ScalarEvolution.cpp revision 980e9f399de8428550faa66835a789ba22e037de
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 || SA->getNumOperands() != 2 || SA->getOperand(0) != Step) 1074 return 0; 1075 1076 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1077 // same three conditions that getSignExtendedExpr checks. 1078 1079 // 1. NSW flags on the step increment. 1080 const SCEV *PreStart = SA->getOperand(1); 1081 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1082 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1083 1084 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1085 return PreStart; 1086 1087 // 2. Direct overflow check on the step operation's expression. 1088 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1089 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1090 const SCEV *OperandExtendedStart = 1091 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1092 SE->getSignExtendExpr(Step, WideTy)); 1093 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1094 // Cache knowledge of PreAR NSW. 1095 if (PreAR) 1096 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1097 // FIXME: this optimization needs a unit test 1098 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1099 return PreStart; 1100 } 1101 1102 // 3. Loop precondition. 1103 ICmpInst::Predicate Pred; 1104 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1105 1106 if (OverflowLimit && 1107 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1108 return PreStart; 1109 } 1110 return 0; 1111} 1112 1113// Get the normalized sign-extended expression for this AddRec's Start. 1114static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1115 Type *Ty, 1116 ScalarEvolution *SE) { 1117 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1118 if (!PreStart) 1119 return SE->getSignExtendExpr(AR->getStart(), Ty); 1120 1121 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1122 SE->getSignExtendExpr(PreStart, Ty)); 1123} 1124 1125const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1126 Type *Ty) { 1127 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1128 "This is not an extending conversion!"); 1129 assert(isSCEVable(Ty) && 1130 "This is not a conversion to a SCEVable type!"); 1131 Ty = getEffectiveSCEVType(Ty); 1132 1133 // Fold if the operand is constant. 1134 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1135 return getConstant( 1136 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1137 getEffectiveSCEVType(Ty)))); 1138 1139 // sext(sext(x)) --> sext(x) 1140 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1141 return getSignExtendExpr(SS->getOperand(), Ty); 1142 1143 // sext(zext(x)) --> zext(x) 1144 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1145 return getZeroExtendExpr(SZ->getOperand(), Ty); 1146 1147 // Before doing any expensive analysis, check to see if we've already 1148 // computed a SCEV for this Op and Ty. 1149 FoldingSetNodeID ID; 1150 ID.AddInteger(scSignExtend); 1151 ID.AddPointer(Op); 1152 ID.AddPointer(Ty); 1153 void *IP = 0; 1154 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1155 1156 // If the input value is provably positive, build a zext instead. 1157 if (isKnownNonNegative(Op)) 1158 return getZeroExtendExpr(Op, Ty); 1159 1160 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1161 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1162 // It's possible the bits taken off by the truncate were all sign bits. If 1163 // so, we should be able to simplify this further. 1164 const SCEV *X = ST->getOperand(); 1165 ConstantRange CR = getSignedRange(X); 1166 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1167 unsigned NewBits = getTypeSizeInBits(Ty); 1168 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1169 CR.sextOrTrunc(NewBits))) 1170 return getTruncateOrSignExtend(X, Ty); 1171 } 1172 1173 // If the input value is a chrec scev, and we can prove that the value 1174 // did not overflow the old, smaller, value, we can sign extend all of the 1175 // operands (often constants). This allows analysis of something like 1176 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1177 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1178 if (AR->isAffine()) { 1179 const SCEV *Start = AR->getStart(); 1180 const SCEV *Step = AR->getStepRecurrence(*this); 1181 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1182 const Loop *L = AR->getLoop(); 1183 1184 // If we have special knowledge that this addrec won't overflow, 1185 // we don't need to do any further analysis. 1186 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1187 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1188 getSignExtendExpr(Step, Ty), 1189 L, SCEV::FlagNSW); 1190 1191 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1192 // Note that this serves two purposes: It filters out loops that are 1193 // simply not analyzable, and it covers the case where this code is 1194 // being called from within backedge-taken count analysis, such that 1195 // attempting to ask for the backedge-taken count would likely result 1196 // in infinite recursion. In the later case, the analysis code will 1197 // cope with a conservative value, and it will take care to purge 1198 // that value once it has finished. 1199 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1200 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1201 // Manually compute the final value for AR, checking for 1202 // overflow. 1203 1204 // Check whether the backedge-taken count can be losslessly casted to 1205 // the addrec's type. The count is always unsigned. 1206 const SCEV *CastedMaxBECount = 1207 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1208 const SCEV *RecastedMaxBECount = 1209 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1210 if (MaxBECount == RecastedMaxBECount) { 1211 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1212 // Check whether Start+Step*MaxBECount has no signed overflow. 1213 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1214 const SCEV *Add = getAddExpr(Start, SMul); 1215 const SCEV *OperandExtendedAdd = 1216 getAddExpr(getSignExtendExpr(Start, WideTy), 1217 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1218 getSignExtendExpr(Step, WideTy))); 1219 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1220 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1221 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1222 // Return the expression with the addrec on the outside. 1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1224 getSignExtendExpr(Step, Ty), 1225 L, AR->getNoWrapFlags()); 1226 } 1227 // Similar to above, only this time treat the step value as unsigned. 1228 // This covers loops that count up with an unsigned step. 1229 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1230 Add = getAddExpr(Start, UMul); 1231 OperandExtendedAdd = 1232 getAddExpr(getSignExtendExpr(Start, WideTy), 1233 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1234 getZeroExtendExpr(Step, WideTy))); 1235 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1236 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1237 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1238 // Return the expression with the addrec on the outside. 1239 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1240 getZeroExtendExpr(Step, Ty), 1241 L, AR->getNoWrapFlags()); 1242 } 1243 } 1244 1245 // If the backedge is guarded by a comparison with the pre-inc value 1246 // the addrec is safe. Also, if the entry is guarded by a comparison 1247 // with the start value and the backedge is guarded by a comparison 1248 // with the post-inc value, the addrec is safe. 1249 ICmpInst::Predicate Pred; 1250 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1251 if (OverflowLimit && 1252 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1253 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1254 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1255 OverflowLimit)))) { 1256 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1259 getSignExtendExpr(Step, Ty), 1260 L, AR->getNoWrapFlags()); 1261 } 1262 } 1263 } 1264 1265 // The cast wasn't folded; create an explicit cast node. 1266 // Recompute the insert position, as it may have been invalidated. 1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1268 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1269 Op, Ty); 1270 UniqueSCEVs.InsertNode(S, IP); 1271 return S; 1272} 1273 1274/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1275/// unspecified bits out to the given type. 1276/// 1277const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1278 Type *Ty) { 1279 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1280 "This is not an extending conversion!"); 1281 assert(isSCEVable(Ty) && 1282 "This is not a conversion to a SCEVable type!"); 1283 Ty = getEffectiveSCEVType(Ty); 1284 1285 // Sign-extend negative constants. 1286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1287 if (SC->getValue()->getValue().isNegative()) 1288 return getSignExtendExpr(Op, Ty); 1289 1290 // Peel off a truncate cast. 1291 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1292 const SCEV *NewOp = T->getOperand(); 1293 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1294 return getAnyExtendExpr(NewOp, Ty); 1295 return getTruncateOrNoop(NewOp, Ty); 1296 } 1297 1298 // Next try a zext cast. If the cast is folded, use it. 1299 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1300 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1301 return ZExt; 1302 1303 // Next try a sext cast. If the cast is folded, use it. 1304 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1305 if (!isa<SCEVSignExtendExpr>(SExt)) 1306 return SExt; 1307 1308 // Force the cast to be folded into the operands of an addrec. 1309 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1310 SmallVector<const SCEV *, 4> Ops; 1311 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1312 I != E; ++I) 1313 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1314 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1315 } 1316 1317 // As a special case, fold anyext(undef) to undef. We don't want to 1318 // know too much about SCEVUnknowns, but this special case is handy 1319 // and harmless. 1320 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1321 if (isa<UndefValue>(U->getValue())) 1322 return getSCEV(UndefValue::get(Ty)); 1323 1324 // If the expression is obviously signed, use the sext cast value. 1325 if (isa<SCEVSMaxExpr>(Op)) 1326 return SExt; 1327 1328 // Absent any other information, use the zext cast value. 1329 return ZExt; 1330} 1331 1332/// CollectAddOperandsWithScales - Process the given Ops list, which is 1333/// a list of operands to be added under the given scale, update the given 1334/// map. This is a helper function for getAddRecExpr. As an example of 1335/// what it does, given a sequence of operands that would form an add 1336/// expression like this: 1337/// 1338/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1339/// 1340/// where A and B are constants, update the map with these values: 1341/// 1342/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1343/// 1344/// and add 13 + A*B*29 to AccumulatedConstant. 1345/// This will allow getAddRecExpr to produce this: 1346/// 1347/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1348/// 1349/// This form often exposes folding opportunities that are hidden in 1350/// the original operand list. 1351/// 1352/// Return true iff it appears that any interesting folding opportunities 1353/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1354/// the common case where no interesting opportunities are present, and 1355/// is also used as a check to avoid infinite recursion. 1356/// 1357static bool 1358CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1359 SmallVector<const SCEV *, 8> &NewOps, 1360 APInt &AccumulatedConstant, 1361 const SCEV *const *Ops, size_t NumOperands, 1362 const APInt &Scale, 1363 ScalarEvolution &SE) { 1364 bool Interesting = false; 1365 1366 // Iterate over the add operands. They are sorted, with constants first. 1367 unsigned i = 0; 1368 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1369 ++i; 1370 // Pull a buried constant out to the outside. 1371 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1372 Interesting = true; 1373 AccumulatedConstant += Scale * C->getValue()->getValue(); 1374 } 1375 1376 // Next comes everything else. We're especially interested in multiplies 1377 // here, but they're in the middle, so just visit the rest with one loop. 1378 for (; i != NumOperands; ++i) { 1379 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1380 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1381 APInt NewScale = 1382 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1383 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1384 // A multiplication of a constant with another add; recurse. 1385 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1386 Interesting |= 1387 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1388 Add->op_begin(), Add->getNumOperands(), 1389 NewScale, SE); 1390 } else { 1391 // A multiplication of a constant with some other value. Update 1392 // the map. 1393 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1394 const SCEV *Key = SE.getMulExpr(MulOps); 1395 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1396 M.insert(std::make_pair(Key, NewScale)); 1397 if (Pair.second) { 1398 NewOps.push_back(Pair.first->first); 1399 } else { 1400 Pair.first->second += NewScale; 1401 // The map already had an entry for this value, which may indicate 1402 // a folding opportunity. 1403 Interesting = true; 1404 } 1405 } 1406 } else { 1407 // An ordinary operand. Update the map. 1408 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1409 M.insert(std::make_pair(Ops[i], Scale)); 1410 if (Pair.second) { 1411 NewOps.push_back(Pair.first->first); 1412 } else { 1413 Pair.first->second += Scale; 1414 // The map already had an entry for this value, which may indicate 1415 // a folding opportunity. 1416 Interesting = true; 1417 } 1418 } 1419 } 1420 1421 return Interesting; 1422} 1423 1424namespace { 1425 struct APIntCompare { 1426 bool operator()(const APInt &LHS, const APInt &RHS) const { 1427 return LHS.ult(RHS); 1428 } 1429 }; 1430} 1431 1432/// getAddExpr - Get a canonical add expression, or something simpler if 1433/// possible. 1434const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1435 SCEV::NoWrapFlags Flags) { 1436 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1437 "only nuw or nsw allowed"); 1438 assert(!Ops.empty() && "Cannot get empty add!"); 1439 if (Ops.size() == 1) return Ops[0]; 1440#ifndef NDEBUG 1441 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1442 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1443 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1444 "SCEVAddExpr operand types don't match!"); 1445#endif 1446 1447 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1448 // And vice-versa. 1449 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1450 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1451 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1452 bool All = true; 1453 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1454 E = Ops.end(); I != E; ++I) 1455 if (!isKnownNonNegative(*I)) { 1456 All = false; 1457 break; 1458 } 1459 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1460 } 1461 1462 // Sort by complexity, this groups all similar expression types together. 1463 GroupByComplexity(Ops, LI); 1464 1465 // If there are any constants, fold them together. 1466 unsigned Idx = 0; 1467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1468 ++Idx; 1469 assert(Idx < Ops.size()); 1470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1471 // We found two constants, fold them together! 1472 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1473 RHSC->getValue()->getValue()); 1474 if (Ops.size() == 2) return Ops[0]; 1475 Ops.erase(Ops.begin()+1); // Erase the folded element 1476 LHSC = cast<SCEVConstant>(Ops[0]); 1477 } 1478 1479 // If we are left with a constant zero being added, strip it off. 1480 if (LHSC->getValue()->isZero()) { 1481 Ops.erase(Ops.begin()); 1482 --Idx; 1483 } 1484 1485 if (Ops.size() == 1) return Ops[0]; 1486 } 1487 1488 // Okay, check to see if the same value occurs in the operand list more than 1489 // once. If so, merge them together into an multiply expression. Since we 1490 // sorted the list, these values are required to be adjacent. 1491 Type *Ty = Ops[0]->getType(); 1492 bool FoundMatch = false; 1493 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1494 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1495 // Scan ahead to count how many equal operands there are. 1496 unsigned Count = 2; 1497 while (i+Count != e && Ops[i+Count] == Ops[i]) 1498 ++Count; 1499 // Merge the values into a multiply. 1500 const SCEV *Scale = getConstant(Ty, Count); 1501 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1502 if (Ops.size() == Count) 1503 return Mul; 1504 Ops[i] = Mul; 1505 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1506 --i; e -= Count - 1; 1507 FoundMatch = true; 1508 } 1509 if (FoundMatch) 1510 return getAddExpr(Ops, Flags); 1511 1512 // Check for truncates. If all the operands are truncated from the same 1513 // type, see if factoring out the truncate would permit the result to be 1514 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1515 // if the contents of the resulting outer trunc fold to something simple. 1516 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1517 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1518 Type *DstType = Trunc->getType(); 1519 Type *SrcType = Trunc->getOperand()->getType(); 1520 SmallVector<const SCEV *, 8> LargeOps; 1521 bool Ok = true; 1522 // Check all the operands to see if they can be represented in the 1523 // source type of the truncate. 1524 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1525 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1526 if (T->getOperand()->getType() != SrcType) { 1527 Ok = false; 1528 break; 1529 } 1530 LargeOps.push_back(T->getOperand()); 1531 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1532 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1533 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1534 SmallVector<const SCEV *, 8> LargeMulOps; 1535 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1536 if (const SCEVTruncateExpr *T = 1537 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1538 if (T->getOperand()->getType() != SrcType) { 1539 Ok = false; 1540 break; 1541 } 1542 LargeMulOps.push_back(T->getOperand()); 1543 } else if (const SCEVConstant *C = 1544 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1545 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1546 } else { 1547 Ok = false; 1548 break; 1549 } 1550 } 1551 if (Ok) 1552 LargeOps.push_back(getMulExpr(LargeMulOps)); 1553 } else { 1554 Ok = false; 1555 break; 1556 } 1557 } 1558 if (Ok) { 1559 // Evaluate the expression in the larger type. 1560 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1561 // If it folds to something simple, use it. Otherwise, don't. 1562 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1563 return getTruncateExpr(Fold, DstType); 1564 } 1565 } 1566 1567 // Skip past any other cast SCEVs. 1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1569 ++Idx; 1570 1571 // If there are add operands they would be next. 1572 if (Idx < Ops.size()) { 1573 bool DeletedAdd = false; 1574 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1575 // If we have an add, expand the add operands onto the end of the operands 1576 // list. 1577 Ops.erase(Ops.begin()+Idx); 1578 Ops.append(Add->op_begin(), Add->op_end()); 1579 DeletedAdd = true; 1580 } 1581 1582 // If we deleted at least one add, we added operands to the end of the list, 1583 // and they are not necessarily sorted. Recurse to resort and resimplify 1584 // any operands we just acquired. 1585 if (DeletedAdd) 1586 return getAddExpr(Ops); 1587 } 1588 1589 // Skip over the add expression until we get to a multiply. 1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1591 ++Idx; 1592 1593 // Check to see if there are any folding opportunities present with 1594 // operands multiplied by constant values. 1595 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1596 uint64_t BitWidth = getTypeSizeInBits(Ty); 1597 DenseMap<const SCEV *, APInt> M; 1598 SmallVector<const SCEV *, 8> NewOps; 1599 APInt AccumulatedConstant(BitWidth, 0); 1600 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1601 Ops.data(), Ops.size(), 1602 APInt(BitWidth, 1), *this)) { 1603 // Some interesting folding opportunity is present, so its worthwhile to 1604 // re-generate the operands list. Group the operands by constant scale, 1605 // to avoid multiplying by the same constant scale multiple times. 1606 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1607 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1608 E = NewOps.end(); I != E; ++I) 1609 MulOpLists[M.find(*I)->second].push_back(*I); 1610 // Re-generate the operands list. 1611 Ops.clear(); 1612 if (AccumulatedConstant != 0) 1613 Ops.push_back(getConstant(AccumulatedConstant)); 1614 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1615 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1616 if (I->first != 0) 1617 Ops.push_back(getMulExpr(getConstant(I->first), 1618 getAddExpr(I->second))); 1619 if (Ops.empty()) 1620 return getConstant(Ty, 0); 1621 if (Ops.size() == 1) 1622 return Ops[0]; 1623 return getAddExpr(Ops); 1624 } 1625 } 1626 1627 // If we are adding something to a multiply expression, make sure the 1628 // something is not already an operand of the multiply. If so, merge it into 1629 // the multiply. 1630 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1631 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1632 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1633 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1634 if (isa<SCEVConstant>(MulOpSCEV)) 1635 continue; 1636 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1637 if (MulOpSCEV == Ops[AddOp]) { 1638 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1639 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1640 if (Mul->getNumOperands() != 2) { 1641 // If the multiply has more than two operands, we must get the 1642 // Y*Z term. 1643 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1644 Mul->op_begin()+MulOp); 1645 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1646 InnerMul = getMulExpr(MulOps); 1647 } 1648 const SCEV *One = getConstant(Ty, 1); 1649 const SCEV *AddOne = getAddExpr(One, InnerMul); 1650 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1651 if (Ops.size() == 2) return OuterMul; 1652 if (AddOp < Idx) { 1653 Ops.erase(Ops.begin()+AddOp); 1654 Ops.erase(Ops.begin()+Idx-1); 1655 } else { 1656 Ops.erase(Ops.begin()+Idx); 1657 Ops.erase(Ops.begin()+AddOp-1); 1658 } 1659 Ops.push_back(OuterMul); 1660 return getAddExpr(Ops); 1661 } 1662 1663 // Check this multiply against other multiplies being added together. 1664 for (unsigned OtherMulIdx = Idx+1; 1665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1666 ++OtherMulIdx) { 1667 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1668 // If MulOp occurs in OtherMul, we can fold the two multiplies 1669 // together. 1670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1671 OMulOp != e; ++OMulOp) 1672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1674 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1675 if (Mul->getNumOperands() != 2) { 1676 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1677 Mul->op_begin()+MulOp); 1678 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1679 InnerMul1 = getMulExpr(MulOps); 1680 } 1681 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1682 if (OtherMul->getNumOperands() != 2) { 1683 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1684 OtherMul->op_begin()+OMulOp); 1685 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1686 InnerMul2 = getMulExpr(MulOps); 1687 } 1688 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1689 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1690 if (Ops.size() == 2) return OuterMul; 1691 Ops.erase(Ops.begin()+Idx); 1692 Ops.erase(Ops.begin()+OtherMulIdx-1); 1693 Ops.push_back(OuterMul); 1694 return getAddExpr(Ops); 1695 } 1696 } 1697 } 1698 } 1699 1700 // If there are any add recurrences in the operands list, see if any other 1701 // added values are loop invariant. If so, we can fold them into the 1702 // recurrence. 1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1704 ++Idx; 1705 1706 // Scan over all recurrences, trying to fold loop invariants into them. 1707 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1708 // Scan all of the other operands to this add and add them to the vector if 1709 // they are loop invariant w.r.t. the recurrence. 1710 SmallVector<const SCEV *, 8> LIOps; 1711 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1712 const Loop *AddRecLoop = AddRec->getLoop(); 1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1714 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1715 LIOps.push_back(Ops[i]); 1716 Ops.erase(Ops.begin()+i); 1717 --i; --e; 1718 } 1719 1720 // If we found some loop invariants, fold them into the recurrence. 1721 if (!LIOps.empty()) { 1722 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1723 LIOps.push_back(AddRec->getStart()); 1724 1725 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1726 AddRec->op_end()); 1727 AddRecOps[0] = getAddExpr(LIOps); 1728 1729 // Build the new addrec. Propagate the NUW and NSW flags if both the 1730 // outer add and the inner addrec are guaranteed to have no overflow. 1731 // Always propagate NW. 1732 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1733 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1734 1735 // If all of the other operands were loop invariant, we are done. 1736 if (Ops.size() == 1) return NewRec; 1737 1738 // Otherwise, add the folded AddRec by the non-invariant parts. 