isMaxValue()) { 5036 Pred = ICmpInst::ICMP_EQ; 5037 RHS = getConstant(RA + 1); 5038 Changed = true; 5039 break; 5040 } 5041 if (RA.isMaxValue()) goto trivially_false; 5042 break; 5043 case ICmpInst::ICMP_ULT: 5044 if (RA.isMaxValue()) { 5045 Pred = ICmpInst::ICMP_NE; 5046 Changed = true; 5047 break; 5048 } 5049 if ((RA - 1).isMinValue()) { 5050 Pred = ICmpInst::ICMP_EQ; 5051 RHS = getConstant(RA - 1); 5052 Changed = true; 5053 break; 5054 } 5055 if (RA.isMinValue()) goto trivially_false; 5056 break; 5057 case ICmpInst::ICMP_SGT: 5058 if (RA.isMinSignedValue()) { 5059 Pred = ICmpInst::ICMP_NE; 5060 Changed = true; 5061 break; 5062 } 5063 if ((RA + 1).isMaxSignedValue()) { 5064 Pred = ICmpInst::ICMP_EQ; 5065 RHS = getConstant(RA + 1); 5066 Changed = true; 5067 break; 5068 } 5069 if (RA.isMaxSignedValue()) goto trivially_false; 5070 break; 5071 case ICmpInst::ICMP_SLT: 5072 if (RA.isMaxSignedValue()) { 5073 Pred = ICmpInst::ICMP_NE; 5074 Changed = true; 5075 break; 5076 } 5077 if ((RA - 1).isMinSignedValue()) { 5078 Pred = ICmpInst::ICMP_EQ; 5079 RHS = getConstant(RA - 1); 5080 Changed = true; 5081 break; 5082 } 5083 if (RA.isMinSignedValue()) goto trivially_false; 5084 break; 5085 } 5086 } 5087 5088 // Check for obvious equality. 5089 if (HasSameValue(LHS, RHS)) { 5090 if (ICmpInst::isTrueWhenEqual(Pred)) 5091 goto trivially_true; 5092 if (ICmpInst::isFalseWhenEqual(Pred)) 5093 goto trivially_false; 5094 } 5095 5096 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5097 // adding or subtracting 1 from one of the operands. 5098 switch (Pred) { 5099 case ICmpInst::ICMP_SLE: 5100 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5101 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5102 /*HasNUW=*/false, /*HasNSW=*/true); 5103 Pred = ICmpInst::ICMP_SLT; 5104 Changed = true; 5105 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5106 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5107 /*HasNUW=*/false, /*HasNSW=*/true); 5108 Pred = ICmpInst::ICMP_SLT; 5109 Changed = true; 5110 } 5111 break; 5112 case ICmpInst::ICMP_SGE: 5113 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5114 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5115 /*HasNUW=*/false, /*HasNSW=*/true); 5116 Pred = ICmpInst::ICMP_SGT; 5117 Changed = true; 5118 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5119 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5120 /*HasNUW=*/false, /*HasNSW=*/true); 5121 Pred = ICmpInst::ICMP_SGT; 5122 Changed = true; 5123 } 5124 break; 5125 case ICmpInst::ICMP_ULE: 5126 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5127 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5128 /*HasNUW=*/true, /*HasNSW=*/false); 5129 Pred = ICmpInst::ICMP_ULT; 5130 Changed = true; 5131 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5132 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5133 /*HasNUW=*/true, /*HasNSW=*/false); 5134 Pred = ICmpInst::ICMP_ULT; 5135 Changed = true; 5136 } 5137 break; 5138 case ICmpInst::ICMP_UGE: 5139 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5140 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5141 /*HasNUW=*/true, /*HasNSW=*/false); 5142 Pred = ICmpInst::ICMP_UGT; 5143 Changed = true; 5144 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5145 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5146 /*HasNUW=*/true, /*HasNSW=*/false); 5147 Pred = ICmpInst::ICMP_UGT; 5148 Changed = true; 5149 } 5150 break; 5151 default: 5152 break; 5153 } 5154 5155 // TODO: More simplifications are possible here. 5156 5157 return Changed; 5158 5159trivially_true: 5160 // Return 0 == 0. 5161 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5162 Pred = ICmpInst::ICMP_EQ; 5163 return true; 5164 5165trivially_false: 5166 // Return 0 != 0. 5167 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); 5168 Pred = ICmpInst::ICMP_NE; 5169 return true; 5170} 5171 5172bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5173 return getSignedRange(S).getSignedMax().isNegative(); 5174} 5175 5176bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5177 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5178} 5179 5180bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5181 return !getSignedRange(S).getSignedMin().isNegative(); 5182} 5183 5184bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5185 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5186} 5187 5188bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5189 return isKnownNegative(S) || isKnownPositive(S); 5190} 5191 5192bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5193 const SCEV *LHS, const SCEV *RHS) { 5194 // Canonicalize the inputs first. 