ScalarEvolution.cpp revision ecb35ece5c42d89057da3c2c7bc2e95f08b1dbef
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 switch (NAry->getSCEVType()) { 192 case scAddExpr: 193 case scMulExpr: 194 if (NAry->getNoWrapFlags(FlagNUW)) 195 OS << "<nuw>"; 196 if (NAry->getNoWrapFlags(FlagNSW)) 197 OS << "<nsw>"; 198 } 199 return; 200 } 201 case scUDivExpr: { 202 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); 203 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; 204 return; 205 } 206 case scUnknown: { 207 const SCEVUnknown *U = cast<SCEVUnknown>(this); 208 Type *AllocTy; 209 if (U->isSizeOf(AllocTy)) { 210 OS << "sizeof(" << *AllocTy << ")"; 211 return; 212 } 213 if (U->isAlignOf(AllocTy)) { 214 OS << "alignof(" << *AllocTy << ")"; 215 return; 216 } 217 218 Type *CTy; 219 Constant *FieldNo; 220 if (U->isOffsetOf(CTy, FieldNo)) { 221 OS << "offsetof(" << *CTy << ", "; 222 WriteAsOperand(OS, FieldNo, false); 223 OS << ")"; 224 return; 225 } 226 227 // Otherwise just print it normally. 228 WriteAsOperand(OS, U->getValue(), false); 229 return; 230 } 231 case scCouldNotCompute: 232 OS << "***COULDNOTCOMPUTE***"; 233 return; 234 default: break; 235 } 236 llvm_unreachable("Unknown SCEV kind!"); 237} 238 239Type *SCEV::getType() const { 240 switch (getSCEVType()) { 241 case scConstant: 242 return cast<SCEVConstant>(this)->getType(); 243 case scTruncate: 244 case scZeroExtend: 245 case scSignExtend: 246 return cast<SCEVCastExpr>(this)->getType(); 247 case scAddRecExpr: 248 case scMulExpr: 249 case scUMaxExpr: 250 case scSMaxExpr: 251 return cast<SCEVNAryExpr>(this)->getType(); 252 case scAddExpr: 253 return cast<SCEVAddExpr>(this)->getType(); 254 case scUDivExpr: 255 return cast<SCEVUDivExpr>(this)->getType(); 256 case scUnknown: 257 return cast<SCEVUnknown>(this)->getType(); 258 case scCouldNotCompute: 259 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 260 return 0; 261 default: break; 262 } 263 llvm_unreachable("Unknown SCEV kind!"); 264 return 0; 265} 266 267bool SCEV::isZero() const { 268 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 269 return SC->getValue()->isZero(); 270 return false; 271} 272 273bool SCEV::isOne() const { 274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 275 return SC->getValue()->isOne(); 276 return false; 277} 278 279bool SCEV::isAllOnesValue() const { 280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) 281 return SC->getValue()->isAllOnesValue(); 282 return false; 283} 284 285SCEVCouldNotCompute::SCEVCouldNotCompute() : 286 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 287 288bool SCEVCouldNotCompute::classof(const SCEV *S) { 289 return S->getSCEVType() == scCouldNotCompute; 290} 291 292const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { 293 FoldingSetNodeID ID; 294 ID.AddInteger(scConstant); 295 ID.AddPointer(V); 296 void *IP = 0; 297 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 298 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); 299 UniqueSCEVs.InsertNode(S, IP); 300 return S; 301} 302 303const SCEV *ScalarEvolution::getConstant(const APInt& Val) { 304 return getConstant(ConstantInt::get(getContext(), Val)); 305} 306 307const SCEV * 308ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) { 309 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); 310 return getConstant(ConstantInt::get(ITy, V, isSigned)); 311} 312 313SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, 314 unsigned SCEVTy, const SCEV *op, Type *ty) 315 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} 316 317SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, 318 const SCEV *op, Type *ty) 319 : SCEVCastExpr(ID, scTruncate, op, ty) { 320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 321 (Ty->isIntegerTy() || Ty->isPointerTy()) && 322 "Cannot truncate non-integer value!"); 323} 324 325SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, 326 const SCEV *op, Type *ty) 327 : SCEVCastExpr(ID, scZeroExtend, op, ty) { 328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 329 (Ty->isIntegerTy() || Ty->isPointerTy()) && 330 "Cannot zero extend non-integer value!"); 331} 332 333SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, 334 const SCEV *op, Type *ty) 335 : SCEVCastExpr(ID, scSignExtend, op, ty) { 336 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && 337 (Ty->isIntegerTy() || Ty->isPointerTy()) && 338 "Cannot sign extend non-integer value!"); 339} 340 341void SCEVUnknown::deleted() { 342 // Clear this SCEVUnknown from various maps. 343 SE->forgetMemoizedResults(this); 344 345 // Remove this SCEVUnknown from the uniquing map. 346 SE->UniqueSCEVs.RemoveNode(this); 347 348 // Release the value. 349 setValPtr(0); 350} 351 352void SCEVUnknown::allUsesReplacedWith(Value *New) { 353 // Clear this SCEVUnknown from various maps. 354 SE->forgetMemoizedResults(this); 355 356 // Remove this SCEVUnknown from the uniquing map. 357 SE->UniqueSCEVs.RemoveNode(this); 358 359 // Update this SCEVUnknown to point to the new value. This is needed 360 // because there may still be outstanding SCEVs which still point to 361 // this SCEVUnknown. 362 setValPtr(New); 363} 364 365bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { 366 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 367 if (VCE->getOpcode() == Instruction::PtrToInt) 368 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 369 if (CE->getOpcode() == Instruction::GetElementPtr && 370 CE->getOperand(0)->isNullValue() && 371 CE->getNumOperands() == 2) 372 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) 373 if (CI->isOne()) { 374 AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) 375 ->getElementType(); 376 return true; 377 } 378 379 return false; 380} 381 382bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { 383 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 384 if (VCE->getOpcode() == Instruction::PtrToInt) 385 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 386 if (CE->getOpcode() == Instruction::GetElementPtr && 387 CE->getOperand(0)->isNullValue()) { 388 Type *Ty = 389 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 390 if (StructType *STy = dyn_cast<StructType>(Ty)) 391 if (!STy->isPacked() && 392 CE->getNumOperands() == 3 && 393 CE->getOperand(1)->isNullValue()) { 394 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) 395 if (CI->isOne() && 396 STy->getNumElements() == 2 && 397 STy->getElementType(0)->isIntegerTy(1)) { 398 AllocTy = STy->getElementType(1); 399 return true; 400 } 401 } 402 } 403 404 return false; 405} 406 407bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { 408 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) 409 if (VCE->getOpcode() == Instruction::PtrToInt) 410 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) 411 if (CE->getOpcode() == Instruction::GetElementPtr && 412 CE->getNumOperands() == 3 && 413 CE->getOperand(0)->isNullValue() && 414 CE->getOperand(1)->isNullValue()) { 415 Type *Ty = 416 cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); 417 // Ignore vector types here so that ScalarEvolutionExpander doesn't 418 // emit getelementptrs that index into vectors. 419 if (Ty->isStructTy() || Ty->isArrayTy()) { 420 CTy = Ty; 421 FieldNo = CE->getOperand(2); 422 return true; 423 } 424 } 425 426 return false; 427} 428 429//===----------------------------------------------------------------------===// 430// SCEV Utilities 431//===----------------------------------------------------------------------===// 432 433namespace { 434 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less 435 /// than the complexity of the RHS. This comparator is used to canonicalize 436 /// expressions. 437 class SCEVComplexityCompare { 438 const LoopInfo *const LI; 439 public: 440 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} 441 442 // Return true or false if LHS is less than, or at least RHS, respectively. 443 bool operator()(const SCEV *LHS, const SCEV *RHS) const { 444 return compare(LHS, RHS) < 0; 445 } 446 447 // Return negative, zero, or positive, if LHS is less than, equal to, or 448 // greater than RHS, respectively. A three-way result allows recursive 449 // comparisons to be more efficient. 450 int compare(const SCEV *LHS, const SCEV *RHS) const { 451 // Fast-path: SCEVs are uniqued so we can do a quick equality check. 452 if (LHS == RHS) 453 return 0; 454 455 // Primarily, sort the SCEVs by their getSCEVType(). 456 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); 457 if (LType != RType) 458 return (int)LType - (int)RType; 459 460 // Aside from the getSCEVType() ordering, the particular ordering 461 // isn't very important except that it's beneficial to be consistent, 462 // so that (a + b) and (b + a) don't end up as different expressions. 463 switch (LType) { 464 case scUnknown: { 465 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); 466 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); 467 468 // Sort SCEVUnknown values with some loose heuristics. TODO: This is 469 // not as complete as it could be. 470 const Value *LV = LU->getValue(), *RV = RU->getValue(); 471 472 // Order pointer values after integer values. This helps SCEVExpander 473 // form GEPs. 474 bool LIsPointer = LV->getType()->isPointerTy(), 475 RIsPointer = RV->getType()->isPointerTy(); 476 if (LIsPointer != RIsPointer) 477 return (int)LIsPointer - (int)RIsPointer; 478 479 // Compare getValueID values. 480 unsigned LID = LV->getValueID(), 481 RID = RV->getValueID(); 482 if (LID != RID) 483 return (int)LID - (int)RID; 484 485 // Sort arguments by their position. 486 if (const Argument *LA = dyn_cast<Argument>(LV)) { 487 const Argument *RA = cast<Argument>(RV); 488 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); 489 return (int)LArgNo - (int)RArgNo; 490 } 491 492 // For instructions, compare their loop depth, and their operand 493 // count. This is pretty loose. 494 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) { 495 const Instruction *RInst = cast<Instruction>(RV); 496 497 // Compare loop depths. 498 const BasicBlock *LParent = LInst->getParent(), 499 *RParent = RInst->getParent(); 500 if (LParent != RParent) { 501 unsigned LDepth = LI->getLoopDepth(LParent), 502 RDepth = LI->getLoopDepth(RParent); 503 if (LDepth != RDepth) 504 return (int)LDepth - (int)RDepth; 505 } 506 507 // Compare the number of operands. 508 unsigned LNumOps = LInst->getNumOperands(), 509 RNumOps = RInst->getNumOperands(); 510 return (int)LNumOps - (int)RNumOps; 511 } 512 513 return 0; 514 } 515 516 case scConstant: { 517 const SCEVConstant *LC = cast<SCEVConstant>(LHS); 518 const SCEVConstant *RC = cast<SCEVConstant>(RHS); 519 520 // Compare constant values. 521 const APInt &LA = LC->getValue()->getValue(); 522 const APInt &RA = RC->getValue()->getValue(); 523 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); 524 if (LBitWidth != RBitWidth) 525 return (int)LBitWidth - (int)RBitWidth; 526 return LA.ult(RA) ? -1 : 1; 527 } 528 529 case scAddRecExpr: { 530 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS); 531 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); 532 533 // Compare addrec loop depths. 534 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); 535 if (LLoop != RLoop) { 536 unsigned LDepth = LLoop->getLoopDepth(), 537 RDepth = RLoop->getLoopDepth(); 538 if (LDepth != RDepth) 539 return (int)LDepth - (int)RDepth; 540 } 541 542 // Addrec complexity grows with operand count. 543 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); 544 if (LNumOps != RNumOps) 545 return (int)LNumOps - (int)RNumOps; 546 547 // Lexicographically compare. 548 for (unsigned i = 0; i != LNumOps; ++i) { 549 long X = compare(LA->getOperand(i), RA->getOperand(i)); 550 if (X != 0) 551 return X; 552 } 553 554 return 0; 555 } 556 557 case scAddExpr: 558 case scMulExpr: 559 case scSMaxExpr: 560 case scUMaxExpr: { 561 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS); 562 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); 563 564 // Lexicographically compare n-ary expressions. 565 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); 566 for (unsigned i = 0; i != LNumOps; ++i) { 567 if (i >= RNumOps) 568 return 1; 569 long X = compare(LC->getOperand(i), RC->getOperand(i)); 570 if (X != 0) 571 return X; 572 } 573 return (int)LNumOps - (int)RNumOps; 574 } 575 576 case scUDivExpr: { 577 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS); 578 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); 579 580 // Lexicographically compare udiv expressions. 581 long X = compare(LC->getLHS(), RC->getLHS()); 582 if (X != 0) 583 return X; 584 return compare(LC->getRHS(), RC->getRHS()); 585 } 586 587 case scTruncate: 588 case scZeroExtend: 589 case scSignExtend: { 590 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); 591 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); 592 593 // Compare cast expressions by operand. 594 return compare(LC->getOperand(), RC->getOperand()); 595 } 596 597 default: 598 break; 599 } 600 601 llvm_unreachable("Unknown SCEV kind!"); 602 return 0; 603 } 604 }; 605} 606 607/// GroupByComplexity - Given a list of SCEV objects, order them by their 608/// complexity, and group objects of the same complexity together by value. 609/// When this routine is finished, we know that any duplicates in the vector are 610/// consecutive and that complexity is monotonically increasing. 611/// 612/// Note that we go take special precautions to ensure that we get deterministic 613/// results from this routine. In other words, we don't want the results of 614/// this to depend on where the addresses of various SCEV objects happened to 615/// land in memory. 616/// 617static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, 618 LoopInfo *LI) { 619 if (Ops.size() < 2) return; // Noop 620 if (Ops.size() == 2) { 621 // This is the common case, which also happens to be trivially simple. 622 // Special case it. 623 const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; 624 if (SCEVComplexityCompare(LI)(RHS, LHS)) 625 std::swap(LHS, RHS); 626 return; 627 } 628 629 // Do the rough sort by complexity. 630 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); 631 632 // Now that we are sorted by complexity, group elements of the same 633 // complexity. Note that this is, at worst, N^2, but the vector is likely to 634 // be extremely short in practice. Note that we take this approach because we 635 // do not want to depend on the addresses of the objects we are grouping. 636 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { 637 const SCEV *S = Ops[i]; 638 unsigned Complexity = S->getSCEVType(); 639 640 // If there are any objects of the same complexity and same value as this 641 // one, group them. 642 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { 643 if (Ops[j] == S) { // Found a duplicate. 644 // Move it to immediately after i'th element. 645 std::swap(Ops[i+1], Ops[j]); 646 ++i; // no need to rescan it. 647 if (i == e-2) return; // Done! 648 } 649 } 650 } 651} 652 653 654 655//===----------------------------------------------------------------------===// 656// Simple SCEV method implementations 657//===----------------------------------------------------------------------===// 658 659/// BinomialCoefficient - Compute BC(It, K). The result has width W. 660/// Assume, K > 0. 661static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, 662 ScalarEvolution &SE, 663 Type *ResultTy) { 664 // Handle the simplest case efficiently. 665 if (K == 1) 666 return SE.getTruncateOrZeroExtend(It, ResultTy); 667 668 // We are using the following formula for BC(It, K): 669 // 670 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! 671 // 672 // Suppose, W is the bitwidth of the return value. We must be prepared for 673 // overflow. Hence, we must assure that the result of our computation is 674 // equal to the accurate one modulo 2^W. Unfortunately, division isn't 675 // safe in modular arithmetic. 676 // 677 // However, this code doesn't use exactly that formula; the formula it uses 678 // is something like the following, where T is the number of factors of 2 in 679 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is 680 // exponentiation: 681 // 682 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) 683 // 684 // This formula is trivially equivalent to the previous formula. However, 685 // this formula can be implemented much more efficiently. The trick is that 686 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular 687 // arithmetic. To do exact division in modular arithmetic, all we have 688 // to do is multiply by the inverse. Therefore, this step can be done at 689 // width W. 690 // 691 // The next issue is how to safely do the division by 2^T. The way this 692 // is done is by doing the multiplication step at a width of at least W + T 693 // bits. This way, the bottom W+T bits of the product are accurate. Then, 694 // when we perform the division by 2^T (which is equivalent to a right shift 695 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get 696 // truncated out after the division by 2^T. 697 // 698 // In comparison to just directly using the first formula, this technique 699 // is much more efficient; using the first formula requires W * K bits, 700 // but this formula less than W + K bits. Also, the first formula requires 701 // a division step, whereas this formula only requires multiplies and shifts. 702 // 703 // It doesn't matter whether the subtraction step is done in the calculation 704 // width or the input iteration count's width; if the subtraction overflows, 705 // the result must be zero anyway. We prefer here to do it in the width of 706 // the induction variable because it helps a lot for certain cases; CodeGen 707 // isn't smart enough to ignore the overflow, which leads to much less 708 // efficient code if the width of the subtraction is wider than the native 709 // register width. 710 // 711 // (It's possible to not widen at all by pulling out factors of 2 before 712 // the multiplication; for example, K=2 can be calculated as 713 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires 714 // extra arithmetic, so it's not an obvious win, and it gets 715 // much more complicated for K > 3.) 716 717 // Protection from insane SCEVs; this bound is conservative, 718 // but it probably doesn't matter. 719 if (K > 1000) 720 return SE.getCouldNotCompute(); 721 722 unsigned W = SE.getTypeSizeInBits(ResultTy); 723 724 // Calculate K! / 2^T and T; we divide out the factors of two before 725 // multiplying for calculating K! / 2^T to avoid overflow. 726 // Other overflow doesn't matter because we only care about the bottom 727 // W bits of the result. 728 APInt OddFactorial(W, 1); 729 unsigned T = 1; 730 for (unsigned i = 3; i <= K; ++i) { 731 APInt Mult(W, i); 732 unsigned TwoFactors = Mult.countTrailingZeros(); 733 T += TwoFactors; 734 Mult = Mult.lshr(TwoFactors); 735 OddFactorial *= Mult; 736 } 737 738 // We need at least W + T bits for the multiplication step 739 unsigned CalculationBits = W + T; 740 741 // Calculate 2^T, at width T+W. 742 APInt DivFactor = APInt(CalculationBits, 1).shl(T); 743 744 // Calculate the multiplicative inverse of K! / 2^T; 745 // this multiplication factor will perform the exact division by 746 // K! / 2^T. 747 APInt Mod = APInt::getSignedMinValue(W+1); 748 APInt MultiplyFactor = OddFactorial.zext(W+1); 749 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); 750 MultiplyFactor = MultiplyFactor.trunc(W); 751 752 // Calculate the product, at width T+W 753 IntegerType *CalculationTy = IntegerType::get(SE.getContext(), 754 CalculationBits); 755 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); 756 for (unsigned i = 1; i != K; ++i) { 757 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); 758 Dividend = SE.getMulExpr(Dividend, 759 SE.getTruncateOrZeroExtend(S, CalculationTy)); 760 } 761 762 // Divide by 2^T 763 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); 764 765 // Truncate the result, and divide by K! / 2^T. 766 767 return SE.getMulExpr(SE.getConstant(MultiplyFactor), 768 SE.getTruncateOrZeroExtend(DivResult, ResultTy)); 769} 770 771/// evaluateAtIteration - Return the value of this chain of recurrences at 772/// the specified iteration number. We can evaluate this recurrence by 773/// multiplying each element in the chain by the binomial coefficient 774/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: 775/// 776/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) 777/// 778/// where BC(It, k) stands for binomial coefficient. 779/// 780const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, 781 ScalarEvolution &SE) const { 782 const SCEV *Result = getStart(); 783 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { 784 // The computation is correct in the face of overflow provided that the 785 // multiplication is performed _after_ the evaluation of the binomial 786 // coefficient. 787 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); 788 if (isa<SCEVCouldNotCompute>(Coeff)) 789 return Coeff; 790 791 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); 792 } 793 return Result; 794} 795 796//===----------------------------------------------------------------------===// 797// SCEV Expression folder implementations 798//===----------------------------------------------------------------------===// 799 800const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 801 Type *Ty) { 802 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && 803 "This is not a truncating conversion!"); 804 assert(isSCEVable(Ty) && 805 "This is not a conversion to a SCEVable type!"); 806 Ty = getEffectiveSCEVType(Ty); 807 808 FoldingSetNodeID ID; 809 ID.AddInteger(scTruncate); 810 ID.AddPointer(Op); 811 ID.AddPointer(Ty); 812 void *IP = 0; 813 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 814 815 // Fold if the operand is constant. 816 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 817 return getConstant( 818 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), 819 getEffectiveSCEVType(Ty)))); 820 821 // trunc(trunc(x)) --> trunc(x) 822 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) 823 return getTruncateExpr(ST->getOperand(), Ty); 824 825 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing 826 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 827 return getTruncateOrSignExtend(SS->getOperand(), Ty); 828 829 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing 830 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 831 return getTruncateOrZeroExtend(SZ->getOperand(), Ty); 832 833 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can 834 // eliminate all the truncates. 835 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) { 836 SmallVector<const SCEV *, 4> Operands; 837 bool hasTrunc = false; 838 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { 839 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); 840 hasTrunc = isa<SCEVTruncateExpr>(S); 841 Operands.push_back(S); 842 } 843 if (!hasTrunc) 844 return getAddExpr(Operands); 845 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 846 } 847 848 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can 849 // eliminate all the truncates. 850 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) { 851 SmallVector<const SCEV *, 4> Operands; 852 bool hasTrunc = false; 853 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { 854 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); 855 hasTrunc = isa<SCEVTruncateExpr>(S); 856 Operands.push_back(S); 857 } 858 if (!hasTrunc) 859 return getMulExpr(Operands); 860 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. 861 } 862 863 // If the input value is a chrec scev, truncate the chrec's operands. 864 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { 865 SmallVector<const SCEV *, 4> Operands; 866 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 867 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); 868 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); 869 } 870 871 // As a special case, fold trunc(undef) to undef. We don't want to 872 // know too much about SCEVUnknowns, but this special case is handy 873 // and harmless. 874 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 875 if (isa<UndefValue>(U->getValue())) 876 return getSCEV(UndefValue::get(Ty)); 877 878 // The cast wasn't folded; create an explicit cast node. We can reuse 879 // the existing insert position since if we get here, we won't have 880 // made any changes which would invalidate it. 881 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), 882 Op, Ty); 883 UniqueSCEVs.InsertNode(S, IP); 884 return S; 885} 886 887const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 888 Type *Ty) { 889 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 890 "This is not an extending conversion!"); 891 assert(isSCEVable(Ty) && 892 "This is not a conversion to a SCEVable type!"); 893 Ty = getEffectiveSCEVType(Ty); 894 895 // Fold if the operand is constant. 896 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 897 return getConstant( 898 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), 899 getEffectiveSCEVType(Ty)))); 900 901 // zext(zext(x)) --> zext(x) 902 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 903 return getZeroExtendExpr(SZ->getOperand(), Ty); 904 905 // Before doing any expensive analysis, check to see if we've already 906 // computed a SCEV for this Op and Ty. 907 FoldingSetNodeID ID; 908 ID.AddInteger(scZeroExtend); 909 ID.AddPointer(Op); 910 ID.AddPointer(Ty); 911 void *IP = 0; 912 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 913 914 // zext(trunc(x)) --> zext(x) or x or trunc(x) 915 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 916 // It's possible the bits taken off by the truncate were all zero bits. If 917 // so, we should be able to simplify this further. 918 const SCEV *X = ST->getOperand(); 919 ConstantRange CR = getUnsignedRange(X); 920 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 921 unsigned NewBits = getTypeSizeInBits(Ty); 922 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( 923 CR.zextOrTrunc(NewBits))) 924 return getTruncateOrZeroExtend(X, Ty); 925 } 926 927 // If the input value is a chrec scev, and we can prove that the value 928 // did not overflow the old, smaller, value, we can zero extend all of the 929 // operands (often constants). This allows analysis of something like 930 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } 931 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 932 if (AR->isAffine()) { 933 const SCEV *Start = AR->getStart(); 934 const SCEV *Step = AR->getStepRecurrence(*this); 935 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 936 const Loop *L = AR->getLoop(); 937 938 // If we have special knowledge that this addrec won't overflow, 939 // we don't need to do any further analysis. 940 if (AR->getNoWrapFlags(SCEV::FlagNUW)) 941 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 942 getZeroExtendExpr(Step, Ty), 943 L, AR->getNoWrapFlags()); 944 945 // Check whether the backedge-taken count is SCEVCouldNotCompute. 946 // Note that this serves two purposes: It filters out loops that are 947 // simply not analyzable, and it covers the case where this code is 948 // being called from within backedge-taken count analysis, such that 949 // attempting to ask for the backedge-taken count would likely result 950 // in infinite recursion. In the later case, the analysis code will 951 // cope with a conservative value, and it will take care to purge 952 // that value once it has finished. 953 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 954 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 955 // Manually compute the final value for AR, checking for 956 // overflow. 957 958 // Check whether the backedge-taken count can be losslessly casted to 959 // the addrec's type. The count is always unsigned. 960 const SCEV *CastedMaxBECount = 961 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 962 const SCEV *RecastedMaxBECount = 963 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 964 if (MaxBECount == RecastedMaxBECount) { 965 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 966 // Check whether Start+Step*MaxBECount has no unsigned overflow. 967 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); 968 const SCEV *Add = getAddExpr(Start, ZMul); 969 const SCEV *OperandExtendedAdd = 970 getAddExpr(getZeroExtendExpr(Start, WideTy), 971 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 972 getZeroExtendExpr(Step, WideTy))); 973 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 974 // Cache knowledge of AR NUW, which is propagated to this AddRec. 975 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 976 // Return the expression with the addrec on the outside. 977 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 978 getZeroExtendExpr(Step, Ty), 979 L, AR->getNoWrapFlags()); 980 } 981 // Similar to above, only this time treat the step value as signed. 982 // This covers loops that count down. 983 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 984 Add = getAddExpr(Start, SMul); 985 OperandExtendedAdd = 986 getAddExpr(getZeroExtendExpr(Start, WideTy), 987 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 988 getSignExtendExpr(Step, WideTy))); 989 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) { 990 // Cache knowledge of AR NW, which is propagated to this AddRec. 991 // Negative step causes unsigned wrap, but it still can't self-wrap. 992 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 993 // Return the expression with the addrec on the outside. 994 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 995 getSignExtendExpr(Step, Ty), 996 L, AR->getNoWrapFlags()); 997 } 998 } 999 1000 // If the backedge is guarded by a comparison with the pre-inc value 1001 // the addrec is safe. Also, if the entry is guarded by a comparison 1002 // with the start value and the backedge is guarded by a comparison 1003 // with the post-inc value, the addrec is safe. 1004 if (isKnownPositive(Step)) { 1005 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - 1006 getUnsignedRange(Step).getUnsignedMax()); 1007 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || 1008 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && 1009 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, 1010 AR->getPostIncExpr(*this), N))) { 1011 // Cache knowledge of AR NUW, which is propagated to this AddRec. 1012 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); 1013 // Return the expression with the addrec on the outside. 1014 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1015 getZeroExtendExpr(Step, Ty), 1016 L, AR->getNoWrapFlags()); 1017 } 1018 } else if (isKnownNegative(Step)) { 1019 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - 1020 getSignedRange(Step).getSignedMin()); 1021 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || 1022 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && 1023 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, 1024 AR->getPostIncExpr(*this), N))) { 1025 // Cache knowledge of AR NW, which is propagated to this AddRec. 1026 // Negative step causes unsigned wrap, but it still can't self-wrap. 1027 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); 1028 // Return the expression with the addrec on the outside. 1029 return getAddRecExpr(getZeroExtendExpr(Start, Ty), 1030 getSignExtendExpr(Step, Ty), 1031 L, AR->getNoWrapFlags()); 1032 } 1033 } 1034 } 1035 } 1036 1037 // The cast wasn't folded; create an explicit cast node. 1038 // Recompute the insert position, as it may have been invalidated. 1039 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1040 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), 1041 Op, Ty); 1042 UniqueSCEVs.InsertNode(S, IP); 1043 return S; 1044} 1045 1046// Get the limit of a recurrence such that incrementing by Step cannot cause 1047// signed overflow as long as the value of the recurrence within the loop does 1048// not exceed this limit before incrementing. 