ScalarEvolution.cpp revision 5c6fc1cab774244fba2746b84f2b86d71b897733
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/InstructionSimplify.h" 73#include "llvm/Analysis/LoopInfo.h" 74#include "llvm/Analysis/ValueTracking.h" 75#include "llvm/Assembly/Writer.h" 76#include "llvm/Target/TargetData.h" 77#include "llvm/Support/CommandLine.h" 78#include "llvm/Support/ConstantRange.h" 79#include "llvm/Support/Debug.h" 80#include "llvm/Support/ErrorHandling.h" 81#include "llvm/Support/GetElementPtrTypeIterator.h" 82#include "llvm/Support/InstIterator.h" 83#include "llvm/Support/MathExtras.h" 84#include "llvm/Support/raw_ostream.h" 85#include "llvm/ADT/Statistic.h" 86#include "llvm/ADT/STLExtras.h" 87#include "llvm/ADT/SmallPtrSet.h" 88#include <algorithm> 89using namespace llvm; 90 91STATISTIC(NumArrayLenItCounts, 92 "Number of trip counts computed with array length"); 93STATISTIC(NumTripCountsComputed, 94 "Number of loops with predictable loop counts"); 95STATISTIC(NumTripCountsNotComputed, 96 "Number of loops without predictable loop counts"); 97STATISTIC(NumBruteForceTripCountsComputed, 98 "Number of loops with trip counts computed by force"); 99 100static cl::opt<unsigned> 101MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, 102 cl::desc("Maximum number of iterations SCEV will " 103 "symbolically execute a constant " 104 "derived loop"), 105 cl::init(100)); 106 107INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", 108 "Scalar Evolution Analysis", false, true) 109INITIALIZE_PASS_DEPENDENCY(LoopInfo) 110INITIALIZE_PASS_DEPENDENCY(DominatorTree) 111INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", 112 "Scalar Evolution Analysis", false, true) 113char ScalarEvolution::ID = 0; 114 115//===----------------------------------------------------------------------===// 116// SCEV class definitions 117//===----------------------------------------------------------------------===// 118 119//===----------------------------------------------------------------------===// 120// Implementation of the SCEV class. 121// 122 123void SCEV::dump() const { 124 print(dbgs()); 125 dbgs() << '\n'; 126} 127 128void SCEV::print(raw_ostream &OS) const { 129 switch (getSCEVType()) { 130 case scConstant: 131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false); 132 return; 133 case scTruncate: { 134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); 135 const SCEV *Op = Trunc->getOperand(); 136 OS << "(trunc " << *Op->getType() << " " << *Op << " to " 137 << *Trunc->getType() << ")"; 138 return; 139 } 140 case scZeroExtend: { 141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); 142 const SCEV *Op = ZExt->getOperand(); 143 OS << "(zext " << *Op->getType() << " " << *Op << " to " 144 << *ZExt->getType() << ")"; 145 return; 146 } 147 case scSignExtend: { 148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); 149 const SCEV *Op = SExt->getOperand(); 150 OS << "(sext " << *Op->getType() << " " << *Op << " to " 151 << *SExt->getType() << ")"; 152 return; 153 } 154 case scAddRecExpr: { 155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this); 156 OS << "{" << *AR->getOperand(0); 157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) 158 OS << ",+," << *AR->getOperand(i); 159 OS << "}<"; 160 if (AR->hasNoUnsignedWrap()) 161 OS << "nuw><"; 162 if (AR->hasNoSignedWrap()) 163 OS << "nsw><"; 164 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 165 OS << ">"; 166 return; 167 } 168 case scAddExpr: 169 case scMulExpr: 170 case scUMaxExpr: 171 case scSMaxExpr: { 172 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 173 const char *OpStr = 0; 174 switch (NAry->getSCEVType()) { 175 case scAddExpr: OpStr = " + "; break; 176 case scMulExpr: OpStr = " * "; break; 177 case scUMaxExpr: OpStr = " umax "; break; 178 case scSMaxExpr: OpStr = " smax "; break; 179 } 180 OS << "("; 181 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 182 I != E; ++I) { 183 OS << **I; 184 if (llvm::next(I) != E) 185 OS << OpStr; 186 } 187 OS << ")"; 188 return; 189 } 190 case scUDivExpr: { 191 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 192 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 193 return; 194 } 195 case scUnknown: { 196 const SCEVUnknown *U = cast<SCEVUnknown>(this); 197 const Type *AllocTy; 198 if (U->isSizeOf(AllocTy)) { 199 OS << "sizeof(" << *AllocTy << ")"; 200 return; 201 } 202 if (U->isAlignOf(AllocTy)) { 203 OS << "alignof(" << *AllocTy << ")"; 204 return; 205 } 206 207 const Type *CTy; 208 Constant *FieldNo; 209 if (U->isOffsetOf(CTy, FieldNo)) { 210 OS << "offsetof(" << *CTy << ", "; 211 WriteAsOperand(OS, FieldNo, false); 212 OS << ")"; 213 return; 214 } 215 216 // Otherwise just print it normally. 217 WriteAsOperand(OS, U->getValue(), false); 218 return; 219 } 220 case scCouldNotCompute: 221 OS << "***COULDNOTCOMPUTE***"; 222 return; 223 default: break; 224 } 225 llvm_unreachable("Unknown SCEV kind!"); 226} 227 228const Type *SCEV::getType() const { 229 switch (getSCEVType()) { 230 case scConstant: 231 return cast<SCEVConstant>(this)->getType(); 232 case scTruncate: 233 case scZeroExtend: 234 case scSignExtend: 235 return cast<SCEVCastExpr>(this)->getType(); 236 case scAddRecExpr: 237 case scMulExpr: 238 case scUMaxExpr: 239 case scSMaxExpr: 240 return cast<SCEVNAryExpr>(this)->getType(); 241 case scAddExpr: 242 return cast<SCEVAddExpr>(this)->getType(); 243 case scUDivExpr: 244 return cast<SCEVUDivExpr>(this)->getType(); 245 case scUnknown: 246 return cast<SCEVUnknown>(this)->getType(); 247 case scCouldNotCompute: 248 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 249 return 0; 250 default: break; 251 } 252 llvm_unreachable("Unknown SCEV kind!"); 253 return 0; 254} 255 256bool SCEV::isZero() const { 257 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 258 return SC->getValue()->isZero(); 259 return false; 260} 261 262bool SCEV::isOne() const { 263 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 264 return SC->getValue()->isOne(); 265 return false; 266} 267 268bool SCEV::isAllOnesValue() const { 269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 270 return SC->getValue()->isAllOnesValue(); 271 return false; 272} 273 274SCEVCouldNotCompute::SCEVCouldNotCompute() : 275 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 276 277bool SCEVCouldNotCompute::classof(const SCEV *S) { 278 return S->getSCEVType() == scCouldNotCompute; 279} 280 281const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 282 FoldingSetNodeID ID; 283 ID.AddInteger(scConstant); 284 ID.AddPointer(V); 285 void *IP = 0; 286 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 287 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 288 UniqueSCEVs.InsertNode(S, IP); 289 return S; 290} 291 292const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 293 return getConstant(ConstantInt::get(getContext(), Val)); 294} 295 296const SCEV * 297ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { 298 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 299 return getConstant(ConstantInt::get(ITy, V, isSigned)); 300} 301 302SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 303 unsigned SCEVTy, const SCEV *op, const Type *ty) 304 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 305 306SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 307 const SCEV *op, const Type *ty) 308 : SCEVCastExpr(ID, scTruncate, op, ty) { 309 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 310 (Ty->isIntegerTy() || Ty->isPointerTy()) && 311 "Cannot truncate non-integer value!"); 312} 313 314SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 315 const SCEV *op, const Type *ty) 316 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 317 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 318 (Ty->isIntegerTy() || Ty->isPointerTy()) && 319 "Cannot zero extend non-integer value!"); 320} 321 322SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 323 const SCEV *op, const Type *ty) 324 : SCEVCastExpr(ID, scSignExtend, op, ty) { 325 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 326 (Ty->isIntegerTy() || Ty->isPointerTy()) && 327 "Cannot sign extend non-integer value!"); 328} 329 330void SCEVUnknown::deleted() { 331 // Clear this SCEVUnknown from various maps. 332 SE->forgetMemoizedResults(this); 333 334 // Remove this SCEVUnknown from the uniquing map. 335 SE->UniqueSCEVs.RemoveNode(this); 336 337 // Release the value. 338 setValPtr(0); 339} 340 341void SCEVUnknown::allUsesReplacedWith(Value *New) { 342 // Clear this SCEVUnknown from various maps. 343 SE->forgetMemoizedResults(this); 344 345 // Remove this SCEVUnknown from the uniquing map. 346 SE->UniqueSCEVs.RemoveNode(this); 347 348 // Update this SCEVUnknown to point to the new value. This is needed 349 // because there may still be outstanding SCEVs which still point to 350 // this SCEVUnknown. 351 setValPtr(New); 352} 353 354bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { 355 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 356 if (VCE->getOpcode() == Instruction::PtrToInt) 357 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 358 if (CE->getOpcode() == Instruction::GetElementPtr && 359 CE->getOperand(0)->isNullValue() && 360 CE->getNumOperands() == 2) 361 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 362 if (CI->isOne()) { 363 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 364 ->getElementType(); 365 return true; 366 } 367 368 return false; 369} 370 371bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { 372 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 373 if (VCE->getOpcode() == Instruction::PtrToInt) 374 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 375 if (CE->getOpcode() == Instruction::GetElementPtr && 376 CE->getOperand(0)->isNullValue()) { 377 const Type *Ty = 378 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 379 if (const StructType *STy = dyn_cast<StructType>(Ty)) 380 if (!STy->isPacked() && 381 CE->getNumOperands() == 3 && 382 CE->getOperand(1)->isNullValue()) { 383 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 384 if (CI->isOne() && 385 STy->getNumElements() == 2 && 386 STy->getElementType(0)->isIntegerTy(1)) { 387 AllocTy = STy->getElementType(1); 388 return true; 389 } 390 } 391 } 392 393 return false; 394} 395 396bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { 397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 398 if (VCE->getOpcode() == Instruction::PtrToInt) 399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 400 if (CE->getOpcode() == Instruction::GetElementPtr && 401 CE->getNumOperands() == 3 && 402 CE->getOperand(0)->isNullValue() && 403 CE->getOperand(1)->isNullValue()) { 404 const Type *Ty = 405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 406 // Ignore vector types here so that ScalarEvolutionExpander doesn't 407 // emit getelementptrs that index into vectors. 408 if (Ty->isStructTy() || Ty->isArrayTy()) { 409 CTy = Ty; 410 FieldNo = CE->getOperand(2); 411 return true; 412 } 413 } 414 415 return false; 416} 417 418//===----------------------------------------------------------------------===// 419// SCEV Utilities 420//===----------------------------------------------------------------------===// 421 422namespace { 423 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 424 /// than the complexity of the RHS. This comparator is used to canonicalize 425 /// expressions. 426 class SCEVComplexityCompare { 427 const LoopInfo *const LI; 428 public: 429 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 430 431 // Return true or false if LHS is less than, or at least RHS, respectively. 432 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 433 return compare(LHS, RHS) < 0; 434 } 435 436 // Return negative, zero, or positive, if LHS is less than, equal to, or 437 // greater than RHS, respectively. A three-way result allows recursive 438 // comparisons to be more efficient. 439 int compare(const SCEV *LHS, const SCEV *RHS) const { 440 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 441 if (LHS == RHS) 442 return 0; 443 444 // Primarily, sort the SCEVs by their getSCEVType(). 445 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 446 if (LType != RType) 447 return (int)LType - (int)RType; 448 449 // Aside from the getSCEVType() ordering, the particular ordering 450 // isn't very important except that it's beneficial to be consistent, 451 // so that (a + b) and (b + a) don't end up as different expressions. 452 switch (LType) { 453 case scUnknown: { 454 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 455 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 456 457 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 458 // not as complete as it could be. 459 const Value *LV = LU->getValue(), *RV = RU->getValue(); 460 461 // Order pointer values after integer values. This helps SCEVExpander 462 // form GEPs. 463 bool LIsPointer = LV->getType()->isPointerTy(), 464 RIsPointer = RV->getType()->isPointerTy(); 465 if (LIsPointer != RIsPointer) 466 return (int)LIsPointer - (int)RIsPointer; 467 468 // Compare getValueID values. 469 unsigned LID = LV->getValueID(), 470 RID = RV->getValueID(); 471 if (LID != RID) 472 return (int)LID - (int)RID; 473 474 // Sort arguments by their position. 475 if (const Argument *LA = dyn_cast<Argument>(LV)) { 476 const Argument *RA = cast<Argument>(RV); 477 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 478 return (int)LArgNo - (int)RArgNo; 479 } 480 481 // For instructions, compare their loop depth, and their operand 482 // count. This is pretty loose. 483 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 484 const Instruction *RInst = cast<Instruction>(RV); 485 486 // Compare loop depths. 487 const BasicBlock *LParent = LInst->getParent(), 488 *RParent = RInst->getParent(); 489 if (LParent != RParent) { 490 unsigned LDepth = LI->getLoopDepth(LParent), 491 RDepth = LI->getLoopDepth(RParent); 492 if (LDepth != RDepth) 493 return (int)LDepth - (int)RDepth; 494 } 495 496 // Compare the number of operands. 497 unsigned LNumOps = LInst->getNumOperands(), 498 RNumOps = RInst->getNumOperands(); 499 return (int)LNumOps - (int)RNumOps; 500 } 501 502 return 0; 503 } 504 505 case scConstant: { 506 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 507 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 508 509 // Compare constant values. 510 const APInt &LA = LC->getValue()->getValue(); 511 const APInt &RA = RC->getValue()->getValue(); 512 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 513 if (LBitWidth != RBitWidth) 514 return (int)LBitWidth - (int)RBitWidth; 515 return LA.ult(RA) ? -1 : 1; 516 } 517 518 case scAddRecExpr: { 519 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 520 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 521 522 // Compare addrec loop depths. 523 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 524 if (LLoop != RLoop) { 525 unsigned LDepth = LLoop->getLoopDepth(), 526 RDepth = RLoop->getLoopDepth(); 527 if (LDepth != RDepth) 528 return (int)LDepth - (int)RDepth; 529 } 530 531 // Addrec complexity grows with operand count. 532 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 533 if (LNumOps != RNumOps) 534 return (int)LNumOps - (int)RNumOps; 535 536 // Lexicographically compare. 537 for (unsigned i = 0; i != LNumOps; ++i) { 538 long X = compare(LA->getOperand(i), RA->getOperand(i)); 539 if (X != 0) 540 return X; 541 } 542 543 return 0; 544 } 545 546 case scAddExpr: 547 case scMulExpr: 548 case scSMaxExpr: 549 case scUMaxExpr: { 550 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 551 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 552 553 // Lexicographically compare n-ary expressions. 554 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 555 for (unsigned i = 0; i != LNumOps; ++i) { 556 if (i >= RNumOps) 557 return 1; 558 long X = compare(LC->getOperand(i), RC->getOperand(i)); 559 if (X != 0) 560 return X; 561 } 562 return (int)LNumOps - (int)RNumOps; 563 } 564 565 case scUDivExpr: { 566 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 567 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 568 569 // Lexicographically compare udiv expressions. 570 long X = compare(LC->getLHS(), RC->getLHS()); 571 if (X != 0) 572 return X; 573 return compare(LC->getRHS(), RC->getRHS()); 574 } 575 576 case scTruncate: 577 case scZeroExtend: 578 case scSignExtend: { 579 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 580 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 581 582 // Compare cast expressions by operand. 583 return compare(LC->getOperand(), RC->getOperand()); 584 } 585 586 default: 587 break; 588 } 589 590 llvm_unreachable("Unknown SCEV kind!"); 591 return 0; 592 } 593 }; 594} 595 596/// GroupByComplexity - Given a list of SCEV objects, order them by their 597/// complexity, and group objects of the same complexity together by value. 598/// When this routine is finished, we know that any duplicates in the vector are 599/// consecutive and that complexity is monotonically increasing. 600/// 601/// Note that we go take special precautions to ensure that we get deterministic 602/// results from this routine. In other words, we don't want the results of 603/// this to depend on where the addresses of various SCEV objects happened to 604/// land in memory. 605/// 606static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 607 LoopInfo *LI) { 608 if (Ops.size() < 2) return; // Noop 609 if (Ops.size() == 2) { 610 // This is the common case, which also happens to be trivially simple. 611 // Special case it. 612 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 613 if (SCEVComplexityCompare(LI)(RHS, LHS)) 614 std::swap(LHS, RHS); 615 return; 616 } 617 618 // Do the rough sort by complexity. 619 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 620 621 // Now that we are sorted by complexity, group elements of the same 622 // complexity. Note that this is, at worst, N^2, but the vector is likely to 623 // be extremely short in practice. Note that we take this approach because we 624 // do not want to depend on the addresses of the objects we are grouping. 625 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 626 const SCEV *S = Ops[i]; 627 unsigned Complexity = S->getSCEVType(); 628 629 // If there are any objects of the same complexity and same value as this 630 // one, group them. 631 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 632 if (Ops[j] == S) { // Found a duplicate. 633 // Move it to immediately after i'th element. 634 std::swap(Ops[i+1], Ops[j]); 635 ++i; // no need to rescan it. 636 if (i == e-2) return; // Done! 637 } 638 } 639 } 640} 641 642 643 644//===----------------------------------------------------------------------===// 645// Simple SCEV method implementations 646//===----------------------------------------------------------------------===// 647 648/// BinomialCoefficient - Compute BC(It, K). The result has width W. 649/// Assume, K > 0. 650static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 651 ScalarEvolution &SE, 652 const Type* ResultTy) { 653 // Handle the simplest case efficiently. 654 if (K == 1) 655 return SE.getTruncateOrZeroExtend(It, ResultTy); 656 657 // We are using the following formula for BC(It, K): 658 // 659 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 660 // 661 // Suppose, W is the bitwidth of the return value. We must be prepared for 662 // overflow. Hence, we must assure that the result of our computation is 663 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 664 // safe in modular arithmetic. 665 // 666 // However, this code doesn't use exactly that formula; the formula it uses 667 // is something like the following, where T is the number of factors of 2 in 668 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 669 // exponentiation: 670 // 671 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 672 // 673 // This formula is trivially equivalent to the previous formula. However, 674 // this formula can be implemented much more efficiently. The trick is that 675 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 676 // arithmetic. To do exact division in modular arithmetic, all we have 677 // to do is multiply by the inverse. Therefore, this step can be done at 678 // width W. 679 // 680 // The next issue is how to safely do the division by 2^T. The way this 681 // is done is by doing the multiplication step at a width of at least W + T 682 // bits. This way, the bottom W+T bits of the product are accurate. Then, 683 // when we perform the division by 2^T (which is equivalent to a right shift 684 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 685 // truncated out after the division by 2^T. 686 // 687 // In comparison to just directly using the first formula, this technique 688 // is much more efficient; using the first formula requires W * K bits, 689 // but this formula less than W + K bits. Also, the first formula requires 690 // a division step, whereas this formula only requires multiplies and shifts. 691 // 692 // It doesn't matter whether the subtraction step is done in the calculation 693 // width or the input iteration count's width; if the subtraction overflows, 694 // the result must be zero anyway. We prefer here to do it in the width of 695 // the induction variable because it helps a lot for certain cases; CodeGen 696 // isn't smart enough to ignore the overflow, which leads to much less 697 // efficient code if the width of the subtraction is wider than the native 698 // register width. 699 // 700 // (It's possible to not widen at all by pulling out factors of 2 before 701 // the multiplication; for example, K=2 can be calculated as 702 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 703 // extra arithmetic, so it's not an obvious win, and it gets 704 // much more complicated for K > 3.) 705 706 // Protection from insane SCEVs; this bound is conservative, 707 // but it probably doesn't matter. 708 if (K > 1000) 709 return SE.getCouldNotCompute(); 710 711 unsigned W = SE.getTypeSizeInBits(ResultTy); 712 713 // Calculate K! / 2^T and T; we divide out the factors of two before 714 // multiplying for calculating K! / 2^T to avoid overflow. 715 // Other overflow doesn't matter because we only care about the bottom 716 // W bits of the result. 717 APInt OddFactorial(W, 1); 718 unsigned T = 1; 719 for (unsigned i = 3; i <= K; ++i) { 720 APInt Mult(W, i); 721 unsigned TwoFactors = Mult.countTrailingZeros(); 722 T += TwoFactors; 723 Mult = Mult.lshr(TwoFactors); 724 OddFactorial *= Mult; 725 } 726 727 // We need at least W + T bits for the multiplication step 728 unsigned CalculationBits = W + T; 729 730 // Calculate 2^T, at width T+W. 731 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 732 733 // Calculate the multiplicative inverse of K! / 2^T; 734 // this multiplication factor will perform the exact division by 735 // K! / 2^T. 736 APInt Mod = APInt::getSignedMinValue(W+1); 737 APInt MultiplyFactor = OddFactorial.zext(W+1); 738 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 739 MultiplyFactor = MultiplyFactor.trunc(W); 740 741 // Calculate the product, at width T+W 742 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 743 CalculationBits); 744 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 745 for (unsigned i = 1; i != K; ++i) { 746 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 747 Dividend = SE.getMulExpr(Dividend, 748 SE.getTruncateOrZeroExtend(S, CalculationTy)); 749 } 750 751 // Divide by 2^T 752 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 753 754 // Truncate the result, and divide by K! / 2^T. 755 756 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 757 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 758} 759 760/// evaluateAtIteration - Return the value of this chain of recurrences at 761/// the specified iteration number. We can evaluate this recurrence by 762/// multiplying each element in the chain by the binomial coefficient 763/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 764/// 765/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 766/// 767/// where BC(It, k) stands for binomial coefficient. 768/// 769const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 770 ScalarEvolution &SE) const { 771 const SCEV *Result = getStart(); 772 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 773 // The computation is correct in the face of overflow provided that the 774 // multiplication is performed _after_ the evaluation of the binomial 775 // coefficient. 776 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 777 if (isa<SCEVCouldNotCompute>(Coeff)) 778 return Coeff; 779 780 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 781 } 782 return Result; 783} 784 785//===----------------------------------------------------------------------===// 786// SCEV Expression folder implementations 787//===----------------------------------------------------------------------===// 788 789const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 790 const Type *Ty) { 791 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 792 "This is not a truncating conversion!"); 793 assert(isSCEVable(Ty) && 794 "This is not a conversion to a SCEVable type!"); 795 Ty = getEffectiveSCEVType(Ty); 796 797 FoldingSetNodeID ID; 798 ID.AddInteger(scTruncate); 799 ID.AddPointer(Op); 800 ID.AddPointer(Ty); 801 void *IP = 0; 802 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 803 804 // Fold if the operand is constant. 805 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 806 return getConstant( 807 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 808 getEffectiveSCEVType(Ty)))); 809 810 // trunc(trunc(x)) --> trunc(x) 811 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 812 return getTruncateExpr(ST->getOperand(), Ty); 813 814 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 815 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 816 return getTruncateOrSignExtend(SS->getOperand(), Ty); 817 818 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 819 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 820 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 821 822 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 823 // eliminate all the truncates. 824 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 825 SmallVector<const SCEV *, 4> Operands; 826 bool hasTrunc = false; 827 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 828 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 829 hasTrunc = isa<SCEVTruncateExpr>(S); 830 Operands.push_back(S); 831 } 832 if (!hasTrunc) 833 return getAddExpr(Operands, false, false); 834 } 835 836 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 837 // eliminate all the truncates. 838 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 839 SmallVector<const SCEV *, 4> Operands; 840 bool hasTrunc = false; 841 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 842 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 843 hasTrunc = isa<SCEVTruncateExpr>(S); 844 Operands.push_back(S); 845 } 846 if (!hasTrunc) 847 return getMulExpr(Operands, false, false); 848 } 849 850 // If the input value is a chrec scev, truncate the chrec's operands. 851 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 852 SmallVector<const SCEV *, 4> Operands; 853 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 854 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 855 return getAddRecExpr(Operands, AddRec->getLoop()); 856 } 857 858 // As a special case, fold trunc(undef) to undef. We don't want to 859 // know too much about SCEVUnknowns, but this special case is handy 860 // and harmless. 861 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 862 if (isa<UndefValue>(U->getValue())) 863 return getSCEV(UndefValue::get(Ty)); 864 865 // The cast wasn't folded; create an explicit cast node. We can reuse 866 // the existing insert position since if we get here, we won't have 867 // made any changes which would invalidate it. 868 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 869 Op, Ty); 870 UniqueSCEVs.InsertNode(S, IP); 871 return S; 872} 873 874const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 875 const Type *Ty) { 876 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 877 "This is not an extending conversion!"); 878 assert(isSCEVable(Ty) && 879 "This is not a conversion to a SCEVable type!"); 880 Ty = getEffectiveSCEVType(Ty); 881 882 // Fold if the operand is constant. 883 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 884 return getConstant( 885 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 886 getEffectiveSCEVType(Ty)))); 887 888 // zext(zext(x)) --> zext(x) 889 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 890 return getZeroExtendExpr(SZ->getOperand(), Ty); 891 892 // Before doing any expensive analysis, check to see if we've already 893 // computed a SCEV for this Op and Ty. 894 FoldingSetNodeID ID; 895 ID.AddInteger(scZeroExtend); 896 ID.AddPointer(Op); 897 ID.AddPointer(Ty); 898 void *IP = 0; 899 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 900 901 // If the input value is a chrec scev, and we can prove that the value 902 // did not overflow the old, smaller, value, we can zero extend all of the 903 // operands (often constants). This allows analysis of something like 904 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 905 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 906 if (AR->isAffine()) { 907 const SCEV *Start = AR->getStart(); 908 const SCEV *Step = AR->getStepRecurrence(*this); 909 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 910 const Loop *L = AR->getLoop(); 911 912 // If we have special knowledge that this addrec won't overflow, 913 // we don't need to do any further analysis. 