5195 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5196 5197 // If LHS or RHS is an addrec, check to see if the condition is true in 5198 // every iteration of the loop. 5199 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5200 if (isLoopEntryGuardedByCond( 5201 AR->getLoop(), Pred, AR->getStart(), RHS) && 5202 isLoopBackedgeGuardedByCond( 5203 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5204 return true; 5205 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5206 if (isLoopEntryGuardedByCond( 5207 AR->getLoop(), Pred, LHS, AR->getStart()) && 5208 isLoopBackedgeGuardedByCond( 5209 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5210 return true; 5211 5212 // Otherwise see what can be done with known constant ranges. 5213 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5214} 5215 5216bool 5217ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5218 const SCEV *LHS, const SCEV *RHS) { 5219 if (HasSameValue(LHS, RHS)) 5220 return ICmpInst::isTrueWhenEqual(Pred); 5221 5222 // This code is split out from isKnownPredicate because it is called from 5223 // within isLoopEntryGuardedByCond. 5224 switch (Pred) { 5225 default: 5226 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5227 break; 5228 case ICmpInst::ICMP_SGT: 5229 Pred = ICmpInst::ICMP_SLT; 5230 std::swap(LHS, RHS); 5231 case ICmpInst::ICMP_SLT: { 5232 ConstantRange LHSRange = getSignedRange(LHS); 5233 ConstantRange RHSRange = getSignedRange(RHS); 5234 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5235 return true; 5236 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5237 return false; 5238 break; 5239 } 5240 case ICmpInst::ICMP_SGE: 5241 Pred = ICmpInst::ICMP_SLE; 5242 std::swap(LHS, RHS); 5243 case ICmpInst::ICMP_SLE: { 5244 ConstantRange LHSRange = getSignedRange(LHS); 5245 ConstantRange RHSRange = getSignedRange(RHS); 5246 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5247 return true; 5248 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5249 return false; 5250 break; 5251 } 5252 case ICmpInst::ICMP_UGT: 5253 Pred = ICmpInst::ICMP_ULT; 5254 std::swap(LHS, RHS); 5255 case ICmpInst::ICMP_ULT: { 5256 ConstantRange LHSRange = getUnsignedRange(LHS); 5257 ConstantRange RHSRange = getUnsignedRange(RHS); 5258 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5259 return true; 5260 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5261 return false; 5262 break; 5263 } 5264 case ICmpInst::ICMP_UGE: 5265 Pred = ICmpInst::ICMP_ULE; 5266 std::swap(LHS, RHS); 5267 case ICmpInst::ICMP_ULE: { 5268 ConstantRange LHSRange = getUnsignedRange(LHS); 5269 ConstantRange RHSRange = getUnsignedRange(RHS); 5270 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5271 return true; 5272 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5273 return false; 5274 break; 5275 } 5276 case ICmpInst::ICMP_NE: { 5277 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5278 return true; 5279 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5280 return true; 5281 5282 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5283 if (isKnownNonZero(Diff)) 5284 return true; 5285 break; 5286 } 5287 case ICmpInst::ICMP_EQ: 5288 // The check at the top of the function catches the case where 5289 // the values are known to be equal. 5290 break; 5291 } 5292 return false; 5293} 5294 5295/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5296/// protected by a conditional between LHS and RHS. This is used to 5297/// to eliminate casts. 5298bool 5299ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5300 ICmpInst::Predicate Pred, 5301 const SCEV *LHS, const SCEV *RHS) { 5302 // Interpret a null as meaning no loop, where there is obviously no guard 5303 // (interprocedural conditions notwithstanding). 5304 if (!L) return true; 5305 5306 BasicBlock *Latch = L->getLoopLatch(); 5307 if (!Latch) 5308 return false; 5309 5310 BranchInst *LoopContinuePredicate = 5311 dyn_cast<BranchInst>(Latch->getTerminator()); 5312 if (!LoopContinuePredicate || 5313 LoopContinuePredicate->isUnconditional()) 5314 return false; 5315 5316 return isImpliedCond(Pred, LHS, RHS, 5317 LoopContinuePredicate->getCondition(), 5318 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5319} 5320 5321/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5322/// by a conditional between LHS and RHS. This is used to help avoid max 5323/// expressions in loop trip counts, and to eliminate casts. 5324bool 5325ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5326 ICmpInst::Predicate Pred, 5327 const SCEV *LHS, const SCEV *RHS) { 5328 // Interpret a null as meaning no loop, where there is obviously no guard 5329 // (interprocedural conditions notwithstanding). 5330 if (!L) return false; 5331 5332 // Starting at the loop predecessor, climb up the predecessor chain, as long 5333 // as there are predecessors that can be found that have unique successors 5334 // leading to the original header. 