1049static const SCEV *getOverflowLimitForStep(const SCEV *Step, 1050 ICmpInst::Predicate *Pred, 1051 ScalarEvolution *SE) { 1052 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); 1053 if (SE->isKnownPositive(Step)) { 1054 *Pred = ICmpInst::ICMP_SLT; 1055 return SE->getConstant(APInt::getSignedMinValue(BitWidth) - 1056 SE->getSignedRange(Step).getSignedMax()); 1057 } 1058 if (SE->isKnownNegative(Step)) { 1059 *Pred = ICmpInst::ICMP_SGT; 1060 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - 1061 SE->getSignedRange(Step).getSignedMin()); 1062 } 1063 return 0; 1064} 1065 1066// The recurrence AR has been shown to have no signed wrap. Typically, if we can 1067// prove NSW for AR, then we can just as easily prove NSW for its preincrement 1068// or postincrement sibling. This allows normalizing a sign extended AddRec as 1069// such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a 1070// result, the expression "Step + sext(PreIncAR)" is congruent with 1071// "sext(PostIncAR)" 1072static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR, 1073 Type *Ty, 1074 ScalarEvolution *SE) { 1075 const Loop *L = AR->getLoop(); 1076 const SCEV *Start = AR->getStart(); 1077 const SCEV *Step = AR->getStepRecurrence(*SE); 1078 1079 // Check for a simple looking step prior to loop entry. 1080 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start); 1081 if (!SA) 1082 return 0; 1083 1084 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV 1085 // subtraction is expensive. For this purpose, perform a quick and dirty 1086 // difference, by checking for Step in the operand list. 1087 SmallVector<const SCEV *, 4> DiffOps; 1088 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end(); 1089 I != E; ++I) { 1090 if (*I != Step) 1091 DiffOps.push_back(*I); 1092 } 1093 if (DiffOps.size() == SA->getNumOperands()) 1094 return 0; 1095 1096 // This is a postinc AR. Check for overflow on the preinc recurrence using the 1097 // same three conditions that getSignExtendedExpr checks. 1098 1099 // 1. NSW flags on the step increment. 1100 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags()); 1101 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>( 1102 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); 1103 1104 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW)) 1105 return PreStart; 1106 1107 // 2. Direct overflow check on the step operation's expression. 1108 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); 1109 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); 1110 const SCEV *OperandExtendedStart = 1111 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy), 1112 SE->getSignExtendExpr(Step, WideTy)); 1113 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) { 1114 // Cache knowledge of PreAR NSW. 1115 if (PreAR) 1116 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW); 1117 // FIXME: this optimization needs a unit test 1118 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n"); 1119 return PreStart; 1120 } 1121 1122 // 3. Loop precondition. 1123 ICmpInst::Predicate Pred; 1124 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE); 1125 1126 if (OverflowLimit && 1127 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { 1128 return PreStart; 1129 } 1130 return 0; 1131} 1132 1133// Get the normalized sign-extended expression for this AddRec's Start. 1134static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR, 1135 Type *Ty, 1136 ScalarEvolution *SE) { 1137 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE); 1138 if (!PreStart) 1139 return SE->getSignExtendExpr(AR->getStart(), Ty); 1140 1141 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty), 1142 SE->getSignExtendExpr(PreStart, Ty)); 1143} 1144 1145const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, 1146 Type *Ty) { 1147 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1148 "This is not an extending conversion!"); 1149 assert(isSCEVable(Ty) && 1150 "This is not a conversion to a SCEVable type!"); 1151 Ty = getEffectiveSCEVType(Ty); 1152 1153 // Fold if the operand is constant. 1154 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1155 return getConstant( 1156 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), 1157 getEffectiveSCEVType(Ty)))); 1158 1159 // sext(sext(x)) --> sext(x) 1160 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) 1161 return getSignExtendExpr(SS->getOperand(), Ty); 1162 1163 // sext(zext(x)) --> zext(x) 1164 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) 1165 return getZeroExtendExpr(SZ->getOperand(), Ty); 1166 1167 // Before doing any expensive analysis, check to see if we've already 1168 // computed a SCEV for this Op and Ty. 1169 FoldingSetNodeID ID; 1170 ID.AddInteger(scSignExtend); 1171 ID.AddPointer(Op); 1172 ID.AddPointer(Ty); 1173 void *IP = 0; 1174 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1175 1176 // If the input value is provably positive, build a zext instead. 1177 if (isKnownNonNegative(Op)) 1178 return getZeroExtendExpr(Op, Ty); 1179 1180 // sext(trunc(x)) --> sext(x) or x or trunc(x) 1181 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) { 1182 // It's possible the bits taken off by the truncate were all sign bits. If 1183 // so, we should be able to simplify this further. 1184 const SCEV *X = ST->getOperand(); 1185 ConstantRange CR = getSignedRange(X); 1186 unsigned TruncBits = getTypeSizeInBits(ST->getType()); 1187 unsigned NewBits = getTypeSizeInBits(Ty); 1188 if (CR.truncate(TruncBits).signExtend(NewBits).contains( 1189 CR.sextOrTrunc(NewBits))) 1190 return getTruncateOrSignExtend(X, Ty); 1191 } 1192 1193 // If the input value is a chrec scev, and we can prove that the value 1194 // did not overflow the old, smaller, value, we can sign extend all of the 1195 // operands (often constants). This allows analysis of something like 1196 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } 1197 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) 1198 if (AR->isAffine()) { 1199 const SCEV *Start = AR->getStart(); 1200 const SCEV *Step = AR->getStepRecurrence(*this); 1201 unsigned BitWidth = getTypeSizeInBits(AR->getType()); 1202 const Loop *L = AR->getLoop(); 1203 1204 // If we have special knowledge that this addrec won't overflow, 1205 // we don't need to do any further analysis. 1206 if (AR->getNoWrapFlags(SCEV::FlagNSW)) 1207 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1208 getSignExtendExpr(Step, Ty), 1209 L, SCEV::FlagNSW); 1210 1211 // Check whether the backedge-taken count is SCEVCouldNotCompute. 1212 // Note that this serves two purposes: It filters out loops that are 1213 // simply not analyzable, and it covers the case where this code is 1214 // being called from within backedge-taken count analysis, such that 1215 // attempting to ask for the backedge-taken count would likely result 1216 // in infinite recursion. In the later case, the analysis code will 1217 // cope with a conservative value, and it will take care to purge 1218 // that value once it has finished. 1219 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); 1220 if (!isa<SCEVCouldNotCompute>(MaxBECount)) { 1221 // Manually compute the final value for AR, checking for 1222 // overflow. 1223 1224 // Check whether the backedge-taken count can be losslessly casted to 1225 // the addrec's type. The count is always unsigned. 1226 const SCEV *CastedMaxBECount = 1227 getTruncateOrZeroExtend(MaxBECount, Start->getType()); 1228 const SCEV *RecastedMaxBECount = 1229 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); 1230 if (MaxBECount == RecastedMaxBECount) { 1231 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); 1232 // Check whether Start+Step*MaxBECount has no signed overflow. 1233 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); 1234 const SCEV *Add = getAddExpr(Start, SMul); 1235 const SCEV *OperandExtendedAdd = 1236 getAddExpr(getSignExtendExpr(Start, WideTy), 1237 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1238 getSignExtendExpr(Step, WideTy))); 1239 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1240 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1241 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1242 // Return the expression with the addrec on the outside. 1243 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1244 getSignExtendExpr(Step, Ty), 1245 L, AR->getNoWrapFlags()); 1246 } 1247 // Similar to above, only this time treat the step value as unsigned. 1248 // This covers loops that count up with an unsigned step. 1249 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); 1250 Add = getAddExpr(Start, UMul); 1251 OperandExtendedAdd = 1252 getAddExpr(getSignExtendExpr(Start, WideTy), 1253 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), 1254 getZeroExtendExpr(Step, WideTy))); 1255 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) { 1256 // Cache knowledge of AR NSW, which is propagated to this AddRec. 1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1258 // Return the expression with the addrec on the outside. 1259 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1260 getZeroExtendExpr(Step, Ty), 1261 L, AR->getNoWrapFlags()); 1262 } 1263 } 1264 1265 // If the backedge is guarded by a comparison with the pre-inc value 1266 // the addrec is safe. Also, if the entry is guarded by a comparison 1267 // with the start value and the backedge is guarded by a comparison 1268 // with the post-inc value, the addrec is safe. 1269 ICmpInst::Predicate Pred; 1270 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this); 1271 if (OverflowLimit && 1272 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || 1273 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && 1274 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), 1275 OverflowLimit)))) { 1276 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. 1277 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); 1278 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this), 1279 getSignExtendExpr(Step, Ty), 1280 L, AR->getNoWrapFlags()); 1281 } 1282 } 1283 } 1284 1285 // The cast wasn't folded; create an explicit cast node. 1286 // Recompute the insert position, as it may have been invalidated. 1287 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 1288 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), 1289 Op, Ty); 1290 UniqueSCEVs.InsertNode(S, IP); 1291 return S; 1292} 1293 1294/// getAnyExtendExpr - Return a SCEV for the given operand extended with 1295/// unspecified bits out to the given type. 1296/// 1297const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, 1298 Type *Ty) { 1299 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && 1300 "This is not an extending conversion!"); 1301 assert(isSCEVable(Ty) && 1302 "This is not a conversion to a SCEVable type!"); 1303 Ty = getEffectiveSCEVType(Ty); 1304 1305 // Sign-extend negative constants. 1306 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) 1307 if (SC->getValue()->getValue().isNegative()) 1308 return getSignExtendExpr(Op, Ty); 1309 1310 // Peel off a truncate cast. 1311 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { 1312 const SCEV *NewOp = T->getOperand(); 1313 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) 1314 return getAnyExtendExpr(NewOp, Ty); 1315 return getTruncateOrNoop(NewOp, Ty); 1316 } 1317 1318 // Next try a zext cast. If the cast is folded, use it. 1319 const SCEV *ZExt = getZeroExtendExpr(Op, Ty); 1320 if (!isa<SCEVZeroExtendExpr>(ZExt)) 1321 return ZExt; 1322 1323 // Next try a sext cast. If the cast is folded, use it. 1324 const SCEV *SExt = getSignExtendExpr(Op, Ty); 1325 if (!isa<SCEVSignExtendExpr>(SExt)) 1326 return SExt; 1327 1328 // Force the cast to be folded into the operands of an addrec. 1329 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { 1330 SmallVector<const SCEV *, 4> Ops; 1331 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 1332 I != E; ++I) 1333 Ops.push_back(getAnyExtendExpr(*I, Ty)); 1334 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); 1335 } 1336 1337 // As a special case, fold anyext(undef) to undef. We don't want to 1338 // know too much about SCEVUnknowns, but this special case is handy 1339 // and harmless. 1340 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op)) 1341 if (isa<UndefValue>(U->getValue())) 1342 return getSCEV(UndefValue::get(Ty)); 1343 1344 // If the expression is obviously signed, use the sext cast value. 1345 if (isa<SCEVSMaxExpr>(Op)) 1346 return SExt; 1347 1348 // Absent any other information, use the zext cast value. 1349 return ZExt; 1350} 1351 1352/// CollectAddOperandsWithScales - Process the given Ops list, which is 1353/// a list of operands to be added under the given scale, update the given 1354/// map. This is a helper function for getAddRecExpr. As an example of 1355/// what it does, given a sequence of operands that would form an add 1356/// expression like this: 1357/// 1358/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) 1359/// 1360/// where A and B are constants, update the map with these values: 1361/// 1362/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) 1363/// 1364/// and add 13 + A*B*29 to AccumulatedConstant. 1365/// This will allow getAddRecExpr to produce this: 1366/// 1367/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) 1368/// 1369/// This form often exposes folding opportunities that are hidden in 1370/// the original operand list. 1371/// 1372/// Return true iff it appears that any interesting folding opportunities 1373/// may be exposed. This helps getAddRecExpr short-circuit extra work in 1374/// the common case where no interesting opportunities are present, and 1375/// is also used as a check to avoid infinite recursion. 1376/// 1377static bool 1378CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, 1379 SmallVector<const SCEV *, 8> &NewOps, 1380 APInt &AccumulatedConstant, 1381 const SCEV *const *Ops, size_t NumOperands, 1382 const APInt &Scale, 1383 ScalarEvolution &SE) { 1384 bool Interesting = false; 1385 1386 // Iterate over the add operands. They are sorted, with constants first. 1387 unsigned i = 0; 1388 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1389 ++i; 1390 // Pull a buried constant out to the outside. 1391 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) 1392 Interesting = true; 1393 AccumulatedConstant += Scale * C->getValue()->getValue(); 1394 } 1395 1396 // Next comes everything else. We're especially interested in multiplies 1397 // here, but they're in the middle, so just visit the rest with one loop. 1398 for (; i != NumOperands; ++i) { 1399 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); 1400 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { 1401 APInt NewScale = 1402 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); 1403 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { 1404 // A multiplication of a constant with another add; recurse. 1405 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); 1406 Interesting |= 1407 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1408 Add->op_begin(), Add->getNumOperands(), 1409 NewScale, SE); 1410 } else { 1411 // A multiplication of a constant with some other value. Update 1412 // the map. 1413 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); 1414 const SCEV *Key = SE.getMulExpr(MulOps); 1415 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1416 M.insert(std::make_pair(Key, NewScale)); 1417 if (Pair.second) { 1418 NewOps.push_back(Pair.first->first); 1419 } else { 1420 Pair.first->second += NewScale; 1421 // The map already had an entry for this value, which may indicate 1422 // a folding opportunity. 1423 Interesting = true; 1424 } 1425 } 1426 } else { 1427 // An ordinary operand. Update the map. 1428 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = 1429 M.insert(std::make_pair(Ops[i], Scale)); 1430 if (Pair.second) { 1431 NewOps.push_back(Pair.first->first); 1432 } else { 1433 Pair.first->second += Scale; 1434 // The map already had an entry for this value, which may indicate 1435 // a folding opportunity. 1436 Interesting = true; 1437 } 1438 } 1439 } 1440 1441 return Interesting; 1442} 1443 1444namespace { 1445 struct APIntCompare { 1446 bool operator()(const APInt &LHS, const APInt &RHS) const { 1447 return LHS.ult(RHS); 1448 } 1449 }; 1450} 1451 1452/// getAddExpr - Get a canonical add expression, or something simpler if 1453/// possible. 1454const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, 1455 SCEV::NoWrapFlags Flags) { 1456 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && 1457 "only nuw or nsw allowed"); 1458 assert(!Ops.empty() && "Cannot get empty add!"); 1459 if (Ops.size() == 1) return Ops[0]; 1460#ifndef NDEBUG 1461 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1462 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1463 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1464 "SCEVAddExpr operand types don't match!"); 1465#endif 1466 1467 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1468 // And vice-versa. 1469 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1470 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1471 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1472 bool All = true; 1473 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1474 E = Ops.end(); I != E; ++I) 1475 if (!isKnownNonNegative(*I)) { 1476 All = false; 1477 break; 1478 } 1479 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1480 } 1481 1482 // Sort by complexity, this groups all similar expression types together. 1483 GroupByComplexity(Ops, LI); 1484 1485 // If there are any constants, fold them together. 1486 unsigned Idx = 0; 1487 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1488 ++Idx; 1489 assert(Idx < Ops.size()); 1490 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1491 // We found two constants, fold them together! 1492 Ops[0] = getConstant(LHSC->getValue()->getValue() + 1493 RHSC->getValue()->getValue()); 1494 if (Ops.size() == 2) return Ops[0]; 1495 Ops.erase(Ops.begin()+1); // Erase the folded element 1496 LHSC = cast<SCEVConstant>(Ops[0]); 1497 } 1498 1499 // If we are left with a constant zero being added, strip it off. 1500 if (LHSC->getValue()->isZero()) { 1501 Ops.erase(Ops.begin()); 1502 --Idx; 1503 } 1504 1505 if (Ops.size() == 1) return Ops[0]; 1506 } 1507 1508 // Okay, check to see if the same value occurs in the operand list more than 1509 // once. If so, merge them together into an multiply expression. Since we 1510 // sorted the list, these values are required to be adjacent. 1511 Type *Ty = Ops[0]->getType(); 1512 bool FoundMatch = false; 1513 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) 1514 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 1515 // Scan ahead to count how many equal operands there are. 1516 unsigned Count = 2; 1517 while (i+Count != e && Ops[i+Count] == Ops[i]) 1518 ++Count; 1519 // Merge the values into a multiply. 1520 const SCEV *Scale = getConstant(Ty, Count); 1521 const SCEV *Mul = getMulExpr(Scale, Ops[i]); 1522 if (Ops.size() == Count) 1523 return Mul; 1524 Ops[i] = Mul; 1525 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); 1526 --i; e -= Count - 1; 1527 FoundMatch = true; 1528 } 1529 if (FoundMatch) 1530 return getAddExpr(Ops, Flags); 1531 1532 // Check for truncates. If all the operands are truncated from the same 1533 // type, see if factoring out the truncate would permit the result to be 1534 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) 1535 // if the contents of the resulting outer trunc fold to something simple. 1536 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { 1537 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); 1538 Type *DstType = Trunc->getType(); 1539 Type *SrcType = Trunc->getOperand()->getType(); 1540 SmallVector<const SCEV *, 8> LargeOps; 1541 bool Ok = true; 1542 // Check all the operands to see if they can be represented in the 1543 // source type of the truncate. 1544 for (unsigned i = 0, e = Ops.size(); i != e; ++i) { 1545 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { 1546 if (T->getOperand()->getType() != SrcType) { 1547 Ok = false; 1548 break; 1549 } 1550 LargeOps.push_back(T->getOperand()); 1551 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { 1552 LargeOps.push_back(getAnyExtendExpr(C, SrcType)); 1553 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { 1554 SmallVector<const SCEV *, 8> LargeMulOps; 1555 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { 1556 if (const SCEVTruncateExpr *T = 1557 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { 1558 if (T->getOperand()->getType() != SrcType) { 1559 Ok = false; 1560 break; 1561 } 1562 LargeMulOps.push_back(T->getOperand()); 1563 } else if (const SCEVConstant *C = 1564 dyn_cast<SCEVConstant>(M->getOperand(j))) { 1565 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); 1566 } else { 1567 Ok = false; 1568 break; 1569 } 1570 } 1571 if (Ok) 1572 LargeOps.push_back(getMulExpr(LargeMulOps)); 1573 } else { 1574 Ok = false; 1575 break; 1576 } 1577 } 1578 if (Ok) { 1579 // Evaluate the expression in the larger type. 1580 const SCEV *Fold = getAddExpr(LargeOps, Flags); 1581 // If it folds to something simple, use it. Otherwise, don't. 1582 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) 1583 return getTruncateExpr(Fold, DstType); 1584 } 1585 } 1586 1587 // Skip past any other cast SCEVs. 1588 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) 1589 ++Idx; 1590 1591 // If there are add operands they would be next. 1592 if (Idx < Ops.size()) { 1593 bool DeletedAdd = false; 1594 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { 1595 // If we have an add, expand the add operands onto the end of the operands 1596 // list. 1597 Ops.erase(Ops.begin()+Idx); 1598 Ops.append(Add->op_begin(), Add->op_end()); 1599 DeletedAdd = true; 1600 } 1601 1602 // If we deleted at least one add, we added operands to the end of the list, 1603 // and they are not necessarily sorted. Recurse to resort and resimplify 1604 // any operands we just acquired. 1605 if (DeletedAdd) 1606 return getAddExpr(Ops); 1607 } 1608 1609 // Skip over the add expression until we get to a multiply. 1610 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1611 ++Idx; 1612 1613 // Check to see if there are any folding opportunities present with 1614 // operands multiplied by constant values. 1615 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { 1616 uint64_t BitWidth = getTypeSizeInBits(Ty); 1617 DenseMap<const SCEV *, APInt> M; 1618 SmallVector<const SCEV *, 8> NewOps; 1619 APInt AccumulatedConstant(BitWidth, 0); 1620 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, 1621 Ops.data(), Ops.size(), 1622 APInt(BitWidth, 1), *this)) { 1623 // Some interesting folding opportunity is present, so its worthwhile to 1624 // re-generate the operands list. Group the operands by constant scale, 1625 // to avoid multiplying by the same constant scale multiple times. 1626 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; 1627 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(), 1628 E = NewOps.end(); I != E; ++I) 1629 MulOpLists[M.find(*I)->second].push_back(*I); 1630 // Re-generate the operands list. 1631 Ops.clear(); 1632 if (AccumulatedConstant != 0) 1633 Ops.push_back(getConstant(AccumulatedConstant)); 1634 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator 1635 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) 1636 if (I->first != 0) 1637 Ops.push_back(getMulExpr(getConstant(I->first), 1638 getAddExpr(I->second))); 1639 if (Ops.empty()) 1640 return getConstant(Ty, 0); 1641 if (Ops.size() == 1) 1642 return Ops[0]; 1643 return getAddExpr(Ops); 1644 } 1645 } 1646 1647 // If we are adding something to a multiply expression, make sure the 1648 // something is not already an operand of the multiply. If so, merge it into 1649 // the multiply. 1650 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { 1651 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); 1652 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { 1653 const SCEV *MulOpSCEV = Mul->getOperand(MulOp); 1654 if (isa<SCEVConstant>(MulOpSCEV)) 1655 continue; 1656 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) 1657 if (MulOpSCEV == Ops[AddOp]) { 1658 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) 1659 const SCEV *InnerMul = Mul->getOperand(MulOp == 0); 1660 if (Mul->getNumOperands() != 2) { 1661 // If the multiply has more than two operands, we must get the 1662 // Y*Z term. 1663 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1664 Mul->op_begin()+MulOp); 1665 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1666 InnerMul = getMulExpr(MulOps); 1667 } 1668 const SCEV *One = getConstant(Ty, 1); 1669 const SCEV *AddOne = getAddExpr(One, InnerMul); 1670 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 1671 if (Ops.size() == 2) return OuterMul; 1672 if (AddOp < Idx) { 1673 Ops.erase(Ops.begin()+AddOp); 1674 Ops.erase(Ops.begin()+Idx-1); 1675 } else { 1676 Ops.erase(Ops.begin()+Idx); 1677 Ops.erase(Ops.begin()+AddOp-1); 1678 } 1679 Ops.push_back(OuterMul); 1680 return getAddExpr(Ops); 1681 } 1682 1683 // Check this multiply against other multiplies being added together. 1684 for (unsigned OtherMulIdx = Idx+1; 1685 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); 1686 ++OtherMulIdx) { 1687 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); 1688 // If MulOp occurs in OtherMul, we can fold the two multiplies 1689 // together. 1690 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); 1691 OMulOp != e; ++OMulOp) 1692 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { 1693 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) 1694 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); 1695 if (Mul->getNumOperands() != 2) { 1696 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), 1697 Mul->op_begin()+MulOp); 1698 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); 1699 InnerMul1 = getMulExpr(MulOps); 1700 } 1701 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); 1702 if (OtherMul->getNumOperands() != 2) { 1703 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), 1704 OtherMul->op_begin()+OMulOp); 1705 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 1706 InnerMul2 = getMulExpr(MulOps); 1707 } 1708 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); 1709 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); 1710 if (Ops.size() == 2) return OuterMul; 1711 Ops.erase(Ops.begin()+Idx); 1712 Ops.erase(Ops.begin()+OtherMulIdx-1); 1713 Ops.push_back(OuterMul); 1714 return getAddExpr(Ops); 1715 } 1716 } 1717 } 1718 } 1719 1720 // If there are any add recurrences in the operands list, see if any other 1721 // added values are loop invariant. If so, we can fold them into the 1722 // recurrence. 1723 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1724 ++Idx; 1725 1726 // Scan over all recurrences, trying to fold loop invariants into them. 1727 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1728 // Scan all of the other operands to this add and add them to the vector if 1729 // they are loop invariant w.r.t. the recurrence. 1730 SmallVector<const SCEV *, 8> LIOps; 1731 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1732 const Loop *AddRecLoop = AddRec->getLoop(); 1733 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1734 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1735 LIOps.push_back(Ops[i]); 1736 Ops.erase(Ops.begin()+i); 1737 --i; --e; 1738 } 1739 1740 // If we found some loop invariants, fold them into the recurrence. 1741 if (!LIOps.empty()) { 1742 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} 1743 LIOps.push_back(AddRec->getStart()); 1744 1745 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1746 AddRec->op_end()); 1747 AddRecOps[0] = getAddExpr(LIOps); 1748 1749 // Build the new addrec. Propagate the NUW and NSW flags if both the 1750 // outer add and the inner addrec are guaranteed to have no overflow. 1751 // Always propagate NW. 1752 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); 1753 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); 1754 1755 // If all of the other operands were loop invariant, we are done. 1756 if (Ops.size() == 1) return NewRec; 1757 1758 // Otherwise, add the folded AddRec by the non-invariant parts. 1759 for (unsigned i = 0;; ++i) 1760 if (Ops[i] == AddRec) { 1761 Ops[i] = NewRec; 1762 break; 1763 } 1764 return getAddExpr(Ops); 1765 } 1766 1767 // Okay, if there weren't any loop invariants to be folded, check to see if 1768 // there are multiple AddRec's with the same loop induction variable being 1769 // added together. If so, we can fold them. 1770 for (unsigned OtherIdx = Idx+1; 1771 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1772 ++OtherIdx) 1773 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 1774 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> 1775 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), 1776 AddRec->op_end()); 1777 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 1778 ++OtherIdx) 1779 if (const SCEVAddRecExpr *OtherAddRec = 1780 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 1781 if (OtherAddRec->getLoop() == AddRecLoop) { 1782 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); 1783 i != e; ++i) { 1784 if (i >= AddRecOps.size()) { 1785 AddRecOps.append(OtherAddRec->op_begin()+i, 1786 OtherAddRec->op_end()); 1787 break; 1788 } 1789 AddRecOps[i] = getAddExpr(AddRecOps[i], 1790 OtherAddRec->getOperand(i)); 1791 } 1792 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 1793 } 1794 // Step size has changed, so we cannot guarantee no self-wraparound. 1795 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 1796 return getAddExpr(Ops); 1797 } 1798 1799 // Otherwise couldn't fold anything into this recurrence. Move onto the 1800 // next one. 1801 } 1802 1803 // Okay, it looks like we really DO need an add expr. Check to see if we 1804 // already have one, otherwise create a new one. 1805 FoldingSetNodeID ID; 1806 ID.AddInteger(scAddExpr); 1807 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1808 ID.AddPointer(Ops[i]); 1809 void *IP = 0; 1810 SCEVAddExpr *S = 1811 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 1812 if (!S) { 1813 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 1814 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 1815 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), 1816 O, Ops.size()); 1817 UniqueSCEVs.InsertNode(S, IP); 1818 } 1819 S->setNoWrapFlags(Flags); 1820 return S; 1821} 1822 1823static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { 1824 uint64_t k = i*j; 1825 if (j > 1 && k / j != i) Overflow = true; 1826 return k; 1827} 1828 1829/// Compute the result of "n choose k", the binomial coefficient. If an 1830/// intermediate computation overflows, Overflow will be set and the return will 1831/// be garbage. Overflow is not cleared on absense of overflow. 1832static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { 1833 // We use the multiplicative formula: 1834 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . 1835 // At each iteration, we take the n-th term of the numeral and divide by the 1836 // (k-n)th term of the denominator. This division will always produce an 1837 // integral result, and helps reduce the chance of overflow in the 1838 // intermediate computations. However, we can still overflow even when the 1839 // final result would fit. 1840 1841 if (n == 0 || n == k) return 1; 1842 if (k > n) return 0; 1843 1844 if (k > n/2) 1845 k = n-k; 1846 1847 uint64_t r = 1; 1848 for (uint64_t i = 1; i <= k; ++i) { 1849 r = umul_ov(r, n-(i-1), Overflow); 1850 r /= i; 1851 } 1852 return r; 1853} 1854 1855/// getMulExpr - Get a canonical multiply expression, or something simpler if 1856/// possible. 1857const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, 1858 SCEV::NoWrapFlags Flags) { 1859 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && 1860 "only nuw or nsw allowed"); 1861 assert(!Ops.empty() && "Cannot get empty mul!"); 1862 if (Ops.size() == 1) return Ops[0]; 1863#ifndef NDEBUG 1864 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 1865 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 1866 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 1867 "SCEVMulExpr operand types don't match!"); 1868#endif 1869 1870 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 1871 // And vice-versa. 1872 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 1873 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 1874 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 1875 bool All = true; 1876 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(), 1877 E = Ops.end(); I != E; ++I) 1878 if (!isKnownNonNegative(*I)) { 1879 All = false; 1880 break; 1881 } 1882 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 1883 } 1884 1885 // Sort by complexity, this groups all similar expression types together. 