1739 for (unsigned i = 0;; ++i) 1740 if (Ops[i] == AddRec) { 1741 Ops[i] = NewRec; 1742 break; 1743 } 1744 return getAddExpr(Ops); 1745 } 1746 1747 // Okay, if there weren't any loop invariants to be folded, check to see if 1748 // there are multiple AddRec's with the same loop induction variable being 1749 // added together. If so, we can fold them. 1750 for (unsigned OtherIdx = Idx+1; 1751 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1752 ++OtherIdx) 1753 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1754 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1756 AddRec->op_end()); 1757 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1758 ++OtherIdx) 1759 if (const SCEVAddRecExpr *OtherAddRec = 1760 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1761 if (OtherAddRec->getLoop() == AddRecLoop) { 1762 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1763 i != e; ++i) { 1764 if (i >= AddRecOps.size()) { 1765 AddRecOps.append(OtherAddRec->op_begin()+i, 1766 OtherAddRec->op_end()); 1767 break; 1768 } 1769 AddRecOps[i] = getAddExpr(AddRecOps[i], 1770 OtherAddRec->getOperand(i)); 1771 } 1772 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1773 } 1774 // Step size has changed, so we cannot guarantee no self-wraparound. 1775 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1776 return getAddExpr(Ops); 1777 } 1778 1779 // Otherwise couldn't fold anything into this recurrence. Move onto the 1780 // next one. 1781 } 1782 1783 // Okay, it looks like we really DO need an add expr. Check to see if we 1784 // already have one, otherwise create a new one. 1785 FoldingSetNodeID ID; 1786 ID.AddInteger(scAddExpr); 1787 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1788 ID.AddPointer(Ops[i]); 1789 void *IP = 0; 1790 SCEVAddExpr *S = 1791 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1792 if (!S) { 1793 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1794 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1795 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1796 O, Ops.size()); 1797 UniqueSCEVs.InsertNode(S, IP); 1798 } 1799 S->setNoWrapFlags(Flags); 1800 return S; 1801} 1802 1803/// getMulExpr - Get a canonical multiply expression, or something simpler if 1804/// possible. 1805const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1806 SCEV::NoWrapFlags Flags) { 1807 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1808 "only nuw or nsw allowed"); 1809 assert(!Ops.empty() && "Cannot get empty mul!"); 1810 if (Ops.size() == 1) return Ops[0]; 1811#ifndef NDEBUG 1812 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1813 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1814 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1815 "SCEVMulExpr operand types don't match!"); 1816#endif 1817 1818 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1819 // And vice-versa. 1820 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1821 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1822 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1823 bool All = true; 1824 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1825 E = Ops.end(); I != E; ++I) 1826 if (!isKnownNonNegative(*I)) { 1827 All = false; 1828 break; 1829 } 1830 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1831 } 1832 1833 // Sort by complexity, this groups all similar expression types together. 1834 GroupByComplexity(Ops, LI); 1835 1836 // If there are any constants, fold them together. 1837 unsigned Idx = 0; 1838 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1839 1840 // C1*(C2+V) -> C1*C2 + C1*V 1841 if (Ops.size() == 2) 1842 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1843 if (Add->getNumOperands() == 2 && 1844 isa<SCEVConstant>(Add->getOperand(0))) 1845 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1846 getMulExpr(LHSC, Add->getOperand(1))); 1847 1848 ++Idx; 1849 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1850 // We found two constants, fold them together! 1851 ConstantInt *Fold = ConstantInt::get(getContext(), 1852 LHSC->getValue()->getValue() * 1853 RHSC->getValue()->getValue()); 1854 Ops[0] = getConstant(Fold); 1855 Ops.erase(Ops.begin()+1); // Erase the folded element 1856 if (Ops.size() == 1) return Ops[0]; 1857 LHSC = cast<SCEVConstant>(Ops[0]); 1858 } 1859 1860 // If we are left with a constant one being multiplied, strip it off. 1861 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1862 Ops.erase(Ops.begin()); 1863 --Idx; 1864 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1865 // If we have a multiply of zero, it will always be zero. 1866 return Ops[0]; 1867 } else if (Ops[0]->isAllOnesValue()) { 1868 // If we have a mul by -1 of an add, try distributing the -1 among the 1869 // add operands. 1870 if (Ops.size() == 2) { 1871 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1872 SmallVector<const SCEV *, 4> NewOps; 1873 bool AnyFolded = false; 1874 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1875 E = Add->op_end(); I != E; ++I) { 1876 const SCEV *Mul = getMulExpr(Ops[0], *I); 1877 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1878 NewOps.push_back(Mul); 1879 } 1880 if (AnyFolded) 1881 return getAddExpr(NewOps); 1882 } 1883 else if (const SCEVAddRecExpr * 1884 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1885 // Negation preserves a recurrence's no self-wrap property. 1886 SmallVector<const SCEV *, 4> Operands; 1887 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1888 E = AddRec->op_end(); I != E; ++I) { 1889 Operands.push_back(getMulExpr(Ops[0], *I)); 1890 } 1891 return getAddRecExpr(Operands, AddRec->getLoop(), 1892 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1893 } 1894 } 1895 } 1896 1897 if (Ops.size() == 1) 1898 return Ops[0]; 1899 } 1900 1901 // Skip over the add expression until we get to a multiply. 1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1903 ++Idx; 1904 1905 // If there are mul operands inline them all into this expression. 1906 if (Idx < Ops.size()) { 1907 bool DeletedMul = false; 1908 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1909 // If we have an mul, expand the mul operands onto the end of the operands 1910 // list. 1911 Ops.erase(Ops.begin()+Idx); 1912 Ops.append(Mul->op_begin(), Mul->op_end()); 1913 DeletedMul = true; 1914 } 1915 1916 // If we deleted at least one mul, we added operands to the end of the list, 1917 // and they are not necessarily sorted. Recurse to resort and resimplify 1918 // any operands we just acquired. 1919 if (DeletedMul) 1920 return getMulExpr(Ops); 1921 } 1922 1923 // If there are any add recurrences in the operands list, see if any other 1924 // added values are loop invariant. If so, we can fold them into the 1925 // recurrence. 1926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1927 ++Idx; 1928 1929 // Scan over all recurrences, trying to fold loop invariants into them. 1930 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1931 // Scan all of the other operands to this mul and add them to the vector if 1932 // they are loop invariant w.r.t. the recurrence. 1933 SmallVector<const SCEV *, 8> LIOps; 1934 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1935 const Loop *AddRecLoop = AddRec->getLoop(); 1936 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1937 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1938 LIOps.push_back(Ops[i]); 1939 Ops.erase(Ops.begin()+i); 1940 --i; --e; 1941 } 1942 1943 // If we found some loop invariants, fold them into the recurrence. 1944 if (!LIOps.empty()) { 1945 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1946 SmallVector<const SCEV *, 4> NewOps; 1947 NewOps.reserve(AddRec->getNumOperands()); 1948 const SCEV *Scale = getMulExpr(LIOps); 1949 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 1950 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 1951 1952 // Build the new addrec. Propagate the NUW and NSW flags if both the 1953 // outer mul and the inner addrec are guaranteed to have no overflow. 1954 // 1955 // No self-wrap cannot be guaranteed after changing the step size, but 1956 // will be inferred if either NUW or NSW is true. 1957 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 1958 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 1959 1960 // If all of the other operands were loop invariant, we are done. 1961 if (Ops.size() == 1) return NewRec; 1962 1963 // Otherwise, multiply the folded AddRec by the non-invariant parts. 1964 for (unsigned i = 0;; ++i) 1965 if (Ops[i] == AddRec) { 1966 Ops[i] = NewRec; 1967 break; 1968 } 1969 return getMulExpr(Ops); 1970 } 1971 1972 // Okay, if there weren't any loop invariants to be folded, check to see if 1973 // there are multiple AddRec's with the same loop induction variable being 1974 // multiplied together. If so, we can fold them. 1975 for (unsigned OtherIdx = Idx+1; 1976 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1977 ++OtherIdx) 1978 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1979 // {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L> 1980 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1981 ++OtherIdx) 1982 if (const SCEVAddRecExpr *OtherAddRec = 1983 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1984 if (OtherAddRec->getLoop() == AddRecLoop) { 1985 const SCEV *A = AddRec->getStart(); 1986 const SCEV *B = AddRec->getStepRecurrence(*this); 1987 const SCEV *C = OtherAddRec->getStart(); 1988 const SCEV *D = OtherAddRec->getStepRecurrence(*this); 1989 const SCEV *NewStart = getMulExpr(A, C); 1990 const SCEV *BD = getMulExpr(B, D); 1991 const SCEV *NewStep = getAddExpr(getMulExpr(A, D), 1992 getMulExpr(B, C), BD); 1993 const SCEV *NewSecondOrderStep = 1994 getMulExpr(BD, getConstant(BD->getType(), 2)); 1995 1996 SmallVector<const SCEV *, 3> AddRecOps; 1997 AddRecOps.push_back(NewStart); 1998 AddRecOps.push_back(NewStep); 1999 AddRecOps.push_back(NewSecondOrderStep); 2000 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, 2001 AddRec->getLoop(), 2002 SCEV::FlagAnyWrap); 2003 if (Ops.size() == 2) return NewAddRec; 2004 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 2005 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2006 } 2007 return getMulExpr(Ops); 2008 } 2009 2010 // Otherwise couldn't fold anything into this recurrence. Move onto the 2011 // next one. 2012 } 2013 2014 // Okay, it looks like we really DO need an mul expr. Check to see if we 2015 // already have one, otherwise create a new one. 2016 FoldingSetNodeID ID; 2017 ID.AddInteger(scMulExpr); 2018 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2019 ID.AddPointer(Ops[i]); 2020 void *IP = 0; 2021 SCEVMulExpr *S = 2022 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2023 if (!S) { 2024 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2025 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2026 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2027 O, Ops.size()); 2028 UniqueSCEVs.InsertNode(S, IP); 2029 } 2030 S->setNoWrapFlags(Flags); 2031 return S; 2032} 2033 2034/// getUDivExpr - Get a canonical unsigned division expression, or something 2035/// simpler if possible. 2036const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2037 const SCEV *RHS) { 2038 assert(getEffectiveSCEVType(LHS->getType()) == 2039 getEffectiveSCEVType(RHS->getType()) && 2040 "SCEVUDivExpr operand types don't match!"); 2041 2042 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2043 if (RHSC->getValue()->equalsInt(1)) 2044 return LHS; // X udiv 1 --> x 2045 // If the denominator is zero, the result of the udiv is undefined. Don't 2046 // try to analyze it, because the resolution chosen here may differ from 2047 // the resolution chosen in other parts of the compiler. 2048 if (!RHSC->getValue()->isZero()) { 2049 // Determine if the division can be folded into the operands of 2050 // its operands. 2051 // TODO: Generalize this to non-constants by using known-bits information. 2052 Type *Ty = LHS->getType(); 2053 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2054 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2055 // For non-power-of-two values, effectively round the value up to the 2056 // nearest power of two. 2057 if (!RHSC->getValue()->getValue().isPowerOf2()) 2058 ++MaxShiftAmt; 2059 IntegerType *ExtTy = 2060 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2061 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2062 if (const SCEVConstant *Step = 2063 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2064 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2065 const APInt &StepInt = Step->getValue()->getValue(); 2066 const APInt &DivInt = RHSC->getValue()->getValue(); 2067 if (!StepInt.urem(DivInt) && 2068 getZeroExtendExpr(AR, ExtTy) == 2069 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2070 getZeroExtendExpr(Step, ExtTy), 2071 AR->getLoop(), SCEV::FlagAnyWrap)) { 2072 SmallVector<const SCEV *, 4> Operands; 2073 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2074 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2075 return getAddRecExpr(Operands, AR->getLoop(), 2076 SCEV::FlagNW); 2077 } 2078 /// Get a canonical UDivExpr for a recurrence. 2079 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2080 // We can currently only fold X%N if X is constant. 2081 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2082 if (StartC && !DivInt.urem(StepInt) && 2083 getZeroExtendExpr(AR, ExtTy) == 2084 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2085 getZeroExtendExpr(Step, ExtTy), 2086 AR->getLoop(), SCEV::FlagAnyWrap)) { 2087 const APInt &StartInt = StartC->getValue()->getValue(); 2088 const APInt &StartRem = StartInt.urem(StepInt); 2089 if (StartRem != 0) 2090 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2091 AR->getLoop(), SCEV::FlagNW); 2092 } 2093 } 2094 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2095 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2096 SmallVector<const SCEV *, 4> Operands; 2097 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2098 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2099 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2100 // Find an operand that's safely divisible. 2101 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2102 const SCEV *Op = M->getOperand(i); 2103 const SCEV *Div = getUDivExpr(Op, RHSC); 2104 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2105 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2106 M->op_end()); 2107 Operands[i] = Div; 2108 return getMulExpr(Operands); 2109 } 2110 } 2111 } 2112 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2113 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2114 SmallVector<const SCEV *, 4> Operands; 2115 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2116 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2117 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2118 Operands.clear(); 2119 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2120 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2121 if (isa<SCEVUDivExpr>(Op) || 2122 getMulExpr(Op, RHS) != A->getOperand(i)) 2123 break; 2124 Operands.push_back(Op); 2125 } 2126 if (Operands.size() == A->getNumOperands()) 2127 return getAddExpr(Operands); 2128 } 2129 } 2130 2131 // Fold if both operands are constant. 2132 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2133 Constant *LHSCV = LHSC->getValue(); 2134 Constant *RHSCV = RHSC->getValue(); 2135 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2136 RHSCV))); 2137 } 2138 } 2139 } 2140 2141 FoldingSetNodeID ID; 2142 ID.AddInteger(scUDivExpr); 2143 ID.AddPointer(LHS); 2144 ID.AddPointer(RHS); 2145 void *IP = 0; 2146 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2147 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2148 LHS, RHS); 2149 UniqueSCEVs.InsertNode(S, IP); 2150 return S; 2151} 2152 2153 2154/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2155/// Simplify the expression as much as possible. 2156const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2157 const Loop *L, 2158 SCEV::NoWrapFlags Flags) { 2159 SmallVector<const SCEV *, 4> Operands; 2160 Operands.push_back(Start); 2161 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2162 if (StepChrec->getLoop() == L) { 2163 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2164 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2165 } 2166 2167 Operands.push_back(Step); 2168 return getAddRecExpr(Operands, L, Flags); 2169} 2170 2171/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2172/// Simplify the expression as much as possible. 2173const SCEV * 2174ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2175 const Loop *L, SCEV::NoWrapFlags Flags) { 2176 if (Operands.size() == 1) return Operands[0]; 2177#ifndef NDEBUG 2178 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2179 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2180 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2181 "SCEVAddRecExpr operand types don't match!"); 2182 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2183 assert(isLoopInvariant(Operands[i], L) && 2184 "SCEVAddRecExpr operand is not loop-invariant!"); 2185#endif 2186 2187 if (Operands.back()->isZero()) { 2188 Operands.pop_back(); 2189 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2190 } 2191 2192 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2193 // use that information to infer NUW and NSW flags. However, computing a 2194 // BE count requires calling getAddRecExpr, so we may not yet have a 2195 // meaningful BE count at this point (and if we don't, we'd be stuck 2196 // with a SCEVCouldNotCompute as the cached BE count). 2197 2198 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2199 // And vice-versa. 2200 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2201 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2202 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2203 bool All = true; 2204 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2205 E = Operands.end(); I != E; ++I) 2206 if (!isKnownNonNegative(*I)) { 2207 All = false; 2208 break; 2209 } 2210 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2211 } 2212 2213 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2214 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2215 const Loop *NestedLoop = NestedAR->getLoop(); 2216 if (L->contains(NestedLoop) ? 2217 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2218 (!NestedLoop->contains(L) && 2219 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2220 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2221 NestedAR->op_end()); 2222 Operands[0] = NestedAR->getStart(); 2223 // AddRecs require their operands be loop-invariant with respect to their 2224 // loops. Don't perform this transformation if it would break this 2225 // requirement. 2226 bool AllInvariant = true; 2227 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2228 if (!isLoopInvariant(Operands[i], L)) { 2229 AllInvariant = false; 2230 break; 2231 } 2232 if (AllInvariant) { 2233 // Create a recurrence for the outer loop with the same step size. 2234 // 2235 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2236 // inner recurrence has the same property. 2237 SCEV::NoWrapFlags OuterFlags = 2238 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2239 2240 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2241 AllInvariant = true; 2242 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2243 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2244 AllInvariant = false; 2245 break; 2246 } 2247 if (AllInvariant) { 2248 // Ok, both add recurrences are valid after the transformation. 2249 // 2250 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2251 // the outer recurrence has the same property. 2252 SCEV::NoWrapFlags InnerFlags = 2253 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2254 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2255 } 2256 } 2257 // Reset Operands to its original state. 2258 Operands[0] = NestedAR; 2259 } 2260 } 2261 2262 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2263 // already have one, otherwise create a new one. 2264 FoldingSetNodeID ID; 2265 ID.AddInteger(scAddRecExpr); 2266 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2267 ID.AddPointer(Operands[i]); 2268 ID.AddPointer(L); 2269 void *IP = 0; 2270 SCEVAddRecExpr *S = 2271 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2272 if (!S) { 2273 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2274 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2275 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2276 O, Operands.size(), L); 2277 UniqueSCEVs.InsertNode(S, IP); 2278 } 2279 S->setNoWrapFlags(Flags); 2280 return S; 2281} 2282 2283const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2284 const SCEV *RHS) { 2285 SmallVector<const SCEV *, 2> Ops; 2286 Ops.push_back(LHS); 2287 Ops.push_back(RHS); 2288 return getSMaxExpr(Ops); 2289} 2290 2291const SCEV * 2292ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2293 assert(!Ops.empty() && "Cannot get empty smax!"); 2294 if (Ops.size() == 1) return Ops[0]; 2295#ifndef NDEBUG 2296 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2297 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2298 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2299 "SCEVSMaxExpr operand types don't match!"); 2300#endif 2301 2302 // Sort by complexity, this groups all similar expression types together. 2303 GroupByComplexity(Ops, LI); 2304 2305 // If there are any constants, fold them together. 2306 unsigned Idx = 0; 2307 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2308 ++Idx; 2309 assert(Idx < Ops.size()); 2310 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2311 // We found two constants, fold them together! 2312 ConstantInt *Fold = ConstantInt::get(getContext(), 2313 APIntOps::smax(LHSC->getValue()->getValue(), 2314 RHSC->getValue()->getValue())); 2315 Ops[0] = getConstant(Fold); 2316 Ops.erase(Ops.begin()+1); // Erase the folded element 2317 if (Ops.size() == 1) return Ops[0]; 2318 LHSC = cast<SCEVConstant>(Ops[0]); 2319 } 2320 2321 // If we are left with a constant minimum-int, strip it off. 2322 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2323 Ops.erase(Ops.begin()); 2324 --Idx; 2325 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2326 // If we have an smax with a constant maximum-int, it will always be 2327 // maximum-int. 2328 return Ops[0]; 2329 } 2330 2331 if (Ops.size() == 1) return Ops[0]; 2332 } 2333 2334 // Find the first SMax 2335 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2336 ++Idx; 2337 2338 // Check to see if one of the operands is an SMax. If so, expand its operands 2339 // onto our operand list, and recurse to simplify. 2340 if (Idx < Ops.size()) { 2341 bool DeletedSMax = false; 2342 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2343 Ops.erase(Ops.begin()+Idx); 2344 Ops.append(SMax->op_begin(), SMax->op_end()); 2345 DeletedSMax = true; 2346 } 2347 2348 if (DeletedSMax) 2349 return getSMaxExpr(Ops); 2350 } 2351 2352 // Okay, check to see if the same value occurs in the operand list twice. If 2353 // so, delete one. Since we sorted the list, these values are required to 2354 // be adjacent. 2355 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2356 // X smax Y smax Y --> X smax Y 2357 // X smax Y --> X, if X is always greater than Y 2358 if (Ops[i] == Ops[i+1] || 2359 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2360 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2361 --i; --e; 2362 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2363 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2364 --i; --e; 2365 } 2366 2367 if (Ops.size() == 1) return Ops[0]; 2368 2369 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2370 2371 // Okay, it looks like we really DO need an smax expr. Check to see if we 2372 // already have one, otherwise create a new one. 2373 FoldingSetNodeID ID; 2374 ID.AddInteger(scSMaxExpr); 2375 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2376 ID.AddPointer(Ops[i]); 2377 void *IP = 0; 2378 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2379 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2380 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2381 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2382 O, Ops.size()); 2383 UniqueSCEVs.InsertNode(S, IP); 2384 return S; 2385} 2386 2387const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2388 const SCEV *RHS) { 2389 SmallVector<const SCEV *, 2> Ops; 2390 Ops.push_back(LHS); 2391 Ops.push_back(RHS); 2392 return getUMaxExpr(Ops); 2393} 2394 2395const SCEV * 2396ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2397 assert(!Ops.empty() && "Cannot get empty umax!"); 2398 if (Ops.size() == 1) return Ops[0]; 2399#ifndef NDEBUG 2400 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2401 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2402 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2403 "SCEVUMaxExpr operand types don't match!"); 2404#endif 2405 2406 // Sort by complexity, this groups all similar expression types together. 2407 GroupByComplexity(Ops, LI); 2408 2409 // If there are any constants, fold them together. 2410 unsigned Idx = 0; 2411 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2412 ++Idx; 2413 assert(Idx < Ops.size()); 2414 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2415 // We found two constants, fold them together! 2416 ConstantInt *Fold = ConstantInt::get(getContext(), 2417 APIntOps::umax(LHSC->getValue()->getValue(), 2418 RHSC->getValue()->getValue())); 2419 Ops[0] = getConstant(Fold); 2420 Ops.erase(Ops.begin()+1); // Erase the folded element 2421 if (Ops.size() == 1) return Ops[0]; 2422 LHSC = cast<SCEVConstant>(Ops[0]); 2423 } 2424 2425 // If we are left with a constant minimum-int, strip it off. 2426 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2427 Ops.erase(Ops.begin()); 2428 --Idx; 2429 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2430 // If we have an umax with a constant maximum-int, it will always be 2431 // maximum-int. 2432 return Ops[0]; 2433 } 2434 2435 if (Ops.size() == 1) return Ops[0]; 2436 } 2437 2438 // Find the first UMax 2439 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2440 ++Idx; 2441 2442 // Check to see if one of the operands is a UMax. If so, expand its operands 2443 // onto our operand list, and recurse to simplify. 