5335 for (std::pair<BasicBlock *, BasicBlock *> 5336 Pair(L->getLoopPredecessor(), L->getHeader()); 5337 Pair.first; 5338 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5339 5340 BranchInst *LoopEntryPredicate = 5341 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5342 if (!LoopEntryPredicate || 5343 LoopEntryPredicate->isUnconditional()) 5344 continue; 5345 5346 if (isImpliedCond(Pred, LHS, RHS, 5347 LoopEntryPredicate->getCondition(), 5348 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5349 return true; 5350 } 5351 5352 return false; 5353} 5354 5355/// isImpliedCond - Test whether the condition described by Pred, LHS, 5356/// and RHS is true whenever the given Cond value evaluates to true. 5357bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5358 const SCEV *LHS, const SCEV *RHS, 5359 Value *FoundCondValue, 5360 bool Inverse) { 5361 // Recursively handle And and Or conditions. 5362 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5363 if (BO->getOpcode() == Instruction::And) { 5364 if (!Inverse) 5365 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5366 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5367 } else if (BO->getOpcode() == Instruction::Or) { 5368 if (Inverse) 5369 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5370 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5371 } 5372 } 5373 5374 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5375 if (!ICI) return false; 5376 5377 // Bail if the ICmp's operands' types are wider than the needed type 5378 // before attempting to call getSCEV on them. This avoids infinite 5379 // recursion, since the analysis of widening casts can require loop 5380 // exit condition information for overflow checking, which would 5381 // lead back here. 5382 if (getTypeSizeInBits(LHS->getType()) < 5383 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5384 return false; 5385 5386 // Now that we found a conditional branch that dominates the loop, check to 5387 // see if it is the comparison we are looking for. 5388 ICmpInst::Predicate FoundPred; 5389 if (Inverse) 5390 FoundPred = ICI->getInversePredicate(); 5391 else 5392 FoundPred = ICI->getPredicate(); 5393 5394 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5395 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5396 5397 // Balance the types. The case where FoundLHS' type is wider than 5398 // LHS' type is checked for above. 5399 if (getTypeSizeInBits(LHS->getType()) > 5400 getTypeSizeInBits(FoundLHS->getType())) { 5401 if (CmpInst::isSigned(Pred)) { 5402 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5403 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5404 } else { 5405 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5406 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5407 } 5408 } 5409 5410 // Canonicalize the query to match the way instcombine will have 5411 // canonicalized the comparison. 5412 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5413 if (LHS == RHS) 5414 return CmpInst::isTrueWhenEqual(Pred); 5415 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5416 if (FoundLHS == FoundRHS) 5417 return CmpInst::isFalseWhenEqual(Pred); 5418 5419 // Check to see if we can make the LHS or RHS match. 5420 if (LHS == FoundRHS || RHS == FoundLHS) { 5421 if (isa<SCEVConstant>(RHS)) { 5422 std::swap(FoundLHS, FoundRHS); 5423 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5424 } else { 5425 std::swap(LHS, RHS); 5426 Pred = ICmpInst::getSwappedPredicate(Pred); 5427 } 5428 } 5429 5430 // Check whether the found predicate is the same as the desired predicate. 5431 if (FoundPred == Pred) 5432 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5433 5434 // Check whether swapping the found predicate makes it the same as the 5435 // desired predicate. 5436 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5437 if (isa<SCEVConstant>(RHS)) 5438 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5439 else 5440 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5441 RHS, LHS, FoundLHS, FoundRHS); 5442 } 5443 5444 // Check whether the actual condition is beyond sufficient. 5445 if (FoundPred == ICmpInst::ICMP_EQ) 5446 if (ICmpInst::isTrueWhenEqual(Pred)) 5447 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5448 return true; 5449 if (Pred == ICmpInst::ICMP_NE) 5450 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5451 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5452 return true; 5453 5454 // Otherwise assume the worst. 