1886 GroupByComplexity(Ops, LI); 1887 1888 // If there are any constants, fold them together. 1889 unsigned Idx = 0; 1890 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 1891 1892 // C1*(C2+V) -> C1*C2 + C1*V 1893 if (Ops.size() == 2) 1894 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) 1895 if (Add->getNumOperands() == 2 && 1896 isa<SCEVConstant>(Add->getOperand(0))) 1897 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), 1898 getMulExpr(LHSC, Add->getOperand(1))); 1899 1900 ++Idx; 1901 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 1902 // We found two constants, fold them together! 1903 ConstantInt *Fold = ConstantInt::get(getContext(), 1904 LHSC->getValue()->getValue() * 1905 RHSC->getValue()->getValue()); 1906 Ops[0] = getConstant(Fold); 1907 Ops.erase(Ops.begin()+1); // Erase the folded element 1908 if (Ops.size() == 1) return Ops[0]; 1909 LHSC = cast<SCEVConstant>(Ops[0]); 1910 } 1911 1912 // If we are left with a constant one being multiplied, strip it off. 1913 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { 1914 Ops.erase(Ops.begin()); 1915 --Idx; 1916 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { 1917 // If we have a multiply of zero, it will always be zero. 1918 return Ops[0]; 1919 } else if (Ops[0]->isAllOnesValue()) { 1920 // If we have a mul by -1 of an add, try distributing the -1 among the 1921 // add operands. 1922 if (Ops.size() == 2) { 1923 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { 1924 SmallVector<const SCEV *, 4> NewOps; 1925 bool AnyFolded = false; 1926 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), 1927 E = Add->op_end(); I != E; ++I) { 1928 const SCEV *Mul = getMulExpr(Ops[0], *I); 1929 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; 1930 NewOps.push_back(Mul); 1931 } 1932 if (AnyFolded) 1933 return getAddExpr(NewOps); 1934 } 1935 else if (const SCEVAddRecExpr * 1936 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { 1937 // Negation preserves a recurrence's no self-wrap property. 1938 SmallVector<const SCEV *, 4> Operands; 1939 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), 1940 E = AddRec->op_end(); I != E; ++I) { 1941 Operands.push_back(getMulExpr(Ops[0], *I)); 1942 } 1943 return getAddRecExpr(Operands, AddRec->getLoop(), 1944 AddRec->getNoWrapFlags(SCEV::FlagNW)); 1945 } 1946 } 1947 } 1948 1949 if (Ops.size() == 1) 1950 return Ops[0]; 1951 } 1952 1953 // Skip over the add expression until we get to a multiply. 1954 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) 1955 ++Idx; 1956 1957 // If there are mul operands inline them all into this expression. 1958 if (Idx < Ops.size()) { 1959 bool DeletedMul = false; 1960 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { 1961 // If we have an mul, expand the mul operands onto the end of the operands 1962 // list. 1963 Ops.erase(Ops.begin()+Idx); 1964 Ops.append(Mul->op_begin(), Mul->op_end()); 1965 DeletedMul = true; 1966 } 1967 1968 // If we deleted at least one mul, we added operands to the end of the list, 1969 // and they are not necessarily sorted. Recurse to resort and resimplify 1970 // any operands we just acquired. 1971 if (DeletedMul) 1972 return getMulExpr(Ops); 1973 } 1974 1975 // If there are any add recurrences in the operands list, see if any other 1976 // added values are loop invariant. If so, we can fold them into the 1977 // recurrence. 1978 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) 1979 ++Idx; 1980 1981 // Scan over all recurrences, trying to fold loop invariants into them. 1982 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { 1983 // Scan all of the other operands to this mul and add them to the vector if 1984 // they are loop invariant w.r.t. the recurrence. 1985 SmallVector<const SCEV *, 8> LIOps; 1986 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); 1987 const Loop *AddRecLoop = AddRec->getLoop(); 1988 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 1989 if (isLoopInvariant(Ops[i], AddRecLoop)) { 1990 LIOps.push_back(Ops[i]); 1991 Ops.erase(Ops.begin()+i); 1992 --i; --e; 1993 } 1994 1995 // If we found some loop invariants, fold them into the recurrence. 1996 if (!LIOps.empty()) { 1997 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} 1998 SmallVector<const SCEV *, 4> NewOps; 1999 NewOps.reserve(AddRec->getNumOperands()); 2000 const SCEV *Scale = getMulExpr(LIOps); 2001 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) 2002 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); 2003 2004 // Build the new addrec. Propagate the NUW and NSW flags if both the 2005 // outer mul and the inner addrec are guaranteed to have no overflow. 2006 // 2007 // No self-wrap cannot be guaranteed after changing the step size, but 2008 // will be inferred if either NUW or NSW is true. 2009 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); 2010 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); 2011 2012 // If all of the other operands were loop invariant, we are done. 2013 if (Ops.size() == 1) return NewRec; 2014 2015 // Otherwise, multiply the folded AddRec by the non-invariant parts. 2016 for (unsigned i = 0;; ++i) 2017 if (Ops[i] == AddRec) { 2018 Ops[i] = NewRec; 2019 break; 2020 } 2021 return getMulExpr(Ops); 2022 } 2023 2024 // Okay, if there weren't any loop invariants to be folded, check to see if 2025 // there are multiple AddRec's with the same loop induction variable being 2026 // multiplied together. If so, we can fold them. 2027 for (unsigned OtherIdx = Idx+1; 2028 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2029 ++OtherIdx) { 2030 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { 2031 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L> 2032 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ 2033 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z 2034 // ]]],+,...up to x=2n}. 2035 // Note that the arguments to choose() are always integers with values 2036 // known at compile time, never SCEV objects. 2037 // 2038 // The implementation avoids pointless extra computations when the two 2039 // addrec's are of different length (mathematically, it's equivalent to 2040 // an infinite stream of zeros on the right). 2041 bool OpsModified = false; 2042 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); 2043 ++OtherIdx) 2044 if (const SCEVAddRecExpr *OtherAddRec = 2045 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx])) 2046 if (OtherAddRec->getLoop() == AddRecLoop) { 2047 bool Overflow = false; 2048 Type *Ty = AddRec->getType(); 2049 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; 2050 SmallVector<const SCEV*, 7> AddRecOps; 2051 for (int x = 0, xe = AddRec->getNumOperands() + 2052 OtherAddRec->getNumOperands() - 1; 2053 x != xe && !Overflow; ++x) { 2054 const SCEV *Term = getConstant(Ty, 0); 2055 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { 2056 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); 2057 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), 2058 ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); 2059 z < ze && !Overflow; ++z) { 2060 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); 2061 uint64_t Coeff; 2062 if (LargerThan64Bits) 2063 Coeff = umul_ov(Coeff1, Coeff2, Overflow); 2064 else 2065 Coeff = Coeff1*Coeff2; 2066 const SCEV *CoeffTerm = getConstant(Ty, Coeff); 2067 const SCEV *Term1 = AddRec->getOperand(y-z); 2068 const SCEV *Term2 = OtherAddRec->getOperand(z); 2069 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2)); 2070 } 2071 } 2072 AddRecOps.push_back(Term); 2073 } 2074 if (!Overflow) { 2075 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, 2076 AddRec->getLoop(), 2077 SCEV::FlagAnyWrap); 2078 if (Ops.size() == 2) return NewAddRec; 2079 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec); 2080 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; 2081 OpsModified = true; 2082 } 2083 } 2084 if (OpsModified) 2085 return getMulExpr(Ops); 2086 } 2087 } 2088 2089 // Otherwise couldn't fold anything into this recurrence. Move onto the 2090 // next one. 2091 } 2092 2093 // Okay, it looks like we really DO need an mul expr. Check to see if we 2094 // already have one, otherwise create a new one. 2095 FoldingSetNodeID ID; 2096 ID.AddInteger(scMulExpr); 2097 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2098 ID.AddPointer(Ops[i]); 2099 void *IP = 0; 2100 SCEVMulExpr *S = 2101 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2102 if (!S) { 2103 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2104 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2105 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), 2106 O, Ops.size()); 2107 UniqueSCEVs.InsertNode(S, IP); 2108 } 2109 S->setNoWrapFlags(Flags); 2110 return S; 2111} 2112 2113/// getUDivExpr - Get a canonical unsigned division expression, or something 2114/// simpler if possible. 2115const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, 2116 const SCEV *RHS) { 2117 assert(getEffectiveSCEVType(LHS->getType()) == 2118 getEffectiveSCEVType(RHS->getType()) && 2119 "SCEVUDivExpr operand types don't match!"); 2120 2121 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 2122 if (RHSC->getValue()->equalsInt(1)) 2123 return LHS; // X udiv 1 --> x 2124 // If the denominator is zero, the result of the udiv is undefined. Don't 2125 // try to analyze it, because the resolution chosen here may differ from 2126 // the resolution chosen in other parts of the compiler. 2127 if (!RHSC->getValue()->isZero()) { 2128 // Determine if the division can be folded into the operands of 2129 // its operands. 2130 // TODO: Generalize this to non-constants by using known-bits information. 2131 Type *Ty = LHS->getType(); 2132 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); 2133 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; 2134 // For non-power-of-two values, effectively round the value up to the 2135 // nearest power of two. 2136 if (!RHSC->getValue()->getValue().isPowerOf2()) 2137 ++MaxShiftAmt; 2138 IntegerType *ExtTy = 2139 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); 2140 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 2141 if (const SCEVConstant *Step = 2142 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) { 2143 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. 2144 const APInt &StepInt = Step->getValue()->getValue(); 2145 const APInt &DivInt = RHSC->getValue()->getValue(); 2146 if (!StepInt.urem(DivInt) && 2147 getZeroExtendExpr(AR, ExtTy) == 2148 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2149 getZeroExtendExpr(Step, ExtTy), 2150 AR->getLoop(), SCEV::FlagAnyWrap)) { 2151 SmallVector<const SCEV *, 4> Operands; 2152 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) 2153 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); 2154 return getAddRecExpr(Operands, AR->getLoop(), 2155 SCEV::FlagNW); 2156 } 2157 /// Get a canonical UDivExpr for a recurrence. 2158 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. 2159 // We can currently only fold X%N if X is constant. 2160 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart()); 2161 if (StartC && !DivInt.urem(StepInt) && 2162 getZeroExtendExpr(AR, ExtTy) == 2163 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), 2164 getZeroExtendExpr(Step, ExtTy), 2165 AR->getLoop(), SCEV::FlagAnyWrap)) { 2166 const APInt &StartInt = StartC->getValue()->getValue(); 2167 const APInt &StartRem = StartInt.urem(StepInt); 2168 if (StartRem != 0) 2169 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, 2170 AR->getLoop(), SCEV::FlagNW); 2171 } 2172 } 2173 // (A*B)/C --> A*(B/C) if safe and B/C can be folded. 2174 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { 2175 SmallVector<const SCEV *, 4> Operands; 2176 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) 2177 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); 2178 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) 2179 // Find an operand that's safely divisible. 2180 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { 2181 const SCEV *Op = M->getOperand(i); 2182 const SCEV *Div = getUDivExpr(Op, RHSC); 2183 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { 2184 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), 2185 M->op_end()); 2186 Operands[i] = Div; 2187 return getMulExpr(Operands); 2188 } 2189 } 2190 } 2191 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. 2192 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) { 2193 SmallVector<const SCEV *, 4> Operands; 2194 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) 2195 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); 2196 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { 2197 Operands.clear(); 2198 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { 2199 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); 2200 if (isa<SCEVUDivExpr>(Op) || 2201 getMulExpr(Op, RHS) != A->getOperand(i)) 2202 break; 2203 Operands.push_back(Op); 2204 } 2205 if (Operands.size() == A->getNumOperands()) 2206 return getAddExpr(Operands); 2207 } 2208 } 2209 2210 // Fold if both operands are constant. 2211 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 2212 Constant *LHSCV = LHSC->getValue(); 2213 Constant *RHSCV = RHSC->getValue(); 2214 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, 2215 RHSCV))); 2216 } 2217 } 2218 } 2219 2220 FoldingSetNodeID ID; 2221 ID.AddInteger(scUDivExpr); 2222 ID.AddPointer(LHS); 2223 ID.AddPointer(RHS); 2224 void *IP = 0; 2225 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2226 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), 2227 LHS, RHS); 2228 UniqueSCEVs.InsertNode(S, IP); 2229 return S; 2230} 2231 2232 2233/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2234/// Simplify the expression as much as possible. 2235const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step, 2236 const Loop *L, 2237 SCEV::NoWrapFlags Flags) { 2238 SmallVector<const SCEV *, 4> Operands; 2239 Operands.push_back(Start); 2240 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) 2241 if (StepChrec->getLoop() == L) { 2242 Operands.append(StepChrec->op_begin(), StepChrec->op_end()); 2243 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); 2244 } 2245 2246 Operands.push_back(Step); 2247 return getAddRecExpr(Operands, L, Flags); 2248} 2249 2250/// getAddRecExpr - Get an add recurrence expression for the specified loop. 2251/// Simplify the expression as much as possible. 2252const SCEV * 2253ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, 2254 const Loop *L, SCEV::NoWrapFlags Flags) { 2255 if (Operands.size() == 1) return Operands[0]; 2256#ifndef NDEBUG 2257 Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); 2258 for (unsigned i = 1, e = Operands.size(); i != e; ++i) 2259 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && 2260 "SCEVAddRecExpr operand types don't match!"); 2261 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2262 assert(isLoopInvariant(Operands[i], L) && 2263 "SCEVAddRecExpr operand is not loop-invariant!"); 2264#endif 2265 2266 if (Operands.back()->isZero()) { 2267 Operands.pop_back(); 2268 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X 2269 } 2270 2271 // It's tempting to want to call getMaxBackedgeTakenCount count here and 2272 // use that information to infer NUW and NSW flags. However, computing a 2273 // BE count requires calling getAddRecExpr, so we may not yet have a 2274 // meaningful BE count at this point (and if we don't, we'd be stuck 2275 // with a SCEVCouldNotCompute as the cached BE count). 2276 2277 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. 2278 // And vice-versa. 2279 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; 2280 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask); 2281 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) { 2282 bool All = true; 2283 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(), 2284 E = Operands.end(); I != E; ++I) 2285 if (!isKnownNonNegative(*I)) { 2286 All = false; 2287 break; 2288 } 2289 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); 2290 } 2291 2292 // Canonicalize nested AddRecs in by nesting them in order of loop depth. 2293 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { 2294 const Loop *NestedLoop = NestedAR->getLoop(); 2295 if (L->contains(NestedLoop) ? 2296 (L->getLoopDepth() < NestedLoop->getLoopDepth()) : 2297 (!NestedLoop->contains(L) && 2298 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { 2299 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), 2300 NestedAR->op_end()); 2301 Operands[0] = NestedAR->getStart(); 2302 // AddRecs require their operands be loop-invariant with respect to their 2303 // loops. Don't perform this transformation if it would break this 2304 // requirement. 2305 bool AllInvariant = true; 2306 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2307 if (!isLoopInvariant(Operands[i], L)) { 2308 AllInvariant = false; 2309 break; 2310 } 2311 if (AllInvariant) { 2312 // Create a recurrence for the outer loop with the same step size. 2313 // 2314 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the 2315 // inner recurrence has the same property. 2316 SCEV::NoWrapFlags OuterFlags = 2317 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); 2318 2319 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); 2320 AllInvariant = true; 2321 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) 2322 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { 2323 AllInvariant = false; 2324 break; 2325 } 2326 if (AllInvariant) { 2327 // Ok, both add recurrences are valid after the transformation. 2328 // 2329 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if 2330 // the outer recurrence has the same property. 2331 SCEV::NoWrapFlags InnerFlags = 2332 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); 2333 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); 2334 } 2335 } 2336 // Reset Operands to its original state. 2337 Operands[0] = NestedAR; 2338 } 2339 } 2340 2341 // Okay, it looks like we really DO need an addrec expr. Check to see if we 2342 // already have one, otherwise create a new one. 2343 FoldingSetNodeID ID; 2344 ID.AddInteger(scAddRecExpr); 2345 for (unsigned i = 0, e = Operands.size(); i != e; ++i) 2346 ID.AddPointer(Operands[i]); 2347 ID.AddPointer(L); 2348 void *IP = 0; 2349 SCEVAddRecExpr *S = 2350 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); 2351 if (!S) { 2352 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); 2353 std::uninitialized_copy(Operands.begin(), Operands.end(), O); 2354 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), 2355 O, Operands.size(), L); 2356 UniqueSCEVs.InsertNode(S, IP); 2357 } 2358 S->setNoWrapFlags(Flags); 2359 return S; 2360} 2361 2362const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, 2363 const SCEV *RHS) { 2364 SmallVector<const SCEV *, 2> Ops; 2365 Ops.push_back(LHS); 2366 Ops.push_back(RHS); 2367 return getSMaxExpr(Ops); 2368} 2369 2370const SCEV * 2371ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2372 assert(!Ops.empty() && "Cannot get empty smax!"); 2373 if (Ops.size() == 1) return Ops[0]; 2374#ifndef NDEBUG 2375 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2376 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2377 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2378 "SCEVSMaxExpr operand types don't match!"); 2379#endif 2380 2381 // Sort by complexity, this groups all similar expression types together. 2382 GroupByComplexity(Ops, LI); 2383 2384 // If there are any constants, fold them together. 2385 unsigned Idx = 0; 2386 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2387 ++Idx; 2388 assert(Idx < Ops.size()); 2389 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2390 // We found two constants, fold them together! 2391 ConstantInt *Fold = ConstantInt::get(getContext(), 2392 APIntOps::smax(LHSC->getValue()->getValue(), 2393 RHSC->getValue()->getValue())); 2394 Ops[0] = getConstant(Fold); 2395 Ops.erase(Ops.begin()+1); // Erase the folded element 2396 if (Ops.size() == 1) return Ops[0]; 2397 LHSC = cast<SCEVConstant>(Ops[0]); 2398 } 2399 2400 // If we are left with a constant minimum-int, strip it off. 2401 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { 2402 Ops.erase(Ops.begin()); 2403 --Idx; 2404 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { 2405 // If we have an smax with a constant maximum-int, it will always be 2406 // maximum-int. 2407 return Ops[0]; 2408 } 2409 2410 if (Ops.size() == 1) return Ops[0]; 2411 } 2412 2413 // Find the first SMax 2414 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) 2415 ++Idx; 2416 2417 // Check to see if one of the operands is an SMax. If so, expand its operands 2418 // onto our operand list, and recurse to simplify. 2419 if (Idx < Ops.size()) { 2420 bool DeletedSMax = false; 2421 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { 2422 Ops.erase(Ops.begin()+Idx); 2423 Ops.append(SMax->op_begin(), SMax->op_end()); 2424 DeletedSMax = true; 2425 } 2426 2427 if (DeletedSMax) 2428 return getSMaxExpr(Ops); 2429 } 2430 2431 // Okay, check to see if the same value occurs in the operand list twice. If 2432 // so, delete one. Since we sorted the list, these values are required to 2433 // be adjacent. 2434 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2435 // X smax Y smax Y --> X smax Y 2436 // X smax Y --> X, if X is always greater than Y 2437 if (Ops[i] == Ops[i+1] || 2438 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { 2439 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2440 --i; --e; 2441 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { 2442 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2443 --i; --e; 2444 } 2445 2446 if (Ops.size() == 1) return Ops[0]; 2447 2448 assert(!Ops.empty() && "Reduced smax down to nothing!"); 2449 2450 // Okay, it looks like we really DO need an smax expr. Check to see if we 2451 // already have one, otherwise create a new one. 2452 FoldingSetNodeID ID; 2453 ID.AddInteger(scSMaxExpr); 2454 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2455 ID.AddPointer(Ops[i]); 2456 void *IP = 0; 2457 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2458 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2459 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2460 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), 2461 O, Ops.size()); 2462 UniqueSCEVs.InsertNode(S, IP); 2463 return S; 2464} 2465 2466const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, 2467 const SCEV *RHS) { 2468 SmallVector<const SCEV *, 2> Ops; 2469 Ops.push_back(LHS); 2470 Ops.push_back(RHS); 2471 return getUMaxExpr(Ops); 2472} 2473 2474const SCEV * 2475ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { 2476 assert(!Ops.empty() && "Cannot get empty umax!"); 2477 if (Ops.size() == 1) return Ops[0]; 2478#ifndef NDEBUG 2479 Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); 2480 for (unsigned i = 1, e = Ops.size(); i != e; ++i) 2481 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && 2482 "SCEVUMaxExpr operand types don't match!"); 2483#endif 2484 2485 // Sort by complexity, this groups all similar expression types together. 2486 GroupByComplexity(Ops, LI); 2487 2488 // If there are any constants, fold them together. 2489 unsigned Idx = 0; 2490 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { 2491 ++Idx; 2492 assert(Idx < Ops.size()); 2493 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { 2494 // We found two constants, fold them together! 2495 ConstantInt *Fold = ConstantInt::get(getContext(), 2496 APIntOps::umax(LHSC->getValue()->getValue(), 2497 RHSC->getValue()->getValue())); 2498 Ops[0] = getConstant(Fold); 2499 Ops.erase(Ops.begin()+1); // Erase the folded element 2500 if (Ops.size() == 1) return Ops[0]; 2501 LHSC = cast<SCEVConstant>(Ops[0]); 2502 } 2503 2504 // If we are left with a constant minimum-int, strip it off. 2505 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { 2506 Ops.erase(Ops.begin()); 2507 --Idx; 2508 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { 2509 // If we have an umax with a constant maximum-int, it will always be 2510 // maximum-int. 2511 return Ops[0]; 2512 } 2513 2514 if (Ops.size() == 1) return Ops[0]; 2515 } 2516 2517 // Find the first UMax 2518 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) 2519 ++Idx; 2520 2521 // Check to see if one of the operands is a UMax. If so, expand its operands 2522 // onto our operand list, and recurse to simplify. 2523 if (Idx < Ops.size()) { 2524 bool DeletedUMax = false; 2525 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { 2526 Ops.erase(Ops.begin()+Idx); 2527 Ops.append(UMax->op_begin(), UMax->op_end()); 2528 DeletedUMax = true; 2529 } 2530 2531 if (DeletedUMax) 2532 return getUMaxExpr(Ops); 2533 } 2534 2535 // Okay, check to see if the same value occurs in the operand list twice. If 2536 // so, delete one. Since we sorted the list, these values are required to 2537 // be adjacent. 2538 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) 2539 // X umax Y umax Y --> X umax Y 2540 // X umax Y --> X, if X is always greater than Y 2541 if (Ops[i] == Ops[i+1] || 2542 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { 2543 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); 2544 --i; --e; 2545 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { 2546 Ops.erase(Ops.begin()+i, Ops.begin()+i+1); 2547 --i; --e; 2548 } 2549 2550 if (Ops.size() == 1) return Ops[0]; 2551 2552 assert(!Ops.empty() && "Reduced umax down to nothing!"); 2553 2554 // Okay, it looks like we really DO need a umax expr. Check to see if we 2555 // already have one, otherwise create a new one. 2556 FoldingSetNodeID ID; 2557 ID.AddInteger(scUMaxExpr); 2558 for (unsigned i = 0, e = Ops.size(); i != e; ++i) 2559 ID.AddPointer(Ops[i]); 2560 void *IP = 0; 2561 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; 2562 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); 2563 std::uninitialized_copy(Ops.begin(), Ops.end(), O); 2564 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), 2565 O, Ops.size()); 2566 UniqueSCEVs.InsertNode(S, IP); 2567 return S; 2568} 2569 2570const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, 2571 const SCEV *RHS) { 2572 // ~smax(~x, ~y) == smin(x, y). 2573 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2574} 2575 2576const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, 2577 const SCEV *RHS) { 2578 // ~umax(~x, ~y) == umin(x, y) 2579 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); 2580} 2581 2582const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) { 2583 // If we have TargetData, we can bypass creating a target-independent 2584 // constant expression and then folding it back into a ConstantInt. 2585 // This is just a compile-time optimization. 2586 if (TD) 2587 return getConstant(TD->getIntPtrType(getContext()), 2588 TD->getTypeAllocSize(AllocTy)); 2589 2590 Constant *C = ConstantExpr::getSizeOf(AllocTy); 2591 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2592 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2593 C = Folded; 2594 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2595 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2596} 2597 2598const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) { 2599 Constant *C = ConstantExpr::getAlignOf(AllocTy); 2600 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2601 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2602 C = Folded; 2603 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); 2604 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2605} 2606 2607const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, 2608 unsigned FieldNo) { 2609 // If we have TargetData, we can bypass creating a target-independent 2610 // constant expression and then folding it back into a ConstantInt. 2611 // This is just a compile-time optimization. 2612 if (TD) 2613 return getConstant(TD->getIntPtrType(getContext()), 2614 TD->getStructLayout(STy)->getElementOffset(FieldNo)); 2615 2616 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); 2617 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2618 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2619 C = Folded; 2620 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 2621 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2622} 2623 2624const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy, 2625 Constant *FieldNo) { 2626 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); 2627 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) 2628 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD)) 2629 C = Folded; 2630 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); 2631 return getTruncateOrZeroExtend(getSCEV(C), Ty); 2632} 2633 2634const SCEV *ScalarEvolution::getUnknown(Value *V) { 2635 // Don't attempt to do anything other than create a SCEVUnknown object 2636 // here. createSCEV only calls getUnknown after checking for all other 2637 // interesting possibilities, and any other code that calls getUnknown 2638 // is doing so in order to hide a value from SCEV canonicalization. 2639 2640 FoldingSetNodeID ID; 2641 ID.AddInteger(scUnknown); 2642 ID.AddPointer(V); 2643 void *IP = 0; 2644 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { 2645 assert(cast<SCEVUnknown>(S)->getValue() == V && 2646 "Stale SCEVUnknown in uniquing map!"); 2647 return S; 2648 } 2649 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, 2650 FirstUnknown); 2651 FirstUnknown = cast<SCEVUnknown>(S); 2652 UniqueSCEVs.InsertNode(S, IP); 2653 return S; 2654} 2655 2656//===----------------------------------------------------------------------===// 2657// Basic SCEV Analysis and PHI Idiom Recognition Code 2658// 2659 2660/// isSCEVable - Test if values of the given type are analyzable within 2661/// the SCEV framework. This primarily includes integer types, and it 2662/// can optionally include pointer types if the ScalarEvolution class 2663/// has access to target-specific information. 2664bool ScalarEvolution::isSCEVable(Type *Ty) const { 2665 // Integers and pointers are always SCEVable. 2666 return Ty->isIntegerTy() || Ty->isPointerTy(); 2667} 2668 2669/// getTypeSizeInBits - Return the size in bits of the specified type, 2670/// for which isSCEVable must return true. 2671uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const { 2672 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2673 2674 // If we have a TargetData, use it! 2675 if (TD) 2676 return TD->getTypeSizeInBits(Ty); 2677 2678 // Integer types have fixed sizes. 2679 if (Ty->isIntegerTy()) 2680 return Ty->getPrimitiveSizeInBits(); 2681 2682 // The only other support type is pointer. Without TargetData, conservatively 2683 // assume pointers are 64-bit. 2684 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); 2685 return 64; 2686} 2687 2688/// getEffectiveSCEVType - Return a type with the same bitwidth as 2689/// the given type and which represents how SCEV will treat the given 2690/// type, for which isSCEVable must return true. For pointer types, 2691/// this is the pointer-sized integer type. 2692Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const { 2693 assert(isSCEVable(Ty) && "Type is not SCEVable!"); 2694 2695 if (Ty->isIntegerTy()) 2696 return Ty; 2697 2698 // The only other support type is pointer. 2699 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); 2700 if (TD) return TD->getIntPtrType(getContext()); 2701 2702 // Without TargetData, conservatively assume pointers are 64-bit. 2703 return Type::getInt64Ty(getContext()); 2704} 2705 2706const SCEV *ScalarEvolution::getCouldNotCompute() { 2707 return &CouldNotCompute; 2708} 2709 2710/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the 2711/// expression and create a new one. 2712const SCEV *ScalarEvolution::getSCEV(Value *V) { 2713 assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); 2714 2715 ValueExprMapType::const_iterator I = ValueExprMap.find(V); 2716 if (I != ValueExprMap.end()) return I->second; 2717 const SCEV *S = createSCEV(V); 2718 2719 // The process of creating a SCEV for V may have caused other SCEVs 2720 // to have been created, so it's necessary to insert the new entry 2721 // from scratch, rather than trying to remember the insert position 2722 // above. 