ScalarEvolution.cpp revision 1cbae18cf60c023840aab605958eea635c837f16
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->getNoWrapFlags(FlagNUW)) 161 OS << "nuw><"; 162 if (AR->getNoWrapFlags(FlagNSW)) 163 OS << "nsw><"; 164 if (AR->getNoWrapFlags(FlagNW) && 165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) 166 OS << "nw><"; 167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false); 168 OS << ">"; 169 return; 170 } 171 case scAddExpr: 172 case scMulExpr: 173 case scUMaxExpr: 174 case scSMaxExpr: { 175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this); 176 const char *OpStr = 0; 177 switch (NAry->getSCEVType()) { 178 case scAddExpr: OpStr = " + "; break; 179 case scMulExpr: OpStr = " * "; break; 180 case scUMaxExpr: OpStr = " umax "; break; 181 case scSMaxExpr: OpStr = " smax "; break; 182 } 183 OS << "("; 184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 185 I != E; ++I) { 186 OS << **I; 187 if (llvm::next(I) != E) 188 OS << OpStr; 189 } 190 OS << ")"; 191 return; 192 } 193 case scUDivExpr: { 194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 196 return; 197 } 198 case scUnknown: { 199 const SCEVUnknown *U = cast<SCEVUnknown>(this); 200 Type *AllocTy; 201 if (U->isSizeOf(AllocTy)) { 202 OS << "sizeof(" << *AllocTy << ")"; 203 return; 204 } 205 if (U->isAlignOf(AllocTy)) { 206 OS << "alignof(" << *AllocTy << ")"; 207 return; 208 } 209 210 Type *CTy; 211 Constant *FieldNo; 212 if (U->isOffsetOf(CTy, FieldNo)) { 213 OS << "offsetof(" << *CTy << ", "; 214 WriteAsOperand(OS, FieldNo, false); 215 OS << ")"; 216 return; 217 } 218 219 // Otherwise just print it normally. 220 WriteAsOperand(OS, U->getValue(), false); 221 return; 222 } 223 case scCouldNotCompute: 224 OS << "***COULDNOTCOMPUTE***"; 225 return; 226 default: break; 227 } 228 llvm_unreachable("Unknown SCEV kind!"); 229} 230 231Type *SCEV::getType() const { 232 switch (getSCEVType()) { 233 case scConstant: 234 return cast<SCEVConstant>(this)->getType(); 235 case scTruncate: 236 case scZeroExtend: 237 case scSignExtend: 238 return cast<SCEVCastExpr>(this)->getType(); 239 case scAddRecExpr: 240 case scMulExpr: 241 case scUMaxExpr: 242 case scSMaxExpr: 243 return cast<SCEVNAryExpr>(this)->getType(); 244 case scAddExpr: 245 return cast<SCEVAddExpr>(this)->getType(); 246 case scUDivExpr: 247 return cast<SCEVUDivExpr>(this)->getType(); 248 case scUnknown: 249 return cast<SCEVUnknown>(this)->getType(); 250 case scCouldNotCompute: 251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 252 return 0; 253 default: break; 254 } 255 llvm_unreachable("Unknown SCEV kind!"); 256 return 0; 257} 258 259bool SCEV::isZero() const { 260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 261 return SC->getValue()->isZero(); 262 return false; 263} 264 265bool SCEV::isOne() const { 266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 267 return SC->getValue()->isOne(); 268 return false; 269} 270 271bool SCEV::isAllOnesValue() const { 272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 273 return SC->getValue()->isAllOnesValue(); 274 return false; 275} 276 277SCEVCouldNotCompute::SCEVCouldNotCompute() : 278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 279 280bool SCEVCouldNotCompute::classof(const SCEV *S) { 281 return S->getSCEVType() == scCouldNotCompute; 282} 283 284const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 285 FoldingSetNodeID ID; 286 ID.AddInteger(scConstant); 287 ID.AddPointer(V); 288 void *IP = 0; 289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 291 UniqueSCEVs.InsertNode(S, IP); 292 return S; 293} 294 295const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 296 return getConstant(ConstantInt::get(getContext(), Val)); 297} 298 299const SCEV * 300ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 301 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 302 return getConstant(ConstantInt::get(ITy, V, isSigned)); 303} 304 305SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 306 unsigned SCEVTy, const SCEV *op, Type *ty) 307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 308 309SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 310 const SCEV *op, Type *ty) 311 : SCEVCastExpr(ID, scTruncate, op, ty) { 312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 313 (Ty->isIntegerTy() || Ty->isPointerTy()) && 314 "Cannot truncate non-integer value!"); 315} 316 317SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 318 const SCEV *op, Type *ty) 319 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 321 (Ty->isIntegerTy() || Ty->isPointerTy()) && 322 "Cannot zero extend non-integer value!"); 323} 324 325SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 326 const SCEV *op, Type *ty) 327 : SCEVCastExpr(ID, scSignExtend, op, ty) { 328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 329 (Ty->isIntegerTy() || Ty->isPointerTy()) && 330 "Cannot sign extend non-integer value!"); 331} 332 333void SCEVUnknown::deleted() { 334 // Clear this SCEVUnknown from various maps. 335 SE->forgetMemoizedResults(this); 336 337 // Remove this SCEVUnknown from the uniquing map. 338 SE->UniqueSCEVs.RemoveNode(this); 339 340 // Release the value. 341 setValPtr(0); 342} 343 344void SCEVUnknown::allUsesReplacedWith(Value *New) { 345 // Clear this SCEVUnknown from various maps. 346 SE->forgetMemoizedResults(this); 347 348 // Remove this SCEVUnknown from the uniquing map. 349 SE->UniqueSCEVs.RemoveNode(this); 350 351 // Update this SCEVUnknown to point to the new value. This is needed 352 // because there may still be outstanding SCEVs which still point to 353 // this SCEVUnknown. 354 setValPtr(New); 355} 356 357bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 359 if (VCE->getOpcode() == Instruction::PtrToInt) 360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 361 if (CE->getOpcode() == Instruction::GetElementPtr && 362 CE->getOperand(0)->isNullValue() && 363 CE->getNumOperands() == 2) 364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 365 if (CI->isOne()) { 366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 367 ->getElementType(); 368 return true; 369 } 370 371 return false; 372} 373 374bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 376 if (VCE->getOpcode() == Instruction::PtrToInt) 377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 378 if (CE->getOpcode() == Instruction::GetElementPtr && 379 CE->getOperand(0)->isNullValue()) { 380 Type *Ty = 381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 382 if (StructType *STy = dyn_cast<StructType>(Ty)) 383 if (!STy->isPacked() && 384 CE->getNumOperands() == 3 && 385 CE->getOperand(1)->isNullValue()) { 386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 387 if (CI->isOne() && 388 STy->getNumElements() == 2 && 389 STy->getElementType(0)->isIntegerTy(1)) { 390 AllocTy = STy->getElementType(1); 391 return true; 392 } 393 } 394 } 395 396 return false; 397} 398 399bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 401 if (VCE->getOpcode() == Instruction::PtrToInt) 402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 403 if (CE->getOpcode() == Instruction::GetElementPtr && 404 CE->getNumOperands() == 3 && 405 CE->getOperand(0)->isNullValue() && 406 CE->getOperand(1)->isNullValue()) { 407 Type *Ty = 408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 409 // Ignore vector types here so that ScalarEvolutionExpander doesn't 410 // emit getelementptrs that index into vectors. 411 if (Ty->isStructTy() || Ty->isArrayTy()) { 412 CTy = Ty; 413 FieldNo = CE->getOperand(2); 414 return true; 415 } 416 } 417 418 return false; 419} 420 421//===----------------------------------------------------------------------===// 422// SCEV Utilities 423//===----------------------------------------------------------------------===// 424 425namespace { 426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 427 /// than the complexity of the RHS. This comparator is used to canonicalize 428 /// expressions. 429 class SCEVComplexityCompare { 430 const LoopInfo *const LI; 431 public: 432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 433 434 // Return true or false if LHS is less than, or at least RHS, respectively. 435 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 436 return compare(LHS, RHS) < 0; 437 } 438 439 // Return negative, zero, or positive, if LHS is less than, equal to, or 440 // greater than RHS, respectively. A three-way result allows recursive 441 // comparisons to be more efficient. 442 int compare(const SCEV *LHS, const SCEV *RHS) const { 443 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 444 if (LHS == RHS) 445 return 0; 446 447 // Primarily, sort the SCEVs by their getSCEVType(). 448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 449 if (LType != RType) 450 return (int)LType - (int)RType; 451 452 // Aside from the getSCEVType() ordering, the particular ordering 453 // isn't very important except that it's beneficial to be consistent, 454 // so that (a + b) and (b + a) don't end up as different expressions. 455 switch (LType) { 456 case scUnknown: { 457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 459 460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 461 // not as complete as it could be. 462 const Value *LV = LU->getValue(), *RV = RU->getValue(); 463 464 // Order pointer values after integer values. This helps SCEVExpander 465 // form GEPs. 466 bool LIsPointer = LV->getType()->isPointerTy(), 467 RIsPointer = RV->getType()->isPointerTy(); 468 if (LIsPointer != RIsPointer) 469 return (int)LIsPointer - (int)RIsPointer; 470 471 // Compare getValueID values. 472 unsigned LID = LV->getValueID(), 473 RID = RV->getValueID(); 474 if (LID != RID) 475 return (int)LID - (int)RID; 476 477 // Sort arguments by their position. 478 if (const Argument *LA = dyn_cast<Argument>(LV)) { 479 const Argument *RA = cast<Argument>(RV); 480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 481 return (int)LArgNo - (int)RArgNo; 482 } 483 484 // For instructions, compare their loop depth, and their operand 485 // count. This is pretty loose. 486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 487 const Instruction *RInst = cast<Instruction>(RV); 488 489 // Compare loop depths. 490 const BasicBlock *LParent = LInst->getParent(), 491 *RParent = RInst->getParent(); 492 if (LParent != RParent) { 493 unsigned LDepth = LI->getLoopDepth(LParent), 494 RDepth = LI->getLoopDepth(RParent); 495 if (LDepth != RDepth) 496 return (int)LDepth - (int)RDepth; 497 } 498 499 // Compare the number of operands. 500 unsigned LNumOps = LInst->getNumOperands(), 501 RNumOps = RInst->getNumOperands(); 502 return (int)LNumOps - (int)RNumOps; 503 } 504 505 return 0; 506 } 507 508 case scConstant: { 509 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 510 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 511 512 // Compare constant values. 513 const APInt &LA = LC->getValue()->getValue(); 514 const APInt &RA = RC->getValue()->getValue(); 515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 516 if (LBitWidth != RBitWidth) 517 return (int)LBitWidth - (int)RBitWidth; 518 return LA.ult(RA) ? -1 : 1; 519 } 520 521 case scAddRecExpr: { 522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 524 525 // Compare addrec loop depths. 526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 527 if (LLoop != RLoop) { 528 unsigned LDepth = LLoop->getLoopDepth(), 529 RDepth = RLoop->getLoopDepth(); 530 if (LDepth != RDepth) 531 return (int)LDepth - (int)RDepth; 532 } 533 534 // Addrec complexity grows with operand count. 535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 536 if (LNumOps != RNumOps) 537 return (int)LNumOps - (int)RNumOps; 538 539 // Lexicographically compare. 540 for (unsigned i = 0; i != LNumOps; ++i) { 541 long X = compare(LA->getOperand(i), RA->getOperand(i)); 542 if (X != 0) 543 return X; 544 } 545 546 return 0; 547 } 548 549 case scAddExpr: 550 case scMulExpr: 551 case scSMaxExpr: 552 case scUMaxExpr: { 553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 555 556 // Lexicographically compare n-ary expressions. 557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 558 for (unsigned i = 0; i != LNumOps; ++i) { 559 if (i >= RNumOps) 560 return 1; 561 long X = compare(LC->getOperand(i), RC->getOperand(i)); 562 if (X != 0) 563 return X; 564 } 565 return (int)LNumOps - (int)RNumOps; 566 } 567 568 case scUDivExpr: { 569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 571 572 // Lexicographically compare udiv expressions. 573 long X = compare(LC->getLHS(), RC->getLHS()); 574 if (X != 0) 575 return X; 576 return compare(LC->getRHS(), RC->getRHS()); 577 } 578 579 case scTruncate: 580 case scZeroExtend: 581 case scSignExtend: { 582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 584 585 // Compare cast expressions by operand. 586 return compare(LC->getOperand(), RC->getOperand()); 587 } 588 589 default: 590 break; 591 } 592 593 llvm_unreachable("Unknown SCEV kind!"); 594 return 0; 595 } 596 }; 597} 598 599/// GroupByComplexity - Given a list of SCEV objects, order them by their 600/// complexity, and group objects of the same complexity together by value. 601/// When this routine is finished, we know that any duplicates in the vector are 602/// consecutive and that complexity is monotonically increasing. 603/// 604/// Note that we go take special precautions to ensure that we get deterministic 605/// results from this routine. In other words, we don't want the results of 606/// this to depend on where the addresses of various SCEV objects happened to 607/// land in memory. 608/// 609static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 610 LoopInfo *LI) { 611 if (Ops.size() < 2) return; // Noop 612 if (Ops.size() == 2) { 613 // This is the common case, which also happens to be trivially simple. 614 // Special case it. 615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 616 if (SCEVComplexityCompare(LI)(RHS, LHS)) 617 std::swap(LHS, RHS); 618 return; 619 } 620 621 // Do the rough sort by complexity. 622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 623 624 // Now that we are sorted by complexity, group elements of the same 625 // complexity. Note that this is, at worst, N^2, but the vector is likely to 626 // be extremely short in practice. Note that we take this approach because we 627 // do not want to depend on the addresses of the objects we are grouping. 628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 629 const SCEV *S = Ops[i]; 630 unsigned Complexity = S->getSCEVType(); 631 632 // If there are any objects of the same complexity and same value as this 633 // one, group them. 634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 635 if (Ops[j] == S) { // Found a duplicate. 636 // Move it to immediately after i'th element. 637 std::swap(Ops[i+1], Ops[j]); 638 ++i; // no need to rescan it. 639 if (i == e-2) return; // Done! 640 } 641 } 642 } 643} 644 645 646 647//===----------------------------------------------------------------------===// 648// Simple SCEV method implementations 649//===----------------------------------------------------------------------===// 650 651/// BinomialCoefficient - Compute BC(It, K). The result has width W. 652/// Assume, K > 0. 653static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 654 ScalarEvolution &SE, 655 Type *ResultTy) { 656 // Handle the simplest case efficiently. 657 if (K == 1) 658 return SE.getTruncateOrZeroExtend(It, ResultTy); 659 660 // We are using the following formula for BC(It, K): 661 // 662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 663 // 664 // Suppose, W is the bitwidth of the return value. We must be prepared for 665 // overflow. Hence, we must assure that the result of our computation is 666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 667 // safe in modular arithmetic. 668 // 669 // However, this code doesn't use exactly that formula; the formula it uses 670 // is something like the following, where T is the number of factors of 2 in 671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 672 // exponentiation: 673 // 674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 675 // 676 // This formula is trivially equivalent to the previous formula. However, 677 // this formula can be implemented much more efficiently. The trick is that 678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 679 // arithmetic. To do exact division in modular arithmetic, all we have 680 // to do is multiply by the inverse. Therefore, this step can be done at 681 // width W. 682 // 683 // The next issue is how to safely do the division by 2^T. The way this 684 // is done is by doing the multiplication step at a width of at least W + T 685 // bits. This way, the bottom W+T bits of the product are accurate. Then, 686 // when we perform the division by 2^T (which is equivalent to a right shift 687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 688 // truncated out after the division by 2^T. 689 // 690 // In comparison to just directly using the first formula, this technique 691 // is much more efficient; using the first formula requires W * K bits, 692 // but this formula less than W + K bits. Also, the first formula requires 693 // a division step, whereas this formula only requires multiplies and shifts. 694 // 695 // It doesn't matter whether the subtraction step is done in the calculation 696 // width or the input iteration count's width; if the subtraction overflows, 697 // the result must be zero anyway. We prefer here to do it in the width of 698 // the induction variable because it helps a lot for certain cases; CodeGen 699 // isn't smart enough to ignore the overflow, which leads to much less 700 // efficient code if the width of the subtraction is wider than the native 701 // register width. 702 // 703 // (It's possible to not widen at all by pulling out factors of 2 before 704 // the multiplication; for example, K=2 can be calculated as 705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 706 // extra arithmetic, so it's not an obvious win, and it gets 707 // much more complicated for K > 3.) 708 709 // Protection from insane SCEVs; this bound is conservative, 710 // but it probably doesn't matter. 711 if (K > 1000) 712 return SE.getCouldNotCompute(); 713 714 unsigned W = SE.getTypeSizeInBits(ResultTy); 715 716 // Calculate K! / 2^T and T; we divide out the factors of two before 717 // multiplying for calculating K! / 2^T to avoid overflow. 718 // Other overflow doesn't matter because we only care about the bottom 719 // W bits of the result. 720 APInt OddFactorial(W, 1); 721 unsigned T = 1; 722 for (unsigned i = 3; i <= K; ++i) { 723 APInt Mult(W, i); 724 unsigned TwoFactors = Mult.countTrailingZeros(); 725 T += TwoFactors; 726 Mult = Mult.lshr(TwoFactors); 727 OddFactorial *= Mult; 728 } 729 730 // We need at least W + T bits for the multiplication step 731 unsigned CalculationBits = W + T; 732 733 // Calculate 2^T, at width T+W. 734 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 735 736 // Calculate the multiplicative inverse of K! / 2^T; 737 // this multiplication factor will perform the exact division by 738 // K! / 2^T. 739 APInt Mod = APInt::getSignedMinValue(W+1); 740 APInt MultiplyFactor = OddFactorial.zext(W+1); 741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 742 MultiplyFactor = MultiplyFactor.trunc(W); 743 744 // Calculate the product, at width T+W 745 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 746 CalculationBits); 747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 748 for (unsigned i = 1; i != K; ++i) { 749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 750 Dividend = SE.getMulExpr(Dividend, 751 SE.getTruncateOrZeroExtend(S, CalculationTy)); 752 } 753 754 // Divide by 2^T 755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 756 757 // Truncate the result, and divide by K! / 2^T. 758 759 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 760 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 761} 762 763/// evaluateAtIteration - Return the value of this chain of recurrences at 764/// the specified iteration number. We can evaluate this recurrence by 765/// multiplying each element in the chain by the binomial coefficient 766/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 767/// 768/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 769/// 770/// where BC(It, k) stands for binomial coefficient. 771/// 772const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 773 ScalarEvolution &SE) const { 774 const SCEV *Result = getStart(); 775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 776 // The computation is correct in the face of overflow provided that the 777 // multiplication is performed _after_ the evaluation of the binomial 778 // coefficient. 779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 780 if (isa<SCEVCouldNotCompute>(Coeff)) 781 return Coeff; 782 783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 784 } 785 return Result; 786} 787 788//===----------------------------------------------------------------------===// 789// SCEV Expression folder implementations 790//===----------------------------------------------------------------------===// 791 792const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 793 Type *Ty) { 794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 795 "This is not a truncating conversion!"); 796 assert(isSCEVable(Ty) && 797 "This is not a conversion to a SCEVable type!"); 798 Ty = getEffectiveSCEVType(Ty); 799 800 FoldingSetNodeID ID; 801 ID.AddInteger(scTruncate); 802 ID.AddPointer(Op); 803 ID.AddPointer(Ty); 804 void *IP = 0; 805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 806 807 // Fold if the operand is constant. 808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 809 return getConstant( 810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 811 getEffectiveSCEVType(Ty)))); 812 813 // trunc(trunc(x)) --> trunc(x) 814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 815 return getTruncateExpr(ST->getOperand(), Ty); 816 817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 819 return getTruncateOrSignExtend(SS->getOperand(), Ty); 820 821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 824 825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 826 // eliminate all the truncates. 827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 828 SmallVector<const SCEV *, 4> Operands; 829 bool hasTrunc = false; 830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 832 hasTrunc = isa<SCEVTruncateExpr>(S); 833 Operands.push_back(S); 834 } 835 if (!hasTrunc) 836 return getAddExpr(Operands); 837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 838 } 839 840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 841 // eliminate all the truncates. 842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 843 SmallVector<const SCEV *, 4> Operands; 844 bool hasTrunc = false; 845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 847 hasTrunc = isa<SCEVTruncateExpr>(S); 848 Operands.push_back(S); 849 } 850 if (!hasTrunc) 851 return getMulExpr(Operands); 852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 853 } 854 855 // If the input value is a chrec scev, truncate the chrec's operands. 856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 857 SmallVector<const SCEV *, 4> Operands; 858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 861 } 862 863 // As a special case, fold trunc(undef) to undef. We don't want to 864 // know too much about SCEVUnknowns, but this special case is handy 865 // and harmless. 866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 867 if (isa<UndefValue>(U->getValue())) 868 return getSCEV(UndefValue::get(Ty)); 869 870 // The cast wasn't folded; create an explicit cast node. We can reuse 871 // the existing insert position since if we get here, we won't have 872 // made any changes which would invalidate it. 873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 874 Op, Ty); 875 UniqueSCEVs.InsertNode(S, IP); 876 return S; 877} 878 879const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 880 Type *Ty) { 881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 882 "This is not an extending conversion!"); 883 assert(isSCEVable(Ty) && 884 "This is not a conversion to a SCEVable type!"); 885 Ty = getEffectiveSCEVType(Ty); 886 887 // Fold if the operand is constant. 888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 889 return getConstant( 890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 891 getEffectiveSCEVType(Ty)))); 892 893 // zext(zext(x)) --> zext(x) 894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 895 return getZeroExtendExpr(SZ->getOperand(), Ty); 896 897 // Before doing any expensive analysis, check to see if we've already 898 // computed a SCEV for this Op and Ty. 899 FoldingSetNodeID ID; 900 ID.AddInteger(scZeroExtend); 901 ID.AddPointer(Op); 902 ID.AddPointer(Ty); 903 void *IP = 0; 904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 905 906 // zext(trunc(x)) --> zext(x) or x or trunc(x) 907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 908 // It's possible the bits taken off by the truncate were all zero bits. If 909 // so, we should be able to simplify this further. 910 const SCEV *X = ST->getOperand(); 911 ConstantRange CR = getUnsignedRange(X); 912 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 913 unsigned NewBits = getTypeSizeInBits(Ty); 914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 915 CR.zextOrTrunc(NewBits))) 916 return getTruncateOrZeroExtend(X, Ty); 917 } 918 919 // If the input value is a chrec scev, and we can prove that the value 920 // did not overflow the old, smaller, value, we can zero extend all of the 921 // operands (often constants). This allows analysis of something like 922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 924 if (AR->isAffine()) { 925 const SCEV *Start = AR->getStart(); 926 const SCEV *Step = AR->getStepRecurrence(*this); 927 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 928 const Loop *L = AR->getLoop(); 929 930 // If we have special knowledge that this addrec won't overflow, 931 // we don't need to do any further analysis. 932 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 933 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 934 getZeroExtendExpr(Step, Ty), 935 L, AR->getNoWrapFlags()); 936 937 // Check whether the backedge-taken count is SCEVCouldNotCompute. 938 // Note that this serves two purposes: It filters out loops that are 939 // simply not analyzable, and it covers the case where this code is 940 // being called from within backedge-taken count analysis, such that 941 // attempting to ask for the backedge-taken count would likely result 942 // in infinite recursion. In the later case, the analysis code will 943 // cope with a conservative value, and it will take care to purge 944 // that value once it has finished. 945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 947 // Manually compute the final value for AR, checking for 948 // overflow. 949 950 // Check whether the backedge-taken count can be losslessly casted to 951 // the addrec's type. The count is always unsigned. 952 const SCEV *CastedMaxBECount = 953 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 954 const SCEV *RecastedMaxBECount = 955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 956 if (MaxBECount == RecastedMaxBECount) { 957 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 958 // Check whether Start+Step*MaxBECount has no unsigned overflow. 959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 960 const SCEV *Add = getAddExpr(Start, ZMul); 961 const SCEV *OperandExtendedAdd = 962 getAddExpr(getZeroExtendExpr(Start, WideTy), 963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 964 getZeroExtendExpr(Step, WideTy))); 965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 966 // Cache knowledge of AR NUW, which is propagated to this AddRec. 967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 968 // Return the expression with the addrec on the outside. 969 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 970 getZeroExtendExpr(Step, Ty), 971 L, AR->getNoWrapFlags()); 972 } 973 // Similar to above, only this time treat the step value as signed. 974 // This covers loops that count down. 975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 976 Add = getAddExpr(Start, SMul); 977 OperandExtendedAdd = 978 getAddExpr(getZeroExtendExpr(Start, WideTy), 979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 980 getSignExtendExpr(Step, WideTy))); 981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 982 // Cache knowledge of AR NW, which is propagated to this AddRec. 983 // Negative step causes unsigned wrap, but it still can't self-wrap. 984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 985 // Return the expression with the addrec on the outside. 986 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 987 getSignExtendExpr(Step, Ty), 988 L, AR->getNoWrapFlags()); 989 } 990 } 991 992 // If the backedge is guarded by a comparison with the pre-inc value 993 // the addrec is safe. Also, if the entry is guarded by a comparison 994 // with the start value and the backedge is guarded by a comparison 995 // with the post-inc value, the addrec is safe. 996 if (isKnownPositive(Step)) { 997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 998 getUnsignedRange(Step).getUnsignedMax()); 999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1002 AR->getPostIncExpr(*this), N))) { 1003 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1005 // Return the expression with the addrec on the outside. 1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1007 getZeroExtendExpr(Step, Ty), 1008 L, AR->getNoWrapFlags()); 1009 } 1010 } else if (isKnownNegative(Step)) { 1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1012 getSignedRange(Step).getSignedMin()); 1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1016 AR->getPostIncExpr(*this), N))) { 1017 // Cache knowledge of AR NW, which is propagated to this AddRec. 1018 // Negative step causes unsigned wrap, but it still can't self-wrap. 1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1020 // Return the expression with the addrec on the outside. 1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1022 getSignExtendExpr(Step, Ty), 1023 L, AR->getNoWrapFlags()); 1024 } 1025 } 1026 } 1027 } 1028 1029 // The cast wasn't folded; create an explicit cast node. 1030 // Recompute the insert position, as it may have been invalidated. 