914 if (AR->hasNoUnsignedWrap()) 915 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 916 getZeroExtendExpr(Step, Ty), 917 L); 918 919 // Check whether the backedge-taken count is SCEVCouldNotCompute. 920 // Note that this serves two purposes: It filters out loops that are 921 // simply not analyzable, and it covers the case where this code is 922 // being called from within backedge-taken count analysis, such that 923 // attempting to ask for the backedge-taken count would likely result 924 // in infinite recursion. In the later case, the analysis code will 925 // cope with a conservative value, and it will take care to purge 926 // that value once it has finished. 927 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 928 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 929 // Manually compute the final value for AR, checking for 930 // overflow. 931 932 // Check whether the backedge-taken count can be losslessly casted to 933 // the addrec's type. The count is always unsigned. 934 const SCEV *CastedMaxBECount = 935 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 936 const SCEV *RecastedMaxBECount = 937 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 938 if (MaxBECount == RecastedMaxBECount) { 939 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 940 // Check whether Start+Step*MaxBECount has no unsigned overflow. 941 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 942 const SCEV *Add = getAddExpr(Start, ZMul); 943 const SCEV *OperandExtendedAdd = 944 getAddExpr(getZeroExtendExpr(Start, WideTy), 945 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 946 getZeroExtendExpr(Step, WideTy))); 947 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 948 // Return the expression with the addrec on the outside. 949 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 950 getZeroExtendExpr(Step, Ty), 951 L); 952 953 // Similar to above, only this time treat the step value as signed. 954 // This covers loops that count down. 955 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 956 Add = getAddExpr(Start, SMul); 957 OperandExtendedAdd = 958 getAddExpr(getZeroExtendExpr(Start, WideTy), 959 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 960 getSignExtendExpr(Step, WideTy))); 961 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) 962 // Return the expression with the addrec on the outside. 963 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 964 getSignExtendExpr(Step, Ty), 965 L); 966 } 967 968 // If the backedge is guarded by a comparison with the pre-inc value 969 // the addrec is safe. Also, if the entry is guarded by a comparison 970 // with the start value and the backedge is guarded by a comparison 971 // with the post-inc value, the addrec is safe. 972 if (isKnownPositive(Step)) { 973 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 974 getUnsignedRange(Step).getUnsignedMax()); 975 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 976 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 977 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 978 AR->getPostIncExpr(*this), N))) 979 // Return the expression with the addrec on the outside. 980 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 981 getZeroExtendExpr(Step, Ty), 982 L); 983 } else if (isKnownNegative(Step)) { 984 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 985 getSignedRange(Step).getSignedMin()); 986 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 987 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 988 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 989 AR->getPostIncExpr(*this), N))) 990 // Return the expression with the addrec on the outside. 991 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 992 getSignExtendExpr(Step, Ty), 993 L); 994 } 995 } 996 } 997 998 // The cast wasn't folded; create an explicit cast node. 999 // Recompute the insert position, as it may have been invalidated. 1000 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1001 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1002 Op, Ty); 1003 UniqueSCEVs.InsertNode(S, IP); 1004 return S; 1005} 1006 1007const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1008 const Type *Ty) { 1009 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1010 "This is not an extending conversion!"); 1011 assert(isSCEVable(Ty) && 1012 "This is not a conversion to a SCEVable type!"); 1013 Ty = getEffectiveSCEVType(Ty); 1014 1015 // Fold if the operand is constant. 1016 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1017 return getConstant( 1018 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1019 getEffectiveSCEVType(Ty)))); 1020 1021 // sext(sext(x)) --> sext(x) 1022 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1023 return getSignExtendExpr(SS->getOperand(), Ty); 1024 1025 // sext(zext(x)) --> zext(x) 1026 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1027 return getZeroExtendExpr(SZ->getOperand(), Ty); 1028 1029 // Before doing any expensive analysis, check to see if we've already 1030 // computed a SCEV for this Op and Ty. 1031 FoldingSetNodeID ID; 1032 ID.AddInteger(scSignExtend); 1033 ID.AddPointer(Op); 1034 ID.AddPointer(Ty); 1035 void *IP = 0; 1036 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1037 1038 // If the input value is a chrec scev, and we can prove that the value 1039 // did not overflow the old, smaller, value, we can sign extend all of the 1040 // operands (often constants). This allows analysis of something like 1041 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1042 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1043 if (AR->isAffine()) { 1044 const SCEV *Start = AR->getStart(); 1045 const SCEV *Step = AR->getStepRecurrence(*this); 1046 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1047 const Loop *L = AR->getLoop(); 1048 1049 // If we have special knowledge that this addrec won't overflow, 1050 // we don't need to do any further analysis. 1051 if (AR->hasNoSignedWrap()) 1052 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1053 getSignExtendExpr(Step, Ty), 1054 L); 1055 1056 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1057 // Note that this serves two purposes: It filters out loops that are 1058 // simply not analyzable, and it covers the case where this code is 1059 // being called from within backedge-taken count analysis, such that 1060 // attempting to ask for the backedge-taken count would likely result 1061 // in infinite recursion. In the later case, the analysis code will 1062 // cope with a conservative value, and it will take care to purge 1063 // that value once it has finished. 1064 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1065 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1066 // Manually compute the final value for AR, checking for 1067 // overflow. 1068 1069 // Check whether the backedge-taken count can be losslessly casted to 1070 // the addrec's type. The count is always unsigned. 1071 const SCEV *CastedMaxBECount = 1072 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1073 const SCEV *RecastedMaxBECount = 1074 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1075 if (MaxBECount == RecastedMaxBECount) { 1076 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1077 // Check whether Start+Step*MaxBECount has no signed overflow. 1078 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1079 const SCEV *Add = getAddExpr(Start, SMul); 1080 const SCEV *OperandExtendedAdd = 1081 getAddExpr(getSignExtendExpr(Start, WideTy), 1082 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1083 getSignExtendExpr(Step, WideTy))); 1084 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1085 // Return the expression with the addrec on the outside. 1086 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1087 getSignExtendExpr(Step, Ty), 1088 L); 1089 1090 // Similar to above, only this time treat the step value as unsigned. 1091 // This covers loops that count up with an unsigned step. 1092 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1093 Add = getAddExpr(Start, UMul); 1094 OperandExtendedAdd = 1095 getAddExpr(getSignExtendExpr(Start, WideTy), 1096 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1097 getZeroExtendExpr(Step, WideTy))); 1098 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) 1099 // Return the expression with the addrec on the outside. 1100 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1101 getZeroExtendExpr(Step, Ty), 1102 L); 1103 } 1104 1105 // If the backedge is guarded by a comparison with the pre-inc value 1106 // the addrec is safe. Also, if the entry is guarded by a comparison 1107 // with the start value and the backedge is guarded by a comparison 1108 // with the post-inc value, the addrec is safe. 1109 if (isKnownPositive(Step)) { 1110 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - 1111 getSignedRange(Step).getSignedMax()); 1112 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || 1113 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && 1114 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, 1115 AR->getPostIncExpr(*this), N))) 1116 // Return the expression with the addrec on the outside. 1117 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1118 getSignExtendExpr(Step, Ty), 1119 L); 1120 } else if (isKnownNegative(Step)) { 1121 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - 1122 getSignedRange(Step).getSignedMin()); 1123 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || 1124 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && 1125 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, 1126 AR->getPostIncExpr(*this), N))) 1127 // Return the expression with the addrec on the outside. 1128 return getAddRecExpr(getSignExtendExpr(Start, Ty), 1129 getSignExtendExpr(Step, Ty), 1130 L); 1131 } 1132 } 1133 } 1134 1135 // The cast wasn't folded; create an explicit cast node. 1136 // Recompute the insert position, as it may have been invalidated. 1137 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1138 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1139 Op, Ty); 1140 UniqueSCEVs.InsertNode(S, IP); 1141 return S; 1142} 1143 1144/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1145/// unspecified bits out to the given type. 1146/// 1147const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1148 const Type *Ty) { 1149 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1150 "This is not an extending conversion!"); 1151 assert(isSCEVable(Ty) && 1152 "This is not a conversion to a SCEVable type!"); 1153 Ty = getEffectiveSCEVType(Ty); 1154 1155 // Sign-extend negative constants. 1156 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1157 if (SC->getValue()->getValue().isNegative()) 1158 return getSignExtendExpr(Op, Ty); 1159 1160 // Peel off a truncate cast. 1161 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1162 const SCEV *NewOp = T->getOperand(); 1163 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1164 return getAnyExtendExpr(NewOp, Ty); 1165 return getTruncateOrNoop(NewOp, Ty); 1166 } 1167 1168 // Next try a zext cast. If the cast is folded, use it. 1169 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1170 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1171 return ZExt; 1172 1173 // Next try a sext cast. If the cast is folded, use it. 1174 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1175 if (!isa<SCEVSignExtendExpr>(SExt)) 1176 return SExt; 1177 1178 // Force the cast to be folded into the operands of an addrec. 1179 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1180 SmallVector<const SCEV *, 4> Ops; 1181 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1182 I != E; ++I) 1183 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1184 return getAddRecExpr(Ops, AR->getLoop()); 1185 } 1186 1187 // As a special case, fold anyext(undef) to undef. We don't want to 1188 // know too much about SCEVUnknowns, but this special case is handy 1189 // and harmless. 1190 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1191 if (isa<UndefValue>(U->getValue())) 1192 return getSCEV(UndefValue::get(Ty)); 1193 1194 // If the expression is obviously signed, use the sext cast value. 1195 if (isa<SCEVSMaxExpr>(Op)) 1196 return SExt; 1197 1198 // Absent any other information, use the zext cast value. 1199 return ZExt; 1200} 1201 1202/// CollectAddOperandsWithScales - Process the given Ops list, which is 1203/// a list of operands to be added under the given scale, update the given 1204/// map. This is a helper function for getAddRecExpr. As an example of 1205/// what it does, given a sequence of operands that would form an add 1206/// expression like this: 1207/// 1208/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1209/// 1210/// where A and B are constants, update the map with these values: 1211/// 1212/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1213/// 1214/// and add 13 + A*B*29 to AccumulatedConstant. 1215/// This will allow getAddRecExpr to produce this: 1216/// 1217/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1218/// 1219/// This form often exposes folding opportunities that are hidden in 1220/// the original operand list. 1221/// 1222/// Return true iff it appears that any interesting folding opportunities 1223/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1224/// the common case where no interesting opportunities are present, and 1225/// is also used as a check to avoid infinite recursion. 1226/// 1227static bool 1228CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1229 SmallVector<const SCEV *, 8> &NewOps, 1230 APInt &AccumulatedConstant, 1231 const SCEV *const *Ops, size_t NumOperands, 1232 const APInt &Scale, 1233 ScalarEvolution &SE) { 1234 bool Interesting = false; 1235 1236 // Iterate over the add operands. They are sorted, with constants first. 1237 unsigned i = 0; 1238 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1239 ++i; 1240 // Pull a buried constant out to the outside. 1241 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1242 Interesting = true; 1243 AccumulatedConstant += Scale * C->getValue()->getValue(); 1244 } 1245 1246 // Next comes everything else. We're especially interested in multiplies 1247 // here, but they're in the middle, so just visit the rest with one loop. 1248 for (; i != NumOperands; ++i) { 1249 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1250 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1251 APInt NewScale = 1252 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1253 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1254 // A multiplication of a constant with another add; recurse. 1255 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1256 Interesting |= 1257 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1258 Add->op_begin(), Add->getNumOperands(), 1259 NewScale, SE); 1260 } else { 1261 // A multiplication of a constant with some other value. Update 1262 // the map. 1263 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1264 const SCEV *Key = SE.getMulExpr(MulOps); 1265 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1266 M.insert(std::make_pair(Key, NewScale)); 1267 if (Pair.second) { 1268 NewOps.push_back(Pair.first->first); 1269 } else { 1270 Pair.first->second += NewScale; 1271 // The map already had an entry for this value, which may indicate 1272 // a folding opportunity. 1273 Interesting = true; 1274 } 1275 } 1276 } else { 1277 // An ordinary operand. Update the map. 1278 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1279 M.insert(std::make_pair(Ops[i], Scale)); 1280 if (Pair.second) { 1281 NewOps.push_back(Pair.first->first); 1282 } else { 1283 Pair.first->second += Scale; 1284 // The map already had an entry for this value, which may indicate 1285 // a folding opportunity. 1286 Interesting = true; 1287 } 1288 } 1289 } 1290 1291 return Interesting; 1292} 1293 1294namespace { 1295 struct APIntCompare { 1296 bool operator()(const APInt &LHS, const APInt &RHS) const { 1297 return LHS.ult(RHS); 1298 } 1299 }; 1300} 1301 1302/// getAddExpr - Get a canonical add expression, or something simpler if 1303/// possible. 1304const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1305 bool HasNUW, bool HasNSW) { 1306 assert(!Ops.empty() && "Cannot get empty add!"); 1307 if (Ops.size() == 1) return Ops[0]; 1308#ifndef NDEBUG 1309 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1310 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1311 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1312 "SCEVAddExpr operand types don't match!"); 1313#endif 1314 1315 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1316 if (!HasNUW && HasNSW) { 1317 bool All = true; 1318 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1319 E = Ops.end(); I != E; ++I) 1320 if (!isKnownNonNegative(*I)) { 1321 All = false; 1322 break; 1323 } 1324 if (All) HasNUW = true; 1325 } 1326 1327 // Sort by complexity, this groups all similar expression types together. 1328 GroupByComplexity(Ops, LI); 1329 1330 // If there are any constants, fold them together. 1331 unsigned Idx = 0; 1332 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1333 ++Idx; 1334 assert(Idx < Ops.size()); 1335 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1336 // We found two constants, fold them together! 1337 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1338 RHSC->getValue()->getValue()); 1339 if (Ops.size() == 2) return Ops[0]; 1340 Ops.erase(Ops.begin()+1); // Erase the folded element 1341 LHSC = cast<SCEVConstant>(Ops[0]); 1342 } 1343 1344 // If we are left with a constant zero being added, strip it off. 1345 if (LHSC->getValue()->isZero()) { 1346 Ops.erase(Ops.begin()); 1347 --Idx; 1348 } 1349 1350 if (Ops.size() == 1) return Ops[0]; 1351 } 1352 1353 // Okay, check to see if the same value occurs in the operand list more than 1354 // once. If so, merge them together into an multiply expression. Since we 1355 // sorted the list, these values are required to be adjacent. 1356 const Type *Ty = Ops[0]->getType(); 1357 bool FoundMatch = false; 1358 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1359 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1360 // Scan ahead to count how many equal operands there are. 1361 unsigned Count = 2; 1362 while (i+Count != e && Ops[i+Count] == Ops[i]) 1363 ++Count; 1364 // Merge the values into a multiply. 1365 const SCEV *Scale = getConstant(Ty, Count); 1366 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1367 if (Ops.size() == Count) 1368 return Mul; 1369 Ops[i] = Mul; 1370 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1371 --i; e -= Count - 1; 1372 FoundMatch = true; 1373 } 1374 if (FoundMatch) 1375 return getAddExpr(Ops, HasNUW, HasNSW); 1376 1377 // Check for truncates. If all the operands are truncated from the same 1378 // type, see if factoring out the truncate would permit the result to be 1379 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1380 // if the contents of the resulting outer trunc fold to something simple. 1381 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1382 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1383 const Type *DstType = Trunc->getType(); 1384 const Type *SrcType = Trunc->getOperand()->getType(); 1385 SmallVector<const SCEV *, 8> LargeOps; 1386 bool Ok = true; 1387 // Check all the operands to see if they can be represented in the 1388 // source type of the truncate. 1389 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1390 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1391 if (T->getOperand()->getType() != SrcType) { 1392 Ok = false; 1393 break; 1394 } 1395 LargeOps.push_back(T->getOperand()); 1396 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1397 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1398 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1399 SmallVector<const SCEV *, 8> LargeMulOps; 1400 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1401 if (const SCEVTruncateExpr *T = 1402 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1403 if (T->getOperand()->getType() != SrcType) { 1404 Ok = false; 1405 break; 1406 } 1407 LargeMulOps.push_back(T->getOperand()); 1408 } else if (const SCEVConstant *C = 1409 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1410 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1411 } else { 1412 Ok = false; 1413 break; 1414 } 1415 } 1416 if (Ok) 1417 LargeOps.push_back(getMulExpr(LargeMulOps)); 1418 } else { 1419 Ok = false; 1420 break; 1421 } 1422 } 1423 if (Ok) { 1424 // Evaluate the expression in the larger type. 1425 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); 1426 // If it folds to something simple, use it. Otherwise, don't. 1427 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1428 return getTruncateExpr(Fold, DstType); 1429 } 1430 } 1431 1432 // Skip past any other cast SCEVs. 1433 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1434 ++Idx; 1435 1436 // If there are add operands they would be next. 1437 if (Idx < Ops.size()) { 1438 bool DeletedAdd = false; 1439 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1440 // If we have an add, expand the add operands onto the end of the operands 1441 // list. 1442 Ops.erase(Ops.begin()+Idx); 1443 Ops.append(Add->op_begin(), Add->op_end()); 1444 DeletedAdd = true; 1445 } 1446 1447 // If we deleted at least one add, we added operands to the end of the list, 1448 // and they are not necessarily sorted. Recurse to resort and resimplify 1449 // any operands we just acquired. 1450 if (DeletedAdd) 1451 return getAddExpr(Ops); 1452 } 1453 1454 // Skip over the add expression until we get to a multiply. 1455 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1456 ++Idx; 1457 1458 // Check to see if there are any folding opportunities present with 1459 // operands multiplied by constant values. 1460 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1461 uint64_t BitWidth = getTypeSizeInBits(Ty); 1462 DenseMap<const SCEV *, APInt> M; 1463 SmallVector<const SCEV *, 8> NewOps; 1464 APInt AccumulatedConstant(BitWidth, 0); 1465 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1466 Ops.data(), Ops.size(), 1467 APInt(BitWidth, 1), *this)) { 1468 // Some interesting folding opportunity is present, so its worthwhile to 1469 // re-generate the operands list. Group the operands by constant scale, 1470 // to avoid multiplying by the same constant scale multiple times. 1471 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1472 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1473 E = NewOps.end(); I != E; ++I) 1474 MulOpLists[M.find(*I)->second].push_back(*I); 1475 // Re-generate the operands list. 1476 Ops.clear(); 1477 if (AccumulatedConstant != 0) 1478 Ops.push_back(getConstant(AccumulatedConstant)); 1479 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1480 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1481 if (I->first != 0) 1482 Ops.push_back(getMulExpr(getConstant(I->first), 1483 getAddExpr(I->second))); 1484 if (Ops.empty()) 1485 return getConstant(Ty, 0); 1486 if (Ops.size() == 1) 1487 return Ops[0]; 1488 return getAddExpr(Ops); 1489 } 1490 } 1491 1492 // If we are adding something to a multiply expression, make sure the 1493 // something is not already an operand of the multiply. If so, merge it into 1494 // the multiply. 1495 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1496 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1497 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1498 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1499 if (isa<SCEVConstant>(MulOpSCEV)) 1500 continue; 1501 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1502 if (MulOpSCEV == Ops[AddOp]) { 1503 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1504 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1505 if (Mul->getNumOperands() != 2) { 1506 // If the multiply has more than two operands, we must get the 1507 // Y*Z term. 1508 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1509 Mul->op_begin()+MulOp); 1510 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1511 InnerMul = getMulExpr(MulOps); 1512 } 1513 const SCEV *One = getConstant(Ty, 1); 1514 const SCEV *AddOne = getAddExpr(One, InnerMul); 1515 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1516 if (Ops.size() == 2) return OuterMul; 1517 if (AddOp < Idx) { 1518 Ops.erase(Ops.begin()+AddOp); 1519 Ops.erase(Ops.begin()+Idx-1); 1520 } else { 1521 Ops.erase(Ops.begin()+Idx); 1522 Ops.erase(Ops.begin()+AddOp-1); 1523 } 1524 Ops.push_back(OuterMul); 1525 return getAddExpr(Ops); 1526 } 1527 1528 // Check this multiply against other multiplies being added together. 1529 for (unsigned OtherMulIdx = Idx+1; 1530 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1531 ++OtherMulIdx) { 1532 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1533 // If MulOp occurs in OtherMul, we can fold the two multiplies 1534 // together. 1535 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1536 OMulOp != e; ++OMulOp) 1537 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1538 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1539 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1540 if (Mul->getNumOperands() != 2) { 1541 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1542 Mul->op_begin()+MulOp); 1543 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1544 InnerMul1 = getMulExpr(MulOps); 1545 } 1546 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1547 if (OtherMul->getNumOperands() != 2) { 1548 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1549 OtherMul->op_begin()+OMulOp); 1550 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1551 InnerMul2 = getMulExpr(MulOps); 1552 } 1553 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1554 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1555 if (Ops.size() == 2) return OuterMul; 1556 Ops.erase(Ops.begin()+Idx); 1557 Ops.erase(Ops.begin()+OtherMulIdx-1); 1558 Ops.push_back(OuterMul); 1559 return getAddExpr(Ops); 1560 } 1561 } 1562 } 1563 } 1564 1565 // If there are any add recurrences in the operands list, see if any other 1566 // added values are loop invariant. If so, we can fold them into the 1567 // recurrence. 1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1569 ++Idx; 1570 1571 // Scan over all recurrences, trying to fold loop invariants into them. 1572 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1573 // Scan all of the other operands to this add and add them to the vector if 1574 // they are loop invariant w.r.t. the recurrence. 1575 SmallVector<const SCEV *, 8> LIOps; 1576 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1577 const Loop *AddRecLoop = AddRec->getLoop(); 1578 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1579 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1580 LIOps.push_back(Ops[i]); 1581 Ops.erase(Ops.begin()+i); 1582 --i; --e; 1583 } 1584 1585 // If we found some loop invariants, fold them into the recurrence. 1586 if (!LIOps.empty()) { 1587 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1588 LIOps.push_back(AddRec->getStart()); 1589 1590 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1591 AddRec->op_end()); 1592 AddRecOps[0] = getAddExpr(LIOps); 1593 1594 // Build the new addrec. Propagate the NUW and NSW flags if both the 1595 // outer add and the inner addrec are guaranteed to have no overflow. 1596 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, 1597 HasNUW && AddRec->hasNoUnsignedWrap(), 1598 HasNSW && AddRec->hasNoSignedWrap()); 1599 1600 // If all of the other operands were loop invariant, we are done. 1601 if (Ops.size() == 1) return NewRec; 1602 1603 // Otherwise, add the folded AddRec by the non-liv parts. 