2444 if (Idx < Ops.size()) { 2445 bool DeletedUMax = false; 2446 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2447 Ops.erase(Ops.begin()+Idx); 2448 Ops.append(UMax->op_begin(), UMax->op_end()); 2449 DeletedUMax = true; 2450 } 2451 2452 if (DeletedUMax) 2453 return getUMaxExpr(Ops); 2454 } 2455 2456 // Okay, check to see if the same value occurs in the operand list twice. If 2457 // so, delete one. Since we sorted the list, these values are required to 2458 // be adjacent. 2459 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2460 // X umax Y umax Y --> X umax Y 2461 // X umax Y --> X, if X is always greater than Y 2462 if (Ops[i] == Ops[i+1] || 2463 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2464 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2465 --i; --e; 2466 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2467 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2468 --i; --e; 2469 } 2470 2471 if (Ops.size() == 1) return Ops[0]; 2472 2473 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2474 2475 // Okay, it looks like we really DO need a umax expr. Check to see if we 2476 // already have one, otherwise create a new one. 2477 FoldingSetNodeID ID; 2478 ID.AddInteger(scUMaxExpr); 2479 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2480 ID.AddPointer(Ops[i]); 2481 void *IP = 0; 2482 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2483 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2484 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2485 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2486 O, Ops.size()); 2487 UniqueSCEVs.InsertNode(S, IP); 2488 return S; 2489} 2490 2491const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2492 const SCEV *RHS) { 2493 // ~smax(~x, ~y) == smin(x, y). 2494 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2495} 2496 2497const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2498 const SCEV *RHS) { 2499 // ~umax(~x, ~y) == umin(x, y) 2500 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2501} 2502 2503const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2504 // If we have TargetData, we can bypass creating a target-independent 2505 // constant expression and then folding it back into a ConstantInt. 2506 // This is just a compile-time optimization. 2507 if (TD) 2508 return getConstant(TD->getIntPtrType(getContext()), 2509 TD->getTypeAllocSize(AllocTy)); 2510 2511 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2512 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2513 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2514 C = Folded; 2515 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2516 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2517} 2518 2519const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2520 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2521 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2522 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2523 C = Folded; 2524 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2525 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2526} 2527 2528const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2529 unsigned FieldNo) { 2530 // If we have TargetData, we can bypass creating a target-independent 2531 // constant expression and then folding it back into a ConstantInt. 2532 // This is just a compile-time optimization. 2533 if (TD) 2534 return getConstant(TD->getIntPtrType(getContext()), 2535 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2536 2537 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2538 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2539 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2540 C = Folded; 2541 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2542 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2543} 2544 2545const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2546 Constant *FieldNo) { 2547 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2548 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2549 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2550 C = Folded; 2551 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2552 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2553} 2554 2555const SCEV *ScalarEvolution::getUnknown(Value *V) { 2556 // Don't attempt to do anything other than create a SCEVUnknown object 2557 // here. createSCEV only calls getUnknown after checking for all other 2558 // interesting possibilities, and any other code that calls getUnknown 2559 // is doing so in order to hide a value from SCEV canonicalization. 2560 2561 FoldingSetNodeID ID; 2562 ID.AddInteger(scUnknown); 2563 ID.AddPointer(V); 2564 void *IP = 0; 2565 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2566 assert(cast<SCEVUnknown>(S)->getValue() == V && 2567 "Stale SCEVUnknown in uniquing map!"); 2568 return S; 2569 } 2570 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2571 FirstUnknown); 2572 FirstUnknown = cast<SCEVUnknown>(S); 2573 UniqueSCEVs.InsertNode(S, IP); 2574 return S; 2575} 2576 2577//===----------------------------------------------------------------------===// 2578// Basic SCEV Analysis and PHI Idiom Recognition Code 2579// 2580 2581/// isSCEVable - Test if values of the given type are analyzable within 2582/// the SCEV framework. This primarily includes integer types, and it 2583/// can optionally include pointer types if the ScalarEvolution class 2584/// has access to target-specific information. 2585bool ScalarEvolution::isSCEVable(Type *Ty) const { 2586 // Integers and pointers are always SCEVable. 2587 return Ty->isIntegerTy() || Ty->isPointerTy(); 2588} 2589 2590/// getTypeSizeInBits - Return the size in bits of the specified type, 2591/// for which isSCEVable must return true. 2592uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2593 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2594 2595 // If we have a TargetData, use it! 2596 if (TD) 2597 return TD->getTypeSizeInBits(Ty); 2598 2599 // Integer types have fixed sizes. 2600 if (Ty->isIntegerTy()) 2601 return Ty->getPrimitiveSizeInBits(); 2602 2603 // The only other support type is pointer. Without TargetData, conservatively 2604 // assume pointers are 64-bit. 2605 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2606 return 64; 2607} 2608 2609/// getEffectiveSCEVType - Return a type with the same bitwidth as 2610/// the given type and which represents how SCEV will treat the given 2611/// type, for which isSCEVable must return true. For pointer types, 2612/// this is the pointer-sized integer type. 2613Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2614 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2615 2616 if (Ty->isIntegerTy()) 2617 return Ty; 2618 2619 // The only other support type is pointer. 2620 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2621 if (TD) return TD->getIntPtrType(getContext()); 2622 2623 // Without TargetData, conservatively assume pointers are 64-bit. 2624 return Type::getInt64Ty(getContext()); 2625} 2626 2627const SCEV *ScalarEvolution::getCouldNotCompute() { 2628 return &CouldNotCompute; 2629} 2630 2631/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2632/// expression and create a new one. 2633const SCEV *ScalarEvolution::getSCEV(Value *V) { 2634 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2635 2636 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2637 if (I != ValueExprMap.end()) return I->second; 2638 const SCEV *S = createSCEV(V); 2639 2640 // The process of creating a SCEV for V may have caused other SCEVs 2641 // to have been created, so it's necessary to insert the new entry 2642 // from scratch, rather than trying to remember the insert position 2643 // above. 2644 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2645 return S; 2646} 2647 2648/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2649/// 2650const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2651 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2652 return getConstant( 2653 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2654 2655 Type *Ty = V->getType(); 2656 Ty = getEffectiveSCEVType(Ty); 2657 return getMulExpr(V, 2658 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2659} 2660 2661/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2662const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2663 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2664 return getConstant( 2665 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2666 2667 Type *Ty = V->getType(); 2668 Ty = getEffectiveSCEVType(Ty); 2669 const SCEV *AllOnes = 2670 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2671 return getMinusSCEV(AllOnes, V); 2672} 2673 2674/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2675const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2676 SCEV::NoWrapFlags Flags) { 2677 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2678 2679 // Fast path: X - X --> 0. 2680 if (LHS == RHS) 2681 return getConstant(LHS->getType(), 0); 2682 2683 // X - Y --> X + -Y 2684 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2685} 2686 2687/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2688/// input value to the specified type. If the type must be extended, it is zero 2689/// extended. 2690const SCEV * 2691ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2692 Type *SrcTy = V->getType(); 2693 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2694 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2695 "Cannot truncate or zero extend with non-integer arguments!"); 2696 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2697 return V; // No conversion 2698 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2699 return getTruncateExpr(V, Ty); 2700 return getZeroExtendExpr(V, Ty); 2701} 2702 2703/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2704/// input value to the specified type. If the type must be extended, it is sign 2705/// extended. 2706const SCEV * 2707ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2708 Type *Ty) { 2709 Type *SrcTy = V->getType(); 2710 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2711 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2712 "Cannot truncate or zero extend with non-integer arguments!"); 2713 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2714 return V; // No conversion 2715 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2716 return getTruncateExpr(V, Ty); 2717 return getSignExtendExpr(V, Ty); 2718} 2719 2720/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2721/// input value to the specified type. If the type must be extended, it is zero 2722/// extended. The conversion must not be narrowing. 2723const SCEV * 2724ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2725 Type *SrcTy = V->getType(); 2726 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2727 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2728 "Cannot noop or zero extend with non-integer arguments!"); 2729 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2730 "getNoopOrZeroExtend cannot truncate!"); 2731 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2732 return V; // No conversion 2733 return getZeroExtendExpr(V, Ty); 2734} 2735 2736/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2737/// input value to the specified type. If the type must be extended, it is sign 2738/// extended. The conversion must not be narrowing. 2739const SCEV * 2740ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2741 Type *SrcTy = V->getType(); 2742 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2743 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2744 "Cannot noop or sign extend with non-integer arguments!"); 2745 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2746 "getNoopOrSignExtend cannot truncate!"); 2747 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2748 return V; // No conversion 2749 return getSignExtendExpr(V, Ty); 2750} 2751 2752/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2753/// the input value to the specified type. If the type must be extended, 2754/// it is extended with unspecified bits. The conversion must not be 2755/// narrowing. 2756const SCEV * 2757ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2758 Type *SrcTy = V->getType(); 2759 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2760 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2761 "Cannot noop or any extend with non-integer arguments!"); 2762 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2763 "getNoopOrAnyExtend cannot truncate!"); 2764 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2765 return V; // No conversion 2766 return getAnyExtendExpr(V, Ty); 2767} 2768 2769/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2770/// input value to the specified type. The conversion must not be widening. 2771const SCEV * 2772ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2773 Type *SrcTy = V->getType(); 2774 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2775 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2776 "Cannot truncate or noop with non-integer arguments!"); 2777 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2778 "getTruncateOrNoop cannot extend!"); 2779 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2780 return V; // No conversion 2781 return getTruncateExpr(V, Ty); 2782} 2783 2784/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2785/// the types using zero-extension, and then perform a umax operation 2786/// with them. 2787const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2788 const SCEV *RHS) { 2789 const SCEV *PromotedLHS = LHS; 2790 const SCEV *PromotedRHS = RHS; 2791 2792 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2793 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2794 else 2795 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2796 2797 return getUMaxExpr(PromotedLHS, PromotedRHS); 2798} 2799 2800/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2801/// the types using zero-extension, and then perform a umin operation 2802/// with them. 2803const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2804 const SCEV *RHS) { 2805 const SCEV *PromotedLHS = LHS; 2806 const SCEV *PromotedRHS = RHS; 2807 2808 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2809 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2810 else 2811 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2812 2813 return getUMinExpr(PromotedLHS, PromotedRHS); 2814} 2815 2816/// getPointerBase - Transitively follow the chain of pointer-type operands 2817/// until reaching a SCEV that does not have a single pointer operand. This 2818/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2819/// but corner cases do exist. 2820const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2821 // A pointer operand may evaluate to a nonpointer expression, such as null. 2822 if (!V->getType()->isPointerTy()) 2823 return V; 2824 2825 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2826 return getPointerBase(Cast->getOperand()); 2827 } 2828 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2829 const SCEV *PtrOp = 0; 2830 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2831 I != E; ++I) { 2832 if ((*I)->getType()->isPointerTy()) { 2833 // Cannot find the base of an expression with multiple pointer operands. 2834 if (PtrOp) 2835 return V; 2836 PtrOp = *I; 2837 } 2838 } 2839 if (!PtrOp) 2840 return V; 2841 return getPointerBase(PtrOp); 2842 } 2843 return V; 2844} 2845 2846/// PushDefUseChildren - Push users of the given Instruction 2847/// onto the given Worklist. 2848static void 2849PushDefUseChildren(Instruction *I, 2850 SmallVectorImpl<Instruction *> &Worklist) { 2851 // Push the def-use children onto the Worklist stack. 2852 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2853 UI != UE; ++UI) 2854 Worklist.push_back(cast<Instruction>(*UI)); 2855} 2856 2857/// ForgetSymbolicValue - This looks up computed SCEV values for all 2858/// instructions that depend on the given instruction and removes them from 2859/// the ValueExprMapType map if they reference SymName. This is used during PHI 2860/// resolution. 2861void 2862ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2863 SmallVector<Instruction *, 16> Worklist; 2864 PushDefUseChildren(PN, Worklist); 2865 2866 SmallPtrSet<Instruction *, 8> Visited; 2867 Visited.insert(PN); 2868 while (!Worklist.empty()) { 2869 Instruction *I = Worklist.pop_back_val(); 2870 if (!Visited.insert(I)) continue; 2871 2872 ValueExprMapType::iterator It = 2873 ValueExprMap.find(static_cast<Value *>(I)); 2874 if (It != ValueExprMap.end()) { 2875 const SCEV *Old = It->second; 2876 2877 // Short-circuit the def-use traversal if the symbolic name 2878 // ceases to appear in expressions. 2879 if (Old != SymName && !hasOperand(Old, SymName)) 2880 continue; 2881 2882 // SCEVUnknown for a PHI either means that it has an unrecognized 2883 // structure, it's a PHI that's in the progress of being computed 2884 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2885 // additional loop trip count information isn't going to change anything. 2886 // In the second case, createNodeForPHI will perform the necessary 2887 // updates on its own when it gets to that point. In the third, we do 2888 // want to forget the SCEVUnknown. 2889 if (!isa<PHINode>(I) || 2890 !isa<SCEVUnknown>(Old) || 2891 (I != PN && Old == SymName)) { 2892 forgetMemoizedResults(Old); 2893 ValueExprMap.erase(It); 2894 } 2895 } 2896 2897 PushDefUseChildren(I, Worklist); 2898 } 2899} 2900 2901/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2902/// a loop header, making it a potential recurrence, or it doesn't. 2903/// 2904const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2905 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2906 if (L->getHeader() == PN->getParent()) { 2907 // The loop may have multiple entrances or multiple exits; we can analyze 2908 // this phi as an addrec if it has a unique entry value and a unique 2909 // backedge value. 2910 Value *BEValueV = 0, *StartValueV = 0; 2911 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2912 Value *V = PN->getIncomingValue(i); 2913 if (L->contains(PN->getIncomingBlock(i))) { 2914 if (!BEValueV) { 2915 BEValueV = V; 2916 } else if (BEValueV != V) { 2917 BEValueV = 0; 2918 break; 2919 } 2920 } else if (!StartValueV) { 2921 StartValueV = V; 2922 } else if (StartValueV != V) { 2923 StartValueV = 0; 2924 break; 2925 } 2926 } 2927 if (BEValueV && StartValueV) { 2928 // While we are analyzing this PHI node, handle its value symbolically. 2929 const SCEV *SymbolicName = getUnknown(PN); 2930 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 2931 "PHI node already processed?"); 2932 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 2933 2934 // Using this symbolic name for the PHI, analyze the value coming around 2935 // the back-edge. 2936 const SCEV *BEValue = getSCEV(BEValueV); 2937 2938 // NOTE: If BEValue is loop invariant, we know that the PHI node just 2939 // has a special value for the first iteration of the loop. 2940 2941 // If the value coming around the backedge is an add with the symbolic 2942 // value we just inserted, then we found a simple induction variable! 2943 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 2944 // If there is a single occurrence of the symbolic value, replace it 2945 // with a recurrence. 2946 unsigned FoundIndex = Add->getNumOperands(); 2947 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2948 if (Add->getOperand(i) == SymbolicName) 2949 if (FoundIndex == e) { 2950 FoundIndex = i; 2951 break; 2952 } 2953 2954 if (FoundIndex != Add->getNumOperands()) { 2955 // Create an add with everything but the specified operand. 2956 SmallVector<const SCEV *, 8> Ops; 2957 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 2958 if (i != FoundIndex) 2959 Ops.push_back(Add->getOperand(i)); 2960 const SCEV *Accum = getAddExpr(Ops); 2961 2962 // This is not a valid addrec if the step amount is varying each 2963 // loop iteration, but is not itself an addrec in this loop. 2964 if (isLoopInvariant(Accum, L) || 2965 (isa<SCEVAddRecExpr>(Accum) && 2966 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 2967 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 2968 2969 // If the increment doesn't overflow, then neither the addrec nor 2970 // the post-increment will overflow. 2971 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 2972 if (OBO->hasNoUnsignedWrap()) 2973 Flags = setFlags(Flags, SCEV::FlagNUW); 2974 if (OBO->hasNoSignedWrap()) 2975 Flags = setFlags(Flags, SCEV::FlagNSW); 2976 } else if (const GEPOperator *GEP = 2977 dyn_cast<GEPOperator>(BEValueV)) { 2978 // If the increment is an inbounds GEP, then we know the address 2979 // space cannot be wrapped around. We cannot make any guarantee 2980 // about signed or unsigned overflow because pointers are 2981 // unsigned but we may have a negative index from the base 2982 // pointer. 2983 if (GEP->isInBounds()) 2984 Flags = setFlags(Flags, SCEV::FlagNW); 2985 } 2986 2987 const SCEV *StartVal = getSCEV(StartValueV); 2988 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 2989 2990 // Since the no-wrap flags are on the increment, they apply to the 2991 // post-incremented value as well. 2992 if (isLoopInvariant(Accum, L)) 2993 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 2994 Accum, L, Flags); 2995 2996 // Okay, for the entire analysis of this edge we assumed the PHI 2997 // to be symbolic. We now need to go back and purge all of the 2998 // entries for the scalars that use the symbolic expression. 2999 ForgetSymbolicName(PN, SymbolicName); 3000 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3001 return PHISCEV; 3002 } 3003 } 3004 } else if (const SCEVAddRecExpr *AddRec = 3005 dyn_cast<SCEVAddRecExpr>(BEValue)) { 3006 // Otherwise, this could be a loop like this: 3007 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3008 // In this case, j = {1,+,1} and BEValue is j. 3009 // Because the other in-value of i (0) fits the evolution of BEValue 3010 // i really is an addrec evolution. 3011 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3012 const SCEV *StartVal = getSCEV(StartValueV); 3013 3014 // If StartVal = j.start - j.stride, we can use StartVal as the 3015 // initial step of the addrec evolution. 3016 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3017 AddRec->getOperand(1))) { 3018 // FIXME: For constant StartVal, we should be able to infer 3019 // no-wrap flags. 3020 const SCEV *PHISCEV = 3021 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3022 SCEV::FlagAnyWrap); 3023 3024 // Okay, for the entire analysis of this edge we assumed the PHI 3025 // to be symbolic. We now need to go back and purge all of the 3026 // entries for the scalars that use the symbolic expression. 3027 ForgetSymbolicName(PN, SymbolicName); 3028 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3029 return PHISCEV; 3030 } 3031 } 3032 } 3033 } 3034 } 3035 3036 // If the PHI has a single incoming value, follow that value, unless the 3037 // PHI's incoming blocks are in a different loop, in which case doing so 3038 // risks breaking LCSSA form. Instcombine would normally zap these, but 3039 // it doesn't have DominatorTree information, so it may miss cases. 3040 if (Value *V = SimplifyInstruction(PN, TD, DT)) 3041 if (LI->replacementPreservesLCSSAForm(PN, V)) 3042 return getSCEV(V); 3043 3044 // If it's not a loop phi, we can't handle it yet. 3045 return getUnknown(PN); 3046} 3047 3048/// createNodeForGEP - Expand GEP instructions into add and multiply 3049/// operations. This allows them to be analyzed by regular SCEV code. 3050/// 3051const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3052 3053 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3054 // Add expression, because the Instruction may be guarded by control flow 3055 // and the no-overflow bits may not be valid for the expression in any 3056 // context. 3057 bool isInBounds = GEP->isInBounds(); 3058 3059 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3060 Value *Base = GEP->getOperand(0); 3061 // Don't attempt to analyze GEPs over unsized objects. 3062 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3063 return getUnknown(GEP); 3064 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3065 gep_type_iterator GTI = gep_type_begin(GEP); 3066 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3067 E = GEP->op_end(); 3068 I != E; ++I) { 3069 Value *Index = *I; 3070 // Compute the (potentially symbolic) offset in bytes for this index. 3071 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3072 // For a struct, add the member offset. 3073 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3074 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3075 3076 // Add the field offset to the running total offset. 3077 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3078 } else { 3079 // For an array, add the element offset, explicitly scaled. 3080 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3081 const SCEV *IndexS = getSCEV(Index); 3082 // Getelementptr indices are signed. 3083 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3084 3085 // Multiply the index by the element size to compute the element offset. 3086 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3087 isInBounds ? SCEV::FlagNSW : 3088 SCEV::FlagAnyWrap); 3089 3090 // Add the element offset to the running total offset. 