5455 return false; 5456} 5457 5458/// isImpliedCondOperands - Test whether the condition described by Pred, 5459/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5460/// and FoundRHS is true. 5461bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5462 const SCEV *LHS, const SCEV *RHS, 5463 const SCEV *FoundLHS, 5464 const SCEV *FoundRHS) { 5465 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5466 FoundLHS, FoundRHS) || 5467 // ~x < ~y --> x > y 5468 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5469 getNotSCEV(FoundRHS), 5470 getNotSCEV(FoundLHS)); 5471} 5472 5473/// isImpliedCondOperandsHelper - Test whether the condition described by 5474/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5475/// FoundLHS, and FoundRHS is true. 5476bool 5477ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5478 const SCEV *LHS, const SCEV *RHS, 5479 const SCEV *FoundLHS, 5480 const SCEV *FoundRHS) { 5481 switch (Pred) { 5482 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5483 case ICmpInst::ICMP_EQ: 5484 case ICmpInst::ICMP_NE: 5485 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5486 return true; 5487 break; 5488 case ICmpInst::ICMP_SLT: 5489 case ICmpInst::ICMP_SLE: 5490 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5491 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5492 return true; 5493 break; 5494 case ICmpInst::ICMP_SGT: 5495 case ICmpInst::ICMP_SGE: 5496 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5497 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5498 return true; 5499 break; 5500 case ICmpInst::ICMP_ULT: 5501 case ICmpInst::ICMP_ULE: 5502 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5503 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5504 return true; 5505 break; 5506 case ICmpInst::ICMP_UGT: 5507 case ICmpInst::ICMP_UGE: 5508 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5509 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5510 return true; 5511 break; 5512 } 5513 5514 return false; 5515} 5516 5517/// getBECount - Subtract the end and start values and divide by the step, 5518/// rounding up, to get the number of times the backedge is executed. Return 5519/// CouldNotCompute if an intermediate computation overflows. 5520const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5521 const SCEV *End, 5522 const SCEV *Step, 5523 bool NoWrap) { 5524 assert(!isKnownNegative(Step) && 5525 "This code doesn't handle negative strides yet!"); 5526 5527 const Type *Ty = Start->getType(); 5528 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5529 const SCEV *Diff = getMinusSCEV(End, Start); 5530 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5531 5532 // Add an adjustment to the difference between End and Start so that 5533 // the division will effectively round up. 5534 const SCEV *Add = getAddExpr(Diff, RoundUp); 5535 5536 if (!NoWrap) { 5537 // Check Add for unsigned overflow. 5538 // TODO: More sophisticated things could be done here. 5539 const Type *WideTy = IntegerType::get(getContext(), 5540 getTypeSizeInBits(Ty) + 1); 5541 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5542 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5543 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5544 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5545 return getCouldNotCompute(); 5546 } 5547 5548 return getUDivExpr(Add, Step); 5549} 5550 5551/// HowManyLessThans - Return the number of times a backedge containing the 5552/// specified less-than comparison will execute. If not computable, return 5553/// CouldNotCompute. 5554ScalarEvolution::BackedgeTakenInfo 5555ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5556 const Loop *L, bool isSigned) { 5557 // Only handle: "ADDREC < LoopInvariant". 5558 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); 5559 5560 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5561 if (!AddRec || AddRec->getLoop() != L) 5562 return getCouldNotCompute(); 5563 5564 // Check to see if we have a flag which makes analysis easy. 5565 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5566 AddRec->hasNoUnsignedWrap(); 5567 5568 if (AddRec->isAffine()) { 5569 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5570 const SCEV *Step = AddRec->getStepRecurrence(*this); 5571 5572 if (Step->isZero()) 5573 return getCouldNotCompute(); 5574 if (Step->isOne()) { 5575 // With unit stride, the iteration never steps past the limit value. 5576 } else if (isKnownPositive(Step)) { 5577 // Test whether a positive iteration can step past the limit 5578 // value and past the maximum value for its type in a single step. 5579 // Note that it's not sufficient to check NoWrap here, because even 5580 // though the value after a wrap is undefined, it's not undefined 5581 // behavior, so if wrap does occur, the loop could either terminate or 5582 // loop infinitely, but in either case, the loop is guaranteed to 5583 // iterate at least until the iteration where the wrapping occurs. 