1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1033 Op, Ty); 1034 UniqueSCEVs.InsertNode(S, IP); 1035 return S; 1036} 1037 1038// Get the limit of a recurrence such that incrementing by Step cannot cause 1039// signed overflow as long as the value of the recurrence within the loop does 1040// not exceed this limit before incrementing. 1041static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1042 ICmpInst::Predicate *Pred, 1043 ScalarEvolution *SE) { 1044 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1045 if (SE->isKnownPositive(Step)) { 1046 *Pred = ICmpInst::ICMP_SLT; 1047 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1048 SE->getSignedRange(Step).getSignedMax()); 1049 } 1050 if (SE->isKnownNegative(Step)) { 1051 *Pred = ICmpInst::ICMP_SGT; 1052 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1053 SE->getSignedRange(Step).getSignedMin()); 1054 } 1055 return 0; 1056} 1057 1058// The recurrence AR has been shown to have no signed wrap. Typically, if we can 1059// prove NSW for AR, then we can just as easily prove NSW for its preincrement 1060// or postincrement sibling. This allows normalizing a sign extended AddRec as 1061// such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a 1062// result, the expression "Step + sext(PreIncAR)" is congruent with 1063// "sext(PostIncAR)" 1064static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR, 1065 Type *Ty, 1066 ScalarEvolution *SE) { 1067 const Loop *L = AR->getLoop(); 1068 const SCEV *Start = AR->getStart(); 1069 const SCEV *Step = AR->getStepRecurrence(*SE); 1070 1071 // Check for a simple looking step prior to loop entry. 1072 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1073 if (!SA) 1074 return 0; 1075 1076 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1077 // subtraction is expensive. For this purpose, perform a quick and dirty 1078 // difference, by checking for Step in the operand list. 1079 SmallVector<const SCEV *, 4> DiffOps; 1080 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end(); 1081 I != E; ++I) { 1082 if (*I != Step) 1083 DiffOps.push_back(*I); 1084 } 1085 if (DiffOps.size() == SA->getNumOperands()) 1086 return 0; 1087 1088 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1089 // same three conditions that getSignExtendedExpr checks. 1090 1091 // 1. NSW flags on the step increment. 1092 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags()); 1093 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1094 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1095 1096 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1097 return PreStart; 1098 1099 // 2. Direct overflow check on the step operation's expression. 1100 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1101 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1102 const SCEV *OperandExtendedStart = 1103 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1104 SE->getSignExtendExpr(Step, WideTy)); 1105 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1106 // Cache knowledge of PreAR NSW. 1107 if (PreAR) 1108 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1109 // FIXME: this optimization needs a unit test 1110 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1111 return PreStart; 1112 } 1113 1114 // 3. Loop precondition. 1115 ICmpInst::Predicate Pred; 1116 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1117 1118 if (OverflowLimit && 1119 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1120 return PreStart; 1121 } 1122 return 0; 1123} 1124 1125// Get the normalized sign-extended expression for this AddRec's Start. 1126static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1127 Type *Ty, 1128 ScalarEvolution *SE) { 1129 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1130 if (!PreStart) 1131 return SE->getSignExtendExpr(AR->getStart(), Ty); 1132 1133 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1134 SE->getSignExtendExpr(PreStart, Ty)); 1135} 1136 1137const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1138 Type *Ty) { 1139 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1140 "This is not an extending conversion!"); 1141 assert(isSCEVable(Ty) && 1142 "This is not a conversion to a SCEVable type!"); 1143 Ty = getEffectiveSCEVType(Ty); 1144 1145 // Fold if the operand is constant. 1146 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1147 return getConstant( 1148 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1149 getEffectiveSCEVType(Ty)))); 1150 1151 // sext(sext(x)) --> sext(x) 1152 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1153 return getSignExtendExpr(SS->getOperand(), Ty); 1154 1155 // sext(zext(x)) --> zext(x) 1156 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1157 return getZeroExtendExpr(SZ->getOperand(), Ty); 1158 1159 // Before doing any expensive analysis, check to see if we've already 1160 // computed a SCEV for this Op and Ty. 1161 FoldingSetNodeID ID; 1162 ID.AddInteger(scSignExtend); 1163 ID.AddPointer(Op); 1164 ID.AddPointer(Ty); 1165 void *IP = 0; 1166 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1167 1168 // If the input value is provably positive, build a zext instead. 1169 if (isKnownNonNegative(Op)) 1170 return getZeroExtendExpr(Op, Ty); 1171 1172 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1173 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1174 // It's possible the bits taken off by the truncate were all sign bits. If 1175 // so, we should be able to simplify this further. 1176 const SCEV *X = ST->getOperand(); 1177 ConstantRange CR = getSignedRange(X); 1178 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1179 unsigned NewBits = getTypeSizeInBits(Ty); 1180 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1181 CR.sextOrTrunc(NewBits))) 1182 return getTruncateOrSignExtend(X, Ty); 1183 } 1184 1185 // If the input value is a chrec scev, and we can prove that the value 1186 // did not overflow the old, smaller, value, we can sign extend all of the 1187 // operands (often constants). This allows analysis of something like 1188 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1189 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1190 if (AR->isAffine()) { 1191 const SCEV *Start = AR->getStart(); 1192 const SCEV *Step = AR->getStepRecurrence(*this); 1193 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1194 const Loop *L = AR->getLoop(); 1195 1196 // If we have special knowledge that this addrec won't overflow, 1197 // we don't need to do any further analysis. 1198 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1199 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1200 getSignExtendExpr(Step, Ty), 1201 L, SCEV::FlagNSW); 1202 1203 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1204 // Note that this serves two purposes: It filters out loops that are 1205 // simply not analyzable, and it covers the case where this code is 1206 // being called from within backedge-taken count analysis, such that 1207 // attempting to ask for the backedge-taken count would likely result 1208 // in infinite recursion. In the later case, the analysis code will 1209 // cope with a conservative value, and it will take care to purge 1210 // that value once it has finished. 1211 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1212 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1213 // Manually compute the final value for AR, checking for 1214 // overflow. 1215 1216 // Check whether the backedge-taken count can be losslessly casted to 1217 // the addrec's type. The count is always unsigned. 1218 const SCEV *CastedMaxBECount = 1219 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1220 const SCEV *RecastedMaxBECount = 1221 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1222 if (MaxBECount == RecastedMaxBECount) { 1223 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1224 // Check whether Start+Step*MaxBECount has no signed overflow. 1225 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1226 const SCEV *Add = getAddExpr(Start, SMul); 1227 const SCEV *OperandExtendedAdd = 1228 getAddExpr(getSignExtendExpr(Start, WideTy), 1229 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1230 getSignExtendExpr(Step, WideTy))); 1231 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1232 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1233 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1234 // Return the expression with the addrec on the outside. 1235 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1236 getSignExtendExpr(Step, Ty), 1237 L, AR->getNoWrapFlags()); 1238 } 1239 // Similar to above, only this time treat the step value as unsigned. 1240 // This covers loops that count up with an unsigned step. 1241 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1242 Add = getAddExpr(Start, UMul); 1243 OperandExtendedAdd = 1244 getAddExpr(getSignExtendExpr(Start, WideTy), 1245 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1246 getZeroExtendExpr(Step, WideTy))); 1247 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1248 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1249 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1250 // Return the expression with the addrec on the outside. 1251 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1252 getZeroExtendExpr(Step, Ty), 1253 L, AR->getNoWrapFlags()); 1254 } 1255 } 1256 1257 // If the backedge is guarded by a comparison with the pre-inc value 1258 // the addrec is safe. Also, if the entry is guarded by a comparison 1259 // with the start value and the backedge is guarded by a comparison 1260 // with the post-inc value, the addrec is safe. 1261 ICmpInst::Predicate Pred; 1262 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1263 if (OverflowLimit && 1264 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1265 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1266 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1267 OverflowLimit)))) { 1268 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1269 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1270 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1271 getSignExtendExpr(Step, Ty), 1272 L, AR->getNoWrapFlags()); 1273 } 1274 } 1275 } 1276 1277 // The cast wasn't folded; create an explicit cast node. 1278 // Recompute the insert position, as it may have been invalidated. 1279 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1280 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1281 Op, Ty); 1282 UniqueSCEVs.InsertNode(S, IP); 1283 return S; 1284} 1285 1286/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1287/// unspecified bits out to the given type. 1288/// 1289const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1290 Type *Ty) { 1291 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1292 "This is not an extending conversion!"); 1293 assert(isSCEVable(Ty) && 1294 "This is not a conversion to a SCEVable type!"); 1295 Ty = getEffectiveSCEVType(Ty); 1296 1297 // Sign-extend negative constants. 1298 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1299 if (SC->getValue()->getValue().isNegative()) 1300 return getSignExtendExpr(Op, Ty); 1301 1302 // Peel off a truncate cast. 1303 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1304 const SCEV *NewOp = T->getOperand(); 1305 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1306 return getAnyExtendExpr(NewOp, Ty); 1307 return getTruncateOrNoop(NewOp, Ty); 1308 } 1309 1310 // Next try a zext cast. If the cast is folded, use it. 1311 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1312 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1313 return ZExt; 1314 1315 // Next try a sext cast. If the cast is folded, use it. 1316 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1317 if (!isa<SCEVSignExtendExpr>(SExt)) 1318 return SExt; 1319 1320 // Force the cast to be folded into the operands of an addrec. 1321 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1322 SmallVector<const SCEV *, 4> Ops; 1323 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1324 I != E; ++I) 1325 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1326 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1327 } 1328 1329 // As a special case, fold anyext(undef) to undef. We don't want to 1330 // know too much about SCEVUnknowns, but this special case is handy 1331 // and harmless. 1332 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1333 if (isa<UndefValue>(U->getValue())) 1334 return getSCEV(UndefValue::get(Ty)); 1335 1336 // If the expression is obviously signed, use the sext cast value. 1337 if (isa<SCEVSMaxExpr>(Op)) 1338 return SExt; 1339 1340 // Absent any other information, use the zext cast value. 1341 return ZExt; 1342} 1343 1344/// CollectAddOperandsWithScales - Process the given Ops list, which is 1345/// a list of operands to be added under the given scale, update the given 1346/// map. This is a helper function for getAddRecExpr. As an example of 1347/// what it does, given a sequence of operands that would form an add 1348/// expression like this: 1349/// 1350/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1351/// 1352/// where A and B are constants, update the map with these values: 1353/// 1354/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1355/// 1356/// and add 13 + A*B*29 to AccumulatedConstant. 1357/// This will allow getAddRecExpr to produce this: 1358/// 1359/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1360/// 1361/// This form often exposes folding opportunities that are hidden in 1362/// the original operand list. 1363/// 1364/// Return true iff it appears that any interesting folding opportunities 1365/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1366/// the common case where no interesting opportunities are present, and 1367/// is also used as a check to avoid infinite recursion. 1368/// 1369static bool 1370CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1371 SmallVector<const SCEV *, 8> &NewOps, 1372 APInt &AccumulatedConstant, 1373 const SCEV *const *Ops, size_t NumOperands, 1374 const APInt &Scale, 1375 ScalarEvolution &SE) { 1376 bool Interesting = false; 1377 1378 // Iterate over the add operands. They are sorted, with constants first. 1379 unsigned i = 0; 1380 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1381 ++i; 1382 // Pull a buried constant out to the outside. 1383 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1384 Interesting = true; 1385 AccumulatedConstant += Scale * C->getValue()->getValue(); 1386 } 1387 1388 // Next comes everything else. We're especially interested in multiplies 1389 // here, but they're in the middle, so just visit the rest with one loop. 1390 for (; i != NumOperands; ++i) { 1391 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1392 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1393 APInt NewScale = 1394 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1395 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1396 // A multiplication of a constant with another add; recurse. 1397 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1398 Interesting |= 1399 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1400 Add->op_begin(), Add->getNumOperands(), 1401 NewScale, SE); 1402 } else { 1403 // A multiplication of a constant with some other value. Update 1404 // the map. 1405 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1406 const SCEV *Key = SE.getMulExpr(MulOps); 1407 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1408 M.insert(std::make_pair(Key, NewScale)); 1409 if (Pair.second) { 1410 NewOps.push_back(Pair.first->first); 1411 } else { 1412 Pair.first->second += NewScale; 1413 // The map already had an entry for this value, which may indicate 1414 // a folding opportunity. 1415 Interesting = true; 1416 } 1417 } 1418 } else { 1419 // An ordinary operand. Update the map. 1420 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1421 M.insert(std::make_pair(Ops[i], Scale)); 1422 if (Pair.second) { 1423 NewOps.push_back(Pair.first->first); 1424 } else { 1425 Pair.first->second += Scale; 1426 // The map already had an entry for this value, which may indicate 1427 // a folding opportunity. 1428 Interesting = true; 1429 } 1430 } 1431 } 1432 1433 return Interesting; 1434} 1435 1436namespace { 1437 struct APIntCompare { 1438 bool operator()(const APInt &LHS, const APInt &RHS) const { 1439 return LHS.ult(RHS); 1440 } 1441 }; 1442} 1443 1444/// getAddExpr - Get a canonical add expression, or something simpler if 1445/// possible. 1446const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1447 SCEV::NoWrapFlags Flags) { 1448 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1449 "only nuw or nsw allowed"); 1450 assert(!Ops.empty() && "Cannot get empty add!"); 1451 if (Ops.size() == 1) return Ops[0]; 1452#ifndef NDEBUG 1453 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1454 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1455 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1456 "SCEVAddExpr operand types don't match!"); 1457#endif 1458 1459 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1460 // And vice-versa. 1461 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1462 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1463 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1464 bool All = true; 1465 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1466 E = Ops.end(); I != E; ++I) 1467 if (!isKnownNonNegative(*I)) { 1468 All = false; 1469 break; 1470 } 1471 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1472 } 1473 1474 // Sort by complexity, this groups all similar expression types together. 1475 GroupByComplexity(Ops, LI); 1476 1477 // If there are any constants, fold them together. 1478 unsigned Idx = 0; 1479 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1480 ++Idx; 1481 assert(Idx < Ops.size()); 1482 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1483 // We found two constants, fold them together! 1484 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1485 RHSC->getValue()->getValue()); 1486 if (Ops.size() == 2) return Ops[0]; 1487 Ops.erase(Ops.begin()+1); // Erase the folded element 1488 LHSC = cast<SCEVConstant>(Ops[0]); 1489 } 1490 1491 // If we are left with a constant zero being added, strip it off. 1492 if (LHSC->getValue()->isZero()) { 1493 Ops.erase(Ops.begin()); 1494 --Idx; 1495 } 1496 1497 if (Ops.size() == 1) return Ops[0]; 1498 } 1499 1500 // Okay, check to see if the same value occurs in the operand list more than 1501 // once. If so, merge them together into an multiply expression. Since we 1502 // sorted the list, these values are required to be adjacent. 1503 Type *Ty = Ops[0]->getType(); 1504 bool FoundMatch = false; 1505 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1506 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1507 // Scan ahead to count how many equal operands there are. 1508 unsigned Count = 2; 1509 while (i+Count != e && Ops[i+Count] == Ops[i]) 1510 ++Count; 1511 // Merge the values into a multiply. 1512 const SCEV *Scale = getConstant(Ty, Count); 1513 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1514 if (Ops.size() == Count) 1515 return Mul; 1516 Ops[i] = Mul; 1517 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1518 --i; e -= Count - 1; 1519 FoundMatch = true; 1520 } 1521 if (FoundMatch) 1522 return getAddExpr(Ops, Flags); 1523 1524 // Check for truncates. If all the operands are truncated from the same 1525 // type, see if factoring out the truncate would permit the result to be 1526 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1527 // if the contents of the resulting outer trunc fold to something simple. 1528 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1529 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1530 Type *DstType = Trunc->getType(); 1531 Type *SrcType = Trunc->getOperand()->getType(); 1532 SmallVector<const SCEV *, 8> LargeOps; 1533 bool Ok = true; 1534 // Check all the operands to see if they can be represented in the 1535 // source type of the truncate. 1536 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1537 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1538 if (T->getOperand()->getType() != SrcType) { 1539 Ok = false; 1540 break; 1541 } 1542 LargeOps.push_back(T->getOperand()); 1543 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1544 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1545 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1546 SmallVector<const SCEV *, 8> LargeMulOps; 1547 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1548 if (const SCEVTruncateExpr *T = 1549 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1550 if (T->getOperand()->getType() != SrcType) { 1551 Ok = false; 1552 break; 1553 } 1554 LargeMulOps.push_back(T->getOperand()); 1555 } else if (const SCEVConstant *C = 1556 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1557 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1558 } else { 1559 Ok = false; 1560 break; 1561 } 1562 } 1563 if (Ok) 1564 LargeOps.push_back(getMulExpr(LargeMulOps)); 1565 } else { 1566 Ok = false; 1567 break; 1568 } 1569 } 1570 if (Ok) { 1571 // Evaluate the expression in the larger type. 1572 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1573 // If it folds to something simple, use it. Otherwise, don't. 1574 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1575 return getTruncateExpr(Fold, DstType); 1576 } 1577 } 1578 1579 // Skip past any other cast SCEVs. 1580 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1581 ++Idx; 1582 1583 // If there are add operands they would be next. 1584 if (Idx < Ops.size()) { 1585 bool DeletedAdd = false; 1586 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1587 // If we have an add, expand the add operands onto the end of the operands 1588 // list. 1589 Ops.erase(Ops.begin()+Idx); 1590 Ops.append(Add->op_begin(), Add->op_end()); 1591 DeletedAdd = true; 1592 } 1593 1594 // If we deleted at least one add, we added operands to the end of the list, 1595 // and they are not necessarily sorted. Recurse to resort and resimplify 1596 // any operands we just acquired. 1597 if (DeletedAdd) 1598 return getAddExpr(Ops); 1599 } 1600 1601 // Skip over the add expression until we get to a multiply. 1602 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1603 ++Idx; 1604 1605 // Check to see if there are any folding opportunities present with 1606 // operands multiplied by constant values. 1607 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1608 uint64_t BitWidth = getTypeSizeInBits(Ty); 1609 DenseMap<const SCEV *, APInt> M; 1610 SmallVector<const SCEV *, 8> NewOps; 1611 APInt AccumulatedConstant(BitWidth, 0); 1612 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1613 Ops.data(), Ops.size(), 1614 APInt(BitWidth, 1), *this)) { 1615 // Some interesting folding opportunity is present, so its worthwhile to 1616 // re-generate the operands list. Group the operands by constant scale, 1617 // to avoid multiplying by the same constant scale multiple times. 1618 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1619 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1620 E = NewOps.end(); I != E; ++I) 1621 MulOpLists[M.find(*I)->second].push_back(*I); 1622 // Re-generate the operands list. 1623 Ops.clear(); 1624 if (AccumulatedConstant != 0) 1625 Ops.push_back(getConstant(AccumulatedConstant)); 1626 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1627 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1628 if (I->first != 0) 1629 Ops.push_back(getMulExpr(getConstant(I->first), 1630 getAddExpr(I->second))); 1631 if (Ops.empty()) 1632 return getConstant(Ty, 0); 1633 if (Ops.size() == 1) 1634 return Ops[0]; 1635 return getAddExpr(Ops); 1636 } 1637 } 1638 1639 // If we are adding something to a multiply expression, make sure the 1640 // something is not already an operand of the multiply. If so, merge it into 1641 // the multiply. 1642 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1643 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1644 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1645 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1646 if (isa<SCEVConstant>(MulOpSCEV)) 1647 continue; 1648 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1649 if (MulOpSCEV == Ops[AddOp]) { 1650 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1651 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1652 if (Mul->getNumOperands() != 2) { 1653 // If the multiply has more than two operands, we must get the 1654 // Y*Z term. 1655 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1656 Mul->op_begin()+MulOp); 1657 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1658 InnerMul = getMulExpr(MulOps); 1659 } 1660 const SCEV *One = getConstant(Ty, 1); 1661 const SCEV *AddOne = getAddExpr(One, InnerMul); 1662 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1663 if (Ops.size() == 2) return OuterMul; 1664 if (AddOp < Idx) { 1665 Ops.erase(Ops.begin()+AddOp); 1666 Ops.erase(Ops.begin()+Idx-1); 1667 } else { 1668 Ops.erase(Ops.begin()+Idx); 1669 Ops.erase(Ops.begin()+AddOp-1); 1670 } 1671 Ops.push_back(OuterMul); 1672 return getAddExpr(Ops); 1673 } 1674 1675 // Check this multiply against other multiplies being added together. 1676 for (unsigned OtherMulIdx = Idx+1; 1677 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1678 ++OtherMulIdx) { 1679 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1680 // If MulOp occurs in OtherMul, we can fold the two multiplies 1681 // together. 1682 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1683 OMulOp != e; ++OMulOp) 1684 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1685 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1686 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1687 if (Mul->getNumOperands() != 2) { 1688 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1689 Mul->op_begin()+MulOp); 1690 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1691 InnerMul1 = getMulExpr(MulOps); 1692 } 1693 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1694 if (OtherMul->getNumOperands() != 2) { 1695 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1696 OtherMul->op_begin()+OMulOp); 1697 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1698 InnerMul2 = getMulExpr(MulOps); 1699 } 1700 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1701 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1702 if (Ops.size() == 2) return OuterMul; 1703 Ops.erase(Ops.begin()+Idx); 1704 Ops.erase(Ops.begin()+OtherMulIdx-1); 1705 Ops.push_back(OuterMul); 1706 return getAddExpr(Ops); 1707 } 1708 } 1709 } 1710 } 1711 1712 // If there are any add recurrences in the operands list, see if any other 1713 // added values are loop invariant. If so, we can fold them into the 1714 // recurrence. 1715 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1716 ++Idx; 1717 1718 // Scan over all recurrences, trying to fold loop invariants into them. 1719 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1720 // Scan all of the other operands to this add and add them to the vector if 1721 // they are loop invariant w.r.t. the recurrence. 1722 SmallVector<const SCEV *, 8> LIOps; 1723 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1724 const Loop *AddRecLoop = AddRec->getLoop(); 1725 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1726 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1727 LIOps.push_back(Ops[i]); 1728 Ops.erase(Ops.begin()+i); 1729 --i; --e; 1730 } 1731 1732 // If we found some loop invariants, fold them into the recurrence. 1733 if (!LIOps.empty()) { 1734 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1735 LIOps.push_back(AddRec->getStart()); 1736 1737 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1738 AddRec->op_end()); 1739 AddRecOps[0] = getAddExpr(LIOps); 1740 1741 // Build the new addrec. Propagate the NUW and NSW flags if both the 1742 // outer add and the inner addrec are guaranteed to have no overflow. 1743 // Always propagate NW. 1744 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1745 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1746 1747 // If all of the other operands were loop invariant, we are done. 1748 if (Ops.size() == 1) return NewRec; 1749 1750 // Otherwise, add the folded AddRec by the non-invariant parts. 1751 for (unsigned i = 0;; ++i) 1752 if (Ops[i] == AddRec) { 1753 Ops[i] = NewRec; 1754 break; 1755 } 1756 return getAddExpr(Ops); 1757 } 1758 1759 // Okay, if there weren't any loop invariants to be folded, check to see if 1760 // there are multiple AddRec's with the same loop induction variable being 1761 // added together. If so, we can fold them. 1762 for (unsigned OtherIdx = Idx+1; 1763 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1764 ++OtherIdx) 1765 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1766 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1767 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1768 AddRec->op_end()); 1769 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1770 ++OtherIdx) 1771 if (const SCEVAddRecExpr *OtherAddRec = 1772 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1773 if (OtherAddRec->getLoop() == AddRecLoop) { 1774 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1775 i != e; ++i) { 1776 if (i >= AddRecOps.size()) { 1777 AddRecOps.append(OtherAddRec->op_begin()+i, 1778 OtherAddRec->op_end()); 1779 break; 1780 } 1781 AddRecOps[i] = getAddExpr(AddRecOps[i], 1782 OtherAddRec->getOperand(i)); 1783 } 1784 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1785 } 1786 // Step size has changed, so we cannot guarantee no self-wraparound. 1787 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1788 return getAddExpr(Ops); 1789 } 1790 1791 // Otherwise couldn't fold anything into this recurrence. Move onto the 1792 // next one. 1793 } 1794 1795 // Okay, it looks like we really DO need an add expr. Check to see if we 1796 // already have one, otherwise create a new one. 1797 FoldingSetNodeID ID; 1798 ID.AddInteger(scAddExpr); 1799 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1800 ID.AddPointer(Ops[i]); 1801 void *IP = 0; 1802 SCEVAddExpr *S = 1803 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1804 if (!S) { 1805 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1806 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1807 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1808 O, Ops.size()); 1809 UniqueSCEVs.InsertNode(S, IP); 1810 } 1811 S->setNoWrapFlags(Flags); 1812 return S; 1813} 1814 1815/// getMulExpr - Get a canonical multiply expression, or something simpler if 1816/// possible. 