3091 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3092 } 3093 } 3094 3095 // Get the SCEV for the GEP base. 3096 const SCEV *BaseS = getSCEV(Base); 3097 3098 // Add the total offset from all the GEP indices to the base. 3099 return getAddExpr(BaseS, TotalOffset, 3100 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3101} 3102 3103/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3104/// guaranteed to end in (at every loop iteration). It is, at the same time, 3105/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3106/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3107uint32_t 3108ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3109 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3110 return C->getValue()->getValue().countTrailingZeros(); 3111 3112 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3113 return std::min(GetMinTrailingZeros(T->getOperand()), 3114 (uint32_t)getTypeSizeInBits(T->getType())); 3115 3116 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3117 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3118 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3119 getTypeSizeInBits(E->getType()) : OpRes; 3120 } 3121 3122 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3123 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3124 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3125 getTypeSizeInBits(E->getType()) : OpRes; 3126 } 3127 3128 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3129 // The result is the min of all operands results. 3130 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3131 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3132 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3133 return MinOpRes; 3134 } 3135 3136 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3137 // The result is the sum of all operands results. 3138 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3139 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3140 for (unsigned i = 1, e = M->getNumOperands(); 3141 SumOpRes != BitWidth && i != e; ++i) 3142 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3143 BitWidth); 3144 return SumOpRes; 3145 } 3146 3147 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3148 // The result is the min of all operands results. 3149 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3150 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3151 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3152 return MinOpRes; 3153 } 3154 3155 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3156 // The result is the min of all operands results. 3157 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3158 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3159 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3160 return MinOpRes; 3161 } 3162 3163 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3164 // The result is the min of all operands results. 3165 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3166 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3167 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3168 return MinOpRes; 3169 } 3170 3171 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3172 // For a SCEVUnknown, ask ValueTracking. 3173 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3174 APInt Mask = APInt::getAllOnesValue(BitWidth); 3175 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3176 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3177 return Zeros.countTrailingOnes(); 3178 } 3179 3180 // SCEVUDivExpr 3181 return 0; 3182} 3183 3184/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3185/// 3186ConstantRange 3187ScalarEvolution::getUnsignedRange(const SCEV *S) { 3188 // See if we've computed this range already. 3189 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3190 if (I != UnsignedRanges.end()) 3191 return I->second; 3192 3193 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3194 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3195 3196 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3197 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3198 3199 // If the value has known zeros, the maximum unsigned value will have those 3200 // known zeros as well. 3201 uint32_t TZ = GetMinTrailingZeros(S); 3202 if (TZ != 0) 3203 ConservativeResult = 3204 ConstantRange(APInt::getMinValue(BitWidth), 3205 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3206 3207 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3208 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3209 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3210 X = X.add(getUnsignedRange(Add->getOperand(i))); 3211 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3212 } 3213 3214 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3215 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3216 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3217 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3218 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3219 } 3220 3221 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3222 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3223 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3224 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3225 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3226 } 3227 3228 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3229 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3230 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3231 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3232 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3233 } 3234 3235 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3236 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3237 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3238 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3239 } 3240 3241 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3242 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3243 return setUnsignedRange(ZExt, 3244 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3245 } 3246 3247 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3248 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3249 return setUnsignedRange(SExt, 3250 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3251 } 3252 3253 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3254 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3255 return setUnsignedRange(Trunc, 3256 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3257 } 3258 3259 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3260 // If there's no unsigned wrap, the value will never be less than its 3261 // initial value. 3262 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3263 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3264 if (!C->getValue()->isZero()) 3265 ConservativeResult = 3266 ConservativeResult.intersectWith( 3267 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3268 3269 // TODO: non-affine addrec 3270 if (AddRec->isAffine()) { 3271 Type *Ty = AddRec->getType(); 3272 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3273 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3274 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3275 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3276 3277 const SCEV *Start = AddRec->getStart(); 3278 const SCEV *Step = AddRec->getStepRecurrence(*this); 3279 3280 ConstantRange StartRange = getUnsignedRange(Start); 3281 ConstantRange StepRange = getSignedRange(Step); 3282 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3283 ConstantRange EndRange = 3284 StartRange.add(MaxBECountRange.multiply(StepRange)); 3285 3286 // Check for overflow. This must be done with ConstantRange arithmetic 3287 // because we could be called from within the ScalarEvolution overflow 3288 // checking code. 3289 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3290 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3291 ConstantRange ExtMaxBECountRange = 3292 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3293 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3294 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3295 ExtEndRange) 3296 return setUnsignedRange(AddRec, ConservativeResult); 3297 3298 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3299 EndRange.getUnsignedMin()); 3300 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3301 EndRange.getUnsignedMax()); 3302 if (Min.isMinValue() && Max.isMaxValue()) 3303 return setUnsignedRange(AddRec, ConservativeResult); 3304 return setUnsignedRange(AddRec, 3305 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3306 } 3307 } 3308 3309 return setUnsignedRange(AddRec, ConservativeResult); 3310 } 3311 3312 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3313 // For a SCEVUnknown, ask ValueTracking. 3314 APInt Mask = APInt::getAllOnesValue(BitWidth); 3315 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3316 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3317 if (Ones == ~Zeros + 1) 3318 return setUnsignedRange(U, ConservativeResult); 3319 return setUnsignedRange(U, 3320 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3321 } 3322 3323 return setUnsignedRange(S, ConservativeResult); 3324} 3325 3326/// getSignedRange - Determine the signed range for a particular SCEV. 3327/// 3328ConstantRange 3329ScalarEvolution::getSignedRange(const SCEV *S) { 3330 // See if we've computed this range already. 3331 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3332 if (I != SignedRanges.end()) 3333 return I->second; 3334 3335 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3336 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3337 3338 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3339 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3340 3341 // If the value has known zeros, the maximum signed value will have those 3342 // known zeros as well. 3343 uint32_t TZ = GetMinTrailingZeros(S); 3344 if (TZ != 0) 3345 ConservativeResult = 3346 ConstantRange(APInt::getSignedMinValue(BitWidth), 3347 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3348 3349 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3350 ConstantRange X = getSignedRange(Add->getOperand(0)); 3351 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3352 X = X.add(getSignedRange(Add->getOperand(i))); 3353 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3354 } 3355 3356 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3357 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3358 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3359 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3360 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3361 } 3362 3363 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3364 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3365 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3366 X = X.smax(getSignedRange(SMax->getOperand(i))); 3367 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3368 } 3369 3370 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3371 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3372 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3373 X = X.umax(getSignedRange(UMax->getOperand(i))); 3374 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3375 } 3376 3377 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3378 ConstantRange X = getSignedRange(UDiv->getLHS()); 3379 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3380 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3381 } 3382 3383 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3384 ConstantRange X = getSignedRange(ZExt->getOperand()); 3385 return setSignedRange(ZExt, 3386 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3387 } 3388 3389 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3390 ConstantRange X = getSignedRange(SExt->getOperand()); 3391 return setSignedRange(SExt, 3392 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3393 } 3394 3395 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3396 ConstantRange X = getSignedRange(Trunc->getOperand()); 3397 return setSignedRange(Trunc, 3398 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3399 } 3400 3401 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3402 // If there's no signed wrap, and all the operands have the same sign or 3403 // zero, the value won't ever change sign. 3404 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3405 bool AllNonNeg = true; 3406 bool AllNonPos = true; 3407 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3408 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3409 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3410 } 3411 if (AllNonNeg) 3412 ConservativeResult = ConservativeResult.intersectWith( 3413 ConstantRange(APInt(BitWidth, 0), 3414 APInt::getSignedMinValue(BitWidth))); 3415 else if (AllNonPos) 3416 ConservativeResult = ConservativeResult.intersectWith( 3417 ConstantRange(APInt::getSignedMinValue(BitWidth), 3418 APInt(BitWidth, 1))); 3419 } 3420 3421 // TODO: non-affine addrec 3422 if (AddRec->isAffine()) { 3423 Type *Ty = AddRec->getType(); 3424 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3425 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3426 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3427 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3428 3429 const SCEV *Start = AddRec->getStart(); 3430 const SCEV *Step = AddRec->getStepRecurrence(*this); 3431 3432 ConstantRange StartRange = getSignedRange(Start); 3433 ConstantRange StepRange = getSignedRange(Step); 3434 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3435 ConstantRange EndRange = 3436 StartRange.add(MaxBECountRange.multiply(StepRange)); 3437 3438 // Check for overflow. This must be done with ConstantRange arithmetic 3439 // because we could be called from within the ScalarEvolution overflow 3440 // checking code. 3441 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3442 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3443 ConstantRange ExtMaxBECountRange = 3444 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3445 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3446 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3447 ExtEndRange) 3448 return setSignedRange(AddRec, ConservativeResult); 3449 3450 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3451 EndRange.getSignedMin()); 3452 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3453 EndRange.getSignedMax()); 3454 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3455 return setSignedRange(AddRec, ConservativeResult); 3456 return setSignedRange(AddRec, 3457 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3458 } 3459 } 3460 3461 return setSignedRange(AddRec, ConservativeResult); 3462 } 3463 3464 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3465 // For a SCEVUnknown, ask ValueTracking. 3466 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3467 return setSignedRange(U, ConservativeResult); 3468 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3469 if (NS == 1) 3470 return setSignedRange(U, ConservativeResult); 3471 return setSignedRange(U, ConservativeResult.intersectWith( 3472 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3473 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3474 } 3475 3476 return setSignedRange(S, ConservativeResult); 3477} 3478 3479/// createSCEV - We know that there is no SCEV for the specified value. 3480/// Analyze the expression. 3481/// 3482const SCEV *ScalarEvolution::createSCEV(Value *V) { 3483 if (!isSCEVable(V->getType())) 3484 return getUnknown(V); 3485 3486 unsigned Opcode = Instruction::UserOp1; 3487 if (Instruction *I = dyn_cast<Instruction>(V)) { 3488 Opcode = I->getOpcode(); 3489 3490 // Don't attempt to analyze instructions in blocks that aren't 3491 // reachable. Such instructions don't matter, and they aren't required 3492 // to obey basic rules for definitions dominating uses which this 3493 // analysis depends on. 3494 if (!DT->isReachableFromEntry(I->getParent())) 3495 return getUnknown(V); 3496 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3497 Opcode = CE->getOpcode(); 3498 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3499 return getConstant(CI); 3500 else if (isa<ConstantPointerNull>(V)) 3501 return getConstant(V->getType(), 0); 3502 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3503 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3504 else 3505 return getUnknown(V); 3506 3507 Operator *U = cast<Operator>(V); 3508 switch (Opcode) { 3509 case Instruction::Add: { 3510 // The simple thing to do would be to just call getSCEV on both operands 3511 // and call getAddExpr with the result. However if we're looking at a 3512 // bunch of things all added together, this can be quite inefficient, 3513 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3514 // Instead, gather up all the operands and make a single getAddExpr call. 3515 // LLVM IR canonical form means we need only traverse the left operands. 3516 SmallVector<const SCEV *, 4> AddOps; 3517 AddOps.push_back(getSCEV(U->getOperand(1))); 3518 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3519 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3520 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3521 break; 3522 U = cast<Operator>(Op); 3523 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3524 if (Opcode == Instruction::Sub) 3525 AddOps.push_back(getNegativeSCEV(Op1)); 3526 else 3527 AddOps.push_back(Op1); 3528 } 3529 AddOps.push_back(getSCEV(U->getOperand(0))); 3530 return getAddExpr(AddOps); 3531 } 3532 case Instruction::Mul: { 3533 // See the Add code above. 3534 SmallVector<const SCEV *, 4> MulOps; 3535 MulOps.push_back(getSCEV(U->getOperand(1))); 3536 for (Value *Op = U->getOperand(0); 3537 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3538 Op = U->getOperand(0)) { 3539 U = cast<Operator>(Op); 3540 MulOps.push_back(getSCEV(U->getOperand(1))); 3541 } 3542 MulOps.push_back(getSCEV(U->getOperand(0))); 3543 return getMulExpr(MulOps); 3544 } 3545 case Instruction::UDiv: 3546 return getUDivExpr(getSCEV(U->getOperand(0)), 3547 getSCEV(U->getOperand(1))); 3548 case Instruction::Sub: 3549 return getMinusSCEV(getSCEV(U->getOperand(0)), 3550 getSCEV(U->getOperand(1))); 3551 case Instruction::And: 3552 // For an expression like x&255 that merely masks off the high bits, 3553 // use zext(trunc(x)) as the SCEV expression. 3554 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3555 if (CI->isNullValue()) 3556 return getSCEV(U->getOperand(1)); 3557 if (CI->isAllOnesValue()) 3558 return getSCEV(U->getOperand(0)); 3559 const APInt &A = CI->getValue(); 3560 3561 // Instcombine's ShrinkDemandedConstant may strip bits out of 3562 // constants, obscuring what would otherwise be a low-bits mask. 3563 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3564 // knew about to reconstruct a low-bits mask value. 3565 unsigned LZ = A.countLeadingZeros(); 3566 unsigned BitWidth = A.getBitWidth(); 3567 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3568 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3569 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3570 3571 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3572 3573 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3574 return 3575 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3576 IntegerType::get(getContext(), BitWidth - LZ)), 3577 U->getType()); 3578 } 3579 break; 3580 3581 case Instruction::Or: 3582 // If the RHS of the Or is a constant, we may have something like: 3583 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3584 // optimizations will transparently handle this case. 3585 // 3586 // In order for this transformation to be safe, the LHS must be of the 3587 // form X*(2^n) and the Or constant must be less than 2^n. 3588 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3589 const SCEV *LHS = getSCEV(U->getOperand(0)); 3590 const APInt &CIVal = CI->getValue(); 3591 if (GetMinTrailingZeros(LHS) >= 3592 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3593 // Build a plain add SCEV. 3594 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3595 // If the LHS of the add was an addrec and it has no-wrap flags, 3596 // transfer the no-wrap flags, since an or won't introduce a wrap. 3597 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3598 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3599 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3600 OldAR->getNoWrapFlags()); 3601 } 3602 return S; 3603 } 3604 } 3605 break; 3606 case Instruction::Xor: 3607 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3608 // If the RHS of the xor is a signbit, then this is just an add. 3609 // Instcombine turns add of signbit into xor as a strength reduction step. 3610 if (CI->getValue().isSignBit()) 3611 return getAddExpr(getSCEV(U->getOperand(0)), 3612 getSCEV(U->getOperand(1))); 3613 3614 // If the RHS of xor is -1, then this is a not operation. 3615 if (CI->isAllOnesValue()) 3616 return getNotSCEV(getSCEV(U->getOperand(0))); 3617 3618 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3619 // This is a variant of the check for xor with -1, and it handles 3620 // the case where instcombine has trimmed non-demanded bits out 3621 // of an xor with -1. 3622 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3623 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3624 if (BO->getOpcode() == Instruction::And && 3625 LCI->getValue() == CI->getValue()) 3626 if (const SCEVZeroExtendExpr *Z = 3627 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3628 Type *UTy = U->getType(); 3629 const SCEV *Z0 = Z->getOperand(); 3630 Type *Z0Ty = Z0->getType(); 3631 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3632 3633 // If C is a low-bits mask, the zero extend is serving to 3634 // mask off the high bits. Complement the operand and 3635 // re-apply the zext. 3636 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3637 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3638 3639 // If C is a single bit, it may be in the sign-bit position 3640 // before the zero-extend. In this case, represent the xor 3641 // using an add, which is equivalent, and re-apply the zext. 3642 APInt Trunc = CI->getValue().trunc(Z0TySize); 3643 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3644 Trunc.isSignBit()) 3645 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3646 UTy); 3647 } 3648 } 3649 break; 3650 3651 case Instruction::Shl: 3652 // Turn shift left of a constant amount into a multiply. 3653 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3654 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3655 3656 // If the shift count is not less than the bitwidth, the result of 3657 // the shift is undefined. Don't try to analyze it, because the 3658 // resolution chosen here may differ from the resolution chosen in 3659 // other parts of the compiler. 3660 if (SA->getValue().uge(BitWidth)) 3661 break; 3662 3663 Constant *X = ConstantInt::get(getContext(), 3664 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3665 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3666 } 3667 break; 3668 3669 case Instruction::LShr: 3670 // Turn logical shift right of a constant into a unsigned divide. 3671 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3672 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3673 3674 // If the shift count is not less than the bitwidth, the result of 3675 // the shift is undefined. Don't try to analyze it, because the 3676 // resolution chosen here may differ from the resolution chosen in 3677 // other parts of the compiler. 3678 if (SA->getValue().uge(BitWidth)) 3679 break; 3680 3681 Constant *X = ConstantInt::get(getContext(), 3682 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3683 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3684 } 3685 break; 3686 3687 case Instruction::AShr: 3688 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3689 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3690 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3691 if (L->getOpcode() == Instruction::Shl && 3692 L->getOperand(1) == U->getOperand(1)) { 3693 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3694 3695 // If the shift count is not less than the bitwidth, the result of 3696 // the shift is undefined. Don't try to analyze it, because the 3697 // resolution chosen here may differ from the resolution chosen in 3698 // other parts of the compiler. 3699 if (CI->getValue().uge(BitWidth)) 3700 break; 3701 3702 uint64_t Amt = BitWidth - CI->getZExtValue(); 3703 if (Amt == BitWidth) 3704 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3705 return 3706 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3707 IntegerType::get(getContext(), 3708 Amt)), 3709 U->getType()); 3710 } 3711 break; 3712 3713 case Instruction::Trunc: 3714 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3715 3716 case Instruction::ZExt: 3717 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3718 3719 case Instruction::SExt: 3720 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3721 3722 case Instruction::BitCast: 3723 // BitCasts are no-op casts so we just eliminate the cast. 3724 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3725 return getSCEV(U->getOperand(0)); 3726 break; 3727 3728 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3729 // lead to pointer expressions which cannot safely be expanded to GEPs, 3730 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3731 // simplifying integer expressions. 3732 3733 case Instruction::GetElementPtr: 3734 return createNodeForGEP(cast<GEPOperator>(U)); 3735 3736 case Instruction::PHI: 3737 return createNodeForPHI(cast<PHINode>(U)); 3738 3739 case Instruction::Select: 3740 // This could be a smax or umax that was lowered earlier. 