1604 for (unsigned i = 0;; ++i) 1605 if (Ops[i] == AddRec) { 1606 Ops[i] = NewRec; 1607 break; 1608 } 1609 return getAddExpr(Ops); 1610 } 1611 1612 // Okay, if there weren't any loop invariants to be folded, check to see if 1613 // there are multiple AddRec's with the same loop induction variable being 1614 // added together. If so, we can fold them. 1615 for (unsigned OtherIdx = Idx+1; 1616 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1617 ++OtherIdx) 1618 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1619 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1620 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1621 AddRec->op_end()); 1622 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1623 ++OtherIdx) 1624 if (const SCEVAddRecExpr *OtherAddRec = 1625 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1626 if (OtherAddRec->getLoop() == AddRecLoop) { 1627 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1628 i != e; ++i) { 1629 if (i >= AddRecOps.size()) { 1630 AddRecOps.append(OtherAddRec->op_begin()+i, 1631 OtherAddRec->op_end()); 1632 break; 1633 } 1634 AddRecOps[i] = getAddExpr(AddRecOps[i], 1635 OtherAddRec->getOperand(i)); 1636 } 1637 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1638 } 1639 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop); 1640 return getAddExpr(Ops); 1641 } 1642 1643 // Otherwise couldn't fold anything into this recurrence. Move onto the 1644 // next one. 1645 } 1646 1647 // Okay, it looks like we really DO need an add expr. Check to see if we 1648 // already have one, otherwise create a new one. 1649 FoldingSetNodeID ID; 1650 ID.AddInteger(scAddExpr); 1651 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1652 ID.AddPointer(Ops[i]); 1653 void *IP = 0; 1654 SCEVAddExpr *S = 1655 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1656 if (!S) { 1657 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1658 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1659 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1660 O, Ops.size()); 1661 UniqueSCEVs.InsertNode(S, IP); 1662 } 1663 if (HasNUW) S->setHasNoUnsignedWrap(true); 1664 if (HasNSW) S->setHasNoSignedWrap(true); 1665 return S; 1666} 1667 1668/// getMulExpr - Get a canonical multiply expression, or something simpler if 1669/// possible. 1670const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1671 bool HasNUW, bool HasNSW) { 1672 assert(!Ops.empty() && "Cannot get empty mul!"); 1673 if (Ops.size() == 1) return Ops[0]; 1674#ifndef NDEBUG 1675 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1676 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1677 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1678 "SCEVMulExpr operand types don't match!"); 1679#endif 1680 1681 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 1682 if (!HasNUW && HasNSW) { 1683 bool All = true; 1684 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1685 E = Ops.end(); I != E; ++I) 1686 if (!isKnownNonNegative(*I)) { 1687 All = false; 1688 break; 1689 } 1690 if (All) HasNUW = true; 1691 } 1692 1693 // Sort by complexity, this groups all similar expression types together. 1694 GroupByComplexity(Ops, LI); 1695 1696 // If there are any constants, fold them together. 1697 unsigned Idx = 0; 1698 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1699 1700 // C1*(C2+V) -> C1*C2 + C1*V 1701 if (Ops.size() == 2) 1702 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1703 if (Add->getNumOperands() == 2 && 1704 isa<SCEVConstant>(Add->getOperand(0))) 1705 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1706 getMulExpr(LHSC, Add->getOperand(1))); 1707 1708 ++Idx; 1709 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1710 // We found two constants, fold them together! 1711 ConstantInt *Fold = ConstantInt::get(getContext(), 1712 LHSC->getValue()->getValue() * 1713 RHSC->getValue()->getValue()); 1714 Ops[0] = getConstant(Fold); 1715 Ops.erase(Ops.begin()+1); // Erase the folded element 1716 if (Ops.size() == 1) return Ops[0]; 1717 LHSC = cast<SCEVConstant>(Ops[0]); 1718 } 1719 1720 // If we are left with a constant one being multiplied, strip it off. 1721 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1722 Ops.erase(Ops.begin()); 1723 --Idx; 1724 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1725 // If we have a multiply of zero, it will always be zero. 1726 return Ops[0]; 1727 } else if (Ops[0]->isAllOnesValue()) { 1728 // If we have a mul by -1 of an add, try distributing the -1 among the 1729 // add operands. 1730 if (Ops.size() == 2) 1731 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1732 SmallVector<const SCEV *, 4> NewOps; 1733 bool AnyFolded = false; 1734 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); 1735 I != E; ++I) { 1736 const SCEV *Mul = getMulExpr(Ops[0], *I); 1737 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1738 NewOps.push_back(Mul); 1739 } 1740 if (AnyFolded) 1741 return getAddExpr(NewOps); 1742 } 1743 } 1744 1745 if (Ops.size() == 1) 1746 return Ops[0]; 1747 } 1748 1749 // Skip over the add expression until we get to a multiply. 1750 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1751 ++Idx; 1752 1753 // If there are mul operands inline them all into this expression. 1754 if (Idx < Ops.size()) { 1755 bool DeletedMul = false; 1756 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1757 // If we have an mul, expand the mul operands onto the end of the operands 1758 // list. 1759 Ops.erase(Ops.begin()+Idx); 1760 Ops.append(Mul->op_begin(), Mul->op_end()); 1761 DeletedMul = true; 1762 } 1763 1764 // If we deleted at least one mul, we added operands to the end of the list, 1765 // and they are not necessarily sorted. Recurse to resort and resimplify 1766 // any operands we just acquired. 1767 if (DeletedMul) 1768 return getMulExpr(Ops); 1769 } 1770 1771 // If there are any add recurrences in the operands list, see if any other 1772 // added values are loop invariant. If so, we can fold them into the 1773 // recurrence. 1774 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1775 ++Idx; 1776 1777 // Scan over all recurrences, trying to fold loop invariants into them. 1778 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1779 // Scan all of the other operands to this mul and add them to the vector if 1780 // they are loop invariant w.r.t. the recurrence. 1781 SmallVector<const SCEV *, 8> LIOps; 1782 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1783 const Loop *AddRecLoop = AddRec->getLoop(); 1784 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1785 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1786 LIOps.push_back(Ops[i]); 1787 Ops.erase(Ops.begin()+i); 1788 --i; --e; 1789 } 1790 1791 // If we found some loop invariants, fold them into the recurrence. 1792 if (!LIOps.empty()) { 1793 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1794 SmallVector<const SCEV *, 4> NewOps; 1795 NewOps.reserve(AddRec->getNumOperands()); 1796 const SCEV *Scale = getMulExpr(LIOps); 1797 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1798 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1799 1800 // Build the new addrec. Propagate the NUW and NSW flags if both the 1801 // outer mul and the inner addrec are guaranteed to have no overflow. 1802 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, 1803 HasNUW && AddRec->hasNoUnsignedWrap(), 1804 HasNSW && AddRec->hasNoSignedWrap()); 1805 1806 // If all of the other operands were loop invariant, we are done. 1807 if (Ops.size() == 1) return NewRec; 1808 1809 // Otherwise, multiply the folded AddRec by the non-liv parts. 1810 for (unsigned i = 0;; ++i) 1811 if (Ops[i] == AddRec) { 1812 Ops[i] = NewRec; 1813 break; 1814 } 1815 return getMulExpr(Ops); 1816 } 1817 1818 // Okay, if there weren't any loop invariants to be folded, check to see if 1819 // there are multiple AddRec's with the same loop induction variable being 1820 // multiplied together. If so, we can fold them. 1821 for (unsigned OtherIdx = Idx+1; 1822 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1823 ++OtherIdx) 1824 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1825 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> --> 1826 // {A*C,+,F*D + G*B + B*D}<L> 1827 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1828 ++OtherIdx) 1829 if (const SCEVAddRecExpr *OtherAddRec = 1830 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1831 if (OtherAddRec->getLoop() == AddRecLoop) { 1832 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; 1833 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart()); 1834 const SCEV *B = F->getStepRecurrence(*this); 1835 const SCEV *D = G->getStepRecurrence(*this); 1836 const SCEV *NewStep = getAddExpr(getMulExpr(F, D), 1837 getMulExpr(G, B), 1838 getMulExpr(B, D)); 1839 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, 1840 F->getLoop()); 1841 if (Ops.size() == 2) return NewAddRec; 1842 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 1843 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1844 } 1845 return getMulExpr(Ops); 1846 } 1847 1848 // Otherwise couldn't fold anything into this recurrence. Move onto the 1849 // next one. 1850 } 1851 1852 // Okay, it looks like we really DO need an mul expr. Check to see if we 1853 // already have one, otherwise create a new one. 1854 FoldingSetNodeID ID; 1855 ID.AddInteger(scMulExpr); 1856 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1857 ID.AddPointer(Ops[i]); 1858 void *IP = 0; 1859 SCEVMulExpr *S = 1860 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1861 if (!S) { 1862 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1863 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1864 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 1865 O, Ops.size()); 1866 UniqueSCEVs.InsertNode(S, IP); 1867 } 1868 if (HasNUW) S->setHasNoUnsignedWrap(true); 1869 if (HasNSW) S->setHasNoSignedWrap(true); 1870 return S; 1871} 1872 1873/// getUDivExpr - Get a canonical unsigned division expression, or something 1874/// simpler if possible. 1875const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 1876 const SCEV *RHS) { 1877 assert(getEffectiveSCEVType(LHS->getType()) == 1878 getEffectiveSCEVType(RHS->getType()) && 1879 "SCEVUDivExpr operand types don't match!"); 1880 1881 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 1882 if (RHSC->getValue()->equalsInt(1)) 1883 return LHS; // X udiv 1 --> x 1884 // If the denominator is zero, the result of the udiv is undefined. Don't 1885 // try to analyze it, because the resolution chosen here may differ from 1886 // the resolution chosen in other parts of the compiler. 1887 if (!RHSC->getValue()->isZero()) { 1888 // Determine if the division can be folded into the operands of 1889 // its operands. 1890 // TODO: Generalize this to non-constants by using known-bits information. 1891 const Type *Ty = LHS->getType(); 1892 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 1893 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 1894 // For non-power-of-two values, effectively round the value up to the 1895 // nearest power of two. 1896 if (!RHSC->getValue()->getValue().isPowerOf2()) 1897 ++MaxShiftAmt; 1898 const IntegerType *ExtTy = 1899 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 1900 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 1901 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 1902 if (const SCEVConstant *Step = 1903 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) 1904 if (!Step->getValue()->getValue() 1905 .urem(RHSC->getValue()->getValue()) && 1906 getZeroExtendExpr(AR, ExtTy) == 1907 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 1908 getZeroExtendExpr(Step, ExtTy), 1909 AR->getLoop())) { 1910 SmallVector<const SCEV *, 4> Operands; 1911 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 1912 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 1913 return getAddRecExpr(Operands, AR->getLoop()); 1914 } 1915 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 1916 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 1917 SmallVector<const SCEV *, 4> Operands; 1918 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 1919 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 1920 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 1921 // Find an operand that's safely divisible. 1922 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 1923 const SCEV *Op = M->getOperand(i); 1924 const SCEV *Div = getUDivExpr(Op, RHSC); 1925 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 1926 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 1927 M->op_end()); 1928 Operands[i] = Div; 1929 return getMulExpr(Operands); 1930 } 1931 } 1932 } 1933 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 1934 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { 1935 SmallVector<const SCEV *, 4> Operands; 1936 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 1937 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 1938 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 1939 Operands.clear(); 1940 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 1941 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 1942 if (isa<SCEVUDivExpr>(Op) || 1943 getMulExpr(Op, RHS) != A->getOperand(i)) 1944 break; 1945 Operands.push_back(Op); 1946 } 1947 if (Operands.size() == A->getNumOperands()) 1948 return getAddExpr(Operands); 1949 } 1950 } 1951 1952 // Fold if both operands are constant. 1953 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 1954 Constant *LHSCV = LHSC->getValue(); 1955 Constant *RHSCV = RHSC->getValue(); 1956 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 1957 RHSCV))); 1958 } 1959 } 1960 } 1961 1962 FoldingSetNodeID ID; 1963 ID.AddInteger(scUDivExpr); 1964 ID.AddPointer(LHS); 1965 ID.AddPointer(RHS); 1966 void *IP = 0; 1967 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1968 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 1969 LHS, RHS); 1970 UniqueSCEVs.InsertNode(S, IP); 1971 return S; 1972} 1973 1974 1975/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1976/// Simplify the expression as much as possible. 1977const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, 1978 const SCEV *Step, const Loop *L, 1979 bool HasNUW, bool HasNSW) { 1980 SmallVector<const SCEV *, 4> Operands; 1981 Operands.push_back(Start); 1982 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 1983 if (StepChrec->getLoop() == L) { 1984 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 1985 return getAddRecExpr(Operands, L); 1986 } 1987 1988 Operands.push_back(Step); 1989 return getAddRecExpr(Operands, L, HasNUW, HasNSW); 1990} 1991 1992/// getAddRecExpr - Get an add recurrence expression for the specified loop. 1993/// Simplify the expression as much as possible. 1994const SCEV * 1995ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 1996 const Loop *L, 1997 bool HasNUW, bool HasNSW) { 1998 if (Operands.size() == 1) return Operands[0]; 1999#ifndef NDEBUG 2000 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2001 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2002 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2003 "SCEVAddRecExpr operand types don't match!"); 2004 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2005 assert(isLoopInvariant(Operands[i], L) && 2006 "SCEVAddRecExpr operand is not loop-invariant!"); 2007#endif 2008 2009 if (Operands.back()->isZero()) { 2010 Operands.pop_back(); 2011 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X 2012 } 2013 2014 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2015 // use that information to infer NUW and NSW flags. However, computing a 2016 // BE count requires calling getAddRecExpr, so we may not yet have a 2017 // meaningful BE count at this point (and if we don't, we'd be stuck 2018 // with a SCEVCouldNotCompute as the cached BE count). 2019 2020 // If HasNSW is true and all the operands are non-negative, infer HasNUW. 2021 if (!HasNUW && HasNSW) { 2022 bool All = true; 2023 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2024 E = Operands.end(); I != E; ++I) 2025 if (!isKnownNonNegative(*I)) { 2026 All = false; 2027 break; 2028 } 2029 if (All) HasNUW = true; 2030 } 2031 2032 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2033 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2034 const Loop *NestedLoop = NestedAR->getLoop(); 2035 if (L->contains(NestedLoop) ? 2036 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2037 (!NestedLoop->contains(L) && 2038 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2039 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2040 NestedAR->op_end()); 2041 Operands[0] = NestedAR->getStart(); 2042 // AddRecs require their operands be loop-invariant with respect to their 2043 // loops. Don't perform this transformation if it would break this 2044 // requirement. 2045 bool AllInvariant = true; 2046 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2047 if (!isLoopInvariant(Operands[i], L)) { 2048 AllInvariant = false; 2049 break; 2050 } 2051 if (AllInvariant) { 2052 NestedOperands[0] = getAddRecExpr(Operands, L); 2053 AllInvariant = true; 2054 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2055 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2056 AllInvariant = false; 2057 break; 2058 } 2059 if (AllInvariant) 2060 // Ok, both add recurrences are valid after the transformation. 2061 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); 2062 } 2063 // Reset Operands to its original state. 2064 Operands[0] = NestedAR; 2065 } 2066 } 2067 2068 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2069 // already have one, otherwise create a new one. 2070 FoldingSetNodeID ID; 2071 ID.AddInteger(scAddRecExpr); 2072 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2073 ID.AddPointer(Operands[i]); 2074 ID.AddPointer(L); 2075 void *IP = 0; 2076 SCEVAddRecExpr *S = 2077 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2078 if (!S) { 2079 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2080 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2081 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2082 O, Operands.size(), L); 2083 UniqueSCEVs.InsertNode(S, IP); 2084 } 2085 if (HasNUW) S->setHasNoUnsignedWrap(true); 2086 if (HasNSW) S->setHasNoSignedWrap(true); 2087 return S; 2088} 2089 2090const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2091 const SCEV *RHS) { 2092 SmallVector<const SCEV *, 2> Ops; 2093 Ops.push_back(LHS); 2094 Ops.push_back(RHS); 2095 return getSMaxExpr(Ops); 2096} 2097 2098const SCEV * 2099ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2100 assert(!Ops.empty() && "Cannot get empty smax!"); 2101 if (Ops.size() == 1) return Ops[0]; 2102#ifndef NDEBUG 2103 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2104 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2105 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2106 "SCEVSMaxExpr operand types don't match!"); 2107#endif 2108 2109 // Sort by complexity, this groups all similar expression types together. 2110 GroupByComplexity(Ops, LI); 2111 2112 // If there are any constants, fold them together. 2113 unsigned Idx = 0; 2114 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2115 ++Idx; 2116 assert(Idx < Ops.size()); 2117 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2118 // We found two constants, fold them together! 2119 ConstantInt *Fold = ConstantInt::get(getContext(), 2120 APIntOps::smax(LHSC->getValue()->getValue(), 2121 RHSC->getValue()->getValue())); 2122 Ops[0] = getConstant(Fold); 2123 Ops.erase(Ops.begin()+1); // Erase the folded element 2124 if (Ops.size() == 1) return Ops[0]; 2125 LHSC = cast<SCEVConstant>(Ops[0]); 2126 } 2127 2128 // If we are left with a constant minimum-int, strip it off. 2129 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2130 Ops.erase(Ops.begin()); 2131 --Idx; 2132 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2133 // If we have an smax with a constant maximum-int, it will always be 2134 // maximum-int. 2135 return Ops[0]; 2136 } 2137 2138 if (Ops.size() == 1) return Ops[0]; 2139 } 2140 2141 // Find the first SMax 2142 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2143 ++Idx; 2144 2145 // Check to see if one of the operands is an SMax. If so, expand its operands 2146 // onto our operand list, and recurse to simplify. 2147 if (Idx < Ops.size()) { 2148 bool DeletedSMax = false; 2149 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2150 Ops.erase(Ops.begin()+Idx); 2151 Ops.append(SMax->op_begin(), SMax->op_end()); 2152 DeletedSMax = true; 2153 } 2154 2155 if (DeletedSMax) 2156 return getSMaxExpr(Ops); 2157 } 2158 2159 // Okay, check to see if the same value occurs in the operand list twice. If 2160 // so, delete one. Since we sorted the list, these values are required to 2161 // be adjacent. 2162 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2163 // X smax Y smax Y --> X smax Y 2164 // X smax Y --> X, if X is always greater than Y 2165 if (Ops[i] == Ops[i+1] || 2166 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2167 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2168 --i; --e; 2169 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2170 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2171 --i; --e; 2172 } 2173 2174 if (Ops.size() == 1) return Ops[0]; 2175 2176 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2177 2178 // Okay, it looks like we really DO need an smax expr. Check to see if we 2179 // already have one, otherwise create a new one. 2180 FoldingSetNodeID ID; 2181 ID.AddInteger(scSMaxExpr); 2182 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2183 ID.AddPointer(Ops[i]); 2184 void *IP = 0; 2185 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2186 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2187 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2188 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2189 O, Ops.size()); 2190 UniqueSCEVs.InsertNode(S, IP); 2191 return S; 2192} 2193 2194const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2195 const SCEV *RHS) { 2196 SmallVector<const SCEV *, 2> Ops; 2197 Ops.push_back(LHS); 2198 Ops.push_back(RHS); 2199 return getUMaxExpr(Ops); 2200} 2201 2202const SCEV * 2203ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2204 assert(!Ops.empty() && "Cannot get empty umax!"); 2205 if (Ops.size() == 1) return Ops[0]; 2206#ifndef NDEBUG 2207 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2208 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2209 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2210 "SCEVUMaxExpr operand types don't match!"); 2211#endif 2212 2213 // Sort by complexity, this groups all similar expression types together. 2214 GroupByComplexity(Ops, LI); 2215 2216 // If there are any constants, fold them together. 2217 unsigned Idx = 0; 2218 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2219 ++Idx; 2220 assert(Idx < Ops.size()); 2221 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2222 // We found two constants, fold them together! 2223 ConstantInt *Fold = ConstantInt::get(getContext(), 2224 APIntOps::umax(LHSC->getValue()->getValue(), 2225 RHSC->getValue()->getValue())); 2226 Ops[0] = getConstant(Fold); 2227 Ops.erase(Ops.begin()+1); // Erase the folded element 2228 if (Ops.size() == 1) return Ops[0]; 2229 LHSC = cast<SCEVConstant>(Ops[0]); 2230 } 2231 2232 // If we are left with a constant minimum-int, strip it off. 2233 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2234 Ops.erase(Ops.begin()); 2235 --Idx; 2236 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2237 // If we have an umax with a constant maximum-int, it will always be 2238 // maximum-int. 2239 return Ops[0]; 2240 } 2241 2242 if (Ops.size() == 1) return Ops[0]; 2243 } 2244 2245 // Find the first UMax 2246 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2247 ++Idx; 2248 2249 // Check to see if one of the operands is a UMax. If so, expand its operands 2250 // onto our operand list, and recurse to simplify. 2251 if (Idx < Ops.size()) { 2252 bool DeletedUMax = false; 2253 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2254 Ops.erase(Ops.begin()+Idx); 2255 Ops.append(UMax->op_begin(), UMax->op_end()); 2256 DeletedUMax = true; 2257 } 2258 2259 if (DeletedUMax) 2260 return getUMaxExpr(Ops); 2261 } 2262 2263 // Okay, check to see if the same value occurs in the operand list twice. If 2264 // so, delete one. Since we sorted the list, these values are required to 2265 // be adjacent. 2266 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2267 // X umax Y umax Y --> X umax Y 2268 // X umax Y --> X, if X is always greater than Y 2269 if (Ops[i] == Ops[i+1] || 2270 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2271 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2272 --i; --e; 2273 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2274 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2275 --i; --e; 2276 } 2277 2278 if (Ops.size() == 1) return Ops[0]; 2279 2280 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2281 2282 // Okay, it looks like we really DO need a umax expr. Check to see if we 2283 // already have one, otherwise create a new one. 2284 FoldingSetNodeID ID; 2285 ID.AddInteger(scUMaxExpr); 2286 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2287 ID.AddPointer(Ops[i]); 2288 void *IP = 0; 2289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2290 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2291 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2292 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2293 O, Ops.size()); 2294 UniqueSCEVs.InsertNode(S, IP); 2295 return S; 2296} 2297 2298const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2299 const SCEV *RHS) { 2300 // ~smax(~x, ~y) == smin(x, y). 2301 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2302} 2303 2304const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2305 const SCEV *RHS) { 2306 // ~umax(~x, ~y) == umin(x, y) 2307 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2308} 2309 2310const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { 2311 // If we have TargetData, we can bypass creating a target-independent 2312 // constant expression and then folding it back into a ConstantInt. 2313 // This is just a compile-time optimization. 2314 if (TD) 2315 return getConstant(TD->getIntPtrType(getContext()), 2316 TD->getTypeAllocSize(AllocTy)); 2317 2318 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2319 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2320 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2321 C = Folded; 2322 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2323 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2324} 2325 2326const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { 2327 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2328 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2329 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2330 C = Folded; 2331 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2332 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2333} 2334 2335const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, 2336 unsigned FieldNo) { 2337 // If we have TargetData, we can bypass creating a target-independent 2338 // constant expression and then folding it back into a ConstantInt. 2339 // This is just a compile-time optimization. 2340 if (TD) 2341 return getConstant(TD->getIntPtrType(getContext()), 2342 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2343 2344 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2345 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2346 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2347 C = Folded; 2348 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2349 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2350} 2351 2352const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, 2353 Constant *FieldNo) { 2354 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2355 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2356 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2357 C = Folded; 2358 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2359 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2360} 2361 2362const SCEV *ScalarEvolution::getUnknown(Value *V) { 2363 // Don't attempt to do anything other than create a SCEVUnknown object 2364 // here. createSCEV only calls getUnknown after checking for all other 2365 // interesting possibilities, and any other code that calls getUnknown 2366 // is doing so in order to hide a value from SCEV canonicalization. 2367 2368 FoldingSetNodeID ID; 2369 ID.AddInteger(scUnknown); 2370 ID.AddPointer(V); 2371 void *IP = 0; 2372 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2373 assert(cast<SCEVUnknown>(S)->getValue() == V && 2374 "Stale SCEVUnknown in uniquing map!"); 2375 return S; 2376 } 2377 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2378 FirstUnknown); 2379 FirstUnknown = cast<SCEVUnknown>(S); 2380 UniqueSCEVs.InsertNode(S, IP); 2381 return S; 2382} 2383 2384//===----------------------------------------------------------------------===// 2385// Basic SCEV Analysis and PHI Idiom Recognition Code 2386// 2387 2388/// isSCEVable - Test if values of the given type are analyzable within 2389/// the SCEV framework. This primarily includes integer types, and it 2390/// can optionally include pointer types if the ScalarEvolution class 2391/// has access to target-specific information. 2392bool ScalarEvolution::isSCEVable(const Type *Ty) const { 2393 // Integers and pointers are always SCEVable. 2394 return Ty->isIntegerTy() || Ty->isPointerTy(); 2395} 2396 2397/// getTypeSizeInBits - Return the size in bits of the specified type, 2398/// for which isSCEVable must return true. 2399uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { 2400 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2401 2402 // If we have a TargetData, use it! 2403 if (TD) 2404 return TD->getTypeSizeInBits(Ty); 2405 2406 // Integer types have fixed sizes. 