2723 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); 2724 return S; 2725} 2726 2727/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V 2728/// 2729const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { 2730 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2731 return getConstant( 2732 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); 2733 2734 Type *Ty = V->getType(); 2735 Ty = getEffectiveSCEVType(Ty); 2736 return getMulExpr(V, 2737 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); 2738} 2739 2740/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V 2741const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { 2742 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) 2743 return getConstant( 2744 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); 2745 2746 Type *Ty = V->getType(); 2747 Ty = getEffectiveSCEVType(Ty); 2748 const SCEV *AllOnes = 2749 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); 2750 return getMinusSCEV(AllOnes, V); 2751} 2752 2753/// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. 2754const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, 2755 SCEV::NoWrapFlags Flags) { 2756 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); 2757 2758 // Fast path: X - X --> 0. 2759 if (LHS == RHS) 2760 return getConstant(LHS->getType(), 0); 2761 2762 // X - Y --> X + -Y 2763 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags); 2764} 2765 2766/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the 2767/// input value to the specified type. If the type must be extended, it is zero 2768/// extended. 2769const SCEV * 2770ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) { 2771 Type *SrcTy = V->getType(); 2772 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2773 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2774 "Cannot truncate or zero extend with non-integer arguments!"); 2775 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2776 return V; // No conversion 2777 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2778 return getTruncateExpr(V, Ty); 2779 return getZeroExtendExpr(V, Ty); 2780} 2781 2782/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the 2783/// input value to the specified type. If the type must be extended, it is sign 2784/// extended. 2785const SCEV * 2786ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, 2787 Type *Ty) { 2788 Type *SrcTy = V->getType(); 2789 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2790 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2791 "Cannot truncate or zero extend with non-integer arguments!"); 2792 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2793 return V; // No conversion 2794 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) 2795 return getTruncateExpr(V, Ty); 2796 return getSignExtendExpr(V, Ty); 2797} 2798 2799/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the 2800/// input value to the specified type. If the type must be extended, it is zero 2801/// extended. The conversion must not be narrowing. 2802const SCEV * 2803ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { 2804 Type *SrcTy = V->getType(); 2805 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2806 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2807 "Cannot noop or zero extend with non-integer arguments!"); 2808 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2809 "getNoopOrZeroExtend cannot truncate!"); 2810 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2811 return V; // No conversion 2812 return getZeroExtendExpr(V, Ty); 2813} 2814 2815/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the 2816/// input value to the specified type. If the type must be extended, it is sign 2817/// extended. The conversion must not be narrowing. 2818const SCEV * 2819ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { 2820 Type *SrcTy = V->getType(); 2821 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2822 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2823 "Cannot noop or sign extend with non-integer arguments!"); 2824 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2825 "getNoopOrSignExtend cannot truncate!"); 2826 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2827 return V; // No conversion 2828 return getSignExtendExpr(V, Ty); 2829} 2830 2831/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of 2832/// the input value to the specified type. If the type must be extended, 2833/// it is extended with unspecified bits. The conversion must not be 2834/// narrowing. 2835const SCEV * 2836ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { 2837 Type *SrcTy = V->getType(); 2838 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2839 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2840 "Cannot noop or any extend with non-integer arguments!"); 2841 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && 2842 "getNoopOrAnyExtend cannot truncate!"); 2843 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2844 return V; // No conversion 2845 return getAnyExtendExpr(V, Ty); 2846} 2847 2848/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the 2849/// input value to the specified type. The conversion must not be widening. 2850const SCEV * 2851ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { 2852 Type *SrcTy = V->getType(); 2853 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && 2854 (Ty->isIntegerTy() || Ty->isPointerTy()) && 2855 "Cannot truncate or noop with non-integer arguments!"); 2856 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && 2857 "getTruncateOrNoop cannot extend!"); 2858 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) 2859 return V; // No conversion 2860 return getTruncateExpr(V, Ty); 2861} 2862 2863/// getUMaxFromMismatchedTypes - Promote the operands to the wider of 2864/// the types using zero-extension, and then perform a umax operation 2865/// with them. 2866const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, 2867 const SCEV *RHS) { 2868 const SCEV *PromotedLHS = LHS; 2869 const SCEV *PromotedRHS = RHS; 2870 2871 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2872 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2873 else 2874 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2875 2876 return getUMaxExpr(PromotedLHS, PromotedRHS); 2877} 2878 2879/// getUMinFromMismatchedTypes - Promote the operands to the wider of 2880/// the types using zero-extension, and then perform a umin operation 2881/// with them. 2882const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, 2883 const SCEV *RHS) { 2884 const SCEV *PromotedLHS = LHS; 2885 const SCEV *PromotedRHS = RHS; 2886 2887 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) 2888 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); 2889 else 2890 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); 2891 2892 return getUMinExpr(PromotedLHS, PromotedRHS); 2893} 2894 2895/// getPointerBase - Transitively follow the chain of pointer-type operands 2896/// until reaching a SCEV that does not have a single pointer operand. This 2897/// returns a SCEVUnknown pointer for well-formed pointer-type expressions, 2898/// but corner cases do exist. 2899const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { 2900 // A pointer operand may evaluate to a nonpointer expression, such as null. 2901 if (!V->getType()->isPointerTy()) 2902 return V; 2903 2904 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { 2905 return getPointerBase(Cast->getOperand()); 2906 } 2907 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { 2908 const SCEV *PtrOp = 0; 2909 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 2910 I != E; ++I) { 2911 if ((*I)->getType()->isPointerTy()) { 2912 // Cannot find the base of an expression with multiple pointer operands. 2913 if (PtrOp) 2914 return V; 2915 PtrOp = *I; 2916 } 2917 } 2918 if (!PtrOp) 2919 return V; 2920 return getPointerBase(PtrOp); 2921 } 2922 return V; 2923} 2924 2925/// PushDefUseChildren - Push users of the given Instruction 2926/// onto the given Worklist. 2927static void 2928PushDefUseChildren(Instruction *I, 2929 SmallVectorImpl<Instruction *> &Worklist) { 2930 // Push the def-use children onto the Worklist stack. 2931 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); 2932 UI != UE; ++UI) 2933 Worklist.push_back(cast<Instruction>(*UI)); 2934} 2935 2936/// ForgetSymbolicValue - This looks up computed SCEV values for all 2937/// instructions that depend on the given instruction and removes them from 2938/// the ValueExprMapType map if they reference SymName. This is used during PHI 2939/// resolution. 2940void 2941ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { 2942 SmallVector<Instruction *, 16> Worklist; 2943 PushDefUseChildren(PN, Worklist); 2944 2945 SmallPtrSet<Instruction *, 8> Visited; 2946 Visited.insert(PN); 2947 while (!Worklist.empty()) { 2948 Instruction *I = Worklist.pop_back_val(); 2949 if (!Visited.insert(I)) continue; 2950 2951 ValueExprMapType::iterator It = 2952 ValueExprMap.find(static_cast<Value *>(I)); 2953 if (It != ValueExprMap.end()) { 2954 const SCEV *Old = It->second; 2955 2956 // Short-circuit the def-use traversal if the symbolic name 2957 // ceases to appear in expressions. 2958 if (Old != SymName && !hasOperand(Old, SymName)) 2959 continue; 2960 2961 // SCEVUnknown for a PHI either means that it has an unrecognized 2962 // structure, it's a PHI that's in the progress of being computed 2963 // by createNodeForPHI, or it's a single-value PHI. In the first case, 2964 // additional loop trip count information isn't going to change anything. 2965 // In the second case, createNodeForPHI will perform the necessary 2966 // updates on its own when it gets to that point. In the third, we do 2967 // want to forget the SCEVUnknown. 2968 if (!isa<PHINode>(I) || 2969 !isa<SCEVUnknown>(Old) || 2970 (I != PN && Old == SymName)) { 2971 forgetMemoizedResults(Old); 2972 ValueExprMap.erase(It); 2973 } 2974 } 2975 2976 PushDefUseChildren(I, Worklist); 2977 } 2978} 2979 2980/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in 2981/// a loop header, making it a potential recurrence, or it doesn't. 2982/// 2983const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { 2984 if (const Loop *L = LI->getLoopFor(PN->getParent())) 2985 if (L->getHeader() == PN->getParent()) { 2986 // The loop may have multiple entrances or multiple exits; we can analyze 2987 // this phi as an addrec if it has a unique entry value and a unique 2988 // backedge value. 2989 Value *BEValueV = 0, *StartValueV = 0; 2990 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { 2991 Value *V = PN->getIncomingValue(i); 2992 if (L->contains(PN->getIncomingBlock(i))) { 2993 if (!BEValueV) { 2994 BEValueV = V; 2995 } else if (BEValueV != V) { 2996 BEValueV = 0; 2997 break; 2998 } 2999 } else if (!StartValueV) { 3000 StartValueV = V; 3001 } else if (StartValueV != V) { 3002 StartValueV = 0; 3003 break; 3004 } 3005 } 3006 if (BEValueV && StartValueV) { 3007 // While we are analyzing this PHI node, handle its value symbolically. 3008 const SCEV *SymbolicName = getUnknown(PN); 3009 assert(ValueExprMap.find(PN) == ValueExprMap.end() && 3010 "PHI node already processed?"); 3011 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); 3012 3013 // Using this symbolic name for the PHI, analyze the value coming around 3014 // the back-edge. 3015 const SCEV *BEValue = getSCEV(BEValueV); 3016 3017 // NOTE: If BEValue is loop invariant, we know that the PHI node just 3018 // has a special value for the first iteration of the loop. 3019 3020 // If the value coming around the backedge is an add with the symbolic 3021 // value we just inserted, then we found a simple induction variable! 3022 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { 3023 // If there is a single occurrence of the symbolic value, replace it 3024 // with a recurrence. 3025 unsigned FoundIndex = Add->getNumOperands(); 3026 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3027 if (Add->getOperand(i) == SymbolicName) 3028 if (FoundIndex == e) { 3029 FoundIndex = i; 3030 break; 3031 } 3032 3033 if (FoundIndex != Add->getNumOperands()) { 3034 // Create an add with everything but the specified operand. 3035 SmallVector<const SCEV *, 8> Ops; 3036 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) 3037 if (i != FoundIndex) 3038 Ops.push_back(Add->getOperand(i)); 3039 const SCEV *Accum = getAddExpr(Ops); 3040 3041 // This is not a valid addrec if the step amount is varying each 3042 // loop iteration, but is not itself an addrec in this loop. 3043 if (isLoopInvariant(Accum, L) || 3044 (isa<SCEVAddRecExpr>(Accum) && 3045 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { 3046 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; 3047 3048 // If the increment doesn't overflow, then neither the addrec nor 3049 // the post-increment will overflow. 3050 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { 3051 if (OBO->hasNoUnsignedWrap()) 3052 Flags = setFlags(Flags, SCEV::FlagNUW); 3053 if (OBO->hasNoSignedWrap()) 3054 Flags = setFlags(Flags, SCEV::FlagNSW); 3055 } else if (const GEPOperator *GEP = 3056 dyn_cast<GEPOperator>(BEValueV)) { 3057 // If the increment is an inbounds GEP, then we know the address 3058 // space cannot be wrapped around. We cannot make any guarantee 3059 // about signed or unsigned overflow because pointers are 3060 // unsigned but we may have a negative index from the base 3061 // pointer. 3062 if (GEP->isInBounds()) 3063 Flags = setFlags(Flags, SCEV::FlagNW); 3064 } 3065 3066 const SCEV *StartVal = getSCEV(StartValueV); 3067 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); 3068 3069 // Since the no-wrap flags are on the increment, they apply to the 3070 // post-incremented value as well. 3071 if (isLoopInvariant(Accum, L)) 3072 (void)getAddRecExpr(getAddExpr(StartVal, Accum), 3073 Accum, L, Flags); 3074 3075 // Okay, for the entire analysis of this edge we assumed the PHI 3076 // to be symbolic. We now need to go back and purge all of the 3077 // entries for the scalars that use the symbolic expression. 3078 ForgetSymbolicName(PN, SymbolicName); 3079 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3080 return PHISCEV; 3081 } 3082 } 3083 } else if (const SCEVAddRecExpr *AddRec = 3084 dyn_cast<SCEVAddRecExpr>(BEValue)) { 3085 // Otherwise, this could be a loop like this: 3086 // i = 0; for (j = 1; ..; ++j) { .... i = j; } 3087 // In this case, j = {1,+,1} and BEValue is j. 3088 // Because the other in-value of i (0) fits the evolution of BEValue 3089 // i really is an addrec evolution. 3090 if (AddRec->getLoop() == L && AddRec->isAffine()) { 3091 const SCEV *StartVal = getSCEV(StartValueV); 3092 3093 // If StartVal = j.start - j.stride, we can use StartVal as the 3094 // initial step of the addrec evolution. 3095 if (StartVal == getMinusSCEV(AddRec->getOperand(0), 3096 AddRec->getOperand(1))) { 3097 // FIXME: For constant StartVal, we should be able to infer 3098 // no-wrap flags. 3099 const SCEV *PHISCEV = 3100 getAddRecExpr(StartVal, AddRec->getOperand(1), L, 3101 SCEV::FlagAnyWrap); 3102 3103 // Okay, for the entire analysis of this edge we assumed the PHI 3104 // to be symbolic. We now need to go back and purge all of the 3105 // entries for the scalars that use the symbolic expression. 3106 ForgetSymbolicName(PN, SymbolicName); 3107 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; 3108 return PHISCEV; 3109 } 3110 } 3111 } 3112 } 3113 } 3114 3115 // If the PHI has a single incoming value, follow that value, unless the 3116 // PHI's incoming blocks are in a different loop, in which case doing so 3117 // risks breaking LCSSA form. Instcombine would normally zap these, but 3118 // it doesn't have DominatorTree information, so it may miss cases. 3119 if (Value *V = SimplifyInstruction(PN, TD, DT)) 3120 if (LI->replacementPreservesLCSSAForm(PN, V)) 3121 return getSCEV(V); 3122 3123 // If it's not a loop phi, we can't handle it yet. 3124 return getUnknown(PN); 3125} 3126 3127/// createNodeForGEP - Expand GEP instructions into add and multiply 3128/// operations. This allows them to be analyzed by regular SCEV code. 3129/// 3130const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { 3131 3132 // Don't blindly transfer the inbounds flag from the GEP instruction to the 3133 // Add expression, because the Instruction may be guarded by control flow 3134 // and the no-overflow bits may not be valid for the expression in any 3135 // context. 3136 bool isInBounds = GEP->isInBounds(); 3137 3138 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); 3139 Value *Base = GEP->getOperand(0); 3140 // Don't attempt to analyze GEPs over unsized objects. 3141 if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) 3142 return getUnknown(GEP); 3143 const SCEV *TotalOffset = getConstant(IntPtrTy, 0); 3144 gep_type_iterator GTI = gep_type_begin(GEP); 3145 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()), 3146 E = GEP->op_end(); 3147 I != E; ++I) { 3148 Value *Index = *I; 3149 // Compute the (potentially symbolic) offset in bytes for this index. 3150 if (StructType *STy = dyn_cast<StructType>(*GTI++)) { 3151 // For a struct, add the member offset. 3152 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); 3153 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo); 3154 3155 // Add the field offset to the running total offset. 3156 TotalOffset = getAddExpr(TotalOffset, FieldOffset); 3157 } else { 3158 // For an array, add the element offset, explicitly scaled. 3159 const SCEV *ElementSize = getSizeOfExpr(*GTI); 3160 const SCEV *IndexS = getSCEV(Index); 3161 // Getelementptr indices are signed. 3162 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); 3163 3164 // Multiply the index by the element size to compute the element offset. 3165 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, 3166 isInBounds ? SCEV::FlagNSW : 3167 SCEV::FlagAnyWrap); 3168 3169 // Add the element offset to the running total offset. 3170 TotalOffset = getAddExpr(TotalOffset, LocalOffset); 3171 } 3172 } 3173 3174 // Get the SCEV for the GEP base. 3175 const SCEV *BaseS = getSCEV(Base); 3176 3177 // Add the total offset from all the GEP indices to the base. 3178 return getAddExpr(BaseS, TotalOffset, 3179 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap); 3180} 3181 3182/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is 3183/// guaranteed to end in (at every loop iteration). It is, at the same time, 3184/// the minimum number of times S is divisible by 2. For example, given {4,+,8} 3185/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. 3186uint32_t 3187ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { 3188 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3189 return C->getValue()->getValue().countTrailingZeros(); 3190 3191 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) 3192 return std::min(GetMinTrailingZeros(T->getOperand()), 3193 (uint32_t)getTypeSizeInBits(T->getType())); 3194 3195 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { 3196 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3197 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3198 getTypeSizeInBits(E->getType()) : OpRes; 3199 } 3200 3201 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { 3202 uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); 3203 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? 3204 getTypeSizeInBits(E->getType()) : OpRes; 3205 } 3206 3207 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { 3208 // The result is the min of all operands results. 3209 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3210 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3211 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3212 return MinOpRes; 3213 } 3214 3215 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { 3216 // The result is the sum of all operands results. 3217 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); 3218 uint32_t BitWidth = getTypeSizeInBits(M->getType()); 3219 for (unsigned i = 1, e = M->getNumOperands(); 3220 SumOpRes != BitWidth && i != e; ++i) 3221 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), 3222 BitWidth); 3223 return SumOpRes; 3224 } 3225 3226 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { 3227 // The result is the min of all operands results. 3228 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); 3229 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) 3230 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); 3231 return MinOpRes; 3232 } 3233 3234 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { 3235 // The result is the min of all operands results. 3236 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3237 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3238 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3239 return MinOpRes; 3240 } 3241 3242 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { 3243 // The result is the min of all operands results. 3244 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); 3245 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) 3246 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); 3247 return MinOpRes; 3248 } 3249 3250 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3251 // For a SCEVUnknown, ask ValueTracking. 3252 unsigned BitWidth = getTypeSizeInBits(U->getType()); 3253 APInt Mask = APInt::getAllOnesValue(BitWidth); 3254 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3255 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); 3256 return Zeros.countTrailingOnes(); 3257 } 3258 3259 // SCEVUDivExpr 3260 return 0; 3261} 3262 3263/// getUnsignedRange - Determine the unsigned range for a particular SCEV. 3264/// 3265ConstantRange 3266ScalarEvolution::getUnsignedRange(const SCEV *S) { 3267 // See if we've computed this range already. 3268 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S); 3269 if (I != UnsignedRanges.end()) 3270 return I->second; 3271 3272 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3273 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue())); 3274 3275 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3276 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3277 3278 // If the value has known zeros, the maximum unsigned value will have those 3279 // known zeros as well. 3280 uint32_t TZ = GetMinTrailingZeros(S); 3281 if (TZ != 0) 3282 ConservativeResult = 3283 ConstantRange(APInt::getMinValue(BitWidth), 3284 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); 3285 3286 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3287 ConstantRange X = getUnsignedRange(Add->getOperand(0)); 3288 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3289 X = X.add(getUnsignedRange(Add->getOperand(i))); 3290 return setUnsignedRange(Add, ConservativeResult.intersectWith(X)); 3291 } 3292 3293 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3294 ConstantRange X = getUnsignedRange(Mul->getOperand(0)); 3295 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3296 X = X.multiply(getUnsignedRange(Mul->getOperand(i))); 3297 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); 3298 } 3299 3300 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3301 ConstantRange X = getUnsignedRange(SMax->getOperand(0)); 3302 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3303 X = X.smax(getUnsignedRange(SMax->getOperand(i))); 3304 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); 3305 } 3306 3307 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3308 ConstantRange X = getUnsignedRange(UMax->getOperand(0)); 3309 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3310 X = X.umax(getUnsignedRange(UMax->getOperand(i))); 3311 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); 3312 } 3313 3314 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3315 ConstantRange X = getUnsignedRange(UDiv->getLHS()); 3316 ConstantRange Y = getUnsignedRange(UDiv->getRHS()); 3317 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3318 } 3319 3320 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3321 ConstantRange X = getUnsignedRange(ZExt->getOperand()); 3322 return setUnsignedRange(ZExt, 3323 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3324 } 3325 3326 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3327 ConstantRange X = getUnsignedRange(SExt->getOperand()); 3328 return setUnsignedRange(SExt, 3329 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3330 } 3331 3332 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3333 ConstantRange X = getUnsignedRange(Trunc->getOperand()); 3334 return setUnsignedRange(Trunc, 3335 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3336 } 3337 3338 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3339 // If there's no unsigned wrap, the value will never be less than its 3340 // initial value. 3341 if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) 3342 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) 3343 if (!C->getValue()->isZero()) 3344 ConservativeResult = 3345 ConservativeResult.intersectWith( 3346 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); 3347 3348 // TODO: non-affine addrec 3349 if (AddRec->isAffine()) { 3350 Type *Ty = AddRec->getType(); 3351 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3352 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3353 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3354 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3355 3356 const SCEV *Start = AddRec->getStart(); 3357 const SCEV *Step = AddRec->getStepRecurrence(*this); 3358 3359 ConstantRange StartRange = getUnsignedRange(Start); 3360 ConstantRange StepRange = getSignedRange(Step); 3361 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3362 ConstantRange EndRange = 3363 StartRange.add(MaxBECountRange.multiply(StepRange)); 3364 3365 // Check for overflow. This must be done with ConstantRange arithmetic 3366 // because we could be called from within the ScalarEvolution overflow 3367 // checking code. 3368 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); 3369 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3370 ConstantRange ExtMaxBECountRange = 3371 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3372 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); 3373 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3374 ExtEndRange) 3375 return setUnsignedRange(AddRec, ConservativeResult); 3376 3377 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), 3378 EndRange.getUnsignedMin()); 3379 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), 3380 EndRange.getUnsignedMax()); 3381 if (Min.isMinValue() && Max.isMaxValue()) 3382 return setUnsignedRange(AddRec, ConservativeResult); 3383 return setUnsignedRange(AddRec, 3384 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3385 } 3386 } 3387 3388 return setUnsignedRange(AddRec, ConservativeResult); 3389 } 3390 3391 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3392 // For a SCEVUnknown, ask ValueTracking. 3393 APInt Mask = APInt::getAllOnesValue(BitWidth); 3394 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); 3395 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); 3396 if (Ones == ~Zeros + 1) 3397 return setUnsignedRange(U, ConservativeResult); 3398 return setUnsignedRange(U, 3399 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); 3400 } 3401 3402 return setUnsignedRange(S, ConservativeResult); 3403} 3404 3405/// getSignedRange - Determine the signed range for a particular SCEV. 3406/// 3407ConstantRange 3408ScalarEvolution::getSignedRange(const SCEV *S) { 3409 // See if we've computed this range already. 3410 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S); 3411 if (I != SignedRanges.end()) 3412 return I->second; 3413 3414 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) 3415 return setSignedRange(C, ConstantRange(C->getValue()->getValue())); 3416 3417 unsigned BitWidth = getTypeSizeInBits(S->getType()); 3418 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); 3419 3420 // If the value has known zeros, the maximum signed value will have those 3421 // known zeros as well. 3422 uint32_t TZ = GetMinTrailingZeros(S); 3423 if (TZ != 0) 3424 ConservativeResult = 3425 ConstantRange(APInt::getSignedMinValue(BitWidth), 3426 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); 3427 3428 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { 3429 ConstantRange X = getSignedRange(Add->getOperand(0)); 3430 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) 3431 X = X.add(getSignedRange(Add->getOperand(i))); 3432 return setSignedRange(Add, ConservativeResult.intersectWith(X)); 3433 } 3434 3435 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { 3436 ConstantRange X = getSignedRange(Mul->getOperand(0)); 3437 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) 3438 X = X.multiply(getSignedRange(Mul->getOperand(i))); 3439 return setSignedRange(Mul, ConservativeResult.intersectWith(X)); 3440 } 3441 3442 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { 3443 ConstantRange X = getSignedRange(SMax->getOperand(0)); 3444 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) 3445 X = X.smax(getSignedRange(SMax->getOperand(i))); 3446 return setSignedRange(SMax, ConservativeResult.intersectWith(X)); 3447 } 3448 3449 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { 3450 ConstantRange X = getSignedRange(UMax->getOperand(0)); 3451 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) 3452 X = X.umax(getSignedRange(UMax->getOperand(i))); 3453 return setSignedRange(UMax, ConservativeResult.intersectWith(X)); 3454 } 3455 3456 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { 3457 ConstantRange X = getSignedRange(UDiv->getLHS()); 3458 ConstantRange Y = getSignedRange(UDiv->getRHS()); 3459 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); 3460 } 3461 3462 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { 3463 ConstantRange X = getSignedRange(ZExt->getOperand()); 3464 return setSignedRange(ZExt, 3465 ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); 3466 } 3467 3468 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { 3469 ConstantRange X = getSignedRange(SExt->getOperand()); 3470 return setSignedRange(SExt, 3471 ConservativeResult.intersectWith(X.signExtend(BitWidth))); 3472 } 3473 3474 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { 3475 ConstantRange X = getSignedRange(Trunc->getOperand()); 3476 return setSignedRange(Trunc, 3477 ConservativeResult.intersectWith(X.truncate(BitWidth))); 3478 } 3479 3480 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { 3481 // If there's no signed wrap, and all the operands have the same sign or 3482 // zero, the value won't ever change sign. 3483 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) { 3484 bool AllNonNeg = true; 3485 bool AllNonPos = true; 3486 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 3487 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; 3488 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; 3489 } 3490 if (AllNonNeg) 3491 ConservativeResult = ConservativeResult.intersectWith( 3492 ConstantRange(APInt(BitWidth, 0), 3493 APInt::getSignedMinValue(BitWidth))); 3494 else if (AllNonPos) 3495 ConservativeResult = ConservativeResult.intersectWith( 3496 ConstantRange(APInt::getSignedMinValue(BitWidth), 3497 APInt(BitWidth, 1))); 3498 } 3499 3500 // TODO: non-affine addrec 3501 if (AddRec->isAffine()) { 3502 Type *Ty = AddRec->getType(); 3503 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); 3504 if (!isa<SCEVCouldNotCompute>(MaxBECount) && 3505 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { 3506 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); 3507 3508 const SCEV *Start = AddRec->getStart(); 3509 const SCEV *Step = AddRec->getStepRecurrence(*this); 3510 3511 ConstantRange StartRange = getSignedRange(Start); 3512 ConstantRange StepRange = getSignedRange(Step); 3513 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); 3514 ConstantRange EndRange = 3515 StartRange.add(MaxBECountRange.multiply(StepRange)); 3516 3517 // Check for overflow. This must be done with ConstantRange arithmetic 3518 // because we could be called from within the ScalarEvolution overflow 3519 // checking code. 3520 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); 3521 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); 3522 ConstantRange ExtMaxBECountRange = 3523 MaxBECountRange.zextOrTrunc(BitWidth*2+1); 3524 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); 3525 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != 3526 ExtEndRange) 3527 return setSignedRange(AddRec, ConservativeResult); 3528 3529 APInt Min = APIntOps::smin(StartRange.getSignedMin(), 3530 EndRange.getSignedMin()); 3531 APInt Max = APIntOps::smax(StartRange.getSignedMax(), 3532 EndRange.getSignedMax()); 3533 if (Min.isMinSignedValue() && Max.isMaxSignedValue()) 3534 return setSignedRange(AddRec, ConservativeResult); 3535 return setSignedRange(AddRec, 3536 ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); 3537 } 3538 } 3539 3540 return setSignedRange(AddRec, ConservativeResult); 3541 } 3542 3543 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { 3544 // For a SCEVUnknown, ask ValueTracking. 3545 if (!U->getValue()->getType()->isIntegerTy() && !TD) 3546 return setSignedRange(U, ConservativeResult); 3547 unsigned NS = ComputeNumSignBits(U->getValue(), TD); 3548 if (NS == 1) 3549 return setSignedRange(U, ConservativeResult); 3550 return setSignedRange(U, ConservativeResult.intersectWith( 3551 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), 3552 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); 3553 } 3554 3555 return setSignedRange(S, ConservativeResult); 3556} 3557 3558/// createSCEV - We know that there is no SCEV for the specified value. 3559/// Analyze the expression. 3560/// 3561const SCEV *ScalarEvolution::createSCEV(Value *V) { 3562 if (!isSCEVable(V->getType())) 3563 return getUnknown(V); 3564 3565 unsigned Opcode = Instruction::UserOp1; 3566 if (Instruction *I = dyn_cast<Instruction>(V)) { 3567 Opcode = I->getOpcode(); 3568 3569 // Don't attempt to analyze instructions in blocks that aren't 3570 // reachable. Such instructions don't matter, and they aren't required 3571 // to obey basic rules for definitions dominating uses which this 3572 // analysis depends on. 3573 if (!DT->isReachableFromEntry(I->getParent())) 3574 return getUnknown(V); 3575 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) 3576 Opcode = CE->getOpcode(); 3577 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) 3578 return getConstant(CI); 3579 else if (isa<ConstantPointerNull>(V)) 3580 return getConstant(V->getType(), 0); 3581 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) 3582 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); 3583 else 3584 return getUnknown(V); 3585 3586 Operator *U = cast<Operator>(V); 3587 switch (Opcode) { 3588 case Instruction::Add: { 3589 // The simple thing to do would be to just call getSCEV on both operands 3590 // and call getAddExpr with the result. However if we're looking at a 3591 // bunch of things all added together, this can be quite inefficient, 3592 // because it leads to N-1 getAddExpr calls for N ultimate operands. 3593 // Instead, gather up all the operands and make a single getAddExpr call. 3594 // LLVM IR canonical form means we need only traverse the left operands. 3595 // 3596 // Don't apply this instruction's NSW or NUW flags to the new 3597 // expression. The instruction may be guarded by control flow that the 3598 // no-wrap behavior depends on. Non-control-equivalent instructions can be 3599 // mapped to the same SCEV expression, and it would be incorrect to transfer 3600 // NSW/NUW semantics to those operations. 3601 SmallVector<const SCEV *, 4> AddOps; 3602 AddOps.push_back(getSCEV(U->getOperand(1))); 3603 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { 3604 unsigned Opcode = Op->getValueID() - Value::InstructionVal; 3605 if (Opcode != Instruction::Add && Opcode != Instruction::Sub) 3606 break; 3607 U = cast<Operator>(Op); 3608 const SCEV *Op1 = getSCEV(U->getOperand(1)); 3609 if (Opcode == Instruction::Sub) 3610 AddOps.push_back(getNegativeSCEV(Op1)); 3611 else 3612 AddOps.push_back(Op1); 3613 } 3614 AddOps.push_back(getSCEV(U->getOperand(0))); 3615 return getAddExpr(AddOps); 3616 } 3617 case Instruction::Mul: { 3618 // Don't transfer NSW/NUW for the same reason as AddExpr. 3619 SmallVector<const SCEV *, 4> MulOps; 3620 MulOps.push_back(getSCEV(U->getOperand(1))); 3621 for (Value *Op = U->getOperand(0); 3622 Op->getValueID() == Instruction::Mul + Value::InstructionVal; 3623 Op = U->getOperand(0)) { 3624 U = cast<Operator>(Op); 3625 MulOps.push_back(getSCEV(U->getOperand(1))); 3626 } 3627 MulOps.push_back(getSCEV(U->getOperand(0))); 3628 return getMulExpr(MulOps); 3629 } 3630 case Instruction::UDiv: 3631 return getUDivExpr(getSCEV(U->getOperand(0)), 3632 getSCEV(U->getOperand(1))); 3633 case Instruction::Sub: 3634 return getMinusSCEV(getSCEV(U->getOperand(0)), 3635 getSCEV(U->getOperand(1))); 3636 case Instruction::And: 3637 // For an expression like x&255 that merely masks off the high bits, 3638 // use zext(trunc(x)) as the SCEV expression. 3639 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3640 if (CI->isNullValue()) 3641 return getSCEV(U->getOperand(1)); 3642 if (CI->isAllOnesValue()) 3643 return getSCEV(U->getOperand(0)); 3644 const APInt &A = CI->getValue(); 3645 3646 // Instcombine's ShrinkDemandedConstant may strip bits out of 3647 // constants, obscuring what would otherwise be a low-bits mask. 3648 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant 3649 // knew about to reconstruct a low-bits mask value. 3650 unsigned LZ = A.countLeadingZeros(); 3651 unsigned BitWidth = A.getBitWidth(); 3652 APInt AllOnes = APInt::getAllOnesValue(BitWidth); 3653 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); 3654 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); 3655 3656 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); 3657 3658 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) 3659 return 3660 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), 3661 IntegerType::get(getContext(), BitWidth - LZ)), 3662 U->getType()); 3663 } 3664 break; 3665 3666 case Instruction::Or: 3667 // If the RHS of the Or is a constant, we may have something like: 3668 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop 3669 // optimizations will transparently handle this case. 3670 // 3671 // In order for this transformation to be safe, the LHS must be of the 3672 // form X*(2^n) and the Or constant must be less than 2^n. 3673 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3674 const SCEV *LHS = getSCEV(U->getOperand(0)); 3675 const APInt &CIVal = CI->getValue(); 3676 if (GetMinTrailingZeros(LHS) >= 3677 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { 3678 // Build a plain add SCEV. 3679 const SCEV *S = getAddExpr(LHS, getSCEV(CI)); 3680 // If the LHS of the add was an addrec and it has no-wrap flags, 3681 // transfer the no-wrap flags, since an or won't introduce a wrap. 3682 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { 3683 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); 3684 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( 3685 OldAR->getNoWrapFlags()); 3686 } 3687 return S; 3688 } 3689 } 3690 break; 3691 case Instruction::Xor: 3692 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { 3693 // If the RHS of the xor is a signbit, then this is just an add. 3694 // Instcombine turns add of signbit into xor as a strength reduction step. 3695 if (CI->getValue().isSignBit()) 3696 return getAddExpr(getSCEV(U->getOperand(0)), 3697 getSCEV(U->getOperand(1))); 3698 3699 // If the RHS of xor is -1, then this is a not operation. 3700 if (CI->isAllOnesValue()) 3701 return getNotSCEV(getSCEV(U->getOperand(0))); 3702 3703 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. 3704 // This is a variant of the check for xor with -1, and it handles 3705 // the case where instcombine has trimmed non-demanded bits out 3706 // of an xor with -1. 3707 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) 3708 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) 3709 if (BO->getOpcode() == Instruction::And && 3710 LCI->getValue() == CI->getValue()) 3711 if (const SCEVZeroExtendExpr *Z = 3712 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { 3713 Type *UTy = U->getType(); 3714 const SCEV *Z0 = Z->getOperand(); 3715 Type *Z0Ty = Z0->getType(); 3716 unsigned Z0TySize = getTypeSizeInBits(Z0Ty); 3717 3718 // If C is a low-bits mask, the zero extend is serving to 3719 // mask off the high bits. Complement the operand and 3720 // re-apply the zext. 3721 if (APIntOps::isMask(Z0TySize, CI->getValue())) 3722 return getZeroExtendExpr(getNotSCEV(Z0), UTy); 3723 3724 // If C is a single bit, it may be in the sign-bit position 3725 // before the zero-extend. In this case, represent the xor 3726 // using an add, which is equivalent, and re-apply the zext. 3727 APInt Trunc = CI->getValue().trunc(Z0TySize); 3728 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() && 3729 Trunc.isSignBit()) 3730 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), 3731 UTy); 3732 } 3733 } 3734 break; 3735 3736 case Instruction::Shl: 3737 // Turn shift left of a constant amount into a multiply. 3738 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3739 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3740 3741 // If the shift count is not less than the bitwidth, the result of 3742 // the shift is undefined. Don't try to analyze it, because the 3743 // resolution chosen here may differ from the resolution chosen in 3744 // other parts of the compiler. 3745 if (SA->getValue().uge(BitWidth)) 3746 break; 3747 3748 Constant *X = ConstantInt::get(getContext(), 3749 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3750 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3751 } 3752 break; 3753 3754 case Instruction::LShr: 3755 // Turn logical shift right of a constant into a unsigned divide. 3756 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { 3757 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); 3758 3759 // If the shift count is not less than the bitwidth, the result of 3760 // the shift is undefined. Don't try to analyze it, because the 3761 // resolution chosen here may differ from the resolution chosen in 3762 // other parts of the compiler. 3763 if (SA->getValue().uge(BitWidth)) 3764 break; 3765 3766 Constant *X = ConstantInt::get(getContext(), 3767 APInt(BitWidth, 1).shl(SA->getZExtValue())); 3768 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); 3769 } 3770 break; 3771 3772 case Instruction::AShr: 3773 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. 3774 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) 3775 if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) 3776 if (L->getOpcode() == Instruction::Shl && 3777 L->getOperand(1) == U->getOperand(1)) { 3778 uint64_t BitWidth = getTypeSizeInBits(U->getType()); 3779 3780 // If the shift count is not less than the bitwidth, the result of 3781 // the shift is undefined. Don't try to analyze it, because the 3782 // resolution chosen here may differ from the resolution chosen in 3783 // other parts of the compiler. 3784 if (CI->getValue().uge(BitWidth)) 3785 break; 3786 3787 uint64_t Amt = BitWidth - CI->getZExtValue(); 3788 if (Amt == BitWidth) 3789 return getSCEV(L->getOperand(0)); // shift by zero --> noop 3790 return 3791 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), 3792 IntegerType::get(getContext(), 3793 Amt)), 3794 U->getType()); 3795 } 3796 break; 3797 3798 case Instruction::Trunc: 3799 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); 3800 3801 case Instruction::ZExt: 3802 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3803 3804 case Instruction::SExt: 3805 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); 3806 3807 case Instruction::BitCast: 3808 // BitCasts are no-op casts so we just eliminate the cast. 3809 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) 3810 return getSCEV(U->getOperand(0)); 3811 break; 3812 3813 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can 3814 // lead to pointer expressions which cannot safely be expanded to GEPs, 3815 // because ScalarEvolution doesn't respect the GEP aliasing rules when 3816 // simplifying integer expressions. 3817 3818 case Instruction::GetElementPtr: 3819 return createNodeForGEP(cast<GEPOperator>(U)); 3820 3821 case Instruction::PHI: 3822 return createNodeForPHI(cast<PHINode>(U)); 3823 3824 case Instruction::Select: 3825 // This could be a smax or umax that was lowered earlier. 3826 // Try to recover it. 3827 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { 3828 Value *LHS = ICI->getOperand(0); 3829 Value *RHS = ICI->getOperand(1); 3830 switch (ICI->getPredicate()) { 3831 case ICmpInst::ICMP_SLT: 3832 case ICmpInst::ICMP_SLE: 3833 std::swap(LHS, RHS); 3834 // fall through 3835 case ICmpInst::ICMP_SGT: 3836 case ICmpInst::ICMP_SGE: 3837 // a >s b ? a+x : b+x -> smax(a, b)+x 3838 // a >s b ? b+x : a+x -> smin(a, b)+x 3839 if (LHS->getType() == U->getType()) { 3840 const SCEV *LS = getSCEV(LHS); 3841 const SCEV *RS = getSCEV(RHS); 3842 const SCEV *LA = getSCEV(U->getOperand(1)); 3843 const SCEV *RA = getSCEV(U->getOperand(2)); 3844 const SCEV *LDiff = getMinusSCEV(LA, LS); 3845 const SCEV *RDiff = getMinusSCEV(RA, RS); 3846 if (LDiff == RDiff) 3847 return getAddExpr(getSMaxExpr(LS, RS), LDiff); 3848 LDiff = getMinusSCEV(LA, RS); 3849 RDiff = getMinusSCEV(RA, LS); 3850 if (LDiff == RDiff) 3851 return getAddExpr(getSMinExpr(LS, RS), LDiff); 3852 } 3853 break; 3854 case ICmpInst::ICMP_ULT: 3855 case ICmpInst::ICMP_ULE: 3856 std::swap(LHS, RHS); 3857 // fall through 3858 case ICmpInst::ICMP_UGT: 3859 case ICmpInst::ICMP_UGE: 3860 // a >u b ? a+x : b+x -> umax(a, b)+x 3861 // a >u b ? b+x : a+x -> umin(a, b)+x 3862 if (LHS->getType() == U->getType()) { 3863 const SCEV *LS = getSCEV(LHS); 3864 const SCEV *RS = getSCEV(RHS); 3865 const SCEV *LA = getSCEV(U->getOperand(1)); 3866 const SCEV *RA = getSCEV(U->getOperand(2)); 3867 const SCEV *LDiff = getMinusSCEV(LA, LS); 3868 const SCEV *RDiff = getMinusSCEV(RA, RS); 3869 if (LDiff == RDiff) 3870 return getAddExpr(getUMaxExpr(LS, RS), LDiff); 3871 LDiff = getMinusSCEV(LA, RS); 3872 RDiff = getMinusSCEV(RA, LS); 3873 if (LDiff == RDiff) 3874 return getAddExpr(getUMinExpr(LS, RS), LDiff); 3875 } 3876 break; 3877 case ICmpInst::ICMP_NE: 3878 // n != 0 ? n+x : 1+x -> umax(n, 1)+x 3879 if (LHS->getType() == U->getType() && 3880 isa<ConstantInt>(RHS) && 3881 cast<ConstantInt>(RHS)->isZero()) { 3882 const SCEV *One = getConstant(LHS->getType(), 1); 3883 const SCEV *LS = getSCEV(LHS); 3884 const SCEV *LA = getSCEV(U->getOperand(1)); 3885 const SCEV *RA = getSCEV(U->getOperand(2)); 3886 const SCEV *LDiff = getMinusSCEV(LA, LS); 3887 const SCEV *RDiff = getMinusSCEV(RA, One); 3888 if (LDiff == RDiff) 3889 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3890 } 3891 break; 3892 case ICmpInst::ICMP_EQ: 3893 // n == 0 ? 1+x : n+x -> umax(n, 1)+x 3894 if (LHS->getType() == U->getType() && 3895 isa<ConstantInt>(RHS) && 3896 cast<ConstantInt>(RHS)->isZero()) { 3897 const SCEV *One = getConstant(LHS->getType(), 1); 3898 const SCEV *LS = getSCEV(LHS); 3899 const SCEV *LA = getSCEV(U->getOperand(1)); 3900 const SCEV *RA = getSCEV(U->getOperand(2)); 3901 const SCEV *LDiff = getMinusSCEV(LA, One); 3902 const SCEV *RDiff = getMinusSCEV(RA, LS); 3903 if (LDiff == RDiff) 3904 return getAddExpr(getUMaxExpr(One, LS), LDiff); 3905 } 3906 break; 3907 default: 3908 break; 3909 } 3910 } 3911 3912 default: // We cannot analyze this expression. 3913 break; 3914 } 3915 3916 return getUnknown(V); 3917} 3918 3919 3920 3921//===----------------------------------------------------------------------===// 3922// Iteration Count Computation Code 3923// 3924 3925/// getSmallConstantTripCount - Returns the maximum trip count of this loop as a 3926/// normal unsigned value, if possible. Returns 0 if the trip count is unknown 3927/// or not constant. Will also return 0 if the maximum trip count is very large 3928/// (>= 2^32) 3929unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, 3930 BasicBlock *ExitBlock) { 3931 const SCEVConstant *ExitCount = 3932 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock)); 3933 if (!ExitCount) 3934 return 0; 3935 3936 ConstantInt *ExitConst = ExitCount->getValue(); 3937 3938 // Guard against huge trip counts. 3939 if (ExitConst->getValue().getActiveBits() > 32) 3940 return 0; 3941 3942 // In case of integer overflow, this returns 0, which is correct. 3943 return ((unsigned)ExitConst->getZExtValue()) + 1; 3944} 3945 3946/// getSmallConstantTripMultiple - Returns the largest constant divisor of the 3947/// trip count of this loop as a normal unsigned value, if possible. This 3948/// means that the actual trip count is always a multiple of the returned 3949/// value (don't forget the trip count could very well be zero as well!). 3950/// 3951/// Returns 1 if the trip count is unknown or not guaranteed to be the 3952/// multiple of a constant (which is also the case if the trip count is simply 3953/// constant, use getSmallConstantTripCount for that case), Will also return 1 3954/// if the trip count is very large (>= 2^32). 3955unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L, 3956 BasicBlock *ExitBlock) { 3957 const SCEV *ExitCount = getExitCount(L, ExitBlock); 3958 if (ExitCount == getCouldNotCompute()) 3959 return 1; 3960 3961 // Get the trip count from the BE count by adding 1. 3962 const SCEV *TCMul = getAddExpr(ExitCount, 3963 getConstant(ExitCount->getType(), 1)); 3964 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt 3965 // to factor simple cases. 3966 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul)) 3967 TCMul = Mul->getOperand(0); 3968 3969 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul); 3970 if (!MulC) 3971 return 1; 3972 3973 ConstantInt *Result = MulC->getValue(); 3974 3975 // Guard against huge trip counts. 3976 if (!Result || Result->getValue().getActiveBits() > 32) 3977 return 1; 3978 3979 return (unsigned)Result->getZExtValue(); 3980} 3981 3982// getExitCount - Get the expression for the number of loop iterations for which 3983// this loop is guaranteed not to exit via ExitintBlock. Otherwise return 3984// SCEVCouldNotCompute. 3985const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { 3986 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); 3987} 3988 3989/// getBackedgeTakenCount - If the specified loop has a predictable 3990/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute 3991/// object. The backedge-taken count is the number of times the loop header 3992/// will be branched to from within the loop. This is one less than the 3993/// trip count of the loop, since it doesn't count the first iteration, 3994/// when the header is branched to from outside the loop. 3995/// 3996/// Note that it is not valid to call this method on a loop without a 3997/// loop-invariant backedge-taken count (see 3998/// hasLoopInvariantBackedgeTakenCount). 3999/// 4000const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { 4001 return getBackedgeTakenInfo(L).getExact(this); 4002} 4003 4004/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except 4005/// return the least SCEV value that is known never to be less than the 4006/// actual backedge taken count. 4007const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { 4008 return getBackedgeTakenInfo(L).getMax(this); 4009} 4010 4011/// PushLoopPHIs - Push PHI nodes in the header of the given loop 4012/// onto the given Worklist. 4013static void 4014PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { 4015 BasicBlock *Header = L->getHeader(); 4016 4017 // Push all Loop-header PHIs onto the Worklist stack. 4018 for (BasicBlock::iterator I = Header->begin(); 4019 PHINode *PN = dyn_cast<PHINode>(I); ++I) 4020 Worklist.push_back(PN); 4021} 4022 4023const ScalarEvolution::BackedgeTakenInfo & 4024ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { 4025 // Initially insert an invalid entry for this loop. If the insertion 4026 // succeeds, proceed to actually compute a backedge-taken count and 4027 // update the value. The temporary CouldNotCompute value tells SCEV 4028 // code elsewhere that it shouldn't attempt to request a new 4029 // backedge-taken count, which could result in infinite recursion. 4030 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = 4031 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); 4032 if (!Pair.second) 4033 return Pair.first->second; 4034 4035 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it 4036 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result 4037 // must be cleared in this scope. 4038 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); 4039 4040 if (Result.getExact(this) != getCouldNotCompute()) { 4041 assert(isLoopInvariant(Result.getExact(this), L) && 4042 isLoopInvariant(Result.getMax(this), L) && 4043 "Computed backedge-taken count isn't loop invariant for loop!"); 4044 ++NumTripCountsComputed; 4045 } 4046 else if (Result.getMax(this) == getCouldNotCompute() && 4047 isa<PHINode>(L->getHeader()->begin())) { 4048 // Only count loops that have phi nodes as not being computable. 4049 ++NumTripCountsNotComputed; 4050 } 4051 4052 // Now that we know more about the trip count for this loop, forget any 4053 // existing SCEV values for PHI nodes in this loop since they are only 4054 // conservative estimates made without the benefit of trip count 4055 // information. This is similar to the code in forgetLoop, except that 4056 // it handles SCEVUnknown PHI nodes specially. 4057 if (Result.hasAnyInfo()) { 4058 SmallVector<Instruction *, 16> Worklist; 4059 PushLoopPHIs(L, Worklist); 4060 4061 SmallPtrSet<Instruction *, 8> Visited; 4062 while (!Worklist.empty()) { 4063 Instruction *I = Worklist.pop_back_val(); 4064 if (!Visited.insert(I)) continue; 4065 4066 ValueExprMapType::iterator It = 4067 ValueExprMap.find(static_cast<Value *>(I)); 4068 if (It != ValueExprMap.end()) { 4069 const SCEV *Old = It->second; 4070 4071 // SCEVUnknown for a PHI either means that it has an unrecognized 4072 // structure, or it's a PHI that's in the progress of being computed 4073 // by createNodeForPHI. In the former case, additional loop trip 4074 // count information isn't going to change anything. In the later 4075 // case, createNodeForPHI will perform the necessary updates on its 4076 // own when it gets to that point. 4077 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) { 4078 forgetMemoizedResults(Old); 4079 ValueExprMap.erase(It); 4080 } 4081 if (PHINode *PN = dyn_cast<PHINode>(I)) 4082 ConstantEvolutionLoopExitValue.erase(PN); 4083 } 4084 4085 PushDefUseChildren(I, Worklist); 4086 } 4087 } 4088 4089 // Re-lookup the insert position, since the call to 4090 // ComputeBackedgeTakenCount above could result in a 4091 // recusive call to getBackedgeTakenInfo (on a different 4092 // loop), which would invalidate the iterator computed 4093 // earlier. 4094 return BackedgeTakenCounts.find(L)->second = Result; 4095} 4096 4097/// forgetLoop - This method should be called by the client when it has 4098/// changed a loop in a way that may effect ScalarEvolution's ability to 4099/// compute a trip count, or if the loop is deleted. 4100void ScalarEvolution::forgetLoop(const Loop *L) { 4101 // Drop any stored trip count value. 4102 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos = 4103 BackedgeTakenCounts.find(L); 4104 if (BTCPos != BackedgeTakenCounts.end()) { 4105 BTCPos->second.clear(); 4106 BackedgeTakenCounts.erase(BTCPos); 4107 } 4108 4109 // Drop information about expressions based on loop-header PHIs. 4110 SmallVector<Instruction *, 16> Worklist; 4111 PushLoopPHIs(L, Worklist); 4112 4113 SmallPtrSet<Instruction *, 8> Visited; 4114 while (!Worklist.empty()) { 4115 Instruction *I = Worklist.pop_back_val(); 4116 if (!Visited.insert(I)) continue; 4117 4118 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4119 if (It != ValueExprMap.end()) { 4120 forgetMemoizedResults(It->second); 4121 ValueExprMap.erase(It); 4122 if (PHINode *PN = dyn_cast<PHINode>(I)) 4123 ConstantEvolutionLoopExitValue.erase(PN); 4124 } 4125 4126 PushDefUseChildren(I, Worklist); 4127 } 4128 4129 // Forget all contained loops too, to avoid dangling entries in the 4130 // ValuesAtScopes map. 4131 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 4132 forgetLoop(*I); 4133} 4134 4135/// forgetValue - This method should be called by the client when it has 4136/// changed a value in a way that may effect its value, or which may 4137/// disconnect it from a def-use chain linking it to a loop. 4138void ScalarEvolution::forgetValue(Value *V) { 4139 Instruction *I = dyn_cast<Instruction>(V); 4140 if (!I) return; 4141 4142 // Drop information about expressions based on loop-header PHIs. 4143 SmallVector<Instruction *, 16> Worklist; 4144 Worklist.push_back(I); 4145 4146 SmallPtrSet<Instruction *, 8> Visited; 4147 while (!Worklist.empty()) { 4148 I = Worklist.pop_back_val(); 4149 if (!Visited.insert(I)) continue; 4150 4151 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I)); 4152 if (It != ValueExprMap.end()) { 4153 forgetMemoizedResults(It->second); 4154 ValueExprMap.erase(It); 4155 if (PHINode *PN = dyn_cast<PHINode>(I)) 4156 ConstantEvolutionLoopExitValue.erase(PN); 4157 } 4158 4159 PushDefUseChildren(I, Worklist); 4160 } 4161} 4162 4163/// getExact - Get the exact loop backedge taken count considering all loop 4164/// exits. A computable result can only be return for loops with a single exit. 4165/// Returning the minimum taken count among all exits is incorrect because one 4166/// of the loop's exit limit's may have been skipped. HowFarToZero assumes that 4167/// the limit of each loop test is never skipped. This is a valid assumption as 4168/// long as the loop exits via that test. For precise results, it is the 4169/// caller's responsibility to specify the relevant loop exit using 4170/// getExact(ExitingBlock, SE). 4171const SCEV * 4172ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { 4173 // If any exits were not computable, the loop is not computable. 4174 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); 4175 4176 // We need exactly one computable exit. 4177 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); 4178 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); 4179 4180 const SCEV *BECount = 0; 4181 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4182 ENT != 0; ENT = ENT->getNextExit()) { 4183 4184 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); 4185 4186 if (!BECount) 4187 BECount = ENT->ExactNotTaken; 4188 else if (BECount != ENT->ExactNotTaken) 4189 return SE->getCouldNotCompute(); 4190 } 4191 assert(BECount && "Invalid not taken count for loop exit"); 4192 return BECount; 4193} 4194 4195/// getExact - Get the exact not taken count for this loop exit. 4196const SCEV * 4197ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, 4198 ScalarEvolution *SE) const { 4199 for (const ExitNotTakenInfo *ENT = &ExitNotTaken; 4200 ENT != 0; ENT = ENT->getNextExit()) { 4201 4202 if (ENT->ExitingBlock == ExitingBlock) 4203 return ENT->ExactNotTaken; 4204 } 4205 return SE->getCouldNotCompute(); 4206} 4207 4208/// getMax - Get the max backedge taken count for the loop. 4209const SCEV * 4210ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { 4211 return Max ? Max : SE->getCouldNotCompute(); 4212} 4213 4214/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each 4215/// computable exit into a persistent ExitNotTakenInfo array. 4216ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( 4217 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts, 4218 bool Complete, const SCEV *MaxCount) : Max(MaxCount) { 4219 4220 if (!Complete) 4221 ExitNotTaken.setIncomplete(); 4222 4223 unsigned NumExits = ExitCounts.size(); 4224 if (NumExits == 0) return; 4225 4226 ExitNotTaken.ExitingBlock = ExitCounts[0].first; 4227 ExitNotTaken.ExactNotTaken = ExitCounts[0].second; 4228 if (NumExits == 1) return; 4229 4230 // Handle the rare case of multiple computable exits. 4231 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; 4232 4233 ExitNotTakenInfo *PrevENT = &ExitNotTaken; 4234 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { 4235 PrevENT->setNextExit(ENT); 4236 ENT->ExitingBlock = ExitCounts[i].first; 4237 ENT->ExactNotTaken = ExitCounts[i].second; 4238 } 4239} 4240 4241/// clear - Invalidate this result and free the ExitNotTakenInfo array. 4242void ScalarEvolution::BackedgeTakenInfo::clear() { 4243 ExitNotTaken.ExitingBlock = 0; 4244 ExitNotTaken.ExactNotTaken = 0; 4245 delete[] ExitNotTaken.getNextExit(); 4246} 4247 4248/// ComputeBackedgeTakenCount - Compute the number of times the backedge 4249/// of the specified loop will execute. 4250ScalarEvolution::BackedgeTakenInfo 4251ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { 4252 SmallVector<BasicBlock *, 8> ExitingBlocks; 4253 L->getExitingBlocks(ExitingBlocks); 4254 4255 // Examine all exits and pick the most conservative values. 4256 const SCEV *MaxBECount = getCouldNotCompute(); 4257 bool CouldComputeBECount = true; 4258 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts; 4259 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { 4260 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]); 4261 if (EL.Exact == getCouldNotCompute()) 4262 // We couldn't compute an exact value for this exit, so 4263 // we won't be able to compute an exact value for the loop. 4264 CouldComputeBECount = false; 4265 else 4266 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact)); 4267 4268 if (MaxBECount == getCouldNotCompute()) 4269 MaxBECount = EL.Max; 4270 else if (EL.Max != getCouldNotCompute()) { 4271 // We cannot take the "min" MaxBECount, because non-unit stride loops may 4272 // skip some loop tests. Taking the max over the exits is sufficiently 4273 // conservative. TODO: We could do better taking into consideration 4274 // that (1) the loop has unit stride (2) the last loop test is 4275 // less-than/greater-than (3) any loop test is less-than/greater-than AND 4276 // falls-through some constant times less then the other tests. 4277 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max); 4278 } 4279 } 4280 4281 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); 4282} 4283 4284/// ComputeExitLimit - Compute the number of times the backedge of the specified 4285/// loop will execute if it exits via the specified block. 4286ScalarEvolution::ExitLimit 4287ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { 4288 4289 // Okay, we've chosen an exiting block. See what condition causes us to 4290 // exit at this block. 4291 // 4292 // FIXME: we should be able to handle switch instructions (with a single exit) 4293 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); 4294 if (ExitBr == 0) return getCouldNotCompute(); 4295 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); 4296 4297 // At this point, we know we have a conditional branch that determines whether 4298 // the loop is exited. However, we don't know if the branch is executed each 4299 // time through the loop. If not, then the execution count of the branch will 4300 // not be equal to the trip count of the loop. 4301 // 4302 // Currently we check for this by checking to see if the Exit branch goes to 4303 // the loop header. If so, we know it will always execute the same number of 4304 // times as the loop. We also handle the case where the exit block *is* the 4305 // loop header. This is common for un-rotated loops. 4306 // 4307 // If both of those tests fail, walk up the unique predecessor chain to the 4308 // header, stopping if there is an edge that doesn't exit the loop. If the 4309 // header is reached, the execution count of the branch will be equal to the 4310 // trip count of the loop. 4311 // 4312 // More extensive analysis could be done to handle more cases here. 4313 // 4314 if (ExitBr->getSuccessor(0) != L->getHeader() && 4315 ExitBr->getSuccessor(1) != L->getHeader() && 4316 ExitBr->getParent() != L->getHeader()) { 4317 // The simple checks failed, try climbing the unique predecessor chain 4318 // up to the header. 4319 bool Ok = false; 4320 for (BasicBlock *BB = ExitBr->getParent(); BB; ) { 4321 BasicBlock *Pred = BB->getUniquePredecessor(); 4322 if (!Pred) 4323 return getCouldNotCompute(); 4324 TerminatorInst *PredTerm = Pred->getTerminator(); 4325 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { 4326 BasicBlock *PredSucc = PredTerm->getSuccessor(i); 4327 if (PredSucc == BB) 4328 continue; 4329 // If the predecessor has a successor that isn't BB and isn't 4330 // outside the loop, assume the worst. 