5584 const SCEV *One = getConstant(Step->getType(), 1); 5585 if (isSigned) { 5586 APInt Max = APInt::getSignedMaxValue(BitWidth); 5587 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5588 .slt(getSignedRange(RHS).getSignedMax())) 5589 return getCouldNotCompute(); 5590 } else { 5591 APInt Max = APInt::getMaxValue(BitWidth); 5592 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5593 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5594 return getCouldNotCompute(); 5595 } 5596 } else 5597 // TODO: Handle negative strides here and below. 5598 return getCouldNotCompute(); 5599 5600 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5601 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5602 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5603 // treat m-n as signed nor unsigned due to overflow possibility. 5604 5605 // First, we get the value of the LHS in the first iteration: n 5606 const SCEV *Start = AddRec->getOperand(0); 5607 5608 // Determine the minimum constant start value. 5609 const SCEV *MinStart = getConstant(isSigned ? 5610 getSignedRange(Start).getSignedMin() : 5611 getUnsignedRange(Start).getUnsignedMin()); 5612 5613 // If we know that the condition is true in order to enter the loop, 5614 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5615 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5616 // the division must round up. 5617 const SCEV *End = RHS; 5618 if (!isLoopEntryGuardedByCond(L, 5619 isSigned ? ICmpInst::ICMP_SLT : 5620 ICmpInst::ICMP_ULT, 5621 getMinusSCEV(Start, Step), RHS)) 5622 End = isSigned ? getSMaxExpr(RHS, Start) 5623 : getUMaxExpr(RHS, Start); 5624 5625 // Determine the maximum constant end value. 5626 const SCEV *MaxEnd = getConstant(isSigned ? 5627 getSignedRange(End).getSignedMax() : 5628 getUnsignedRange(End).getUnsignedMax()); 5629 5630 // If MaxEnd is within a step of the maximum integer value in its type, 5631 // adjust it down to the minimum value which would produce the same effect. 5632 // This allows the subsequent ceiling division of (N+(step-1))/step to 5633 // compute the correct value. 5634 const SCEV *StepMinusOne = getMinusSCEV(Step, 5635 getConstant(Step->getType(), 1)); 5636 MaxEnd = isSigned ? 5637 getSMinExpr(MaxEnd, 5638 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5639 StepMinusOne)) : 5640 getUMinExpr(MaxEnd, 5641 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5642 StepMinusOne)); 5643 5644 // Finally, we subtract these two values and divide, rounding up, to get 5645 // the number of times the backedge is executed. 5646 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5647 5648 // The maximum backedge count is similar, except using the minimum start 5649 // value and the maximum end value. 5650 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5651 5652 return BackedgeTakenInfo(BECount, MaxBECount); 5653 } 5654 5655 return getCouldNotCompute(); 5656} 5657 5658/// getNumIterationsInRange - Return the number of iterations of this loop that 5659/// produce values in the specified constant range. Another way of looking at 5660/// this is that it returns the first iteration number where the value is not in 5661/// the condition, thus computing the exit count. If the iteration count can't 5662/// be computed, an instance of SCEVCouldNotCompute is returned. 5663const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5664 ScalarEvolution &SE) const { 5665 if (Range.isFullSet()) // Infinite loop. 5666 return SE.getCouldNotCompute(); 5667 5668 // If the start is a non-zero constant, shift the range to simplify things. 5669 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5670 if (!SC->getValue()->isZero()) { 5671 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5672 Operands[0] = SE.getConstant(SC->getType(), 0); 5673 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5674 if (const SCEVAddRecExpr *ShiftedAddRec = 5675 dyn_cast<SCEVAddRecExpr>(Shifted)) 5676 return ShiftedAddRec->getNumIterationsInRange( 5677 Range.subtract(SC->getValue()->getValue()), SE); 5678 // This is strange and shouldn't happen. 5679 return SE.getCouldNotCompute(); 5680 } 5681 5682 // The only time we can solve this is when we have all constant indices. 5683 // Otherwise, we cannot determine the overflow conditions. 5684 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5685 if (!isa<SCEVConstant>(getOperand(i))) 5686 return SE.getCouldNotCompute(); 5687 5688 5689 // Okay at this point we know that all elements of the chrec are constants and 5690 // that the start element is zero. 5691 5692 // First check to see if the range contains zero. If not, the first 5693 // iteration exits. 