2407 if (Ty->isIntegerTy()) 2408 return Ty->getPrimitiveSizeInBits(); 2409 2410 // The only other support type is pointer. Without TargetData, conservatively 2411 // assume pointers are 64-bit. 2412 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2413 return 64; 2414} 2415 2416/// getEffectiveSCEVType - Return a type with the same bitwidth as 2417/// the given type and which represents how SCEV will treat the given 2418/// type, for which isSCEVable must return true. For pointer types, 2419/// this is the pointer-sized integer type. 2420const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { 2421 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2422 2423 if (Ty->isIntegerTy()) 2424 return Ty; 2425 2426 // The only other support type is pointer. 2427 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2428 if (TD) return TD->getIntPtrType(getContext()); 2429 2430 // Without TargetData, conservatively assume pointers are 64-bit. 2431 return Type::getInt64Ty(getContext()); 2432} 2433 2434const SCEV *ScalarEvolution::getCouldNotCompute() { 2435 return &CouldNotCompute; 2436} 2437 2438/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2439/// expression and create a new one. 2440const SCEV *ScalarEvolution::getSCEV(Value *V) { 2441 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2442 2443 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2444 if (I != ValueExprMap.end()) return I->second; 2445 const SCEV *S = createSCEV(V); 2446 2447 // The process of creating a SCEV for V may have caused other SCEVs 2448 // to have been created, so it's necessary to insert the new entry 2449 // from scratch, rather than trying to remember the insert position 2450 // above. 2451 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2452 return S; 2453} 2454 2455/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2456/// 2457const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2458 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2459 return getConstant( 2460 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2461 2462 const Type *Ty = V->getType(); 2463 Ty = getEffectiveSCEVType(Ty); 2464 return getMulExpr(V, 2465 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2466} 2467 2468/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2469const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2470 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2471 return getConstant( 2472 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2473 2474 const Type *Ty = V->getType(); 2475 Ty = getEffectiveSCEVType(Ty); 2476 const SCEV *AllOnes = 2477 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2478 return getMinusSCEV(AllOnes, V); 2479} 2480 2481/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1, 2482/// and thus the HasNUW and HasNSW bits apply to the resultant add, not 2483/// whether the sub would have overflowed. 2484const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2485 bool HasNUW, bool HasNSW) { 2486 // Fast path: X - X --> 0. 2487 if (LHS == RHS) 2488 return getConstant(LHS->getType(), 0); 2489 2490 // X - Y --> X + -Y 2491 return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW); 2492} 2493 2494/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2495/// input value to the specified type. If the type must be extended, it is zero 2496/// extended. 2497const SCEV * 2498ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) { 2499 const Type *SrcTy = V->getType(); 2500 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2501 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2502 "Cannot truncate or zero extend with non-integer arguments!"); 2503 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2504 return V; // No conversion 2505 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2506 return getTruncateExpr(V, Ty); 2507 return getZeroExtendExpr(V, Ty); 2508} 2509 2510/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2511/// input value to the specified type. If the type must be extended, it is sign 2512/// extended. 2513const SCEV * 2514ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2515 const Type *Ty) { 2516 const Type *SrcTy = V->getType(); 2517 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2518 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2519 "Cannot truncate or zero extend with non-integer arguments!"); 2520 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2521 return V; // No conversion 2522 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2523 return getTruncateExpr(V, Ty); 2524 return getSignExtendExpr(V, Ty); 2525} 2526 2527/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2528/// input value to the specified type. If the type must be extended, it is zero 2529/// extended. The conversion must not be narrowing. 2530const SCEV * 2531ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { 2532 const Type *SrcTy = V->getType(); 2533 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2534 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2535 "Cannot noop or zero extend with non-integer arguments!"); 2536 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2537 "getNoopOrZeroExtend cannot truncate!"); 2538 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2539 return V; // No conversion 2540 return getZeroExtendExpr(V, Ty); 2541} 2542 2543/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2544/// input value to the specified type. If the type must be extended, it is sign 2545/// extended. The conversion must not be narrowing. 2546const SCEV * 2547ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { 2548 const Type *SrcTy = V->getType(); 2549 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2550 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2551 "Cannot noop or sign extend with non-integer arguments!"); 2552 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2553 "getNoopOrSignExtend cannot truncate!"); 2554 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2555 return V; // No conversion 2556 return getSignExtendExpr(V, Ty); 2557} 2558 2559/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2560/// the input value to the specified type. If the type must be extended, 2561/// it is extended with unspecified bits. The conversion must not be 2562/// narrowing. 2563const SCEV * 2564ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { 2565 const Type *SrcTy = V->getType(); 2566 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2567 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2568 "Cannot noop or any extend with non-integer arguments!"); 2569 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2570 "getNoopOrAnyExtend cannot truncate!"); 2571 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2572 return V; // No conversion 2573 return getAnyExtendExpr(V, Ty); 2574} 2575 2576/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2577/// input value to the specified type. The conversion must not be widening. 2578const SCEV * 2579ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { 2580 const Type *SrcTy = V->getType(); 2581 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2582 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2583 "Cannot truncate or noop with non-integer arguments!"); 2584 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2585 "getTruncateOrNoop cannot extend!"); 2586 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2587 return V; // No conversion 2588 return getTruncateExpr(V, Ty); 2589} 2590 2591/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2592/// the types using zero-extension, and then perform a umax operation 2593/// with them. 2594const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2595 const SCEV *RHS) { 2596 const SCEV *PromotedLHS = LHS; 2597 const SCEV *PromotedRHS = RHS; 2598 2599 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2600 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2601 else 2602 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2603 2604 return getUMaxExpr(PromotedLHS, PromotedRHS); 2605} 2606 2607/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2608/// the types using zero-extension, and then perform a umin operation 2609/// with them. 2610const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2611 const SCEV *RHS) { 2612 const SCEV *PromotedLHS = LHS; 2613 const SCEV *PromotedRHS = RHS; 2614 2615 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2616 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2617 else 2618 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2619 2620 return getUMinExpr(PromotedLHS, PromotedRHS); 2621} 2622 2623/// PushDefUseChildren - Push users of the given Instruction 2624/// onto the given Worklist. 2625static void 2626PushDefUseChildren(Instruction *I, 2627 SmallVectorImpl<Instruction *> &Worklist) { 2628 // Push the def-use children onto the Worklist stack. 2629 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2630 UI != UE; ++UI) 2631 Worklist.push_back(cast<Instruction>(*UI)); 2632} 2633 2634/// ForgetSymbolicValue - This looks up computed SCEV values for all 2635/// instructions that depend on the given instruction and removes them from 2636/// the ValueExprMapType map if they reference SymName. This is used during PHI 2637/// resolution. 2638void 2639ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2640 SmallVector<Instruction *, 16> Worklist; 2641 PushDefUseChildren(PN, Worklist); 2642 2643 SmallPtrSet<Instruction *, 8> Visited; 2644 Visited.insert(PN); 2645 while (!Worklist.empty()) { 2646 Instruction *I = Worklist.pop_back_val(); 2647 if (!Visited.insert(I)) continue; 2648 2649 ValueExprMapType::iterator It = 2650 ValueExprMap.find(static_cast<Value *>(I)); 2651 if (It != ValueExprMap.end()) { 2652 const SCEV *Old = It->second; 2653 2654 // Short-circuit the def-use traversal if the symbolic name 2655 // ceases to appear in expressions. 2656 if (Old != SymName && !hasOperand(Old, SymName)) 2657 continue; 2658 2659 // SCEVUnknown for a PHI either means that it has an unrecognized 2660 // structure, it's a PHI that's in the progress of being computed 2661 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2662 // additional loop trip count information isn't going to change anything. 2663 // In the second case, createNodeForPHI will perform the necessary 2664 // updates on its own when it gets to that point. In the third, we do 2665 // want to forget the SCEVUnknown. 2666 if (!isa<PHINode>(I) || 2667 !isa<SCEVUnknown>(Old) || 2668 (I != PN && Old == SymName)) { 2669 forgetMemoizedResults(Old); 2670 ValueExprMap.erase(It); 2671 } 2672 } 2673 2674 PushDefUseChildren(I, Worklist); 2675 } 2676} 2677 2678/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2679/// a loop header, making it a potential recurrence, or it doesn't. 2680/// 2681const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2682 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2683 if (L->getHeader() == PN->getParent()) { 2684 // The loop may have multiple entrances or multiple exits; we can analyze 2685 // this phi as an addrec if it has a unique entry value and a unique 2686 // backedge value. 2687 Value *BEValueV = 0, *StartValueV = 0; 2688 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2689 Value *V = PN->getIncomingValue(i); 2690 if (L->contains(PN->getIncomingBlock(i))) { 2691 if (!BEValueV) { 2692 BEValueV = V; 2693 } else if (BEValueV != V) { 2694 BEValueV = 0; 2695 break; 2696 } 2697 } else if (!StartValueV) { 2698 StartValueV = V; 2699 } else if (StartValueV != V) { 2700 StartValueV = 0; 2701 break; 2702 } 2703 } 2704 if (BEValueV && StartValueV) { 2705 // While we are analyzing this PHI node, handle its value symbolically. 2706 const SCEV *SymbolicName = getUnknown(PN); 2707 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2708 "PHI node already processed?"); 2709 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2710 2711 // Using this symbolic name for the PHI, analyze the value coming around 2712 // the back-edge. 2713 const SCEV *BEValue = getSCEV(BEValueV); 2714 2715 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2716 // has a special value for the first iteration of the loop. 2717 2718 // If the value coming around the backedge is an add with the symbolic 2719 // value we just inserted, then we found a simple induction variable! 2720 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2721 // If there is a single occurrence of the symbolic value, replace it 2722 // with a recurrence. 2723 unsigned FoundIndex = Add->getNumOperands(); 2724 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2725 if (Add->getOperand(i) == SymbolicName) 2726 if (FoundIndex == e) { 2727 FoundIndex = i; 2728 break; 2729 } 2730 2731 if (FoundIndex != Add->getNumOperands()) { 2732 // Create an add with everything but the specified operand. 2733 SmallVector<const SCEV *, 8> Ops; 2734 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2735 if (i != FoundIndex) 2736 Ops.push_back(Add->getOperand(i)); 2737 const SCEV *Accum = getAddExpr(Ops); 2738 2739 // This is not a valid addrec if the step amount is varying each 2740 // loop iteration, but is not itself an addrec in this loop. 2741 if (isLoopInvariant(Accum, L) || 2742 (isa<SCEVAddRecExpr>(Accum) && 2743 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2744 bool HasNUW = false; 2745 bool HasNSW = false; 2746 2747 // If the increment doesn't overflow, then neither the addrec nor 2748 // the post-increment will overflow. 2749 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2750 if (OBO->hasNoUnsignedWrap()) 2751 HasNUW = true; 2752 if (OBO->hasNoSignedWrap()) 2753 HasNSW = true; 2754 } else if (const GEPOperator *GEP = 2755 dyn_cast<GEPOperator>(BEValueV)) { 2756 // If the increment is a GEP, then we know it won't perform an 2757 // unsigned overflow, because the address space cannot be 2758 // wrapped around. 2759 HasNUW |= GEP->isInBounds(); 2760 } 2761 2762 const SCEV *StartVal = getSCEV(StartValueV); 2763 const SCEV *PHISCEV = 2764 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); 2765 2766 // Since the no-wrap flags are on the increment, they apply to the 2767 // post-incremented value as well. 2768 if (isLoopInvariant(Accum, L)) 2769 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2770 Accum, L, HasNUW, HasNSW); 2771 2772 // Okay, for the entire analysis of this edge we assumed the PHI 2773 // to be symbolic. We now need to go back and purge all of the 2774 // entries for the scalars that use the symbolic expression. 2775 ForgetSymbolicName(PN, SymbolicName); 2776 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2777 return PHISCEV; 2778 } 2779 } 2780 } else if (const SCEVAddRecExpr *AddRec = 2781 dyn_cast<SCEVAddRecExpr>(BEValue)) { 2782 // Otherwise, this could be a loop like this: 2783 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 2784 // In this case, j = {1,+,1} and BEValue is j. 2785 // Because the other in-value of i (0) fits the evolution of BEValue 2786 // i really is an addrec evolution. 2787 if (AddRec->getLoop() == L && AddRec->isAffine()) { 2788 const SCEV *StartVal = getSCEV(StartValueV); 2789 2790 // If StartVal = j.start - j.stride, we can use StartVal as the 2791 // initial step of the addrec evolution. 2792 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 2793 AddRec->getOperand(1))) { 2794 const SCEV *PHISCEV = 2795 getAddRecExpr(StartVal, AddRec->getOperand(1), L); 2796 2797 // Okay, for the entire analysis of this edge we assumed the PHI 2798 // to be symbolic. We now need to go back and purge all of the 2799 // entries for the scalars that use the symbolic expression. 2800 ForgetSymbolicName(PN, SymbolicName); 2801 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 2802 return PHISCEV; 2803 } 2804 } 2805 } 2806 } 2807 } 2808 2809 // If the PHI has a single incoming value, follow that value, unless the 2810 // PHI's incoming blocks are in a different loop, in which case doing so 2811 // risks breaking LCSSA form. Instcombine would normally zap these, but 2812 // it doesn't have DominatorTree information, so it may miss cases. 2813 if (Value *V = SimplifyInstruction(PN, TD, DT)) 2814 if (LI->replacementPreservesLCSSAForm(PN, V)) 2815 return getSCEV(V); 2816 2817 // If it's not a loop phi, we can't handle it yet. 2818 return getUnknown(PN); 2819} 2820 2821/// createNodeForGEP - Expand GEP instructions into add and multiply 2822/// operations. This allows them to be analyzed by regular SCEV code. 2823/// 2824const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 2825 2826 // Don't blindly transfer the inbounds flag from the GEP instruction to the 2827 // Add expression, because the Instruction may be guarded by control flow 2828 // and the no-overflow bits may not be valid for the expression in any 2829 // context. 2830 2831 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 2832 Value *Base = GEP->getOperand(0); 2833 // Don't attempt to analyze GEPs over unsized objects. 2834 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 2835 return getUnknown(GEP); 2836 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 2837 gep_type_iterator GTI = gep_type_begin(GEP); 2838 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 2839 E = GEP->op_end(); 2840 I != E; ++I) { 2841 Value *Index = *I; 2842 // Compute the (potentially symbolic) offset in bytes for this index. 2843 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { 2844 // For a struct, add the member offset. 2845 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 2846 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 2847 2848 // Add the field offset to the running total offset. 2849 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 2850 } else { 2851 // For an array, add the element offset, explicitly scaled. 2852 const SCEV *ElementSize = getSizeOfExpr(*GTI); 2853 const SCEV *IndexS = getSCEV(Index); 2854 // Getelementptr indices are signed. 2855 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 2856 2857 // Multiply the index by the element size to compute the element offset. 2858 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize); 2859 2860 // Add the element offset to the running total offset. 2861 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 2862 } 2863 } 2864 2865 // Get the SCEV for the GEP base. 2866 const SCEV *BaseS = getSCEV(Base); 2867 2868 // Add the total offset from all the GEP indices to the base. 2869 return getAddExpr(BaseS, TotalOffset); 2870} 2871 2872/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 2873/// guaranteed to end in (at every loop iteration). It is, at the same time, 2874/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 2875/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 2876uint32_t 2877ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 2878 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2879 return C->getValue()->getValue().countTrailingZeros(); 2880 2881 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 2882 return std::min(GetMinTrailingZeros(T->getOperand()), 2883 (uint32_t)getTypeSizeInBits(T->getType())); 2884 2885 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 2886 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2887 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2888 getTypeSizeInBits(E->getType()) : OpRes; 2889 } 2890 2891 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 2892 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 2893 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 2894 getTypeSizeInBits(E->getType()) : OpRes; 2895 } 2896 2897 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 2898 // The result is the min of all operands results. 2899 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2900 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2901 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2902 return MinOpRes; 2903 } 2904 2905 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 2906 // The result is the sum of all operands results. 2907 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 2908 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 2909 for (unsigned i = 1, e = M->getNumOperands(); 2910 SumOpRes != BitWidth && i != e; ++i) 2911 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 2912 BitWidth); 2913 return SumOpRes; 2914 } 2915 2916 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 2917 // The result is the min of all operands results. 2918 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 2919 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 2920 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 2921 return MinOpRes; 2922 } 2923 2924 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 2925 // The result is the min of all operands results. 2926 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2927 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2928 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2929 return MinOpRes; 2930 } 2931 2932 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 2933 // The result is the min of all operands results. 2934 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 2935 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 2936 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 2937 return MinOpRes; 2938 } 2939 2940 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 2941 // For a SCEVUnknown, ask ValueTracking. 2942 unsigned BitWidth = getTypeSizeInBits(U->getType()); 2943 APInt Mask = APInt::getAllOnesValue(BitWidth); 2944 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 2945 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 2946 return Zeros.countTrailingOnes(); 2947 } 2948 2949 // SCEVUDivExpr 2950 return 0; 2951} 2952 2953/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 2954/// 2955ConstantRange 2956ScalarEvolution::getUnsignedRange(const SCEV *S) { 2957 // See if we've computed this range already. 2958 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 2959 if (I != UnsignedRanges.end()) 2960 return I->second; 2961 2962 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 2963 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 2964 2965 unsigned BitWidth = getTypeSizeInBits(S->getType()); 2966 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 2967 2968 // If the value has known zeros, the maximum unsigned value will have those 2969 // known zeros as well. 2970 uint32_t TZ = GetMinTrailingZeros(S); 2971 if (TZ != 0) 2972 ConservativeResult = 2973 ConstantRange(APInt::getMinValue(BitWidth), 2974 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 2975 2976 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 2977 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 2978 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 2979 X = X.add(getUnsignedRange(Add->getOperand(i))); 2980 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 2981 } 2982 2983 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 2984 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 2985 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 2986 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 2987 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 2988 } 2989 2990 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 2991 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 2992 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 2993 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 2994 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 2995 } 2996 2997 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 2998 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 2999 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3000 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3001 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3002 } 3003 3004 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3005 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3006 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3007 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3008 } 3009 3010 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3011 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3012 return setUnsignedRange(ZExt, 3013 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3014 } 3015 3016 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3017 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3018 return setUnsignedRange(SExt, 3019 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3020 } 3021 3022 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3023 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3024 return setUnsignedRange(Trunc, 3025 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3026 } 3027 3028 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3029 // If there's no unsigned wrap, the value will never be less than its 3030 // initial value. 3031 if (AddRec->hasNoUnsignedWrap()) 3032 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3033 if (!C->getValue()->isZero()) 3034 ConservativeResult = 3035 ConservativeResult.intersectWith( 3036 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3037 3038 // TODO: non-affine addrec 3039 if (AddRec->isAffine()) { 3040 const Type *Ty = AddRec->getType(); 3041 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3042 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3043 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3044 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3045 3046 const SCEV *Start = AddRec->getStart(); 3047 const SCEV *Step = AddRec->getStepRecurrence(*this); 3048 3049 ConstantRange StartRange = getUnsignedRange(Start); 3050 ConstantRange StepRange = getSignedRange(Step); 3051 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3052 ConstantRange EndRange = 3053 StartRange.add(MaxBECountRange.multiply(StepRange)); 3054 3055 // Check for overflow. This must be done with ConstantRange arithmetic 3056 // because we could be called from within the ScalarEvolution overflow 3057 // checking code. 3058 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3059 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3060 ConstantRange ExtMaxBECountRange = 3061 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3062 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3063 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3064 ExtEndRange) 3065 return setUnsignedRange(AddRec, ConservativeResult); 3066 3067 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3068 EndRange.getUnsignedMin()); 3069 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3070 EndRange.getUnsignedMax()); 3071 if (Min.isMinValue() && Max.isMaxValue()) 3072 return setUnsignedRange(AddRec, ConservativeResult); 3073 return setUnsignedRange(AddRec, 3074 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3075 } 3076 } 3077 3078 return setUnsignedRange(AddRec, ConservativeResult); 3079 } 3080 3081 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3082 // For a SCEVUnknown, ask ValueTracking. 