1817const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1818 SCEV::NoWrapFlags Flags) { 1819 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1820 "only nuw or nsw allowed"); 1821 assert(!Ops.empty() && "Cannot get empty mul!"); 1822 if (Ops.size() == 1) return Ops[0]; 1823#ifndef NDEBUG 1824 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1825 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1826 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1827 "SCEVMulExpr operand types don't match!"); 1828#endif 1829 1830 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1831 // And vice-versa. 1832 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1833 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1834 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1835 bool All = true; 1836 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1837 E = Ops.end(); I != E; ++I) 1838 if (!isKnownNonNegative(*I)) { 1839 All = false; 1840 break; 1841 } 1842 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1843 } 1844 1845 // Sort by complexity, this groups all similar expression types together. 1846 GroupByComplexity(Ops, LI); 1847 1848 // If there are any constants, fold them together. 1849 unsigned Idx = 0; 1850 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1851 1852 // C1*(C2+V) -> C1*C2 + C1*V 1853 if (Ops.size() == 2) 1854 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1855 if (Add->getNumOperands() == 2 && 1856 isa<SCEVConstant>(Add->getOperand(0))) 1857 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1858 getMulExpr(LHSC, Add->getOperand(1))); 1859 1860 ++Idx; 1861 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1862 // We found two constants, fold them together! 1863 ConstantInt *Fold = ConstantInt::get(getContext(), 1864 LHSC->getValue()->getValue() * 1865 RHSC->getValue()->getValue()); 1866 Ops[0] = getConstant(Fold); 1867 Ops.erase(Ops.begin()+1); // Erase the folded element 1868 if (Ops.size() == 1) return Ops[0]; 1869 LHSC = cast<SCEVConstant>(Ops[0]); 1870 } 1871 1872 // If we are left with a constant one being multiplied, strip it off. 1873 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1874 Ops.erase(Ops.begin()); 1875 --Idx; 1876 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1877 // If we have a multiply of zero, it will always be zero. 1878 return Ops[0]; 1879 } else if (Ops[0]->isAllOnesValue()) { 1880 // If we have a mul by -1 of an add, try distributing the -1 among the 1881 // add operands. 1882 if (Ops.size() == 2) { 1883 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1884 SmallVector<const SCEV *, 4> NewOps; 1885 bool AnyFolded = false; 1886 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1887 E = Add->op_end(); I != E; ++I) { 1888 const SCEV *Mul = getMulExpr(Ops[0], *I); 1889 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1890 NewOps.push_back(Mul); 1891 } 1892 if (AnyFolded) 1893 return getAddExpr(NewOps); 1894 } 1895 else if (const SCEVAddRecExpr * 1896 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1897 // Negation preserves a recurrence's no self-wrap property. 1898 SmallVector<const SCEV *, 4> Operands; 1899 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1900 E = AddRec->op_end(); I != E; ++I) { 1901 Operands.push_back(getMulExpr(Ops[0], *I)); 1902 } 1903 return getAddRecExpr(Operands, AddRec->getLoop(), 1904 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1905 } 1906 } 1907 } 1908 1909 if (Ops.size() == 1) 1910 return Ops[0]; 1911 } 1912 1913 // Skip over the add expression until we get to a multiply. 1914 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1915 ++Idx; 1916 1917 // If there are mul operands inline them all into this expression. 1918 if (Idx < Ops.size()) { 1919 bool DeletedMul = false; 1920 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1921 // If we have an mul, expand the mul operands onto the end of the operands 1922 // list. 1923 Ops.erase(Ops.begin()+Idx); 1924 Ops.append(Mul->op_begin(), Mul->op_end()); 1925 DeletedMul = true; 1926 } 1927 1928 // If we deleted at least one mul, we added operands to the end of the list, 1929 // and they are not necessarily sorted. Recurse to resort and resimplify 1930 // any operands we just acquired. 1931 if (DeletedMul) 1932 return getMulExpr(Ops); 1933 } 1934 1935 // If there are any add recurrences in the operands list, see if any other 1936 // added values are loop invariant. If so, we can fold them into the 1937 // recurrence. 1938 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1939 ++Idx; 1940 1941 // Scan over all recurrences, trying to fold loop invariants into them. 1942 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1943 // Scan all of the other operands to this mul and add them to the vector if 1944 // they are loop invariant w.r.t. the recurrence. 1945 SmallVector<const SCEV *, 8> LIOps; 1946 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1947 const Loop *AddRecLoop = AddRec->getLoop(); 1948 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1949 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1950 LIOps.push_back(Ops[i]); 1951 Ops.erase(Ops.begin()+i); 1952 --i; --e; 1953 } 1954 1955 // If we found some loop invariants, fold them into the recurrence. 1956 if (!LIOps.empty()) { 1957 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1958 SmallVector<const SCEV *, 4> NewOps; 1959 NewOps.reserve(AddRec->getNumOperands()); 1960 const SCEV *Scale = getMulExpr(LIOps); 1961 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1962 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1963 1964 // Build the new addrec. Propagate the NUW and NSW flags if both the 1965 // outer mul and the inner addrec are guaranteed to have no overflow. 1966 // 1967 // No self-wrap cannot be guaranteed after changing the step size, but 1968 // will be inferred if either NUW or NSW is true. 1969 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 1970 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 1971 1972 // If all of the other operands were loop invariant, we are done. 1973 if (Ops.size() == 1) return NewRec; 1974 1975 // Otherwise, multiply the folded AddRec by the non-invariant parts. 1976 for (unsigned i = 0;; ++i) 1977 if (Ops[i] == AddRec) { 1978 Ops[i] = NewRec; 1979 break; 1980 } 1981 return getMulExpr(Ops); 1982 } 1983 1984 // Okay, if there weren't any loop invariants to be folded, check to see if 1985 // there are multiple AddRec's with the same loop induction variable being 1986 // multiplied together. If so, we can fold them. 1987 for (unsigned OtherIdx = Idx+1; 1988 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1989 ++OtherIdx) { 1990 bool Retry = false; 1991 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1992 // {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L> 1993 // 1994 // {A,+,B} * {C,+,D} = A+It*B * C+It*D = A*C + (A*D + B*C)*It + B*D*It^2 1995 // Given an equation of the form x + y*It + z*It^2 (above), we want to 1996 // express it in terms of {X,+,Y,+,Z}. 1997 // {X,+,Y,+,Z} = X + Y*It + Z*(It^2 - It)/2. 1998 // Rearranging, X = x, Y = y+z, Z = 2z. 1999 // 2000 // x = A*C, y = (A*D + B*C), z = B*D. 2001 // Therefore X = A*C, Y = A*D + B*C + B*D and Z = 2*B*D. 2002 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2003 ++OtherIdx) 2004 if (const SCEVAddRecExpr *OtherAddRec = 2005 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 2006 if (OtherAddRec->getLoop() == AddRecLoop) { 2007 const SCEV *A = AddRec->getStart(); 2008 const SCEV *B = AddRec->getStepRecurrence(*this); 2009 const SCEV *C = OtherAddRec->getStart(); 2010 const SCEV *D = OtherAddRec->getStepRecurrence(*this); 2011 const SCEV *NewStart = getMulExpr(A, C); 2012 const SCEV *BD = getMulExpr(B, D); 2013 const SCEV *NewStep = getAddExpr(getMulExpr(A, D), 2014 getMulExpr(B, C), BD); 2015 const SCEV *NewSecondOrderStep = 2016 getMulExpr(BD, getConstant(BD->getType(), 2)); 2017 2018 // This can happen when AddRec or OtherAddRec have >3 operands. 2019 // TODO: support these add-recs. 2020 if (isLoopInvariant(NewStart, AddRecLoop) && 2021 isLoopInvariant(NewStep, AddRecLoop) && 2022 isLoopInvariant(NewSecondOrderStep, AddRecLoop)) { 2023 SmallVector<const SCEV *, 3> AddRecOps; 2024 AddRecOps.push_back(NewStart); 2025 AddRecOps.push_back(NewStep); 2026 AddRecOps.push_back(NewSecondOrderStep); 2027 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, 2028 AddRec->getLoop(), 2029 SCEV::FlagAnyWrap); 2030 if (Ops.size() == 2) return NewAddRec; 2031 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 2032 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2033 Retry = true; 2034 } 2035 } 2036 if (Retry) 2037 return getMulExpr(Ops); 2038 } 2039 } 2040 2041 // Otherwise couldn't fold anything into this recurrence. Move onto the 2042 // next one. 2043 } 2044 2045 // Okay, it looks like we really DO need an mul expr. Check to see if we 2046 // already have one, otherwise create a new one. 2047 FoldingSetNodeID ID; 2048 ID.AddInteger(scMulExpr); 2049 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2050 ID.AddPointer(Ops[i]); 2051 void *IP = 0; 2052 SCEVMulExpr *S = 2053 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2054 if (!S) { 2055 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2056 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2057 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2058 O, Ops.size()); 2059 UniqueSCEVs.InsertNode(S, IP); 2060 } 2061 S->setNoWrapFlags(Flags); 2062 return S; 2063} 2064 2065/// getUDivExpr - Get a canonical unsigned division expression, or something 2066/// simpler if possible. 2067const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2068 const SCEV *RHS) { 2069 assert(getEffectiveSCEVType(LHS->getType()) == 2070 getEffectiveSCEVType(RHS->getType()) && 2071 "SCEVUDivExpr operand types don't match!"); 2072 2073 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2074 if (RHSC->getValue()->equalsInt(1)) 2075 return LHS; // X udiv 1 --> x 2076 // If the denominator is zero, the result of the udiv is undefined. Don't 2077 // try to analyze it, because the resolution chosen here may differ from 2078 // the resolution chosen in other parts of the compiler. 2079 if (!RHSC->getValue()->isZero()) { 2080 // Determine if the division can be folded into the operands of 2081 // its operands. 2082 // TODO: Generalize this to non-constants by using known-bits information. 2083 Type *Ty = LHS->getType(); 2084 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2085 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2086 // For non-power-of-two values, effectively round the value up to the 2087 // nearest power of two. 2088 if (!RHSC->getValue()->getValue().isPowerOf2()) 2089 ++MaxShiftAmt; 2090 IntegerType *ExtTy = 2091 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2092 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2093 if (const SCEVConstant *Step = 2094 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2095 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2096 const APInt &StepInt = Step->getValue()->getValue(); 2097 const APInt &DivInt = RHSC->getValue()->getValue(); 2098 if (!StepInt.urem(DivInt) && 2099 getZeroExtendExpr(AR, ExtTy) == 2100 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2101 getZeroExtendExpr(Step, ExtTy), 2102 AR->getLoop(), SCEV::FlagAnyWrap)) { 2103 SmallVector<const SCEV *, 4> Operands; 2104 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2105 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2106 return getAddRecExpr(Operands, AR->getLoop(), 2107 SCEV::FlagNW); 2108 } 2109 /// Get a canonical UDivExpr for a recurrence. 2110 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2111 // We can currently only fold X%N if X is constant. 2112 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2113 if (StartC && !DivInt.urem(StepInt) && 2114 getZeroExtendExpr(AR, ExtTy) == 2115 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2116 getZeroExtendExpr(Step, ExtTy), 2117 AR->getLoop(), SCEV::FlagAnyWrap)) { 2118 const APInt &StartInt = StartC->getValue()->getValue(); 2119 const APInt &StartRem = StartInt.urem(StepInt); 2120 if (StartRem != 0) 2121 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2122 AR->getLoop(), SCEV::FlagNW); 2123 } 2124 } 2125 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2126 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2127 SmallVector<const SCEV *, 4> Operands; 2128 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2129 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2130 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2131 // Find an operand that's safely divisible. 2132 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2133 const SCEV *Op = M->getOperand(i); 2134 const SCEV *Div = getUDivExpr(Op, RHSC); 2135 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2136 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2137 M->op_end()); 2138 Operands[i] = Div; 2139 return getMulExpr(Operands); 2140 } 2141 } 2142 } 2143 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2144 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2145 SmallVector<const SCEV *, 4> Operands; 2146 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2147 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2148 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2149 Operands.clear(); 2150 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2151 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2152 if (isa<SCEVUDivExpr>(Op) || 2153 getMulExpr(Op, RHS) != A->getOperand(i)) 2154 break; 2155 Operands.push_back(Op); 2156 } 2157 if (Operands.size() == A->getNumOperands()) 2158 return getAddExpr(Operands); 2159 } 2160 } 2161 2162 // Fold if both operands are constant. 2163 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2164 Constant *LHSCV = LHSC->getValue(); 2165 Constant *RHSCV = RHSC->getValue(); 2166 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2167 RHSCV))); 2168 } 2169 } 2170 } 2171 2172 FoldingSetNodeID ID; 2173 ID.AddInteger(scUDivExpr); 2174 ID.AddPointer(LHS); 2175 ID.AddPointer(RHS); 2176 void *IP = 0; 2177 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2178 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2179 LHS, RHS); 2180 UniqueSCEVs.InsertNode(S, IP); 2181 return S; 2182} 2183 2184 2185/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2186/// Simplify the expression as much as possible. 2187const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2188 const Loop *L, 2189 SCEV::NoWrapFlags Flags) { 2190 SmallVector<const SCEV *, 4> Operands; 2191 Operands.push_back(Start); 2192 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2193 if (StepChrec->getLoop() == L) { 2194 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2195 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2196 } 2197 2198 Operands.push_back(Step); 2199 return getAddRecExpr(Operands, L, Flags); 2200} 2201 2202/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2203/// Simplify the expression as much as possible. 2204const SCEV * 2205ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2206 const Loop *L, SCEV::NoWrapFlags Flags) { 2207 if (Operands.size() == 1) return Operands[0]; 2208#ifndef NDEBUG 2209 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2210 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2211 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2212 "SCEVAddRecExpr operand types don't match!"); 2213 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2214 assert(isLoopInvariant(Operands[i], L) && 2215 "SCEVAddRecExpr operand is not loop-invariant!"); 2216#endif 2217 2218 if (Operands.back()->isZero()) { 2219 Operands.pop_back(); 2220 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2221 } 2222 2223 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2224 // use that information to infer NUW and NSW flags. However, computing a 2225 // BE count requires calling getAddRecExpr, so we may not yet have a 2226 // meaningful BE count at this point (and if we don't, we'd be stuck 2227 // with a SCEVCouldNotCompute as the cached BE count). 2228 2229 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2230 // And vice-versa. 2231 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2232 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2233 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2234 bool All = true; 2235 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2236 E = Operands.end(); I != E; ++I) 2237 if (!isKnownNonNegative(*I)) { 2238 All = false; 2239 break; 2240 } 2241 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2242 } 2243 2244 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2245 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2246 const Loop *NestedLoop = NestedAR->getLoop(); 2247 if (L->contains(NestedLoop) ? 2248 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2249 (!NestedLoop->contains(L) && 2250 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2251 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2252 NestedAR->op_end()); 2253 Operands[0] = NestedAR->getStart(); 2254 // AddRecs require their operands be loop-invariant with respect to their 2255 // loops. Don't perform this transformation if it would break this 2256 // requirement. 2257 bool AllInvariant = true; 2258 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2259 if (!isLoopInvariant(Operands[i], L)) { 2260 AllInvariant = false; 2261 break; 2262 } 2263 if (AllInvariant) { 2264 // Create a recurrence for the outer loop with the same step size. 2265 // 2266 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2267 // inner recurrence has the same property. 2268 SCEV::NoWrapFlags OuterFlags = 2269 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2270 2271 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2272 AllInvariant = true; 2273 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2274 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2275 AllInvariant = false; 2276 break; 2277 } 2278 if (AllInvariant) { 2279 // Ok, both add recurrences are valid after the transformation. 2280 // 2281 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2282 // the outer recurrence has the same property. 2283 SCEV::NoWrapFlags InnerFlags = 2284 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2285 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2286 } 2287 } 2288 // Reset Operands to its original state. 2289 Operands[0] = NestedAR; 2290 } 2291 } 2292 2293 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2294 // already have one, otherwise create a new one. 2295 FoldingSetNodeID ID; 2296 ID.AddInteger(scAddRecExpr); 2297 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2298 ID.AddPointer(Operands[i]); 2299 ID.AddPointer(L); 2300 void *IP = 0; 2301 SCEVAddRecExpr *S = 2302 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2303 if (!S) { 2304 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2305 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2306 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2307 O, Operands.size(), L); 2308 UniqueSCEVs.InsertNode(S, IP); 2309 } 2310 S->setNoWrapFlags(Flags); 2311 return S; 2312} 2313 2314const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2315 const SCEV *RHS) { 2316 SmallVector<const SCEV *, 2> Ops; 2317 Ops.push_back(LHS); 2318 Ops.push_back(RHS); 2319 return getSMaxExpr(Ops); 2320} 2321 2322const SCEV * 2323ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2324 assert(!Ops.empty() && "Cannot get empty smax!"); 2325 if (Ops.size() == 1) return Ops[0]; 2326#ifndef NDEBUG 2327 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2328 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2329 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2330 "SCEVSMaxExpr operand types don't match!"); 2331#endif 2332 2333 // Sort by complexity, this groups all similar expression types together. 2334 GroupByComplexity(Ops, LI); 2335 2336 // If there are any constants, fold them together. 2337 unsigned Idx = 0; 2338 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2339 ++Idx; 2340 assert(Idx < Ops.size()); 2341 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2342 // We found two constants, fold them together! 2343 ConstantInt *Fold = ConstantInt::get(getContext(), 2344 APIntOps::smax(LHSC->getValue()->getValue(), 2345 RHSC->getValue()->getValue())); 2346 Ops[0] = getConstant(Fold); 2347 Ops.erase(Ops.begin()+1); // Erase the folded element 2348 if (Ops.size() == 1) return Ops[0]; 2349 LHSC = cast<SCEVConstant>(Ops[0]); 2350 } 2351 2352 // If we are left with a constant minimum-int, strip it off. 2353 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2354 Ops.erase(Ops.begin()); 2355 --Idx; 2356 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2357 // If we have an smax with a constant maximum-int, it will always be 2358 // maximum-int. 2359 return Ops[0]; 2360 } 2361 2362 if (Ops.size() == 1) return Ops[0]; 2363 } 2364 2365 // Find the first SMax 2366 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2367 ++Idx; 2368 2369 // Check to see if one of the operands is an SMax. If so, expand its operands 2370 // onto our operand list, and recurse to simplify. 2371 if (Idx < Ops.size()) { 2372 bool DeletedSMax = false; 2373 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2374 Ops.erase(Ops.begin()+Idx); 2375 Ops.append(SMax->op_begin(), SMax->op_end()); 2376 DeletedSMax = true; 2377 } 2378 2379 if (DeletedSMax) 2380 return getSMaxExpr(Ops); 2381 } 2382 2383 // Okay, check to see if the same value occurs in the operand list twice. If 2384 // so, delete one. Since we sorted the list, these values are required to 2385 // be adjacent. 2386 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2387 // X smax Y smax Y --> X smax Y 2388 // X smax Y --> X, if X is always greater than Y 2389 if (Ops[i] == Ops[i+1] || 2390 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2391 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2392 --i; --e; 2393 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2394 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2395 --i; --e; 2396 } 2397 2398 if (Ops.size() == 1) return Ops[0]; 2399 2400 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2401 2402 // Okay, it looks like we really DO need an smax expr. Check to see if we 2403 // already have one, otherwise create a new one. 2404 FoldingSetNodeID ID; 2405 ID.AddInteger(scSMaxExpr); 2406 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2407 ID.AddPointer(Ops[i]); 2408 void *IP = 0; 2409 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2410 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2411 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2412 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2413 O, Ops.size()); 2414 UniqueSCEVs.InsertNode(S, IP); 2415 return S; 2416} 2417 2418const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2419 const SCEV *RHS) { 2420 SmallVector<const SCEV *, 2> Ops; 2421 Ops.push_back(LHS); 2422 Ops.push_back(RHS); 2423 return getUMaxExpr(Ops); 2424} 2425 2426const SCEV * 2427ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2428 assert(!Ops.empty() && "Cannot get empty umax!"); 2429 if (Ops.size() == 1) return Ops[0]; 2430#ifndef NDEBUG 2431 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2432 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2433 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2434 "SCEVUMaxExpr operand types don't match!"); 2435#endif 2436 2437 // Sort by complexity, this groups all similar expression types together. 2438 GroupByComplexity(Ops, LI); 2439 2440 // If there are any constants, fold them together. 2441 unsigned Idx = 0; 2442 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2443 ++Idx; 2444 assert(Idx < Ops.size()); 2445 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2446 // We found two constants, fold them together! 2447 ConstantInt *Fold = ConstantInt::get(getContext(), 2448 APIntOps::umax(LHSC->getValue()->getValue(), 2449 RHSC->getValue()->getValue())); 2450 Ops[0] = getConstant(Fold); 2451 Ops.erase(Ops.begin()+1); // Erase the folded element 2452 if (Ops.size() == 1) return Ops[0]; 2453 LHSC = cast<SCEVConstant>(Ops[0]); 2454 } 2455 2456 // If we are left with a constant minimum-int, strip it off. 2457 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2458 Ops.erase(Ops.begin()); 2459 --Idx; 2460 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2461 // If we have an umax with a constant maximum-int, it will always be 2462 // maximum-int. 2463 return Ops[0]; 2464 } 2465 2466 if (Ops.size() == 1) return Ops[0]; 2467 } 2468 2469 // Find the first UMax 2470 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2471 ++Idx; 2472 2473 // Check to see if one of the operands is a UMax. If so, expand its operands 2474 // onto our operand list, and recurse to simplify. 2475 if (Idx < Ops.size()) { 2476 bool DeletedUMax = false; 2477 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2478 Ops.erase(Ops.begin()+Idx); 2479 Ops.append(UMax->op_begin(), UMax->op_end()); 2480 DeletedUMax = true; 2481 } 2482 2483 if (DeletedUMax) 2484 return getUMaxExpr(Ops); 2485 } 2486 2487 // Okay, check to see if the same value occurs in the operand list twice. If 2488 // so, delete one. Since we sorted the list, these values are required to 2489 // be adjacent. 2490 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2491 // X umax Y umax Y --> X umax Y 2492 // X umax Y --> X, if X is always greater than Y 2493 if (Ops[i] == Ops[i+1] || 2494 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2495 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2496 --i; --e; 2497 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2498 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2499 --i; --e; 2500 } 2501 2502 if (Ops.size() == 1) return Ops[0]; 2503 2504 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2505 2506 // Okay, it looks like we really DO need a umax expr. Check to see if we 2507 // already have one, otherwise create a new one. 2508 FoldingSetNodeID ID; 2509 ID.AddInteger(scUMaxExpr); 2510 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2511 ID.AddPointer(Ops[i]); 2512 void *IP = 0; 2513 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2514 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2515 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2516 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2517 O, Ops.size()); 2518 UniqueSCEVs.InsertNode(S, IP); 2519 return S; 2520} 2521 2522const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2523 const SCEV *RHS) { 2524 // ~smax(~x, ~y) == smin(x, y). 2525 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2526} 2527 2528const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2529 const SCEV *RHS) { 2530 // ~umax(~x, ~y) == umin(x, y) 2531 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2532} 2533 2534const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2535 // If we have TargetData, we can bypass creating a target-independent 2536 // constant expression and then folding it back into a ConstantInt. 2537 // This is just a compile-time optimization. 2538 if (TD) 2539 return getConstant(TD->getIntPtrType(getContext()), 2540 TD->getTypeAllocSize(AllocTy)); 2541 2542 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2543 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2544 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2545 C = Folded; 2546 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2547 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2548} 2549 2550const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2551 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2552 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2553 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2554 C = Folded; 2555 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2556 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2557} 2558 2559const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2560 unsigned FieldNo) { 2561 // If we have TargetData, we can bypass creating a target-independent 2562 // constant expression and then folding it back into a ConstantInt. 2563 // This is just a compile-time optimization. 2564 if (TD) 2565 return getConstant(TD->getIntPtrType(getContext()), 2566 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2567 2568 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2569 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2570 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2571 C = Folded; 2572 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2573 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2574} 2575 2576const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2577 Constant *FieldNo) { 2578 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2579 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2580 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2581 C = Folded; 2582 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2583 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2584} 2585 2586const SCEV *ScalarEvolution::getUnknown(Value *V) { 2587 // Don't attempt to do anything other than create a SCEVUnknown object 2588 // here. createSCEV only calls getUnknown after checking for all other 2589 // interesting possibilities, and any other code that calls getUnknown 2590 // is doing so in order to hide a value from SCEV canonicalization. 2591 2592 FoldingSetNodeID ID; 2593 ID.AddInteger(scUnknown); 2594 ID.AddPointer(V); 2595 void *IP = 0; 2596 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2597 assert(cast<SCEVUnknown>(S)->getValue() == V && 2598 "Stale SCEVUnknown in uniquing map!"); 2599 return S; 2600 } 2601 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2602 FirstUnknown); 2603 FirstUnknown = cast<SCEVUnknown>(S); 2604 UniqueSCEVs.InsertNode(S, IP); 2605 return S; 2606} 2607 2608//===----------------------------------------------------------------------===// 2609// Basic SCEV Analysis and PHI Idiom Recognition Code 2610// 2611 2612/// isSCEVable - Test if values of the given type are analyzable within 2613/// the SCEV framework. This primarily includes integer types, and it 2614/// can optionally include pointer types if the ScalarEvolution class 2615/// has access to target-specific information. 