3741 // Try to recover it. 3742 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3743 Value *LHS = ICI->getOperand(0); 3744 Value *RHS = ICI->getOperand(1); 3745 switch (ICI->getPredicate()) { 3746 case ICmpInst::ICMP_SLT: 3747 case ICmpInst::ICMP_SLE: 3748 std::swap(LHS, RHS); 3749 // fall through 3750 case ICmpInst::ICMP_SGT: 3751 case ICmpInst::ICMP_SGE: 3752 // a >s b ? a+x : b+x -> smax(a, b)+x 3753 // a >s b ? b+x : a+x -> smin(a, b)+x 3754 if (LHS->getType() == U->getType()) { 3755 const SCEV *LS = getSCEV(LHS); 3756 const SCEV *RS = getSCEV(RHS); 3757 const SCEV *LA = getSCEV(U->getOperand(1)); 3758 const SCEV *RA = getSCEV(U->getOperand(2)); 3759 const SCEV *LDiff = getMinusSCEV(LA, LS); 3760 const SCEV *RDiff = getMinusSCEV(RA, RS); 3761 if (LDiff == RDiff) 3762 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3763 LDiff = getMinusSCEV(LA, RS); 3764 RDiff = getMinusSCEV(RA, LS); 3765 if (LDiff == RDiff) 3766 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3767 } 3768 break; 3769 case ICmpInst::ICMP_ULT: 3770 case ICmpInst::ICMP_ULE: 3771 std::swap(LHS, RHS); 3772 // fall through 3773 case ICmpInst::ICMP_UGT: 3774 case ICmpInst::ICMP_UGE: 3775 // a >u b ? a+x : b+x -> umax(a, b)+x 3776 // a >u b ? b+x : a+x -> umin(a, b)+x 3777 if (LHS->getType() == U->getType()) { 3778 const SCEV *LS = getSCEV(LHS); 3779 const SCEV *RS = getSCEV(RHS); 3780 const SCEV *LA = getSCEV(U->getOperand(1)); 3781 const SCEV *RA = getSCEV(U->getOperand(2)); 3782 const SCEV *LDiff = getMinusSCEV(LA, LS); 3783 const SCEV *RDiff = getMinusSCEV(RA, RS); 3784 if (LDiff == RDiff) 3785 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3786 LDiff = getMinusSCEV(LA, RS); 3787 RDiff = getMinusSCEV(RA, LS); 3788 if (LDiff == RDiff) 3789 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3790 } 3791 break; 3792 case ICmpInst::ICMP_NE: 3793 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3794 if (LHS->getType() == U->getType() && 3795 isa<ConstantInt>(RHS) && 3796 cast<ConstantInt>(RHS)->isZero()) { 3797 const SCEV *One = getConstant(LHS->getType(), 1); 3798 const SCEV *LS = getSCEV(LHS); 3799 const SCEV *LA = getSCEV(U->getOperand(1)); 3800 const SCEV *RA = getSCEV(U->getOperand(2)); 3801 const SCEV *LDiff = getMinusSCEV(LA, LS); 3802 const SCEV *RDiff = getMinusSCEV(RA, One); 3803 if (LDiff == RDiff) 3804 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3805 } 3806 break; 3807 case ICmpInst::ICMP_EQ: 3808 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3809 if (LHS->getType() == U->getType() && 3810 isa<ConstantInt>(RHS) && 3811 cast<ConstantInt>(RHS)->isZero()) { 3812 const SCEV *One = getConstant(LHS->getType(), 1); 3813 const SCEV *LS = getSCEV(LHS); 3814 const SCEV *LA = getSCEV(U->getOperand(1)); 3815 const SCEV *RA = getSCEV(U->getOperand(2)); 3816 const SCEV *LDiff = getMinusSCEV(LA, One); 3817 const SCEV *RDiff = getMinusSCEV(RA, LS); 3818 if (LDiff == RDiff) 3819 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3820 } 3821 break; 3822 default: 3823 break; 3824 } 3825 } 3826 3827 default: // We cannot analyze this expression. 3828 break; 3829 } 3830 3831 return getUnknown(V); 3832} 3833 3834 3835 3836//===----------------------------------------------------------------------===// 3837// Iteration Count Computation Code 3838// 3839 3840/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 3841/// normal unsigned value, if possible. Returns 0 if the trip count is unknown 3842/// or not constant. Will also return 0 if the maximum trip count is very large 3843/// (>= 2^32) 3844unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, 3845 BasicBlock *ExitBlock) { 3846 const SCEVConstant *ExitCount = 3847 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock)); 3848 if (!ExitCount) 3849 return 0; 3850 3851 ConstantInt *ExitConst = ExitCount->getValue(); 3852 3853 // Guard against huge trip counts. 3854 if (ExitConst->getValue().getActiveBits() > 32) 3855 return 0; 3856 3857 // In case of integer overflow, this returns 0, which is correct. 3858 return ((unsigned)ExitConst->getZExtValue()) + 1; 3859} 3860 3861/// getSmallConstantTripMultiple - Returns the largest constant divisor of the 3862/// trip count of this loop as a normal unsigned value, if possible. This 3863/// means that the actual trip count is always a multiple of the returned 3864/// value (don't forget the trip count could very well be zero as well!). 3865/// 3866/// Returns 1 if the trip count is unknown or not guaranteed to be the 3867/// multiple of a constant (which is also the case if the trip count is simply 3868/// constant, use getSmallConstantTripCount for that case), Will also return 1 3869/// if the trip count is very large (>= 2^32). 3870unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L, 3871 BasicBlock *ExitBlock) { 3872 const SCEV *ExitCount = getExitCount(L, ExitBlock); 3873 if (ExitCount == getCouldNotCompute()) 3874 return 1; 3875 3876 // Get the trip count from the BE count by adding 1. 3877 const SCEV *TCMul = getAddExpr(ExitCount, 3878 getConstant(ExitCount->getType(), 1)); 3879 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 3880 // to factor simple cases. 3881 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 3882 TCMul = Mul->getOperand(0); 3883 3884 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 3885 if (!MulC) 3886 return 1; 3887 3888 ConstantInt *Result = MulC->getValue(); 3889 3890 // Guard against huge trip counts. 3891 if (!Result || Result->getValue().getActiveBits() > 32) 3892 return 1; 3893 3894 return (unsigned)Result->getZExtValue(); 3895} 3896 3897// getExitCount - Get the expression for the number of loop iterations for which 3898// this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3899// SCEVCouldNotCompute. 3900const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3901 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3902} 3903 3904/// getBackedgeTakenCount - If the specified loop has a predictable 3905/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3906/// object. The backedge-taken count is the number of times the loop header 3907/// will be branched to from within the loop. This is one less than the 3908/// trip count of the loop, since it doesn't count the first iteration, 3909/// when the header is branched to from outside the loop. 3910/// 3911/// Note that it is not valid to call this method on a loop without a 3912/// loop-invariant backedge-taken count (see 3913/// hasLoopInvariantBackedgeTakenCount). 3914/// 3915const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 3916 return getBackedgeTakenInfo(L).getExact(this); 3917} 3918 3919/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 3920/// return the least SCEV value that is known never to be less than the 3921/// actual backedge taken count. 3922const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 3923 return getBackedgeTakenInfo(L).getMax(this); 3924} 3925 3926/// PushLoopPHIs - Push PHI nodes in the header of the given loop 3927/// onto the given Worklist. 3928static void 3929PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 3930 BasicBlock *Header = L->getHeader(); 3931 3932 // Push all Loop-header PHIs onto the Worklist stack. 3933 for (BasicBlock::iterator I = Header->begin(); 3934 PHINode *PN = dyn_cast<PHINode>(I); ++I) 3935 Worklist.push_back(PN); 3936} 3937 3938const ScalarEvolution::BackedgeTakenInfo & 3939ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 3940 // Initially insert an invalid entry for this loop. If the insertion 3941 // succeeds, proceed to actually compute a backedge-taken count and 3942 // update the value. The temporary CouldNotCompute value tells SCEV 3943 // code elsewhere that it shouldn't attempt to request a new 3944 // backedge-taken count, which could result in infinite recursion. 3945 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 3946 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 3947 if (!Pair.second) 3948 return Pair.first->second; 3949 3950 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 3951 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 3952 // must be cleared in this scope. 3953 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 3954 3955 if (Result.getExact(this) != getCouldNotCompute()) { 3956 assert(isLoopInvariant(Result.getExact(this), L) && 3957 isLoopInvariant(Result.getMax(this), L) && 3958 "Computed backedge-taken count isn't loop invariant for loop!"); 3959 ++NumTripCountsComputed; 3960 } 3961 else if (Result.getMax(this) == getCouldNotCompute() && 3962 isa<PHINode>(L->getHeader()->begin())) { 3963 // Only count loops that have phi nodes as not being computable. 3964 ++NumTripCountsNotComputed; 3965 } 3966 3967 // Now that we know more about the trip count for this loop, forget any 3968 // existing SCEV values for PHI nodes in this loop since they are only 3969 // conservative estimates made without the benefit of trip count 3970 // information. This is similar to the code in forgetLoop, except that 3971 // it handles SCEVUnknown PHI nodes specially. 3972 if (Result.hasAnyInfo()) { 3973 SmallVector<Instruction *, 16> Worklist; 3974 PushLoopPHIs(L, Worklist); 3975 3976 SmallPtrSet<Instruction *, 8> Visited; 3977 while (!Worklist.empty()) { 3978 Instruction *I = Worklist.pop_back_val(); 3979 if (!Visited.insert(I)) continue; 3980 3981 ValueExprMapType::iterator It = 3982 ValueExprMap.find(static_cast<Value *>(I)); 3983 if (It != ValueExprMap.end()) { 3984 const SCEV *Old = It->second; 3985 3986 // SCEVUnknown for a PHI either means that it has an unrecognized 3987 // structure, or it's a PHI that's in the progress of being computed 3988 // by createNodeForPHI. In the former case, additional loop trip 3989 // count information isn't going to change anything. In the later 3990 // case, createNodeForPHI will perform the necessary updates on its 3991 // own when it gets to that point. 3992 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 3993 forgetMemoizedResults(Old); 3994 ValueExprMap.erase(It); 3995 } 3996 if (PHINode *PN = dyn_cast<PHINode>(I)) 3997 ConstantEvolutionLoopExitValue.erase(PN); 3998 } 3999 4000 PushDefUseChildren(I, Worklist); 4001 } 4002 } 4003 4004 // Re-lookup the insert position, since the call to 4005 // ComputeBackedgeTakenCount above could result in a 4006 // recusive call to getBackedgeTakenInfo (on a different 4007 // loop), which would invalidate the iterator computed 4008 // earlier. 4009 return BackedgeTakenCounts.find(L)->second = Result; 4010} 4011 4012/// forgetLoop - This method should be called by the client when it has 4013/// changed a loop in a way that may effect ScalarEvolution's ability to 4014/// compute a trip count, or if the loop is deleted. 4015void ScalarEvolution::forgetLoop(const Loop *L) { 4016 // Drop any stored trip count value. 4017 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4018 BackedgeTakenCounts.find(L); 4019 if (BTCPos != BackedgeTakenCounts.end()) { 4020 BTCPos->second.clear(); 4021 BackedgeTakenCounts.erase(BTCPos); 4022 } 4023 4024 // Drop information about expressions based on loop-header PHIs. 4025 SmallVector<Instruction *, 16> Worklist; 4026 PushLoopPHIs(L, Worklist); 4027 4028 SmallPtrSet<Instruction *, 8> Visited; 4029 while (!Worklist.empty()) { 4030 Instruction *I = Worklist.pop_back_val(); 4031 if (!Visited.insert(I)) continue; 4032 4033 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4034 if (It != ValueExprMap.end()) { 4035 forgetMemoizedResults(It->second); 4036 ValueExprMap.erase(It); 4037 if (PHINode *PN = dyn_cast<PHINode>(I)) 4038 ConstantEvolutionLoopExitValue.erase(PN); 4039 } 4040 4041 PushDefUseChildren(I, Worklist); 4042 } 4043 4044 // Forget all contained loops too, to avoid dangling entries in the 4045 // ValuesAtScopes map. 4046 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4047 forgetLoop(*I); 4048} 4049 4050/// forgetValue - This method should be called by the client when it has 4051/// changed a value in a way that may effect its value, or which may 4052/// disconnect it from a def-use chain linking it to a loop. 4053void ScalarEvolution::forgetValue(Value *V) { 4054 Instruction *I = dyn_cast<Instruction>(V); 4055 if (!I) return; 4056 4057 // Drop information about expressions based on loop-header PHIs. 4058 SmallVector<Instruction *, 16> Worklist; 4059 Worklist.push_back(I); 4060 4061 SmallPtrSet<Instruction *, 8> Visited; 4062 while (!Worklist.empty()) { 4063 I = Worklist.pop_back_val(); 4064 if (!Visited.insert(I)) continue; 4065 4066 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4067 if (It != ValueExprMap.end()) { 4068 forgetMemoizedResults(It->second); 4069 ValueExprMap.erase(It); 4070 if (PHINode *PN = dyn_cast<PHINode>(I)) 4071 ConstantEvolutionLoopExitValue.erase(PN); 4072 } 4073 4074 PushDefUseChildren(I, Worklist); 4075 } 4076} 4077 4078/// getExact - Get the exact loop backedge taken count considering all loop 4079/// exits. If all exits are computable, this is the minimum computed count. 4080const SCEV * 4081ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4082 // If any exits were not computable, the loop is not computable. 4083 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4084 4085 // We need at least one computable exit. 4086 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4087 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4088 4089 const SCEV *BECount = 0; 4090 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4091 ENT != 0; ENT = ENT->getNextExit()) { 4092 4093 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4094 4095 if (!BECount) 4096 BECount = ENT->ExactNotTaken; 4097 else 4098 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken); 4099 } 4100 assert(BECount && "Invalid not taken count for loop exit"); 4101 return BECount; 4102} 4103 4104/// getExact - Get the exact not taken count for this loop exit. 4105const SCEV * 4106ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4107 ScalarEvolution *SE) const { 4108 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4109 ENT != 0; ENT = ENT->getNextExit()) { 4110 4111 if (ENT->ExitingBlock == ExitingBlock) 4112 return ENT->ExactNotTaken; 4113 } 4114 return SE->getCouldNotCompute(); 4115} 4116 4117/// getMax - Get the max backedge taken count for the loop. 4118const SCEV * 4119ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4120 return Max ? Max : SE->getCouldNotCompute(); 4121} 4122 4123/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4124/// computable exit into a persistent ExitNotTakenInfo array. 4125ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4126 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4127 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4128 4129 if (!Complete) 4130 ExitNotTaken.setIncomplete(); 4131 4132 unsigned NumExits = ExitCounts.size(); 4133 if (NumExits == 0) return; 4134 4135 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4136 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4137 if (NumExits == 1) return; 4138 4139 // Handle the rare case of multiple computable exits. 4140 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4141 4142 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4143 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4144 PrevENT->setNextExit(ENT); 4145 ENT->ExitingBlock = ExitCounts[i].first; 4146 ENT->ExactNotTaken = ExitCounts[i].second; 4147 } 4148} 4149 4150/// clear - Invalidate this result and free the ExitNotTakenInfo array. 4151void ScalarEvolution::BackedgeTakenInfo::clear() { 4152 ExitNotTaken.ExitingBlock = 0; 4153 ExitNotTaken.ExactNotTaken = 0; 4154 delete[] ExitNotTaken.getNextExit(); 4155} 4156 4157/// ComputeBackedgeTakenCount - Compute the number of times the backedge 4158/// of the specified loop will execute. 4159ScalarEvolution::BackedgeTakenInfo 4160ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4161 SmallVector<BasicBlock *, 8> ExitingBlocks; 4162 L->getExitingBlocks(ExitingBlocks); 4163 4164 // Examine all exits and pick the most conservative values. 4165 const SCEV *MaxBECount = getCouldNotCompute(); 4166 bool CouldComputeBECount = true; 4167 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4168 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4169 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4170 if (EL.Exact == getCouldNotCompute()) 4171 // We couldn't compute an exact value for this exit, so 4172 // we won't be able to compute an exact value for the loop. 4173 CouldComputeBECount = false; 4174 else 4175 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4176 4177 if (MaxBECount == getCouldNotCompute()) 4178 MaxBECount = EL.Max; 4179 else if (EL.Max != getCouldNotCompute()) 4180 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max); 4181 } 4182 4183 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4184} 4185 4186/// ComputeExitLimit - Compute the number of times the backedge of the specified 4187/// loop will execute if it exits via the specified block. 4188ScalarEvolution::ExitLimit 4189ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4190 4191 // Okay, we've chosen an exiting block. See what condition causes us to 4192 // exit at this block. 4193 // 4194 // FIXME: we should be able to handle switch instructions (with a single exit) 4195 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4196 if (ExitBr == 0) return getCouldNotCompute(); 4197 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4198 4199 // At this point, we know we have a conditional branch that determines whether 4200 // the loop is exited. However, we don't know if the branch is executed each 4201 // time through the loop. If not, then the execution count of the branch will 4202 // not be equal to the trip count of the loop. 4203 // 4204 // Currently we check for this by checking to see if the Exit branch goes to 4205 // the loop header. If so, we know it will always execute the same number of 4206 // times as the loop. We also handle the case where the exit block *is* the 4207 // loop header. This is common for un-rotated loops. 4208 // 4209 // If both of those tests fail, walk up the unique predecessor chain to the 4210 // header, stopping if there is an edge that doesn't exit the loop. If the 4211 // header is reached, the execution count of the branch will be equal to the 4212 // trip count of the loop. 4213 // 4214 // More extensive analysis could be done to handle more cases here. 4215 // 4216 if (ExitBr->getSuccessor(0) != L->getHeader() && 4217 ExitBr->getSuccessor(1) != L->getHeader() && 4218 ExitBr->getParent() != L->getHeader()) { 4219 // The simple checks failed, try climbing the unique predecessor chain 4220 // up to the header. 4221 bool Ok = false; 4222 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4223 BasicBlock *Pred = BB->getUniquePredecessor(); 4224 if (!Pred) 4225 return getCouldNotCompute(); 4226 TerminatorInst *PredTerm = Pred->getTerminator(); 4227 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4228 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4229 if (PredSucc == BB) 4230 continue; 4231 // If the predecessor has a successor that isn't BB and isn't 4232 // outside the loop, assume the worst. 4233 if (L->contains(PredSucc)) 4234 return getCouldNotCompute(); 4235 } 4236 if (Pred == L->getHeader()) { 4237 Ok = true; 4238 break; 4239 } 4240 BB = Pred; 4241 } 4242 if (!Ok) 4243 return getCouldNotCompute(); 4244 } 4245 4246 // Proceed to the next level to examine the exit condition expression. 4247 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4248 ExitBr->getSuccessor(0), 4249 ExitBr->getSuccessor(1)); 4250} 4251 4252/// ComputeExitLimitFromCond - Compute the number of times the 4253/// backedge of the specified loop will execute if its exit condition 4254/// were a conditional branch of ExitCond, TBB, and FBB. 4255ScalarEvolution::ExitLimit 4256ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4257 Value *ExitCond, 4258 BasicBlock *TBB, 4259 BasicBlock *FBB) { 4260 // Check if the controlling expression for this loop is an And or Or. 4261 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4262 if (BO->getOpcode() == Instruction::And) { 4263 // Recurse on the operands of the and. 4264 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4265 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4266 const SCEV *BECount = getCouldNotCompute(); 4267 const SCEV *MaxBECount = getCouldNotCompute(); 4268 if (L->contains(TBB)) { 4269 // Both conditions must be true for the loop to continue executing. 4270 // Choose the less conservative count. 4271 if (EL0.Exact == getCouldNotCompute() || 4272 EL1.Exact == getCouldNotCompute()) 4273 BECount = getCouldNotCompute(); 4274 else 4275 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4276 if (EL0.Max == getCouldNotCompute()) 4277 MaxBECount = EL1.Max; 4278 else if (EL1.Max == getCouldNotCompute()) 4279 MaxBECount = EL0.Max; 4280 else 4281 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4282 } else { 4283 // Both conditions must be true at the same time for the loop to exit. 4284 // For now, be conservative. 4285 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4286 if (EL0.Max == EL1.Max) 4287 MaxBECount = EL0.Max; 4288 if (EL0.Exact == EL1.Exact) 4289 BECount = EL0.Exact; 4290 } 4291 4292 return ExitLimit(BECount, MaxBECount); 4293 } 4294 if (BO->getOpcode() == Instruction::Or) { 4295 // Recurse on the operands of the or. 4296 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4297 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4298 const SCEV *BECount = getCouldNotCompute(); 4299 const SCEV *MaxBECount = getCouldNotCompute(); 4300 if (L->contains(FBB)) { 4301 // Both conditions must be false for the loop to continue executing. 4302 // Choose the less conservative count. 4303 if (EL0.Exact == getCouldNotCompute() || 4304 EL1.Exact == getCouldNotCompute()) 4305 BECount = getCouldNotCompute(); 4306 else 4307 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4308 if (EL0.Max == getCouldNotCompute()) 4309 MaxBECount = EL1.Max; 4310 else if (EL1.Max == getCouldNotCompute()) 4311 MaxBECount = EL0.Max; 4312 else 4313 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4314 } else { 4315 // Both conditions must be false at the same time for the loop to exit. 4316 // For now, be conservative. 4317 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4318 if (EL0.Max == EL1.Max) 4319 MaxBECount = EL0.Max; 4320 if (EL0.Exact == EL1.Exact) 4321 BECount = EL0.Exact; 4322 } 4323 4324 return ExitLimit(BECount, MaxBECount); 4325 } 4326 } 4327 4328 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4329 // Proceed to the next level to examine the icmp. 4330 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4331 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4332 4333 // Check for a constant condition. These are normally stripped out by 4334 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4335 // preserve the CFG and is temporarily leaving constant conditions 4336 // in place. 4337 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4338 if (L->contains(FBB) == !CI->getZExtValue()) 4339 // The backedge is always taken. 4340 return getCouldNotCompute(); 4341 else 4342 // The backedge is never taken. 4343 return getConstant(CI->getType(), 0); 4344 } 4345 4346 // If it's not an integer or pointer comparison then compute it the hard way. 4347 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4348} 4349 4350/// ComputeExitLimitFromICmp - Compute the number of times the 4351/// backedge of the specified loop will execute if its exit condition 4352/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4353ScalarEvolution::ExitLimit 4354ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4355 ICmpInst *ExitCond, 4356 BasicBlock *TBB, 4357 BasicBlock *FBB) { 4358 4359 // If the condition was exit on true, convert the condition to exit on false 4360 ICmpInst::Predicate Cond; 4361 if (!L->contains(FBB)) 4362 Cond = ExitCond->getPredicate(); 4363 else 4364 Cond = ExitCond->getInversePredicate(); 4365 4366 // Handle common loops like: for (X = "string"; *X; ++X) 4367 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4368 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4369 ExitLimit ItCnt = 4370 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4371 if (ItCnt.hasAnyInfo()) 4372 return ItCnt; 4373 } 4374 4375 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4376 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4377 4378 // Try to evaluate any dependencies out of the loop. 4379 LHS = getSCEVAtScope(LHS, L); 4380 RHS = getSCEVAtScope(RHS, L); 4381 4382 // At this point, we would like to compute how many iterations of the 4383 // loop the predicate will return true for these inputs. 4384 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4385 // If there is a loop-invariant, force it into the RHS. 4386 std::swap(LHS, RHS); 4387 Cond = ICmpInst::getSwappedPredicate(Cond); 4388 } 4389 4390 // Simplify the operands before analyzing them. 4391 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4392 4393 // If we have a comparison of a chrec against a constant, try to use value 4394 // ranges to answer this query. 4395 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4396 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4397 if (AddRec->getLoop() == L) { 4398 // Form the constant range. 4399 ConstantRange CompRange( 4400 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4401 4402 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4403 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4404 } 4405 4406 switch (Cond) { 4407 case ICmpInst::ICMP_NE: { // while (X != Y) 4408 // Convert to: while (X-Y != 0) 4409 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4410 if (EL.hasAnyInfo()) return EL; 4411 break; 4412 } 4413 case ICmpInst::ICMP_EQ: { // while (X == Y) 4414 // Convert to: while (X-Y == 0) 4415 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4416 if (EL.hasAnyInfo()) return EL; 4417 break; 4418 } 4419 case ICmpInst::ICMP_SLT: { 4420 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4421 if (EL.hasAnyInfo()) return EL; 4422 break; 4423 } 4424 case ICmpInst::ICMP_SGT: { 4425 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4426 getNotSCEV(RHS), L, true); 4427 if (EL.hasAnyInfo()) return EL; 4428 break; 4429 } 4430 case ICmpInst::ICMP_ULT: { 4431 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4432 if (EL.hasAnyInfo()) return EL; 4433 break; 4434 } 4435 case ICmpInst::ICMP_UGT: { 4436 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4437 getNotSCEV(RHS), L, false); 4438 if (EL.hasAnyInfo()) return EL; 4439 break; 4440 } 4441 default: 4442#if 0 4443 dbgs() << "ComputeBackedgeTakenCount "; 4444 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4445 dbgs() << "[unsigned] "; 4446 dbgs() << *LHS << " " 4447 << Instruction::getOpcodeName(Instruction::ICmp) 4448 << " " << *RHS << "\n"; 4449#endif 4450 break; 4451 } 4452 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4453} 4454 4455static ConstantInt * 4456EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4457 ScalarEvolution &SE) { 4458 const SCEV *InVal = SE.getConstant(C); 4459 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4460 assert(isa<SCEVConstant>(Val) && 4461 "Evaluation of SCEV at constant didn't fold correctly?"); 4462 return cast<SCEVConstant>(Val)->getValue(); 4463} 4464 4465/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4466/// and a GEP expression (missing the pointer index) indexing into it, return 4467/// the addressed element of the initializer or null if the index expression is 4468/// invalid. 