4331 if (L->contains(PredSucc)) 4332 return getCouldNotCompute(); 4333 } 4334 if (Pred == L->getHeader()) { 4335 Ok = true; 4336 break; 4337 } 4338 BB = Pred; 4339 } 4340 if (!Ok) 4341 return getCouldNotCompute(); 4342 } 4343 4344 // Proceed to the next level to examine the exit condition expression. 4345 return ComputeExitLimitFromCond(L, ExitBr->getCondition(), 4346 ExitBr->getSuccessor(0), 4347 ExitBr->getSuccessor(1)); 4348} 4349 4350/// ComputeExitLimitFromCond - Compute the number of times the 4351/// backedge of the specified loop will execute if its exit condition 4352/// were a conditional branch of ExitCond, TBB, and FBB. 4353ScalarEvolution::ExitLimit 4354ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, 4355 Value *ExitCond, 4356 BasicBlock *TBB, 4357 BasicBlock *FBB) { 4358 // Check if the controlling expression for this loop is an And or Or. 4359 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { 4360 if (BO->getOpcode() == Instruction::And) { 4361 // Recurse on the operands of the and. 4362 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4363 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4364 const SCEV *BECount = getCouldNotCompute(); 4365 const SCEV *MaxBECount = getCouldNotCompute(); 4366 if (L->contains(TBB)) { 4367 // Both conditions must be true for the loop to continue executing. 4368 // Choose the less conservative count. 4369 if (EL0.Exact == getCouldNotCompute() || 4370 EL1.Exact == getCouldNotCompute()) 4371 BECount = getCouldNotCompute(); 4372 else 4373 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4374 if (EL0.Max == getCouldNotCompute()) 4375 MaxBECount = EL1.Max; 4376 else if (EL1.Max == getCouldNotCompute()) 4377 MaxBECount = EL0.Max; 4378 else 4379 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4380 } else { 4381 // Both conditions must be true at the same time for the loop to exit. 4382 // For now, be conservative. 4383 assert(L->contains(FBB) && "Loop block has no successor in loop!"); 4384 if (EL0.Max == EL1.Max) 4385 MaxBECount = EL0.Max; 4386 if (EL0.Exact == EL1.Exact) 4387 BECount = EL0.Exact; 4388 } 4389 4390 return ExitLimit(BECount, MaxBECount); 4391 } 4392 if (BO->getOpcode() == Instruction::Or) { 4393 // Recurse on the operands of the or. 4394 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB); 4395 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB); 4396 const SCEV *BECount = getCouldNotCompute(); 4397 const SCEV *MaxBECount = getCouldNotCompute(); 4398 if (L->contains(FBB)) { 4399 // Both conditions must be false for the loop to continue executing. 4400 // Choose the less conservative count. 4401 if (EL0.Exact == getCouldNotCompute() || 4402 EL1.Exact == getCouldNotCompute()) 4403 BECount = getCouldNotCompute(); 4404 else 4405 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); 4406 if (EL0.Max == getCouldNotCompute()) 4407 MaxBECount = EL1.Max; 4408 else if (EL1.Max == getCouldNotCompute()) 4409 MaxBECount = EL0.Max; 4410 else 4411 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); 4412 } else { 4413 // Both conditions must be false at the same time for the loop to exit. 4414 // For now, be conservative. 4415 assert(L->contains(TBB) && "Loop block has no successor in loop!"); 4416 if (EL0.Max == EL1.Max) 4417 MaxBECount = EL0.Max; 4418 if (EL0.Exact == EL1.Exact) 4419 BECount = EL0.Exact; 4420 } 4421 4422 return ExitLimit(BECount, MaxBECount); 4423 } 4424 } 4425 4426 // With an icmp, it may be feasible to compute an exact backedge-taken count. 4427 // Proceed to the next level to examine the icmp. 4428 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) 4429 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB); 4430 4431 // Check for a constant condition. These are normally stripped out by 4432 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to 4433 // preserve the CFG and is temporarily leaving constant conditions 4434 // in place. 4435 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { 4436 if (L->contains(FBB) == !CI->getZExtValue()) 4437 // The backedge is always taken. 4438 return getCouldNotCompute(); 4439 else 4440 // The backedge is never taken. 4441 return getConstant(CI->getType(), 0); 4442 } 4443 4444 // If it's not an integer or pointer comparison then compute it the hard way. 4445 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4446} 4447 4448/// ComputeExitLimitFromICmp - Compute the number of times the 4449/// backedge of the specified loop will execute if its exit condition 4450/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. 4451ScalarEvolution::ExitLimit 4452ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, 4453 ICmpInst *ExitCond, 4454 BasicBlock *TBB, 4455 BasicBlock *FBB) { 4456 4457 // If the condition was exit on true, convert the condition to exit on false 4458 ICmpInst::Predicate Cond; 4459 if (!L->contains(FBB)) 4460 Cond = ExitCond->getPredicate(); 4461 else 4462 Cond = ExitCond->getInversePredicate(); 4463 4464 // Handle common loops like: for (X = "string"; *X; ++X) 4465 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) 4466 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { 4467 ExitLimit ItCnt = 4468 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond); 4469 if (ItCnt.hasAnyInfo()) 4470 return ItCnt; 4471 } 4472 4473 const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); 4474 const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); 4475 4476 // Try to evaluate any dependencies out of the loop. 4477 LHS = getSCEVAtScope(LHS, L); 4478 RHS = getSCEVAtScope(RHS, L); 4479 4480 // At this point, we would like to compute how many iterations of the 4481 // loop the predicate will return true for these inputs. 4482 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) { 4483 // If there is a loop-invariant, force it into the RHS. 4484 std::swap(LHS, RHS); 4485 Cond = ICmpInst::getSwappedPredicate(Cond); 4486 } 4487 4488 // Simplify the operands before analyzing them. 4489 (void)SimplifyICmpOperands(Cond, LHS, RHS); 4490 4491 // If we have a comparison of a chrec against a constant, try to use value 4492 // ranges to answer this query. 4493 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) 4494 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) 4495 if (AddRec->getLoop() == L) { 4496 // Form the constant range. 4497 ConstantRange CompRange( 4498 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); 4499 4500 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); 4501 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; 4502 } 4503 4504 switch (Cond) { 4505 case ICmpInst::ICMP_NE: { // while (X != Y) 4506 // Convert to: while (X-Y != 0) 4507 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L); 4508 if (EL.hasAnyInfo()) return EL; 4509 break; 4510 } 4511 case ICmpInst::ICMP_EQ: { // while (X == Y) 4512 // Convert to: while (X-Y == 0) 4513 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); 4514 if (EL.hasAnyInfo()) return EL; 4515 break; 4516 } 4517 case ICmpInst::ICMP_SLT: { 4518 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true); 4519 if (EL.hasAnyInfo()) return EL; 4520 break; 4521 } 4522 case ICmpInst::ICMP_SGT: { 4523 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4524 getNotSCEV(RHS), L, true); 4525 if (EL.hasAnyInfo()) return EL; 4526 break; 4527 } 4528 case ICmpInst::ICMP_ULT: { 4529 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false); 4530 if (EL.hasAnyInfo()) return EL; 4531 break; 4532 } 4533 case ICmpInst::ICMP_UGT: { 4534 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS), 4535 getNotSCEV(RHS), L, false); 4536 if (EL.hasAnyInfo()) return EL; 4537 break; 4538 } 4539 default: 4540#if 0 4541 dbgs() << "ComputeBackedgeTakenCount "; 4542 if (ExitCond->getOperand(0)->getType()->isUnsigned()) 4543 dbgs() << "[unsigned] "; 4544 dbgs() << *LHS << " " 4545 << Instruction::getOpcodeName(Instruction::ICmp) 4546 << " " << *RHS << "\n"; 4547#endif 4548 break; 4549 } 4550 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); 4551} 4552 4553static ConstantInt * 4554EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, 4555 ScalarEvolution &SE) { 4556 const SCEV *InVal = SE.getConstant(C); 4557 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); 4558 assert(isa<SCEVConstant>(Val) && 4559 "Evaluation of SCEV at constant didn't fold correctly?"); 4560 return cast<SCEVConstant>(Val)->getValue(); 4561} 4562 4563/// GetAddressedElementFromGlobal - Given a global variable with an initializer 4564/// and a GEP expression (missing the pointer index) indexing into it, return 4565/// the addressed element of the initializer or null if the index expression is 4566/// invalid. 4567static Constant * 4568GetAddressedElementFromGlobal(GlobalVariable *GV, 4569 const std::vector<ConstantInt*> &Indices) { 4570 Constant *Init = GV->getInitializer(); 4571 for (unsigned i = 0, e = Indices.size(); i != e; ++i) { 4572 uint64_t Idx = Indices[i]->getZExtValue(); 4573 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { 4574 assert(Idx < CS->getNumOperands() && "Bad struct index!"); 4575 Init = cast<Constant>(CS->getOperand(Idx)); 4576 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { 4577 if (Idx >= CA->getNumOperands()) return 0; // Bogus program 4578 Init = cast<Constant>(CA->getOperand(Idx)); 4579 } else if (isa<ConstantAggregateZero>(Init)) { 4580 if (StructType *STy = dyn_cast<StructType>(Init->getType())) { 4581 assert(Idx < STy->getNumElements() && "Bad struct index!"); 4582 Init = Constant::getNullValue(STy->getElementType(Idx)); 4583 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { 4584 if (Idx >= ATy->getNumElements()) return 0; // Bogus program 4585 Init = Constant::getNullValue(ATy->getElementType()); 4586 } else { 4587 llvm_unreachable("Unknown constant aggregate type!"); 4588 } 4589 return 0; 4590 } else { 4591 return 0; // Unknown initializer type 4592 } 4593 } 4594 return Init; 4595} 4596 4597/// ComputeLoadConstantCompareExitLimit - Given an exit condition of 4598/// 'icmp op load X, cst', try to see if we can compute the backedge 4599/// execution count. 4600ScalarEvolution::ExitLimit 4601ScalarEvolution::ComputeLoadConstantCompareExitLimit( 4602 LoadInst *LI, 4603 Constant *RHS, 4604 const Loop *L, 4605 ICmpInst::Predicate predicate) { 4606 4607 if (LI->isVolatile()) return getCouldNotCompute(); 4608 4609 // Check to see if the loaded pointer is a getelementptr of a global. 4610 // TODO: Use SCEV instead of manually grubbing with GEPs. 4611 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); 4612 if (!GEP) return getCouldNotCompute(); 4613 4614 // Make sure that it is really a constant global we are gepping, with an 4615 // initializer, and make sure the first IDX is really 0. 4616 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); 4617 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || 4618 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || 4619 !cast<Constant>(GEP->getOperand(1))->isNullValue()) 4620 return getCouldNotCompute(); 4621 4622 // Okay, we allow one non-constant index into the GEP instruction. 4623 Value *VarIdx = 0; 4624 std::vector<ConstantInt*> Indexes; 4625 unsigned VarIdxNum = 0; 4626 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) 4627 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { 4628 Indexes.push_back(CI); 4629 } else if (!isa<ConstantInt>(GEP->getOperand(i))) { 4630 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. 4631 VarIdx = GEP->getOperand(i); 4632 VarIdxNum = i-2; 4633 Indexes.push_back(0); 4634 } 4635 4636 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. 4637 // Check to see if X is a loop variant variable value now. 4638 const SCEV *Idx = getSCEV(VarIdx); 4639 Idx = getSCEVAtScope(Idx, L); 4640 4641 // We can only recognize very limited forms of loop index expressions, in 4642 // particular, only affine AddRec's like {C1,+,C2}. 4643 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); 4644 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || 4645 !isa<SCEVConstant>(IdxExpr->getOperand(0)) || 4646 !isa<SCEVConstant>(IdxExpr->getOperand(1))) 4647 return getCouldNotCompute(); 4648 4649 unsigned MaxSteps = MaxBruteForceIterations; 4650 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { 4651 ConstantInt *ItCst = ConstantInt::get( 4652 cast<IntegerType>(IdxExpr->getType()), IterationNum); 4653 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); 4654 4655 // Form the GEP offset. 4656 Indexes[VarIdxNum] = Val; 4657 4658 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); 4659 if (Result == 0) break; // Cannot compute! 4660 4661 // Evaluate the condition for this iteration. 4662 Result = ConstantExpr::getICmp(predicate, Result, RHS); 4663 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure 4664 if (cast<ConstantInt>(Result)->getValue().isMinValue()) { 4665#if 0 4666 dbgs() << "\n***\n*** Computed loop count " << *ItCst 4667 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() 4668 << "***\n"; 4669#endif 4670 ++NumArrayLenItCounts; 4671 return getConstant(ItCst); // Found terminating iteration! 4672 } 4673 } 4674 return getCouldNotCompute(); 4675} 4676 4677 4678/// CanConstantFold - Return true if we can constant fold an instruction of the 4679/// specified type, assuming that all operands were constants. 4680static bool CanConstantFold(const Instruction *I) { 4681 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || 4682 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || 4683 isa<LoadInst>(I)) 4684 return true; 4685 4686 if (const CallInst *CI = dyn_cast<CallInst>(I)) 4687 if (const Function *F = CI->getCalledFunction()) 4688 return canConstantFoldCallTo(F); 4689 return false; 4690} 4691 4692/// Determine whether this instruction can constant evolve within this loop 4693/// assuming its operands can all constant evolve. 4694static bool canConstantEvolve(Instruction *I, const Loop *L) { 4695 // An instruction outside of the loop can't be derived from a loop PHI. 4696 if (!L->contains(I)) return false; 4697 4698 if (isa<PHINode>(I)) { 4699 if (L->getHeader() == I->getParent()) 4700 return true; 4701 else 4702 // We don't currently keep track of the control flow needed to evaluate 4703 // PHIs, so we cannot handle PHIs inside of loops. 4704 return false; 4705 } 4706 4707 // If we won't be able to constant fold this expression even if the operands 4708 // are constants, bail early. 4709 return CanConstantFold(I); 4710} 4711 4712/// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by 4713/// recursing through each instruction operand until reaching a loop header phi. 4714static PHINode * 4715getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, 4716 DenseMap<Instruction *, PHINode *> &PHIMap) { 4717 4718 // Otherwise, we can evaluate this instruction if all of its operands are 4719 // constant or derived from a PHI node themselves. 4720 PHINode *PHI = 0; 4721 for (Instruction::op_iterator OpI = UseInst->op_begin(), 4722 OpE = UseInst->op_end(); OpI != OpE; ++OpI) { 4723 4724 if (isa<Constant>(*OpI)) continue; 4725 4726 Instruction *OpInst = dyn_cast<Instruction>(*OpI); 4727 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0; 4728 4729 PHINode *P = dyn_cast<PHINode>(OpInst); 4730 if (!P) 4731 // If this operand is already visited, reuse the prior result. 4732 // We may have P != PHI if this is the deepest point at which the 4733 // inconsistent paths meet. 4734 P = PHIMap.lookup(OpInst); 4735 if (!P) { 4736 // Recurse and memoize the results, whether a phi is found or not. 4737 // This recursive call invalidates pointers into PHIMap. 4738 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap); 4739 PHIMap[OpInst] = P; 4740 } 4741 if (P == 0) return 0; // Not evolving from PHI 4742 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs. 4743 PHI = P; 4744 } 4745 // This is a expression evolving from a constant PHI! 4746 return PHI; 4747} 4748 4749/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node 4750/// in the loop that V is derived from. We allow arbitrary operations along the 4751/// way, but the operands of an operation must either be constants or a value 4752/// derived from a constant PHI. If this expression does not fit with these 4753/// constraints, return null. 4754static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { 4755 Instruction *I = dyn_cast<Instruction>(V); 4756 if (I == 0 || !canConstantEvolve(I, L)) return 0; 4757 4758 if (PHINode *PN = dyn_cast<PHINode>(I)) { 4759 return PN; 4760 } 4761 4762 // Record non-constant instructions contained by the loop. 4763 DenseMap<Instruction *, PHINode *> PHIMap; 4764 return getConstantEvolvingPHIOperands(I, L, PHIMap); 4765} 4766 4767/// EvaluateExpression - Given an expression that passes the 4768/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node 4769/// in the loop has the value PHIVal. If we can't fold this expression for some 4770/// reason, return null. 4771static Constant *EvaluateExpression(Value *V, const Loop *L, 4772 DenseMap<Instruction *, Constant *> &Vals, 4773 const TargetData *TD) { 4774 // Convenient constant check, but redundant for recursive calls. 4775 if (Constant *C = dyn_cast<Constant>(V)) return C; 4776 Instruction *I = dyn_cast<Instruction>(V); 4777 if (!I) return 0; 4778 4779 if (Constant *C = Vals.lookup(I)) return C; 4780 4781 // An instruction inside the loop depends on a value outside the loop that we 4782 // weren't given a mapping for, or a value such as a call inside the loop. 4783 if (!canConstantEvolve(I, L)) return 0; 4784 4785 // An unmapped PHI can be due to a branch or another loop inside this loop, 4786 // or due to this not being the initial iteration through a loop where we 4787 // couldn't compute the evolution of this particular PHI last time. 4788 if (isa<PHINode>(I)) return 0; 4789 4790 std::vector<Constant*> Operands(I->getNumOperands()); 4791 4792 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 4793 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); 4794 if (!Operand) { 4795 Operands[i] = dyn_cast<Constant>(I->getOperand(i)); 4796 if (!Operands[i]) return 0; 4797 continue; 4798 } 4799 Constant *C = EvaluateExpression(Operand, L, Vals, TD); 4800 Vals[Operand] = C; 4801 if (!C) return 0; 4802 Operands[i] = C; 4803 } 4804 4805 if (CmpInst *CI = dyn_cast<CmpInst>(I)) 4806 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], 4807 Operands[1], TD); 4808 if (LoadInst *LI = dyn_cast<LoadInst>(I)) { 4809 if (!LI->isVolatile()) 4810 return ConstantFoldLoadFromConstPtr(Operands[0], TD); 4811 } 4812 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD); 4813} 4814 4815/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is 4816/// in the header of its containing loop, we know the loop executes a 4817/// constant number of times, and the PHI node is just a recurrence 4818/// involving constants, fold it. 4819Constant * 4820ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, 4821 const APInt &BEs, 4822 const Loop *L) { 4823 DenseMap<PHINode*, Constant*>::const_iterator I = 4824 ConstantEvolutionLoopExitValue.find(PN); 4825 if (I != ConstantEvolutionLoopExitValue.end()) 4826 return I->second; 4827 4828 if (BEs.ugt(MaxBruteForceIterations)) 4829 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. 4830 4831 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; 4832 4833 DenseMap<Instruction *, Constant *> CurrentIterVals; 4834 BasicBlock *Header = L->getHeader(); 4835 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 4836 4837 // Since the loop is canonicalized, the PHI node must have two entries. One 4838 // entry must be a constant (coming in from outside of the loop), and the 4839 // second must be derived from the same PHI. 4840 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4841 PHINode *PHI = 0; 4842 for (BasicBlock::iterator I = Header->begin(); 4843 (PHI = dyn_cast<PHINode>(I)); ++I) { 4844 Constant *StartCST = 4845 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 4846 if (StartCST == 0) continue; 4847 CurrentIterVals[PHI] = StartCST; 4848 } 4849 if (!CurrentIterVals.count(PN)) 4850 return RetVal = 0; 4851 4852 Value *BEValue = PN->getIncomingValue(SecondIsBackedge); 4853 4854 // Execute the loop symbolically to determine the exit value. 4855 if (BEs.getActiveBits() >= 32) 4856 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! 4857 4858 unsigned NumIterations = BEs.getZExtValue(); // must be in range 4859 unsigned IterationNum = 0; 4860 for (; ; ++IterationNum) { 4861 if (IterationNum == NumIterations) 4862 return RetVal = CurrentIterVals[PN]; // Got exit value! 4863 4864 // Compute the value of the PHIs for the next iteration. 4865 // EvaluateExpression adds non-phi values to the CurrentIterVals map. 4866 DenseMap<Instruction *, Constant *> NextIterVals; 4867 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD); 4868 if (NextPHI == 0) 4869 return 0; // Couldn't evaluate! 4870 NextIterVals[PN] = NextPHI; 4871 4872 bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; 4873 4874 // Also evaluate the other PHI nodes. However, we don't get to stop if we 4875 // cease to be able to evaluate one of them or if they stop evolving, 4876 // because that doesn't necessarily prevent us from computing PN. 4877 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; 4878 for (DenseMap<Instruction *, Constant *>::const_iterator 4879 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 4880 PHINode *PHI = dyn_cast<PHINode>(I->first); 4881 if (!PHI || PHI == PN || PHI->getParent() != Header) continue; 4882 PHIsToCompute.push_back(std::make_pair(PHI, I->second)); 4883 } 4884 // We use two distinct loops because EvaluateExpression may invalidate any 4885 // iterators into CurrentIterVals. 4886 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator 4887 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) { 4888 PHINode *PHI = I->first; 4889 Constant *&NextPHI = NextIterVals[PHI]; 4890 if (!NextPHI) { // Not already computed. 4891 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 4892 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD); 4893 } 4894 if (NextPHI != I->second) 4895 StoppedEvolving = false; 4896 } 4897 4898 // If all entries in CurrentIterVals == NextIterVals then we can stop 4899 // iterating, the loop can't continue to change. 4900 if (StoppedEvolving) 4901 return RetVal = CurrentIterVals[PN]; 4902 4903 CurrentIterVals.swap(NextIterVals); 4904 } 4905} 4906 4907/// ComputeExitCountExhaustively - If the loop is known to execute a 4908/// constant number of times (the condition evolves only from constants), 4909/// try to evaluate a few iterations of the loop until we get the exit 4910/// condition gets a value of ExitWhen (true or false). If we cannot 4911/// evaluate the trip count of the loop, return getCouldNotCompute(). 4912const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L, 4913 Value *Cond, 4914 bool ExitWhen) { 4915 PHINode *PN = getConstantEvolvingPHI(Cond, L); 4916 if (PN == 0) return getCouldNotCompute(); 4917 4918 // If the loop is canonicalized, the PHI will have exactly two entries. 4919 // That's the only form we support here. 4920 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); 4921 4922 DenseMap<Instruction *, Constant *> CurrentIterVals; 4923 BasicBlock *Header = L->getHeader(); 4924 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); 4925 4926 // One entry must be a constant (coming in from outside of the loop), and the 4927 // second must be derived from the same PHI. 4928 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); 4929 PHINode *PHI = 0; 4930 for (BasicBlock::iterator I = Header->begin(); 4931 (PHI = dyn_cast<PHINode>(I)); ++I) { 4932 Constant *StartCST = 4933 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge)); 4934 if (StartCST == 0) continue; 4935 CurrentIterVals[PHI] = StartCST; 4936 } 4937 if (!CurrentIterVals.count(PN)) 4938 return getCouldNotCompute(); 4939 4940 // Okay, we find a PHI node that defines the trip count of this loop. Execute 4941 // the loop symbolically to determine when the condition gets a value of 4942 // "ExitWhen". 4943 4944 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. 4945 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ 4946 ConstantInt *CondVal = 4947 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, 4948 CurrentIterVals, TD)); 4949 4950 // Couldn't symbolically evaluate. 4951 if (!CondVal) return getCouldNotCompute(); 4952 4953 if (CondVal->getValue() == uint64_t(ExitWhen)) { 4954 ++NumBruteForceTripCountsComputed; 4955 return getConstant(Type::getInt32Ty(getContext()), IterationNum); 4956 } 4957 4958 // Update all the PHI nodes for the next iteration. 4959 DenseMap<Instruction *, Constant *> NextIterVals; 4960 4961 // Create a list of which PHIs we need to compute. We want to do this before 4962 // calling EvaluateExpression on them because that may invalidate iterators 4963 // into CurrentIterVals. 4964 SmallVector<PHINode *, 8> PHIsToCompute; 4965 for (DenseMap<Instruction *, Constant *>::const_iterator 4966 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ 4967 PHINode *PHI = dyn_cast<PHINode>(I->first); 4968 if (!PHI || PHI->getParent() != Header) continue; 4969 PHIsToCompute.push_back(PHI); 4970 } 4971 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(), 4972 E = PHIsToCompute.end(); I != E; ++I) { 4973 PHINode *PHI = *I; 4974 Constant *&NextPHI = NextIterVals[PHI]; 4975 if (NextPHI) continue; // Already computed! 4976 4977 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); 4978 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD); 4979 } 4980 CurrentIterVals.swap(NextIterVals); 4981 } 4982 4983 // Too many iterations were needed to evaluate. 4984 return getCouldNotCompute(); 4985} 4986 4987/// getSCEVAtScope - Return a SCEV expression for the specified value 4988/// at the specified scope in the program. The L value specifies a loop 4989/// nest to evaluate the expression at, where null is the top-level or a 4990/// specified loop is immediately inside of the loop. 4991/// 4992/// This method can be used to compute the exit value for a variable defined 4993/// in a loop by querying what the value will hold in the parent loop. 4994/// 4995/// In the case that a relevant loop exit value cannot be computed, the 4996/// original value V is returned. 4997const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { 4998 // Check to see if we've folded this expression at this loop before. 4999 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; 5000 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = 5001 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); 5002 if (!Pair.second) 5003 return Pair.first->second ? Pair.first->second : V; 5004 5005 // Otherwise compute it. 5006 const SCEV *C = computeSCEVAtScope(V, L); 5007 ValuesAtScopes[V][L] = C; 5008 return C; 5009} 5010 5011/// This builds up a Constant using the ConstantExpr interface. That way, we 5012/// will return Constants for objects which aren't represented by a 5013/// SCEVConstant, because SCEVConstant is restricted to ConstantInt. 5014/// Returns NULL if the SCEV isn't representable as a Constant. 5015static Constant *BuildConstantFromSCEV(const SCEV *V) { 5016 switch (V->getSCEVType()) { 5017 default: // TODO: smax, umax. 5018 case scCouldNotCompute: 5019 case scAddRecExpr: 5020 break; 5021 case scConstant: 5022 return cast<SCEVConstant>(V)->getValue(); 5023 case scUnknown: 5024 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); 5025 case scSignExtend: { 5026 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); 5027 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) 5028 return ConstantExpr::getSExt(CastOp, SS->getType()); 5029 break; 5030 } 5031 case scZeroExtend: { 5032 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); 5033 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) 5034 return ConstantExpr::getZExt(CastOp, SZ->getType()); 5035 break; 5036 } 5037 case scTruncate: { 5038 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); 5039 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) 5040 return ConstantExpr::getTrunc(CastOp, ST->getType()); 5041 break; 5042 } 5043 case scAddExpr: { 5044 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); 5045 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { 5046 if (C->getType()->isPointerTy()) 5047 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext())); 5048 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { 5049 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); 5050 if (!C2) return 0; 5051 5052 // First pointer! 5053 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { 5054 std::swap(C, C2); 5055 // The offsets have been converted to bytes. We can add bytes to an 5056 // i8* by GEP with the byte count in the first index. 5057 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext())); 5058 } 5059 5060 // Don't bother trying to sum two pointers. We probably can't 5061 // statically compute a load that results from it anyway. 5062 if (C2->getType()->isPointerTy()) 5063 return 0; 5064 5065 if (C->getType()->isPointerTy()) { 5066 if (cast<PointerType>(C->getType())->getElementType()->isStructTy()) 5067 C2 = ConstantExpr::getIntegerCast( 5068 C2, Type::getInt32Ty(C->getContext()), true); 5069 C = ConstantExpr::getGetElementPtr(C, C2); 5070 } else 5071 C = ConstantExpr::getAdd(C, C2); 5072 } 5073 return C; 5074 } 5075 break; 5076 } 5077 case scMulExpr: { 5078 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); 5079 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { 5080 // Don't bother with pointers at all. 5081 if (C->getType()->isPointerTy()) return 0; 5082 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { 5083 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); 5084 if (!C2 || C2->getType()->isPointerTy()) return 0; 5085 C = ConstantExpr::getMul(C, C2); 5086 } 5087 return C; 5088 } 5089 break; 5090 } 5091 case scUDivExpr: { 5092 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); 5093 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) 5094 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) 5095 if (LHS->getType() == RHS->getType()) 5096 return ConstantExpr::getUDiv(LHS, RHS); 5097 break; 5098 } 5099 } 5100 return 0; 5101} 5102 5103const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { 5104 if (isa<SCEVConstant>(V)) return V; 5105 5106 // If this instruction is evolved from a constant-evolving PHI, compute the 5107 // exit value from the loop without using SCEVs. 5108 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { 5109 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { 5110 const Loop *LI = (*this->LI)[I->getParent()]; 5111 if (LI && LI->getParentLoop() == L) // Looking for loop exit value. 5112 if (PHINode *PN = dyn_cast<PHINode>(I)) 5113 if (PN->getParent() == LI->getHeader()) { 5114 // Okay, there is no closed form solution for the PHI node. Check 5115 // to see if the loop that contains it has a known backedge-taken 5116 // count. If so, we may be able to force computation of the exit 5117 // value. 5118 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); 5119 if (const SCEVConstant *BTCC = 5120 dyn_cast<SCEVConstant>(BackedgeTakenCount)) { 5121 // Okay, we know how many times the containing loop executes. If 5122 // this is a constant evolving PHI node, get the final value at 5123 // the specified iteration number. 5124 Constant *RV = getConstantEvolutionLoopExitValue(PN, 5125 BTCC->getValue()->getValue(), 5126 LI); 5127 if (RV) return getSCEV(RV); 5128 } 5129 } 5130 5131 // Okay, this is an expression that we cannot symbolically evaluate 5132 // into a SCEV. Check to see if it's possible to symbolically evaluate 5133 // the arguments into constants, and if so, try to constant propagate the 5134 // result. This is particularly useful for computing loop exit values. 5135 if (CanConstantFold(I)) { 5136 SmallVector<Constant *, 4> Operands; 5137 bool MadeImprovement = false; 5138 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { 5139 Value *Op = I->getOperand(i); 5140 if (Constant *C = dyn_cast<Constant>(Op)) { 5141 Operands.push_back(C); 5142 continue; 5143 } 5144 5145 // If any of the operands is non-constant and if they are 5146 // non-integer and non-pointer, don't even try to analyze them 5147 // with scev techniques. 