2616bool ScalarEvolution::isSCEVable(Type *Ty) const { 2617 // Integers and pointers are always SCEVable. 2618 return Ty->isIntegerTy() || Ty->isPointerTy(); 2619} 2620 2621/// getTypeSizeInBits - Return the size in bits of the specified type, 2622/// for which isSCEVable must return true. 2623uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2624 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2625 2626 // If we have a TargetData, use it! 2627 if (TD) 2628 return TD->getTypeSizeInBits(Ty); 2629 2630 // Integer types have fixed sizes. 2631 if (Ty->isIntegerTy()) 2632 return Ty->getPrimitiveSizeInBits(); 2633 2634 // The only other support type is pointer. Without TargetData, conservatively 2635 // assume pointers are 64-bit. 2636 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2637 return 64; 2638} 2639 2640/// getEffectiveSCEVType - Return a type with the same bitwidth as 2641/// the given type and which represents how SCEV will treat the given 2642/// type, for which isSCEVable must return true. For pointer types, 2643/// this is the pointer-sized integer type. 2644Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2645 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2646 2647 if (Ty->isIntegerTy()) 2648 return Ty; 2649 2650 // The only other support type is pointer. 2651 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2652 if (TD) return TD->getIntPtrType(getContext()); 2653 2654 // Without TargetData, conservatively assume pointers are 64-bit. 2655 return Type::getInt64Ty(getContext()); 2656} 2657 2658const SCEV *ScalarEvolution::getCouldNotCompute() { 2659 return &CouldNotCompute; 2660} 2661 2662/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2663/// expression and create a new one. 2664const SCEV *ScalarEvolution::getSCEV(Value *V) { 2665 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2666 2667 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2668 if (I != ValueExprMap.end()) return I->second; 2669 const SCEV *S = createSCEV(V); 2670 2671 // The process of creating a SCEV for V may have caused other SCEVs 2672 // to have been created, so it's necessary to insert the new entry 2673 // from scratch, rather than trying to remember the insert position 2674 // above. 2675 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2676 return S; 2677} 2678 2679/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2680/// 2681const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2682 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2683 return getConstant( 2684 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2685 2686 Type *Ty = V->getType(); 2687 Ty = getEffectiveSCEVType(Ty); 2688 return getMulExpr(V, 2689 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2690} 2691 2692/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2693const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2694 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2695 return getConstant( 2696 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2697 2698 Type *Ty = V->getType(); 2699 Ty = getEffectiveSCEVType(Ty); 2700 const SCEV *AllOnes = 2701 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2702 return getMinusSCEV(AllOnes, V); 2703} 2704 2705/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2706const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2707 SCEV::NoWrapFlags Flags) { 2708 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2709 2710 // Fast path: X - X --> 0. 2711 if (LHS == RHS) 2712 return getConstant(LHS->getType(), 0); 2713 2714 // X - Y --> X + -Y 2715 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2716} 2717 2718/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2719/// input value to the specified type. If the type must be extended, it is zero 2720/// extended. 2721const SCEV * 2722ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2723 Type *SrcTy = V->getType(); 2724 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2725 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2726 "Cannot truncate or zero extend with non-integer arguments!"); 2727 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2728 return V; // No conversion 2729 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2730 return getTruncateExpr(V, Ty); 2731 return getZeroExtendExpr(V, Ty); 2732} 2733 2734/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2735/// input value to the specified type. If the type must be extended, it is sign 2736/// extended. 2737const SCEV * 2738ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2739 Type *Ty) { 2740 Type *SrcTy = V->getType(); 2741 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2742 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2743 "Cannot truncate or zero extend with non-integer arguments!"); 2744 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2745 return V; // No conversion 2746 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2747 return getTruncateExpr(V, Ty); 2748 return getSignExtendExpr(V, Ty); 2749} 2750 2751/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2752/// input value to the specified type. If the type must be extended, it is zero 2753/// extended. The conversion must not be narrowing. 2754const SCEV * 2755ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2756 Type *SrcTy = V->getType(); 2757 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2758 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2759 "Cannot noop or zero extend with non-integer arguments!"); 2760 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2761 "getNoopOrZeroExtend cannot truncate!"); 2762 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2763 return V; // No conversion 2764 return getZeroExtendExpr(V, Ty); 2765} 2766 2767/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2768/// input value to the specified type. If the type must be extended, it is sign 2769/// extended. The conversion must not be narrowing. 2770const SCEV * 2771ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2772 Type *SrcTy = V->getType(); 2773 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2774 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2775 "Cannot noop or sign extend with non-integer arguments!"); 2776 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2777 "getNoopOrSignExtend cannot truncate!"); 2778 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2779 return V; // No conversion 2780 return getSignExtendExpr(V, Ty); 2781} 2782 2783/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2784/// the input value to the specified type. If the type must be extended, 2785/// it is extended with unspecified bits. The conversion must not be 2786/// narrowing. 2787const SCEV * 2788ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2789 Type *SrcTy = V->getType(); 2790 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2791 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2792 "Cannot noop or any extend with non-integer arguments!"); 2793 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2794 "getNoopOrAnyExtend cannot truncate!"); 2795 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2796 return V; // No conversion 2797 return getAnyExtendExpr(V, Ty); 2798} 2799 2800/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2801/// input value to the specified type. The conversion must not be widening. 2802const SCEV * 2803ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2804 Type *SrcTy = V->getType(); 2805 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2806 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2807 "Cannot truncate or noop with non-integer arguments!"); 2808 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2809 "getTruncateOrNoop cannot extend!"); 2810 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2811 return V; // No conversion 2812 return getTruncateExpr(V, Ty); 2813} 2814 2815/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2816/// the types using zero-extension, and then perform a umax operation 2817/// with them. 2818const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2819 const SCEV *RHS) { 2820 const SCEV *PromotedLHS = LHS; 2821 const SCEV *PromotedRHS = RHS; 2822 2823 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2824 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2825 else 2826 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2827 2828 return getUMaxExpr(PromotedLHS, PromotedRHS); 2829} 2830 2831/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2832/// the types using zero-extension, and then perform a umin operation 2833/// with them. 2834const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2835 const SCEV *RHS) { 2836 const SCEV *PromotedLHS = LHS; 2837 const SCEV *PromotedRHS = RHS; 2838 2839 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2840 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2841 else 2842 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2843 2844 return getUMinExpr(PromotedLHS, PromotedRHS); 2845} 2846 2847/// getPointerBase - Transitively follow the chain of pointer-type operands 2848/// until reaching a SCEV that does not have a single pointer operand. This 2849/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2850/// but corner cases do exist. 2851const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2852 // A pointer operand may evaluate to a nonpointer expression, such as null. 2853 if (!V->getType()->isPointerTy()) 2854 return V; 2855 2856 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2857 return getPointerBase(Cast->getOperand()); 2858 } 2859 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2860 const SCEV *PtrOp = 0; 2861 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2862 I != E; ++I) { 2863 if ((*I)->getType()->isPointerTy()) { 2864 // Cannot find the base of an expression with multiple pointer operands. 2865 if (PtrOp) 2866 return V; 2867 PtrOp = *I; 2868 } 2869 } 2870 if (!PtrOp) 2871 return V; 2872 return getPointerBase(PtrOp); 2873 } 2874 return V; 2875} 2876 2877/// PushDefUseChildren - Push users of the given Instruction 2878/// onto the given Worklist. 2879static void 2880PushDefUseChildren(Instruction *I, 2881 SmallVectorImpl<Instruction *> &Worklist) { 2882 // Push the def-use children onto the Worklist stack. 2883 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2884 UI != UE; ++UI) 2885 Worklist.push_back(cast<Instruction>(*UI)); 2886} 2887 2888/// ForgetSymbolicValue - This looks up computed SCEV values for all 2889/// instructions that depend on the given instruction and removes them from 2890/// the ValueExprMapType map if they reference SymName. This is used during PHI 2891/// resolution. 2892void 2893ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2894 SmallVector<Instruction *, 16> Worklist; 2895 PushDefUseChildren(PN, Worklist); 2896 2897 SmallPtrSet<Instruction *, 8> Visited; 2898 Visited.insert(PN); 2899 while (!Worklist.empty()) { 2900 Instruction *I = Worklist.pop_back_val(); 2901 if (!Visited.insert(I)) continue; 2902 2903 ValueExprMapType::iterator It = 2904 ValueExprMap.find(static_cast<Value *>(I)); 2905 if (It != ValueExprMap.end()) { 2906 const SCEV *Old = It->second; 2907 2908 // Short-circuit the def-use traversal if the symbolic name 2909 // ceases to appear in expressions. 2910 if (Old != SymName && !hasOperand(Old, SymName)) 2911 continue; 2912 2913 // SCEVUnknown for a PHI either means that it has an unrecognized 2914 // structure, it's a PHI that's in the progress of being computed 2915 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2916 // additional loop trip count information isn't going to change anything. 2917 // In the second case, createNodeForPHI will perform the necessary 2918 // updates on its own when it gets to that point. In the third, we do 2919 // want to forget the SCEVUnknown. 2920 if (!isa<PHINode>(I) || 2921 !isa<SCEVUnknown>(Old) || 2922 (I != PN && Old == SymName)) { 2923 forgetMemoizedResults(Old); 2924 ValueExprMap.erase(It); 2925 } 2926 } 2927 2928 PushDefUseChildren(I, Worklist); 2929 } 2930} 2931 2932/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2933/// a loop header, making it a potential recurrence, or it doesn't. 2934/// 2935const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2936 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2937 if (L->getHeader() == PN->getParent()) { 2938 // The loop may have multiple entrances or multiple exits; we can analyze 2939 // this phi as an addrec if it has a unique entry value and a unique 2940 // backedge value. 2941 Value *BEValueV = 0, *StartValueV = 0; 2942 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2943 Value *V = PN->getIncomingValue(i); 2944 if (L->contains(PN->getIncomingBlock(i))) { 2945 if (!BEValueV) { 2946 BEValueV = V; 2947 } else if (BEValueV != V) { 2948 BEValueV = 0; 2949 break; 2950 } 2951 } else if (!StartValueV) { 2952 StartValueV = V; 2953 } else if (StartValueV != V) { 2954 StartValueV = 0; 2955 break; 2956 } 2957 } 2958 if (BEValueV && StartValueV) { 2959 // While we are analyzing this PHI node, handle its value symbolically. 2960 const SCEV *SymbolicName = getUnknown(PN); 2961 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2962 "PHI node already processed?"); 2963 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2964 2965 // Using this symbolic name for the PHI, analyze the value coming around 2966 // the back-edge. 2967 const SCEV *BEValue = getSCEV(BEValueV); 2968 2969 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2970 // has a special value for the first iteration of the loop. 2971 2972 // If the value coming around the backedge is an add with the symbolic 2973 // value we just inserted, then we found a simple induction variable! 2974 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2975 // If there is a single occurrence of the symbolic value, replace it 2976 // with a recurrence. 2977 unsigned FoundIndex = Add->getNumOperands(); 2978 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2979 if (Add->getOperand(i) == SymbolicName) 2980 if (FoundIndex == e) { 2981 FoundIndex = i; 2982 break; 2983 } 2984 2985 if (FoundIndex != Add->getNumOperands()) { 2986 // Create an add with everything but the specified operand. 2987 SmallVector<const SCEV *, 8> Ops; 2988 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2989 if (i != FoundIndex) 2990 Ops.push_back(Add->getOperand(i)); 2991 const SCEV *Accum = getAddExpr(Ops); 2992 2993 // This is not a valid addrec if the step amount is varying each 2994 // loop iteration, but is not itself an addrec in this loop. 2995 if (isLoopInvariant(Accum, L) || 2996 (isa<SCEVAddRecExpr>(Accum) && 2997 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2998 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 2999 3000 // If the increment doesn't overflow, then neither the addrec nor 3001 // the post-increment will overflow. 3002 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 3003 if (OBO->hasNoUnsignedWrap()) 3004 Flags = setFlags(Flags, SCEV::FlagNUW); 3005 if (OBO->hasNoSignedWrap()) 3006 Flags = setFlags(Flags, SCEV::FlagNSW); 3007 } else if (const GEPOperator *GEP = 3008 dyn_cast<GEPOperator>(BEValueV)) { 3009 // If the increment is an inbounds GEP, then we know the address 3010 // space cannot be wrapped around. We cannot make any guarantee 3011 // about signed or unsigned overflow because pointers are 3012 // unsigned but we may have a negative index from the base 3013 // pointer. 3014 if (GEP->isInBounds()) 3015 Flags = setFlags(Flags, SCEV::FlagNW); 3016 } 3017 3018 const SCEV *StartVal = getSCEV(StartValueV); 3019 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 3020 3021 // Since the no-wrap flags are on the increment, they apply to the 3022 // post-incremented value as well. 3023 if (isLoopInvariant(Accum, L)) 3024 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 3025 Accum, L, Flags); 3026 3027 // Okay, for the entire analysis of this edge we assumed the PHI 3028 // to be symbolic. We now need to go back and purge all of the 3029 // entries for the scalars that use the symbolic expression. 3030 ForgetSymbolicName(PN, SymbolicName); 3031 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3032 return PHISCEV; 3033 } 3034 } 3035 } else if (const SCEVAddRecExpr *AddRec = 3036 dyn_cast<SCEVAddRecExpr>(BEValue)) { 3037 // Otherwise, this could be a loop like this: 3038 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3039 // In this case, j = {1,+,1} and BEValue is j. 3040 // Because the other in-value of i (0) fits the evolution of BEValue 3041 // i really is an addrec evolution. 3042 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3043 const SCEV *StartVal = getSCEV(StartValueV); 3044 3045 // If StartVal = j.start - j.stride, we can use StartVal as the 3046 // initial step of the addrec evolution. 3047 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3048 AddRec->getOperand(1))) { 3049 // FIXME: For constant StartVal, we should be able to infer 3050 // no-wrap flags. 3051 const SCEV *PHISCEV = 3052 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3053 SCEV::FlagAnyWrap); 3054 3055 // Okay, for the entire analysis of this edge we assumed the PHI 3056 // to be symbolic. We now need to go back and purge all of the 3057 // entries for the scalars that use the symbolic expression. 3058 ForgetSymbolicName(PN, SymbolicName); 3059 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3060 return PHISCEV; 3061 } 3062 } 3063 } 3064 } 3065 } 3066 3067 // If the PHI has a single incoming value, follow that value, unless the 3068 // PHI's incoming blocks are in a different loop, in which case doing so 3069 // risks breaking LCSSA form. Instcombine would normally zap these, but 3070 // it doesn't have DominatorTree information, so it may miss cases. 3071 if (Value *V = SimplifyInstruction(PN, TD, DT)) 3072 if (LI->replacementPreservesLCSSAForm(PN, V)) 3073 return getSCEV(V); 3074 3075 // If it's not a loop phi, we can't handle it yet. 3076 return getUnknown(PN); 3077} 3078 3079/// createNodeForGEP - Expand GEP instructions into add and multiply 3080/// operations. This allows them to be analyzed by regular SCEV code. 3081/// 3082const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3083 3084 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3085 // Add expression, because the Instruction may be guarded by control flow 3086 // and the no-overflow bits may not be valid for the expression in any 3087 // context. 3088 bool isInBounds = GEP->isInBounds(); 3089 3090 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3091 Value *Base = GEP->getOperand(0); 3092 // Don't attempt to analyze GEPs over unsized objects. 3093 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3094 return getUnknown(GEP); 3095 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3096 gep_type_iterator GTI = gep_type_begin(GEP); 3097 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3098 E = GEP->op_end(); 3099 I != E; ++I) { 3100 Value *Index = *I; 3101 // Compute the (potentially symbolic) offset in bytes for this index. 3102 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3103 // For a struct, add the member offset. 3104 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3105 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3106 3107 // Add the field offset to the running total offset. 3108 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3109 } else { 3110 // For an array, add the element offset, explicitly scaled. 3111 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3112 const SCEV *IndexS = getSCEV(Index); 3113 // Getelementptr indices are signed. 3114 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3115 3116 // Multiply the index by the element size to compute the element offset. 3117 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3118 isInBounds ? SCEV::FlagNSW : 3119 SCEV::FlagAnyWrap); 3120 3121 // Add the element offset to the running total offset. 3122 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3123 } 3124 } 3125 3126 // Get the SCEV for the GEP base. 3127 const SCEV *BaseS = getSCEV(Base); 3128 3129 // Add the total offset from all the GEP indices to the base. 3130 return getAddExpr(BaseS, TotalOffset, 3131 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3132} 3133 3134/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3135/// guaranteed to end in (at every loop iteration). It is, at the same time, 3136/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3137/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3138uint32_t 3139ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3140 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3141 return C->getValue()->getValue().countTrailingZeros(); 3142 3143 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3144 return std::min(GetMinTrailingZeros(T->getOperand()), 3145 (uint32_t)getTypeSizeInBits(T->getType())); 3146 3147 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3148 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3149 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3150 getTypeSizeInBits(E->getType()) : OpRes; 3151 } 3152 3153 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3154 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3155 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3156 getTypeSizeInBits(E->getType()) : OpRes; 3157 } 3158 3159 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3160 // The result is the min of all operands results. 3161 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3162 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3163 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3164 return MinOpRes; 3165 } 3166 3167 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3168 // The result is the sum of all operands results. 3169 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3170 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3171 for (unsigned i = 1, e = M->getNumOperands(); 3172 SumOpRes != BitWidth && i != e; ++i) 3173 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3174 BitWidth); 3175 return SumOpRes; 3176 } 3177 3178 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3179 // The result is the min of all operands results. 3180 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3181 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3182 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3183 return MinOpRes; 3184 } 3185 3186 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3187 // The result is the min of all operands results. 3188 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3189 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3190 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3191 return MinOpRes; 3192 } 3193 3194 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3195 // The result is the min of all operands results. 3196 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3197 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3198 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3199 return MinOpRes; 3200 } 3201 3202 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3203 // For a SCEVUnknown, ask ValueTracking. 3204 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3205 APInt Mask = APInt::getAllOnesValue(BitWidth); 3206 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3207 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3208 return Zeros.countTrailingOnes(); 3209 } 3210 3211 // SCEVUDivExpr 3212 return 0; 3213} 3214 3215/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3216/// 3217ConstantRange 3218ScalarEvolution::getUnsignedRange(const SCEV *S) { 3219 // See if we've computed this range already. 3220 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3221 if (I != UnsignedRanges.end()) 3222 return I->second; 3223 3224 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3225 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3226 3227 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3228 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3229 3230 // If the value has known zeros, the maximum unsigned value will have those 3231 // known zeros as well. 3232 uint32_t TZ = GetMinTrailingZeros(S); 3233 if (TZ != 0) 3234 ConservativeResult = 3235 ConstantRange(APInt::getMinValue(BitWidth), 3236 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3237 3238 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3239 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3240 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3241 X = X.add(getUnsignedRange(Add->getOperand(i))); 3242 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3243 } 3244 3245 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3246 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3247 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3248 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3249 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3250 } 3251 3252 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3253 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3254 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3255 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3256 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3257 } 3258 3259 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3260 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3261 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3262 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3263 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3264 } 3265 3266 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3267 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3268 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3269 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3270 } 3271 3272 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3273 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3274 return setUnsignedRange(ZExt, 3275 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3276 } 3277 3278 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3279 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3280 return setUnsignedRange(SExt, 3281 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3282 } 3283 3284 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3285 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3286 return setUnsignedRange(Trunc, 3287 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3288 } 3289 3290 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3291 // If there's no unsigned wrap, the value will never be less than its 3292 // initial value. 3293 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3294 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3295 if (!C->getValue()->isZero()) 3296 ConservativeResult = 3297 ConservativeResult.intersectWith( 3298 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3299 3300 // TODO: non-affine addrec 3301 if (AddRec->isAffine()) { 3302 Type *Ty = AddRec->getType(); 3303 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3304 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3305 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3306 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3307 3308 const SCEV *Start = AddRec->getStart(); 3309 const SCEV *Step = AddRec->getStepRecurrence(*this); 3310 3311 ConstantRange StartRange = getUnsignedRange(Start); 3312 ConstantRange StepRange = getSignedRange(Step); 3313 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3314 ConstantRange EndRange = 3315 StartRange.add(MaxBECountRange.multiply(StepRange)); 3316 3317 // Check for overflow. This must be done with ConstantRange arithmetic 3318 // because we could be called from within the ScalarEvolution overflow 3319 // checking code. 3320 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3321 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3322 ConstantRange ExtMaxBECountRange = 3323 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3324 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3325 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3326 ExtEndRange) 3327 return setUnsignedRange(AddRec, ConservativeResult); 3328 3329 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3330 EndRange.getUnsignedMin()); 3331 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3332 EndRange.getUnsignedMax()); 3333 if (Min.isMinValue() && Max.isMaxValue()) 3334 return setUnsignedRange(AddRec, ConservativeResult); 3335 return setUnsignedRange(AddRec, 3336 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3337 } 3338 } 3339 3340 return setUnsignedRange(AddRec, ConservativeResult); 3341 } 3342 3343 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3344 // For a SCEVUnknown, ask ValueTracking. 3345 APInt Mask = APInt::getAllOnesValue(BitWidth); 3346 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3347 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3348 if (Ones == ~Zeros + 1) 3349 return setUnsignedRange(U, ConservativeResult); 3350 return setUnsignedRange(U, 3351 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3352 } 3353 3354 return setUnsignedRange(S, ConservativeResult); 3355} 3356 3357/// getSignedRange - Determine the signed range for a particular SCEV. 3358/// 3359ConstantRange 3360ScalarEvolution::getSignedRange(const SCEV *S) { 3361 // See if we've computed this range already. 