3083 APInt Mask = APInt::getAllOnesValue(BitWidth); 3084 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3085 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3086 if (Ones == ~Zeros + 1) 3087 return setUnsignedRange(U, ConservativeResult); 3088 return setUnsignedRange(U, 3089 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3090 } 3091 3092 return setUnsignedRange(S, ConservativeResult); 3093} 3094 3095/// getSignedRange - Determine the signed range for a particular SCEV. 3096/// 3097ConstantRange 3098ScalarEvolution::getSignedRange(const SCEV *S) { 3099 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3100 if (I != SignedRanges.end()) 3101 return I->second; 3102 3103 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3104 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3105 3106 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3107 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3108 3109 // If the value has known zeros, the maximum signed value will have those 3110 // known zeros as well. 3111 uint32_t TZ = GetMinTrailingZeros(S); 3112 if (TZ != 0) 3113 ConservativeResult = 3114 ConstantRange(APInt::getSignedMinValue(BitWidth), 3115 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3116 3117 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3118 ConstantRange X = getSignedRange(Add->getOperand(0)); 3119 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3120 X = X.add(getSignedRange(Add->getOperand(i))); 3121 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3122 } 3123 3124 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3125 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3126 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3127 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3128 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3129 } 3130 3131 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3132 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3133 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3134 X = X.smax(getSignedRange(SMax->getOperand(i))); 3135 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3136 } 3137 3138 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3139 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3140 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3141 X = X.umax(getSignedRange(UMax->getOperand(i))); 3142 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3143 } 3144 3145 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3146 ConstantRange X = getSignedRange(UDiv->getLHS()); 3147 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3148 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3149 } 3150 3151 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3152 ConstantRange X = getSignedRange(ZExt->getOperand()); 3153 return setSignedRange(ZExt, 3154 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3155 } 3156 3157 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3158 ConstantRange X = getSignedRange(SExt->getOperand()); 3159 return setSignedRange(SExt, 3160 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3161 } 3162 3163 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3164 ConstantRange X = getSignedRange(Trunc->getOperand()); 3165 return setSignedRange(Trunc, 3166 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3167 } 3168 3169 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3170 // If there's no signed wrap, and all the operands have the same sign or 3171 // zero, the value won't ever change sign. 3172 if (AddRec->hasNoSignedWrap()) { 3173 bool AllNonNeg = true; 3174 bool AllNonPos = true; 3175 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3176 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3177 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3178 } 3179 if (AllNonNeg) 3180 ConservativeResult = ConservativeResult.intersectWith( 3181 ConstantRange(APInt(BitWidth, 0), 3182 APInt::getSignedMinValue(BitWidth))); 3183 else if (AllNonPos) 3184 ConservativeResult = ConservativeResult.intersectWith( 3185 ConstantRange(APInt::getSignedMinValue(BitWidth), 3186 APInt(BitWidth, 1))); 3187 } 3188 3189 // TODO: non-affine addrec 3190 if (AddRec->isAffine()) { 3191 const Type *Ty = AddRec->getType(); 3192 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3193 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3194 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3195 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3196 3197 const SCEV *Start = AddRec->getStart(); 3198 const SCEV *Step = AddRec->getStepRecurrence(*this); 3199 3200 ConstantRange StartRange = getSignedRange(Start); 3201 ConstantRange StepRange = getSignedRange(Step); 3202 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3203 ConstantRange EndRange = 3204 StartRange.add(MaxBECountRange.multiply(StepRange)); 3205 3206 // Check for overflow. This must be done with ConstantRange arithmetic 3207 // because we could be called from within the ScalarEvolution overflow 3208 // checking code. 3209 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3210 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3211 ConstantRange ExtMaxBECountRange = 3212 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3213 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3214 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3215 ExtEndRange) 3216 return setSignedRange(AddRec, ConservativeResult); 3217 3218 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3219 EndRange.getSignedMin()); 3220 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3221 EndRange.getSignedMax()); 3222 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3223 return setSignedRange(AddRec, ConservativeResult); 3224 return setSignedRange(AddRec, 3225 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3226 } 3227 } 3228 3229 return setSignedRange(AddRec, ConservativeResult); 3230 } 3231 3232 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3233 // For a SCEVUnknown, ask ValueTracking. 3234 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3235 return setSignedRange(U, ConservativeResult); 3236 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3237 if (NS == 1) 3238 return setSignedRange(U, ConservativeResult); 3239 return setSignedRange(U, ConservativeResult.intersectWith( 3240 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3241 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3242 } 3243 3244 return setSignedRange(S, ConservativeResult); 3245} 3246 3247/// createSCEV - We know that there is no SCEV for the specified value. 3248/// Analyze the expression. 3249/// 3250const SCEV *ScalarEvolution::createSCEV(Value *V) { 3251 if (!isSCEVable(V->getType())) 3252 return getUnknown(V); 3253 3254 unsigned Opcode = Instruction::UserOp1; 3255 if (Instruction *I = dyn_cast<Instruction>(V)) { 3256 Opcode = I->getOpcode(); 3257 3258 // Don't attempt to analyze instructions in blocks that aren't 3259 // reachable. Such instructions don't matter, and they aren't required 3260 // to obey basic rules for definitions dominating uses which this 3261 // analysis depends on. 3262 if (!DT->isReachableFromEntry(I->getParent())) 3263 return getUnknown(V); 3264 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3265 Opcode = CE->getOpcode(); 3266 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3267 return getConstant(CI); 3268 else if (isa<ConstantPointerNull>(V)) 3269 return getConstant(V->getType(), 0); 3270 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3271 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3272 else 3273 return getUnknown(V); 3274 3275 Operator *U = cast<Operator>(V); 3276 switch (Opcode) { 3277 case Instruction::Add: { 3278 // The simple thing to do would be to just call getSCEV on both operands 3279 // and call getAddExpr with the result. However if we're looking at a 3280 // bunch of things all added together, this can be quite inefficient, 3281 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3282 // Instead, gather up all the operands and make a single getAddExpr call. 3283 // LLVM IR canonical form means we need only traverse the left operands. 3284 SmallVector<const SCEV *, 4> AddOps; 3285 AddOps.push_back(getSCEV(U->getOperand(1))); 3286 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3287 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3288 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3289 break; 3290 U = cast<Operator>(Op); 3291 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3292 if (Opcode == Instruction::Sub) 3293 AddOps.push_back(getNegativeSCEV(Op1)); 3294 else 3295 AddOps.push_back(Op1); 3296 } 3297 AddOps.push_back(getSCEV(U->getOperand(0))); 3298 return getAddExpr(AddOps); 3299 } 3300 case Instruction::Mul: { 3301 // See the Add code above. 3302 SmallVector<const SCEV *, 4> MulOps; 3303 MulOps.push_back(getSCEV(U->getOperand(1))); 3304 for (Value *Op = U->getOperand(0); 3305 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3306 Op = U->getOperand(0)) { 3307 U = cast<Operator>(Op); 3308 MulOps.push_back(getSCEV(U->getOperand(1))); 3309 } 3310 MulOps.push_back(getSCEV(U->getOperand(0))); 3311 return getMulExpr(MulOps); 3312 } 3313 case Instruction::UDiv: 3314 return getUDivExpr(getSCEV(U->getOperand(0)), 3315 getSCEV(U->getOperand(1))); 3316 case Instruction::Sub: 3317 return getMinusSCEV(getSCEV(U->getOperand(0)), 3318 getSCEV(U->getOperand(1))); 3319 case Instruction::And: 3320 // For an expression like x&255 that merely masks off the high bits, 3321 // use zext(trunc(x)) as the SCEV expression. 3322 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3323 if (CI->isNullValue()) 3324 return getSCEV(U->getOperand(1)); 3325 if (CI->isAllOnesValue()) 3326 return getSCEV(U->getOperand(0)); 3327 const APInt &A = CI->getValue(); 3328 3329 // Instcombine's ShrinkDemandedConstant may strip bits out of 3330 // constants, obscuring what would otherwise be a low-bits mask. 3331 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3332 // knew about to reconstruct a low-bits mask value. 3333 unsigned LZ = A.countLeadingZeros(); 3334 unsigned BitWidth = A.getBitWidth(); 3335 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3336 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3337 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3338 3339 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3340 3341 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3342 return 3343 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3344 IntegerType::get(getContext(), BitWidth - LZ)), 3345 U->getType()); 3346 } 3347 break; 3348 3349 case Instruction::Or: 3350 // If the RHS of the Or is a constant, we may have something like: 3351 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3352 // optimizations will transparently handle this case. 3353 // 3354 // In order for this transformation to be safe, the LHS must be of the 3355 // form X*(2^n) and the Or constant must be less than 2^n. 3356 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3357 const SCEV *LHS = getSCEV(U->getOperand(0)); 3358 const APInt &CIVal = CI->getValue(); 3359 if (GetMinTrailingZeros(LHS) >= 3360 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3361 // Build a plain add SCEV. 3362 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3363 // If the LHS of the add was an addrec and it has no-wrap flags, 3364 // transfer the no-wrap flags, since an or won't introduce a wrap. 3365 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3366 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3367 if (OldAR->hasNoUnsignedWrap()) 3368 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); 3369 if (OldAR->hasNoSignedWrap()) 3370 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); 3371 } 3372 return S; 3373 } 3374 } 3375 break; 3376 case Instruction::Xor: 3377 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3378 // If the RHS of the xor is a signbit, then this is just an add. 3379 // Instcombine turns add of signbit into xor as a strength reduction step. 3380 if (CI->getValue().isSignBit()) 3381 return getAddExpr(getSCEV(U->getOperand(0)), 3382 getSCEV(U->getOperand(1))); 3383 3384 // If the RHS of xor is -1, then this is a not operation. 3385 if (CI->isAllOnesValue()) 3386 return getNotSCEV(getSCEV(U->getOperand(0))); 3387 3388 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3389 // This is a variant of the check for xor with -1, and it handles 3390 // the case where instcombine has trimmed non-demanded bits out 3391 // of an xor with -1. 3392 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3393 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3394 if (BO->getOpcode() == Instruction::And && 3395 LCI->getValue() == CI->getValue()) 3396 if (const SCEVZeroExtendExpr *Z = 3397 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3398 const Type *UTy = U->getType(); 3399 const SCEV *Z0 = Z->getOperand(); 3400 const Type *Z0Ty = Z0->getType(); 3401 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3402 3403 // If C is a low-bits mask, the zero extend is serving to 3404 // mask off the high bits. Complement the operand and 3405 // re-apply the zext. 3406 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3407 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3408 3409 // If C is a single bit, it may be in the sign-bit position 3410 // before the zero-extend. In this case, represent the xor 3411 // using an add, which is equivalent, and re-apply the zext. 3412 APInt Trunc = CI->getValue().trunc(Z0TySize); 3413 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3414 Trunc.isSignBit()) 3415 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3416 UTy); 3417 } 3418 } 3419 break; 3420 3421 case Instruction::Shl: 3422 // Turn shift left of a constant amount into a multiply. 3423 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3424 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3425 3426 // If the shift count is not less than the bitwidth, the result of 3427 // the shift is undefined. Don't try to analyze it, because the 3428 // resolution chosen here may differ from the resolution chosen in 3429 // other parts of the compiler. 3430 if (SA->getValue().uge(BitWidth)) 3431 break; 3432 3433 Constant *X = ConstantInt::get(getContext(), 3434 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3435 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3436 } 3437 break; 3438 3439 case Instruction::LShr: 3440 // Turn logical shift right of a constant into a unsigned divide. 3441 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3442 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3443 3444 // If the shift count is not less than the bitwidth, the result of 3445 // the shift is undefined. Don't try to analyze it, because the 3446 // resolution chosen here may differ from the resolution chosen in 3447 // other parts of the compiler. 3448 if (SA->getValue().uge(BitWidth)) 3449 break; 3450 3451 Constant *X = ConstantInt::get(getContext(), 3452 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3453 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3454 } 3455 break; 3456 3457 case Instruction::AShr: 3458 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3459 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3460 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3461 if (L->getOpcode() == Instruction::Shl && 3462 L->getOperand(1) == U->getOperand(1)) { 3463 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3464 3465 // If the shift count is not less than the bitwidth, the result of 3466 // the shift is undefined. Don't try to analyze it, because the 3467 // resolution chosen here may differ from the resolution chosen in 3468 // other parts of the compiler. 3469 if (CI->getValue().uge(BitWidth)) 3470 break; 3471 3472 uint64_t Amt = BitWidth - CI->getZExtValue(); 3473 if (Amt == BitWidth) 3474 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3475 return 3476 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3477 IntegerType::get(getContext(), 3478 Amt)), 3479 U->getType()); 3480 } 3481 break; 3482 3483 case Instruction::Trunc: 3484 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3485 3486 case Instruction::ZExt: 3487 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3488 3489 case Instruction::SExt: 3490 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3491 3492 case Instruction::BitCast: 3493 // BitCasts are no-op casts so we just eliminate the cast. 3494 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3495 return getSCEV(U->getOperand(0)); 3496 break; 3497 3498 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3499 // lead to pointer expressions which cannot safely be expanded to GEPs, 3500 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3501 // simplifying integer expressions. 3502 3503 case Instruction::GetElementPtr: 3504 return createNodeForGEP(cast<GEPOperator>(U)); 3505 3506 case Instruction::PHI: 3507 return createNodeForPHI(cast<PHINode>(U)); 3508 3509 case Instruction::Select: 3510 // This could be a smax or umax that was lowered earlier. 3511 // Try to recover it. 3512 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3513 Value *LHS = ICI->getOperand(0); 3514 Value *RHS = ICI->getOperand(1); 3515 switch (ICI->getPredicate()) { 3516 case ICmpInst::ICMP_SLT: 3517 case ICmpInst::ICMP_SLE: 3518 std::swap(LHS, RHS); 3519 // fall through 3520 case ICmpInst::ICMP_SGT: 3521 case ICmpInst::ICMP_SGE: 3522 // a >s b ? a+x : b+x -> smax(a, b)+x 3523 // a >s b ? b+x : a+x -> smin(a, b)+x 3524 if (LHS->getType() == U->getType()) { 3525 const SCEV *LS = getSCEV(LHS); 3526 const SCEV *RS = getSCEV(RHS); 3527 const SCEV *LA = getSCEV(U->getOperand(1)); 3528 const SCEV *RA = getSCEV(U->getOperand(2)); 3529 const SCEV *LDiff = getMinusSCEV(LA, LS); 3530 const SCEV *RDiff = getMinusSCEV(RA, RS); 3531 if (LDiff == RDiff) 3532 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3533 LDiff = getMinusSCEV(LA, RS); 3534 RDiff = getMinusSCEV(RA, LS); 3535 if (LDiff == RDiff) 3536 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3537 } 3538 break; 3539 case ICmpInst::ICMP_ULT: 3540 case ICmpInst::ICMP_ULE: 3541 std::swap(LHS, RHS); 3542 // fall through 3543 case ICmpInst::ICMP_UGT: 3544 case ICmpInst::ICMP_UGE: 3545 // a >u b ? a+x : b+x -> umax(a, b)+x 3546 // a >u b ? b+x : a+x -> umin(a, b)+x 3547 if (LHS->getType() == U->getType()) { 3548 const SCEV *LS = getSCEV(LHS); 3549 const SCEV *RS = getSCEV(RHS); 3550 const SCEV *LA = getSCEV(U->getOperand(1)); 3551 const SCEV *RA = getSCEV(U->getOperand(2)); 3552 const SCEV *LDiff = getMinusSCEV(LA, LS); 3553 const SCEV *RDiff = getMinusSCEV(RA, RS); 3554 if (LDiff == RDiff) 3555 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3556 LDiff = getMinusSCEV(LA, RS); 3557 RDiff = getMinusSCEV(RA, LS); 3558 if (LDiff == RDiff) 3559 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3560 } 3561 break; 3562 case ICmpInst::ICMP_NE: 3563 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3564 if (LHS->getType() == U->getType() && 3565 isa<ConstantInt>(RHS) && 3566 cast<ConstantInt>(RHS)->isZero()) { 3567 const SCEV *One = getConstant(LHS->getType(), 1); 3568 const SCEV *LS = getSCEV(LHS); 3569 const SCEV *LA = getSCEV(U->getOperand(1)); 3570 const SCEV *RA = getSCEV(U->getOperand(2)); 3571 const SCEV *LDiff = getMinusSCEV(LA, LS); 3572 const SCEV *RDiff = getMinusSCEV(RA, One); 3573 if (LDiff == RDiff) 3574 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3575 } 3576 break; 3577 case ICmpInst::ICMP_EQ: 3578 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3579 if (LHS->getType() == U->getType() && 3580 isa<ConstantInt>(RHS) && 3581 cast<ConstantInt>(RHS)->isZero()) { 3582 const SCEV *One = getConstant(LHS->getType(), 1); 3583 const SCEV *LS = getSCEV(LHS); 3584 const SCEV *LA = getSCEV(U->getOperand(1)); 3585 const SCEV *RA = getSCEV(U->getOperand(2)); 3586 const SCEV *LDiff = getMinusSCEV(LA, One); 3587 const SCEV *RDiff = getMinusSCEV(RA, LS); 3588 if (LDiff == RDiff) 3589 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3590 } 3591 break; 3592 default: 3593 break; 3594 } 3595 } 3596 3597 default: // We cannot analyze this expression. 3598 break; 3599 } 3600 3601 return getUnknown(V); 3602} 3603 3604 3605 3606//===----------------------------------------------------------------------===// 3607// Iteration Count Computation Code 3608// 3609 3610/// getBackedgeTakenCount - If the specified loop has a predictable 3611/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3612/// object. The backedge-taken count is the number of times the loop header 3613/// will be branched to from within the loop. This is one less than the 3614/// trip count of the loop, since it doesn't count the first iteration, 3615/// when the header is branched to from outside the loop. 3616/// 3617/// Note that it is not valid to call this method on a loop without a 3618/// loop-invariant backedge-taken count (see 3619/// hasLoopInvariantBackedgeTakenCount). 3620/// 3621const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3622 return getBackedgeTakenInfo(L).Exact; 3623} 3624 3625/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3626/// return the least SCEV value that is known never to be less than the 3627/// actual backedge taken count. 3628const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3629 return getBackedgeTakenInfo(L).Max; 3630} 3631 3632/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3633/// onto the given Worklist. 3634static void 3635PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3636 BasicBlock *Header = L->getHeader(); 3637 3638 // Push all Loop-header PHIs onto the Worklist stack. 3639 for (BasicBlock::iterator I = Header->begin(); 3640 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3641 Worklist.push_back(PN); 3642} 3643 3644const ScalarEvolution::BackedgeTakenInfo & 3645ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3646 // Initially insert a CouldNotCompute for this loop. If the insertion 3647 // succeeds, proceed to actually compute a backedge-taken count and 3648 // update the value. The temporary CouldNotCompute value tells SCEV 3649 // code elsewhere that it shouldn't attempt to request a new 3650 // backedge-taken count, which could result in infinite recursion. 3651 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3652 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); 3653 if (!Pair.second) 3654 return Pair.first->second; 3655 3656 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); 3657 if (BECount.Exact != getCouldNotCompute()) { 3658 assert(isLoopInvariant(BECount.Exact, L) && 3659 isLoopInvariant(BECount.Max, L) && 3660 "Computed backedge-taken count isn't loop invariant for loop!"); 3661 ++NumTripCountsComputed; 3662 3663 // Update the value in the map. 3664 Pair.first->second = BECount; 3665 } else { 3666 if (BECount.Max != getCouldNotCompute()) 3667 // Update the value in the map. 3668 Pair.first->second = BECount; 3669 if (isa<PHINode>(L->getHeader()->begin())) 3670 // Only count loops that have phi nodes as not being computable. 3671 ++NumTripCountsNotComputed; 3672 } 3673 3674 // Now that we know more about the trip count for this loop, forget any 3675 // existing SCEV values for PHI nodes in this loop since they are only 3676 // conservative estimates made without the benefit of trip count 3677 // information. This is similar to the code in forgetLoop, except that 3678 // it handles SCEVUnknown PHI nodes specially. 3679 if (BECount.hasAnyInfo()) { 3680 SmallVector<Instruction *, 16> Worklist; 3681 PushLoopPHIs(L, Worklist); 3682 3683 SmallPtrSet<Instruction *, 8> Visited; 3684 while (!Worklist.empty()) { 3685 Instruction *I = Worklist.pop_back_val(); 3686 if (!Visited.insert(I)) continue; 3687 3688 ValueExprMapType::iterator It = 3689 ValueExprMap.find(static_cast<Value *>(I)); 3690 if (It != ValueExprMap.end()) { 3691 const SCEV *Old = It->second; 3692 3693 // SCEVUnknown for a PHI either means that it has an unrecognized 3694 // structure, or it's a PHI that's in the progress of being computed 3695 // by createNodeForPHI. In the former case, additional loop trip 3696 // count information isn't going to change anything. In the later 3697 // case, createNodeForPHI will perform the necessary updates on its 3698 // own when it gets to that point. 3699 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3700 forgetMemoizedResults(Old); 3701 ValueExprMap.erase(It); 3702 } 3703 if (PHINode *PN = dyn_cast<PHINode>(I)) 3704 ConstantEvolutionLoopExitValue.erase(PN); 3705 } 3706 3707 PushDefUseChildren(I, Worklist); 3708 } 3709 } 3710 return Pair.first->second; 3711} 3712 3713/// forgetLoop - This method should be called by the client when it has 3714/// changed a loop in a way that may effect ScalarEvolution's ability to 3715/// compute a trip count, or if the loop is deleted. 3716void ScalarEvolution::forgetLoop(const Loop *L) { 3717 // Drop any stored trip count value. 3718 BackedgeTakenCounts.erase(L); 3719 3720 // Drop information about expressions based on loop-header PHIs. 3721 SmallVector<Instruction *, 16> Worklist; 3722 PushLoopPHIs(L, Worklist); 3723 3724 SmallPtrSet<Instruction *, 8> Visited; 3725 while (!Worklist.empty()) { 3726 Instruction *I = Worklist.pop_back_val(); 3727 if (!Visited.insert(I)) continue; 3728 3729 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3730 if (It != ValueExprMap.end()) { 3731 forgetMemoizedResults(It->second); 3732 ValueExprMap.erase(It); 3733 if (PHINode *PN = dyn_cast<PHINode>(I)) 3734 ConstantEvolutionLoopExitValue.erase(PN); 3735 } 3736 3737 PushDefUseChildren(I, Worklist); 3738 } 3739 3740 // Forget all contained loops too, to avoid dangling entries in the 3741 // ValuesAtScopes map. 3742 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 3743 forgetLoop(*I); 3744} 3745 3746/// forgetValue - This method should be called by the client when it has 3747/// changed a value in a way that may effect its value, or which may 3748/// disconnect it from a def-use chain linking it to a loop. 3749void ScalarEvolution::forgetValue(Value *V) { 3750 Instruction *I = dyn_cast<Instruction>(V); 3751 if (!I) return; 3752 3753 // Drop information about expressions based on loop-header PHIs. 3754 SmallVector<Instruction *, 16> Worklist; 3755 Worklist.push_back(I); 3756 3757 SmallPtrSet<Instruction *, 8> Visited; 3758 while (!Worklist.empty()) { 3759 I = Worklist.pop_back_val(); 3760 if (!Visited.insert(I)) continue; 3761 3762 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 3763 if (It != ValueExprMap.end()) { 3764 forgetMemoizedResults(It->second); 3765 ValueExprMap.erase(It); 3766 if (PHINode *PN = dyn_cast<PHINode>(I)) 3767 ConstantEvolutionLoopExitValue.erase(PN); 3768 } 3769 3770 PushDefUseChildren(I, Worklist); 3771 } 3772} 3773 3774/// ComputeBackedgeTakenCount - Compute the number of times the backedge 3775/// of the specified loop will execute. 3776ScalarEvolution::BackedgeTakenInfo 3777ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 3778 SmallVector<BasicBlock *, 8> ExitingBlocks; 3779 L->getExitingBlocks(ExitingBlocks); 3780 3781 // Examine all exits and pick the most conservative values. 3782 const SCEV *BECount = getCouldNotCompute(); 3783 const SCEV *MaxBECount = getCouldNotCompute(); 3784 bool CouldNotComputeBECount = false; 3785 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 3786 BackedgeTakenInfo NewBTI = 3787 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); 3788 3789 if (NewBTI.Exact == getCouldNotCompute()) { 3790 // We couldn't compute an exact value for this exit, so 3791 // we won't be able to compute an exact value for the loop. 3792 CouldNotComputeBECount = true; 3793 BECount = getCouldNotCompute(); 3794 } else if (!CouldNotComputeBECount) { 3795 if (BECount == getCouldNotCompute()) 3796 BECount = NewBTI.Exact; 3797 else 3798 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); 3799 } 3800 if (MaxBECount == getCouldNotCompute()) 3801 MaxBECount = NewBTI.Max; 3802 else if (NewBTI.Max != getCouldNotCompute()) 3803 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); 3804 } 3805 3806 return BackedgeTakenInfo(BECount, MaxBECount); 3807} 3808 3809/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge 3810/// of the specified loop will execute if it exits via the specified block. 3811ScalarEvolution::BackedgeTakenInfo 3812ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, 3813 BasicBlock *ExitingBlock) { 3814 3815 // Okay, we've chosen an exiting block. See what condition causes us to 3816 // exit at this block. 3817 // 3818 // FIXME: we should be able to handle switch instructions (with a single exit) 3819 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 3820 if (ExitBr == 0) return getCouldNotCompute(); 3821 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 3822 3823 // At this point, we know we have a conditional branch that determines whether 3824 // the loop is exited. However, we don't know if the branch is executed each 3825 // time through the loop. If not, then the execution count of the branch will 3826 // not be equal to the trip count of the loop. 3827 // 3828 // Currently we check for this by checking to see if the Exit branch goes to 3829 // the loop header. If so, we know it will always execute the same number of 3830 // times as the loop. We also handle the case where the exit block *is* the 3831 // loop header. This is common for un-rotated loops. 3832 // 3833 // If both of those tests fail, walk up the unique predecessor chain to the 3834 // header, stopping if there is an edge that doesn't exit the loop. If the 3835 // header is reached, the execution count of the branch will be equal to the 3836 // trip count of the loop. 3837 // 3838 // More extensive analysis could be done to handle more cases here. 3839 // 3840 if (ExitBr->getSuccessor(0) != L->getHeader() && 3841 ExitBr->getSuccessor(1) != L->getHeader() && 3842 ExitBr->getParent() != L->getHeader()) { 3843 // The simple checks failed, try climbing the unique predecessor chain 3844 // up to the header. 3845 bool Ok = false; 3846 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 3847 BasicBlock *Pred = BB->getUniquePredecessor(); 3848 if (!Pred) 3849 return getCouldNotCompute(); 3850 TerminatorInst *PredTerm = Pred->getTerminator(); 3851 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 3852 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 3853 if (PredSucc == BB) 3854 continue; 3855 // If the predecessor has a successor that isn't BB and isn't 3856 // outside the loop, assume the worst. 3857 if (L->contains(PredSucc)) 3858 return getCouldNotCompute(); 3859 } 3860 if (Pred == L->getHeader()) { 3861 Ok = true; 3862 break; 3863 } 3864 BB = Pred; 3865 } 3866 if (!Ok) 3867 return getCouldNotCompute(); 3868 } 3869 3870 // Proceed to the next level to examine the exit condition expression. 3871 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), 3872 ExitBr->getSuccessor(0), 3873 ExitBr->getSuccessor(1)); 3874} 3875 3876/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the 3877/// backedge of the specified loop will execute if its exit condition 3878/// were a conditional branch of ExitCond, TBB, and FBB. 3879ScalarEvolution::BackedgeTakenInfo 3880ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, 3881 Value *ExitCond, 3882 BasicBlock *TBB, 3883 BasicBlock *FBB) { 3884 // Check if the controlling expression for this loop is an And or Or. 3885 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 3886 if (BO->getOpcode() == Instruction::And) { 3887 // Recurse on the operands of the and. 3888 BackedgeTakenInfo BTI0 = 3889 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3890 BackedgeTakenInfo BTI1 = 3891 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3892 const SCEV *BECount = getCouldNotCompute(); 3893 const SCEV *MaxBECount = getCouldNotCompute(); 3894 if (L->contains(TBB)) { 3895 // Both conditions must be true for the loop to continue executing. 