4469static Constant * 4470GetAddressedElementFromGlobal(GlobalVariable *GV, 4471 const std::vector<ConstantInt*> &Indices) { 4472 Constant *Init = GV->getInitializer(); 4473 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4474 uint64_t Idx = Indices[i]->getZExtValue(); 4475 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4476 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4477 Init = cast<Constant>(CS->getOperand(Idx)); 4478 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4479 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4480 Init = cast<Constant>(CA->getOperand(Idx)); 4481 } else if (isa<ConstantAggregateZero>(Init)) { 4482 if (StructType *STy = dyn_cast<StructType>(Init->getType())) { 4483 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4484 Init = Constant::getNullValue(STy->getElementType(Idx)); 4485 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4486 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4487 Init = Constant::getNullValue(ATy->getElementType()); 4488 } else { 4489 llvm_unreachable("Unknown constant aggregate type!"); 4490 } 4491 return 0; 4492 } else { 4493 return 0; // Unknown initializer type 4494 } 4495 } 4496 return Init; 4497} 4498 4499/// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4500/// 'icmp op load X, cst', try to see if we can compute the backedge 4501/// execution count. 4502ScalarEvolution::ExitLimit 4503ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4504 LoadInst *LI, 4505 Constant *RHS, 4506 const Loop *L, 4507 ICmpInst::Predicate predicate) { 4508 4509 if (LI->isVolatile()) return getCouldNotCompute(); 4510 4511 // Check to see if the loaded pointer is a getelementptr of a global. 4512 // TODO: Use SCEV instead of manually grubbing with GEPs. 4513 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4514 if (!GEP) return getCouldNotCompute(); 4515 4516 // Make sure that it is really a constant global we are gepping, with an 4517 // initializer, and make sure the first IDX is really 0. 4518 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4519 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4520 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4521 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4522 return getCouldNotCompute(); 4523 4524 // Okay, we allow one non-constant index into the GEP instruction. 4525 Value *VarIdx = 0; 4526 std::vector<ConstantInt*> Indexes; 4527 unsigned VarIdxNum = 0; 4528 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4529 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4530 Indexes.push_back(CI); 4531 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4532 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4533 VarIdx = GEP->getOperand(i); 4534 VarIdxNum = i-2; 4535 Indexes.push_back(0); 4536 } 4537 4538 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4539 // Check to see if X is a loop variant variable value now. 4540 const SCEV *Idx = getSCEV(VarIdx); 4541 Idx = getSCEVAtScope(Idx, L); 4542 4543 // We can only recognize very limited forms of loop index expressions, in 4544 // particular, only affine AddRec's like {C1,+,C2}. 4545 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4546 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4547 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4548 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4549 return getCouldNotCompute(); 4550 4551 unsigned MaxSteps = MaxBruteForceIterations; 4552 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4553 ConstantInt *ItCst = ConstantInt::get( 4554 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4555 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4556 4557 // Form the GEP offset. 4558 Indexes[VarIdxNum] = Val; 4559 4560 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4561 if (Result == 0) break; // Cannot compute! 4562 4563 // Evaluate the condition for this iteration. 4564 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4565 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4566 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4567#if 0 4568 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4569 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4570 << "***\n"; 4571#endif 4572 ++NumArrayLenItCounts; 4573 return getConstant(ItCst); // Found terminating iteration! 4574 } 4575 } 4576 return getCouldNotCompute(); 4577} 4578 4579 4580/// CanConstantFold - Return true if we can constant fold an instruction of the 4581/// specified type, assuming that all operands were constants. 4582static bool CanConstantFold(const Instruction *I) { 4583 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4584 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) 4585 return true; 4586 4587 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4588 if (const Function *F = CI->getCalledFunction()) 4589 return canConstantFoldCallTo(F); 4590 return false; 4591} 4592 4593/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4594/// in the loop that V is derived from. We allow arbitrary operations along the 4595/// way, but the operands of an operation must either be constants or a value 4596/// derived from a constant PHI. If this expression does not fit with these 4597/// constraints, return null. 4598static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4599 // If this is not an instruction, or if this is an instruction outside of the 4600 // loop, it can't be derived from a loop PHI. 4601 Instruction *I = dyn_cast<Instruction>(V); 4602 if (I == 0 || !L->contains(I)) return 0; 4603 4604 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4605 if (L->getHeader() == I->getParent()) 4606 return PN; 4607 else 4608 // We don't currently keep track of the control flow needed to evaluate 4609 // PHIs, so we cannot handle PHIs inside of loops. 4610 return 0; 4611 } 4612 4613 // If we won't be able to constant fold this expression even if the operands 4614 // are constants, return early. 4615 if (!CanConstantFold(I)) return 0; 4616 4617 // Otherwise, we can evaluate this instruction if all of its operands are 4618 // constant or derived from a PHI node themselves. 4619 PHINode *PHI = 0; 4620 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) 4621 if (!isa<Constant>(I->getOperand(Op))) { 4622 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); 4623 if (P == 0) return 0; // Not evolving from PHI 4624 if (PHI == 0) 4625 PHI = P; 4626 else if (PHI != P) 4627 return 0; // Evolving from multiple different PHIs. 4628 } 4629 4630 // This is a expression evolving from a constant PHI! 4631 return PHI; 4632} 4633 4634/// EvaluateExpression - Given an expression that passes the 4635/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4636/// in the loop has the value PHIVal. If we can't fold this expression for some 4637/// reason, return null. 4638static Constant *EvaluateExpression(Value *V, Constant *PHIVal, 4639 const TargetData *TD) { 4640 if (isa<PHINode>(V)) return PHIVal; 4641 if (Constant *C = dyn_cast<Constant>(V)) return C; 4642 Instruction *I = cast<Instruction>(V); 4643 4644 std::vector<Constant*> Operands(I->getNumOperands()); 4645 4646 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4647 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); 4648 if (Operands[i] == 0) return 0; 4649 } 4650 4651 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4652 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4653 Operands[1], TD); 4654 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD); 4655} 4656 4657/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4658/// in the header of its containing loop, we know the loop executes a 4659/// constant number of times, and the PHI node is just a recurrence 4660/// involving constants, fold it. 4661Constant * 4662ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4663 const APInt &BEs, 4664 const Loop *L) { 4665 DenseMap<PHINode*, Constant*>::const_iterator I = 4666 ConstantEvolutionLoopExitValue.find(PN); 4667 if (I != ConstantEvolutionLoopExitValue.end()) 4668 return I->second; 4669 4670 if (BEs.ugt(MaxBruteForceIterations)) 4671 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4672 4673 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4674 4675 // Since the loop is canonicalized, the PHI node must have two entries. One 4676 // entry must be a constant (coming in from outside of the loop), and the 4677 // second must be derived from the same PHI. 4678 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4679 Constant *StartCST = 4680 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4681 if (StartCST == 0) 4682 return RetVal = 0; // Must be a constant. 4683 4684 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4685 if (getConstantEvolvingPHI(BEValue, L) != PN && 4686 !isa<Constant>(BEValue)) 4687 return RetVal = 0; // Not derived from same PHI. 4688 4689 // Execute the loop symbolically to determine the exit value. 4690 if (BEs.getActiveBits() >= 32) 4691 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4692 4693 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4694 unsigned IterationNum = 0; 4695 for (Constant *PHIVal = StartCST; ; ++IterationNum) { 4696 if (IterationNum == NumIterations) 4697 return RetVal = PHIVal; // Got exit value! 4698 4699 // Compute the value of the PHI node for the next iteration. 4700 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4701 if (NextPHI == PHIVal) 4702 return RetVal = NextPHI; // Stopped evolving! 4703 if (NextPHI == 0) 4704 return 0; // Couldn't evaluate! 4705 PHIVal = NextPHI; 4706 } 4707} 4708 4709/// ComputeExitCountExhaustively - If the loop is known to execute a 4710/// constant number of times (the condition evolves only from constants), 4711/// try to evaluate a few iterations of the loop until we get the exit 4712/// condition gets a value of ExitWhen (true or false). If we cannot 4713/// evaluate the trip count of the loop, return getCouldNotCompute(). 4714const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4715 Value *Cond, 4716 bool ExitWhen) { 4717 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4718 if (PN == 0) return getCouldNotCompute(); 4719 4720 // If the loop is canonicalized, the PHI will have exactly two entries. 4721 // That's the only form we support here. 4722 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4723 4724 // One entry must be a constant (coming in from outside of the loop), and the 4725 // second must be derived from the same PHI. 4726 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4727 Constant *StartCST = 4728 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); 4729 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. 4730 4731 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4732 if (getConstantEvolvingPHI(BEValue, L) != PN && 4733 !isa<Constant>(BEValue)) 4734 return getCouldNotCompute(); // Not derived from same PHI. 4735 4736 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4737 // the loop symbolically to determine when the condition gets a value of 4738 // "ExitWhen". 4739 unsigned IterationNum = 0; 4740 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4741 for (Constant *PHIVal = StartCST; 4742 IterationNum != MaxIterations; ++IterationNum) { 4743 ConstantInt *CondVal = 4744 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); 4745 4746 // Couldn't symbolically evaluate. 4747 if (!CondVal) return getCouldNotCompute(); 4748 4749 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4750 ++NumBruteForceTripCountsComputed; 4751 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4752 } 4753 4754 // Compute the value of the PHI node for the next iteration. 4755 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); 4756 if (NextPHI == 0 || NextPHI == PHIVal) 4757 return getCouldNotCompute();// Couldn't evaluate or not making progress... 4758 PHIVal = NextPHI; 4759 } 4760 4761 // Too many iterations were needed to evaluate. 4762 return getCouldNotCompute(); 4763} 4764 4765/// getSCEVAtScope - Return a SCEV expression for the specified value 4766/// at the specified scope in the program. The L value specifies a loop 4767/// nest to evaluate the expression at, where null is the top-level or a 4768/// specified loop is immediately inside of the loop. 4769/// 4770/// This method can be used to compute the exit value for a variable defined 4771/// in a loop by querying what the value will hold in the parent loop. 4772/// 4773/// In the case that a relevant loop exit value cannot be computed, the 4774/// original value V is returned. 4775const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4776 // Check to see if we've folded this expression at this loop before. 4777 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 4778 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 4779 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 4780 if (!Pair.second) 4781 return Pair.first->second ? Pair.first->second : V; 4782 4783 // Otherwise compute it. 4784 const SCEV *C = computeSCEVAtScope(V, L); 4785 ValuesAtScopes[V][L] = C; 4786 return C; 4787} 4788 4789const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 4790 if (isa<SCEVConstant>(V)) return V; 4791 4792 // If this instruction is evolved from a constant-evolving PHI, compute the 4793 // exit value from the loop without using SCEVs. 4794 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 4795 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 4796 const Loop *LI = (*this->LI)[I->getParent()]; 4797 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 4798 if (PHINode *PN = dyn_cast<PHINode>(I)) 4799 if (PN->getParent() == LI->getHeader()) { 4800 // Okay, there is no closed form solution for the PHI node. Check 4801 // to see if the loop that contains it has a known backedge-taken 4802 // count. If so, we may be able to force computation of the exit 4803 // value. 4804 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 4805 if (const SCEVConstant *BTCC = 4806 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 4807 // Okay, we know how many times the containing loop executes. If 4808 // this is a constant evolving PHI node, get the final value at 4809 // the specified iteration number. 4810 Constant *RV = getConstantEvolutionLoopExitValue(PN, 4811 BTCC->getValue()->getValue(), 4812 LI); 4813 if (RV) return getSCEV(RV); 4814 } 4815 } 4816 4817 // Okay, this is an expression that we cannot symbolically evaluate 4818 // into a SCEV. Check to see if it's possible to symbolically evaluate 4819 // the arguments into constants, and if so, try to constant propagate the 4820 // result. This is particularly useful for computing loop exit values. 4821 if (CanConstantFold(I)) { 4822 SmallVector<Constant *, 4> Operands; 4823 bool MadeImprovement = false; 4824 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4825 Value *Op = I->getOperand(i); 4826 if (Constant *C = dyn_cast<Constant>(Op)) { 4827 Operands.push_back(C); 4828 continue; 4829 } 4830 4831 // If any of the operands is non-constant and if they are 4832 // non-integer and non-pointer, don't even try to analyze them 4833 // with scev techniques. 4834 if (!isSCEVable(Op->getType())) 4835 return V; 4836 4837 const SCEV *OrigV = getSCEV(Op); 4838 const SCEV *OpV = getSCEVAtScope(OrigV, L); 4839 MadeImprovement |= OrigV != OpV; 4840 4841 Constant *C = 0; 4842 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) 4843 C = SC->getValue(); 4844 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) 4845 C = dyn_cast<Constant>(SU->getValue()); 4846 if (!C) return V; 4847 if (C->getType() != Op->getType()) 4848 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 4849 Op->getType(), 4850 false), 4851 C, Op->getType()); 4852 Operands.push_back(C); 4853 } 4854 4855 // Check to see if getSCEVAtScope actually made an improvement. 4856 if (MadeImprovement) { 4857 Constant *C = 0; 4858 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 4859 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 4860 Operands[0], Operands[1], TD); 4861 else 4862 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 4863 Operands, TD); 4864 if (!C) return V; 4865 return getSCEV(C); 4866 } 4867 } 4868 } 4869 4870 // This is some other type of SCEVUnknown, just return it. 4871 return V; 4872 } 4873 4874 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 4875 // Avoid performing the look-up in the common case where the specified 4876 // expression has no loop-variant portions. 4877 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 4878 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4879 if (OpAtScope != Comm->getOperand(i)) { 4880 // Okay, at least one of these operands is loop variant but might be 4881 // foldable. Build a new instance of the folded commutative expression. 4882 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 4883 Comm->op_begin()+i); 4884 NewOps.push_back(OpAtScope); 4885 4886 for (++i; i != e; ++i) { 4887 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 4888 NewOps.push_back(OpAtScope); 4889 } 4890 if (isa<SCEVAddExpr>(Comm)) 4891 return getAddExpr(NewOps); 4892 if (isa<SCEVMulExpr>(Comm)) 4893 return getMulExpr(NewOps); 4894 if (isa<SCEVSMaxExpr>(Comm)) 4895 return getSMaxExpr(NewOps); 4896 if (isa<SCEVUMaxExpr>(Comm)) 4897 return getUMaxExpr(NewOps); 4898 llvm_unreachable("Unknown commutative SCEV type!"); 4899 } 4900 } 4901 // If we got here, all operands are loop invariant. 4902 return Comm; 4903 } 4904 4905 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 4906 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 4907 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 4908 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 4909 return Div; // must be loop invariant 4910 return getUDivExpr(LHS, RHS); 4911 } 4912 4913 // If this is a loop recurrence for a loop that does not contain L, then we 4914 // are dealing with the final value computed by the loop. 4915 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 4916 // First, attempt to evaluate each operand. 4917 // Avoid performing the look-up in the common case where the specified 4918 // expression has no loop-variant portions. 4919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 4920 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 4921 if (OpAtScope == AddRec->getOperand(i)) 4922 continue; 4923 4924 // Okay, at least one of these operands is loop variant but might be 4925 // foldable. Build a new instance of the folded commutative expression. 4926 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 4927 AddRec->op_begin()+i); 4928 NewOps.push_back(OpAtScope); 4929 for (++i; i != e; ++i) 4930 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 4931 4932 const SCEV *FoldedRec = 4933 getAddRecExpr(NewOps, AddRec->getLoop(), 4934 AddRec->getNoWrapFlags(SCEV::FlagNW)); 4935 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 4936 // The addrec may be folded to a nonrecurrence, for example, if the 4937 // induction variable is multiplied by zero after constant folding. Go 4938 // ahead and return the folded value. 4939 if (!AddRec) 4940 return FoldedRec; 4941 break; 4942 } 4943 4944 // If the scope is outside the addrec's loop, evaluate it by using the 4945 // loop exit value of the addrec. 4946 if (!AddRec->getLoop()->contains(L)) { 4947 // To evaluate this recurrence, we need to know how many times the AddRec 4948 // loop iterates. Compute this now. 4949 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 4950 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 4951 4952 // Then, evaluate the AddRec. 4953 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 4954 } 4955 4956 return AddRec; 4957 } 4958 4959 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 4960 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4961 if (Op == Cast->getOperand()) 4962 return Cast; // must be loop invariant 4963 return getZeroExtendExpr(Op, Cast->getType()); 4964 } 4965 4966 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 4967 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4968 if (Op == Cast->getOperand()) 4969 return Cast; // must be loop invariant 4970 return getSignExtendExpr(Op, Cast->getType()); 4971 } 4972 4973 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 4974 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 4975 if (Op == Cast->getOperand()) 4976 return Cast; // must be loop invariant 4977 return getTruncateExpr(Op, Cast->getType()); 4978 } 4979 4980 llvm_unreachable("Unknown SCEV type!"); 4981 return 0; 4982} 4983 4984/// getSCEVAtScope - This is a convenience function which does 4985/// getSCEVAtScope(getSCEV(V), L). 4986const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 4987 return getSCEVAtScope(getSCEV(V), L); 4988} 4989 4990/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 4991/// following equation: 4992/// 4993/// A * X = B (mod N) 4994/// 4995/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 4996/// A and B isn't important. 4997/// 4998/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 4999static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 5000 ScalarEvolution &SE) { 5001 uint32_t BW = A.getBitWidth(); 5002 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 5003 assert(A != 0 && "A must be non-zero."); 5004 5005 // 1. D = gcd(A, N) 5006 // 5007 // The gcd of A and N may have only one prime factor: 2. The number of 5008 // trailing zeros in A is its multiplicity 5009 uint32_t Mult2 = A.countTrailingZeros(); 5010 // D = 2^Mult2 5011 5012 // 2. Check if B is divisible by D. 5013 // 5014 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5015 // is not less than multiplicity of this prime factor for D. 5016 if (B.countTrailingZeros() < Mult2) 5017 return SE.getCouldNotCompute(); 5018 5019 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5020 // modulo (N / D). 5021 // 5022 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5023 // bit width during computations. 5024 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5025 APInt Mod(BW + 1, 0); 5026 Mod.setBit(BW - Mult2); // Mod = N / D 5027 APInt I = AD.multiplicativeInverse(Mod); 5028 5029 // 4. Compute the minimum unsigned root of the equation: 5030 // I * (B / D) mod (N / D) 5031 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5032 5033 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5034 // bits. 5035 return SE.getConstant(Result.trunc(BW)); 5036} 5037 5038/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5039/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5040/// might be the same) or two SCEVCouldNotCompute objects. 5041/// 5042static std::pair<const SCEV *,const SCEV *> 5043SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5044 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5045 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5046 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5047 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5048 5049 // We currently can only solve this if the coefficients are constants. 5050 if (!LC || !MC || !NC) { 5051 const SCEV *CNC = SE.getCouldNotCompute(); 5052 return std::make_pair(CNC, CNC); 5053 } 5054 5055 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5056 const APInt &L = LC->getValue()->getValue(); 5057 const APInt &M = MC->getValue()->getValue(); 5058 const APInt &N = NC->getValue()->getValue(); 5059 APInt Two(BitWidth, 2); 5060 APInt Four(BitWidth, 4); 5061 5062 { 5063 using namespace APIntOps; 5064 const APInt& C = L; 5065 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 5066 // The B coefficient is M-N/2 5067 APInt B(M); 5068 B -= sdiv(N,Two); 5069 5070 // The A coefficient is N/2 5071 APInt A(N.sdiv(Two)); 5072 5073 // Compute the B^2-4ac term. 5074 APInt SqrtTerm(B); 5075 SqrtTerm *= B; 5076 SqrtTerm -= Four * (A * C); 5077 5078 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 5079 // integer value or else APInt::sqrt() will assert. 5080 APInt SqrtVal(SqrtTerm.sqrt()); 5081 5082 // Compute the two solutions for the quadratic formula. 5083 // The divisions must be performed as signed divisions. 5084 APInt NegB(-B); 5085 APInt TwoA( A << 1 ); 5086 if (TwoA.isMinValue()) { 5087 const SCEV *CNC = SE.getCouldNotCompute(); 5088 return std::make_pair(CNC, CNC); 5089 } 5090 5091 LLVMContext &Context = SE.getContext(); 5092 5093 ConstantInt *Solution1 = 5094 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5095 ConstantInt *Solution2 = 5096 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5097 5098 return std::make_pair(SE.getConstant(Solution1), 5099 SE.getConstant(Solution2)); 5100 } // end APIntOps namespace 5101} 5102 5103/// HowFarToZero - Return the number of times a backedge comparing the specified 5104/// value to zero will execute. If not computable, return CouldNotCompute. 5105/// 5106/// This is only used for loops with a "x != y" exit test. The exit condition is 5107/// now expressed as a single expression, V = x-y. So the exit test is 5108/// effectively V != 0. We know and take advantage of the fact that this 5109/// expression only being used in a comparison by zero context. 5110ScalarEvolution::ExitLimit 5111ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5112 // If the value is a constant 5113 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5114 // If the value is already zero, the branch will execute zero times. 5115 if (C->getValue()->isZero()) return C; 5116 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5117 } 5118 5119 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5120 if (!AddRec || AddRec->getLoop() != L) 5121 return getCouldNotCompute(); 5122 5123 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5124 // the quadratic equation to solve it. 5125 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5126 std::pair<const SCEV *,const SCEV *> Roots = 5127 SolveQuadraticEquation(AddRec, *this); 5128 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5129 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5130 if (R1 && R2) { 5131#if 0 5132 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5133 << " sol#2: " << *R2 << "\n"; 5134#endif 5135 // Pick the smallest positive root value. 