5694 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5695 if (!Range.contains(APInt(BitWidth, 0))) 5696 return SE.getConstant(getType(), 0); 5697 5698 if (isAffine()) { 5699 // If this is an affine expression then we have this situation: 5700 // Solve {0,+,A} in Range === Ax in Range 5701 5702 // We know that zero is in the range. If A is positive then we know that 5703 // the upper value of the range must be the first possible exit value. 5704 // If A is negative then the lower of the range is the last possible loop 5705 // value. Also note that we already checked for a full range. 5706 APInt One(BitWidth,1); 5707 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5708 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5709 5710 // The exit value should be (End+A)/A. 5711 APInt ExitVal = (End + A).udiv(A); 5712 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5713 5714 // Evaluate at the exit value. If we really did fall out of the valid 5715 // range, then we computed our trip count, otherwise wrap around or other 5716 // things must have happened. 5717 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5718 if (Range.contains(Val->getValue())) 5719 return SE.getCouldNotCompute(); // Something strange happened 5720 5721 // Ensure that the previous value is in the range. This is a sanity check. 5722 assert(Range.contains( 5723 EvaluateConstantChrecAtConstant(this, 5724 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5725 "Linear scev computation is off in a bad way!"); 5726 return SE.getConstant(ExitValue); 5727 } else if (isQuadratic()) { 5728 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5729 // quadratic equation to solve it. To do this, we must frame our problem in 5730 // terms of figuring out when zero is crossed, instead of when 5731 // Range.getUpper() is crossed. 5732 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5733 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5734 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5735 5736 // Next, solve the constructed addrec 5737 std::pair<const SCEV *,const SCEV *> Roots = 5738 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5739 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5740 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5741 if (R1) { 5742 // Pick the smallest positive root value. 5743 if (ConstantInt *CB = 5744 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5745 R1->getValue(), R2->getValue()))) { 5746 if (CB->getZExtValue() == false) 5747 std::swap(R1, R2); // R1 is the minimum root now. 5748 5749 // Make sure the root is not off by one. The returned iteration should 5750 // not be in the range, but the previous one should be. When solving 5751 // for "X*X < 5", for example, we should not return a root of 2. 5752 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5753 R1->getValue(), 5754 SE); 5755 if (Range.contains(R1Val->getValue())) { 5756 // The next iteration must be out of the range... 5757 ConstantInt *NextVal = 5758 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5759 5760 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5761 if (!Range.contains(R1Val->getValue())) 5762 return SE.getConstant(NextVal); 5763 return SE.getCouldNotCompute(); // Something strange happened 5764 } 5765 5766 // If R1 was not in the range, then it is a good return value. Make 5767 // sure that R1-1 WAS in the range though, just in case. 5768 ConstantInt *NextVal = 5769 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5770 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5771 if (Range.contains(R1Val->getValue())) 5772 return R1; 5773 return SE.getCouldNotCompute(); // Something strange happened 5774 } 5775 } 5776 } 5777 5778 return SE.getCouldNotCompute(); 5779} 5780 5781 5782 5783//===----------------------------------------------------------------------===// 5784// SCEVCallbackVH Class Implementation 5785//===----------------------------------------------------------------------===// 5786 5787void ScalarEvolution::SCEVCallbackVH::deleted() { 5788 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5789 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5790 SE->ConstantEvolutionLoopExitValue.erase(PN); 5791 SE->ValueExprMap.erase(getValPtr()); 5792 // this now dangles! 5793} 5794 5795void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5796 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5797 5798 // Forget all the expressions associated with users of the old value, 5799 // so that future queries will recompute the expressions using the new 5800 // value. 