5148 if (!isSCEVable(Op->getType())) 5149 return V; 5150 5151 const SCEV *OrigV = getSCEV(Op); 5152 const SCEV *OpV = getSCEVAtScope(OrigV, L); 5153 MadeImprovement |= OrigV != OpV; 5154 5155 Constant *C = BuildConstantFromSCEV(OpV); 5156 if (!C) return V; 5157 if (C->getType() != Op->getType()) 5158 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, 5159 Op->getType(), 5160 false), 5161 C, Op->getType()); 5162 Operands.push_back(C); 5163 } 5164 5165 // Check to see if getSCEVAtScope actually made an improvement. 5166 if (MadeImprovement) { 5167 Constant *C = 0; 5168 if (const CmpInst *CI = dyn_cast<CmpInst>(I)) 5169 C = ConstantFoldCompareInstOperands(CI->getPredicate(), 5170 Operands[0], Operands[1], TD); 5171 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) { 5172 if (!LI->isVolatile()) 5173 C = ConstantFoldLoadFromConstPtr(Operands[0], TD); 5174 } else 5175 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), 5176 Operands, TD); 5177 if (!C) return V; 5178 return getSCEV(C); 5179 } 5180 } 5181 } 5182 5183 // This is some other type of SCEVUnknown, just return it. 5184 return V; 5185 } 5186 5187 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { 5188 // Avoid performing the look-up in the common case where the specified 5189 // expression has no loop-variant portions. 5190 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { 5191 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5192 if (OpAtScope != Comm->getOperand(i)) { 5193 // Okay, at least one of these operands is loop variant but might be 5194 // foldable. Build a new instance of the folded commutative expression. 5195 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), 5196 Comm->op_begin()+i); 5197 NewOps.push_back(OpAtScope); 5198 5199 for (++i; i != e; ++i) { 5200 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); 5201 NewOps.push_back(OpAtScope); 5202 } 5203 if (isa<SCEVAddExpr>(Comm)) 5204 return getAddExpr(NewOps); 5205 if (isa<SCEVMulExpr>(Comm)) 5206 return getMulExpr(NewOps); 5207 if (isa<SCEVSMaxExpr>(Comm)) 5208 return getSMaxExpr(NewOps); 5209 if (isa<SCEVUMaxExpr>(Comm)) 5210 return getUMaxExpr(NewOps); 5211 llvm_unreachable("Unknown commutative SCEV type!"); 5212 } 5213 } 5214 // If we got here, all operands are loop invariant. 5215 return Comm; 5216 } 5217 5218 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { 5219 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); 5220 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); 5221 if (LHS == Div->getLHS() && RHS == Div->getRHS()) 5222 return Div; // must be loop invariant 5223 return getUDivExpr(LHS, RHS); 5224 } 5225 5226 // If this is a loop recurrence for a loop that does not contain L, then we 5227 // are dealing with the final value computed by the loop. 5228 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { 5229 // First, attempt to evaluate each operand. 5230 // Avoid performing the look-up in the common case where the specified 5231 // expression has no loop-variant portions. 5232 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { 5233 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); 5234 if (OpAtScope == AddRec->getOperand(i)) 5235 continue; 5236 5237 // Okay, at least one of these operands is loop variant but might be 5238 // foldable. Build a new instance of the folded commutative expression. 5239 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(), 5240 AddRec->op_begin()+i); 5241 NewOps.push_back(OpAtScope); 5242 for (++i; i != e; ++i) 5243 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); 5244 5245 const SCEV *FoldedRec = 5246 getAddRecExpr(NewOps, AddRec->getLoop(), 5247 AddRec->getNoWrapFlags(SCEV::FlagNW)); 5248 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec); 5249 // The addrec may be folded to a nonrecurrence, for example, if the 5250 // induction variable is multiplied by zero after constant folding. Go 5251 // ahead and return the folded value. 5252 if (!AddRec) 5253 return FoldedRec; 5254 break; 5255 } 5256 5257 // If the scope is outside the addrec's loop, evaluate it by using the 5258 // loop exit value of the addrec. 5259 if (!AddRec->getLoop()->contains(L)) { 5260 // To evaluate this recurrence, we need to know how many times the AddRec 5261 // loop iterates. Compute this now. 5262 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); 5263 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; 5264 5265 // Then, evaluate the AddRec. 5266 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); 5267 } 5268 5269 return AddRec; 5270 } 5271 5272 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { 5273 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5274 if (Op == Cast->getOperand()) 5275 return Cast; // must be loop invariant 5276 return getZeroExtendExpr(Op, Cast->getType()); 5277 } 5278 5279 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { 5280 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5281 if (Op == Cast->getOperand()) 5282 return Cast; // must be loop invariant 5283 return getSignExtendExpr(Op, Cast->getType()); 5284 } 5285 5286 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { 5287 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); 5288 if (Op == Cast->getOperand()) 5289 return Cast; // must be loop invariant 5290 return getTruncateExpr(Op, Cast->getType()); 5291 } 5292 5293 llvm_unreachable("Unknown SCEV type!"); 5294 return 0; 5295} 5296 5297/// getSCEVAtScope - This is a convenience function which does 5298/// getSCEVAtScope(getSCEV(V), L). 5299const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { 5300 return getSCEVAtScope(getSCEV(V), L); 5301} 5302 5303/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the 5304/// following equation: 5305/// 5306/// A * X = B (mod N) 5307/// 5308/// where N = 2^BW and BW is the common bit width of A and B. The signedness of 5309/// A and B isn't important. 5310/// 5311/// If the equation does not have a solution, SCEVCouldNotCompute is returned. 5312static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, 5313 ScalarEvolution &SE) { 5314 uint32_t BW = A.getBitWidth(); 5315 assert(BW == B.getBitWidth() && "Bit widths must be the same."); 5316 assert(A != 0 && "A must be non-zero."); 5317 5318 // 1. D = gcd(A, N) 5319 // 5320 // The gcd of A and N may have only one prime factor: 2. The number of 5321 // trailing zeros in A is its multiplicity 5322 uint32_t Mult2 = A.countTrailingZeros(); 5323 // D = 2^Mult2 5324 5325 // 2. Check if B is divisible by D. 5326 // 5327 // B is divisible by D if and only if the multiplicity of prime factor 2 for B 5328 // is not less than multiplicity of this prime factor for D. 5329 if (B.countTrailingZeros() < Mult2) 5330 return SE.getCouldNotCompute(); 5331 5332 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic 5333 // modulo (N / D). 5334 // 5335 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this 5336 // bit width during computations. 5337 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D 5338 APInt Mod(BW + 1, 0); 5339 Mod.setBit(BW - Mult2); // Mod = N / D 5340 APInt I = AD.multiplicativeInverse(Mod); 5341 5342 // 4. Compute the minimum unsigned root of the equation: 5343 // I * (B / D) mod (N / D) 5344 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); 5345 5346 // The result is guaranteed to be less than 2^BW so we may truncate it to BW 5347 // bits. 5348 return SE.getConstant(Result.trunc(BW)); 5349} 5350 5351/// SolveQuadraticEquation - Find the roots of the quadratic equation for the 5352/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which 5353/// might be the same) or two SCEVCouldNotCompute objects. 5354/// 5355static std::pair<const SCEV *,const SCEV *> 5356SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { 5357 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); 5358 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); 5359 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); 5360 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); 5361 5362 // We currently can only solve this if the coefficients are constants. 5363 if (!LC || !MC || !NC) { 5364 const SCEV *CNC = SE.getCouldNotCompute(); 5365 return std::make_pair(CNC, CNC); 5366 } 5367 5368 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); 5369 const APInt &L = LC->getValue()->getValue(); 5370 const APInt &M = MC->getValue()->getValue(); 5371 const APInt &N = NC->getValue()->getValue(); 5372 APInt Two(BitWidth, 2); 5373 APInt Four(BitWidth, 4); 5374 5375 { 5376 using namespace APIntOps; 5377 const APInt& C = L; 5378 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C 5379 // The B coefficient is M-N/2 5380 APInt B(M); 5381 B -= sdiv(N,Two); 5382 5383 // The A coefficient is N/2 5384 APInt A(N.sdiv(Two)); 5385 5386 // Compute the B^2-4ac term. 5387 APInt SqrtTerm(B); 5388 SqrtTerm *= B; 5389 SqrtTerm -= Four * (A * C); 5390 5391 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest 5392 // integer value or else APInt::sqrt() will assert. 5393 APInt SqrtVal(SqrtTerm.sqrt()); 5394 5395 // Compute the two solutions for the quadratic formula. 5396 // The divisions must be performed as signed divisions. 5397 APInt NegB(-B); 5398 APInt TwoA(A << 1); 5399 if (TwoA.isMinValue()) { 5400 const SCEV *CNC = SE.getCouldNotCompute(); 5401 return std::make_pair(CNC, CNC); 5402 } 5403 5404 LLVMContext &Context = SE.getContext(); 5405 5406 ConstantInt *Solution1 = 5407 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); 5408 ConstantInt *Solution2 = 5409 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); 5410 5411 return std::make_pair(SE.getConstant(Solution1), 5412 SE.getConstant(Solution2)); 5413 } // end APIntOps namespace 5414} 5415 5416/// HowFarToZero - Return the number of times a backedge comparing the specified 5417/// value to zero will execute. If not computable, return CouldNotCompute. 5418/// 5419/// This is only used for loops with a "x != y" exit test. The exit condition is 5420/// now expressed as a single expression, V = x-y. So the exit test is 5421/// effectively V != 0. We know and take advantage of the fact that this 5422/// expression only being used in a comparison by zero context. 5423ScalarEvolution::ExitLimit 5424ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { 5425 // If the value is a constant 5426 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5427 // If the value is already zero, the branch will execute zero times. 5428 if (C->getValue()->isZero()) return C; 5429 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5430 } 5431 5432 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); 5433 if (!AddRec || AddRec->getLoop() != L) 5434 return getCouldNotCompute(); 5435 5436 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of 5437 // the quadratic equation to solve it. 5438 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { 5439 std::pair<const SCEV *,const SCEV *> Roots = 5440 SolveQuadraticEquation(AddRec, *this); 5441 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 5442 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 5443 if (R1 && R2) { 5444#if 0 5445 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 5446 << " sol#2: " << *R2 << "\n"; 5447#endif 5448 // Pick the smallest positive root value. 5449 if (ConstantInt *CB = 5450 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT, 5451 R1->getValue(), 5452 R2->getValue()))) { 5453 if (CB->getZExtValue() == false) 5454 std::swap(R1, R2); // R1 is the minimum root now. 5455 5456 // We can only use this value if the chrec ends up with an exact zero 5457 // value at this index. When solving for "X*X != 5", for example, we 5458 // should not accept a root of 2. 5459 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); 5460 if (Val->isZero()) 5461 return R1; // We found a quadratic root! 5462 } 5463 } 5464 return getCouldNotCompute(); 5465 } 5466 5467 // Otherwise we can only handle this if it is affine. 5468 if (!AddRec->isAffine()) 5469 return getCouldNotCompute(); 5470 5471 // If this is an affine expression, the execution count of this branch is 5472 // the minimum unsigned root of the following equation: 5473 // 5474 // Start + Step*N = 0 (mod 2^BW) 5475 // 5476 // equivalent to: 5477 // 5478 // Step*N = -Start (mod 2^BW) 5479 // 5480 // where BW is the common bit width of Start and Step. 5481 5482 // Get the initial value for the loop. 5483 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop()); 5484 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop()); 5485 5486 // For now we handle only constant steps. 5487 // 5488 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the 5489 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap 5490 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. 5491 // We have not yet seen any such cases. 5492 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step); 5493 if (StepC == 0) 5494 return getCouldNotCompute(); 5495 5496 // For positive steps (counting up until unsigned overflow): 5497 // N = -Start/Step (as unsigned) 5498 // For negative steps (counting down to zero): 5499 // N = Start/-Step 5500 // First compute the unsigned distance from zero in the direction of Step. 5501 bool CountDown = StepC->getValue()->getValue().isNegative(); 5502 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); 5503 5504 // Handle unitary steps, which cannot wraparound. 5505 // 1*N = -Start; -1*N = Start (mod 2^BW), so: 5506 // N = Distance (as unsigned) 5507 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) { 5508 ConstantRange CR = getUnsignedRange(Start); 5509 const SCEV *MaxBECount; 5510 if (!CountDown && CR.getUnsignedMin().isMinValue()) 5511 // When counting up, the worst starting value is 1, not 0. 5512 MaxBECount = CR.getUnsignedMax().isMinValue() 5513 ? getConstant(APInt::getMinValue(CR.getBitWidth())) 5514 : getConstant(APInt::getMaxValue(CR.getBitWidth())); 5515 else 5516 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax() 5517 : -CR.getUnsignedMin()); 5518 return ExitLimit(Distance, MaxBECount); 5519 } 5520 5521 // If the recurrence is known not to wraparound, unsigned divide computes the 5522 // back edge count. We know that the value will either become zero (and thus 5523 // the loop terminates), that the loop will terminate through some other exit 5524 // condition first, or that the loop has undefined behavior. This means 5525 // we can't "miss" the exit value, even with nonunit stride. 5526 // 5527 // FIXME: Prove that loops always exhibits *acceptable* undefined 5528 // behavior. Loops must exhibit defined behavior until a wrapped value is 5529 // actually used. So the trip count computed by udiv could be smaller than the 5530 // number of well-defined iterations. 5531 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) { 5532 // FIXME: We really want an "isexact" bit for udiv. 5533 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); 5534 } 5535 // Then, try to solve the above equation provided that Start is constant. 5536 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) 5537 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), 5538 -StartC->getValue()->getValue(), 5539 *this); 5540 return getCouldNotCompute(); 5541} 5542 5543/// HowFarToNonZero - Return the number of times a backedge checking the 5544/// specified value for nonzero will execute. If not computable, return 5545/// CouldNotCompute 5546ScalarEvolution::ExitLimit 5547ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { 5548 // Loops that look like: while (X == 0) are very strange indeed. We don't 5549 // handle them yet except for the trivial case. This could be expanded in the 5550 // future as needed. 5551 5552 // If the value is a constant, check to see if it is known to be non-zero 5553 // already. If so, the backedge will execute zero times. 5554 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { 5555 if (!C->getValue()->isNullValue()) 5556 return getConstant(C->getType(), 0); 5557 return getCouldNotCompute(); // Otherwise it will loop infinitely. 5558 } 5559 5560 // We could implement others, but I really doubt anyone writes loops like 5561 // this, and if they did, they would already be constant folded. 5562 return getCouldNotCompute(); 5563} 5564 5565/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB 5566/// (which may not be an immediate predecessor) which has exactly one 5567/// successor from which BB is reachable, or null if no such block is 5568/// found. 5569/// 5570std::pair<BasicBlock *, BasicBlock *> 5571ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { 5572 // If the block has a unique predecessor, then there is no path from the 5573 // predecessor to the block that does not go through the direct edge 5574 // from the predecessor to the block. 5575 if (BasicBlock *Pred = BB->getSinglePredecessor()) 5576 return std::make_pair(Pred, BB); 5577 5578 // A loop's header is defined to be a block that dominates the loop. 5579 // If the header has a unique predecessor outside the loop, it must be 5580 // a block that has exactly one successor that can reach the loop. 5581 if (Loop *L = LI->getLoopFor(BB)) 5582 return std::make_pair(L->getLoopPredecessor(), L->getHeader()); 5583 5584 return std::pair<BasicBlock *, BasicBlock *>(); 5585} 5586 5587/// HasSameValue - SCEV structural equivalence is usually sufficient for 5588/// testing whether two expressions are equal, however for the purposes of 5589/// looking for a condition guarding a loop, it can be useful to be a little 5590/// more general, since a front-end may have replicated the controlling 5591/// expression. 5592/// 5593static bool HasSameValue(const SCEV *A, const SCEV *B) { 5594 // Quick check to see if they are the same SCEV. 5595 if (A == B) return true; 5596 5597 // Otherwise, if they're both SCEVUnknown, it's possible that they hold 5598 // two different instructions with the same value. Check for this case. 5599 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) 5600 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) 5601 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) 5602 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) 5603 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) 5604 return true; 5605 5606 // Otherwise assume they may have a different value. 5607 return false; 5608} 5609 5610/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with 5611/// predicate Pred. Return true iff any changes were made. 5612/// 5613bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, 5614 const SCEV *&LHS, const SCEV *&RHS) { 5615 bool Changed = false; 5616 5617 // Canonicalize a constant to the right side. 5618 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { 5619 // Check for both operands constant. 5620 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { 5621 if (ConstantExpr::getICmp(Pred, 5622 LHSC->getValue(), 5623 RHSC->getValue())->isNullValue()) 5624 goto trivially_false; 5625 else 5626 goto trivially_true; 5627 } 5628 // Otherwise swap the operands to put the constant on the right. 5629 std::swap(LHS, RHS); 5630 Pred = ICmpInst::getSwappedPredicate(Pred); 5631 Changed = true; 5632 } 5633 5634 // If we're comparing an addrec with a value which is loop-invariant in the 5635 // addrec's loop, put the addrec on the left. Also make a dominance check, 5636 // as both operands could be addrecs loop-invariant in each other's loop. 5637 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { 5638 const Loop *L = AR->getLoop(); 5639 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 5640 std::swap(LHS, RHS); 5641 Pred = ICmpInst::getSwappedPredicate(Pred); 5642 Changed = true; 5643 } 5644 } 5645 5646 // If there's a constant operand, canonicalize comparisons with boundary 5647 // cases, and canonicalize *-or-equal comparisons to regular comparisons. 5648 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { 5649 const APInt &RA = RC->getValue()->getValue(); 5650 switch (Pred) { 5651 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5652 case ICmpInst::ICMP_EQ: 5653 case ICmpInst::ICMP_NE: 5654 break; 5655 case ICmpInst::ICMP_UGE: 5656 if ((RA - 1).isMinValue()) { 5657 Pred = ICmpInst::ICMP_NE; 5658 RHS = getConstant(RA - 1); 5659 Changed = true; 5660 break; 5661 } 5662 if (RA.isMaxValue()) { 5663 Pred = ICmpInst::ICMP_EQ; 5664 Changed = true; 5665 break; 5666 } 5667 if (RA.isMinValue()) goto trivially_true; 5668 5669 Pred = ICmpInst::ICMP_UGT; 5670 RHS = getConstant(RA - 1); 5671 Changed = true; 5672 break; 5673 case ICmpInst::ICMP_ULE: 5674 if ((RA + 1).isMaxValue()) { 5675 Pred = ICmpInst::ICMP_NE; 5676 RHS = getConstant(RA + 1); 5677 Changed = true; 5678 break; 5679 } 5680 if (RA.isMinValue()) { 5681 Pred = ICmpInst::ICMP_EQ; 5682 Changed = true; 5683 break; 5684 } 5685 if (RA.isMaxValue()) goto trivially_true; 5686 5687 Pred = ICmpInst::ICMP_ULT; 5688 RHS = getConstant(RA + 1); 5689 Changed = true; 5690 break; 5691 case ICmpInst::ICMP_SGE: 5692 if ((RA - 1).isMinSignedValue()) { 5693 Pred = ICmpInst::ICMP_NE; 5694 RHS = getConstant(RA - 1); 5695 Changed = true; 5696 break; 5697 } 5698 if (RA.isMaxSignedValue()) { 5699 Pred = ICmpInst::ICMP_EQ; 5700 Changed = true; 5701 break; 5702 } 5703 if (RA.isMinSignedValue()) goto trivially_true; 5704 5705 Pred = ICmpInst::ICMP_SGT; 5706 RHS = getConstant(RA - 1); 5707 Changed = true; 5708 break; 5709 case ICmpInst::ICMP_SLE: 5710 if ((RA + 1).isMaxSignedValue()) { 5711 Pred = ICmpInst::ICMP_NE; 5712 RHS = getConstant(RA + 1); 5713 Changed = true; 5714 break; 5715 } 5716 if (RA.isMinSignedValue()) { 5717 Pred = ICmpInst::ICMP_EQ; 5718 Changed = true; 5719 break; 5720 } 5721 if (RA.isMaxSignedValue()) goto trivially_true; 5722 5723 Pred = ICmpInst::ICMP_SLT; 5724 RHS = getConstant(RA + 1); 5725 Changed = true; 5726 break; 5727 case ICmpInst::ICMP_UGT: 5728 if (RA.isMinValue()) { 5729 Pred = ICmpInst::ICMP_NE; 5730 Changed = true; 5731 break; 5732 } 5733 if ((RA + 1).isMaxValue()) { 5734 Pred = ICmpInst::ICMP_EQ; 5735 RHS = getConstant(RA + 1); 5736 Changed = true; 5737 break; 5738 } 5739 if (RA.isMaxValue()) goto trivially_false; 5740 break; 5741 case ICmpInst::ICMP_ULT: 5742 if (RA.isMaxValue()) { 5743 Pred = ICmpInst::ICMP_NE; 5744 Changed = true; 5745 break; 5746 } 5747 if ((RA - 1).isMinValue()) { 5748 Pred = ICmpInst::ICMP_EQ; 5749 RHS = getConstant(RA - 1); 5750 Changed = true; 5751 break; 5752 } 5753 if (RA.isMinValue()) goto trivially_false; 5754 break; 5755 case ICmpInst::ICMP_SGT: 5756 if (RA.isMinSignedValue()) { 5757 Pred = ICmpInst::ICMP_NE; 5758 Changed = true; 5759 break; 5760 } 5761 if ((RA + 1).isMaxSignedValue()) { 5762 Pred = ICmpInst::ICMP_EQ; 5763 RHS = getConstant(RA + 1); 5764 Changed = true; 5765 break; 5766 } 5767 if (RA.isMaxSignedValue()) goto trivially_false; 5768 break; 5769 case ICmpInst::ICMP_SLT: 5770 if (RA.isMaxSignedValue()) { 5771 Pred = ICmpInst::ICMP_NE; 5772 Changed = true; 5773 break; 5774 } 5775 if ((RA - 1).isMinSignedValue()) { 5776 Pred = ICmpInst::ICMP_EQ; 5777 RHS = getConstant(RA - 1); 5778 Changed = true; 5779 break; 5780 } 5781 if (RA.isMinSignedValue()) goto trivially_false; 5782 break; 5783 } 5784 } 5785 5786 // Check for obvious equality. 5787 if (HasSameValue(LHS, RHS)) { 5788 if (ICmpInst::isTrueWhenEqual(Pred)) 5789 goto trivially_true; 5790 if (ICmpInst::isFalseWhenEqual(Pred)) 5791 goto trivially_false; 5792 } 5793 5794 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by 5795 // adding or subtracting 1 from one of the operands. 5796 switch (Pred) { 5797 case ICmpInst::ICMP_SLE: 5798 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { 5799 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5800 SCEV::FlagNSW); 5801 Pred = ICmpInst::ICMP_SLT; 5802 Changed = true; 5803 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { 5804 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5805 SCEV::FlagNSW); 5806 Pred = ICmpInst::ICMP_SLT; 5807 Changed = true; 5808 } 5809 break; 5810 case ICmpInst::ICMP_SGE: 5811 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { 5812 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5813 SCEV::FlagNSW); 5814 Pred = ICmpInst::ICMP_SGT; 5815 Changed = true; 5816 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { 5817 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5818 SCEV::FlagNSW); 5819 Pred = ICmpInst::ICMP_SGT; 5820 Changed = true; 5821 } 5822 break; 5823 case ICmpInst::ICMP_ULE: 5824 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { 5825 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, 5826 SCEV::FlagNUW); 5827 Pred = ICmpInst::ICMP_ULT; 5828 Changed = true; 5829 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { 5830 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, 5831 SCEV::FlagNUW); 5832 Pred = ICmpInst::ICMP_ULT; 5833 Changed = true; 5834 } 5835 break; 5836 case ICmpInst::ICMP_UGE: 5837 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { 5838 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, 5839 SCEV::FlagNUW); 5840 Pred = ICmpInst::ICMP_UGT; 5841 Changed = true; 5842 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { 5843 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, 5844 SCEV::FlagNUW); 5845 Pred = ICmpInst::ICMP_UGT; 5846 Changed = true; 5847 } 5848 break; 5849 default: 5850 break; 5851 } 5852 5853 // TODO: More simplifications are possible here. 5854 5855 return Changed; 5856 5857trivially_true: 5858 // Return 0 == 0. 5859 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5860 Pred = ICmpInst::ICMP_EQ; 5861 return true; 5862 5863trivially_false: 5864 // Return 0 != 0. 5865 LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 5866 Pred = ICmpInst::ICMP_NE; 5867 return true; 5868} 5869 5870bool ScalarEvolution::isKnownNegative(const SCEV *S) { 5871 return getSignedRange(S).getSignedMax().isNegative(); 5872} 5873 5874bool ScalarEvolution::isKnownPositive(const SCEV *S) { 5875 return getSignedRange(S).getSignedMin().isStrictlyPositive(); 5876} 5877 5878bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { 5879 return !getSignedRange(S).getSignedMin().isNegative(); 5880} 5881 5882bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { 5883 return !getSignedRange(S).getSignedMax().isStrictlyPositive(); 5884} 5885 5886bool ScalarEvolution::isKnownNonZero(const SCEV *S) { 5887 return isKnownNegative(S) || isKnownPositive(S); 5888} 5889 5890bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, 5891 const SCEV *LHS, const SCEV *RHS) { 5892 // Canonicalize the inputs first. 5893 (void)SimplifyICmpOperands(Pred, LHS, RHS); 5894 5895 // If LHS or RHS is an addrec, check to see if the condition is true in 5896 // every iteration of the loop. 5897 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) 5898 if (isLoopEntryGuardedByCond( 5899 AR->getLoop(), Pred, AR->getStart(), RHS) && 5900 isLoopBackedgeGuardedByCond( 5901 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) 5902 return true; 5903 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) 5904 if (isLoopEntryGuardedByCond( 5905 AR->getLoop(), Pred, LHS, AR->getStart()) && 5906 isLoopBackedgeGuardedByCond( 5907 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) 5908 return true; 5909 5910 // Otherwise see what can be done with known constant ranges. 5911 return isKnownPredicateWithRanges(Pred, LHS, RHS); 5912} 5913 5914bool 5915ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, 5916 const SCEV *LHS, const SCEV *RHS) { 5917 if (HasSameValue(LHS, RHS)) 5918 return ICmpInst::isTrueWhenEqual(Pred); 5919 5920 // This code is split out from isKnownPredicate because it is called from 5921 // within isLoopEntryGuardedByCond. 5922 switch (Pred) { 5923 default: 5924 llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 5925 break; 5926 case ICmpInst::ICMP_SGT: 5927 Pred = ICmpInst::ICMP_SLT; 5928 std::swap(LHS, RHS); 5929 case ICmpInst::ICMP_SLT: { 5930 ConstantRange LHSRange = getSignedRange(LHS); 5931 ConstantRange RHSRange = getSignedRange(RHS); 5932 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) 5933 return true; 5934 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) 5935 return false; 5936 break; 5937 } 5938 case ICmpInst::ICMP_SGE: 5939 Pred = ICmpInst::ICMP_SLE; 5940 std::swap(LHS, RHS); 5941 case ICmpInst::ICMP_SLE: { 5942 ConstantRange LHSRange = getSignedRange(LHS); 5943 ConstantRange RHSRange = getSignedRange(RHS); 5944 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) 5945 return true; 5946 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) 5947 return false; 5948 break; 5949 } 5950 case ICmpInst::ICMP_UGT: 5951 Pred = ICmpInst::ICMP_ULT; 5952 std::swap(LHS, RHS); 5953 case ICmpInst::ICMP_ULT: { 5954 ConstantRange LHSRange = getUnsignedRange(LHS); 5955 ConstantRange RHSRange = getUnsignedRange(RHS); 5956 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) 5957 return true; 5958 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) 5959 return false; 5960 break; 5961 } 5962 case ICmpInst::ICMP_UGE: 5963 Pred = ICmpInst::ICMP_ULE; 5964 std::swap(LHS, RHS); 5965 case ICmpInst::ICMP_ULE: { 5966 ConstantRange LHSRange = getUnsignedRange(LHS); 5967 ConstantRange RHSRange = getUnsignedRange(RHS); 5968 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) 5969 return true; 5970 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) 5971 return false; 5972 break; 5973 } 5974 case ICmpInst::ICMP_NE: { 5975 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) 5976 return true; 5977 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) 5978 return true; 5979 5980 const SCEV *Diff = getMinusSCEV(LHS, RHS); 5981 if (isKnownNonZero(Diff)) 5982 return true; 5983 break; 5984 } 5985 case ICmpInst::ICMP_EQ: 5986 // The check at the top of the function catches the case where 5987 // the values are known to be equal. 5988 break; 5989 } 5990 return false; 5991} 5992 5993/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is 5994/// protected by a conditional between LHS and RHS. This is used to 5995/// to eliminate casts. 5996bool 5997ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, 5998 ICmpInst::Predicate Pred, 5999 const SCEV *LHS, const SCEV *RHS) { 6000 // Interpret a null as meaning no loop, where there is obviously no guard 6001 // (interprocedural conditions notwithstanding). 6002 if (!L) return true; 6003 6004 BasicBlock *Latch = L->getLoopLatch(); 6005 if (!Latch) 6006 return false; 6007 6008 BranchInst *LoopContinuePredicate = 6009 dyn_cast<BranchInst>(Latch->getTerminator()); 6010 if (!LoopContinuePredicate || 6011 LoopContinuePredicate->isUnconditional()) 6012 return false; 6013 6014 return isImpliedCond(Pred, LHS, RHS, 6015 LoopContinuePredicate->getCondition(), 6016 LoopContinuePredicate->getSuccessor(0) != L->getHeader()); 6017} 6018 6019/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected 6020/// by a conditional between LHS and RHS. This is used to help avoid max 6021/// expressions in loop trip counts, and to eliminate casts. 6022bool 6023ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, 6024 ICmpInst::Predicate Pred, 6025 const SCEV *LHS, const SCEV *RHS) { 6026 // Interpret a null as meaning no loop, where there is obviously no guard 6027 // (interprocedural conditions notwithstanding). 6028 if (!L) return false; 6029 6030 // Starting at the loop predecessor, climb up the predecessor chain, as long 6031 // as there are predecessors that can be found that have unique successors 6032 // leading to the original header. 6033 for (std::pair<BasicBlock *, BasicBlock *> 6034 Pair(L->getLoopPredecessor(), L->getHeader()); 6035 Pair.first; 6036 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { 6037 6038 BranchInst *LoopEntryPredicate = 6039 dyn_cast<BranchInst>(Pair.first->getTerminator()); 6040 if (!LoopEntryPredicate || 6041 LoopEntryPredicate->isUnconditional()) 6042 continue; 6043 6044 if (isImpliedCond(Pred, LHS, RHS, 6045 LoopEntryPredicate->getCondition(), 6046 LoopEntryPredicate->getSuccessor(0) != Pair.second)) 6047 return true; 6048 } 6049 6050 return false; 6051} 6052 6053/// isImpliedCond - Test whether the condition described by Pred, LHS, 6054/// and RHS is true whenever the given Cond value evaluates to true. 6055bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, 6056 const SCEV *LHS, const SCEV *RHS, 6057 Value *FoundCondValue, 6058 bool Inverse) { 6059 // Recursively handle And and Or conditions. 