3362 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3363 if (I != SignedRanges.end()) 3364 return I->second; 3365 3366 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3367 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3368 3369 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3370 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3371 3372 // If the value has known zeros, the maximum signed value will have those 3373 // known zeros as well. 3374 uint32_t TZ = GetMinTrailingZeros(S); 3375 if (TZ != 0) 3376 ConservativeResult = 3377 ConstantRange(APInt::getSignedMinValue(BitWidth), 3378 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3379 3380 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3381 ConstantRange X = getSignedRange(Add->getOperand(0)); 3382 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3383 X = X.add(getSignedRange(Add->getOperand(i))); 3384 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3385 } 3386 3387 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3388 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3389 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3390 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3391 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3392 } 3393 3394 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3395 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3396 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3397 X = X.smax(getSignedRange(SMax->getOperand(i))); 3398 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3399 } 3400 3401 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3402 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3403 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3404 X = X.umax(getSignedRange(UMax->getOperand(i))); 3405 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3406 } 3407 3408 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3409 ConstantRange X = getSignedRange(UDiv->getLHS()); 3410 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3411 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3412 } 3413 3414 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3415 ConstantRange X = getSignedRange(ZExt->getOperand()); 3416 return setSignedRange(ZExt, 3417 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3418 } 3419 3420 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3421 ConstantRange X = getSignedRange(SExt->getOperand()); 3422 return setSignedRange(SExt, 3423 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3424 } 3425 3426 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3427 ConstantRange X = getSignedRange(Trunc->getOperand()); 3428 return setSignedRange(Trunc, 3429 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3430 } 3431 3432 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3433 // If there's no signed wrap, and all the operands have the same sign or 3434 // zero, the value won't ever change sign. 3435 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3436 bool AllNonNeg = true; 3437 bool AllNonPos = true; 3438 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3439 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3440 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3441 } 3442 if (AllNonNeg) 3443 ConservativeResult = ConservativeResult.intersectWith( 3444 ConstantRange(APInt(BitWidth, 0), 3445 APInt::getSignedMinValue(BitWidth))); 3446 else if (AllNonPos) 3447 ConservativeResult = ConservativeResult.intersectWith( 3448 ConstantRange(APInt::getSignedMinValue(BitWidth), 3449 APInt(BitWidth, 1))); 3450 } 3451 3452 // TODO: non-affine addrec 3453 if (AddRec->isAffine()) { 3454 Type *Ty = AddRec->getType(); 3455 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3456 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3457 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3458 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3459 3460 const SCEV *Start = AddRec->getStart(); 3461 const SCEV *Step = AddRec->getStepRecurrence(*this); 3462 3463 ConstantRange StartRange = getSignedRange(Start); 3464 ConstantRange StepRange = getSignedRange(Step); 3465 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3466 ConstantRange EndRange = 3467 StartRange.add(MaxBECountRange.multiply(StepRange)); 3468 3469 // Check for overflow. This must be done with ConstantRange arithmetic 3470 // because we could be called from within the ScalarEvolution overflow 3471 // checking code. 3472 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3473 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3474 ConstantRange ExtMaxBECountRange = 3475 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3476 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3477 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3478 ExtEndRange) 3479 return setSignedRange(AddRec, ConservativeResult); 3480 3481 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3482 EndRange.getSignedMin()); 3483 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3484 EndRange.getSignedMax()); 3485 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3486 return setSignedRange(AddRec, ConservativeResult); 3487 return setSignedRange(AddRec, 3488 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3489 } 3490 } 3491 3492 return setSignedRange(AddRec, ConservativeResult); 3493 } 3494 3495 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3496 // For a SCEVUnknown, ask ValueTracking. 3497 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3498 return setSignedRange(U, ConservativeResult); 3499 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3500 if (NS == 1) 3501 return setSignedRange(U, ConservativeResult); 3502 return setSignedRange(U, ConservativeResult.intersectWith( 3503 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3504 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3505 } 3506 3507 return setSignedRange(S, ConservativeResult); 3508} 3509 3510/// createSCEV - We know that there is no SCEV for the specified value. 3511/// Analyze the expression. 3512/// 3513const SCEV *ScalarEvolution::createSCEV(Value *V) { 3514 if (!isSCEVable(V->getType())) 3515 return getUnknown(V); 3516 3517 unsigned Opcode = Instruction::UserOp1; 3518 if (Instruction *I = dyn_cast<Instruction>(V)) { 3519 Opcode = I->getOpcode(); 3520 3521 // Don't attempt to analyze instructions in blocks that aren't 3522 // reachable. Such instructions don't matter, and they aren't required 3523 // to obey basic rules for definitions dominating uses which this 3524 // analysis depends on. 3525 if (!DT->isReachableFromEntry(I->getParent())) 3526 return getUnknown(V); 3527 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3528 Opcode = CE->getOpcode(); 3529 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3530 return getConstant(CI); 3531 else if (isa<ConstantPointerNull>(V)) 3532 return getConstant(V->getType(), 0); 3533 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3534 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3535 else 3536 return getUnknown(V); 3537 3538 Operator *U = cast<Operator>(V); 3539 switch (Opcode) { 3540 case Instruction::Add: { 3541 // The simple thing to do would be to just call getSCEV on both operands 3542 // and call getAddExpr with the result. However if we're looking at a 3543 // bunch of things all added together, this can be quite inefficient, 3544 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3545 // Instead, gather up all the operands and make a single getAddExpr call. 3546 // LLVM IR canonical form means we need only traverse the left operands. 3547 SmallVector<const SCEV *, 4> AddOps; 3548 AddOps.push_back(getSCEV(U->getOperand(1))); 3549 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3550 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3551 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3552 break; 3553 U = cast<Operator>(Op); 3554 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3555 if (Opcode == Instruction::Sub) 3556 AddOps.push_back(getNegativeSCEV(Op1)); 3557 else 3558 AddOps.push_back(Op1); 3559 } 3560 AddOps.push_back(getSCEV(U->getOperand(0))); 3561 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 3562 OverflowingBinaryOperator *OBO = cast<OverflowingBinaryOperator>(V); 3563 if (OBO->hasNoSignedWrap()) 3564 setFlags(Flags, SCEV::FlagNSW); 3565 if (OBO->hasNoUnsignedWrap()) 3566 setFlags(Flags, SCEV::FlagNUW); 3567 return getAddExpr(AddOps, Flags); 3568 } 3569 case Instruction::Mul: { 3570 // See the Add code above. 3571 SmallVector<const SCEV *, 4> MulOps; 3572 MulOps.push_back(getSCEV(U->getOperand(1))); 3573 for (Value *Op = U->getOperand(0); 3574 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3575 Op = U->getOperand(0)) { 3576 U = cast<Operator>(Op); 3577 MulOps.push_back(getSCEV(U->getOperand(1))); 3578 } 3579 MulOps.push_back(getSCEV(U->getOperand(0))); 3580 return getMulExpr(MulOps); 3581 } 3582 case Instruction::UDiv: 3583 return getUDivExpr(getSCEV(U->getOperand(0)), 3584 getSCEV(U->getOperand(1))); 3585 case Instruction::Sub: 3586 return getMinusSCEV(getSCEV(U->getOperand(0)), 3587 getSCEV(U->getOperand(1))); 3588 case Instruction::And: 3589 // For an expression like x&255 that merely masks off the high bits, 3590 // use zext(trunc(x)) as the SCEV expression. 3591 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3592 if (CI->isNullValue()) 3593 return getSCEV(U->getOperand(1)); 3594 if (CI->isAllOnesValue()) 3595 return getSCEV(U->getOperand(0)); 3596 const APInt &A = CI->getValue(); 3597 3598 // Instcombine's ShrinkDemandedConstant may strip bits out of 3599 // constants, obscuring what would otherwise be a low-bits mask. 3600 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3601 // knew about to reconstruct a low-bits mask value. 3602 unsigned LZ = A.countLeadingZeros(); 3603 unsigned BitWidth = A.getBitWidth(); 3604 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3605 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3606 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3607 3608 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3609 3610 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3611 return 3612 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3613 IntegerType::get(getContext(), BitWidth - LZ)), 3614 U->getType()); 3615 } 3616 break; 3617 3618 case Instruction::Or: 3619 // If the RHS of the Or is a constant, we may have something like: 3620 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3621 // optimizations will transparently handle this case. 3622 // 3623 // In order for this transformation to be safe, the LHS must be of the 3624 // form X*(2^n) and the Or constant must be less than 2^n. 3625 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3626 const SCEV *LHS = getSCEV(U->getOperand(0)); 3627 const APInt &CIVal = CI->getValue(); 3628 if (GetMinTrailingZeros(LHS) >= 3629 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3630 // Build a plain add SCEV. 3631 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3632 // If the LHS of the add was an addrec and it has no-wrap flags, 3633 // transfer the no-wrap flags, since an or won't introduce a wrap. 3634 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3635 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3636 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3637 OldAR->getNoWrapFlags()); 3638 } 3639 return S; 3640 } 3641 } 3642 break; 3643 case Instruction::Xor: 3644 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3645 // If the RHS of the xor is a signbit, then this is just an add. 3646 // Instcombine turns add of signbit into xor as a strength reduction step. 3647 if (CI->getValue().isSignBit()) 3648 return getAddExpr(getSCEV(U->getOperand(0)), 3649 getSCEV(U->getOperand(1))); 3650 3651 // If the RHS of xor is -1, then this is a not operation. 3652 if (CI->isAllOnesValue()) 3653 return getNotSCEV(getSCEV(U->getOperand(0))); 3654 3655 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3656 // This is a variant of the check for xor with -1, and it handles 3657 // the case where instcombine has trimmed non-demanded bits out 3658 // of an xor with -1. 3659 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3660 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3661 if (BO->getOpcode() == Instruction::And && 3662 LCI->getValue() == CI->getValue()) 3663 if (const SCEVZeroExtendExpr *Z = 3664 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3665 Type *UTy = U->getType(); 3666 const SCEV *Z0 = Z->getOperand(); 3667 Type *Z0Ty = Z0->getType(); 3668 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3669 3670 // If C is a low-bits mask, the zero extend is serving to 3671 // mask off the high bits. Complement the operand and 3672 // re-apply the zext. 3673 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3674 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3675 3676 // If C is a single bit, it may be in the sign-bit position 3677 // before the zero-extend. In this case, represent the xor 3678 // using an add, which is equivalent, and re-apply the zext. 3679 APInt Trunc = CI->getValue().trunc(Z0TySize); 3680 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3681 Trunc.isSignBit()) 3682 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3683 UTy); 3684 } 3685 } 3686 break; 3687 3688 case Instruction::Shl: 3689 // Turn shift left of a constant amount into a multiply. 3690 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3691 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3692 3693 // If the shift count is not less than the bitwidth, the result of 3694 // the shift is undefined. Don't try to analyze it, because the 3695 // resolution chosen here may differ from the resolution chosen in 3696 // other parts of the compiler. 3697 if (SA->getValue().uge(BitWidth)) 3698 break; 3699 3700 Constant *X = ConstantInt::get(getContext(), 3701 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3702 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3703 } 3704 break; 3705 3706 case Instruction::LShr: 3707 // Turn logical shift right of a constant into a unsigned divide. 3708 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3709 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3710 3711 // If the shift count is not less than the bitwidth, the result of 3712 // the shift is undefined. Don't try to analyze it, because the 3713 // resolution chosen here may differ from the resolution chosen in 3714 // other parts of the compiler. 3715 if (SA->getValue().uge(BitWidth)) 3716 break; 3717 3718 Constant *X = ConstantInt::get(getContext(), 3719 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3720 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3721 } 3722 break; 3723 3724 case Instruction::AShr: 3725 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3726 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3727 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3728 if (L->getOpcode() == Instruction::Shl && 3729 L->getOperand(1) == U->getOperand(1)) { 3730 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3731 3732 // If the shift count is not less than the bitwidth, the result of 3733 // the shift is undefined. Don't try to analyze it, because the 3734 // resolution chosen here may differ from the resolution chosen in 3735 // other parts of the compiler. 3736 if (CI->getValue().uge(BitWidth)) 3737 break; 3738 3739 uint64_t Amt = BitWidth - CI->getZExtValue(); 3740 if (Amt == BitWidth) 3741 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3742 return 3743 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3744 IntegerType::get(getContext(), 3745 Amt)), 3746 U->getType()); 3747 } 3748 break; 3749 3750 case Instruction::Trunc: 3751 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3752 3753 case Instruction::ZExt: 3754 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3755 3756 case Instruction::SExt: 3757 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3758 3759 case Instruction::BitCast: 3760 // BitCasts are no-op casts so we just eliminate the cast. 3761 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3762 return getSCEV(U->getOperand(0)); 3763 break; 3764 3765 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3766 // lead to pointer expressions which cannot safely be expanded to GEPs, 3767 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3768 // simplifying integer expressions. 3769 3770 case Instruction::GetElementPtr: 3771 return createNodeForGEP(cast<GEPOperator>(U)); 3772 3773 case Instruction::PHI: 3774 return createNodeForPHI(cast<PHINode>(U)); 3775 3776 case Instruction::Select: 3777 // This could be a smax or umax that was lowered earlier. 3778 // Try to recover it. 3779 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3780 Value *LHS = ICI->getOperand(0); 3781 Value *RHS = ICI->getOperand(1); 3782 switch (ICI->getPredicate()) { 3783 case ICmpInst::ICMP_SLT: 3784 case ICmpInst::ICMP_SLE: 3785 std::swap(LHS, RHS); 3786 // fall through 3787 case ICmpInst::ICMP_SGT: 3788 case ICmpInst::ICMP_SGE: 3789 // a >s b ? a+x : b+x -> smax(a, b)+x 3790 // a >s b ? b+x : a+x -> smin(a, b)+x 3791 if (LHS->getType() == U->getType()) { 3792 const SCEV *LS = getSCEV(LHS); 3793 const SCEV *RS = getSCEV(RHS); 3794 const SCEV *LA = getSCEV(U->getOperand(1)); 3795 const SCEV *RA = getSCEV(U->getOperand(2)); 3796 const SCEV *LDiff = getMinusSCEV(LA, LS); 3797 const SCEV *RDiff = getMinusSCEV(RA, RS); 3798 if (LDiff == RDiff) 3799 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3800 LDiff = getMinusSCEV(LA, RS); 3801 RDiff = getMinusSCEV(RA, LS); 3802 if (LDiff == RDiff) 3803 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3804 } 3805 break; 3806 case ICmpInst::ICMP_ULT: 3807 case ICmpInst::ICMP_ULE: 3808 std::swap(LHS, RHS); 3809 // fall through 3810 case ICmpInst::ICMP_UGT: 3811 case ICmpInst::ICMP_UGE: 3812 // a >u b ? a+x : b+x -> umax(a, b)+x 3813 // a >u b ? b+x : a+x -> umin(a, b)+x 3814 if (LHS->getType() == U->getType()) { 3815 const SCEV *LS = getSCEV(LHS); 3816 const SCEV *RS = getSCEV(RHS); 3817 const SCEV *LA = getSCEV(U->getOperand(1)); 3818 const SCEV *RA = getSCEV(U->getOperand(2)); 3819 const SCEV *LDiff = getMinusSCEV(LA, LS); 3820 const SCEV *RDiff = getMinusSCEV(RA, RS); 3821 if (LDiff == RDiff) 3822 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3823 LDiff = getMinusSCEV(LA, RS); 3824 RDiff = getMinusSCEV(RA, LS); 3825 if (LDiff == RDiff) 3826 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3827 } 3828 break; 3829 case ICmpInst::ICMP_NE: 3830 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3831 if (LHS->getType() == U->getType() && 3832 isa<ConstantInt>(RHS) && 3833 cast<ConstantInt>(RHS)->isZero()) { 3834 const SCEV *One = getConstant(LHS->getType(), 1); 3835 const SCEV *LS = getSCEV(LHS); 3836 const SCEV *LA = getSCEV(U->getOperand(1)); 3837 const SCEV *RA = getSCEV(U->getOperand(2)); 3838 const SCEV *LDiff = getMinusSCEV(LA, LS); 3839 const SCEV *RDiff = getMinusSCEV(RA, One); 3840 if (LDiff == RDiff) 3841 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3842 } 3843 break; 3844 case ICmpInst::ICMP_EQ: 3845 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3846 if (LHS->getType() == U->getType() && 3847 isa<ConstantInt>(RHS) && 3848 cast<ConstantInt>(RHS)->isZero()) { 3849 const SCEV *One = getConstant(LHS->getType(), 1); 3850 const SCEV *LS = getSCEV(LHS); 3851 const SCEV *LA = getSCEV(U->getOperand(1)); 3852 const SCEV *RA = getSCEV(U->getOperand(2)); 3853 const SCEV *LDiff = getMinusSCEV(LA, One); 3854 const SCEV *RDiff = getMinusSCEV(RA, LS); 3855 if (LDiff == RDiff) 3856 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3857 } 3858 break; 3859 default: 3860 break; 3861 } 3862 } 3863 3864 default: // We cannot analyze this expression. 3865 break; 3866 } 3867 3868 return getUnknown(V); 3869} 3870 3871 3872 3873//===----------------------------------------------------------------------===// 3874// Iteration Count Computation Code 3875// 3876 3877/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 3878/// normal unsigned value, if possible. Returns 0 if the trip count is unknown 3879/// or not constant. Will also return 0 if the maximum trip count is very large 3880/// (>= 2^32) 3881unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, 3882 BasicBlock *ExitBlock) { 3883 const SCEVConstant *ExitCount = 3884 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock)); 3885 if (!ExitCount) 3886 return 0; 3887 3888 ConstantInt *ExitConst = ExitCount->getValue(); 3889 3890 // Guard against huge trip counts. 3891 if (ExitConst->getValue().getActiveBits() > 32) 3892 return 0; 3893 3894 // In case of integer overflow, this returns 0, which is correct. 3895 return ((unsigned)ExitConst->getZExtValue()) + 1; 3896} 3897 3898/// getSmallConstantTripMultiple - Returns the largest constant divisor of the 3899/// trip count of this loop as a normal unsigned value, if possible. This 3900/// means that the actual trip count is always a multiple of the returned 3901/// value (don't forget the trip count could very well be zero as well!). 3902/// 3903/// Returns 1 if the trip count is unknown or not guaranteed to be the 3904/// multiple of a constant (which is also the case if the trip count is simply 3905/// constant, use getSmallConstantTripCount for that case), Will also return 1 3906/// if the trip count is very large (>= 2^32). 3907unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L, 3908 BasicBlock *ExitBlock) { 3909 const SCEV *ExitCount = getExitCount(L, ExitBlock); 3910 if (ExitCount == getCouldNotCompute()) 3911 return 1; 3912 3913 // Get the trip count from the BE count by adding 1. 3914 const SCEV *TCMul = getAddExpr(ExitCount, 3915 getConstant(ExitCount->getType(), 1)); 3916 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 3917 // to factor simple cases. 3918 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 3919 TCMul = Mul->getOperand(0); 3920 3921 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 3922 if (!MulC) 3923 return 1; 3924 3925 ConstantInt *Result = MulC->getValue(); 3926 3927 // Guard against huge trip counts. 3928 if (!Result || Result->getValue().getActiveBits() > 32) 3929 return 1; 3930 3931 return (unsigned)Result->getZExtValue(); 3932} 3933 3934// getExitCount - Get the expression for the number of loop iterations for which 3935// this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3936// SCEVCouldNotCompute. 3937const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3938 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3939} 3940 3941/// getBackedgeTakenCount - If the specified loop has a predictable 3942/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3943/// object. The backedge-taken count is the number of times the loop header 3944/// will be branched to from within the loop. This is one less than the 3945/// trip count of the loop, since it doesn't count the first iteration, 3946/// when the header is branched to from outside the loop. 3947/// 3948/// Note that it is not valid to call this method on a loop without a 3949/// loop-invariant backedge-taken count (see 3950/// hasLoopInvariantBackedgeTakenCount). 3951/// 3952const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3953 return getBackedgeTakenInfo(L).getExact(this); 3954} 3955 3956/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3957/// return the least SCEV value that is known never to be less than the 3958/// actual backedge taken count. 3959const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3960 return getBackedgeTakenInfo(L).getMax(this); 3961} 3962 3963/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3964/// onto the given Worklist. 3965static void 3966PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3967 BasicBlock *Header = L->getHeader(); 3968 3969 // Push all Loop-header PHIs onto the Worklist stack. 3970 for (BasicBlock::iterator I = Header->begin(); 3971 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3972 Worklist.push_back(PN); 3973} 3974 3975const ScalarEvolution::BackedgeTakenInfo & 3976ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3977 // Initially insert an invalid entry for this loop. If the insertion 3978 // succeeds, proceed to actually compute a backedge-taken count and 3979 // update the value. The temporary CouldNotCompute value tells SCEV 3980 // code elsewhere that it shouldn't attempt to request a new 3981 // backedge-taken count, which could result in infinite recursion. 3982 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3983 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 3984 if (!Pair.second) 3985 return Pair.first->second; 3986 3987 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 3988 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 3989 // must be cleared in this scope. 3990 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 3991 3992 if (Result.getExact(this) != getCouldNotCompute()) { 3993 assert(isLoopInvariant(Result.getExact(this), L) && 3994 isLoopInvariant(Result.getMax(this), L) && 3995 "Computed backedge-taken count isn't loop invariant for loop!"); 3996 ++NumTripCountsComputed; 3997 } 3998 else if (Result.getMax(this) == getCouldNotCompute() && 3999 isa<PHINode>(L->getHeader()->begin())) { 4000 // Only count loops that have phi nodes as not being computable. 4001 ++NumTripCountsNotComputed; 4002 } 4003 4004 // Now that we know more about the trip count for this loop, forget any 4005 // existing SCEV values for PHI nodes in this loop since they are only 4006 // conservative estimates made without the benefit of trip count 4007 // information. This is similar to the code in forgetLoop, except that 4008 // it handles SCEVUnknown PHI nodes specially. 4009 if (Result.hasAnyInfo()) { 4010 SmallVector<Instruction *, 16> Worklist; 4011 PushLoopPHIs(L, Worklist); 4012 4013 SmallPtrSet<Instruction *, 8> Visited; 4014 while (!Worklist.empty()) { 4015 Instruction *I = Worklist.pop_back_val(); 4016 if (!Visited.insert(I)) continue; 4017 4018 ValueExprMapType::iterator It = 4019 ValueExprMap.find(static_cast<Value *>(I)); 4020 if (It != ValueExprMap.end()) { 4021 const SCEV *Old = It->second; 4022 4023 // SCEVUnknown for a PHI either means that it has an unrecognized 4024 // structure, or it's a PHI that's in the progress of being computed 4025 // by createNodeForPHI. In the former case, additional loop trip 4026 // count information isn't going to change anything. In the later 4027 // case, createNodeForPHI will perform the necessary updates on its 4028 // own when it gets to that point. 4029 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 4030 forgetMemoizedResults(Old); 4031 ValueExprMap.erase(It); 4032 } 4033 if (PHINode *PN = dyn_cast<PHINode>(I)) 4034 ConstantEvolutionLoopExitValue.erase(PN); 4035 } 4036 4037 PushDefUseChildren(I, Worklist); 4038 } 4039 } 4040 4041 // Re-lookup the insert position, since the call to 4042 // ComputeBackedgeTakenCount above could result in a 4043 // recusive call to getBackedgeTakenInfo (on a different 4044 // loop), which would invalidate the iterator computed 4045 // earlier. 4046 return BackedgeTakenCounts.find(L)->second = Result; 4047} 4048 4049/// forgetLoop - This method should be called by the client when it has 4050/// changed a loop in a way that may effect ScalarEvolution's ability to 4051/// compute a trip count, or if the loop is deleted. 4052void ScalarEvolution::forgetLoop(const Loop *L) { 4053 // Drop any stored trip count value. 4054 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4055 BackedgeTakenCounts.find(L); 4056 if (BTCPos != BackedgeTakenCounts.end()) { 4057 BTCPos->second.clear(); 4058 BackedgeTakenCounts.erase(BTCPos); 4059 } 4060 4061 // Drop information about expressions based on loop-header PHIs. 4062 SmallVector<Instruction *, 16> Worklist; 4063 PushLoopPHIs(L, Worklist); 4064 4065 SmallPtrSet<Instruction *, 8> Visited; 4066 while (!Worklist.empty()) { 4067 Instruction *I = Worklist.pop_back_val(); 4068 if (!Visited.insert(I)) continue; 4069 4070 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4071 if (It != ValueExprMap.end()) { 4072 forgetMemoizedResults(It->second); 4073 ValueExprMap.erase(It); 4074 if (PHINode *PN = dyn_cast<PHINode>(I)) 4075 ConstantEvolutionLoopExitValue.erase(PN); 4076 } 4077 4078 PushDefUseChildren(I, Worklist); 4079 } 4080 4081 // Forget all contained loops too, to avoid dangling entries in the 4082 // ValuesAtScopes map. 4083 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4084 forgetLoop(*I); 4085} 4086 4087/// forgetValue - This method should be called by the client when it has 4088/// changed a value in a way that may effect its value, or which may 4089/// disconnect it from a def-use chain linking it to a loop. 4090void ScalarEvolution::forgetValue(Value *V) { 4091 Instruction *I = dyn_cast<Instruction>(V); 4092 if (!I) return; 4093 4094 // Drop information about expressions based on loop-header PHIs. 4095 SmallVector<Instruction *, 16> Worklist; 4096 Worklist.push_back(I); 4097 4098 SmallPtrSet<Instruction *, 8> Visited; 4099 while (!Worklist.empty()) { 4100 I = Worklist.pop_back_val(); 4101 if (!Visited.insert(I)) continue; 4102 4103 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4104 if (It != ValueExprMap.end()) { 4105 forgetMemoizedResults(It->second); 4106 ValueExprMap.erase(It); 4107 if (PHINode *PN = dyn_cast<PHINode>(I)) 4108 ConstantEvolutionLoopExitValue.erase(PN); 4109 } 4110 4111 PushDefUseChildren(I, Worklist); 4112 } 4113} 4114 4115/// getExact - Get the exact loop backedge taken count considering all loop 4116/// exits. If all exits are computable, this is the minimum computed count. 4117const SCEV * 4118ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4119 // If any exits were not computable, the loop is not computable. 4120 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4121 4122 // We need at least one computable exit. 4123 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4124 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4125 4126 const SCEV *BECount = 0; 4127 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4128 ENT != 0; ENT = ENT->getNextExit()) { 4129 4130 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4131 4132 if (!BECount) 4133 BECount = ENT->ExactNotTaken; 4134 else 4135 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken); 4136 } 4137 assert(BECount && "Invalid not taken count for loop exit"); 4138 return BECount; 4139} 4140 4141/// getExact - Get the exact not taken count for this loop exit. 4142const SCEV * 4143ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4144 ScalarEvolution *SE) const { 4145 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4146 ENT != 0; ENT = ENT->getNextExit()) { 4147 4148 if (ENT->ExitingBlock == ExitingBlock) 4149 return ENT->ExactNotTaken; 4150 } 4151 return SE->getCouldNotCompute(); 4152} 4153 4154/// getMax - Get the max backedge taken count for the loop. 4155const SCEV * 4156ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4157 return Max ? Max : SE->getCouldNotCompute(); 4158} 4159 4160/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4161/// computable exit into a persistent ExitNotTakenInfo array. 4162ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4163 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4164 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4165 4166 if (!Complete) 4167 ExitNotTaken.setIncomplete(); 4168 4169 unsigned NumExits = ExitCounts.size(); 4170 if (NumExits == 0) return; 4171 4172 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4173 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4174 if (NumExits == 1) return; 4175 4176 // Handle the rare case of multiple computable exits. 