5801 Value *Old = getValPtr(); 5802 SmallVector<User *, 16> Worklist; 5803 SmallPtrSet<User *, 8> Visited; 5804 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5805 UI != UE; ++UI) 5806 Worklist.push_back(*UI); 5807 while (!Worklist.empty()) { 5808 User *U = Worklist.pop_back_val(); 5809 // Deleting the Old value will cause this to dangle. Postpone 5810 // that until everything else is done. 5811 if (U == Old) 5812 continue; 5813 if (!Visited.insert(U)) 5814 continue; 5815 if (PHINode *PN = dyn_cast<PHINode>(U)) 5816 SE->ConstantEvolutionLoopExitValue.erase(PN); 5817 SE->ValueExprMap.erase(U); 5818 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5819 UI != UE; ++UI) 5820 Worklist.push_back(*UI); 5821 } 5822 // Delete the Old value. 5823 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5824 SE->ConstantEvolutionLoopExitValue.erase(PN); 5825 SE->ValueExprMap.erase(Old); 5826 // this now dangles! 5827} 5828 5829ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5830 : CallbackVH(V), SE(se) {} 5831 5832//===----------------------------------------------------------------------===// 5833// ScalarEvolution Class Implementation 5834//===----------------------------------------------------------------------===// 5835 5836ScalarEvolution::ScalarEvolution() 5837 : FunctionPass(ID), FirstUnknown(0) { 5838 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 5839} 5840 5841bool ScalarEvolution::runOnFunction(Function &F) { 5842 this->F = &F; 5843 LI = &getAnalysis<LoopInfo>(); 5844 TD = getAnalysisIfAvailable<TargetData>(); 5845 DT = &getAnalysis<DominatorTree>(); 5846 return false; 5847} 5848 5849void ScalarEvolution::releaseMemory() { 5850 // Iterate through all the SCEVUnknown instances and call their 5851 // destructors, so that they release their references to their values. 5852 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5853 U->~SCEVUnknown(); 5854 FirstUnknown = 0; 5855 5856 ValueExprMap.clear(); 5857 BackedgeTakenCounts.clear(); 5858 ConstantEvolutionLoopExitValue.clear(); 5859 ValuesAtScopes.clear(); 5860 UniqueSCEVs.clear(); 5861 SCEVAllocator.Reset(); 5862} 5863 5864void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5865 AU.setPreservesAll(); 5866 AU.addRequiredTransitive<LoopInfo>(); 5867 AU.addRequiredTransitive<DominatorTree>(); 5868} 5869 5870bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5871 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5872} 5873 5874static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5875 const Loop *L) { 5876 // Print all inner loops first 5877 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5878 PrintLoopInfo(OS, SE, *I); 5879 5880 OS << "Loop "; 5881 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5882 OS << ": "; 5883 5884 SmallVector<BasicBlock *, 8> ExitBlocks; 5885 L->getExitBlocks(ExitBlocks); 5886 if (ExitBlocks.size() != 1) 5887 OS << "<multiple exits> "; 5888 5889 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5890 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5891 } else { 5892 OS << "Unpredictable backedge-taken count. "; 5893 } 5894 5895 OS << "\n" 5896 "Loop "; 5897 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5898 OS << ": "; 5899 5900 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5901 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5902 } else { 5903 OS << "Unpredictable max backedge-taken count. "; 5904 } 5905 5906 OS << "\n"; 5907} 5908 5909void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5910 // ScalarEvolution's implementation of the print method is to print 5911 // out SCEV values of all instructions that are interesting. Doing 5912 // this potentially causes it to create new SCEV objects though, 5913 // which technically conflicts with the const qualifier. This isn't 5914 // observable from outside the class though, so casting away the 5915 // const isn't dangerous. 5916 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5917 5918 OS << "Classifying expressions for: "; 5919 WriteAsOperand(OS, F, /*PrintType=*/false); 5920 OS << "\n"; 5921 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 5922 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 5923 OS << *I << '\n'; 5924 OS << " --> "; 5925 const SCEV *SV = SE.getSCEV(&*I); 5926 SV->print(OS); 5927 5928 const Loop *L = LI->getLoopFor((*I).getParent()); 5929 5930 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 5931 if (AtUse != SV) { 5932 OS << " --> "; 5933 AtUse->print(OS); 5934 } 5935 5936 if (L) { 5937 OS << "\t\t" "Exits: "; 5938 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 5939 if (!ExitValue->isLoopInvariant(L)) { 5940 OS << "<<Unknown>>"; 5941 } else { 5942 OS << *ExitValue; 5943 } 5944 } 5945 5946 OS << "\n"; 5947 } 5948 5949 OS << "Determining loop execution counts for: "; 5950 WriteAsOperand(OS, F, /*PrintType=*/false); 5951 OS << "\n"; 5952 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 5953 PrintLoopInfo(OS, &SE, *I); 5954} 5955 5956