3896 // Choose the less conservative count. 3897 if (BTI0.Exact == getCouldNotCompute() || 3898 BTI1.Exact == getCouldNotCompute()) 3899 BECount = getCouldNotCompute(); 3900 else 3901 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3902 if (BTI0.Max == getCouldNotCompute()) 3903 MaxBECount = BTI1.Max; 3904 else if (BTI1.Max == getCouldNotCompute()) 3905 MaxBECount = BTI0.Max; 3906 else 3907 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3908 } else { 3909 // Both conditions must be true at the same time for the loop to exit. 3910 // For now, be conservative. 3911 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 3912 if (BTI0.Max == BTI1.Max) 3913 MaxBECount = BTI0.Max; 3914 if (BTI0.Exact == BTI1.Exact) 3915 BECount = BTI0.Exact; 3916 } 3917 3918 return BackedgeTakenInfo(BECount, MaxBECount); 3919 } 3920 if (BO->getOpcode() == Instruction::Or) { 3921 // Recurse on the operands of the or. 3922 BackedgeTakenInfo BTI0 = 3923 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); 3924 BackedgeTakenInfo BTI1 = 3925 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); 3926 const SCEV *BECount = getCouldNotCompute(); 3927 const SCEV *MaxBECount = getCouldNotCompute(); 3928 if (L->contains(FBB)) { 3929 // Both conditions must be false for the loop to continue executing. 3930 // Choose the less conservative count. 3931 if (BTI0.Exact == getCouldNotCompute() || 3932 BTI1.Exact == getCouldNotCompute()) 3933 BECount = getCouldNotCompute(); 3934 else 3935 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); 3936 if (BTI0.Max == getCouldNotCompute()) 3937 MaxBECount = BTI1.Max; 3938 else if (BTI1.Max == getCouldNotCompute()) 3939 MaxBECount = BTI0.Max; 3940 else 3941 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); 3942 } else { 3943 // Both conditions must be false at the same time for the loop to exit. 3944 // For now, be conservative. 3945 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 3946 if (BTI0.Max == BTI1.Max) 3947 MaxBECount = BTI0.Max; 3948 if (BTI0.Exact == BTI1.Exact) 3949 BECount = BTI0.Exact; 3950 } 3951 3952 return BackedgeTakenInfo(BECount, MaxBECount); 3953 } 3954 } 3955 3956 // With an icmp, it may be feasible to compute an exact backedge-taken count. 3957 // Proceed to the next level to examine the icmp. 3958 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 3959 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); 3960 3961 // Check for a constant condition. These are normally stripped out by 3962 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 3963 // preserve the CFG and is temporarily leaving constant conditions 3964 // in place. 3965 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 3966 if (L->contains(FBB) == !CI->getZExtValue()) 3967 // The backedge is always taken. 3968 return getCouldNotCompute(); 3969 else 3970 // The backedge is never taken. 3971 return getConstant(CI->getType(), 0); 3972 } 3973 3974 // If it's not an integer or pointer comparison then compute it the hard way. 3975 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 3976} 3977 3978static const SCEVAddRecExpr * 3979isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) { 3980 const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S); 3981 3982 // The SCEV must be an addrec of this loop. 3983 if (!SA || SA->getLoop() != L || !SA->isAffine()) 3984 return 0; 3985 3986 // The SCEV must be known to not wrap in some way to be interesting. 3987 if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap()) 3988 return 0; 3989 3990 // The stride must be a constant so that we know if it is striding up or down. 3991 if (!isa<SCEVConstant>(SA->getOperand(1))) 3992 return 0; 3993 return SA; 3994} 3995 3996/// getMinusSCEVForExitTest - When considering an exit test for a loop with a 3997/// "x != y" exit test, we turn this into a computation that evaluates x-y != 0, 3998/// and this function returns the expression to use for x-y. We know and take 3999/// advantage of the fact that this subtraction is only being used in a 4000/// comparison by zero context. 4001/// 4002static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS, 4003 const Loop *L, ScalarEvolution &SE) { 4004 // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not 4005 // wrap (either NSW or NUW), then we know that the value will either become 4006 // the other one (and thus the loop terminates), that the loop will terminate 4007 // through some other exit condition first, or that the loop has undefined 4008 // behavior. This information is useful when the addrec has a stride that is 4009 // != 1 or -1, because it means we can't "miss" the exit value. 4010 // 4011 // In any of these three cases, it is safe to turn the exit condition into a 4012 // "counting down" AddRec (to zero) by subtracting the two inputs as normal, 4013 // but since we know that the "end cannot be missed" we can force the 4014 // resulting AddRec to be a NUW addrec. Since it is counting down, this means 4015 // that the AddRec *cannot* pass zero. 4016 4017 // See if LHS and RHS are addrec's we can handle. 4018 const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L); 4019 const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L); 4020 4021 // If neither addrec is interesting, just return a minus. 4022 if (RHSA == 0 && LHSA == 0) 4023 return SE.getMinusSCEV(LHS, RHS); 4024 4025 // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS. 4026 if (RHSA && LHSA == 0) { 4027 // Safe because a-b === b-a for comparisons against zero. 4028 std::swap(LHS, RHS); 4029 std::swap(LHSA, RHSA); 4030 } 4031 4032 // Handle the case when only one is advancing in a non-overflowing way. 4033 if (RHSA == 0) { 4034 // If RHS is loop varying, then we can't predict when LHS will cross it. 4035 if (!SE.isLoopInvariant(RHS, L)) 4036 return SE.getMinusSCEV(LHS, RHS); 4037 4038 // If LHS has a positive stride, then we compute RHS-LHS, because the loop 4039 // is counting up until it crosses RHS (which must be larger than LHS). If 4040 // it is negative, we compute LHS-RHS because we're counting down to RHS. 4041 const ConstantInt *Stride = 4042 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4043 if (Stride->getValue().isNegative()) 4044 std::swap(LHS, RHS); 4045 4046 return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/); 4047 } 4048 4049 // If both LHS and RHS are interesting, we have something like: 4050 // a+i*4 != b+i*8. 4051 const ConstantInt *LHSStride = 4052 cast<SCEVConstant>(LHSA->getOperand(1))->getValue(); 4053 const ConstantInt *RHSStride = 4054 cast<SCEVConstant>(RHSA->getOperand(1))->getValue(); 4055 4056 // If the strides are equal, then this is just a (complex) loop invariant 4057 // comparison of a and b. 4058 if (LHSStride == RHSStride) 4059 return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart()); 4060 4061 // If the signs of the strides differ, then the negative stride is counting 4062 // down to the positive stride. 4063 if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){ 4064 if (RHSStride->getValue().isNegative()) 4065 std::swap(LHS, RHS); 4066 } else { 4067 // If LHS's stride is smaller than RHS's stride, then "b" must be less than 4068 // "a" and "b" is RHS is counting up (catching up) to LHS. This is true 4069 // whether the strides are positive or negative. 4070 if (RHSStride->getValue().slt(LHSStride->getValue())) 4071 std::swap(LHS, RHS); 4072 } 4073 4074 return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/); 4075} 4076 4077/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the 4078/// backedge of the specified loop will execute if its exit condition 4079/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4080ScalarEvolution::BackedgeTakenInfo 4081ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, 4082 ICmpInst *ExitCond, 4083 BasicBlock *TBB, 4084 BasicBlock *FBB) { 4085 4086 // If the condition was exit on true, convert the condition to exit on false 4087 ICmpInst::Predicate Cond; 4088 if (!L->contains(FBB)) 4089 Cond = ExitCond->getPredicate(); 4090 else 4091 Cond = ExitCond->getInversePredicate(); 4092 4093 // Handle common loops like: for (X = "string"; *X; ++X) 4094 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4095 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4096 BackedgeTakenInfo ItCnt = 4097 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); 4098 if (ItCnt.hasAnyInfo()) 4099 return ItCnt; 4100 } 4101 4102 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4103 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4104 4105 // Try to evaluate any dependencies out of the loop. 4106 LHS = getSCEVAtScope(LHS, L); 4107 RHS = getSCEVAtScope(RHS, L); 4108 4109 // At this point, we would like to compute how many iterations of the 4110 // loop the predicate will return true for these inputs. 4111 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4112 // If there is a loop-invariant, force it into the RHS. 4113 std::swap(LHS, RHS); 4114 Cond = ICmpInst::getSwappedPredicate(Cond); 4115 } 4116 4117 // Simplify the operands before analyzing them. 4118 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4119 4120 // If we have a comparison of a chrec against a constant, try to use value 4121 // ranges to answer this query. 4122 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4123 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4124 if (AddRec->getLoop() == L) { 4125 // Form the constant range. 4126 ConstantRange CompRange( 4127 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4128 4129 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4130 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4131 } 4132 4133 switch (Cond) { 4134 case ICmpInst::ICMP_NE: { // while (X != Y) 4135 // Convert to: while (X-Y != 0) 4136 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L, 4137 *this), L); 4138 if (BTI.hasAnyInfo()) return BTI; 4139 break; 4140 } 4141 case ICmpInst::ICMP_EQ: { // while (X == Y) 4142 // Convert to: while (X-Y == 0) 4143 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4144 if (BTI.hasAnyInfo()) return BTI; 4145 break; 4146 } 4147 case ICmpInst::ICMP_SLT: { 4148 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); 4149 if (BTI.hasAnyInfo()) return BTI; 4150 break; 4151 } 4152 case ICmpInst::ICMP_SGT: { 4153 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4154 getNotSCEV(RHS), L, true); 4155 if (BTI.hasAnyInfo()) return BTI; 4156 break; 4157 } 4158 case ICmpInst::ICMP_ULT: { 4159 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); 4160 if (BTI.hasAnyInfo()) return BTI; 4161 break; 4162 } 4163 case ICmpInst::ICMP_UGT: { 4164 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), 4165 getNotSCEV(RHS), L, false); 4166 if (BTI.hasAnyInfo()) return BTI; 4167 break; 4168 } 4169 default: 4170#if 0 4171 dbgs() << "ComputeBackedgeTakenCount "; 4172 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4173 dbgs() << "[unsigned] "; 4174 dbgs() << *LHS << " " 4175 << Instruction::getOpcodeName(Instruction::ICmp) 4176 << " " << *RHS << "\n"; 4177#endif 4178 break; 4179 } 4180 return 4181 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); 4182} 4183 4184static ConstantInt * 4185EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4186 ScalarEvolution &SE) { 4187 const SCEV *InVal = SE.getConstant(C); 4188 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4189 assert(isa<SCEVConstant>(Val) && 4190 "Evaluation of SCEV at constant didn't fold correctly?"); 4191 return cast<SCEVConstant>(Val)->getValue(); 4192} 4193 4194/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4195/// and a GEP expression (missing the pointer index) indexing into it, return 4196/// the addressed element of the initializer or null if the index expression is 4197/// invalid. 4198static Constant * 4199GetAddressedElementFromGlobal(GlobalVariable *GV, 4200 const std::vector<ConstantInt*> &Indices) { 4201 Constant *Init = GV->getInitializer(); 4202 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4203 uint64_t Idx = Indices[i]->getZExtValue(); 4204 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4205 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4206 Init = cast<Constant>(CS->getOperand(Idx)); 4207 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4208 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4209 Init = cast<Constant>(CA->getOperand(Idx)); 4210 } else if (isa<ConstantAggregateZero>(Init)) { 4211 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { 4212 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4213 Init = Constant::getNullValue(STy->getElementType(Idx)); 4214 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4215 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4216 Init = Constant::getNullValue(ATy->getElementType()); 4217 } else { 4218 llvm_unreachable("Unknown constant aggregate type!"); 4219 } 4220 return 0; 4221 } else { 4222 return 0; // Unknown initializer type 4223 } 4224 } 4225 return Init; 4226} 4227 4228/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of 4229/// 'icmp op load X, cst', try to see if we can compute the backedge 4230/// execution count. 4231ScalarEvolution::BackedgeTakenInfo 4232ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( 4233 LoadInst *LI, 4234 Constant *RHS, 4235 const Loop *L, 4236 ICmpInst::Predicate predicate) { 4237 if (LI->isVolatile()) return getCouldNotCompute(); 4238 4239 // Check to see if the loaded pointer is a getelementptr of a global. 4240 // TODO: Use SCEV instead of manually grubbing with GEPs. 4241 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4242 if (!GEP) return getCouldNotCompute(); 4243 4244 // Make sure that it is really a constant global we are gepping, with an 4245 // initializer, and make sure the first IDX is really 0. 4246 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4247 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4248 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4249 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4250 return getCouldNotCompute(); 4251 4252 // Okay, we allow one non-constant index into the GEP instruction. 4253 Value *VarIdx = 0; 4254 std::vector<ConstantInt*> Indexes; 4255 unsigned VarIdxNum = 0; 4256 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4257 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4258 Indexes.push_back(CI); 4259 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4260 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4261 VarIdx = GEP->getOperand(i); 4262 VarIdxNum = i-2; 4263 Indexes.push_back(0); 4264 } 4265 4266 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4267 // Check to see if X is a loop variant variable value now. 4268 const SCEV *Idx = getSCEV(VarIdx); 4269 Idx = getSCEVAtScope(Idx, L); 4270 4271 // We can only recognize very limited forms of loop index expressions, in 4272 // particular, only affine AddRec's like {C1,+,C2}. 4273 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4274 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4275 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4276 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4277 return getCouldNotCompute(); 4278 4279 unsigned MaxSteps = MaxBruteForceIterations; 4280 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4281 ConstantInt *ItCst = ConstantInt::get( 4282 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4283 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4284 4285 // Form the GEP offset. 4286 Indexes[VarIdxNum] = Val; 4287 4288 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4289 if (Result == 0) break; // Cannot compute! 4290 4291 // Evaluate the condition for this iteration. 4292 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4293 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4294 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4295#if 0 4296 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4297 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4298 << "***\n"; 4299#endif 4300 ++NumArrayLenItCounts; 4301 return getConstant(ItCst); // Found terminating iteration! 4302 } 4303 } 4304 return getCouldNotCompute(); 4305} 4306 4307 4308/// CanConstantFold - Return true if we can constant fold an instruction of the 4309/// specified type, assuming that all operands were constants. 4310static bool CanConstantFold(const Instruction *I) { 4311 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4312 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4313 return true; 4314 4315 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4316 if (const Function *F = CI->getCalledFunction()) 4317 return canConstantFoldCallTo(F); 4318 return false; 4319} 4320 4321/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4322/// in the loop that V is derived from. We allow arbitrary operations along the 4323/// way, but the operands of an operation must either be constants or a value 4324/// derived from a constant PHI. If this expression does not fit with these 4325/// constraints, return null. 4326static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4327 // If this is not an instruction, or if this is an instruction outside of the 4328 // loop, it can't be derived from a loop PHI. 4329 Instruction *I = dyn_cast<Instruction>(V); 4330 if (I == 0 || !L->contains(I)) return 0; 4331 4332 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4333 if (L->getHeader() == I->getParent()) 4334 return PN; 4335 else 4336 // We don't currently keep track of the control flow needed to evaluate 4337 // PHIs, so we cannot handle PHIs inside of loops. 4338 return 0; 4339 } 4340 4341 // If we won't be able to constant fold this expression even if the operands 4342 // are constants, return early. 4343 if (!CanConstantFold(I)) return 0; 4344 4345 // Otherwise, we can evaluate this instruction if all of its operands are 4346 // constant or derived from a PHI node themselves. 4347 PHINode *PHI = 0; 4348 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4349 if (!isa<Constant>(I->getOperand(Op))) { 4350 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4351 if (P == 0) return 0; // Not evolving from PHI 4352 if (PHI == 0) 4353 PHI = P; 4354 else if (PHI != P) 4355 return 0; // Evolving from multiple different PHIs. 4356 } 4357 4358 // This is a expression evolving from a constant PHI! 4359 return PHI; 4360} 4361 4362/// EvaluateExpression - Given an expression that passes the 4363/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4364/// in the loop has the value PHIVal. If we can't fold this expression for some 4365/// reason, return null. 4366static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4367 const TargetData *TD) { 4368 if (isa<PHINode>(V)) return PHIVal; 4369 if (Constant *C = dyn_cast<Constant>(V)) return C; 4370 Instruction *I = cast<Instruction>(V); 4371 4372 std::vector<Constant*> Operands(I->getNumOperands()); 4373 4374 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4375 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4376 if (Operands[i] == 0) return 0; 4377 } 4378 4379 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4380 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4381 Operands[1], TD); 4382 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4383 &Operands[0], Operands.size(), TD); 4384} 4385 4386/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4387/// in the header of its containing loop, we know the loop executes a 4388/// constant number of times, and the PHI node is just a recurrence 4389/// involving constants, fold it. 4390Constant * 4391ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4392 const APInt &BEs, 4393 const Loop *L) { 4394 std::map<PHINode*, Constant*>::const_iterator I = 4395 ConstantEvolutionLoopExitValue.find(PN); 4396 if (I != ConstantEvolutionLoopExitValue.end()) 4397 return I->second; 4398 4399 if (BEs.ugt(MaxBruteForceIterations)) 4400 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4401 4402 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4403 4404 // Since the loop is canonicalized, the PHI node must have two entries. One 4405 // entry must be a constant (coming in from outside of the loop), and the 4406 // second must be derived from the same PHI. 4407 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4408 Constant *StartCST = 4409 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4410 if (StartCST == 0) 4411 return RetVal = 0; // Must be a constant. 4412 4413 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4414 if (getConstantEvolvingPHI(BEValue, L) != PN && 4415 !isa<Constant>(BEValue)) 4416 return RetVal = 0; // Not derived from same PHI. 4417 4418 // Execute the loop symbolically to determine the exit value. 4419 if (BEs.getActiveBits() >= 32) 4420 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4421 4422 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4423 unsigned IterationNum = 0; 4424 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4425 if (IterationNum == NumIterations) 4426 return RetVal = PHIVal; // Got exit value! 4427 4428 // Compute the value of the PHI node for the next iteration. 4429 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4430 if (NextPHI == PHIVal) 4431 return RetVal = NextPHI; // Stopped evolving! 4432 if (NextPHI == 0) 4433 return 0; // Couldn't evaluate! 4434 PHIVal = NextPHI; 4435 } 4436} 4437 4438/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a 4439/// constant number of times (the condition evolves only from constants), 4440/// try to evaluate a few iterations of the loop until we get the exit 4441/// condition gets a value of ExitWhen (true or false). If we cannot 4442/// evaluate the trip count of the loop, return getCouldNotCompute(). 4443const SCEV * 4444ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, 4445 Value *Cond, 4446 bool ExitWhen) { 4447 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4448 if (PN == 0) return getCouldNotCompute(); 4449 4450 // If the loop is canonicalized, the PHI will have exactly two entries. 4451 // That's the only form we support here. 4452 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4453 4454 // One entry must be a constant (coming in from outside of the loop), and the 4455 // second must be derived from the same PHI. 4456 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4457 Constant *StartCST = 4458 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4459 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4460 4461 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4462 if (getConstantEvolvingPHI(BEValue, L) != PN && 4463 !isa<Constant>(BEValue)) 4464 return getCouldNotCompute(); // Not derived from same PHI. 4465 4466 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4467 // the loop symbolically to determine when the condition gets a value of 4468 // "ExitWhen". 4469 unsigned IterationNum = 0; 4470 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4471 for (Constant *PHIVal = StartCST; 4472 IterationNum != MaxIterations; ++IterationNum) { 4473 ConstantInt *CondVal = 4474 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4475 4476 // Couldn't symbolically evaluate. 4477 if (!CondVal) return getCouldNotCompute(); 4478 4479 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4480 ++NumBruteForceTripCountsComputed; 4481 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4482 } 4483 4484 // Compute the value of the PHI node for the next iteration. 4485 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4486 if (NextPHI == 0 || NextPHI == PHIVal) 4487 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4488 PHIVal = NextPHI; 4489 } 4490 4491 // Too many iterations were needed to evaluate. 4492 return getCouldNotCompute(); 4493} 4494 4495/// getSCEVAtScope - Return a SCEV expression for the specified value 4496/// at the specified scope in the program. The L value specifies a loop 4497/// nest to evaluate the expression at, where null is the top-level or a 4498/// specified loop is immediately inside of the loop. 4499/// 4500/// This method can be used to compute the exit value for a variable defined 4501/// in a loop by querying what the value will hold in the parent loop. 4502/// 4503/// In the case that a relevant loop exit value cannot be computed, the 4504/// original value V is returned. 4505const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4506 // Check to see if we've folded this expression at this loop before. 4507 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4508 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4509 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4510 if (!Pair.second) 4511 return Pair.first->second ? Pair.first->second : V; 4512 4513 // Otherwise compute it. 4514 const SCEV *C = computeSCEVAtScope(V, L); 4515 ValuesAtScopes[V][L] = C; 4516 return C; 4517} 4518 4519const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4520 if (isa<SCEVConstant>(V)) return V; 4521 4522 // If this instruction is evolved from a constant-evolving PHI, compute the 4523 // exit value from the loop without using SCEVs. 4524 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4525 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4526 const Loop *LI = (*this->LI)[I->getParent()]; 4527 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4528 if (PHINode *PN = dyn_cast<PHINode>(I)) 4529 if (PN->getParent() == LI->getHeader()) { 4530 // Okay, there is no closed form solution for the PHI node. Check 4531 // to see if the loop that contains it has a known backedge-taken 4532 // count. If so, we may be able to force computation of the exit 4533 // value. 4534 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4535 if (const SCEVConstant *BTCC = 4536 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4537 // Okay, we know how many times the containing loop executes. If 4538 // this is a constant evolving PHI node, get the final value at 4539 // the specified iteration number. 4540 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4541 BTCC->getValue()->getValue(), 4542 LI); 4543 if (RV) return getSCEV(RV); 4544 } 4545 } 4546 4547 // Okay, this is an expression that we cannot symbolically evaluate 4548 // into a SCEV. Check to see if it's possible to symbolically evaluate 4549 // the arguments into constants, and if so, try to constant propagate the 4550 // result. This is particularly useful for computing loop exit values. 4551 if (CanConstantFold(I)) { 4552 SmallVector<Constant *, 4> Operands; 4553 bool MadeImprovement = false; 4554 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4555 Value *Op = I->getOperand(i); 4556 if (Constant *C = dyn_cast<Constant>(Op)) { 4557 Operands.push_back(C); 4558 continue; 4559 } 4560 4561 // If any of the operands is non-constant and if they are 4562 // non-integer and non-pointer, don't even try to analyze them 4563 // with scev techniques. 4564 if (!isSCEVable(Op->getType())) 4565 return V; 4566 4567 const SCEV *OrigV = getSCEV(Op); 4568 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4569 MadeImprovement |= OrigV != OpV; 4570 4571 Constant *C = 0; 4572 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4573 C = SC->getValue(); 4574 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4575 C = dyn_cast<Constant>(SU->getValue()); 4576 if (!C) return V; 4577 if (C->getType() != Op->getType()) 4578 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4579 Op->getType(), 4580 false), 4581 C, Op->getType()); 4582 Operands.push_back(C); 4583 } 4584 4585 // Check to see if getSCEVAtScope actually made an improvement. 4586 if (MadeImprovement) { 4587 Constant *C = 0; 4588 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4589 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4590 Operands[0], Operands[1], TD); 4591 else 4592 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4593 &Operands[0], Operands.size(), TD); 4594 if (!C) return V; 4595 return getSCEV(C); 4596 } 4597 } 4598 } 4599 4600 // This is some other type of SCEVUnknown, just return it. 4601 return V; 4602 } 4603 4604 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4605 // Avoid performing the look-up in the common case where the specified 4606 // expression has no loop-variant portions. 4607 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4608 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4609 if (OpAtScope != Comm->getOperand(i)) { 4610 // Okay, at least one of these operands is loop variant but might be 4611 // foldable. Build a new instance of the folded commutative expression. 4612 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4613 Comm->op_begin()+i); 4614 NewOps.push_back(OpAtScope); 4615 4616 for (++i; i != e; ++i) { 4617 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4618 NewOps.push_back(OpAtScope); 4619 } 4620 if (isa<SCEVAddExpr>(Comm)) 4621 return getAddExpr(NewOps); 4622 if (isa<SCEVMulExpr>(Comm)) 4623 return getMulExpr(NewOps); 4624 if (isa<SCEVSMaxExpr>(Comm)) 4625 return getSMaxExpr(NewOps); 4626 if (isa<SCEVUMaxExpr>(Comm)) 4627 return getUMaxExpr(NewOps); 4628 llvm_unreachable("Unknown commutative SCEV type!"); 4629 } 4630 } 4631 // If we got here, all operands are loop invariant. 