4177 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4178 4179 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4180 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4181 PrevENT->setNextExit(ENT); 4182 ENT->ExitingBlock = ExitCounts[i].first; 4183 ENT->ExactNotTaken = ExitCounts[i].second; 4184 } 4185} 4186 4187/// clear - Invalidate this result and free the ExitNotTakenInfo array. 4188void ScalarEvolution::BackedgeTakenInfo::clear() { 4189 ExitNotTaken.ExitingBlock = 0; 4190 ExitNotTaken.ExactNotTaken = 0; 4191 delete[] ExitNotTaken.getNextExit(); 4192} 4193 4194/// ComputeBackedgeTakenCount - Compute the number of times the backedge 4195/// of the specified loop will execute. 4196ScalarEvolution::BackedgeTakenInfo 4197ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4198 SmallVector<BasicBlock *, 8> ExitingBlocks; 4199 L->getExitingBlocks(ExitingBlocks); 4200 4201 // Examine all exits and pick the most conservative values. 4202 const SCEV *MaxBECount = getCouldNotCompute(); 4203 bool CouldComputeBECount = true; 4204 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4205 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4206 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4207 if (EL.Exact == getCouldNotCompute()) 4208 // We couldn't compute an exact value for this exit, so 4209 // we won't be able to compute an exact value for the loop. 4210 CouldComputeBECount = false; 4211 else 4212 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4213 4214 if (MaxBECount == getCouldNotCompute()) 4215 MaxBECount = EL.Max; 4216 else if (EL.Max != getCouldNotCompute()) 4217 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max); 4218 } 4219 4220 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4221} 4222 4223/// ComputeExitLimit - Compute the number of times the backedge of the specified 4224/// loop will execute if it exits via the specified block. 4225ScalarEvolution::ExitLimit 4226ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4227 4228 // Okay, we've chosen an exiting block. See what condition causes us to 4229 // exit at this block. 4230 // 4231 // FIXME: we should be able to handle switch instructions (with a single exit) 4232 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4233 if (ExitBr == 0) return getCouldNotCompute(); 4234 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4235 4236 // At this point, we know we have a conditional branch that determines whether 4237 // the loop is exited. However, we don't know if the branch is executed each 4238 // time through the loop. If not, then the execution count of the branch will 4239 // not be equal to the trip count of the loop. 4240 // 4241 // Currently we check for this by checking to see if the Exit branch goes to 4242 // the loop header. If so, we know it will always execute the same number of 4243 // times as the loop. We also handle the case where the exit block *is* the 4244 // loop header. This is common for un-rotated loops. 4245 // 4246 // If both of those tests fail, walk up the unique predecessor chain to the 4247 // header, stopping if there is an edge that doesn't exit the loop. If the 4248 // header is reached, the execution count of the branch will be equal to the 4249 // trip count of the loop. 4250 // 4251 // More extensive analysis could be done to handle more cases here. 4252 // 4253 if (ExitBr->getSuccessor(0) != L->getHeader() && 4254 ExitBr->getSuccessor(1) != L->getHeader() && 4255 ExitBr->getParent() != L->getHeader()) { 4256 // The simple checks failed, try climbing the unique predecessor chain 4257 // up to the header. 4258 bool Ok = false; 4259 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4260 BasicBlock *Pred = BB->getUniquePredecessor(); 4261 if (!Pred) 4262 return getCouldNotCompute(); 4263 TerminatorInst *PredTerm = Pred->getTerminator(); 4264 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4265 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4266 if (PredSucc == BB) 4267 continue; 4268 // If the predecessor has a successor that isn't BB and isn't 4269 // outside the loop, assume the worst. 4270 if (L->contains(PredSucc)) 4271 return getCouldNotCompute(); 4272 } 4273 if (Pred == L->getHeader()) { 4274 Ok = true; 4275 break; 4276 } 4277 BB = Pred; 4278 } 4279 if (!Ok) 4280 return getCouldNotCompute(); 4281 } 4282 4283 // Proceed to the next level to examine the exit condition expression. 4284 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4285 ExitBr->getSuccessor(0), 4286 ExitBr->getSuccessor(1)); 4287} 4288 4289/// ComputeExitLimitFromCond - Compute the number of times the 4290/// backedge of the specified loop will execute if its exit condition 4291/// were a conditional branch of ExitCond, TBB, and FBB. 4292ScalarEvolution::ExitLimit 4293ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4294 Value *ExitCond, 4295 BasicBlock *TBB, 4296 BasicBlock *FBB) { 4297 // Check if the controlling expression for this loop is an And or Or. 4298 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4299 if (BO->getOpcode() == Instruction::And) { 4300 // Recurse on the operands of the and. 4301 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4302 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4303 const SCEV *BECount = getCouldNotCompute(); 4304 const SCEV *MaxBECount = getCouldNotCompute(); 4305 if (L->contains(TBB)) { 4306 // Both conditions must be true for the loop to continue executing. 4307 // Choose the less conservative count. 4308 if (EL0.Exact == getCouldNotCompute() || 4309 EL1.Exact == getCouldNotCompute()) 4310 BECount = getCouldNotCompute(); 4311 else 4312 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4313 if (EL0.Max == getCouldNotCompute()) 4314 MaxBECount = EL1.Max; 4315 else if (EL1.Max == getCouldNotCompute()) 4316 MaxBECount = EL0.Max; 4317 else 4318 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4319 } else { 4320 // Both conditions must be true at the same time for the loop to exit. 4321 // For now, be conservative. 4322 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4323 if (EL0.Max == EL1.Max) 4324 MaxBECount = EL0.Max; 4325 if (EL0.Exact == EL1.Exact) 4326 BECount = EL0.Exact; 4327 } 4328 4329 return ExitLimit(BECount, MaxBECount); 4330 } 4331 if (BO->getOpcode() == Instruction::Or) { 4332 // Recurse on the operands of the or. 4333 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4334 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4335 const SCEV *BECount = getCouldNotCompute(); 4336 const SCEV *MaxBECount = getCouldNotCompute(); 4337 if (L->contains(FBB)) { 4338 // Both conditions must be false for the loop to continue executing. 4339 // Choose the less conservative count. 4340 if (EL0.Exact == getCouldNotCompute() || 4341 EL1.Exact == getCouldNotCompute()) 4342 BECount = getCouldNotCompute(); 4343 else 4344 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4345 if (EL0.Max == getCouldNotCompute()) 4346 MaxBECount = EL1.Max; 4347 else if (EL1.Max == getCouldNotCompute()) 4348 MaxBECount = EL0.Max; 4349 else 4350 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4351 } else { 4352 // Both conditions must be false at the same time for the loop to exit. 4353 // For now, be conservative. 4354 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4355 if (EL0.Max == EL1.Max) 4356 MaxBECount = EL0.Max; 4357 if (EL0.Exact == EL1.Exact) 4358 BECount = EL0.Exact; 4359 } 4360 4361 return ExitLimit(BECount, MaxBECount); 4362 } 4363 } 4364 4365 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4366 // Proceed to the next level to examine the icmp. 4367 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4368 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4369 4370 // Check for a constant condition. These are normally stripped out by 4371 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4372 // preserve the CFG and is temporarily leaving constant conditions 4373 // in place. 4374 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4375 if (L->contains(FBB) == !CI->getZExtValue()) 4376 // The backedge is always taken. 4377 return getCouldNotCompute(); 4378 else 4379 // The backedge is never taken. 4380 return getConstant(CI->getType(), 0); 4381 } 4382 4383 // If it's not an integer or pointer comparison then compute it the hard way. 4384 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4385} 4386 4387/// ComputeExitLimitFromICmp - Compute the number of times the 4388/// backedge of the specified loop will execute if its exit condition 4389/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4390ScalarEvolution::ExitLimit 4391ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4392 ICmpInst *ExitCond, 4393 BasicBlock *TBB, 4394 BasicBlock *FBB) { 4395 4396 // If the condition was exit on true, convert the condition to exit on false 4397 ICmpInst::Predicate Cond; 4398 if (!L->contains(FBB)) 4399 Cond = ExitCond->getPredicate(); 4400 else 4401 Cond = ExitCond->getInversePredicate(); 4402 4403 // Handle common loops like: for (X = "string"; *X; ++X) 4404 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4405 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4406 ExitLimit ItCnt = 4407 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4408 if (ItCnt.hasAnyInfo()) 4409 return ItCnt; 4410 } 4411 4412 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4413 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4414 4415 // Try to evaluate any dependencies out of the loop. 4416 LHS = getSCEVAtScope(LHS, L); 4417 RHS = getSCEVAtScope(RHS, L); 4418 4419 // At this point, we would like to compute how many iterations of the 4420 // loop the predicate will return true for these inputs. 4421 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4422 // If there is a loop-invariant, force it into the RHS. 4423 std::swap(LHS, RHS); 4424 Cond = ICmpInst::getSwappedPredicate(Cond); 4425 } 4426 4427 // Simplify the operands before analyzing them. 4428 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4429 4430 // If we have a comparison of a chrec against a constant, try to use value 4431 // ranges to answer this query. 4432 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4433 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4434 if (AddRec->getLoop() == L) { 4435 // Form the constant range. 4436 ConstantRange CompRange( 4437 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4438 4439 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4440 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4441 } 4442 4443 switch (Cond) { 4444 case ICmpInst::ICMP_NE: { // while (X != Y) 4445 // Convert to: while (X-Y != 0) 4446 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4447 if (EL.hasAnyInfo()) return EL; 4448 break; 4449 } 4450 case ICmpInst::ICMP_EQ: { // while (X == Y) 4451 // Convert to: while (X-Y == 0) 4452 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4453 if (EL.hasAnyInfo()) return EL; 4454 break; 4455 } 4456 case ICmpInst::ICMP_SLT: { 4457 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4458 if (EL.hasAnyInfo()) return EL; 4459 break; 4460 } 4461 case ICmpInst::ICMP_SGT: { 4462 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4463 getNotSCEV(RHS), L, true); 4464 if (EL.hasAnyInfo()) return EL; 4465 break; 4466 } 4467 case ICmpInst::ICMP_ULT: { 4468 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4469 if (EL.hasAnyInfo()) return EL; 4470 break; 4471 } 4472 case ICmpInst::ICMP_UGT: { 4473 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4474 getNotSCEV(RHS), L, false); 4475 if (EL.hasAnyInfo()) return EL; 4476 break; 4477 } 4478 default: 4479#if 0 4480 dbgs() << "ComputeBackedgeTakenCount "; 4481 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4482 dbgs() << "[unsigned] "; 4483 dbgs() << *LHS << " " 4484 << Instruction::getOpcodeName(Instruction::ICmp) 4485 << " " << *RHS << "\n"; 4486#endif 4487 break; 4488 } 4489 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4490} 4491 4492static ConstantInt * 4493EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4494 ScalarEvolution &SE) { 4495 const SCEV *InVal = SE.getConstant(C); 4496 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4497 assert(isa<SCEVConstant>(Val) && 4498 "Evaluation of SCEV at constant didn't fold correctly?"); 4499 return cast<SCEVConstant>(Val)->getValue(); 4500} 4501 4502/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4503/// and a GEP expression (missing the pointer index) indexing into it, return 4504/// the addressed element of the initializer or null if the index expression is 4505/// invalid. 4506static Constant * 4507GetAddressedElementFromGlobal(GlobalVariable *GV, 4508 const std::vector<ConstantInt*> &Indices) { 4509 Constant *Init = GV->getInitializer(); 4510 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4511 uint64_t Idx = Indices[i]->getZExtValue(); 4512 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4513 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4514 Init = cast<Constant>(CS->getOperand(Idx)); 4515 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4516 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4517 Init = cast<Constant>(CA->getOperand(Idx)); 4518 } else if (isa<ConstantAggregateZero>(Init)) { 4519 if (StructType *STy = dyn_cast<StructType>(Init->getType())) { 4520 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4521 Init = Constant::getNullValue(STy->getElementType(Idx)); 4522 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4523 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4524 Init = Constant::getNullValue(ATy->getElementType()); 4525 } else { 4526 llvm_unreachable("Unknown constant aggregate type!"); 4527 } 4528 return 0; 4529 } else { 4530 return 0; // Unknown initializer type 4531 } 4532 } 4533 return Init; 4534} 4535 4536/// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4537/// 'icmp op load X, cst', try to see if we can compute the backedge 4538/// execution count. 4539ScalarEvolution::ExitLimit 4540ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4541 LoadInst *LI, 4542 Constant *RHS, 4543 const Loop *L, 4544 ICmpInst::Predicate predicate) { 4545 4546 if (LI->isVolatile()) return getCouldNotCompute(); 4547 4548 // Check to see if the loaded pointer is a getelementptr of a global. 4549 // TODO: Use SCEV instead of manually grubbing with GEPs. 4550 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4551 if (!GEP) return getCouldNotCompute(); 4552 4553 // Make sure that it is really a constant global we are gepping, with an 4554 // initializer, and make sure the first IDX is really 0. 4555 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4556 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4557 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4558 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4559 return getCouldNotCompute(); 4560 4561 // Okay, we allow one non-constant index into the GEP instruction. 4562 Value *VarIdx = 0; 4563 std::vector<ConstantInt*> Indexes; 4564 unsigned VarIdxNum = 0; 4565 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4566 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4567 Indexes.push_back(CI); 4568 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4569 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4570 VarIdx = GEP->getOperand(i); 4571 VarIdxNum = i-2; 4572 Indexes.push_back(0); 4573 } 4574 4575 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4576 // Check to see if X is a loop variant variable value now. 4577 const SCEV *Idx = getSCEV(VarIdx); 4578 Idx = getSCEVAtScope(Idx, L); 4579 4580 // We can only recognize very limited forms of loop index expressions, in 4581 // particular, only affine AddRec's like {C1,+,C2}. 4582 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4583 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4584 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4585 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4586 return getCouldNotCompute(); 4587 4588 unsigned MaxSteps = MaxBruteForceIterations; 4589 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4590 ConstantInt *ItCst = ConstantInt::get( 4591 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4592 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4593 4594 // Form the GEP offset. 4595 Indexes[VarIdxNum] = Val; 4596 4597 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4598 if (Result == 0) break; // Cannot compute! 4599 4600 // Evaluate the condition for this iteration. 4601 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4602 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4603 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4604#if 0 4605 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4606 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4607 << "***\n"; 4608#endif 4609 ++NumArrayLenItCounts; 4610 return getConstant(ItCst); // Found terminating iteration! 4611 } 4612 } 4613 return getCouldNotCompute(); 4614} 4615 4616 4617/// CanConstantFold - Return true if we can constant fold an instruction of the 4618/// specified type, assuming that all operands were constants. 4619static bool CanConstantFold(const Instruction *I) { 4620 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4621 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4622 return true; 4623 4624 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4625 if (const Function *F = CI->getCalledFunction()) 4626 return canConstantFoldCallTo(F); 4627 return false; 4628} 4629 4630/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4631/// in the loop that V is derived from. We allow arbitrary operations along the 4632/// way, but the operands of an operation must either be constants or a value 4633/// derived from a constant PHI. If this expression does not fit with these 4634/// constraints, return null. 4635static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4636 // If this is not an instruction, or if this is an instruction outside of the 4637 // loop, it can't be derived from a loop PHI. 4638 Instruction *I = dyn_cast<Instruction>(V); 4639 if (I == 0 || !L->contains(I)) return 0; 4640 4641 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4642 if (L->getHeader() == I->getParent()) 4643 return PN; 4644 else 4645 // We don't currently keep track of the control flow needed to evaluate 4646 // PHIs, so we cannot handle PHIs inside of loops. 4647 return 0; 4648 } 4649 4650 // If we won't be able to constant fold this expression even if the operands 4651 // are constants, return early. 4652 if (!CanConstantFold(I)) return 0; 4653 4654 // Otherwise, we can evaluate this instruction if all of its operands are 4655 // constant or derived from a PHI node themselves. 4656 PHINode *PHI = 0; 4657 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4658 if (!isa<Constant>(I->getOperand(Op))) { 4659 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4660 if (P == 0) return 0; // Not evolving from PHI 4661 if (PHI == 0) 4662 PHI = P; 4663 else if (PHI != P) 4664 return 0; // Evolving from multiple different PHIs. 4665 } 4666 4667 // This is a expression evolving from a constant PHI! 4668 return PHI; 4669} 4670 4671/// EvaluateExpression - Given an expression that passes the 4672/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4673/// in the loop has the value PHIVal. If we can't fold this expression for some 4674/// reason, return null. 4675static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4676 const TargetData *TD) { 4677 if (isa<PHINode>(V)) return PHIVal; 4678 if (Constant *C = dyn_cast<Constant>(V)) return C; 4679 Instruction *I = cast<Instruction>(V); 4680 4681 std::vector<Constant*> Operands(I->getNumOperands()); 4682 4683 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4684 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4685 if (Operands[i] == 0) return 0; 4686 } 4687 4688 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4689 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4690 Operands[1], TD); 4691 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD); 4692} 4693 4694/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4695/// in the header of its containing loop, we know the loop executes a 4696/// constant number of times, and the PHI node is just a recurrence 4697/// involving constants, fold it. 4698Constant * 4699ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4700 const APInt &BEs, 4701 const Loop *L) { 4702 DenseMap<PHINode*, Constant*>::const_iterator I = 4703 ConstantEvolutionLoopExitValue.find(PN); 4704 if (I != ConstantEvolutionLoopExitValue.end()) 4705 return I->second; 4706 4707 if (BEs.ugt(MaxBruteForceIterations)) 4708 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4709 4710 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4711 4712 // Since the loop is canonicalized, the PHI node must have two entries. One 4713 // entry must be a constant (coming in from outside of the loop), and the 4714 // second must be derived from the same PHI. 4715 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4716 Constant *StartCST = 4717 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4718 if (StartCST == 0) 4719 return RetVal = 0; // Must be a constant. 4720 4721 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4722 if (getConstantEvolvingPHI(BEValue, L) != PN && 4723 !isa<Constant>(BEValue)) 4724 return RetVal = 0; // Not derived from same PHI. 4725 4726 // Execute the loop symbolically to determine the exit value. 4727 if (BEs.getActiveBits() >= 32) 4728 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4729 4730 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4731 unsigned IterationNum = 0; 4732 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4733 if (IterationNum == NumIterations) 4734 return RetVal = PHIVal; // Got exit value! 4735 4736 // Compute the value of the PHI node for the next iteration. 4737 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4738 if (NextPHI == PHIVal) 4739 return RetVal = NextPHI; // Stopped evolving! 4740 if (NextPHI == 0) 4741 return 0; // Couldn't evaluate! 4742 PHIVal = NextPHI; 4743 } 4744} 4745 4746/// ComputeExitCountExhaustively - If the loop is known to execute a 4747/// constant number of times (the condition evolves only from constants), 4748/// try to evaluate a few iterations of the loop until we get the exit 4749/// condition gets a value of ExitWhen (true or false). If we cannot 4750/// evaluate the trip count of the loop, return getCouldNotCompute(). 4751const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4752 Value *Cond, 4753 bool ExitWhen) { 4754 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4755 if (PN == 0) return getCouldNotCompute(); 4756 4757 // If the loop is canonicalized, the PHI will have exactly two entries. 4758 // That's the only form we support here. 4759 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4760 4761 // One entry must be a constant (coming in from outside of the loop), and the 4762 // second must be derived from the same PHI. 4763 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4764 Constant *StartCST = 4765 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4766 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4767 4768 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4769 if (getConstantEvolvingPHI(BEValue, L) != PN && 4770 !isa<Constant>(BEValue)) 4771 return getCouldNotCompute(); // Not derived from same PHI. 4772 4773 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4774 // the loop symbolically to determine when the condition gets a value of 4775 // "ExitWhen". 4776 unsigned IterationNum = 0; 4777 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4778 for (Constant *PHIVal = StartCST; 4779 IterationNum != MaxIterations; ++IterationNum) { 4780 ConstantInt *CondVal = 4781 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4782 4783 // Couldn't symbolically evaluate. 4784 if (!CondVal) return getCouldNotCompute(); 4785 4786 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4787 ++NumBruteForceTripCountsComputed; 4788 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4789 } 4790 4791 // Compute the value of the PHI node for the next iteration. 4792 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4793 if (NextPHI == 0 || NextPHI == PHIVal) 4794 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4795 PHIVal = NextPHI; 4796 } 4797 4798 // Too many iterations were needed to evaluate. 4799 return getCouldNotCompute(); 4800} 4801 4802/// getSCEVAtScope - Return a SCEV expression for the specified value 4803/// at the specified scope in the program. The L value specifies a loop 4804/// nest to evaluate the expression at, where null is the top-level or a 4805/// specified loop is immediately inside of the loop. 4806/// 4807/// This method can be used to compute the exit value for a variable defined 4808/// in a loop by querying what the value will hold in the parent loop. 4809/// 4810/// In the case that a relevant loop exit value cannot be computed, the 4811/// original value V is returned. 4812const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4813 // Check to see if we've folded this expression at this loop before. 4814 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4815 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4816 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4817 if (!Pair.second) 4818 return Pair.first->second ? Pair.first->second : V; 4819 4820 // Otherwise compute it. 4821 const SCEV *C = computeSCEVAtScope(V, L); 4822 ValuesAtScopes[V][L] = C; 4823 return C; 4824} 4825 4826const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4827 if (isa<SCEVConstant>(V)) return V; 4828 4829 // If this instruction is evolved from a constant-evolving PHI, compute the 4830 // exit value from the loop without using SCEVs. 4831 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4832 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4833 const Loop *LI = (*this->LI)[I->getParent()]; 4834 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4835 if (PHINode *PN = dyn_cast<PHINode>(I)) 4836 if (PN->getParent() == LI->getHeader()) { 4837 // Okay, there is no closed form solution for the PHI node. Check 4838 // to see if the loop that contains it has a known backedge-taken 4839 // count. If so, we may be able to force computation of the exit 4840 // value. 4841 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4842 if (const SCEVConstant *BTCC = 4843 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4844 // Okay, we know how many times the containing loop executes. If 4845 // this is a constant evolving PHI node, get the final value at 4846 // the specified iteration number. 4847 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4848 BTCC->getValue()->getValue(), 4849 LI); 4850 if (RV) return getSCEV(RV); 4851 } 4852 } 4853 4854 // Okay, this is an expression that we cannot symbolically evaluate 4855 // into a SCEV. Check to see if it's possible to symbolically evaluate 4856 // the arguments into constants, and if so, try to constant propagate the 4857 // result. This is particularly useful for computing loop exit values. 4858 if (CanConstantFold(I)) { 4859 SmallVector<Constant *, 4> Operands; 4860 bool MadeImprovement = false; 4861 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4862 Value *Op = I->getOperand(i); 4863 if (Constant *C = dyn_cast<Constant>(Op)) { 4864 Operands.push_back(C); 4865 continue; 4866 } 4867 4868 // If any of the operands is non-constant and if they are 4869 // non-integer and non-pointer, don't even try to analyze them 4870 // with scev techniques. 4871 if (!isSCEVable(Op->getType())) 4872 return V; 4873 4874 const SCEV *OrigV = getSCEV(Op); 4875 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4876 MadeImprovement |= OrigV != OpV; 4877 4878 Constant *C = 0; 4879 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4880 C = SC->getValue(); 4881 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4882 C = dyn_cast<Constant>(SU->getValue()); 4883 if (!C) return V; 4884 if (C->getType() != Op->getType()) 4885 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4886 Op->getType(), 4887 false), 4888 C, Op->getType()); 4889 Operands.push_back(C); 4890 } 4891 4892 // Check to see if getSCEVAtScope actually made an improvement. 4893 if (MadeImprovement) { 4894 Constant *C = 0; 4895 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4896 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4897 Operands[0], Operands[1], TD); 4898 else 4899 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4900 Operands, TD); 4901 if (!C) return V; 4902 return getSCEV(C); 4903 } 4904 } 4905 } 4906 4907 // This is some other type of SCEVUnknown, just return it. 4908 return V; 4909 } 4910 4911 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4912 // Avoid performing the look-up in the common case where the specified 4913 // expression has no loop-variant portions. 4914 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4915 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4916 if (OpAtScope != Comm->getOperand(i)) { 4917 // Okay, at least one of these operands is loop variant but might be 4918 // foldable. Build a new instance of the folded commutative expression. 4919 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4920 Comm->op_begin()+i); 4921 NewOps.push_back(OpAtScope); 4922 4923 for (++i; i != e; ++i) { 4924 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4925 NewOps.push_back(OpAtScope); 4926 } 4927 if (isa<SCEVAddExpr>(Comm)) 4928 return getAddExpr(NewOps); 4929 if (isa<SCEVMulExpr>(Comm)) 4930 return getMulExpr(NewOps); 4931 if (isa<SCEVSMaxExpr>(Comm)) 4932 return getSMaxExpr(NewOps); 4933 if (isa<SCEVUMaxExpr>(Comm)) 4934 return getUMaxExpr(NewOps); 4935 llvm_unreachable("Unknown commutative SCEV type!"); 4936 } 4937 } 4938 // If we got here, all operands are loop invariant. 4939 return Comm; 4940 } 4941 4942 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4943 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4944 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4945 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4946 return Div; // must be loop invariant 4947 return getUDivExpr(LHS, RHS); 4948 } 4949 4950 // If this is a loop recurrence for a loop that does not contain L, then we 4951 // are dealing with the final value computed by the loop. 4952 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4953 // First, attempt to evaluate each operand. 