6060 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { 6061 if (BO->getOpcode() == Instruction::And) { 6062 if (!Inverse) 6063 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6064 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6065 } else if (BO->getOpcode() == Instruction::Or) { 6066 if (Inverse) 6067 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || 6068 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); 6069 } 6070 } 6071 6072 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue); 6073 if (!ICI) return false; 6074 6075 // Bail if the ICmp's operands' types are wider than the needed type 6076 // before attempting to call getSCEV on them. This avoids infinite 6077 // recursion, since the analysis of widening casts can require loop 6078 // exit condition information for overflow checking, which would 6079 // lead back here. 6080 if (getTypeSizeInBits(LHS->getType()) < 6081 getTypeSizeInBits(ICI->getOperand(0)->getType())) 6082 return false; 6083 6084 // Now that we found a conditional branch that dominates the loop, check to 6085 // see if it is the comparison we are looking for. 6086 ICmpInst::Predicate FoundPred; 6087 if (Inverse) 6088 FoundPred = ICI->getInversePredicate(); 6089 else 6090 FoundPred = ICI->getPredicate(); 6091 6092 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); 6093 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); 6094 6095 // Balance the types. The case where FoundLHS' type is wider than 6096 // LHS' type is checked for above. 6097 if (getTypeSizeInBits(LHS->getType()) > 6098 getTypeSizeInBits(FoundLHS->getType())) { 6099 if (CmpInst::isSigned(Pred)) { 6100 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); 6101 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); 6102 } else { 6103 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); 6104 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); 6105 } 6106 } 6107 6108 // Canonicalize the query to match the way instcombine will have 6109 // canonicalized the comparison. 6110 if (SimplifyICmpOperands(Pred, LHS, RHS)) 6111 if (LHS == RHS) 6112 return CmpInst::isTrueWhenEqual(Pred); 6113 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) 6114 if (FoundLHS == FoundRHS) 6115 return CmpInst::isFalseWhenEqual(Pred); 6116 6117 // Check to see if we can make the LHS or RHS match. 6118 if (LHS == FoundRHS || RHS == FoundLHS) { 6119 if (isa<SCEVConstant>(RHS)) { 6120 std::swap(FoundLHS, FoundRHS); 6121 FoundPred = ICmpInst::getSwappedPredicate(FoundPred); 6122 } else { 6123 std::swap(LHS, RHS); 6124 Pred = ICmpInst::getSwappedPredicate(Pred); 6125 } 6126 } 6127 6128 // Check whether the found predicate is the same as the desired predicate. 6129 if (FoundPred == Pred) 6130 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); 6131 6132 // Check whether swapping the found predicate makes it the same as the 6133 // desired predicate. 6134 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { 6135 if (isa<SCEVConstant>(RHS)) 6136 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); 6137 else 6138 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), 6139 RHS, LHS, FoundLHS, FoundRHS); 6140 } 6141 6142 // Check whether the actual condition is beyond sufficient. 6143 if (FoundPred == ICmpInst::ICMP_EQ) 6144 if (ICmpInst::isTrueWhenEqual(Pred)) 6145 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) 6146 return true; 6147 if (Pred == ICmpInst::ICMP_NE) 6148 if (!ICmpInst::isTrueWhenEqual(FoundPred)) 6149 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) 6150 return true; 6151 6152 // Otherwise assume the worst. 6153 return false; 6154} 6155 6156/// isImpliedCondOperands - Test whether the condition described by Pred, 6157/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, 6158/// and FoundRHS is true. 6159bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, 6160 const SCEV *LHS, const SCEV *RHS, 6161 const SCEV *FoundLHS, 6162 const SCEV *FoundRHS) { 6163 return isImpliedCondOperandsHelper(Pred, LHS, RHS, 6164 FoundLHS, FoundRHS) || 6165 // ~x < ~y --> x > y 6166 isImpliedCondOperandsHelper(Pred, LHS, RHS, 6167 getNotSCEV(FoundRHS), 6168 getNotSCEV(FoundLHS)); 6169} 6170 6171/// isImpliedCondOperandsHelper - Test whether the condition described by 6172/// Pred, LHS, and RHS is true whenever the condition described by Pred, 6173/// FoundLHS, and FoundRHS is true. 6174bool 6175ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, 6176 const SCEV *LHS, const SCEV *RHS, 6177 const SCEV *FoundLHS, 6178 const SCEV *FoundRHS) { 6179 switch (Pred) { 6180 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); 6181 case ICmpInst::ICMP_EQ: 6182 case ICmpInst::ICMP_NE: 6183 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) 6184 return true; 6185 break; 6186 case ICmpInst::ICMP_SLT: 6187 case ICmpInst::ICMP_SLE: 6188 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && 6189 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) 6190 return true; 6191 break; 6192 case ICmpInst::ICMP_SGT: 6193 case ICmpInst::ICMP_SGE: 6194 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && 6195 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) 6196 return true; 6197 break; 6198 case ICmpInst::ICMP_ULT: 6199 case ICmpInst::ICMP_ULE: 6200 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && 6201 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) 6202 return true; 6203 break; 6204 case ICmpInst::ICMP_UGT: 6205 case ICmpInst::ICMP_UGE: 6206 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && 6207 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) 6208 return true; 6209 break; 6210 } 6211 6212 return false; 6213} 6214 6215/// getBECount - Subtract the end and start values and divide by the step, 6216/// rounding up, to get the number of times the backedge is executed. Return 6217/// CouldNotCompute if an intermediate computation overflows. 6218const SCEV *ScalarEvolution::getBECount(const SCEV *Start, 6219 const SCEV *End, 6220 const SCEV *Step, 6221 bool NoWrap) { 6222 assert(!isKnownNegative(Step) && 6223 "This code doesn't handle negative strides yet!"); 6224 6225 Type *Ty = Start->getType(); 6226 6227 // When Start == End, we have an exact BECount == 0. Short-circuit this case 6228 // here because SCEV may not be able to determine that the unsigned division 6229 // after rounding is zero. 6230 if (Start == End) 6231 return getConstant(Ty, 0); 6232 6233 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); 6234 const SCEV *Diff = getMinusSCEV(End, Start); 6235 const SCEV *RoundUp = getAddExpr(Step, NegOne); 6236 6237 // Add an adjustment to the difference between End and Start so that 6238 // the division will effectively round up. 6239 const SCEV *Add = getAddExpr(Diff, RoundUp); 6240 6241 if (!NoWrap) { 6242 // Check Add for unsigned overflow. 6243 // TODO: More sophisticated things could be done here. 6244 Type *WideTy = IntegerType::get(getContext(), 6245 getTypeSizeInBits(Ty) + 1); 6246 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); 6247 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); 6248 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); 6249 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) 6250 return getCouldNotCompute(); 6251 } 6252 6253 return getUDivExpr(Add, Step); 6254} 6255 6256/// HowManyLessThans - Return the number of times a backedge containing the 6257/// specified less-than comparison will execute. If not computable, return 6258/// CouldNotCompute. 6259ScalarEvolution::ExitLimit 6260ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, 6261 const Loop *L, bool isSigned) { 6262 // Only handle: "ADDREC < LoopInvariant". 6263 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); 6264 6265 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); 6266 if (!AddRec || AddRec->getLoop() != L) 6267 return getCouldNotCompute(); 6268 6269 // Check to see if we have a flag which makes analysis easy. 6270 bool NoWrap = isSigned ? 6271 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) : 6272 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW)); 6273 6274 if (AddRec->isAffine()) { 6275 unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); 6276 const SCEV *Step = AddRec->getStepRecurrence(*this); 6277 6278 if (Step->isZero()) 6279 return getCouldNotCompute(); 6280 if (Step->isOne()) { 6281 // With unit stride, the iteration never steps past the limit value. 6282 } else if (isKnownPositive(Step)) { 6283 // Test whether a positive iteration can step past the limit 6284 // value and past the maximum value for its type in a single step. 6285 // Note that it's not sufficient to check NoWrap here, because even 6286 // though the value after a wrap is undefined, it's not undefined 6287 // behavior, so if wrap does occur, the loop could either terminate or 6288 // loop infinitely, but in either case, the loop is guaranteed to 6289 // iterate at least until the iteration where the wrapping occurs. 6290 const SCEV *One = getConstant(Step->getType(), 1); 6291 if (isSigned) { 6292 APInt Max = APInt::getSignedMaxValue(BitWidth); 6293 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) 6294 .slt(getSignedRange(RHS).getSignedMax())) 6295 return getCouldNotCompute(); 6296 } else { 6297 APInt Max = APInt::getMaxValue(BitWidth); 6298 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) 6299 .ult(getUnsignedRange(RHS).getUnsignedMax())) 6300 return getCouldNotCompute(); 6301 } 6302 } else 6303 // TODO: Handle negative strides here and below. 6304 return getCouldNotCompute(); 6305 6306 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant 6307 // m. So, we count the number of iterations in which {n,+,s} < m is true. 6308 // Note that we cannot simply return max(m-n,0)/s because it's not safe to 6309 // treat m-n as signed nor unsigned due to overflow possibility. 6310 6311 // First, we get the value of the LHS in the first iteration: n 6312 const SCEV *Start = AddRec->getOperand(0); 6313 6314 // Determine the minimum constant start value. 6315 const SCEV *MinStart = getConstant(isSigned ? 6316 getSignedRange(Start).getSignedMin() : 6317 getUnsignedRange(Start).getUnsignedMin()); 6318 6319 // If we know that the condition is true in order to enter the loop, 6320 // then we know that it will run exactly (m-n)/s times. Otherwise, we 6321 // only know that it will execute (max(m,n)-n)/s times. In both cases, 6322 // the division must round up. 6323 const SCEV *End = RHS; 6324 if (!isLoopEntryGuardedByCond(L, 6325 isSigned ? ICmpInst::ICMP_SLT : 6326 ICmpInst::ICMP_ULT, 6327 getMinusSCEV(Start, Step), RHS)) 6328 End = isSigned ? getSMaxExpr(RHS, Start) 6329 : getUMaxExpr(RHS, Start); 6330 6331 // Determine the maximum constant end value. 6332 const SCEV *MaxEnd = getConstant(isSigned ? 6333 getSignedRange(End).getSignedMax() : 6334 getUnsignedRange(End).getUnsignedMax()); 6335 6336 // If MaxEnd is within a step of the maximum integer value in its type, 6337 // adjust it down to the minimum value which would produce the same effect. 6338 // This allows the subsequent ceiling division of (N+(step-1))/step to 6339 // compute the correct value. 6340 const SCEV *StepMinusOne = getMinusSCEV(Step, 6341 getConstant(Step->getType(), 1)); 6342 MaxEnd = isSigned ? 6343 getSMinExpr(MaxEnd, 6344 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), 6345 StepMinusOne)) : 6346 getUMinExpr(MaxEnd, 6347 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), 6348 StepMinusOne)); 6349 6350 // Finally, we subtract these two values and divide, rounding up, to get 6351 // the number of times the backedge is executed. 6352 const SCEV *BECount = getBECount(Start, End, Step, NoWrap); 6353 6354 // The maximum backedge count is similar, except using the minimum start 6355 // value and the maximum end value. 6356 // If we already have an exact constant BECount, use it instead. 6357 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount 6358 : getBECount(MinStart, MaxEnd, Step, NoWrap); 6359 6360 // If the stride is nonconstant, and NoWrap == true, then 6361 // getBECount(MinStart, MaxEnd) may not compute. This would result in an 6362 // exact BECount and invalid MaxBECount, which should be avoided to catch 6363 // more optimization opportunities. 6364 if (isa<SCEVCouldNotCompute>(MaxBECount)) 6365 MaxBECount = BECount; 6366 6367 return ExitLimit(BECount, MaxBECount); 6368 } 6369 6370 return getCouldNotCompute(); 6371} 6372 6373/// getNumIterationsInRange - Return the number of iterations of this loop that 6374/// produce values in the specified constant range. Another way of looking at 6375/// this is that it returns the first iteration number where the value is not in 6376/// the condition, thus computing the exit count. If the iteration count can't 6377/// be computed, an instance of SCEVCouldNotCompute is returned. 6378const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, 6379 ScalarEvolution &SE) const { 6380 if (Range.isFullSet()) // Infinite loop. 6381 return SE.getCouldNotCompute(); 6382 6383 // If the start is a non-zero constant, shift the range to simplify things. 6384 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) 6385 if (!SC->getValue()->isZero()) { 6386 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); 6387 Operands[0] = SE.getConstant(SC->getType(), 0); 6388 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), 6389 getNoWrapFlags(FlagNW)); 6390 if (const SCEVAddRecExpr *ShiftedAddRec = 6391 dyn_cast<SCEVAddRecExpr>(Shifted)) 6392 return ShiftedAddRec->getNumIterationsInRange( 6393 Range.subtract(SC->getValue()->getValue()), SE); 6394 // This is strange and shouldn't happen. 6395 return SE.getCouldNotCompute(); 6396 } 6397 6398 // The only time we can solve this is when we have all constant indices. 6399 // Otherwise, we cannot determine the overflow conditions. 6400 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) 6401 if (!isa<SCEVConstant>(getOperand(i))) 6402 return SE.getCouldNotCompute(); 6403 6404 6405 // Okay at this point we know that all elements of the chrec are constants and 6406 // that the start element is zero. 6407 6408 // First check to see if the range contains zero. If not, the first 6409 // iteration exits. 6410 unsigned BitWidth = SE.getTypeSizeInBits(getType()); 6411 if (!Range.contains(APInt(BitWidth, 0))) 6412 return SE.getConstant(getType(), 0); 6413 6414 if (isAffine()) { 6415 // If this is an affine expression then we have this situation: 6416 // Solve {0,+,A} in Range === Ax in Range 6417 6418 // We know that zero is in the range. If A is positive then we know that 6419 // the upper value of the range must be the first possible exit value. 6420 // If A is negative then the lower of the range is the last possible loop 6421 // value. Also note that we already checked for a full range. 6422 APInt One(BitWidth,1); 6423 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); 6424 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); 6425 6426 // The exit value should be (End+A)/A. 6427 APInt ExitVal = (End + A).udiv(A); 6428 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); 6429 6430 // Evaluate at the exit value. If we really did fall out of the valid 6431 // range, then we computed our trip count, otherwise wrap around or other 6432 // things must have happened. 6433 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); 6434 if (Range.contains(Val->getValue())) 6435 return SE.getCouldNotCompute(); // Something strange happened 6436 6437 // Ensure that the previous value is in the range. This is a sanity check. 6438 assert(Range.contains( 6439 EvaluateConstantChrecAtConstant(this, 6440 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && 6441 "Linear scev computation is off in a bad way!"); 6442 return SE.getConstant(ExitValue); 6443 } else if (isQuadratic()) { 6444 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the 6445 // quadratic equation to solve it. To do this, we must frame our problem in 6446 // terms of figuring out when zero is crossed, instead of when 6447 // Range.getUpper() is crossed. 6448 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); 6449 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); 6450 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), 6451 // getNoWrapFlags(FlagNW) 6452 FlagAnyWrap); 6453 6454 // Next, solve the constructed addrec 6455 std::pair<const SCEV *,const SCEV *> Roots = 6456 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); 6457 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); 6458 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); 6459 if (R1) { 6460 // Pick the smallest positive root value. 6461 if (ConstantInt *CB = 6462 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, 6463 R1->getValue(), R2->getValue()))) { 6464 if (CB->getZExtValue() == false) 6465 std::swap(R1, R2); // R1 is the minimum root now. 6466 6467 // Make sure the root is not off by one. The returned iteration should 6468 // not be in the range, but the previous one should be. When solving 6469 // for "X*X < 5", for example, we should not return a root of 2. 6470 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, 6471 R1->getValue(), 6472 SE); 6473 if (Range.contains(R1Val->getValue())) { 6474 // The next iteration must be out of the range... 6475 ConstantInt *NextVal = 6476 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); 6477 6478 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6479 if (!Range.contains(R1Val->getValue())) 6480 return SE.getConstant(NextVal); 6481 return SE.getCouldNotCompute(); // Something strange happened 6482 } 6483 6484 // If R1 was not in the range, then it is a good return value. Make 6485 // sure that R1-1 WAS in the range though, just in case. 6486 ConstantInt *NextVal = 6487 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); 6488 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); 6489 if (Range.contains(R1Val->getValue())) 6490 return R1; 6491 return SE.getCouldNotCompute(); // Something strange happened 6492 } 6493 } 6494 } 6495 6496 return SE.getCouldNotCompute(); 6497} 6498 6499 6500 6501//===----------------------------------------------------------------------===// 6502// SCEVCallbackVH Class Implementation 6503//===----------------------------------------------------------------------===// 6504 6505void ScalarEvolution::SCEVCallbackVH::deleted() { 6506 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6507 if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) 6508 SE->ConstantEvolutionLoopExitValue.erase(PN); 6509 SE->ValueExprMap.erase(getValPtr()); 6510 // this now dangles! 6511} 6512 6513void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 6514 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); 6515 6516 // Forget all the expressions associated with users of the old value, 6517 // so that future queries will recompute the expressions using the new 6518 // value. 6519 Value *Old = getValPtr(); 6520 SmallVector<User *, 16> Worklist; 6521 SmallPtrSet<User *, 8> Visited; 6522 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); 6523 UI != UE; ++UI) 6524 Worklist.push_back(*UI); 6525 while (!Worklist.empty()) { 6526 User *U = Worklist.pop_back_val(); 6527 // Deleting the Old value will cause this to dangle. Postpone 6528 // that until everything else is done. 6529 if (U == Old) 6530 continue; 6531 if (!Visited.insert(U)) 6532 continue; 6533 if (PHINode *PN = dyn_cast<PHINode>(U)) 6534 SE->ConstantEvolutionLoopExitValue.erase(PN); 6535 SE->ValueExprMap.erase(U); 6536 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); 6537 UI != UE; ++UI) 6538 Worklist.push_back(*UI); 6539 } 6540 // Delete the Old value. 6541 if (PHINode *PN = dyn_cast<PHINode>(Old)) 6542 SE->ConstantEvolutionLoopExitValue.erase(PN); 6543 SE->ValueExprMap.erase(Old); 6544 // this now dangles! 6545} 6546 6547ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) 6548 : CallbackVH(V), SE(se) {} 6549 6550//===----------------------------------------------------------------------===// 6551// ScalarEvolution Class Implementation 6552//===----------------------------------------------------------------------===// 6553 6554ScalarEvolution::ScalarEvolution() 6555 : FunctionPass(ID), FirstUnknown(0) { 6556 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); 6557} 6558 6559bool ScalarEvolution::runOnFunction(Function &F) { 6560 this->F = &F; 6561 LI = &getAnalysis<LoopInfo>(); 6562 TD = getAnalysisIfAvailable<TargetData>(); 6563 DT = &getAnalysis<DominatorTree>(); 6564 return false; 6565} 6566 6567void ScalarEvolution::releaseMemory() { 6568 // Iterate through all the SCEVUnknown instances and call their 6569 // destructors, so that they release their references to their values. 6570 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) 6571 U->~SCEVUnknown(); 6572 FirstUnknown = 0; 6573 6574 ValueExprMap.clear(); 6575 6576 // Free any extra memory created for ExitNotTakenInfo in the unlikely event 6577 // that a loop had multiple computable exits. 6578 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I = 6579 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); 6580 I != E; ++I) { 6581 I->second.clear(); 6582 } 6583 6584 BackedgeTakenCounts.clear(); 6585 ConstantEvolutionLoopExitValue.clear(); 6586 ValuesAtScopes.clear(); 6587 LoopDispositions.clear(); 6588 BlockDispositions.clear(); 6589 UnsignedRanges.clear(); 6590 SignedRanges.clear(); 6591 UniqueSCEVs.clear(); 6592 SCEVAllocator.Reset(); 6593} 6594 6595void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { 6596 AU.setPreservesAll(); 6597 AU.addRequiredTransitive<LoopInfo>(); 6598 AU.addRequiredTransitive<DominatorTree>(); 6599} 6600 6601bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { 6602 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); 6603} 6604 6605static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, 6606 const Loop *L) { 6607 // Print all inner loops first 6608 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) 6609 PrintLoopInfo(OS, SE, *I); 6610 6611 OS << "Loop "; 6612 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6613 OS << ": "; 6614 6615 SmallVector<BasicBlock *, 8> ExitBlocks; 6616 L->getExitBlocks(ExitBlocks); 6617 if (ExitBlocks.size() != 1) 6618 OS << "<multiple exits> "; 6619 6620 if (SE->hasLoopInvariantBackedgeTakenCount(L)) { 6621 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); 6622 } else { 6623 OS << "Unpredictable backedge-taken count. "; 6624 } 6625 6626 OS << "\n" 6627 "Loop "; 6628 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); 6629 OS << ": "; 6630 6631 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { 6632 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); 6633 } else { 6634 OS << "Unpredictable max backedge-taken count. "; 6635 } 6636 6637 OS << "\n"; 6638} 6639 6640void ScalarEvolution::print(raw_ostream &OS, const Module *) const { 6641 // ScalarEvolution's implementation of the print method is to print 6642 // out SCEV values of all instructions that are interesting. Doing 6643 // this potentially causes it to create new SCEV objects though, 6644 // which technically conflicts with the const qualifier. This isn't 6645 // observable from outside the class though, so casting away the 6646 // const isn't dangerous. 6647 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); 6648 6649 OS << "Classifying expressions for: "; 6650 WriteAsOperand(OS, F, /*PrintType=*/false); 6651 OS << "\n"; 6652 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) 6653 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { 6654 OS << *I << '\n'; 6655 OS << " --> "; 6656 const SCEV *SV = SE.getSCEV(&*I); 6657 SV->print(OS); 6658 6659 const Loop *L = LI->getLoopFor((*I).getParent()); 6660 6661 const SCEV *AtUse = SE.getSCEVAtScope(SV, L); 6662 if (AtUse != SV) { 6663 OS << " --> "; 6664 AtUse->print(OS); 6665 } 6666 6667 if (L) { 6668 OS << "\t\t" "Exits: "; 6669 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); 6670 if (!SE.isLoopInvariant(ExitValue, L)) { 6671 OS << "<<Unknown>>"; 6672 } else { 6673 OS << *ExitValue; 6674 } 6675 } 6676 6677 OS << "\n"; 6678 } 6679 6680 OS << "Determining loop execution counts for: "; 6681 WriteAsOperand(OS, F, /*PrintType=*/false); 6682 OS << "\n"; 6683 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) 6684 PrintLoopInfo(OS, &SE, *I); 6685} 6686 6687ScalarEvolution::LoopDisposition 6688ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { 6689 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S]; 6690 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair = 6691 Values.insert(std::make_pair(L, LoopVariant)); 6692 if (!Pair.second) 6693 return Pair.first->second; 6694 6695 LoopDisposition D = computeLoopDisposition(S, L); 6696 return LoopDispositions[S][L] = D; 6697} 6698 6699ScalarEvolution::LoopDisposition 6700ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { 6701 switch (S->getSCEVType()) { 6702 case scConstant: 6703 return LoopInvariant; 6704 case scTruncate: 6705 case scZeroExtend: 6706 case scSignExtend: 6707 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); 6708 case scAddRecExpr: { 6709 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6710 6711 // If L is the addrec's loop, it's computable. 6712 if (AR->getLoop() == L) 6713 return LoopComputable; 6714 6715 // Add recurrences are never invariant in the function-body (null loop). 6716 if (!L) 6717 return LoopVariant; 6718 6719 // This recurrence is variant w.r.t. L if L contains AR's loop. 6720 if (L->contains(AR->getLoop())) 6721 return LoopVariant; 6722 6723 // This recurrence is invariant w.r.t. L if AR's loop contains L. 6724 if (AR->getLoop()->contains(L)) 6725 return LoopInvariant; 6726 6727 // This recurrence is variant w.r.t. L if any of its operands 6728 // are variant. 6729 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); 6730 I != E; ++I) 6731 if (!isLoopInvariant(*I, L)) 6732 return LoopVariant; 6733 6734 // Otherwise it's loop-invariant. 6735 return LoopInvariant; 6736 } 6737 case scAddExpr: 6738 case scMulExpr: 6739 case scUMaxExpr: 6740 case scSMaxExpr: { 6741 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6742 bool HasVarying = false; 6743 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6744 I != E; ++I) { 6745 LoopDisposition D = getLoopDisposition(*I, L); 6746 if (D == LoopVariant) 6747 return LoopVariant; 6748 if (D == LoopComputable) 6749 HasVarying = true; 6750 } 6751 return HasVarying ? LoopComputable : LoopInvariant; 6752 } 6753 case scUDivExpr: { 6754 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6755 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); 6756 if (LD == LoopVariant) 6757 return LoopVariant; 6758 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); 6759 if (RD == LoopVariant) 6760 return LoopVariant; 6761 return (LD == LoopInvariant && RD == LoopInvariant) ? 6762 LoopInvariant : LoopComputable; 6763 } 6764 case scUnknown: 6765 // All non-instruction values are loop invariant. All instructions are loop 6766 // invariant if they are not contained in the specified loop. 6767 // Instructions are never considered invariant in the function body 6768 // (null loop) because they are defined within the "loop". 6769 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) 6770 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; 6771 return LoopInvariant; 6772 case scCouldNotCompute: 6773 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6774 return LoopVariant; 6775 default: break; 6776 } 6777 llvm_unreachable("Unknown SCEV kind!"); 6778 return LoopVariant; 6779} 6780 6781bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { 6782 return getLoopDisposition(S, L) == LoopInvariant; 6783} 6784 6785bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { 6786 return getLoopDisposition(S, L) == LoopComputable; 6787} 6788 6789ScalarEvolution::BlockDisposition 6790ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6791 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S]; 6792 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool> 6793 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock)); 6794 if (!Pair.second) 6795 return Pair.first->second; 6796 6797 BlockDisposition D = computeBlockDisposition(S, BB); 6798 return BlockDispositions[S][BB] = D; 6799} 6800 6801ScalarEvolution::BlockDisposition 6802ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { 6803 switch (S->getSCEVType()) { 6804 case scConstant: 6805 return ProperlyDominatesBlock; 6806 case scTruncate: 6807 case scZeroExtend: 6808 case scSignExtend: 6809 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB); 6810 case scAddRecExpr: { 6811 // This uses a "dominates" query instead of "properly dominates" query 6812 // to test for proper dominance too, because the instruction which 6813 // produces the addrec's value is a PHI, and a PHI effectively properly 6814 // dominates its entire containing block. 6815 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S); 6816 if (!DT->dominates(AR->getLoop()->getHeader(), BB)) 6817 return DoesNotDominateBlock; 6818 } 6819 // FALL THROUGH into SCEVNAryExpr handling. 6820 case scAddExpr: 6821 case scMulExpr: 6822 case scUMaxExpr: 6823 case scSMaxExpr: { 6824 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6825 bool Proper = true; 6826 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6827 I != E; ++I) { 6828 BlockDisposition D = getBlockDisposition(*I, BB); 6829 if (D == DoesNotDominateBlock) 6830 return DoesNotDominateBlock; 6831 if (D == DominatesBlock) 6832 Proper = false; 6833 } 6834 return Proper ? ProperlyDominatesBlock : DominatesBlock; 6835 } 6836 case scUDivExpr: { 6837 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6838 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6839 BlockDisposition LD = getBlockDisposition(LHS, BB); 6840 if (LD == DoesNotDominateBlock) 6841 return DoesNotDominateBlock; 6842 BlockDisposition RD = getBlockDisposition(RHS, BB); 6843 if (RD == DoesNotDominateBlock) 6844 return DoesNotDominateBlock; 6845 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? 6846 ProperlyDominatesBlock : DominatesBlock; 6847 } 6848 case scUnknown: 6849 if (Instruction *I = 6850 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) { 6851 if (I->getParent() == BB) 6852 return DominatesBlock; 6853 if (DT->properlyDominates(I->getParent(), BB)) 6854 return ProperlyDominatesBlock; 6855 return DoesNotDominateBlock; 6856 } 6857 return ProperlyDominatesBlock; 6858 case scCouldNotCompute: 6859 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6860 return DoesNotDominateBlock; 6861 default: break; 6862 } 6863 llvm_unreachable("Unknown SCEV kind!"); 6864 return DoesNotDominateBlock; 6865} 6866 6867bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { 6868 return getBlockDisposition(S, BB) >= DominatesBlock; 6869} 6870 6871bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { 6872 return getBlockDisposition(S, BB) == ProperlyDominatesBlock; 6873} 6874 6875bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { 6876 switch (S->getSCEVType()) { 6877 case scConstant: 6878 return false; 6879 case scTruncate: 6880 case scZeroExtend: 6881 case scSignExtend: { 6882 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S); 6883 const SCEV *CastOp = Cast->getOperand(); 6884 return Op == CastOp || hasOperand(CastOp, Op); 6885 } 6886 case scAddRecExpr: 6887 case scAddExpr: 6888 case scMulExpr: 6889 case scUMaxExpr: 6890 case scSMaxExpr: { 6891 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S); 6892 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); 6893 I != E; ++I) { 6894 const SCEV *NAryOp = *I; 6895 if (NAryOp == Op || hasOperand(NAryOp, Op)) 6896 return true; 6897 } 6898 return false; 6899 } 6900 case scUDivExpr: { 6901 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S); 6902 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); 6903 return LHS == Op || hasOperand(LHS, Op) || 6904 RHS == Op || hasOperand(RHS, Op); 6905 } 6906 case scUnknown: 6907 return false; 6908 case scCouldNotCompute: 6909 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); 6910 return false; 6911 default: break; 6912 } 6913 llvm_unreachable("Unknown SCEV kind!"); 6914 return false; 6915} 6916 6917void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { 6918 ValuesAtScopes.erase(S); 6919 LoopDispositions.erase(S); 6920 BlockDispositions.erase(S); 6921 UnsignedRanges.erase(S); 6922 SignedRanges.erase(S); 6923} 6924