4632 return Comm; 4633 } 4634 4635 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4636 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4637 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4638 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4639 return Div; // must be loop invariant 4640 return getUDivExpr(LHS, RHS); 4641 } 4642 4643 // If this is a loop recurrence for a loop that does not contain L, then we 4644 // are dealing with the final value computed by the loop. 4645 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4646 // First, attempt to evaluate each operand. 4647 // Avoid performing the look-up in the common case where the specified 4648 // expression has no loop-variant portions. 4649 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4650 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4651 if (OpAtScope == AddRec->getOperand(i)) 4652 continue; 4653 4654 // Okay, at least one of these operands is loop variant but might be 4655 // foldable. Build a new instance of the folded commutative expression. 4656 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4657 AddRec->op_begin()+i); 4658 NewOps.push_back(OpAtScope); 4659 for (++i; i != e; ++i) 4660 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4661 4662 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop())); 4663 break; 4664 } 4665 4666 // If the scope is outside the addrec's loop, evaluate it by using the 4667 // loop exit value of the addrec. 4668 if (!AddRec->getLoop()->contains(L)) { 4669 // To evaluate this recurrence, we need to know how many times the AddRec 4670 // loop iterates. Compute this now. 4671 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4672 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4673 4674 // Then, evaluate the AddRec. 4675 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4676 } 4677 4678 return AddRec; 4679 } 4680 4681 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4682 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4683 if (Op == Cast->getOperand()) 4684 return Cast; // must be loop invariant 4685 return getZeroExtendExpr(Op, Cast->getType()); 4686 } 4687 4688 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4689 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4690 if (Op == Cast->getOperand()) 4691 return Cast; // must be loop invariant 4692 return getSignExtendExpr(Op, Cast->getType()); 4693 } 4694 4695 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4696 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4697 if (Op == Cast->getOperand()) 4698 return Cast; // must be loop invariant 4699 return getTruncateExpr(Op, Cast->getType()); 4700 } 4701 4702 llvm_unreachable("Unknown SCEV type!"); 4703 return 0; 4704} 4705 4706/// getSCEVAtScope - This is a convenience function which does 4707/// getSCEVAtScope(getSCEV(V), L). 4708const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4709 return getSCEVAtScope(getSCEV(V), L); 4710} 4711 4712/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4713/// following equation: 4714/// 4715/// A * X = B (mod N) 4716/// 4717/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4718/// A and B isn't important. 4719/// 4720/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4721static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 4722 ScalarEvolution &SE) { 4723 uint32_t BW = A.getBitWidth(); 4724 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 4725 assert(A != 0 && "A must be non-zero."); 4726 4727 // 1. D = gcd(A, N) 4728 // 4729 // The gcd of A and N may have only one prime factor: 2. The number of 4730 // trailing zeros in A is its multiplicity 4731 uint32_t Mult2 = A.countTrailingZeros(); 4732 // D = 2^Mult2 4733 4734 // 2. Check if B is divisible by D. 4735 // 4736 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 4737 // is not less than multiplicity of this prime factor for D. 4738 if (B.countTrailingZeros() < Mult2) 4739 return SE.getCouldNotCompute(); 4740 4741 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 4742 // modulo (N / D). 4743 // 4744 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 4745 // bit width during computations. 4746 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 4747 APInt Mod(BW + 1, 0); 4748 Mod.setBit(BW - Mult2); // Mod = N / D 4749 APInt I = AD.multiplicativeInverse(Mod); 4750 4751 // 4. Compute the minimum unsigned root of the equation: 4752 // I * (B / D) mod (N / D) 4753 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 4754 4755 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 4756 // bits. 4757 return SE.getConstant(Result.trunc(BW)); 4758} 4759 4760/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 4761/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 4762/// might be the same) or two SCEVCouldNotCompute objects. 4763/// 4764static std::pair<const SCEV *,const SCEV *> 4765SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 4766 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 4767 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 4768 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 4769 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 4770 4771 // We currently can only solve this if the coefficients are constants. 4772 if (!LC || !MC || !NC) { 4773 const SCEV *CNC = SE.getCouldNotCompute(); 4774 return std::make_pair(CNC, CNC); 4775 } 4776 4777 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 4778 const APInt &L = LC->getValue()->getValue(); 4779 const APInt &M = MC->getValue()->getValue(); 4780 const APInt &N = NC->getValue()->getValue(); 4781 APInt Two(BitWidth, 2); 4782 APInt Four(BitWidth, 4); 4783 4784 { 4785 using namespace APIntOps; 4786 const APInt& C = L; 4787 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 4788 // The B coefficient is M-N/2 4789 APInt B(M); 4790 B -= sdiv(N,Two); 4791 4792 // The A coefficient is N/2 4793 APInt A(N.sdiv(Two)); 4794 4795 // Compute the B^2-4ac term. 4796 APInt SqrtTerm(B); 4797 SqrtTerm *= B; 4798 SqrtTerm -= Four * (A * C); 4799 4800 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 4801 // integer value or else APInt::sqrt() will assert. 4802 APInt SqrtVal(SqrtTerm.sqrt()); 4803 4804 // Compute the two solutions for the quadratic formula. 4805 // The divisions must be performed as signed divisions. 4806 APInt NegB(-B); 4807 APInt TwoA( A << 1 ); 4808 if (TwoA.isMinValue()) { 4809 const SCEV *CNC = SE.getCouldNotCompute(); 4810 return std::make_pair(CNC, CNC); 4811 } 4812 4813 LLVMContext &Context = SE.getContext(); 4814 4815 ConstantInt *Solution1 = 4816 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 4817 ConstantInt *Solution2 = 4818 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 4819 4820 return std::make_pair(SE.getConstant(Solution1), 4821 SE.getConstant(Solution2)); 4822 } // end APIntOps namespace 4823} 4824 4825/// HowFarToZero - Return the number of times a backedge comparing the specified 4826/// value to zero will execute. If not computable, return CouldNotCompute. 4827ScalarEvolution::BackedgeTakenInfo 4828ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 4829 // If the value is a constant 4830 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4831 // If the value is already zero, the branch will execute zero times. 4832 if (C->getValue()->isZero()) return C; 4833 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4834 } 4835 4836 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 4837 if (!AddRec || AddRec->getLoop() != L) 4838 return getCouldNotCompute(); 4839 4840 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 4841 // the quadratic equation to solve it. 4842 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 4843 std::pair<const SCEV *,const SCEV *> Roots = 4844 SolveQuadraticEquation(AddRec, *this); 4845 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 4846 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 4847 if (R1 && R2) { 4848#if 0 4849 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 4850 << " sol#2: " << *R2 << "\n"; 4851#endif 4852 // Pick the smallest positive root value. 4853 if (ConstantInt *CB = 4854 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 4855 R1->getValue(), 4856 R2->getValue()))) { 4857 if (CB->getZExtValue() == false) 4858 std::swap(R1, R2); // R1 is the minimum root now. 4859 4860 // We can only use this value if the chrec ends up with an exact zero 4861 // value at this index. When solving for "X*X != 5", for example, we 4862 // should not accept a root of 2. 4863 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 4864 if (Val->isZero()) 4865 return R1; // We found a quadratic root! 4866 } 4867 } 4868 return getCouldNotCompute(); 4869 } 4870 4871 // Otherwise we can only handle this if it is affine. 4872 if (!AddRec->isAffine()) 4873 return getCouldNotCompute(); 4874 4875 // If this is an affine expression, the execution count of this branch is 4876 // the minimum unsigned root of the following equation: 4877 // 4878 // Start + Step*N = 0 (mod 2^BW) 4879 // 4880 // equivalent to: 4881 // 4882 // Step*N = -Start (mod 2^BW) 4883 // 4884 // where BW is the common bit width of Start and Step. 4885 4886 // Get the initial value for the loop. 4887 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 4888 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 4889 4890 // If the AddRec is NUW, then (in an unsigned sense) it cannot be counting up 4891 // to wrap to 0, it must be counting down to equal 0. Also, while counting 4892 // down, it cannot "miss" 0 (which would cause it to wrap), regardless of what 4893 // the stride is. As such, NUW addrec's will always become zero in 4894 // "start / -stride" steps, and we know that the division is exact. 4895 if (AddRec->hasNoUnsignedWrap()) 4896 // FIXME: We really want an "isexact" bit for udiv. 4897 return getUDivExpr(Start, getNegativeSCEV(Step)); 4898 4899 // For now we handle only constant steps. 4900 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 4901 if (StepC == 0) 4902 return getCouldNotCompute(); 4903 4904 // First, handle unitary steps. 4905 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: 4906 return getNegativeSCEV(Start); // N = -Start (as unsigned) 4907 4908 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: 4909 return Start; // N = Start (as unsigned) 4910 4911 // Then, try to solve the above equation provided that Start is constant. 4912 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 4913 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 4914 -StartC->getValue()->getValue(), 4915 *this); 4916 return getCouldNotCompute(); 4917} 4918 4919/// HowFarToNonZero - Return the number of times a backedge checking the 4920/// specified value for nonzero will execute. If not computable, return 4921/// CouldNotCompute 4922ScalarEvolution::BackedgeTakenInfo 4923ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 4924 // Loops that look like: while (X == 0) are very strange indeed. We don't 4925 // handle them yet except for the trivial case. This could be expanded in the 4926 // future as needed. 4927 4928 // If the value is a constant, check to see if it is known to be non-zero 4929 // already. If so, the backedge will execute zero times. 4930 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 4931 if (!C->getValue()->isNullValue()) 4932 return getConstant(C->getType(), 0); 4933 return getCouldNotCompute(); // Otherwise it will loop infinitely. 4934 } 4935 4936 // We could implement others, but I really doubt anyone writes loops like 4937 // this, and if they did, they would already be constant folded. 4938 return getCouldNotCompute(); 4939} 4940 4941/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 4942/// (which may not be an immediate predecessor) which has exactly one 4943/// successor from which BB is reachable, or null if no such block is 4944/// found. 4945/// 4946std::pair<BasicBlock *, BasicBlock *> 4947ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 4948 // If the block has a unique predecessor, then there is no path from the 4949 // predecessor to the block that does not go through the direct edge 4950 // from the predecessor to the block. 4951 if (BasicBlock *Pred = BB->getSinglePredecessor()) 4952 return std::make_pair(Pred, BB); 4953 4954 // A loop's header is defined to be a block that dominates the loop. 4955 // If the header has a unique predecessor outside the loop, it must be 4956 // a block that has exactly one successor that can reach the loop. 4957 if (Loop *L = LI->getLoopFor(BB)) 4958 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 4959 4960 return std::pair<BasicBlock *, BasicBlock *>(); 4961} 4962 4963/// HasSameValue - SCEV structural equivalence is usually sufficient for 4964/// testing whether two expressions are equal, however for the purposes of 4965/// looking for a condition guarding a loop, it can be useful to be a little 4966/// more general, since a front-end may have replicated the controlling 4967/// expression. 4968/// 4969static bool HasSameValue(const SCEV *A, const SCEV *B) { 4970 // Quick check to see if they are the same SCEV. 4971 if (A == B) return true; 4972 4973 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 4974 // two different instructions with the same value. Check for this case. 4975 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 4976 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 4977 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 4978 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 4979 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 4980 return true; 4981 4982 // Otherwise assume they may have a different value. 4983 return false; 4984} 4985 4986/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 4987/// predicate Pred. Return true iff any changes were made. 4988/// 4989bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 4990 const SCEV *&LHS, const SCEV *&RHS) { 4991 bool Changed = false; 4992 4993 // Canonicalize a constant to the right side. 4994 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 4995 // Check for both operands constant. 4996 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 4997 if (ConstantExpr::getICmp(Pred, 4998 LHSC->getValue(), 4999 RHSC->getValue())->isNullValue()) 5000 goto trivially_false; 5001 else 5002 goto trivially_true; 5003 } 5004 // Otherwise swap the operands to put the constant on the right. 5005 std::swap(LHS, RHS); 5006 Pred = ICmpInst::getSwappedPredicate(Pred); 5007 Changed = true; 5008 } 5009 5010 // If we're comparing an addrec with a value which is loop-invariant in the 5011 // addrec's loop, put the addrec on the left. Also make a dominance check, 5012 // as both operands could be addrecs loop-invariant in each other's loop. 5013 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5014 const Loop *L = AR->getLoop(); 5015 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5016 std::swap(LHS, RHS); 5017 Pred = ICmpInst::getSwappedPredicate(Pred); 5018 Changed = true; 5019 } 5020 } 5021 5022 // If there's a constant operand, canonicalize comparisons with boundary 5023 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5024 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5025 const APInt &RA = RC->getValue()->getValue(); 5026 switch (Pred) { 5027 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5028 case ICmpInst::ICMP_EQ: 5029 case ICmpInst::ICMP_NE: 5030 break; 5031 case ICmpInst::ICMP_UGE: 5032 if ((RA - 1).isMinValue()) { 5033 Pred = ICmpInst::ICMP_NE; 5034 RHS = getConstant(RA - 1); 5035 Changed = true; 5036 break; 5037 } 5038 if (RA.isMaxValue()) { 5039 Pred = ICmpInst::ICMP_EQ; 5040 Changed = true; 5041 break; 5042 } 5043 if (RA.isMinValue()) goto trivially_true; 5044 5045 Pred = ICmpInst::ICMP_UGT; 5046 RHS = getConstant(RA - 1); 5047 Changed = true; 5048 break; 5049 case ICmpInst::ICMP_ULE: 5050 if ((RA + 1).isMaxValue()) { 5051 Pred = ICmpInst::ICMP_NE; 5052 RHS = getConstant(RA + 1); 5053 Changed = true; 5054 break; 5055 } 5056 if (RA.isMinValue()) { 5057 Pred = ICmpInst::ICMP_EQ; 5058 Changed = true; 5059 break; 5060 } 5061 if (RA.isMaxValue()) goto trivially_true; 5062 5063 Pred = ICmpInst::ICMP_ULT; 5064 RHS = getConstant(RA + 1); 5065 Changed = true; 5066 break; 5067 case ICmpInst::ICMP_SGE: 5068 if ((RA - 1).isMinSignedValue()) { 5069 Pred = ICmpInst::ICMP_NE; 5070 RHS = getConstant(RA - 1); 5071 Changed = true; 5072 break; 5073 } 5074 if (RA.isMaxSignedValue()) { 5075 Pred = ICmpInst::ICMP_EQ; 5076 Changed = true; 5077 break; 5078 } 5079 if (RA.isMinSignedValue()) goto trivially_true; 5080 5081 Pred = ICmpInst::ICMP_SGT; 5082 RHS = getConstant(RA - 1); 5083 Changed = true; 5084 break; 5085 case ICmpInst::ICMP_SLE: 5086 if ((RA + 1).isMaxSignedValue()) { 5087 Pred = ICmpInst::ICMP_NE; 5088 RHS = getConstant(RA + 1); 5089 Changed = true; 5090 break; 5091 } 5092 if (RA.isMinSignedValue()) { 5093 Pred = ICmpInst::ICMP_EQ; 5094 Changed = true; 5095 break; 5096 } 5097 if (RA.isMaxSignedValue()) goto trivially_true; 5098 5099 Pred = ICmpInst::ICMP_SLT; 5100 RHS = getConstant(RA + 1); 5101 Changed = true; 5102 break; 5103 case ICmpInst::ICMP_UGT: 5104 if (RA.isMinValue()) { 5105 Pred = ICmpInst::ICMP_NE; 5106 Changed = true; 5107 break; 5108 } 5109 if ((RA + 1).isMaxValue()) { 5110 Pred = ICmpInst::ICMP_EQ; 5111 RHS = getConstant(RA + 1); 5112 Changed = true; 5113 break; 5114 } 5115 if (RA.isMaxValue()) goto trivially_false; 5116 break; 5117 case ICmpInst::ICMP_ULT: 5118 if (RA.isMaxValue()) { 5119 Pred = ICmpInst::ICMP_NE; 5120 Changed = true; 5121 break; 5122 } 5123 if ((RA - 1).isMinValue()) { 5124 Pred = ICmpInst::ICMP_EQ; 5125 RHS = getConstant(RA - 1); 5126 Changed = true; 5127 break; 5128 } 5129 if (RA.isMinValue()) goto trivially_false; 5130 break; 5131 case ICmpInst::ICMP_SGT: 5132 if (RA.isMinSignedValue()) { 5133 Pred = ICmpInst::ICMP_NE; 5134 Changed = true; 5135 break; 5136 } 5137 if ((RA + 1).isMaxSignedValue()) { 5138 Pred = ICmpInst::ICMP_EQ; 5139 RHS = getConstant(RA + 1); 5140 Changed = true; 5141 break; 5142 } 5143 if (RA.isMaxSignedValue()) goto trivially_false; 5144 break; 5145 case ICmpInst::ICMP_SLT: 5146 if (RA.isMaxSignedValue()) { 5147 Pred = ICmpInst::ICMP_NE; 5148 Changed = true; 5149 break; 5150 } 5151 if ((RA - 1).isMinSignedValue()) { 5152 Pred = ICmpInst::ICMP_EQ; 5153 RHS = getConstant(RA - 1); 5154 Changed = true; 5155 break; 5156 } 5157 if (RA.isMinSignedValue()) goto trivially_false; 5158 break; 5159 } 5160 } 5161 5162 // Check for obvious equality. 5163 if (HasSameValue(LHS, RHS)) { 5164 if (ICmpInst::isTrueWhenEqual(Pred)) 5165 goto trivially_true; 5166 if (ICmpInst::isFalseWhenEqual(Pred)) 5167 goto trivially_false; 5168 } 5169 5170 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5171 // adding or subtracting 1 from one of the operands. 5172 switch (Pred) { 5173 case ICmpInst::ICMP_SLE: 5174 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5175 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5176 /*HasNUW=*/false, /*HasNSW=*/true); 5177 Pred = ICmpInst::ICMP_SLT; 5178 Changed = true; 5179 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5180 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5181 /*HasNUW=*/false, /*HasNSW=*/true); 5182 Pred = ICmpInst::ICMP_SLT; 5183 Changed = true; 5184 } 5185 break; 5186 case ICmpInst::ICMP_SGE: 5187 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5188 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5189 /*HasNUW=*/false, /*HasNSW=*/true); 5190 Pred = ICmpInst::ICMP_SGT; 5191 Changed = true; 5192 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5193 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5194 /*HasNUW=*/false, /*HasNSW=*/true); 5195 Pred = ICmpInst::ICMP_SGT; 5196 Changed = true; 5197 } 5198 break; 5199 case ICmpInst::ICMP_ULE: 5200 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5201 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5202 /*HasNUW=*/true, /*HasNSW=*/false); 5203 Pred = ICmpInst::ICMP_ULT; 5204 Changed = true; 5205 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5206 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5207 /*HasNUW=*/true, /*HasNSW=*/false); 5208 Pred = ICmpInst::ICMP_ULT; 5209 Changed = true; 5210 } 5211 break; 5212 case ICmpInst::ICMP_UGE: 5213 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5214 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5215 /*HasNUW=*/true, /*HasNSW=*/false); 5216 Pred = ICmpInst::ICMP_UGT; 5217 Changed = true; 5218 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5219 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5220 /*HasNUW=*/true, /*HasNSW=*/false); 5221 Pred = ICmpInst::ICMP_UGT; 5222 Changed = true; 5223 } 5224 break; 5225 default: 5226 break; 5227 } 5228 5229 // TODO: More simplifications are possible here. 5230 5231 return Changed; 5232 5233trivially_true: 5234 // Return 0 == 0. 5235 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5236 Pred = ICmpInst::ICMP_EQ; 5237 return true; 5238 5239trivially_false: 5240 // Return 0 != 0. 5241 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5242 Pred = ICmpInst::ICMP_NE; 5243 return true; 5244} 5245 5246bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5247 return getSignedRange(S).getSignedMax().isNegative(); 5248} 5249 5250bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5251 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5252} 5253 5254bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5255 return !getSignedRange(S).getSignedMin().isNegative(); 5256} 5257 5258bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5259 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5260} 5261 5262bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5263 return isKnownNegative(S) || isKnownPositive(S); 5264} 5265 5266bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5267 const SCEV *LHS, const SCEV *RHS) { 5268 // Canonicalize the inputs first. 5269 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5270 5271 // If LHS or RHS is an addrec, check to see if the condition is true in 5272 // every iteration of the loop. 5273 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5274 if (isLoopEntryGuardedByCond( 5275 AR->getLoop(), Pred, AR->getStart(), RHS) && 5276 isLoopBackedgeGuardedByCond( 5277 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5278 return true; 5279 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5280 if (isLoopEntryGuardedByCond( 5281 AR->getLoop(), Pred, LHS, AR->getStart()) && 5282 isLoopBackedgeGuardedByCond( 5283 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5284 return true; 5285 5286 // Otherwise see what can be done with known constant ranges. 5287 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5288} 5289 5290bool 5291ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5292 const SCEV *LHS, const SCEV *RHS) { 5293 if (HasSameValue(LHS, RHS)) 5294 return ICmpInst::isTrueWhenEqual(Pred); 5295 5296 // This code is split out from isKnownPredicate because it is called from 5297 // within isLoopEntryGuardedByCond. 5298 switch (Pred) { 5299 default: 5300 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5301 break; 5302 case ICmpInst::ICMP_SGT: 5303 Pred = ICmpInst::ICMP_SLT; 5304 std::swap(LHS, RHS); 5305 case ICmpInst::ICMP_SLT: { 5306 ConstantRange LHSRange = getSignedRange(LHS); 5307 ConstantRange RHSRange = getSignedRange(RHS); 5308 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5309 return true; 5310 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5311 return false; 5312 break; 5313 } 5314 case ICmpInst::ICMP_SGE: 5315 Pred = ICmpInst::ICMP_SLE; 5316 std::swap(LHS, RHS); 5317 case ICmpInst::ICMP_SLE: { 5318 ConstantRange LHSRange = getSignedRange(LHS); 5319 ConstantRange RHSRange = getSignedRange(RHS); 5320 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5321 return true; 5322 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5323 return false; 5324 break; 5325 } 5326 case ICmpInst::ICMP_UGT: 5327 Pred = ICmpInst::ICMP_ULT; 5328 std::swap(LHS, RHS); 5329 case ICmpInst::ICMP_ULT: { 5330 ConstantRange LHSRange = getUnsignedRange(LHS); 5331 ConstantRange RHSRange = getUnsignedRange(RHS); 5332 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5333 return true; 5334 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5335 return false; 5336 break; 5337 } 5338 case ICmpInst::ICMP_UGE: 5339 Pred = ICmpInst::ICMP_ULE; 5340 std::swap(LHS, RHS); 5341 case ICmpInst::ICMP_ULE: { 5342 ConstantRange LHSRange = getUnsignedRange(LHS); 5343 ConstantRange RHSRange = getUnsignedRange(RHS); 5344 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5345 return true; 5346 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5347 return false; 5348 break; 5349 } 5350 case ICmpInst::ICMP_NE: { 5351 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5352 return true; 5353 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5354 return true; 5355 5356 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5357 if (isKnownNonZero(Diff)) 5358 return true; 5359 break; 5360 } 5361 case ICmpInst::ICMP_EQ: 5362 // The check at the top of the function catches the case where 5363 // the values are known to be equal. 5364 break; 5365 } 5366 return false; 5367} 5368 5369/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5370/// protected by a conditional between LHS and RHS. This is used to 5371/// to eliminate casts. 5372bool 5373ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5374 ICmpInst::Predicate Pred, 5375 const SCEV *LHS, const SCEV *RHS) { 5376 // Interpret a null as meaning no loop, where there is obviously no guard 5377 // (interprocedural conditions notwithstanding). 5378 if (!L) return true; 5379 5380 BasicBlock *Latch = L->getLoopLatch(); 5381 if (!Latch) 5382 return false; 5383 5384 BranchInst *LoopContinuePredicate = 5385 dyn_cast<BranchInst>(Latch->getTerminator()); 5386 if (!LoopContinuePredicate || 5387 LoopContinuePredicate->isUnconditional()) 5388 return false; 5389 5390 return isImpliedCond(Pred, LHS, RHS, 5391 LoopContinuePredicate->getCondition(), 5392 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5393} 5394 5395/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5396/// by a conditional between LHS and RHS. This is used to help avoid max 5397/// expressions in loop trip counts, and to eliminate casts. 5398bool 5399ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5400 ICmpInst::Predicate Pred, 5401 const SCEV *LHS, const SCEV *RHS) { 5402 // Interpret a null as meaning no loop, where there is obviously no guard 5403 // (interprocedural conditions notwithstanding). 5404 if (!L) return false; 5405 5406 // Starting at the loop predecessor, climb up the predecessor chain, as long 5407 // as there are predecessors that can be found that have unique successors 5408 // leading to the original header. 5409 for (std::pair<BasicBlock *, BasicBlock *> 5410 Pair(L->getLoopPredecessor(), L->getHeader()); 5411 Pair.first; 5412 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5413 5414 BranchInst *LoopEntryPredicate = 5415 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5416 if (!LoopEntryPredicate || 5417 LoopEntryPredicate->isUnconditional()) 5418 continue; 5419 5420 if (isImpliedCond(Pred, LHS, RHS, 5421 LoopEntryPredicate->getCondition(), 5422 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5423 return true; 5424 } 5425 5426 return false; 5427} 5428 5429/// isImpliedCond - Test whether the condition described by Pred, LHS, 5430/// and RHS is true whenever the given Cond value evaluates to true. 5431bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5432 const SCEV *LHS, const SCEV *RHS, 5433 Value *FoundCondValue, 5434 bool Inverse) { 5435 // Recursively handle And and Or conditions. 5436 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5437 if (BO->getOpcode() == Instruction::And) { 5438 if (!Inverse) 5439 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5440 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5441 } else if (BO->getOpcode() == Instruction::Or) { 5442 if (Inverse) 5443 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5444 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5445 } 5446 } 5447 5448 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5449 if (!ICI) return false; 5450 5451 // Bail if the ICmp's operands' types are wider than the needed type 5452 // before attempting to call getSCEV on them. This avoids infinite 5453 // recursion, since the analysis of widening casts can require loop 5454 // exit condition information for overflow checking, which would 5455 // lead back here. 5456 if (getTypeSizeInBits(LHS->getType()) < 5457 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5458 return false; 5459 5460 // Now that we found a conditional branch that dominates the loop, check to 5461 // see if it is the comparison we are looking for. 5462 ICmpInst::Predicate FoundPred; 5463 if (Inverse) 5464 FoundPred = ICI->getInversePredicate(); 5465 else 5466 FoundPred = ICI->getPredicate(); 5467 5468 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5469 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5470 5471 // Balance the types. The case where FoundLHS' type is wider than 5472 // LHS' type is checked for above. 