4954 // Avoid performing the look-up in the common case where the specified 4955 // expression has no loop-variant portions. 4956 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4957 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4958 if (OpAtScope == AddRec->getOperand(i)) 4959 continue; 4960 4961 // Okay, at least one of these operands is loop variant but might be 4962 // foldable. Build a new instance of the folded commutative expression. 4963 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4964 AddRec->op_begin()+i); 4965 NewOps.push_back(OpAtScope); 4966 for (++i; i != e; ++i) 4967 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4968 4969 const SCEV *FoldedRec = 4970 getAddRecExpr(NewOps, AddRec->getLoop(), 4971 AddRec->getNoWrapFlags(SCEV::FlagNW)); 4972 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 4973 // The addrec may be folded to a nonrecurrence, for example, if the 4974 // induction variable is multiplied by zero after constant folding. Go 4975 // ahead and return the folded value. 4976 if (!AddRec) 4977 return FoldedRec; 4978 break; 4979 } 4980 4981 // If the scope is outside the addrec's loop, evaluate it by using the 4982 // loop exit value of the addrec. 4983 if (!AddRec->getLoop()->contains(L)) { 4984 // To evaluate this recurrence, we need to know how many times the AddRec 4985 // loop iterates. Compute this now. 4986 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4987 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4988 4989 // Then, evaluate the AddRec. 4990 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4991 } 4992 4993 return AddRec; 4994 } 4995 4996 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4997 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4998 if (Op == Cast->getOperand()) 4999 return Cast; // must be loop invariant 5000 return getZeroExtendExpr(Op, Cast->getType()); 5001 } 5002 5003 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 5004 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5005 if (Op == Cast->getOperand()) 5006 return Cast; // must be loop invariant 5007 return getSignExtendExpr(Op, Cast->getType()); 5008 } 5009 5010 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 5011 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5012 if (Op == Cast->getOperand()) 5013 return Cast; // must be loop invariant 5014 return getTruncateExpr(Op, Cast->getType()); 5015 } 5016 5017 llvm_unreachable("Unknown SCEV type!"); 5018 return 0; 5019} 5020 5021/// getSCEVAtScope - This is a convenience function which does 5022/// getSCEVAtScope(getSCEV(V), L). 5023const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 5024 return getSCEVAtScope(getSCEV(V), L); 5025} 5026 5027/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 5028/// following equation: 5029/// 5030/// A * X = B (mod N) 5031/// 5032/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 5033/// A and B isn't important. 5034/// 5035/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 5036static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 5037 ScalarEvolution &SE) { 5038 uint32_t BW = A.getBitWidth(); 5039 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 5040 assert(A != 0 && "A must be non-zero."); 5041 5042 // 1. D = gcd(A, N) 5043 // 5044 // The gcd of A and N may have only one prime factor: 2. The number of 5045 // trailing zeros in A is its multiplicity 5046 uint32_t Mult2 = A.countTrailingZeros(); 5047 // D = 2^Mult2 5048 5049 // 2. Check if B is divisible by D. 5050 // 5051 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5052 // is not less than multiplicity of this prime factor for D. 5053 if (B.countTrailingZeros() < Mult2) 5054 return SE.getCouldNotCompute(); 5055 5056 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5057 // modulo (N / D). 5058 // 5059 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5060 // bit width during computations. 5061 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5062 APInt Mod(BW + 1, 0); 5063 Mod.setBit(BW - Mult2); // Mod = N / D 5064 APInt I = AD.multiplicativeInverse(Mod); 5065 5066 // 4. Compute the minimum unsigned root of the equation: 5067 // I * (B / D) mod (N / D) 5068 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5069 5070 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5071 // bits. 5072 return SE.getConstant(Result.trunc(BW)); 5073} 5074 5075/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5076/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5077/// might be the same) or two SCEVCouldNotCompute objects. 5078/// 5079static std::pair<const SCEV *,const SCEV *> 5080SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5081 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5082 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5083 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5084 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5085 5086 // We currently can only solve this if the coefficients are constants. 5087 if (!LC || !MC || !NC) { 5088 const SCEV *CNC = SE.getCouldNotCompute(); 5089 return std::make_pair(CNC, CNC); 5090 } 5091 5092 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5093 const APInt &L = LC->getValue()->getValue(); 5094 const APInt &M = MC->getValue()->getValue(); 5095 const APInt &N = NC->getValue()->getValue(); 5096 APInt Two(BitWidth, 2); 5097 APInt Four(BitWidth, 4); 5098 5099 { 5100 using namespace APIntOps; 5101 const APInt& C = L; 5102 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 5103 // The B coefficient is M-N/2 5104 APInt B(M); 5105 B -= sdiv(N,Two); 5106 5107 // The A coefficient is N/2 5108 APInt A(N.sdiv(Two)); 5109 5110 // Compute the B^2-4ac term. 5111 APInt SqrtTerm(B); 5112 SqrtTerm *= B; 5113 SqrtTerm -= Four * (A * C); 5114 5115 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 5116 // integer value or else APInt::sqrt() will assert. 5117 APInt SqrtVal(SqrtTerm.sqrt()); 5118 5119 // Compute the two solutions for the quadratic formula. 5120 // The divisions must be performed as signed divisions. 5121 APInt NegB(-B); 5122 APInt TwoA(A << 1); 5123 if (TwoA.isMinValue()) { 5124 const SCEV *CNC = SE.getCouldNotCompute(); 5125 return std::make_pair(CNC, CNC); 5126 } 5127 5128 LLVMContext &Context = SE.getContext(); 5129 5130 ConstantInt *Solution1 = 5131 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5132 ConstantInt *Solution2 = 5133 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5134 5135 return std::make_pair(SE.getConstant(Solution1), 5136 SE.getConstant(Solution2)); 5137 } // end APIntOps namespace 5138} 5139 5140/// HowFarToZero - Return the number of times a backedge comparing the specified 5141/// value to zero will execute. If not computable, return CouldNotCompute. 5142/// 5143/// This is only used for loops with a "x != y" exit test. The exit condition is 5144/// now expressed as a single expression, V = x-y. So the exit test is 5145/// effectively V != 0. We know and take advantage of the fact that this 5146/// expression only being used in a comparison by zero context. 5147ScalarEvolution::ExitLimit 5148ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5149 // If the value is a constant 5150 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5151 // If the value is already zero, the branch will execute zero times. 5152 if (C->getValue()->isZero()) return C; 5153 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5154 } 5155 5156 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5157 if (!AddRec || AddRec->getLoop() != L) 5158 return getCouldNotCompute(); 5159 5160 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5161 // the quadratic equation to solve it. 5162 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5163 std::pair<const SCEV *,const SCEV *> Roots = 5164 SolveQuadraticEquation(AddRec, *this); 5165 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5166 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5167 if (R1 && R2) { 5168#if 0 5169 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5170 << " sol#2: " << *R2 << "\n"; 5171#endif 5172 // Pick the smallest positive root value. 5173 if (ConstantInt *CB = 5174 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5175 R1->getValue(), 5176 R2->getValue()))) { 5177 if (CB->getZExtValue() == false) 5178 std::swap(R1, R2); // R1 is the minimum root now. 5179 5180 // We can only use this value if the chrec ends up with an exact zero 5181 // value at this index. When solving for "X*X != 5", for example, we 5182 // should not accept a root of 2. 5183 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5184 if (Val->isZero()) 5185 return R1; // We found a quadratic root! 5186 } 5187 } 5188 return getCouldNotCompute(); 5189 } 5190 5191 // Otherwise we can only handle this if it is affine. 5192 if (!AddRec->isAffine()) 5193 return getCouldNotCompute(); 5194 5195 // If this is an affine expression, the execution count of this branch is 5196 // the minimum unsigned root of the following equation: 5197 // 5198 // Start + Step*N = 0 (mod 2^BW) 5199 // 5200 // equivalent to: 5201 // 5202 // Step*N = -Start (mod 2^BW) 5203 // 5204 // where BW is the common bit width of Start and Step. 5205 5206 // Get the initial value for the loop. 5207 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5208 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5209 5210 // For now we handle only constant steps. 5211 // 5212 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5213 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5214 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5215 // We have not yet seen any such cases. 5216 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5217 if (StepC == 0) 5218 return getCouldNotCompute(); 5219 5220 // For positive steps (counting up until unsigned overflow): 5221 // N = -Start/Step (as unsigned) 5222 // For negative steps (counting down to zero): 5223 // N = Start/-Step 5224 // First compute the unsigned distance from zero in the direction of Step. 5225 bool CountDown = StepC->getValue()->getValue().isNegative(); 5226 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5227 5228 // Handle unitary steps, which cannot wraparound. 5229 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5230 // N = Distance (as unsigned) 5231 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) { 5232 ConstantRange CR = getUnsignedRange(Start); 5233 const SCEV *MaxBECount; 5234 if (!CountDown && CR.getUnsignedMin().isMinValue()) 5235 // When counting up, the worst starting value is 1, not 0. 5236 MaxBECount = CR.getUnsignedMax().isMinValue() 5237 ? getConstant(APInt::getMinValue(CR.getBitWidth())) 5238 : getConstant(APInt::getMaxValue(CR.getBitWidth())); 5239 else 5240 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax() 5241 : -CR.getUnsignedMin()); 5242 return ExitLimit(Distance, MaxBECount); 5243 } 5244 5245 // If the recurrence is known not to wraparound, unsigned divide computes the 5246 // back edge count. We know that the value will either become zero (and thus 5247 // the loop terminates), that the loop will terminate through some other exit 5248 // condition first, or that the loop has undefined behavior. This means 5249 // we can't "miss" the exit value, even with nonunit stride. 5250 // 5251 // FIXME: Prove that loops always exhibits *acceptable* undefined 5252 // behavior. Loops must exhibit defined behavior until a wrapped value is 5253 // actually used. So the trip count computed by udiv could be smaller than the 5254 // number of well-defined iterations. 5255 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) 5256 // FIXME: We really want an "isexact" bit for udiv. 5257 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5258 5259 // Then, try to solve the above equation provided that Start is constant. 5260 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5261 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5262 -StartC->getValue()->getValue(), 5263 *this); 5264 return getCouldNotCompute(); 5265} 5266 5267/// HowFarToNonZero - Return the number of times a backedge checking the 5268/// specified value for nonzero will execute. If not computable, return 5269/// CouldNotCompute 5270ScalarEvolution::ExitLimit 5271ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5272 // Loops that look like: while (X == 0) are very strange indeed. We don't 5273 // handle them yet except for the trivial case. This could be expanded in the 5274 // future as needed. 5275 5276 // If the value is a constant, check to see if it is known to be non-zero 5277 // already. If so, the backedge will execute zero times. 5278 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5279 if (!C->getValue()->isNullValue()) 5280 return getConstant(C->getType(), 0); 5281 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5282 } 5283 5284 // We could implement others, but I really doubt anyone writes loops like 5285 // this, and if they did, they would already be constant folded. 5286 return getCouldNotCompute(); 5287} 5288 5289/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5290/// (which may not be an immediate predecessor) which has exactly one 5291/// successor from which BB is reachable, or null if no such block is 5292/// found. 5293/// 5294std::pair<BasicBlock *, BasicBlock *> 5295ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5296 // If the block has a unique predecessor, then there is no path from the 5297 // predecessor to the block that does not go through the direct edge 5298 // from the predecessor to the block. 5299 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5300 return std::make_pair(Pred, BB); 5301 5302 // A loop's header is defined to be a block that dominates the loop. 5303 // If the header has a unique predecessor outside the loop, it must be 5304 // a block that has exactly one successor that can reach the loop. 5305 if (Loop *L = LI->getLoopFor(BB)) 5306 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5307 5308 return std::pair<BasicBlock *, BasicBlock *>(); 5309} 5310 5311/// HasSameValue - SCEV structural equivalence is usually sufficient for 5312/// testing whether two expressions are equal, however for the purposes of 5313/// looking for a condition guarding a loop, it can be useful to be a little 5314/// more general, since a front-end may have replicated the controlling 5315/// expression. 5316/// 5317static bool HasSameValue(const SCEV *A, const SCEV *B) { 5318 // Quick check to see if they are the same SCEV. 5319 if (A == B) return true; 5320 5321 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5322 // two different instructions with the same value. Check for this case. 5323 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5324 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5325 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5326 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5327 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5328 return true; 5329 5330 // Otherwise assume they may have a different value. 5331 return false; 5332} 5333 5334/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5335/// predicate Pred. Return true iff any changes were made. 5336/// 5337bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5338 const SCEV *&LHS, const SCEV *&RHS) { 5339 bool Changed = false; 5340 5341 // Canonicalize a constant to the right side. 5342 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5343 // Check for both operands constant. 5344 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5345 if (ConstantExpr::getICmp(Pred, 5346 LHSC->getValue(), 5347 RHSC->getValue())->isNullValue()) 5348 goto trivially_false; 5349 else 5350 goto trivially_true; 5351 } 5352 // Otherwise swap the operands to put the constant on the right. 5353 std::swap(LHS, RHS); 5354 Pred = ICmpInst::getSwappedPredicate(Pred); 5355 Changed = true; 5356 } 5357 5358 // If we're comparing an addrec with a value which is loop-invariant in the 5359 // addrec's loop, put the addrec on the left. Also make a dominance check, 5360 // as both operands could be addrecs loop-invariant in each other's loop. 5361 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5362 const Loop *L = AR->getLoop(); 5363 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5364 std::swap(LHS, RHS); 5365 Pred = ICmpInst::getSwappedPredicate(Pred); 5366 Changed = true; 5367 } 5368 } 5369 5370 // If there's a constant operand, canonicalize comparisons with boundary 5371 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5372 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5373 const APInt &RA = RC->getValue()->getValue(); 5374 switch (Pred) { 5375 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5376 case ICmpInst::ICMP_EQ: 5377 case ICmpInst::ICMP_NE: 5378 break; 5379 case ICmpInst::ICMP_UGE: 5380 if ((RA - 1).isMinValue()) { 5381 Pred = ICmpInst::ICMP_NE; 5382 RHS = getConstant(RA - 1); 5383 Changed = true; 5384 break; 5385 } 5386 if (RA.isMaxValue()) { 5387 Pred = ICmpInst::ICMP_EQ; 5388 Changed = true; 5389 break; 5390 } 5391 if (RA.isMinValue()) goto trivially_true; 5392 5393 Pred = ICmpInst::ICMP_UGT; 5394 RHS = getConstant(RA - 1); 5395 Changed = true; 5396 break; 5397 case ICmpInst::ICMP_ULE: 5398 if ((RA + 1).isMaxValue()) { 5399 Pred = ICmpInst::ICMP_NE; 5400 RHS = getConstant(RA + 1); 5401 Changed = true; 5402 break; 5403 } 5404 if (RA.isMinValue()) { 5405 Pred = ICmpInst::ICMP_EQ; 5406 Changed = true; 5407 break; 5408 } 5409 if (RA.isMaxValue()) goto trivially_true; 5410 5411 Pred = ICmpInst::ICMP_ULT; 5412 RHS = getConstant(RA + 1); 5413 Changed = true; 5414 break; 5415 case ICmpInst::ICMP_SGE: 5416 if ((RA - 1).isMinSignedValue()) { 5417 Pred = ICmpInst::ICMP_NE; 5418 RHS = getConstant(RA - 1); 5419 Changed = true; 5420 break; 5421 } 5422 if (RA.isMaxSignedValue()) { 5423 Pred = ICmpInst::ICMP_EQ; 5424 Changed = true; 5425 break; 5426 } 5427 if (RA.isMinSignedValue()) goto trivially_true; 5428 5429 Pred = ICmpInst::ICMP_SGT; 5430 RHS = getConstant(RA - 1); 5431 Changed = true; 5432 break; 5433 case ICmpInst::ICMP_SLE: 5434 if ((RA + 1).isMaxSignedValue()) { 5435 Pred = ICmpInst::ICMP_NE; 5436 RHS = getConstant(RA + 1); 5437 Changed = true; 5438 break; 5439 } 5440 if (RA.isMinSignedValue()) { 5441 Pred = ICmpInst::ICMP_EQ; 5442 Changed = true; 5443 break; 5444 } 5445 if (RA.isMaxSignedValue()) goto trivially_true; 5446 5447 Pred = ICmpInst::ICMP_SLT; 5448 RHS = getConstant(RA + 1); 5449 Changed = true; 5450 break; 5451 case ICmpInst::ICMP_UGT: 5452 if (RA.isMinValue()) { 5453 Pred = ICmpInst::ICMP_NE; 5454 Changed = true; 5455 break; 5456 } 5457 if ((RA + 1).isMaxValue()) { 5458 Pred = ICmpInst::ICMP_EQ; 5459 RHS = getConstant(RA + 1); 5460 Changed = true; 5461 break; 5462 } 5463 if (RA.isMaxValue()) goto trivially_false; 5464 break; 5465 case ICmpInst::ICMP_ULT: 5466 if (RA.isMaxValue()) { 5467 Pred = ICmpInst::ICMP_NE; 5468 Changed = true; 5469 break; 5470 } 5471 if ((RA - 1).isMinValue()) { 5472 Pred = ICmpInst::ICMP_EQ; 5473 RHS = getConstant(RA - 1); 5474 Changed = true; 5475 break; 5476 } 5477 if (RA.isMinValue()) goto trivially_false; 5478 break; 5479 case ICmpInst::ICMP_SGT: 5480 if (RA.isMinSignedValue()) { 5481 Pred = ICmpInst::ICMP_NE; 5482 Changed = true; 5483 break; 5484 } 5485 if ((RA + 1).isMaxSignedValue()) { 5486 Pred = ICmpInst::ICMP_EQ; 5487 RHS = getConstant(RA + 1); 5488 Changed = true; 5489 break; 5490 } 5491 if (RA.isMaxSignedValue()) goto trivially_false; 5492 break; 5493 case ICmpInst::ICMP_SLT: 5494 if (RA.isMaxSignedValue()) { 5495 Pred = ICmpInst::ICMP_NE; 5496 Changed = true; 5497 break; 5498 } 5499 if ((RA - 1).isMinSignedValue()) { 5500 Pred = ICmpInst::ICMP_EQ; 5501 RHS = getConstant(RA - 1); 5502 Changed = true; 5503 break; 5504 } 5505 if (RA.isMinSignedValue()) goto trivially_false; 5506 break; 5507 } 5508 } 5509 5510 // Check for obvious equality. 5511 if (HasSameValue(LHS, RHS)) { 5512 if (ICmpInst::isTrueWhenEqual(Pred)) 5513 goto trivially_true; 5514 if (ICmpInst::isFalseWhenEqual(Pred)) 5515 goto trivially_false; 5516 } 5517 5518 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5519 // adding or subtracting 1 from one of the operands. 5520 switch (Pred) { 5521 case ICmpInst::ICMP_SLE: 5522 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5523 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5524 SCEV::FlagNSW); 5525 Pred = ICmpInst::ICMP_SLT; 5526 Changed = true; 5527 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5528 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5529 SCEV::FlagNSW); 5530 Pred = ICmpInst::ICMP_SLT; 5531 Changed = true; 5532 } 5533 break; 5534 case ICmpInst::ICMP_SGE: 5535 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5536 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5537 SCEV::FlagNSW); 5538 Pred = ICmpInst::ICMP_SGT; 5539 Changed = true; 5540 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5541 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5542 SCEV::FlagNSW); 5543 Pred = ICmpInst::ICMP_SGT; 5544 Changed = true; 5545 } 5546 break; 5547 case ICmpInst::ICMP_ULE: 5548 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5549 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5550 SCEV::FlagNUW); 5551 Pred = ICmpInst::ICMP_ULT; 5552 Changed = true; 5553 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5554 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5555 SCEV::FlagNUW); 5556 Pred = ICmpInst::ICMP_ULT; 5557 Changed = true; 5558 } 5559 break; 5560 case ICmpInst::ICMP_UGE: 5561 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5562 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5563 SCEV::FlagNUW); 5564 Pred = ICmpInst::ICMP_UGT; 5565 Changed = true; 5566 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5567 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5568 SCEV::FlagNUW); 5569 Pred = ICmpInst::ICMP_UGT; 5570 Changed = true; 5571 } 5572 break; 5573 default: 5574 break; 5575 } 5576 5577 // TODO: More simplifications are possible here. 5578 5579 return Changed; 5580 5581trivially_true: 5582 // Return 0 == 0. 5583 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5584 Pred = ICmpInst::ICMP_EQ; 5585 return true; 5586 5587trivially_false: 5588 // Return 0 != 0. 5589 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5590 Pred = ICmpInst::ICMP_NE; 5591 return true; 5592} 5593 5594bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5595 return getSignedRange(S).getSignedMax().isNegative(); 5596} 5597 5598bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5599 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5600} 5601 5602bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5603 return !getSignedRange(S).getSignedMin().isNegative(); 5604} 5605 5606bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5607 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5608} 5609 5610bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5611 return isKnownNegative(S) || isKnownPositive(S); 5612} 5613 5614bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5615 const SCEV *LHS, const SCEV *RHS) { 5616 // Canonicalize the inputs first. 5617 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5618 5619 // If LHS or RHS is an addrec, check to see if the condition is true in 5620 // every iteration of the loop. 5621 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5622 if (isLoopEntryGuardedByCond( 5623 AR->getLoop(), Pred, AR->getStart(), RHS) && 5624 isLoopBackedgeGuardedByCond( 5625 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5626 return true; 5627 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5628 if (isLoopEntryGuardedByCond( 5629 AR->getLoop(), Pred, LHS, AR->getStart()) && 5630 isLoopBackedgeGuardedByCond( 5631 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5632 return true; 5633 5634 // Otherwise see what can be done with known constant ranges. 5635 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5636} 5637 5638bool 5639ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5640 const SCEV *LHS, const SCEV *RHS) { 5641 if (HasSameValue(LHS, RHS)) 5642 return ICmpInst::isTrueWhenEqual(Pred); 5643 5644 // This code is split out from isKnownPredicate because it is called from 5645 // within isLoopEntryGuardedByCond. 5646 switch (Pred) { 5647 default: 5648 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5649 break; 5650 case ICmpInst::ICMP_SGT: 5651 Pred = ICmpInst::ICMP_SLT; 5652 std::swap(LHS, RHS); 5653 case ICmpInst::ICMP_SLT: { 5654 ConstantRange LHSRange = getSignedRange(LHS); 5655 ConstantRange RHSRange = getSignedRange(RHS); 5656 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5657 return true; 5658 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5659 return false; 5660 break; 5661 } 5662 case ICmpInst::ICMP_SGE: 5663 Pred = ICmpInst::ICMP_SLE; 5664 std::swap(LHS, RHS); 5665 case ICmpInst::ICMP_SLE: { 5666 ConstantRange LHSRange = getSignedRange(LHS); 5667 ConstantRange RHSRange = getSignedRange(RHS); 5668 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5669 return true; 5670 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5671 return false; 5672 break; 5673 } 5674 case ICmpInst::ICMP_UGT: 5675 Pred = ICmpInst::ICMP_ULT; 5676 std::swap(LHS, RHS); 5677 case ICmpInst::ICMP_ULT: { 5678 ConstantRange LHSRange = getUnsignedRange(LHS); 5679 ConstantRange RHSRange = getUnsignedRange(RHS); 5680 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5681 return true; 5682 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5683 return false; 5684 break; 5685 } 5686 case ICmpInst::ICMP_UGE: 5687 Pred = ICmpInst::ICMP_ULE; 5688 std::swap(LHS, RHS); 5689 case ICmpInst::ICMP_ULE: { 5690 ConstantRange LHSRange = getUnsignedRange(LHS); 5691 ConstantRange RHSRange = getUnsignedRange(RHS); 5692 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5693 return true; 5694 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5695 return false; 5696 break; 5697 } 5698 case ICmpInst::ICMP_NE: { 5699 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5700 return true; 5701 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5702 return true; 5703 5704 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5705 if (isKnownNonZero(Diff)) 5706 return true; 5707 break; 5708 } 5709 case ICmpInst::ICMP_EQ: 5710 // The check at the top of the function catches the case where 5711 // the values are known to be equal. 5712 break; 5713 } 5714 return false; 5715} 5716 5717/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5718/// protected by a conditional between LHS and RHS. This is used to 5719/// to eliminate casts. 5720bool 5721ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5722 ICmpInst::Predicate Pred, 5723 const SCEV *LHS, const SCEV *RHS) { 5724 // Interpret a null as meaning no loop, where there is obviously no guard 5725 // (interprocedural conditions notwithstanding). 5726 if (!L) return true; 5727 5728 BasicBlock *Latch = L->getLoopLatch(); 5729 if (!Latch) 5730 return false; 5731 5732 BranchInst *LoopContinuePredicate = 5733 dyn_cast<BranchInst>(Latch->getTerminator()); 5734 if (!LoopContinuePredicate || 5735 LoopContinuePredicate->isUnconditional()) 5736 return false; 5737 5738 return isImpliedCond(Pred, LHS, RHS, 5739 LoopContinuePredicate->getCondition(), 5740 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5741} 5742 5743/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5744/// by a conditional between LHS and RHS. This is used to help avoid max 5745/// expressions in loop trip counts, and to eliminate casts. 5746bool 5747ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5748 ICmpInst::Predicate Pred, 5749 const SCEV *LHS, const SCEV *RHS) { 5750 // Interpret a null as meaning no loop, where there is obviously no guard 5751 // (interprocedural conditions notwithstanding). 5752 if (!L) return false; 5753 5754 // Starting at the loop predecessor, climb up the predecessor chain, as long 5755 // as there are predecessors that can be found that have unique successors 5756 // leading to the original header. 5757 for (std::pair<BasicBlock *, BasicBlock *> 5758 Pair(L->getLoopPredecessor(), L->getHeader()); 5759 Pair.first; 5760 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5761 5762 BranchInst *LoopEntryPredicate = 5763 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5764 if (!LoopEntryPredicate || 5765 LoopEntryPredicate->isUnconditional()) 5766 continue; 5767 5768 if (isImpliedCond(Pred, LHS, RHS, 5769 LoopEntryPredicate->getCondition(), 5770 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5771 return true; 5772 } 5773 5774 return false; 5775} 5776 5777/// isImpliedCond - Test whether the condition described by Pred, LHS, 5778/// and RHS is true whenever the given Cond value evaluates to true. 5779bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5780 const SCEV *LHS, const SCEV *RHS, 5781 Value *FoundCondValue, 5782 bool Inverse) { 5783 // Recursively handle And and Or conditions. 5784 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5785 if (BO->getOpcode() == Instruction::And) { 5786 if (!Inverse) 5787 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5788 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5789 } else if (BO->getOpcode() == Instruction::Or) { 5790 if (Inverse) 5791 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5792 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5793 } 5794 } 5795 5796 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5797 if (!ICI) return false; 5798 5799 // Bail if the ICmp's operands' types are wider than the needed type 5800 // before attempting to call getSCEV on them. This avoids infinite 5801 // recursion, since the analysis of widening casts can require loop 5802 // exit condition information for overflow checking, which would 5803 // lead back here. 5804 if (getTypeSizeInBits(LHS->getType()) < 5805 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5806 return false; 5807 5808 // Now that we found a conditional branch that dominates the loop, check to 5809 // see if it is the comparison we are looking for. 5810 ICmpInst::Predicate FoundPred; 5811 if (Inverse) 5812 FoundPred = ICI->getInversePredicate(); 5813 else 5814 FoundPred = ICI->getPredicate(); 5815 5816 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5817 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5818 5819 // Balance the types. The case where FoundLHS' type is wider than 5820 // LHS' type is checked for above. 