5136 if (ConstantInt *CB = 5137 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5138 R1->getValue(), 5139 R2->getValue()))) { 5140 if (CB->getZExtValue() == false) 5141 std::swap(R1, R2); // R1 is the minimum root now. 5142 5143 // We can only use this value if the chrec ends up with an exact zero 5144 // value at this index. When solving for "X*X != 5", for example, we 5145 // should not accept a root of 2. 5146 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5147 if (Val->isZero()) 5148 return R1; // We found a quadratic root! 5149 } 5150 } 5151 return getCouldNotCompute(); 5152 } 5153 5154 // Otherwise we can only handle this if it is affine. 5155 if (!AddRec->isAffine()) 5156 return getCouldNotCompute(); 5157 5158 // If this is an affine expression, the execution count of this branch is 5159 // the minimum unsigned root of the following equation: 5160 // 5161 // Start + Step*N = 0 (mod 2^BW) 5162 // 5163 // equivalent to: 5164 // 5165 // Step*N = -Start (mod 2^BW) 5166 // 5167 // where BW is the common bit width of Start and Step. 5168 5169 // Get the initial value for the loop. 5170 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5171 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5172 5173 // For now we handle only constant steps. 5174 // 5175 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5176 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5177 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5178 // We have not yet seen any such cases. 5179 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5180 if (StepC == 0) 5181 return getCouldNotCompute(); 5182 5183 // For positive steps (counting up until unsigned overflow): 5184 // N = -Start/Step (as unsigned) 5185 // For negative steps (counting down to zero): 5186 // N = Start/-Step 5187 // First compute the unsigned distance from zero in the direction of Step. 5188 bool CountDown = StepC->getValue()->getValue().isNegative(); 5189 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5190 5191 // Handle unitary steps, which cannot wraparound. 5192 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5193 // N = Distance (as unsigned) 5194 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) 5195 return Distance; 5196 5197 // If the recurrence is known not to wraparound, unsigned divide computes the 5198 // back edge count. We know that the value will either become zero (and thus 5199 // the loop terminates), that the loop will terminate through some other exit 5200 // condition first, or that the loop has undefined behavior. This means 5201 // we can't "miss" the exit value, even with nonunit stride. 5202 // 5203 // FIXME: Prove that loops always exhibits *acceptable* undefined 5204 // behavior. Loops must exhibit defined behavior until a wrapped value is 5205 // actually used. So the trip count computed by udiv could be smaller than the 5206 // number of well-defined iterations. 5207 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) 5208 // FIXME: We really want an "isexact" bit for udiv. 5209 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5210 5211 // Then, try to solve the above equation provided that Start is constant. 5212 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5213 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5214 -StartC->getValue()->getValue(), 5215 *this); 5216 return getCouldNotCompute(); 5217} 5218 5219/// HowFarToNonZero - Return the number of times a backedge checking the 5220/// specified value for nonzero will execute. If not computable, return 5221/// CouldNotCompute 5222ScalarEvolution::ExitLimit 5223ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5224 // Loops that look like: while (X == 0) are very strange indeed. We don't 5225 // handle them yet except for the trivial case. This could be expanded in the 5226 // future as needed. 5227 5228 // If the value is a constant, check to see if it is known to be non-zero 5229 // already. If so, the backedge will execute zero times. 5230 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5231 if (!C->getValue()->isNullValue()) 5232 return getConstant(C->getType(), 0); 5233 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5234 } 5235 5236 // We could implement others, but I really doubt anyone writes loops like 5237 // this, and if they did, they would already be constant folded. 5238 return getCouldNotCompute(); 5239} 5240 5241/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5242/// (which may not be an immediate predecessor) which has exactly one 5243/// successor from which BB is reachable, or null if no such block is 5244/// found. 5245/// 5246std::pair<BasicBlock *, BasicBlock *> 5247ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5248 // If the block has a unique predecessor, then there is no path from the 5249 // predecessor to the block that does not go through the direct edge 5250 // from the predecessor to the block. 5251 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5252 return std::make_pair(Pred, BB); 5253 5254 // A loop's header is defined to be a block that dominates the loop. 5255 // If the header has a unique predecessor outside the loop, it must be 5256 // a block that has exactly one successor that can reach the loop. 5257 if (Loop *L = LI->getLoopFor(BB)) 5258 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5259 5260 return std::pair<BasicBlock *, BasicBlock *>(); 5261} 5262 5263/// HasSameValue - SCEV structural equivalence is usually sufficient for 5264/// testing whether two expressions are equal, however for the purposes of 5265/// looking for a condition guarding a loop, it can be useful to be a little 5266/// more general, since a front-end may have replicated the controlling 5267/// expression. 5268/// 5269static bool HasSameValue(const SCEV *A, const SCEV *B) { 5270 // Quick check to see if they are the same SCEV. 5271 if (A == B) return true; 5272 5273 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5274 // two different instructions with the same value. Check for this case. 5275 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5276 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5277 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5278 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5279 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5280 return true; 5281 5282 // Otherwise assume they may have a different value. 5283 return false; 5284} 5285 5286/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5287/// predicate Pred. Return true iff any changes were made. 5288/// 5289bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5290 const SCEV *&LHS, const SCEV *&RHS) { 5291 bool Changed = false; 5292 5293 // Canonicalize a constant to the right side. 5294 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5295 // Check for both operands constant. 5296 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5297 if (ConstantExpr::getICmp(Pred, 5298 LHSC->getValue(), 5299 RHSC->getValue())->isNullValue()) 5300 goto trivially_false; 5301 else 5302 goto trivially_true; 5303 } 5304 // Otherwise swap the operands to put the constant on the right. 5305 std::swap(LHS, RHS); 5306 Pred = ICmpInst::getSwappedPredicate(Pred); 5307 Changed = true; 5308 } 5309 5310 // If we're comparing an addrec with a value which is loop-invariant in the 5311 // addrec's loop, put the addrec on the left. Also make a dominance check, 5312 // as both operands could be addrecs loop-invariant in each other's loop. 5313 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5314 const Loop *L = AR->getLoop(); 5315 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5316 std::swap(LHS, RHS); 5317 Pred = ICmpInst::getSwappedPredicate(Pred); 5318 Changed = true; 5319 } 5320 } 5321 5322 // If there's a constant operand, canonicalize comparisons with boundary 5323 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5324 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5325 const APInt &RA = RC->getValue()->getValue(); 5326 switch (Pred) { 5327 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5328 case ICmpInst::ICMP_EQ: 5329 case ICmpInst::ICMP_NE: 5330 break; 5331 case ICmpInst::ICMP_UGE: 5332 if ((RA - 1).isMinValue()) { 5333 Pred = ICmpInst::ICMP_NE; 5334 RHS = getConstant(RA - 1); 5335 Changed = true; 5336 break; 5337 } 5338 if (RA.isMaxValue()) { 5339 Pred = ICmpInst::ICMP_EQ; 5340 Changed = true; 5341 break; 5342 } 5343 if (RA.isMinValue()) goto trivially_true; 5344 5345 Pred = ICmpInst::ICMP_UGT; 5346 RHS = getConstant(RA - 1); 5347 Changed = true; 5348 break; 5349 case ICmpInst::ICMP_ULE: 5350 if ((RA + 1).isMaxValue()) { 5351 Pred = ICmpInst::ICMP_NE; 5352 RHS = getConstant(RA + 1); 5353 Changed = true; 5354 break; 5355 } 5356 if (RA.isMinValue()) { 5357 Pred = ICmpInst::ICMP_EQ; 5358 Changed = true; 5359 break; 5360 } 5361 if (RA.isMaxValue()) goto trivially_true; 5362 5363 Pred = ICmpInst::ICMP_ULT; 5364 RHS = getConstant(RA + 1); 5365 Changed = true; 5366 break; 5367 case ICmpInst::ICMP_SGE: 5368 if ((RA - 1).isMinSignedValue()) { 5369 Pred = ICmpInst::ICMP_NE; 5370 RHS = getConstant(RA - 1); 5371 Changed = true; 5372 break; 5373 } 5374 if (RA.isMaxSignedValue()) { 5375 Pred = ICmpInst::ICMP_EQ; 5376 Changed = true; 5377 break; 5378 } 5379 if (RA.isMinSignedValue()) goto trivially_true; 5380 5381 Pred = ICmpInst::ICMP_SGT; 5382 RHS = getConstant(RA - 1); 5383 Changed = true; 5384 break; 5385 case ICmpInst::ICMP_SLE: 5386 if ((RA + 1).isMaxSignedValue()) { 5387 Pred = ICmpInst::ICMP_NE; 5388 RHS = getConstant(RA + 1); 5389 Changed = true; 5390 break; 5391 } 5392 if (RA.isMinSignedValue()) { 5393 Pred = ICmpInst::ICMP_EQ; 5394 Changed = true; 5395 break; 5396 } 5397 if (RA.isMaxSignedValue()) goto trivially_true; 5398 5399 Pred = ICmpInst::ICMP_SLT; 5400 RHS = getConstant(RA + 1); 5401 Changed = true; 5402 break; 5403 case ICmpInst::ICMP_UGT: 5404 if (RA.isMinValue()) { 5405 Pred = ICmpInst::ICMP_NE; 5406 Changed = true; 5407 break; 5408 } 5409 if ((RA + 1).isMaxValue()) { 5410 Pred = ICmpInst::ICMP_EQ; 5411 RHS = getConstant(RA + 1); 5412 Changed = true; 5413 break; 5414 } 5415 if (RA.isMaxValue()) goto trivially_false; 5416 break; 5417 case ICmpInst::ICMP_ULT: 5418 if (RA.isMaxValue()) { 5419 Pred = ICmpInst::ICMP_NE; 5420 Changed = true; 5421 break; 5422 } 5423 if ((RA - 1).isMinValue()) { 5424 Pred = ICmpInst::ICMP_EQ; 5425 RHS = getConstant(RA - 1); 5426 Changed = true; 5427 break; 5428 } 5429 if (RA.isMinValue()) goto trivially_false; 5430 break; 5431 case ICmpInst::ICMP_SGT: 5432 if (RA.isMinSignedValue()) { 5433 Pred = ICmpInst::ICMP_NE; 5434 Changed = true; 5435 break; 5436 } 5437 if ((RA + 1).isMaxSignedValue()) { 5438 Pred = ICmpInst::ICMP_EQ; 5439 RHS = getConstant(RA + 1); 5440 Changed = true; 5441 break; 5442 } 5443 if (RA.isMaxSignedValue()) goto trivially_false; 5444 break; 5445 case ICmpInst::ICMP_SLT: 5446 if (RA.isMaxSignedValue()) { 5447 Pred = ICmpInst::ICMP_NE; 5448 Changed = true; 5449 break; 5450 } 5451 if ((RA - 1).isMinSignedValue()) { 5452 Pred = ICmpInst::ICMP_EQ; 5453 RHS = getConstant(RA - 1); 5454 Changed = true; 5455 break; 5456 } 5457 if (RA.isMinSignedValue()) goto trivially_false; 5458 break; 5459 } 5460 } 5461 5462 // Check for obvious equality. 5463 if (HasSameValue(LHS, RHS)) { 5464 if (ICmpInst::isTrueWhenEqual(Pred)) 5465 goto trivially_true; 5466 if (ICmpInst::isFalseWhenEqual(Pred)) 5467 goto trivially_false; 5468 } 5469 5470 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5471 // adding or subtracting 1 from one of the operands. 5472 switch (Pred) { 5473 case ICmpInst::ICMP_SLE: 5474 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5475 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5476 SCEV::FlagNSW); 5477 Pred = ICmpInst::ICMP_SLT; 5478 Changed = true; 5479 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5480 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5481 SCEV::FlagNSW); 5482 Pred = ICmpInst::ICMP_SLT; 5483 Changed = true; 5484 } 5485 break; 5486 case ICmpInst::ICMP_SGE: 5487 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5488 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5489 SCEV::FlagNSW); 5490 Pred = ICmpInst::ICMP_SGT; 5491 Changed = true; 5492 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5493 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5494 SCEV::FlagNSW); 5495 Pred = ICmpInst::ICMP_SGT; 5496 Changed = true; 5497 } 5498 break; 5499 case ICmpInst::ICMP_ULE: 5500 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5501 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5502 SCEV::FlagNUW); 5503 Pred = ICmpInst::ICMP_ULT; 5504 Changed = true; 5505 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5506 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5507 SCEV::FlagNUW); 5508 Pred = ICmpInst::ICMP_ULT; 5509 Changed = true; 5510 } 5511 break; 5512 case ICmpInst::ICMP_UGE: 5513 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5514 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5515 SCEV::FlagNUW); 5516 Pred = ICmpInst::ICMP_UGT; 5517 Changed = true; 5518 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5519 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5520 SCEV::FlagNUW); 5521 Pred = ICmpInst::ICMP_UGT; 5522 Changed = true; 5523 } 5524 break; 5525 default: 5526 break; 5527 } 5528 5529 // TODO: More simplifications are possible here. 5530 5531 return Changed; 5532 5533trivially_true: 5534 // Return 0 == 0. 5535 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5536 Pred = ICmpInst::ICMP_EQ; 5537 return true; 5538 5539trivially_false: 5540 // Return 0 != 0. 5541 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5542 Pred = ICmpInst::ICMP_NE; 5543 return true; 5544} 5545 5546bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5547 return getSignedRange(S).getSignedMax().isNegative(); 5548} 5549 5550bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5551 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5552} 5553 5554bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5555 return !getSignedRange(S).getSignedMin().isNegative(); 5556} 5557 5558bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5559 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5560} 5561 5562bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5563 return isKnownNegative(S) || isKnownPositive(S); 5564} 5565 5566bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5567 const SCEV *LHS, const SCEV *RHS) { 5568 // Canonicalize the inputs first. 5569 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5570 5571 // If LHS or RHS is an addrec, check to see if the condition is true in 5572 // every iteration of the loop. 5573 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5574 if (isLoopEntryGuardedByCond( 5575 AR->getLoop(), Pred, AR->getStart(), RHS) && 5576 isLoopBackedgeGuardedByCond( 5577 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5578 return true; 5579 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5580 if (isLoopEntryGuardedByCond( 5581 AR->getLoop(), Pred, LHS, AR->getStart()) && 5582 isLoopBackedgeGuardedByCond( 5583 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5584 return true; 5585 5586 // Otherwise see what can be done with known constant ranges. 5587 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5588} 5589 5590bool 5591ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5592 const SCEV *LHS, const SCEV *RHS) { 5593 if (HasSameValue(LHS, RHS)) 5594 return ICmpInst::isTrueWhenEqual(Pred); 5595 5596 // This code is split out from isKnownPredicate because it is called from 5597 // within isLoopEntryGuardedByCond. 5598 switch (Pred) { 5599 default: 5600 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5601 break; 5602 case ICmpInst::ICMP_SGT: 5603 Pred = ICmpInst::ICMP_SLT; 5604 std::swap(LHS, RHS); 5605 case ICmpInst::ICMP_SLT: { 5606 ConstantRange LHSRange = getSignedRange(LHS); 5607 ConstantRange RHSRange = getSignedRange(RHS); 5608 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5609 return true; 5610 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5611 return false; 5612 break; 5613 } 5614 case ICmpInst::ICMP_SGE: 5615 Pred = ICmpInst::ICMP_SLE; 5616 std::swap(LHS, RHS); 5617 case ICmpInst::ICMP_SLE: { 5618 ConstantRange LHSRange = getSignedRange(LHS); 5619 ConstantRange RHSRange = getSignedRange(RHS); 5620 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5621 return true; 5622 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5623 return false; 5624 break; 5625 } 5626 case ICmpInst::ICMP_UGT: 5627 Pred = ICmpInst::ICMP_ULT; 5628 std::swap(LHS, RHS); 5629 case ICmpInst::ICMP_ULT: { 5630 ConstantRange LHSRange = getUnsignedRange(LHS); 5631 ConstantRange RHSRange = getUnsignedRange(RHS); 5632 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5633 return true; 5634 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5635 return false; 5636 break; 5637 } 5638 case ICmpInst::ICMP_UGE: 5639 Pred = ICmpInst::ICMP_ULE; 5640 std::swap(LHS, RHS); 5641 case ICmpInst::ICMP_ULE: { 5642 ConstantRange LHSRange = getUnsignedRange(LHS); 5643 ConstantRange RHSRange = getUnsignedRange(RHS); 5644 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5645 return true; 5646 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5647 return false; 5648 break; 5649 } 5650 case ICmpInst::ICMP_NE: { 5651 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5652 return true; 5653 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5654 return true; 5655 5656 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5657 if (isKnownNonZero(Diff)) 5658 return true; 5659 break; 5660 } 5661 case ICmpInst::ICMP_EQ: 5662 // The check at the top of the function catches the case where 5663 // the values are known to be equal. 5664 break; 5665 } 5666 return false; 5667} 5668 5669/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5670/// protected by a conditional between LHS and RHS. This is used to 5671/// to eliminate casts. 5672bool 5673ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5674 ICmpInst::Predicate Pred, 5675 const SCEV *LHS, const SCEV *RHS) { 5676 // Interpret a null as meaning no loop, where there is obviously no guard 5677 // (interprocedural conditions notwithstanding). 5678 if (!L) return true; 5679 5680 BasicBlock *Latch = L->getLoopLatch(); 5681 if (!Latch) 5682 return false; 5683 5684 BranchInst *LoopContinuePredicate = 5685 dyn_cast<BranchInst>(Latch->getTerminator()); 5686 if (!LoopContinuePredicate || 5687 LoopContinuePredicate->isUnconditional()) 5688 return false; 5689 5690 return isImpliedCond(Pred, LHS, RHS, 5691 LoopContinuePredicate->getCondition(), 5692 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 5693} 5694 5695/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 5696/// by a conditional between LHS and RHS. This is used to help avoid max 5697/// expressions in loop trip counts, and to eliminate casts. 5698bool 5699ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 5700 ICmpInst::Predicate Pred, 5701 const SCEV *LHS, const SCEV *RHS) { 5702 // Interpret a null as meaning no loop, where there is obviously no guard 5703 // (interprocedural conditions notwithstanding). 5704 if (!L) return false; 5705 5706 // Starting at the loop predecessor, climb up the predecessor chain, as long 5707 // as there are predecessors that can be found that have unique successors 5708 // leading to the original header. 5709 for (std::pair<BasicBlock *, BasicBlock *> 5710 Pair(L->getLoopPredecessor(), L->getHeader()); 5711 Pair.first; 5712 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 5713 5714 BranchInst *LoopEntryPredicate = 5715 dyn_cast<BranchInst>(Pair.first->getTerminator()); 5716 if (!LoopEntryPredicate || 5717 LoopEntryPredicate->isUnconditional()) 5718 continue; 5719 5720 if (isImpliedCond(Pred, LHS, RHS, 5721 LoopEntryPredicate->getCondition(), 5722 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 5723 return true; 5724 } 5725 5726 return false; 5727} 5728 5729/// isImpliedCond - Test whether the condition described by Pred, LHS, 5730/// and RHS is true whenever the given Cond value evaluates to true. 5731bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 5732 const SCEV *LHS, const SCEV *RHS, 5733 Value *FoundCondValue, 5734 bool Inverse) { 5735 // Recursively handle And and Or conditions. 5736 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 5737 if (BO->getOpcode() == Instruction::And) { 5738 if (!Inverse) 5739 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5740 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5741 } else if (BO->getOpcode() == Instruction::Or) { 5742 if (Inverse) 5743 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 5744 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 5745 } 5746 } 5747 5748 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 5749 if (!ICI) return false; 5750 5751 // Bail if the ICmp's operands' types are wider than the needed type 5752 // before attempting to call getSCEV on them. This avoids infinite 5753 // recursion, since the analysis of widening casts can require loop 5754 // exit condition information for overflow checking, which would 5755 // lead back here. 5756 if (getTypeSizeInBits(LHS->getType()) < 5757 getTypeSizeInBits(ICI->getOperand(0)->getType())) 5758 return false; 5759 5760 // Now that we found a conditional branch that dominates the loop, check to 5761 // see if it is the comparison we are looking for. 5762 ICmpInst::Predicate FoundPred; 5763 if (Inverse) 5764 FoundPred = ICI->getInversePredicate(); 5765 else 5766 FoundPred = ICI->getPredicate(); 5767 5768 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 5769 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 5770 5771 // Balance the types. The case where FoundLHS' type is wider than 5772 // LHS' type is checked for above. 5773 if (getTypeSizeInBits(LHS->getType()) > 5774 getTypeSizeInBits(FoundLHS->getType())) { 5775 if (CmpInst::isSigned(Pred)) { 5776 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 5777 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 5778 } else { 5779 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 5780 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 5781 } 5782 } 5783 5784 // Canonicalize the query to match the way instcombine will have 5785 // canonicalized the comparison. 5786 if (SimplifyICmpOperands(Pred, LHS, RHS)) 5787 if (LHS == RHS) 5788 return CmpInst::isTrueWhenEqual(Pred); 5789 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 5790 if (FoundLHS == FoundRHS) 5791 return CmpInst::isFalseWhenEqual(Pred); 5792 5793 // Check to see if we can make the LHS or RHS match. 5794 if (LHS == FoundRHS || RHS == FoundLHS) { 5795 if (isa<SCEVConstant>(RHS)) { 5796 std::swap(FoundLHS, FoundRHS); 5797 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 5798 } else { 5799 std::swap(LHS, RHS); 5800 Pred = ICmpInst::getSwappedPredicate(Pred); 5801 } 5802 } 5803 5804 // Check whether the found predicate is the same as the desired predicate. 5805 if (FoundPred == Pred) 5806 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 5807 5808 // Check whether swapping the found predicate makes it the same as the 5809 // desired predicate. 5810 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 5811 if (isa<SCEVConstant>(RHS)) 5812 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 5813 else 5814 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 5815 RHS, LHS, FoundLHS, FoundRHS); 5816 } 5817 5818 // Check whether the actual condition is beyond sufficient. 5819 if (FoundPred == ICmpInst::ICMP_EQ) 5820 if (ICmpInst::isTrueWhenEqual(Pred)) 5821 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 5822 return true; 5823 if (Pred == ICmpInst::ICMP_NE) 5824 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 5825 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 5826 return true; 5827 5828 // Otherwise assume the worst. 5829 return false; 5830} 5831 5832/// isImpliedCondOperands - Test whether the condition described by Pred, 5833/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 5834/// and FoundRHS is true. 5835bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 5836 const SCEV *LHS, const SCEV *RHS, 5837 const SCEV *FoundLHS, 5838 const SCEV *FoundRHS) { 5839 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 5840 FoundLHS, FoundRHS) || 5841 // ~x < ~y --> x > y 5842 isImpliedCondOperandsHelper(Pred, LHS, RHS, 5843 getNotSCEV(FoundRHS), 5844 getNotSCEV(FoundLHS)); 5845} 5846 5847/// isImpliedCondOperandsHelper - Test whether the condition described by 5848/// Pred, LHS, and RHS is true whenever the condition described by Pred, 5849/// FoundLHS, and FoundRHS is true. 5850bool 5851ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 5852 const SCEV *LHS, const SCEV *RHS, 5853 const SCEV *FoundLHS, 5854 const SCEV *FoundRHS) { 5855 switch (Pred) { 5856 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5857 case ICmpInst::ICMP_EQ: 5858 case ICmpInst::ICMP_NE: 5859 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 5860 return true; 5861 break; 5862 case ICmpInst::ICMP_SLT: 5863 case ICmpInst::ICMP_SLE: 5864 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 5865 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 5866 return true; 5867 break; 5868 case ICmpInst::ICMP_SGT: 5869 case ICmpInst::ICMP_SGE: 5870 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 5871 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 5872 return true; 5873 break; 5874 case ICmpInst::ICMP_ULT: 5875 case ICmpInst::ICMP_ULE: 5876 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 5877 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 5878 return true; 5879 break; 5880 case ICmpInst::ICMP_UGT: 5881 case ICmpInst::ICMP_UGE: 5882 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 5883 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 5884 return true; 5885 break; 5886 } 5887 5888 return false; 5889} 5890 5891/// getBECount - Subtract the end and start values and divide by the step, 5892/// rounding up, to get the number of times the backedge is executed. Return 5893/// CouldNotCompute if an intermediate computation overflows. 