5473 if (getTypeSizeInBits(LHS->getType()) > 5474 getTypeSizeInBits(FoundLHS->getType())) { 5475 if (CmpInst::isSigned(Pred)) { 5476 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5477 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5478 } else { 5479 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5480 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5481 } 5482 } 5483 5484 // Canonicalize the query to match the way instcombine will have 5485 // canonicalized the comparison. 5486 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5487 if (LHS == RHS) 5488 return CmpInst::isTrueWhenEqual(Pred); 5489 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5490 if (FoundLHS == FoundRHS) 5491 return CmpInst::isFalseWhenEqual(Pred); 5492 5493 // Check to see if we can make the LHS or RHS match. 5494 if (LHS == FoundRHS || RHS == FoundLHS) { 5495 if (isa<SCEVConstant>(RHS)) { 5496 std::swap(FoundLHS, FoundRHS); 5497 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5498 } else { 5499 std::swap(LHS, RHS); 5500 Pred = ICmpInst::getSwappedPredicate(Pred); 5501 } 5502 } 5503 5504 // Check whether the found predicate is the same as the desired predicate. 5505 if (FoundPred == Pred) 5506 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5507 5508 // Check whether swapping the found predicate makes it the same as the 5509 // desired predicate. 5510 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5511 if (isa<SCEVConstant>(RHS)) 5512 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5513 else 5514 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5515 RHS, LHS, FoundLHS, FoundRHS); 5516 } 5517 5518 // Check whether the actual condition is beyond sufficient. 5519 if (FoundPred == ICmpInst::ICMP_EQ) 5520 if (ICmpInst::isTrueWhenEqual(Pred)) 5521 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5522 return true; 5523 if (Pred == ICmpInst::ICMP_NE) 5524 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5525 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5526 return true; 5527 5528 // Otherwise assume the worst. 5529 return false; 5530} 5531 5532/// isImpliedCondOperands - Test whether the condition described by Pred, 5533/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5534/// and FoundRHS is true. 5535bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5536 const SCEV *LHS, const SCEV *RHS, 5537 const SCEV *FoundLHS, 5538 const SCEV *FoundRHS) { 5539 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5540 FoundLHS, FoundRHS) || 5541 // ~x < ~y --> x > y 5542 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5543 getNotSCEV(FoundRHS), 5544 getNotSCEV(FoundLHS)); 5545} 5546 5547/// isImpliedCondOperandsHelper - Test whether the condition described by 5548/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5549/// FoundLHS, and FoundRHS is true. 5550bool 5551ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5552 const SCEV *LHS, const SCEV *RHS, 5553 const SCEV *FoundLHS, 5554 const SCEV *FoundRHS) { 5555 switch (Pred) { 5556 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5557 case ICmpInst::ICMP_EQ: 5558 case ICmpInst::ICMP_NE: 5559 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5560 return true; 5561 break; 5562 case ICmpInst::ICMP_SLT: 5563 case ICmpInst::ICMP_SLE: 5564 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5565 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5566 return true; 5567 break; 5568 case ICmpInst::ICMP_SGT: 5569 case ICmpInst::ICMP_SGE: 5570 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5571 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5572 return true; 5573 break; 5574 case ICmpInst::ICMP_ULT: 5575 case ICmpInst::ICMP_ULE: 5576 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5577 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5578 return true; 5579 break; 5580 case ICmpInst::ICMP_UGT: 5581 case ICmpInst::ICMP_UGE: 5582 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5583 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5584 return true; 5585 break; 5586 } 5587 5588 return false; 5589} 5590 5591/// getBECount - Subtract the end and start values and divide by the step, 5592/// rounding up, to get the number of times the backedge is executed. Return 5593/// CouldNotCompute if an intermediate computation overflows. 5594const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5595 const SCEV *End, 5596 const SCEV *Step, 5597 bool NoWrap) { 5598 assert(!isKnownNegative(Step) && 5599 "This code doesn't handle negative strides yet!"); 5600 5601 const Type *Ty = Start->getType(); 5602 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5603 const SCEV *Diff = getMinusSCEV(End, Start); 5604 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5605 5606 // Add an adjustment to the difference between End and Start so that 5607 // the division will effectively round up. 5608 const SCEV *Add = getAddExpr(Diff, RoundUp); 5609 5610 if (!NoWrap) { 5611 // Check Add for unsigned overflow. 5612 // TODO: More sophisticated things could be done here. 5613 const Type *WideTy = IntegerType::get(getContext(), 5614 getTypeSizeInBits(Ty) + 1); 5615 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5616 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5617 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5618 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5619 return getCouldNotCompute(); 5620 } 5621 5622 return getUDivExpr(Add, Step); 5623} 5624 5625/// HowManyLessThans - Return the number of times a backedge containing the 5626/// specified less-than comparison will execute. If not computable, return 5627/// CouldNotCompute. 5628ScalarEvolution::BackedgeTakenInfo 5629ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5630 const Loop *L, bool isSigned) { 5631 // Only handle: "ADDREC < LoopInvariant". 5632 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5633 5634 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5635 if (!AddRec || AddRec->getLoop() != L) 5636 return getCouldNotCompute(); 5637 5638 // Check to see if we have a flag which makes analysis easy. 5639 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : 5640 AddRec->hasNoUnsignedWrap(); 5641 5642 if (AddRec->isAffine()) { 5643 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5644 const SCEV *Step = AddRec->getStepRecurrence(*this); 5645 5646 if (Step->isZero()) 5647 return getCouldNotCompute(); 5648 if (Step->isOne()) { 5649 // With unit stride, the iteration never steps past the limit value. 5650 } else if (isKnownPositive(Step)) { 5651 // Test whether a positive iteration can step past the limit 5652 // value and past the maximum value for its type in a single step. 5653 // Note that it's not sufficient to check NoWrap here, because even 5654 // though the value after a wrap is undefined, it's not undefined 5655 // behavior, so if wrap does occur, the loop could either terminate or 5656 // loop infinitely, but in either case, the loop is guaranteed to 5657 // iterate at least until the iteration where the wrapping occurs. 5658 const SCEV *One = getConstant(Step->getType(), 1); 5659 if (isSigned) { 5660 APInt Max = APInt::getSignedMaxValue(BitWidth); 5661 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5662 .slt(getSignedRange(RHS).getSignedMax())) 5663 return getCouldNotCompute(); 5664 } else { 5665 APInt Max = APInt::getMaxValue(BitWidth); 5666 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5667 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5668 return getCouldNotCompute(); 5669 } 5670 } else 5671 // TODO: Handle negative strides here and below. 5672 return getCouldNotCompute(); 5673 5674 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5675 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5676 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5677 // treat m-n as signed nor unsigned due to overflow possibility. 5678 5679 // First, we get the value of the LHS in the first iteration: n 5680 const SCEV *Start = AddRec->getOperand(0); 5681 5682 // Determine the minimum constant start value. 5683 const SCEV *MinStart = getConstant(isSigned ? 5684 getSignedRange(Start).getSignedMin() : 5685 getUnsignedRange(Start).getUnsignedMin()); 5686 5687 // If we know that the condition is true in order to enter the loop, 5688 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5689 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5690 // the division must round up. 5691 const SCEV *End = RHS; 5692 if (!isLoopEntryGuardedByCond(L, 5693 isSigned ? ICmpInst::ICMP_SLT : 5694 ICmpInst::ICMP_ULT, 5695 getMinusSCEV(Start, Step), RHS)) 5696 End = isSigned ? getSMaxExpr(RHS, Start) 5697 : getUMaxExpr(RHS, Start); 5698 5699 // Determine the maximum constant end value. 5700 const SCEV *MaxEnd = getConstant(isSigned ? 5701 getSignedRange(End).getSignedMax() : 5702 getUnsignedRange(End).getUnsignedMax()); 5703 5704 // If MaxEnd is within a step of the maximum integer value in its type, 5705 // adjust it down to the minimum value which would produce the same effect. 5706 // This allows the subsequent ceiling division of (N+(step-1))/step to 5707 // compute the correct value. 5708 const SCEV *StepMinusOne = getMinusSCEV(Step, 5709 getConstant(Step->getType(), 1)); 5710 MaxEnd = isSigned ? 5711 getSMinExpr(MaxEnd, 5712 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 5713 StepMinusOne)) : 5714 getUMinExpr(MaxEnd, 5715 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 5716 StepMinusOne)); 5717 5718 // Finally, we subtract these two values and divide, rounding up, to get 5719 // the number of times the backedge is executed. 5720 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 5721 5722 // The maximum backedge count is similar, except using the minimum start 5723 // value and the maximum end value. 5724 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); 5725 5726 return BackedgeTakenInfo(BECount, MaxBECount); 5727 } 5728 5729 return getCouldNotCompute(); 5730} 5731 5732/// getNumIterationsInRange - Return the number of iterations of this loop that 5733/// produce values in the specified constant range. Another way of looking at 5734/// this is that it returns the first iteration number where the value is not in 5735/// the condition, thus computing the exit count. If the iteration count can't 5736/// be computed, an instance of SCEVCouldNotCompute is returned. 5737const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 5738 ScalarEvolution &SE) const { 5739 if (Range.isFullSet()) // Infinite loop. 5740 return SE.getCouldNotCompute(); 5741 5742 // If the start is a non-zero constant, shift the range to simplify things. 5743 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 5744 if (!SC->getValue()->isZero()) { 5745 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 5746 Operands[0] = SE.getConstant(SC->getType(), 0); 5747 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); 5748 if (const SCEVAddRecExpr *ShiftedAddRec = 5749 dyn_cast<SCEVAddRecExpr>(Shifted)) 5750 return ShiftedAddRec->getNumIterationsInRange( 5751 Range.subtract(SC->getValue()->getValue()), SE); 5752 // This is strange and shouldn't happen. 5753 return SE.getCouldNotCompute(); 5754 } 5755 5756 // The only time we can solve this is when we have all constant indices. 5757 // Otherwise, we cannot determine the overflow conditions. 5758 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 5759 if (!isa<SCEVConstant>(getOperand(i))) 5760 return SE.getCouldNotCompute(); 5761 5762 5763 // Okay at this point we know that all elements of the chrec are constants and 5764 // that the start element is zero. 5765 5766 // First check to see if the range contains zero. If not, the first 5767 // iteration exits. 5768 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 5769 if (!Range.contains(APInt(BitWidth, 0))) 5770 return SE.getConstant(getType(), 0); 5771 5772 if (isAffine()) { 5773 // If this is an affine expression then we have this situation: 5774 // Solve {0,+,A} in Range === Ax in Range 5775 5776 // We know that zero is in the range. If A is positive then we know that 5777 // the upper value of the range must be the first possible exit value. 5778 // If A is negative then the lower of the range is the last possible loop 5779 // value. Also note that we already checked for a full range. 5780 APInt One(BitWidth,1); 5781 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 5782 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 5783 5784 // The exit value should be (End+A)/A. 5785 APInt ExitVal = (End + A).udiv(A); 5786 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 5787 5788 // Evaluate at the exit value. If we really did fall out of the valid 5789 // range, then we computed our trip count, otherwise wrap around or other 5790 // things must have happened. 5791 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 5792 if (Range.contains(Val->getValue())) 5793 return SE.getCouldNotCompute(); // Something strange happened 5794 5795 // Ensure that the previous value is in the range. This is a sanity check. 5796 assert(Range.contains( 5797 EvaluateConstantChrecAtConstant(this, 5798 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 5799 "Linear scev computation is off in a bad way!"); 5800 return SE.getConstant(ExitValue); 5801 } else if (isQuadratic()) { 5802 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 5803 // quadratic equation to solve it. To do this, we must frame our problem in 5804 // terms of figuring out when zero is crossed, instead of when 5805 // Range.getUpper() is crossed. 5806 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 5807 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 5808 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); 5809 5810 // Next, solve the constructed addrec 5811 std::pair<const SCEV *,const SCEV *> Roots = 5812 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 5813 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5814 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5815 if (R1) { 5816 // Pick the smallest positive root value. 5817 if (ConstantInt *CB = 5818 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 5819 R1->getValue(), R2->getValue()))) { 5820 if (CB->getZExtValue() == false) 5821 std::swap(R1, R2); // R1 is the minimum root now. 5822 5823 // Make sure the root is not off by one. The returned iteration should 5824 // not be in the range, but the previous one should be. When solving 5825 // for "X*X < 5", for example, we should not return a root of 2. 5826 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 5827 R1->getValue(), 5828 SE); 5829 if (Range.contains(R1Val->getValue())) { 5830 // The next iteration must be out of the range... 5831 ConstantInt *NextVal = 5832 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 5833 5834 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5835 if (!Range.contains(R1Val->getValue())) 5836 return SE.getConstant(NextVal); 5837 return SE.getCouldNotCompute(); // Something strange happened 5838 } 5839 5840 // If R1 was not in the range, then it is a good return value. Make 5841 // sure that R1-1 WAS in the range though, just in case. 5842 ConstantInt *NextVal = 5843 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 5844 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 5845 if (Range.contains(R1Val->getValue())) 5846 return R1; 5847 return SE.getCouldNotCompute(); // Something strange happened 5848 } 5849 } 5850 } 5851 5852 return SE.getCouldNotCompute(); 5853} 5854 5855 5856 5857//===----------------------------------------------------------------------===// 5858// SCEVCallbackVH Class Implementation 5859//===----------------------------------------------------------------------===// 5860 5861void ScalarEvolution::SCEVCallbackVH::deleted() { 5862 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5863 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 5864 SE->ConstantEvolutionLoopExitValue.erase(PN); 5865 SE->ValueExprMap.erase(getValPtr()); 5866 // this now dangles! 5867} 5868 5869void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 5870 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 5871 5872 // Forget all the expressions associated with users of the old value, 5873 // so that future queries will recompute the expressions using the new 5874 // value. 5875 Value *Old = getValPtr(); 5876 SmallVector<User *, 16> Worklist; 5877 SmallPtrSet<User *, 8> Visited; 5878 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 5879 UI != UE; ++UI) 5880 Worklist.push_back(*UI); 5881 while (!Worklist.empty()) { 5882 User *U = Worklist.pop_back_val(); 5883 // Deleting the Old value will cause this to dangle. Postpone 5884 // that until everything else is done. 5885 if (U == Old) 5886 continue; 5887 if (!Visited.insert(U)) 5888 continue; 5889 if (PHINode *PN = dyn_cast<PHINode>(U)) 5890 SE->ConstantEvolutionLoopExitValue.erase(PN); 5891 SE->ValueExprMap.erase(U); 5892 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 5893 UI != UE; ++UI) 5894 Worklist.push_back(*UI); 5895 } 5896 // Delete the Old value. 5897 if (PHINode *PN = dyn_cast<PHINode>(Old)) 5898 SE->ConstantEvolutionLoopExitValue.erase(PN); 5899 SE->ValueExprMap.erase(Old); 5900 // this now dangles! 5901} 5902 5903ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 5904 : CallbackVH(V), SE(se) {} 5905 5906//===----------------------------------------------------------------------===// 5907// ScalarEvolution Class Implementation 5908//===----------------------------------------------------------------------===// 5909 5910ScalarEvolution::ScalarEvolution() 5911 : FunctionPass(ID), FirstUnknown(0) { 5912 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 5913} 5914 5915bool ScalarEvolution::runOnFunction(Function &F) { 5916 this->F = &F; 5917 LI = &getAnalysis<LoopInfo>(); 5918 TD = getAnalysisIfAvailable<TargetData>(); 5919 DT = &getAnalysis<DominatorTree>(); 5920 return false; 5921} 5922 5923void ScalarEvolution::releaseMemory() { 5924 // Iterate through all the SCEVUnknown instances and call their 5925 // destructors, so that they release their references to their values. 5926 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 5927 U->~SCEVUnknown(); 5928 FirstUnknown = 0; 5929 5930 ValueExprMap.clear(); 5931 BackedgeTakenCounts.clear(); 5932 ConstantEvolutionLoopExitValue.clear(); 5933 ValuesAtScopes.clear(); 5934 LoopDispositions.clear(); 5935 BlockDispositions.clear(); 5936 UnsignedRanges.clear(); 5937 SignedRanges.clear(); 5938 UniqueSCEVs.clear(); 5939 SCEVAllocator.Reset(); 5940} 5941 5942void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 5943 AU.setPreservesAll(); 5944 AU.addRequiredTransitive<LoopInfo>(); 5945 AU.addRequiredTransitive<DominatorTree>(); 5946} 5947 5948bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 5949 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 5950} 5951 5952static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 5953 const Loop *L) { 5954 // Print all inner loops first 5955 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 5956 PrintLoopInfo(OS, SE, *I); 5957 5958 OS << "Loop "; 5959 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5960 OS << ": "; 5961 5962 SmallVector<BasicBlock *, 8> ExitBlocks; 5963 L->getExitBlocks(ExitBlocks); 5964 if (ExitBlocks.size() != 1) 5965 OS << "<multiple exits> "; 5966 5967 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 5968 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 5969 } else { 5970 OS << "Unpredictable backedge-taken count. "; 5971 } 5972 5973 OS << "\n" 5974 "Loop "; 5975 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 5976 OS << ": "; 5977 5978 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 5979 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 5980 } else { 5981 OS << "Unpredictable max backedge-taken count. "; 5982 } 5983 5984 OS << "\n"; 5985} 5986 5987void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 5988 // ScalarEvolution's implementation of the print method is to print 5989 // out SCEV values of all instructions that are interesting. Doing 5990 // this potentially causes it to create new SCEV objects though, 5991 // which technically conflicts with the const qualifier. This isn't 5992 // observable from outside the class though, so casting away the 5993 // const isn't dangerous. 5994 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 5995 5996 OS << "Classifying expressions for: "; 5997 WriteAsOperand(OS, F, /*PrintType=*/false); 5998 OS << "\n"; 5999 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6000 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6001 OS << *I << '\n'; 6002 OS << " --> "; 6003 const SCEV *SV = SE.getSCEV(&*I); 6004 SV->print(OS); 6005 6006 const Loop *L = LI->getLoopFor((*I).getParent()); 6007 6008 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6009 if (AtUse != SV) { 6010 OS << " --> "; 6011 AtUse->print(OS); 6012 } 6013 6014 if (L) { 6015 OS << "\t\t" "Exits: "; 6016 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6017 if (!SE.isLoopInvariant(ExitValue, L)) { 6018 OS << "<<Unknown>>"; 6019 } else { 6020 OS << *ExitValue; 6021 } 6022 } 6023 6024 OS << "\n"; 6025 } 6026 6027 OS << "Determining loop execution counts for: "; 6028 WriteAsOperand(OS, F, /*PrintType=*/false); 6029 OS << "\n"; 6030 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6031 PrintLoopInfo(OS, &SE, *I); 6032} 6033 6034ScalarEvolution::LoopDisposition 6035ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6036 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6037 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6038 Values.insert(std::make_pair(L, LoopVariant)); 6039 if (!Pair.second) 6040 return Pair.first->second; 6041 6042 LoopDisposition D = computeLoopDisposition(S, L); 6043 return LoopDispositions[S][L] = D; 6044} 6045 6046ScalarEvolution::LoopDisposition 6047ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6048 switch (S->getSCEVType()) { 6049 case scConstant: 6050 return LoopInvariant; 6051 case scTruncate: 6052 case scZeroExtend: 6053 case scSignExtend: 6054 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6055 case scAddRecExpr: { 6056 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6057 6058 // If L is the addrec's loop, it's computable. 6059 if (AR->getLoop() == L) 6060 return LoopComputable; 6061 6062 // Add recurrences are never invariant in the function-body (null loop). 6063 if (!L) 6064 return LoopVariant; 6065 6066 // This recurrence is variant w.r.t. L if L contains AR's loop. 6067 if (L->contains(AR->getLoop())) 6068 return LoopVariant; 6069 6070 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6071 if (AR->getLoop()->contains(L)) 6072 return LoopInvariant; 6073 6074 // This recurrence is variant w.r.t. L if any of its operands 6075 // are variant. 6076 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6077 I != E; ++I) 6078 if (!isLoopInvariant(*I, L)) 6079 return LoopVariant; 6080 6081 // Otherwise it's loop-invariant. 6082 return LoopInvariant; 6083 } 6084 case scAddExpr: 6085 case scMulExpr: 6086 case scUMaxExpr: 6087 case scSMaxExpr: { 6088 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6089 bool HasVarying = false; 6090 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6091 I != E; ++I) { 6092 LoopDisposition D = getLoopDisposition(*I, L); 6093 if (D == LoopVariant) 6094 return LoopVariant; 6095 if (D == LoopComputable) 6096 HasVarying = true; 6097 } 6098 return HasVarying ? LoopComputable : LoopInvariant; 6099 } 6100 case scUDivExpr: { 6101 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6102 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6103 if (LD == LoopVariant) 6104 return LoopVariant; 6105 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6106 if (RD == LoopVariant) 6107 return LoopVariant; 6108 return (LD == LoopInvariant && RD == LoopInvariant) ? 6109 LoopInvariant : LoopComputable; 6110 } 6111 case scUnknown: 6112 // All non-instruction values are loop invariant. All instructions are loop 6113 // invariant if they are not contained in the specified loop. 6114 // Instructions are never considered invariant in the function body 6115 // (null loop) because they are defined within the "loop". 6116 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6117 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6118 return LoopInvariant; 6119 case scCouldNotCompute: 6120 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6121 return LoopVariant; 6122 default: break; 6123 } 6124 llvm_unreachable("Unknown SCEV kind!"); 6125 return LoopVariant; 6126} 6127 6128bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6129 return getLoopDisposition(S, L) == LoopInvariant; 6130} 6131 6132bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6133 return getLoopDisposition(S, L) == LoopComputable; 6134} 6135 6136ScalarEvolution::BlockDisposition 6137ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6138 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6139 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6140 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6141 if (!Pair.second) 6142 return Pair.first->second; 6143 6144 BlockDisposition D = computeBlockDisposition(S, BB); 6145 return BlockDispositions[S][BB] = D; 6146} 6147 6148ScalarEvolution::BlockDisposition 6149ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6150 switch (S->getSCEVType()) { 6151 case scConstant: 6152 return ProperlyDominatesBlock; 6153 case scTruncate: 6154 case scZeroExtend: 6155 case scSignExtend: 6156 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6157 case scAddRecExpr: { 6158 // This uses a "dominates" query instead of "properly dominates" query 6159 // to test for proper dominance too, because the instruction which 6160 // produces the addrec's value is a PHI, and a PHI effectively properly 6161 // dominates its entire containing block. 6162 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6163 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6164 return DoesNotDominateBlock; 6165 } 6166 // FALL THROUGH into SCEVNAryExpr handling. 6167 case scAddExpr: 6168 case scMulExpr: 6169 case scUMaxExpr: 6170 case scSMaxExpr: { 6171 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6172 bool Proper = true; 6173 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6174 I != E; ++I) { 6175 BlockDisposition D = getBlockDisposition(*I, BB); 6176 if (D == DoesNotDominateBlock) 6177 return DoesNotDominateBlock; 6178 if (D == DominatesBlock) 6179 Proper = false; 6180 } 6181 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6182 } 6183 case scUDivExpr: { 6184 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6185 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6186 BlockDisposition LD = getBlockDisposition(LHS, BB); 6187 if (LD == DoesNotDominateBlock) 6188 return DoesNotDominateBlock; 6189 BlockDisposition RD = getBlockDisposition(RHS, BB); 6190 if (RD == DoesNotDominateBlock) 6191 return DoesNotDominateBlock; 6192 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6193 ProperlyDominatesBlock : DominatesBlock; 6194 } 6195 case scUnknown: 6196 if (Instruction *I = 6197 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6198 if (I->getParent() == BB) 6199 return DominatesBlock; 6200 if (DT->properlyDominates(I->getParent(), BB)) 6201 return ProperlyDominatesBlock; 6202 return DoesNotDominateBlock; 6203 } 6204 return ProperlyDominatesBlock; 6205 case scCouldNotCompute: 6206 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6207 return DoesNotDominateBlock; 6208 default: break; 6209 } 6210 llvm_unreachable("Unknown SCEV kind!"); 6211 return DoesNotDominateBlock; 6212} 6213 6214bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6215 return getBlockDisposition(S, BB) >= DominatesBlock; 6216} 6217 6218bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6219 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6220} 6221 6222bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6223 switch (S->getSCEVType()) { 6224 case scConstant: 6225 return false; 6226 case scTruncate: 6227 case scZeroExtend: 6228 case scSignExtend: { 6229 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6230 const SCEV *CastOp = Cast->getOperand(); 6231 return Op == CastOp || hasOperand(CastOp, Op); 6232 } 6233 case scAddRecExpr: 6234 case scAddExpr: 6235 case scMulExpr: 6236 case scUMaxExpr: 6237 case scSMaxExpr: { 6238 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6239 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6240 I != E; ++I) { 6241 const SCEV *NAryOp = *I; 6242 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6243 return true; 6244 } 6245 return false; 6246 } 6247 case scUDivExpr: { 6248 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6249 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6250 return LHS == Op || hasOperand(LHS, Op) || 6251 RHS == Op || hasOperand(RHS, Op); 6252 } 6253 case scUnknown: 6254 return false; 6255 case scCouldNotCompute: 6256 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6257 return false; 6258 default: break; 6259 } 6260 llvm_unreachable("Unknown SCEV kind!"); 6261 return false; 6262} 6263 6264void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6265 ValuesAtScopes.erase(S); 6266 LoopDispositions.erase(S); 6267 BlockDispositions.erase(S); 6268 UnsignedRanges.erase(S); 6269 SignedRanges.erase(S); 6270} 6271