5821 if (getTypeSizeInBits(LHS->getType()) > 5822 getTypeSizeInBits(FoundLHS->getType())) { 5823 if (CmpInst::isSigned(Pred)) { 5824 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5825 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5826 } else { 5827 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5828 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5829 } 5830 } 5831 5832 // Canonicalize the query to match the way instcombine will have 5833 // canonicalized the comparison. 5834 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5835 if (LHS == RHS) 5836 return CmpInst::isTrueWhenEqual(Pred); 5837 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5838 if (FoundLHS == FoundRHS) 5839 return CmpInst::isFalseWhenEqual(Pred); 5840 5841 // Check to see if we can make the LHS or RHS match. 5842 if (LHS == FoundRHS || RHS == FoundLHS) { 5843 if (isa<SCEVConstant>(RHS)) { 5844 std::swap(FoundLHS, FoundRHS); 5845 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5846 } else { 5847 std::swap(LHS, RHS); 5848 Pred = ICmpInst::getSwappedPredicate(Pred); 5849 } 5850 } 5851 5852 // Check whether the found predicate is the same as the desired predicate. 5853 if (FoundPred == Pred) 5854 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5855 5856 // Check whether swapping the found predicate makes it the same as the 5857 // desired predicate. 5858 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5859 if (isa<SCEVConstant>(RHS)) 5860 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5861 else 5862 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5863 RHS, LHS, FoundLHS, FoundRHS); 5864 } 5865 5866 // Check whether the actual condition is beyond sufficient. 5867 if (FoundPred == ICmpInst::ICMP_EQ) 5868 if (ICmpInst::isTrueWhenEqual(Pred)) 5869 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5870 return true; 5871 if (Pred == ICmpInst::ICMP_NE) 5872 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5873 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5874 return true; 5875 5876 // Otherwise assume the worst. 5877 return false; 5878} 5879 5880/// isImpliedCondOperands - Test whether the condition described by Pred, 5881/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5882/// and FoundRHS is true. 5883bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5884 const SCEV *LHS, const SCEV *RHS, 5885 const SCEV *FoundLHS, 5886 const SCEV *FoundRHS) { 5887 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5888 FoundLHS, FoundRHS) || 5889 // ~x < ~y --> x > y 5890 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5891 getNotSCEV(FoundRHS), 5892 getNotSCEV(FoundLHS)); 5893} 5894 5895/// isImpliedCondOperandsHelper - Test whether the condition described by 5896/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5897/// FoundLHS, and FoundRHS is true. 5898bool 5899ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5900 const SCEV *LHS, const SCEV *RHS, 5901 const SCEV *FoundLHS, 5902 const SCEV *FoundRHS) { 5903 switch (Pred) { 5904 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5905 case ICmpInst::ICMP_EQ: 5906 case ICmpInst::ICMP_NE: 5907 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5908 return true; 5909 break; 5910 case ICmpInst::ICMP_SLT: 5911 case ICmpInst::ICMP_SLE: 5912 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5913 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5914 return true; 5915 break; 5916 case ICmpInst::ICMP_SGT: 5917 case ICmpInst::ICMP_SGE: 5918 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5919 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5920 return true; 5921 break; 5922 case ICmpInst::ICMP_ULT: 5923 case ICmpInst::ICMP_ULE: 5924 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5925 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5926 return true; 5927 break; 5928 case ICmpInst::ICMP_UGT: 5929 case ICmpInst::ICMP_UGE: 5930 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5931 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5932 return true; 5933 break; 5934 } 5935 5936 return false; 5937} 5938 5939/// getBECount - Subtract the end and start values and divide by the step, 5940/// rounding up, to get the number of times the backedge is executed. Return 5941/// CouldNotCompute if an intermediate computation overflows. 5942const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5943 const SCEV *End, 5944 const SCEV *Step, 5945 bool NoWrap) { 5946 assert(!isKnownNegative(Step) && 5947 "This code doesn't handle negative strides yet!"); 5948 5949 Type *Ty = Start->getType(); 5950 5951 // When Start == End, we have an exact BECount == 0. Short-circuit this case 5952 // here because SCEV may not be able to determine that the unsigned division 5953 // after rounding is zero. 5954 if (Start == End) 5955 return getConstant(Ty, 0); 5956 5957 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5958 const SCEV *Diff = getMinusSCEV(End, Start); 5959 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5960 5961 // Add an adjustment to the difference between End and Start so that 5962 // the division will effectively round up. 5963 const SCEV *Add = getAddExpr(Diff, RoundUp); 5964 5965 if (!NoWrap) { 5966 // Check Add for unsigned overflow. 5967 // TODO: More sophisticated things could be done here. 5968 Type *WideTy = IntegerType::get(getContext(), 5969 getTypeSizeInBits(Ty) + 1); 5970 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5971 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5972 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5973 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5974 return getCouldNotCompute(); 5975 } 5976 5977 return getUDivExpr(Add, Step); 5978} 5979 5980/// HowManyLessThans - Return the number of times a backedge containing the 5981/// specified less-than comparison will execute. If not computable, return 5982/// CouldNotCompute. 5983ScalarEvolution::ExitLimit 5984ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5985 const Loop *L, bool isSigned) { 5986 // Only handle: "ADDREC < LoopInvariant". 5987 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5988 5989 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5990 if (!AddRec || AddRec->getLoop() != L) 5991 return getCouldNotCompute(); 5992 5993 // Check to see if we have a flag which makes analysis easy. 5994 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) : 5995 AddRec->getNoWrapFlags(SCEV::FlagNUW); 5996 5997 if (AddRec->isAffine()) { 5998 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5999 const SCEV *Step = AddRec->getStepRecurrence(*this); 6000 6001 if (Step->isZero()) 6002 return getCouldNotCompute(); 6003 if (Step->isOne()) { 6004 // With unit stride, the iteration never steps past the limit value. 6005 } else if (isKnownPositive(Step)) { 6006 // Test whether a positive iteration can step past the limit 6007 // value and past the maximum value for its type in a single step. 6008 // Note that it's not sufficient to check NoWrap here, because even 6009 // though the value after a wrap is undefined, it's not undefined 6010 // behavior, so if wrap does occur, the loop could either terminate or 6011 // loop infinitely, but in either case, the loop is guaranteed to 6012 // iterate at least until the iteration where the wrapping occurs. 6013 const SCEV *One = getConstant(Step->getType(), 1); 6014 if (isSigned) { 6015 APInt Max = APInt::getSignedMaxValue(BitWidth); 6016 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 6017 .slt(getSignedRange(RHS).getSignedMax())) 6018 return getCouldNotCompute(); 6019 } else { 6020 APInt Max = APInt::getMaxValue(BitWidth); 6021 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 6022 .ult(getUnsignedRange(RHS).getUnsignedMax())) 6023 return getCouldNotCompute(); 6024 } 6025 } else 6026 // TODO: Handle negative strides here and below. 6027 return getCouldNotCompute(); 6028 6029 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 6030 // m. So, we count the number of iterations in which {n,+,s} < m is true. 6031 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 6032 // treat m-n as signed nor unsigned due to overflow possibility. 6033 6034 // First, we get the value of the LHS in the first iteration: n 6035 const SCEV *Start = AddRec->getOperand(0); 6036 6037 // Determine the minimum constant start value. 6038 const SCEV *MinStart = getConstant(isSigned ? 6039 getSignedRange(Start).getSignedMin() : 6040 getUnsignedRange(Start).getUnsignedMin()); 6041 6042 // If we know that the condition is true in order to enter the loop, 6043 // then we know that it will run exactly (m-n)/s times. Otherwise, we 6044 // only know that it will execute (max(m,n)-n)/s times. In both cases, 6045 // the division must round up. 6046 const SCEV *End = RHS; 6047 if (!isLoopEntryGuardedByCond(L, 6048 isSigned ? ICmpInst::ICMP_SLT : 6049 ICmpInst::ICMP_ULT, 6050 getMinusSCEV(Start, Step), RHS)) 6051 End = isSigned ? getSMaxExpr(RHS, Start) 6052 : getUMaxExpr(RHS, Start); 6053 6054 // Determine the maximum constant end value. 6055 const SCEV *MaxEnd = getConstant(isSigned ? 6056 getSignedRange(End).getSignedMax() : 6057 getUnsignedRange(End).getUnsignedMax()); 6058 6059 // If MaxEnd is within a step of the maximum integer value in its type, 6060 // adjust it down to the minimum value which would produce the same effect. 6061 // This allows the subsequent ceiling division of (N+(step-1))/step to 6062 // compute the correct value. 6063 const SCEV *StepMinusOne = getMinusSCEV(Step, 6064 getConstant(Step->getType(), 1)); 6065 MaxEnd = isSigned ? 6066 getSMinExpr(MaxEnd, 6067 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 6068 StepMinusOne)) : 6069 getUMinExpr(MaxEnd, 6070 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 6071 StepMinusOne)); 6072 6073 // Finally, we subtract these two values and divide, rounding up, to get 6074 // the number of times the backedge is executed. 6075 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 6076 6077 // The maximum backedge count is similar, except using the minimum start 6078 // value and the maximum end value. 6079 // If we already have an exact constant BECount, use it instead. 6080 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 6081 : getBECount(MinStart, MaxEnd, Step, NoWrap); 6082 6083 // If the stride is nonconstant, and NoWrap == true, then 6084 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 6085 // exact BECount and invalid MaxBECount, which should be avoided to catch 6086 // more optimization opportunities. 6087 if (isa<SCEVCouldNotCompute>(MaxBECount)) 6088 MaxBECount = BECount; 6089 6090 return ExitLimit(BECount, MaxBECount); 6091 } 6092 6093 return getCouldNotCompute(); 6094} 6095 6096/// getNumIterationsInRange - Return the number of iterations of this loop that 6097/// produce values in the specified constant range. Another way of looking at 6098/// this is that it returns the first iteration number where the value is not in 6099/// the condition, thus computing the exit count. If the iteration count can't 6100/// be computed, an instance of SCEVCouldNotCompute is returned. 6101const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 6102 ScalarEvolution &SE) const { 6103 if (Range.isFullSet()) // Infinite loop. 6104 return SE.getCouldNotCompute(); 6105 6106 // If the start is a non-zero constant, shift the range to simplify things. 6107 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 6108 if (!SC->getValue()->isZero()) { 6109 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 6110 Operands[0] = SE.getConstant(SC->getType(), 0); 6111 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 6112 getNoWrapFlags(FlagNW)); 6113 if (const SCEVAddRecExpr *ShiftedAddRec = 6114 dyn_cast<SCEVAddRecExpr>(Shifted)) 6115 return ShiftedAddRec->getNumIterationsInRange( 6116 Range.subtract(SC->getValue()->getValue()), SE); 6117 // This is strange and shouldn't happen. 6118 return SE.getCouldNotCompute(); 6119 } 6120 6121 // The only time we can solve this is when we have all constant indices. 6122 // Otherwise, we cannot determine the overflow conditions. 6123 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 6124 if (!isa<SCEVConstant>(getOperand(i))) 6125 return SE.getCouldNotCompute(); 6126 6127 6128 // Okay at this point we know that all elements of the chrec are constants and 6129 // that the start element is zero. 6130 6131 // First check to see if the range contains zero. If not, the first 6132 // iteration exits. 6133 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6134 if (!Range.contains(APInt(BitWidth, 0))) 6135 return SE.getConstant(getType(), 0); 6136 6137 if (isAffine()) { 6138 // If this is an affine expression then we have this situation: 6139 // Solve {0,+,A} in Range === Ax in Range 6140 6141 // We know that zero is in the range. If A is positive then we know that 6142 // the upper value of the range must be the first possible exit value. 6143 // If A is negative then the lower of the range is the last possible loop 6144 // value. Also note that we already checked for a full range. 6145 APInt One(BitWidth,1); 6146 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6147 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6148 6149 // The exit value should be (End+A)/A. 6150 APInt ExitVal = (End + A).udiv(A); 6151 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6152 6153 // Evaluate at the exit value. If we really did fall out of the valid 6154 // range, then we computed our trip count, otherwise wrap around or other 6155 // things must have happened. 6156 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6157 if (Range.contains(Val->getValue())) 6158 return SE.getCouldNotCompute(); // Something strange happened 6159 6160 // Ensure that the previous value is in the range. This is a sanity check. 6161 assert(Range.contains( 6162 EvaluateConstantChrecAtConstant(this, 6163 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6164 "Linear scev computation is off in a bad way!"); 6165 return SE.getConstant(ExitValue); 6166 } else if (isQuadratic()) { 6167 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6168 // quadratic equation to solve it. To do this, we must frame our problem in 6169 // terms of figuring out when zero is crossed, instead of when 6170 // Range.getUpper() is crossed. 6171 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6172 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6173 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6174 // getNoWrapFlags(FlagNW) 6175 FlagAnyWrap); 6176 6177 // Next, solve the constructed addrec 6178 std::pair<const SCEV *,const SCEV *> Roots = 6179 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6180 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6181 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6182 if (R1) { 6183 // Pick the smallest positive root value. 6184 if (ConstantInt *CB = 6185 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6186 R1->getValue(), R2->getValue()))) { 6187 if (CB->getZExtValue() == false) 6188 std::swap(R1, R2); // R1 is the minimum root now. 6189 6190 // Make sure the root is not off by one. The returned iteration should 6191 // not be in the range, but the previous one should be. When solving 6192 // for "X*X < 5", for example, we should not return a root of 2. 6193 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6194 R1->getValue(), 6195 SE); 6196 if (Range.contains(R1Val->getValue())) { 6197 // The next iteration must be out of the range... 6198 ConstantInt *NextVal = 6199 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6200 6201 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6202 if (!Range.contains(R1Val->getValue())) 6203 return SE.getConstant(NextVal); 6204 return SE.getCouldNotCompute(); // Something strange happened 6205 } 6206 6207 // If R1 was not in the range, then it is a good return value. Make 6208 // sure that R1-1 WAS in the range though, just in case. 6209 ConstantInt *NextVal = 6210 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6211 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6212 if (Range.contains(R1Val->getValue())) 6213 return R1; 6214 return SE.getCouldNotCompute(); // Something strange happened 6215 } 6216 } 6217 } 6218 6219 return SE.getCouldNotCompute(); 6220} 6221 6222 6223 6224//===----------------------------------------------------------------------===// 6225// SCEVCallbackVH Class Implementation 6226//===----------------------------------------------------------------------===// 6227 6228void ScalarEvolution::SCEVCallbackVH::deleted() { 6229 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6230 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6231 SE->ConstantEvolutionLoopExitValue.erase(PN); 6232 SE->ValueExprMap.erase(getValPtr()); 6233 // this now dangles! 6234} 6235 6236void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6237 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6238 6239 // Forget all the expressions associated with users of the old value, 6240 // so that future queries will recompute the expressions using the new 6241 // value. 6242 Value *Old = getValPtr(); 6243 SmallVector<User *, 16> Worklist; 6244 SmallPtrSet<User *, 8> Visited; 6245 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6246 UI != UE; ++UI) 6247 Worklist.push_back(*UI); 6248 while (!Worklist.empty()) { 6249 User *U = Worklist.pop_back_val(); 6250 // Deleting the Old value will cause this to dangle. Postpone 6251 // that until everything else is done. 6252 if (U == Old) 6253 continue; 6254 if (!Visited.insert(U)) 6255 continue; 6256 if (PHINode *PN = dyn_cast<PHINode>(U)) 6257 SE->ConstantEvolutionLoopExitValue.erase(PN); 6258 SE->ValueExprMap.erase(U); 6259 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6260 UI != UE; ++UI) 6261 Worklist.push_back(*UI); 6262 } 6263 // Delete the Old value. 6264 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6265 SE->ConstantEvolutionLoopExitValue.erase(PN); 6266 SE->ValueExprMap.erase(Old); 6267 // this now dangles! 6268} 6269 6270ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6271 : CallbackVH(V), SE(se) {} 6272 6273//===----------------------------------------------------------------------===// 6274// ScalarEvolution Class Implementation 6275//===----------------------------------------------------------------------===// 6276 6277ScalarEvolution::ScalarEvolution() 6278 : FunctionPass(ID), FirstUnknown(0) { 6279 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6280} 6281 6282bool ScalarEvolution::runOnFunction(Function &F) { 6283 this->F = &F; 6284 LI = &getAnalysis<LoopInfo>(); 6285 TD = getAnalysisIfAvailable<TargetData>(); 6286 DT = &getAnalysis<DominatorTree>(); 6287 return false; 6288} 6289 6290void ScalarEvolution::releaseMemory() { 6291 // Iterate through all the SCEVUnknown instances and call their 6292 // destructors, so that they release their references to their values. 6293 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6294 U->~SCEVUnknown(); 6295 FirstUnknown = 0; 6296 6297 ValueExprMap.clear(); 6298 6299 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6300 // that a loop had multiple computable exits. 6301 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6302 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6303 I != E; ++I) { 6304 I->second.clear(); 6305 } 6306 6307 BackedgeTakenCounts.clear(); 6308 ConstantEvolutionLoopExitValue.clear(); 6309 ValuesAtScopes.clear(); 6310 LoopDispositions.clear(); 6311 BlockDispositions.clear(); 6312 UnsignedRanges.clear(); 6313 SignedRanges.clear(); 6314 UniqueSCEVs.clear(); 6315 SCEVAllocator.Reset(); 6316} 6317 6318void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6319 AU.setPreservesAll(); 6320 AU.addRequiredTransitive<LoopInfo>(); 6321 AU.addRequiredTransitive<DominatorTree>(); 6322} 6323 6324bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6325 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6326} 6327 6328static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6329 const Loop *L) { 6330 // Print all inner loops first 6331 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6332 PrintLoopInfo(OS, SE, *I); 6333 6334 OS << "Loop "; 6335 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6336 OS << ": "; 6337 6338 SmallVector<BasicBlock *, 8> ExitBlocks; 6339 L->getExitBlocks(ExitBlocks); 6340 if (ExitBlocks.size() != 1) 6341 OS << "<multiple exits> "; 6342 6343 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6344 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6345 } else { 6346 OS << "Unpredictable backedge-taken count. "; 6347 } 6348 6349 OS << "\n" 6350 "Loop "; 6351 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6352 OS << ": "; 6353 6354 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6355 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6356 } else { 6357 OS << "Unpredictable max backedge-taken count. "; 6358 } 6359 6360 OS << "\n"; 6361} 6362 6363void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6364 // ScalarEvolution's implementation of the print method is to print 6365 // out SCEV values of all instructions that are interesting. Doing 6366 // this potentially causes it to create new SCEV objects though, 6367 // which technically conflicts with the const qualifier. This isn't 6368 // observable from outside the class though, so casting away the 6369 // const isn't dangerous. 6370 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6371 6372 OS << "Classifying expressions for: "; 6373 WriteAsOperand(OS, F, /*PrintType=*/false); 6374 OS << "\n"; 6375 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6376 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6377 OS << *I << '\n'; 6378 OS << " --> "; 6379 const SCEV *SV = SE.getSCEV(&*I); 6380 SV->print(OS); 6381 6382 const Loop *L = LI->getLoopFor((*I).getParent()); 6383 6384 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6385 if (AtUse != SV) { 6386 OS << " --> "; 6387 AtUse->print(OS); 6388 } 6389 6390 if (L) { 6391 OS << "\t\t" "Exits: "; 6392 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6393 if (!SE.isLoopInvariant(ExitValue, L)) { 6394 OS << "<<Unknown>>"; 6395 } else { 6396 OS << *ExitValue; 6397 } 6398 } 6399 6400 OS << "\n"; 6401 } 6402 6403 OS << "Determining loop execution counts for: "; 6404 WriteAsOperand(OS, F, /*PrintType=*/false); 6405 OS << "\n"; 6406 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6407 PrintLoopInfo(OS, &SE, *I); 6408} 6409 6410ScalarEvolution::LoopDisposition 6411ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6412 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6413 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6414 Values.insert(std::make_pair(L, LoopVariant)); 6415 if (!Pair.second) 6416 return Pair.first->second; 6417 6418 LoopDisposition D = computeLoopDisposition(S, L); 6419 return LoopDispositions[S][L] = D; 6420} 6421 6422ScalarEvolution::LoopDisposition 6423ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6424 switch (S->getSCEVType()) { 6425 case scConstant: 6426 return LoopInvariant; 6427 case scTruncate: 6428 case scZeroExtend: 6429 case scSignExtend: 6430 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6431 case scAddRecExpr: { 6432 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6433 6434 // If L is the addrec's loop, it's computable. 6435 if (AR->getLoop() == L) 6436 return LoopComputable; 6437 6438 // Add recurrences are never invariant in the function-body (null loop). 6439 if (!L) 6440 return LoopVariant; 6441 6442 // This recurrence is variant w.r.t. L if L contains AR's loop. 6443 if (L->contains(AR->getLoop())) 6444 return LoopVariant; 6445 6446 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6447 if (AR->getLoop()->contains(L)) 6448 return LoopInvariant; 6449 6450 // This recurrence is variant w.r.t. L if any of its operands 6451 // are variant. 6452 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6453 I != E; ++I) 6454 if (!isLoopInvariant(*I, L)) 6455 return LoopVariant; 6456 6457 // Otherwise it's loop-invariant. 6458 return LoopInvariant; 6459 } 6460 case scAddExpr: 6461 case scMulExpr: 6462 case scUMaxExpr: 6463 case scSMaxExpr: { 6464 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6465 bool HasVarying = false; 6466 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6467 I != E; ++I) { 6468 LoopDisposition D = getLoopDisposition(*I, L); 6469 if (D == LoopVariant) 6470 return LoopVariant; 6471 if (D == LoopComputable) 6472 HasVarying = true; 6473 } 6474 return HasVarying ? LoopComputable : LoopInvariant; 6475 } 6476 case scUDivExpr: { 6477 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6478 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6479 if (LD == LoopVariant) 6480 return LoopVariant; 6481 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6482 if (RD == LoopVariant) 6483 return LoopVariant; 6484 return (LD == LoopInvariant && RD == LoopInvariant) ? 6485 LoopInvariant : LoopComputable; 6486 } 6487 case scUnknown: 6488 // All non-instruction values are loop invariant. All instructions are loop 6489 // invariant if they are not contained in the specified loop. 6490 // Instructions are never considered invariant in the function body 6491 // (null loop) because they are defined within the "loop". 6492 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6493 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6494 return LoopInvariant; 6495 case scCouldNotCompute: 6496 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6497 return LoopVariant; 6498 default: break; 6499 } 6500 llvm_unreachable("Unknown SCEV kind!"); 6501 return LoopVariant; 6502} 6503 6504bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6505 return getLoopDisposition(S, L) == LoopInvariant; 6506} 6507 6508bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6509 return getLoopDisposition(S, L) == LoopComputable; 6510} 6511 6512ScalarEvolution::BlockDisposition 6513ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6514 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6515 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6516 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6517 if (!Pair.second) 6518 return Pair.first->second; 6519 6520 BlockDisposition D = computeBlockDisposition(S, BB); 6521 return BlockDispositions[S][BB] = D; 6522} 6523 6524ScalarEvolution::BlockDisposition 6525ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6526 switch (S->getSCEVType()) { 6527 case scConstant: 6528 return ProperlyDominatesBlock; 6529 case scTruncate: 6530 case scZeroExtend: 6531 case scSignExtend: 6532 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6533 case scAddRecExpr: { 6534 // This uses a "dominates" query instead of "properly dominates" query 6535 // to test for proper dominance too, because the instruction which 6536 // produces the addrec's value is a PHI, and a PHI effectively properly 6537 // dominates its entire containing block. 6538 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6539 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6540 return DoesNotDominateBlock; 6541 } 6542 // FALL THROUGH into SCEVNAryExpr handling. 6543 case scAddExpr: 6544 case scMulExpr: 6545 case scUMaxExpr: 6546 case scSMaxExpr: { 6547 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6548 bool Proper = true; 6549 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6550 I != E; ++I) { 6551 BlockDisposition D = getBlockDisposition(*I, BB); 6552 if (D == DoesNotDominateBlock) 6553 return DoesNotDominateBlock; 6554 if (D == DominatesBlock) 6555 Proper = false; 6556 } 6557 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6558 } 6559 case scUDivExpr: { 6560 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6561 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6562 BlockDisposition LD = getBlockDisposition(LHS, BB); 6563 if (LD == DoesNotDominateBlock) 6564 return DoesNotDominateBlock; 6565 BlockDisposition RD = getBlockDisposition(RHS, BB); 6566 if (RD == DoesNotDominateBlock) 6567 return DoesNotDominateBlock; 6568 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6569 ProperlyDominatesBlock : DominatesBlock; 6570 } 6571 case scUnknown: 6572 if (Instruction *I = 6573 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6574 if (I->getParent() == BB) 6575 return DominatesBlock; 6576 if (DT->properlyDominates(I->getParent(), BB)) 6577 return ProperlyDominatesBlock; 6578 return DoesNotDominateBlock; 6579 } 6580 return ProperlyDominatesBlock; 6581 case scCouldNotCompute: 6582 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6583 return DoesNotDominateBlock; 6584 default: break; 6585 } 6586 llvm_unreachable("Unknown SCEV kind!"); 6587 return DoesNotDominateBlock; 6588} 6589 6590bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6591 return getBlockDisposition(S, BB) >= DominatesBlock; 6592} 6593 6594bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6595 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6596} 6597 6598bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6599 switch (S->getSCEVType()) { 6600 case scConstant: 6601 return false; 6602 case scTruncate: 6603 case scZeroExtend: 6604 case scSignExtend: { 6605 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6606 const SCEV *CastOp = Cast->getOperand(); 6607 return Op == CastOp || hasOperand(CastOp, Op); 6608 } 6609 case scAddRecExpr: 6610 case scAddExpr: 6611 case scMulExpr: 6612 case scUMaxExpr: 6613 case scSMaxExpr: { 6614 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6615 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6616 I != E; ++I) { 6617 const SCEV *NAryOp = *I; 6618 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6619 return true; 6620 } 6621 return false; 6622 } 6623 case scUDivExpr: { 6624 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6625 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6626 return LHS == Op || hasOperand(LHS, Op) || 6627 RHS == Op || hasOperand(RHS, Op); 6628 } 6629 case scUnknown: 6630 return false; 6631 case scCouldNotCompute: 6632 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6633 return false; 6634 default: break; 6635 } 6636 llvm_unreachable("Unknown SCEV kind!"); 6637 return false; 6638} 6639 6640void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6641 ValuesAtScopes.erase(S); 6642 LoopDispositions.erase(S); 6643 BlockDispositions.erase(S); 6644 UnsignedRanges.erase(S); 6645 SignedRanges.erase(S); 6646} 6647