5894const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 5895 const SCEV *End, 5896 const SCEV *Step, 5897 bool NoWrap) { 5898 assert(!isKnownNegative(Step) && 5899 "This code doesn't handle negative strides yet!"); 5900 5901 Type *Ty = Start->getType(); 5902 5903 // When Start == End, we have an exact BECount == 0. Short-circuit this case 5904 // here because SCEV may not be able to determine that the unsigned division 5905 // after rounding is zero. 5906 if (Start == End) 5907 return getConstant(Ty, 0); 5908 5909 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 5910 const SCEV *Diff = getMinusSCEV(End, Start); 5911 const SCEV *RoundUp = getAddExpr(Step, NegOne); 5912 5913 // Add an adjustment to the difference between End and Start so that 5914 // the division will effectively round up. 5915 const SCEV *Add = getAddExpr(Diff, RoundUp); 5916 5917 if (!NoWrap) { 5918 // Check Add for unsigned overflow. 5919 // TODO: More sophisticated things could be done here. 5920 Type *WideTy = IntegerType::get(getContext(), 5921 getTypeSizeInBits(Ty) + 1); 5922 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 5923 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 5924 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 5925 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 5926 return getCouldNotCompute(); 5927 } 5928 5929 return getUDivExpr(Add, Step); 5930} 5931 5932/// HowManyLessThans - Return the number of times a backedge containing the 5933/// specified less-than comparison will execute. If not computable, return 5934/// CouldNotCompute. 5935ScalarEvolution::ExitLimit 5936ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 5937 const Loop *L, bool isSigned) { 5938 // Only handle: "ADDREC < LoopInvariant". 5939 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 5940 5941 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 5942 if (!AddRec || AddRec->getLoop() != L) 5943 return getCouldNotCompute(); 5944 5945 // Check to see if we have a flag which makes analysis easy. 5946 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) : 5947 AddRec->getNoWrapFlags(SCEV::FlagNUW); 5948 5949 if (AddRec->isAffine()) { 5950 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 5951 const SCEV *Step = AddRec->getStepRecurrence(*this); 5952 5953 if (Step->isZero()) 5954 return getCouldNotCompute(); 5955 if (Step->isOne()) { 5956 // With unit stride, the iteration never steps past the limit value. 5957 } else if (isKnownPositive(Step)) { 5958 // Test whether a positive iteration can step past the limit 5959 // value and past the maximum value for its type in a single step. 5960 // Note that it's not sufficient to check NoWrap here, because even 5961 // though the value after a wrap is undefined, it's not undefined 5962 // behavior, so if wrap does occur, the loop could either terminate or 5963 // loop infinitely, but in either case, the loop is guaranteed to 5964 // iterate at least until the iteration where the wrapping occurs. 5965 const SCEV *One = getConstant(Step->getType(), 1); 5966 if (isSigned) { 5967 APInt Max = APInt::getSignedMaxValue(BitWidth); 5968 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 5969 .slt(getSignedRange(RHS).getSignedMax())) 5970 return getCouldNotCompute(); 5971 } else { 5972 APInt Max = APInt::getMaxValue(BitWidth); 5973 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 5974 .ult(getUnsignedRange(RHS).getUnsignedMax())) 5975 return getCouldNotCompute(); 5976 } 5977 } else 5978 // TODO: Handle negative strides here and below. 5979 return getCouldNotCompute(); 5980 5981 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 5982 // m. So, we count the number of iterations in which {n,+,s} < m is true. 5983 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 5984 // treat m-n as signed nor unsigned due to overflow possibility. 5985 5986 // First, we get the value of the LHS in the first iteration: n 5987 const SCEV *Start = AddRec->getOperand(0); 5988 5989 // Determine the minimum constant start value. 5990 const SCEV *MinStart = getConstant(isSigned ? 5991 getSignedRange(Start).getSignedMin() : 5992 getUnsignedRange(Start).getUnsignedMin()); 5993 5994 // If we know that the condition is true in order to enter the loop, 5995 // then we know that it will run exactly (m-n)/s times. Otherwise, we 5996 // only know that it will execute (max(m,n)-n)/s times. In both cases, 5997 // the division must round up. 5998 const SCEV *End = RHS; 5999 if (!isLoopEntryGuardedByCond(L, 6000 isSigned ? ICmpInst::ICMP_SLT : 6001 ICmpInst::ICMP_ULT, 6002 getMinusSCEV(Start, Step), RHS)) 6003 End = isSigned ? getSMaxExpr(RHS, Start) 6004 : getUMaxExpr(RHS, Start); 6005 6006 // Determine the maximum constant end value. 6007 const SCEV *MaxEnd = getConstant(isSigned ? 6008 getSignedRange(End).getSignedMax() : 6009 getUnsignedRange(End).getUnsignedMax()); 6010 6011 // If MaxEnd is within a step of the maximum integer value in its type, 6012 // adjust it down to the minimum value which would produce the same effect. 6013 // This allows the subsequent ceiling division of (N+(step-1))/step to 6014 // compute the correct value. 6015 const SCEV *StepMinusOne = getMinusSCEV(Step, 6016 getConstant(Step->getType(), 1)); 6017 MaxEnd = isSigned ? 6018 getSMinExpr(MaxEnd, 6019 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 6020 StepMinusOne)) : 6021 getUMinExpr(MaxEnd, 6022 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 6023 StepMinusOne)); 6024 6025 // Finally, we subtract these two values and divide, rounding up, to get 6026 // the number of times the backedge is executed. 6027 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 6028 6029 // The maximum backedge count is similar, except using the minimum start 6030 // value and the maximum end value. 6031 // If we already have an exact constant BECount, use it instead. 6032 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 6033 : getBECount(MinStart, MaxEnd, Step, NoWrap); 6034 6035 // If the stride is nonconstant, and NoWrap == true, then 6036 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 6037 // exact BECount and invalid MaxBECount, which should be avoided to catch 6038 // more optimization opportunities. 6039 if (isa<SCEVCouldNotCompute>(MaxBECount)) 6040 MaxBECount = BECount; 6041 6042 return ExitLimit(BECount, MaxBECount); 6043 } 6044 6045 return getCouldNotCompute(); 6046} 6047 6048/// getNumIterationsInRange - Return the number of iterations of this loop that 6049/// produce values in the specified constant range. Another way of looking at 6050/// this is that it returns the first iteration number where the value is not in 6051/// the condition, thus computing the exit count. If the iteration count can't 6052/// be computed, an instance of SCEVCouldNotCompute is returned. 6053const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 6054 ScalarEvolution &SE) const { 6055 if (Range.isFullSet()) // Infinite loop. 6056 return SE.getCouldNotCompute(); 6057 6058 // If the start is a non-zero constant, shift the range to simplify things. 6059 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 6060 if (!SC->getValue()->isZero()) { 6061 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 6062 Operands[0] = SE.getConstant(SC->getType(), 0); 6063 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 6064 getNoWrapFlags(FlagNW)); 6065 if (const SCEVAddRecExpr *ShiftedAddRec = 6066 dyn_cast<SCEVAddRecExpr>(Shifted)) 6067 return ShiftedAddRec->getNumIterationsInRange( 6068 Range.subtract(SC->getValue()->getValue()), SE); 6069 // This is strange and shouldn't happen. 6070 return SE.getCouldNotCompute(); 6071 } 6072 6073 // The only time we can solve this is when we have all constant indices. 6074 // Otherwise, we cannot determine the overflow conditions. 6075 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 6076 if (!isa<SCEVConstant>(getOperand(i))) 6077 return SE.getCouldNotCompute(); 6078 6079 6080 // Okay at this point we know that all elements of the chrec are constants and 6081 // that the start element is zero. 6082 6083 // First check to see if the range contains zero. If not, the first 6084 // iteration exits. 6085 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6086 if (!Range.contains(APInt(BitWidth, 0))) 6087 return SE.getConstant(getType(), 0); 6088 6089 if (isAffine()) { 6090 // If this is an affine expression then we have this situation: 6091 // Solve {0,+,A} in Range === Ax in Range 6092 6093 // We know that zero is in the range. If A is positive then we know that 6094 // the upper value of the range must be the first possible exit value. 6095 // If A is negative then the lower of the range is the last possible loop 6096 // value. Also note that we already checked for a full range. 6097 APInt One(BitWidth,1); 6098 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6099 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6100 6101 // The exit value should be (End+A)/A. 6102 APInt ExitVal = (End + A).udiv(A); 6103 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6104 6105 // Evaluate at the exit value. If we really did fall out of the valid 6106 // range, then we computed our trip count, otherwise wrap around or other 6107 // things must have happened. 6108 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6109 if (Range.contains(Val->getValue())) 6110 return SE.getCouldNotCompute(); // Something strange happened 6111 6112 // Ensure that the previous value is in the range. This is a sanity check. 6113 assert(Range.contains( 6114 EvaluateConstantChrecAtConstant(this, 6115 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6116 "Linear scev computation is off in a bad way!"); 6117 return SE.getConstant(ExitValue); 6118 } else if (isQuadratic()) { 6119 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6120 // quadratic equation to solve it. To do this, we must frame our problem in 6121 // terms of figuring out when zero is crossed, instead of when 6122 // Range.getUpper() is crossed. 6123 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6124 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6125 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6126 // getNoWrapFlags(FlagNW) 6127 FlagAnyWrap); 6128 6129 // Next, solve the constructed addrec 6130 std::pair<const SCEV *,const SCEV *> Roots = 6131 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6132 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6133 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6134 if (R1) { 6135 // Pick the smallest positive root value. 6136 if (ConstantInt *CB = 6137 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6138 R1->getValue(), R2->getValue()))) { 6139 if (CB->getZExtValue() == false) 6140 std::swap(R1, R2); // R1 is the minimum root now. 6141 6142 // Make sure the root is not off by one. The returned iteration should 6143 // not be in the range, but the previous one should be. When solving 6144 // for "X*X < 5", for example, we should not return a root of 2. 6145 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6146 R1->getValue(), 6147 SE); 6148 if (Range.contains(R1Val->getValue())) { 6149 // The next iteration must be out of the range... 6150 ConstantInt *NextVal = 6151 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6152 6153 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6154 if (!Range.contains(R1Val->getValue())) 6155 return SE.getConstant(NextVal); 6156 return SE.getCouldNotCompute(); // Something strange happened 6157 } 6158 6159 // If R1 was not in the range, then it is a good return value. Make 6160 // sure that R1-1 WAS in the range though, just in case. 6161 ConstantInt *NextVal = 6162 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6163 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6164 if (Range.contains(R1Val->getValue())) 6165 return R1; 6166 return SE.getCouldNotCompute(); // Something strange happened 6167 } 6168 } 6169 } 6170 6171 return SE.getCouldNotCompute(); 6172} 6173 6174 6175 6176//===----------------------------------------------------------------------===// 6177// SCEVCallbackVH Class Implementation 6178//===----------------------------------------------------------------------===// 6179 6180void ScalarEvolution::SCEVCallbackVH::deleted() { 6181 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6182 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6183 SE->ConstantEvolutionLoopExitValue.erase(PN); 6184 SE->ValueExprMap.erase(getValPtr()); 6185 // this now dangles! 6186} 6187 6188void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6189 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6190 6191 // Forget all the expressions associated with users of the old value, 6192 // so that future queries will recompute the expressions using the new 6193 // value. 6194 Value *Old = getValPtr(); 6195 SmallVector<User *, 16> Worklist; 6196 SmallPtrSet<User *, 8> Visited; 6197 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6198 UI != UE; ++UI) 6199 Worklist.push_back(*UI); 6200 while (!Worklist.empty()) { 6201 User *U = Worklist.pop_back_val(); 6202 // Deleting the Old value will cause this to dangle. Postpone 6203 // that until everything else is done. 6204 if (U == Old) 6205 continue; 6206 if (!Visited.insert(U)) 6207 continue; 6208 if (PHINode *PN = dyn_cast<PHINode>(U)) 6209 SE->ConstantEvolutionLoopExitValue.erase(PN); 6210 SE->ValueExprMap.erase(U); 6211 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6212 UI != UE; ++UI) 6213 Worklist.push_back(*UI); 6214 } 6215 // Delete the Old value. 6216 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6217 SE->ConstantEvolutionLoopExitValue.erase(PN); 6218 SE->ValueExprMap.erase(Old); 6219 // this now dangles! 6220} 6221 6222ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6223 : CallbackVH(V), SE(se) {} 6224 6225//===----------------------------------------------------------------------===// 6226// ScalarEvolution Class Implementation 6227//===----------------------------------------------------------------------===// 6228 6229ScalarEvolution::ScalarEvolution() 6230 : FunctionPass(ID), FirstUnknown(0) { 6231 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6232} 6233 6234bool ScalarEvolution::runOnFunction(Function &F) { 6235 this->F = &F; 6236 LI = &getAnalysis<LoopInfo>(); 6237 TD = getAnalysisIfAvailable<TargetData>(); 6238 DT = &getAnalysis<DominatorTree>(); 6239 return false; 6240} 6241 6242void ScalarEvolution::releaseMemory() { 6243 // Iterate through all the SCEVUnknown instances and call their 6244 // destructors, so that they release their references to their values. 6245 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6246 U->~SCEVUnknown(); 6247 FirstUnknown = 0; 6248 6249 ValueExprMap.clear(); 6250 6251 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6252 // that a loop had multiple computable exits. 6253 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6254 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6255 I != E; ++I) { 6256 I->second.clear(); 6257 } 6258 6259 BackedgeTakenCounts.clear(); 6260 ConstantEvolutionLoopExitValue.clear(); 6261 ValuesAtScopes.clear(); 6262 LoopDispositions.clear(); 6263 BlockDispositions.clear(); 6264 UnsignedRanges.clear(); 6265 SignedRanges.clear(); 6266 UniqueSCEVs.clear(); 6267 SCEVAllocator.Reset(); 6268} 6269 6270void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6271 AU.setPreservesAll(); 6272 AU.addRequiredTransitive<LoopInfo>(); 6273 AU.addRequiredTransitive<DominatorTree>(); 6274} 6275 6276bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6277 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6278} 6279 6280static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6281 const Loop *L) { 6282 // Print all inner loops first 6283 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6284 PrintLoopInfo(OS, SE, *I); 6285 6286 OS << "Loop "; 6287 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6288 OS << ": "; 6289 6290 SmallVector<BasicBlock *, 8> ExitBlocks; 6291 L->getExitBlocks(ExitBlocks); 6292 if (ExitBlocks.size() != 1) 6293 OS << "<multiple exits> "; 6294 6295 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6296 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6297 } else { 6298 OS << "Unpredictable backedge-taken count. "; 6299 } 6300 6301 OS << "\n" 6302 "Loop "; 6303 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6304 OS << ": "; 6305 6306 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6307 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6308 } else { 6309 OS << "Unpredictable max backedge-taken count. "; 6310 } 6311 6312 OS << "\n"; 6313} 6314 6315void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6316 // ScalarEvolution's implementation of the print method is to print 6317 // out SCEV values of all instructions that are interesting. Doing 6318 // this potentially causes it to create new SCEV objects though, 6319 // which technically conflicts with the const qualifier. This isn't 6320 // observable from outside the class though, so casting away the 6321 // const isn't dangerous. 6322 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6323 6324 OS << "Classifying expressions for: "; 6325 WriteAsOperand(OS, F, /*PrintType=*/false); 6326 OS << "\n"; 6327 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6328 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6329 OS << *I << '\n'; 6330 OS << " --> "; 6331 const SCEV *SV = SE.getSCEV(&*I); 6332 SV->print(OS); 6333 6334 const Loop *L = LI->getLoopFor((*I).getParent()); 6335 6336 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6337 if (AtUse != SV) { 6338 OS << " --> "; 6339 AtUse->print(OS); 6340 } 6341 6342 if (L) { 6343 OS << "\t\t" "Exits: "; 6344 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6345 if (!SE.isLoopInvariant(ExitValue, L)) { 6346 OS << "<<Unknown>>"; 6347 } else { 6348 OS << *ExitValue; 6349 } 6350 } 6351 6352 OS << "\n"; 6353 } 6354 6355 OS << "Determining loop execution counts for: "; 6356 WriteAsOperand(OS, F, /*PrintType=*/false); 6357 OS << "\n"; 6358 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6359 PrintLoopInfo(OS, &SE, *I); 6360} 6361 6362ScalarEvolution::LoopDisposition 6363ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6364 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6365 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6366 Values.insert(std::make_pair(L, LoopVariant)); 6367 if (!Pair.second) 6368 return Pair.first->second; 6369 6370 LoopDisposition D = computeLoopDisposition(S, L); 6371 return LoopDispositions[S][L] = D; 6372} 6373 6374ScalarEvolution::LoopDisposition 6375ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6376 switch (S->getSCEVType()) { 6377 case scConstant: 6378 return LoopInvariant; 6379 case scTruncate: 6380 case scZeroExtend: 6381 case scSignExtend: 6382 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6383 case scAddRecExpr: { 6384 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6385 6386 // If L is the addrec's loop, it's computable. 6387 if (AR->getLoop() == L) 6388 return LoopComputable; 6389 6390 // Add recurrences are never invariant in the function-body (null loop). 6391 if (!L) 6392 return LoopVariant; 6393 6394 // This recurrence is variant w.r.t. L if L contains AR's loop. 6395 if (L->contains(AR->getLoop())) 6396 return LoopVariant; 6397 6398 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6399 if (AR->getLoop()->contains(L)) 6400 return LoopInvariant; 6401 6402 // This recurrence is variant w.r.t. L if any of its operands 6403 // are variant. 6404 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6405 I != E; ++I) 6406 if (!isLoopInvariant(*I, L)) 6407 return LoopVariant; 6408 6409 // Otherwise it's loop-invariant. 6410 return LoopInvariant; 6411 } 6412 case scAddExpr: 6413 case scMulExpr: 6414 case scUMaxExpr: 6415 case scSMaxExpr: { 6416 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6417 bool HasVarying = false; 6418 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6419 I != E; ++I) { 6420 LoopDisposition D = getLoopDisposition(*I, L); 6421 if (D == LoopVariant) 6422 return LoopVariant; 6423 if (D == LoopComputable) 6424 HasVarying = true; 6425 } 6426 return HasVarying ? LoopComputable : LoopInvariant; 6427 } 6428 case scUDivExpr: { 6429 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6430 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6431 if (LD == LoopVariant) 6432 return LoopVariant; 6433 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6434 if (RD == LoopVariant) 6435 return LoopVariant; 6436 return (LD == LoopInvariant && RD == LoopInvariant) ? 6437 LoopInvariant : LoopComputable; 6438 } 6439 case scUnknown: 6440 // All non-instruction values are loop invariant. All instructions are loop 6441 // invariant if they are not contained in the specified loop. 6442 // Instructions are never considered invariant in the function body 6443 // (null loop) because they are defined within the "loop". 6444 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6445 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6446 return LoopInvariant; 6447 case scCouldNotCompute: 6448 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6449 return LoopVariant; 6450 default: break; 6451 } 6452 llvm_unreachable("Unknown SCEV kind!"); 6453 return LoopVariant; 6454} 6455 6456bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6457 return getLoopDisposition(S, L) == LoopInvariant; 6458} 6459 6460bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6461 return getLoopDisposition(S, L) == LoopComputable; 6462} 6463 6464ScalarEvolution::BlockDisposition 6465ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6466 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6467 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6468 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6469 if (!Pair.second) 6470 return Pair.first->second; 6471 6472 BlockDisposition D = computeBlockDisposition(S, BB); 6473 return BlockDispositions[S][BB] = D; 6474} 6475 6476ScalarEvolution::BlockDisposition 6477ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6478 switch (S->getSCEVType()) { 6479 case scConstant: 6480 return ProperlyDominatesBlock; 6481 case scTruncate: 6482 case scZeroExtend: 6483 case scSignExtend: 6484 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6485 case scAddRecExpr: { 6486 // This uses a "dominates" query instead of "properly dominates" query 6487 // to test for proper dominance too, because the instruction which 6488 // produces the addrec's value is a PHI, and a PHI effectively properly 6489 // dominates its entire containing block. 6490 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6491 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6492 return DoesNotDominateBlock; 6493 } 6494 // FALL THROUGH into SCEVNAryExpr handling. 6495 case scAddExpr: 6496 case scMulExpr: 6497 case scUMaxExpr: 6498 case scSMaxExpr: { 6499 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6500 bool Proper = true; 6501 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6502 I != E; ++I) { 6503 BlockDisposition D = getBlockDisposition(*I, BB); 6504 if (D == DoesNotDominateBlock) 6505 return DoesNotDominateBlock; 6506 if (D == DominatesBlock) 6507 Proper = false; 6508 } 6509 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6510 } 6511 case scUDivExpr: { 6512 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6513 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6514 BlockDisposition LD = getBlockDisposition(LHS, BB); 6515 if (LD == DoesNotDominateBlock) 6516 return DoesNotDominateBlock; 6517 BlockDisposition RD = getBlockDisposition(RHS, BB); 6518 if (RD == DoesNotDominateBlock) 6519 return DoesNotDominateBlock; 6520 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6521 ProperlyDominatesBlock : DominatesBlock; 6522 } 6523 case scUnknown: 6524 if (Instruction *I = 6525 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6526 if (I->getParent() == BB) 6527 return DominatesBlock; 6528 if (DT->properlyDominates(I->getParent(), BB)) 6529 return ProperlyDominatesBlock; 6530 return DoesNotDominateBlock; 6531 } 6532 return ProperlyDominatesBlock; 6533 case scCouldNotCompute: 6534 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6535 return DoesNotDominateBlock; 6536 default: break; 6537 } 6538 llvm_unreachable("Unknown SCEV kind!"); 6539 return DoesNotDominateBlock; 6540} 6541 6542bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6543 return getBlockDisposition(S, BB) >= DominatesBlock; 6544} 6545 6546bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6547 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6548} 6549 6550bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6551 switch (S->getSCEVType()) { 6552 case scConstant: 6553 return false; 6554 case scTruncate: 6555 case scZeroExtend: 6556 case scSignExtend: { 6557 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6558 const SCEV *CastOp = Cast->getOperand(); 6559 return Op == CastOp || hasOperand(CastOp, Op); 6560 } 6561 case scAddRecExpr: 6562 case scAddExpr: 6563 case scMulExpr: 6564 case scUMaxExpr: 6565 case scSMaxExpr: { 6566 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6567 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6568 I != E; ++I) { 6569 const SCEV *NAryOp = *I; 6570 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6571 return true; 6572 } 6573 return false; 6574 } 6575 case scUDivExpr: { 6576 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6577 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6578 return LHS == Op || hasOperand(LHS, Op) || 6579 RHS == Op || hasOperand(RHS, Op); 6580 } 6581 case scUnknown: 6582 return false; 6583 case scCouldNotCompute: 6584 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6585 return false; 6586 default: break; 6587 } 6588 llvm_unreachable("Unknown SCEV kind!"); 6589 return false; 6590} 6591 6592void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6593 ValuesAtScopes.erase(S); 6594 LoopDispositions.erase(S); 6595 BlockDispositions.erase(S); 6596 UnsignedRanges.erase(S); 6597 SignedRanges.erase(S); 6598} 6599